DOCTORAL DISSERTATION Soil physical properties under different managements: an analysis through CT-scanning, transport experiments and pressure jumps characterisation Diego Soto Gómez 2019 International mention

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2019

Diego Soto Gómez

DOCTORAL DISSERTATION

Soil physical properties under different managements: an analysis through

CT-scanning, transport experiments and pressure jumps characterisation

Supervised by:

José Eugenio López Periago

Marcos Paradelo Pérez

2019

“International mention”

Agradecementos

Esta tese de doutoramento foi realizada grazas a colaboración de persoas de moi

diversos ámbitos, que me ofreceron ánimo e apoio durante esta época da miña vida.

En primeiro lugar, gustaríame dárllelas grazas ós membros da miña familia e ós meus

amigos, ós que están e ós que se foron xa. A pesar de que viñeron máis ben pouco polo

laboratorio, compartiron a miña ilusión dende o intre que lles dixen que ía facer unha

tese doutoral.

Por suposto, teño moito que agradecer ós meus directores, José Eugenio López Periago

e Marcos Paradelo Pérez, que me axudaron dende un primeiro momento, con moita

paciencia, dende aqueles tempos do proxecto de fin de carreira. Teño que darlles as

grazas tamén por darme liberdade para investigar, cometelos meus propios erros e

continuar polos camiños que eu considerei máis axeitados.

Tamén me gustaría agradecer o apoio que recibín por parte das compañeiras do

laboratorio, que sempre estaban dispostas a axudar ou a tomar un respiro diante dun

café. Non se pode pedir mellor ambiente para traballar.

A miña gratitude tamén se extende ós meus coautores, que compartiron comigo a ardua

tarefa de publicar e responder ós revisores, facendo interesantes comentarios e

dándome consellos que enriqueceron de xeito exponencial a calidade dos artigos.

Grazas, compañeiros de Viborg, por facer que a miña estancia no norte fose produtiva e

moi entretida. Teño que repetir.

Grazas, alumnos de traballo de fin de grado, por axudarme ó longo destes anos coa miña

investigación.

E grazas, Róber, por non deixar que perdese o ánimo e pola paciencia que amosaches e

que segues mostrando agora que se achega o final.

¡Grazas a todos!

Diego Soto

Ourense, España

Table of contents

Resumo ............................................................................................................................ 1

List of symbols and abbreviations .............................................................................. 11

1. Introduction: the concept of soil ......................................................................... 16

2. Soil physics: challenges and objectives of the present work ........................... 23

3. Theoretical background ........................................................................................ 26

4. Materials & methods ............................................................................................ 38

5. Results & Discussion.............................................................................................. 56

6. Summary and general discussion ........................................................................ 83

7. Conclusions and future perspectives ................................................................... 89

8. References .............................................................................................................. 91

9. Supporting papers ................................................................................................ 101

1

Resumo

O termo solo fai referencia á capa da terra que serve de conexión entre a atmosfera e a litosfera.

Está constituído por partículas minerais máis ou menos alteradas, auga con sales e sustancias

suspendidas, aire, materia orgánica e organismos vivos. É o soporte dos ecosistemas terrestres

e presenta unha gran diversidade e funcionalidade. A súa formación depende dunha serie de

factores entre os que se atopan o material de partida, a evolución das condicións climáticas da

zona, o tempo, o relevo, e os organismos presentes. Dependendo de como sexan os factores de

formación, un solo vai desenvolverse dun ou doutro xeito, adquirindo un conxunto de

propiedades físicas, químicas e biolóxicas, que van condicionalo seu funcionamento. As

actividades humanas, cada vez máis diversas, teñen un importante efecto sobre a xénese e a

evolución dos solos, e mesmo poden ameazar algunhas das súas funcións claves, como son a

súa función de soporte para a agricultura e a regulación do ciclo hidrolóxico e o do carbono.

Coñecer a función da estrutura do solo, é dicir, de qué xeito a organización espacial das

partículas e ocos regula a infiltración e a retención da auga, o intercambio de gases, a

distribución e evolución da biota do solo e a súa actividade, a penetración das raíces, a

mobilidade de nutrientes e a súa dinámica, o balance de carbono, e a erosión, constitúen un

conxunto de puntos esenciais sobre o coñecemento do solo sobre o que esta tese pretende

ofrecer algunha resposta.

Existe un debate na comunidade científica acerca do efecto que teñen as diferentes alternativas

de labranza sobre as función do solo e sobre a súa sustentabilidade. Isto é debido á dificultade

de identificar cada un dos diversos tipos de resposta do solo ao manexo xa que cada sistema de

labranza afecta a un conxunto de variables edafolóxicas que son interdependentes. Ó longo

deste traballo imos estudalos efectos dunha labranza convencional sobre as características da

rede porosa e comparalos cos ocasionados por un tipo de manexo ecolóxico no que non se

realiza ningún tipo de labranza. Ó ser parcelas limítrofes, eses solos van ter unhas propiedades

químicas semellantes, pero a estrutura pode estar influenciada polo factor de labranza. Tamén

estudamos como afectan as diferenzas na estrutura xerada polos diferentes manexos á

capacidade filtrante do solo, é dicir, ó seu papel no transporte de solutos e partículas en

suspensión: Con isto, pretendemos atopar relacións entre características físicas da rede porosa

e propiedades relacionadas co transporte.

As mostras que foron empregadas neste estudo poden separarse en tres grupos dependendo

das características da labranza que sobre elas se efectuou: no primeiro grupo temos aquelas

mostras que se obtiveron de solos dedicados a agricultura convencional con arado superficial

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(ST); no segundo grupo atópanse as mostras tomadas dun solo de labranza convencional, cun

manexo semellante ó do solo ST, coa diferenza de que neste caso o arado aínda non fora

realizado na data de mostraxe e os solos obtidos conservaban o sistema radicular (NT); o terceiro

grupo é o de mostras extraídas de solos de agricultura ecolóxica, neste resumo mantense a

abreviatura (O) que se usou de acordo co termo inglés "organic". Esta última foi subdividida

atendendo á densidade de buracos de miñoca que observamos na superficie do mesmo: ó

subgrupo orgánico A (OA) pertencen as mostras tomadas alí onde se apreciaban restos de

alteración superficial producida por miñoca, mentres que as mostras do subgrupo orgánico B

(OB) foron tomadas de forma completamente aleatoria na mesma parcela.

A tomografía computarizada (CT, do inglés, "Computed Tomography") é unha técnica non

invasora coa que se pode obter unha gran cantidade de información sobre a estrutura do solo.

O avance que está a experimentar nos últimos anos este campo mellorou a resolución das

análises CT, aumentando a cantidade de información que se pode obter dun solo sen alteralo.

Ademais, é importante considerar que o seu custo se está a abaratar e cada vez hai unha maior

oferta de servizos de CT e con maiores prestacións en termos de resolución, contraste, e

calidade da reconstrución das imaxes. Un dos obxectivos do presente traballo é extraer a maior

cantidade de información das redes de poros obtidas das análises tomográficas dos solos

sometidos a diferentes tipos de labranza: ST, NT, OA e OB. Grazas á análise CT podemos coñecela

cantidade de poros que ten un solo, a superficie de cada un deses poros, e cuantificala súa

tortuosidade, entre outras moitas características.

Os primeiros resultados obtidos amosan que existen algunhas diferenzas entre os distintos

tratamentos. Por exemplo, o solo dedicado a agricultura convencional sobre o que se realizou

unha labranza superficial (ST) presentou moitas semellanzas co solo de agricultura orgánica sen

arado pero con maior cantidade de poros de miñoca (OA). Estes dous solos teñen unha

porosidade maior que os outros dous (NT e OB), é dicir, as redes porosas dos solos ST e OA

ocupan un volume moito maior xa que están formadas por poros grandes, xerados pola labranza

no caso do solo ST, e pola alta concentración de miñoca no caso do solo OA. As redes porosas

destas dúas zonas tamén se caracterizan pola alta tortuosidade e a curta lonxitude das súas

polas. Neste contexto, cada pola comprende o espazo de poro que existe entre dúas bifurcacións

consecutivas. Ademais, segundo o ton da tomografía, podemos deducir que as matrices dos

solos destas dúas zonas posúen unha densidade media (comparada cos dous solos restantes).

No caso do solo NT, as raíces confírenlle á rede porosa das mostras unha porosidade de pouco

volume, formada por longos poros moi dereitos, é dicir, cunha tortuosidade moi baixa. Estes

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poros presentan tamén unha circularidade1 significativamente máis alta cós demais, cunha

aparencia case cilíndrica. O solo NT presenta unha propiedade bastante curiosa: malia que a súa

densidade aparente é a maior, a densidade da matriz (obtida da tomografía, CTMatrix) e menor.

Isto pode darnos unha idea do enganoso que pode resultar en ocasións o valor da densidade

aparente do solo para estimalo transporte, xa que, como se verá máis adiante, a CTMatrix resultou

ser unha propiedade moito máis sensible ó transporte que a densidade aparente. O último tipo

de solo estudado, a subzona de agricultura orgánica con menor cantidade de buracos de miñoca

(OB), presentou unha rede porosa cunhas características diferentes ás dos demais solos. Esta

zona caracterizouse por posuír unha porosidade máis baixa, menor incluso que a da zona NT,

con poros pouco tortuosos pero máis curtos e distribuídos pouco uniformemente no solo. Neste

solo OB, a porosidade está causada fundamentalmente por algunha galería de miñoca illada,

raíces e outros restos vexetais soterrados e descompostos.

Os datos obtidos a través da análise CT explicados nos parágrafos anteriores ofrecen

información sobre as propiedades macroscópicas das redes de poros que son significativas para

o trasporte, non embargante esta información non explica unha propiedade que tamén ten

influencia no transporte e é inherente ó solo: falamos da complexidade do sistema de poros. A

CT permite obter a información microscópica2 necesaria para estudar esta complexidade. Ó

longo desta tese aplicáronse dúas ferramentas que permiten por unha parte medila

complexidade da porosidade (análise multifractal) e por outra simplificar esta complexidade

identificando os camiños críticos (teoría de percolación). Estas dúas ferramentas poden axudar

a descubrilas relacións entre a complexidade da porosidade e o transporte no solo, relacións

que son coñecidas na teoría. O que se pretende é parametrizala complexidade e empregala para

obter descricións máis completas do solo, mellorando deste xeito a nosa capacidade de facer

predicións relativas á retención e transporte de sustancias.

A análise multifractal baséase no concepto de fractal: un sistema formado por un patrón que se

repite a diferentes escalas e cuxa dimensión non coincide cunha dimensión do espazo euclídeo,

é dicir, posúe unha dimensión fraccionaria (dimensión fractal). Ó analizala rede porosa dun solo,

pódese intuír que se aproxima a un obxecto fractal xa que está formado por estruturas que se

1A circularidade indica a semellanza dunha figura plana cun círculo e está definida por 4 𝜋 𝐴 𝑃−2 , onde A é a área transversal do poro e P o seu perímetro. O valor máximo da circularidade é de 1 para un círculo, e menor para outras figuras.

2 Usase aquí o termo microscópico tomado da física estatística aplicado nun sentido amplo, no cal o efecto colectivo resultante das interaccións de cada elemento individual, neste caso os segmentos de poro, contribúe no comportamento macroscópico.

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repiten, con algún grado de variación, a diferentes escalas. Cada solo podería caracterizarse a

través dunha única dimensión fractal, pero existe un problema: a estrutura do solo non sempre

se repite de forma exactamente igual en tódalas escalas. Deste xeito, esta dimensión fractal

única non describe axeitadamente as variacións que se poden observar a unha determinada

escala de observación. A análise multifractal é unha ferramenta que permite describila

complexidade ó longo de varias escalas de observación. Neste último caso os patróns de

distribución espacial dos poros non se caracterizan mediante unha soa dimensión fractal, senón

que se emprega un espectro multifractal que describe como cambia a dimensión fractal coa

escala.

Ó realizar unha análise dos nosos solos determinamos os espectros multifractais de cada un

deles e, polas súas características, concluímos que tódolos solos estudados presentaron unha

estrutura porosa multifractal. Ademais, de cada espectro obtivemos unha serie de

características que imos empregar para definilas redes porosas das que se extraeron. Un dos

datos máis interesantes obtidos da análise multifractal é a apertura do espectro (Ap), un valor

que reflexa a complexidade do solo. Esta magnitude delimita a cantidade de patróns que

podemos atopar nel: canto maior sexa a apertura do espectro, máis valores necesitamos para

caracterizalos patróns que aparecen no solo, e, polo tanto, máis complexo é este. Outra

característica fundamental que podemos tomar dos espectros multifractais é a simetría

horizontal, que simbolizamos por R-L (do inglés, "right – left"). Este valor indica que tamaños de

poro presentan unha maior complexidade, se os situados á dereita no espectro (valores

positivos segundo o criterio usado), ou os situados a esquerda. A base é a mesma que a usada

para analizala Ap: se a rama dereita do espectro (a que caracteriza patróns en poros pequenos)

é máis longa, necesitamos máis valores para definilos, polo que os poros pequenos presentan

unha maior complexidade. Tendo en conta eses dous aspectos, podemos concluír que a rede de

poros do solo OB é diferente á do resto. Este solo posúe redes porosas con espectros máis

estreitos, asociados a unha menor complexidade, e cunha simetría horizontal con valores

negativos, indicativo de que os poros grandes son máis complexos cós pequenos. O resto de

solos teñen unhas redes porosas máis complexas (ST<OA<NT, en orde de Ap crecente), cunha

clara tendencia a valores de R-L positivos, isto é, poros grandes pero simples e poros pequenos

máis complexos. Tamén cabe destacar que as redes porosas do solo NT teñen uns espectros que

tenden cara á simetría, indicando unha complexidade similar en poros pequenos e grandes.

Por outra banda, unha análise enfocada dende a teoría de percolación permite identificalas

estruturas de poros que poden ter máis peso no transporte. A teoría de percolación é unha rama

da estatística que estuda as conexións entre os límites ou fronteiras dun sistema. Nesta

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investigación as conexións serían os poros, e as fronteiras as superficies superior e inferior das

mostras de solo. O poro que conecta estes dous extremos chámase poro infinito, e se

eliminamos del os poros colgantes, é dicir, aqueles que rematan na matriz ou nos bordes laterais

da mostra, obtemos o espiñazo ou "backbone". O espiñazo é a parte da rede porosa que permite

un paso máis rápido de fluídos e sustancias disoltas e suspendidas en condicións próximas á

saturación, o cal a converte na estrutura candidata responsable do transporte preferencial. Á

hora de extraer o backbone e analizalo hai que ter en conta dúas cousas: a primeira é que pode

conter bucles (ou "loops") que actúan como camiños alternativos equivalentes, e a segunda é

que non contén poros colgantes (ou "end-points") xa que foron eliminados no proceso de

extracción. O que se entende por end-points no caso do espiñazo son entradas e saídas do

sistema, é dicir, poros que conectan ó espiñazo cos extremos (superior e inferior) da mostra de

solo.

Ó realizar unha análise das características obtidas a través do enfoque da teoría de percolación,

observamos que as mostras do solo OB ou non tiñan espiñazo, ou tiñan un que ocupaba un

volume bastante pequeno (unhas catro veces menor que o dos solos ST ou OA). Os espiñazos

xerados por un complexo sistema radicular (NT) teñen tamén pouco volume, pero presentan

unha área maior en proporción, e están constituídos por poros menos tortuosos e dun perímetro

case circular. Como se mencionou anteriormente, os espiñazos dos solos ST e OA son os máis

voluminosos e tortuosos. Como acontecía coa estrutura porosa en xeral, estes dous solos

posúen espiñazos con características similares, a pesar de que o seu manexo é diferente.

Como se explicou nos parágrafos anteriores, a tomografía é un método non destrutivo que fai

posible empregalas mesmas mostras para outros experimentos. Nesta tese, intentamos

combinala análise CT con experimentos de lixiviación (tamén chamados de transporte ou

breakthrough) para identificala influencia da organización tridimensional da estrutura no

transporte de sustancias a través do solo. Así, despois da análise tomográfica, fixemos

experimentos de transporte simulando condicións de fluxo equivalentes ás do campo.

Estableceuse un réxime de fluxo de auga constante e drenaxe libre con cada unha das mostras,

empregando dous tipos de trazadores: micro-esferas fluorescentes de látex de un micrómetro

de diámetro (MS) como trazador particulado, e bromuro (Br−) como trazador soluble. Estes

experimentos de lixiviación baséanse en facer pasar un pulso3 do trazador a través do solo e

3Un pulso refírese a un tipo de condición de contorno na que, durante un experimento de percolación a fluxo constante, a concentración dun trazador increméntase instantaneamente e mantense constante durante un tempo establecido (duración do pulso). Transcorrido ese tempo, a concentración cámbiase instantaneamente ó seu valor inicial, de xeito que se xera unha onda de concentración cadrada na cara superior do solo.

6

analizala evolución da súa concentración no efluente que sae da cara inferior do solo ata que

baixa a niveis non detectables. No caso das partículas, ademais, é necesario determinala

distribución vertical de concentracións para coñecelo seu mecanismo de transporte. Para isto

último, unha vez finalizada a recollida de fraccións do efluente, a columna é seccionada en

láminas horizontais, e en cada unha das seccións determínase a concentración do trazador.

Adicionalmente, tomáronse fotografías de fluorescencia da superficie de cada sección para

localizalos poros polos que se moveron as MS (aqueles coas paredes tinguidas polas partículas).

As curvas de avance (breakthrough curves) de Br− e MS describen a evolución das concentracións

na saída inferior da columna durante o transporte, e permiten identificalos mecanismos

dominantes no transporte. A análise destas curvas indica que o movemento tanto do Br− como

das MS seguiu un modelo de transporte advectivo-difusivo con efectos de dobre porosidade, o

cal reflexa os efectos da coexistencia de zonas móbiles e inmóbiles, e unha transferencia de Br−

e MS entre estas dúas zonas. Os parámetros axustados foron o coeficiente de dispersión (D) e a

dispersividade (d), o coeficiente de reparto para o transporte en condicións de non-equilibrio

(β), e o coeficiente de transferencia de masa entre a fase móbil (os poros) e a fase inmóbil (a

matriz) (ω). Para o transporte das micro-esferas foi necesario introducir un coeficiente cinético

(µ) para simulala súa retención na matriz.

Os resultados do modelado mostraron poucas diferenzas nos parámetros de transporte en

relación cos diferentes manexos do solo. No caso do bromuro, o modelo axustouse

satisfactoriamente en tódalas mostras, pero no caso das micro-esferas tivemos que descartalo

axuste de dúas mostras ó presentar o trazador un comportamento demasiado irregular. Os

valores dos parámetros do modelado (d, D, β e ω) obtidos para as MS foron, en xeral, maiores,

un indicativo de que as partículas, en comparación co bromuro, viaxaron a través do solo

empregando un maior rango de velocidades, e, ademais, a súa retención na matriz foi tamén

maior. Parte das micro-esferas foron capaces de atravesalo solo grazas, en parte, á presenza de

camiños preferenciáis. Mediante a toma de fotografías de fluorescencia que se realizou durante

o seccionado puidemos determinalos poros polos que se moveron as micro-esferas (aqueles que

tiñan as paredes recubertas polas micro-esferas retidas). Coa axuda das tomografías

describimos con maior precisión a forma e as características deses poros. Estes camiños

preferenciáis presentaron unhas propiedades similares independentemente do manexo do solo.

Isto pode deberse ó pequeno tamaño das poboacións de poros estudadas, xa que en cada

mostra só obtivemos de 2 a 6 camiños preferenciáis (unha pequena fracción entre os centenares

de poros presentes nas mostras), ou tamén pode ser porque as partículas só se moven por unha

serie de poros que comparten unha determinada morfoloxía, cun tamaño e cunha tortuosidade

7

axeitadas paro o transporte. A combinación dos experimentos de lixiviación coa análise

tomográfica resulta nunha nova ferramenta que permite obter información sobre a relación

entre a xeometría da rede de poros e o transporte.

Un dos temas de máis interese na física de solos é o do "upscaling" ou escalado das propiedades

implicadas no transporte de sustancias. Isto consiste en coñecer como varían as propiedades do

solo en función das escalas de espazo ou de tempo. Para isto cómpre facer experimentos a

diferentes escalas espazo-temporais. Non embargante, nos experimentos de transporte a escala

de campo (escala grande) precísanse grandes cantidades do trazador, e no caso de estudos de

transporte coloidal, a maioría dos trazadores que se empregan son micro-esferas de plástico.

Tendo en conta os problemas que están a aparecer nos últimos anos coa dispersión dos micro-

plásticos no ambiente, expoñemos a posibilidade de utilizar trazadores coloidais alternativos.

Neste estudo propoñemos a opción se usar as micro-esferas de eumelanina obtidas do saco de

tinta de Sepia officinalis L. Estas eumelaninas son partículas proteicas esféricas que presentan

tamaños que van de 80 a 140 nm, e forman suspensións estables. Ademais, ata o que se coñece,

son inocuas para o ambiente. Para examinar o seu emprego como trazador realizamos

experimentos de transporte en mostras de solo estruturado, da mesma parcela que o solo

empregado para o resto dos experimentos, aínda que dun tamaño máis pequeno (5 x 5 cm,

diámetro por lonxitude), e analizámola concentración de saída mediante fotometría de

absorción. Os resultados mostraron que a tinta de sepia é un trazador axeitado para estudos de

transporte coloidal dado que a cantidade retida no solo foi relativamente baixa (en torno a un

12%). Ademais, trátase dun material sinxelo de medir e presenta alta estabilidade en suspensión

nun rango de pH bastante amplo. Este trazador posúe tamén vantaxes importantes á hora de

empregalo como trazador de virus: ten unha densidade de partícula, composición e tamaño

similar á dalgunhas cápsides víricas. Concluímos, polo tanto, que as micro-esferas de tinta de

sepia poden aplicarse como trazadores que simulan o comportamento dos virus nos solo.

Cómpre indicar que nesta parte non se fixo un escalado do estudo.

Nesta tese tamén se estudou o efecto da xeometría dos poros na dinámica da auga do solo. A

hipótese de partida é que a complexidade da rede de poros tamén podería expresar efectos a

niveis microscópicos (i.e., a escala de poro) que influirían no movemento da auga do solo. Para

isto, colocamos un par de sensores de presión (ou tensiómetros) de alta sensibilidade nas

mostras de solo, co obxectivo de medilas oscilacións rápidas de presión que se poderían producir

durante a drenaxe. Estas variacións coñécense como saltos de presión ou "Haines jumps", e

prodúcense por desprazamentos moi rápidos da interface entre dous fluídos inmiscibles, neste

caso, o auga e o aire do solo, nun medio poroso. Nalgúns dos solos estudados, ó posuír

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macroporos estruturais de gran tamaño como as galerías de miñoca, estas oscilacións poden ser

da orde de 5 hPa. A hipótese que explica a aparición destes saltos basease na presenza dun

escudo capilar que separa os fluídos nas gargantas dos poros. A medida que progresa a drenaxe

da auga do solo, a tensión neses escudos aumenta ata que iguala a presión de burbulla e

rompen, permitindo un desprazamento rápido do fluído no interior do poro. Este

desprazamento produce unha onda da presión moi rápida e unha relaxación máis lenta que se

debe á redistribución do exceso de fluído nos poros máis pequenos. Este proceso que se produce

a unha escala pequena (escala de poro), ten un efecto sobre a auga da mostra enteira (escala

de núcleo de solo). O interese deste fenómeno é que evidencia un proceso que enlaza dúas

escalas, e pode influír tamén na dinámica do trasporte de sustancias no solo.

A última parte da tese consiste en identificar correlacións entre as características estruturais do

solo cas propiedades macroscópicas do solo, e, particularmente, cas que están relacionadas co

transporte a escala macroscópica, como exemplo, as breakthrough curves. Atopamos

correlacións significativas entre aquelas propiedades do solo obtidas a través das tomografías e

as que se determinaron mediante experimentos de transporte e modelado. Un exemplo disto é

a correlación inversa que existe entre o coeficiente de absorción de raios-X da matriz do solo,

medido polo ton da tomografía en HU (CTMatix), e os volumes de poro que tarda o 5% da masa

de bromuro en atravesar verticalmente o solo. Esta correlación indica que canto maior é a

densidade da matriz, menos tempo tarda o trazador en atravesalo solo. Este resultado é

consistente coa hipótese de que, naquelas mostras cuxa matriz é máis densa o transporte

concéntrase nos macroporos do solo, nos cales a velocidade do fluído é maior de acordo coa lei

de Hagen-Poiseuille. Esta hipótese tamén se apoia no feito de que naquelas mostras cunha

matriz máis densa a retención de bromuro é menor. A densidade da matriz do solo é unha

propiedade que tamén se correlaciona coa retención de micro-esferas: aquelas matrices menos

densas favorecen o intercambio de partículas con rexións pouco móbiles. O achegamento das

MS a estas zonas da como resultado a retención de coloides, un proceso consistente co modelo

de transporte de porosidade dual que empregamos.

No caso das propiedades multifractais da rede de poros, as correlacións máis interesantes son

as que se atoparon entre a apertura do espectro e a dispersividade, e entre a apertura e a área

superficial das paredes dos poros. Os solos que teñen unha rede máis complexa (maior apertura)

posúen máis diversidade de estruturas que poden actuar como camiños ao longo da escala de

observación. Esta diversidade de camiños pode xerar un rango maior de velocidades de

transporte nos poros, que se expresa nunha maior dispersividade. Por outra banda, a correlación

entre a apertura do espectro e a área das paredes dos poros ten interese porque demostra que

9

a complexidade pode ter implicacións no transporte, xa que esta superficie controla o fluxo

entre os macroporos e a matriz do solo. Nesta fronteira que constitúen as paredes, solutos e

partículas coloidais poden pasar á matriz e difundir máis lentamente, ou poden continuar polos

macroporos cunha velocidade maior.

Da parte de percolación, as propiedades que resultaron máis interesantes foron aquelas que

caracterizan o espiñazo, sobre todo o volume, a superficie, o número de polas dos poros e os

end-points (que neste caso, recordamos, refírese a entradas e saídas do solo conectadas o

espiñazo). O volume do backbone está inversamente correlacionado coa densidade aparente do

solo seco, o que suxire que a densidade limita dalgún xeito o desenvolvemento do backbone. A

superficie e o número de polas do espiñazo son quizais as dúas propiedades máis interesantes,

xa que se relacionan directamente coa dispersividade de bromuro: unha maior superficie de

poros máis ramificados produce un abano de velocidades maior. A suma dos poros que entran

e saen da mostra de solo, isto é, o número de end-points, relaciónase: directamente, cos valores

dos parámetros do modelo de transporte de Br− (β e ω) e cos volumes de poro que tarda en

chegar un 5% da masa (para os dous trazadores); e inversamente, coa proporción de MS retidas

en poros. A conectividade entre zonas é o fundamento físico que explica estas correlacións: as

entradas e saídas do solo que están conectadas ó backbone determinan tanto o volume de auga

móbil do solo coma o tempo que lle leva os trazadores cruzalo (tempo de residencia), afectando

tamén ó reparto de partículas entre a matriz e os macroporos.

Para rematar coa sección de correlacións cómpre falar dunha variable que se identificou a partir

das fotografías de fluorescencia que se fixeron durante o seccionado: a proporción media de

sección tinguida polo trazador fluorescente (%Stained). Esta magnitude depende da porosidade

e da tortuosidade dos poros: canto máis poroso sexa o solo e máis tortuosos sexan eses poros,

maior será a superficie tinguida. Isto pode explicarse asumindo que as MS se moven de xeito

preferente a través de poros grandes. Ademais, a tortuosidade destes poros favorece o

intercambio de masa coa matriz e, por tanto, as MS esténdense dende a parede do macroporo

cara ó interior da matriz. A %Stained está tamén relacionada co volume do espiñazo, un feito

que apoia o rol deste último no transporte de partículas. Tanto a densidade aparente do solo

seco coma a densidade da parede do poro (determinada mediante análise tomográfica) están

inversamente relacionados coa %Stained, o cal suxire que a densidade da parede do poro

dificulta a penetración das partículas na matriz.

Para concluír, podemos dicir que os diferentes sistemas de labranza non influíron

significativamente na retención de bromuro ou de micro-esferas. Os posibles efectos

10

microscópicos da labranza sobre o transporte non se manifestan a escala macroscópica. Pero

unha análise máis profunda, a escala de macroporo, permitiu atopar moitas diferenzas entre ese

transporte e a distribución no solo dos trazadores. Ademais, estas diferenzas están relacionadas

con algúns dos descritores da complexidade da porosidade. Estes achados afondan no

coñecemento dos mecanismos de transporte a través do solo en relación coa estrutura, e

contribúen a un mellor entendemento dos mecanismos implicados na función filtrante do solo.

11

List of symbols and abbreviations

% Br− Recovered, percentage of bromide recovered after the transport experiments.

% MS Connected paths, percentage of pores larger than 0.24 mm and connected from top to

bottom, used by the particles to cross the columns.

% MS Disconnected paths, percentage of pores larger than 0.24 mm and disconnected from top

to bottom, used by the particles to cross the columns.

% MS Paths, percentage of pores larger than 0.24 mm with the walls covered by microspheres,

therefore, particle preferential pathways.

% of MS Retained in the matrix, percentage of microsphere mass retained in the soil matrix with

respect to the total concentration.

% of MS Retained in the upper half, percentage of microsphere mass retained in the upper half

of the sample with respect to the total concentration.

%Stained, average percentage of soil slices covered by fluorescent stains determined from the

epifluorescence macrophotographs.

Ap, aperture of the entire multifractal spectrum.

BTC, breakthrough curve.

c, concentration.

C, normalisation constant of the probability density function.

C14, soil sample number 14.

C5, soil sample number 5.

CFT, colloidal filtration theory.

ci or c0, initial concentration of the pulse applied during a breakthrough.

CPT, critical pore thickness.

CT Porosity (%), percentage of pores larger than 0.24 mm, extracted from the computed

tomography images using the Sauvola’s auto local threshold method.

CT, computed tomography.

12

CTMatrix, optical density of the matrix measured by the X-ray absorbance using the Hounsfield

scale.

CTPore, optical density of the pores measured by the X-ray absorbance using the Hounsfield scale.

d, dispersivity.

D, in multifractal analysis, is the fractal dimension; in modelling, is the hydrodynamic dispersion

coefficient.

D0, generalized fractal dimension when q = 0.

D1, generalized fractal dimension when q = 1.

D2, generalized fractal dimension when q = 2.

d50, collector diameter.

DBr, dispersion coefficient of the Br−.

dBr, dispersivity for the Br−.

Dmin, generalized fractal dimension for the minimum value of q.

DMS, dispersion coefficient of the microspheres.

dMS, dispersivity coefficient for the microspheres.

Dq, generalized fractal dimension.

DW, deionised water.

f(α), Hausdorff dimension.

f(αmax), value of f(α) for the maximum value of the Holder exponent.

f(αmin), value of f(α) for the minimum value of the Holder exponent.

HU, Hounsfield units.

I, intensity of the X-rays after crossing the sample.

I0, intensity of the X-rays before crossing the sample.

im, immobile liquid region.

ISI, inter-jump interval.

13

Jw, volumetric water flux density.

k value, parameter one of the Sauvola's thresholding.

Katt, first-order attachment coefficient for ink particles.

Kdet, first-order detachment coefficient for ink particles.

m, mobile liquid region.

MAD, median absolute deviation.

MF, multifractal.

MIM, mobile-immobile solute transport.

MS Disconnected/ MS Paths, proportion of pores disconnected from top to bottom used by MS.

MS, microspheres.

N(α), number of squares (or cubes) with the same Holder exponent.

NT, conventional soil management with no tillage after sowing.

O, organic management.

OA, organic management with high earthworm alteration in the surface.

OB, organic management with low earthworm alteration in the surface.

P, in modelling, is the Peclet number; in multifractal analysis, is the probability of a voxel being

occupied; and, in percolation theory, is the percolation probability.

pc, percolation threshold.

PV, pore volume.

PVC, polyvinyl chloride.

q, arbitrary exponent used in multifractals.

R, retardation factor.

r value, parameter two of the Sauvola's thresholding.

R-L, horizontal symmetry of the multifractal spectrum.

RP, retention profile.

14

Satt, concentration of ink particles attached to soil or sand grains.

SEM, scanning electron microscopy.

ST, conventional soil management with shallow tillage after sowing.

T or t, time.

T1, tensiometer one, located at 2 cm of the soil surface.

T2, tensiometer two, located at 7.5 cm of the soil surface.

T5%, 5%-arrival time (in pore volumes).

T5%Br, 5%-arrival time of Br−.

T5%MS, 5%-arrival time of MS.

USDA, United States Department of Agriculture.

V, vertical symmetry of the multifractal spectrum.

x, in CT, thickness of a sample and, in modelling, length.

x0, distance where the straining starts (in our case, the soil surface).

xmax, maximum cutoff of the power-law distribution.

xmin, minimum cutoff of the power-law distribution.

Z, in percolation theory is the coordination number; and in modelling is distance.

ZB, coordination number of the skeleton of the backbone.

ZT, coordination number of network skeleton.

α, in modelling transport, is the first-order mass transfer coefficient for solute exchange between

the mobile and immobile regions; in pressure jump analysis, is the fitting exponent of the best-

fit power-law relationship; and, in multifractal theory, is the Holder exponent.

α0, value of de Holder exponent when q = 0.

αmax, maximum value of the Holder exponent.

αmin, minimum value of the Holder exponent.

β, empirical factor with an optimal value of 0.43.

15

βBr, dimensionless parameter for partitioning in the two-region transport model for the Br−.

βMS, dimensionless parameter for partitioning in the two-region transport model for the

microspheres.

ε, scale.

η, single-collector contact efficiency.

ηD, removal efficiency of a single-collector due to diffusion.

ηG, removal efficiency of a single-collector due to sedimentation.

ηI, removal efficiency of a single-collector due to interception.

θ, volumetric water content.

θs, saturated volumetric water content.

θim, volumetric water contents of the soil in the immobile region.

θm, volumetric water contents of the soil in the mobile region.

µ(q, ε), partition function that normalises the distribution (in multifractal analysis).

µ, in Ct, is the linear attenuation coefficient; in modelling, is the dimensionless first order decay

coefficient for the immobile region.

ξ, zeta potential.

ρb, dry bulk density, mass of air-dried soil per unit of bulk volume.

τ, correlation exponent of the qth order.

ϕ, porosity.

ψatt, dimensionless attachment function (for ink particles).

ω, scaled mass transfer coefficient.

ωBr, scaled mass transfer coefficient for the Br−.

ωMS scaled mass transfer coefficient for the microspheres.

16

1. Introduction: the concept of soil

Soil is a complex concept, and means different things depending on the user: the concept of

"soil" of a geologist is very different from the one of an engineer (White, 2006). Soil is the top

layer of the earth, is an interface between the atmosphere and the lithosphere, and it is

constituted by weathered mineral particles, water, air, organic matter and living organisms

(Figure 1.1). Soil is also the base of the terrestrial ecosystems of the planet, a natural resource

that supports life and presents high frailty and diversity (Wilding and Lin, 2006). The soil is part

of the biosphere and supports a wide variety of animals, plants, and their growth (White, 2006).

Figure 1.1: Scheme of the composition of the soil in volume (adapted from Kalev and Toor, 2018)

a. Formation

The soil is formed as the result of the interaction of several variables known as soil-forming

factors (Jenny, 1941): parent material, organisms, climate, relief, and time. There are other

minor factors, with more localised effects in time and space, such as a fire. The anthropic factor

must also be included, but it encloses a wide variety of processes that cannot be classified as a

single factor.

First, we have to consider the parent material since the weathering of an unaltered rock can

form soil in situ (igneous, sedimentary or metamorphic), or by solid material deposits

transported by wind, water, ice or gravity in fields with a determinate slope. Weathering

involves physical, chemical and biological processes, and is regulated by constituent minerals,

17

temperature, water regime and its chemistry, and the surface of the rock or material exposed,

among others.

The second factor is the soil ecosystem, the communities of plants, animals and microorganisms

that live in it. The vegetation can colonise rock surfaces with minimum weathering, and the soil

formation can follow several routes depending on the composition of the leaves. The fauna also

has a significant role in the soil genesis. A great diversity of bacteria, fungi, invertebrates and

vertebrates controls the decomposition and turnover of the organic matter. They determine the

composition and structure of the soil organo-mineral complexes. In numbers, each gram of soil

supports about 109 bacteria, and each hectare can keep up to 3000 kg of biomass (Ranjard and

Richaume, 2001).

Climate influence on the soil genesis is double: it has a direct impact as a soil-forming factor but

also determines the type of species that inhabit the soil. Moisture and temperature regimes

control the physical and chemical weathering processes. Moisture depends on the

precipitations, their intensity and distribution, the evaporation rate, the shape of the land (relief)

and the permeability of the parent material. Temperature is a function of altitude, latitude and

radiation balance, which controls the rate of chemical weathering reactions and breakdown of

rocks by thermal and icing-deicing cycles.

The topography conditions the characteristics of the ecosystems and the local climate to some

extent. The elevation determines the temperature and the precipitation, and the angle of slope,

together with other factors, establish the drainage (Figure 1.2).

Figure 1.2: Effects of the slope over the drainage (from White, 2006).

18

The time element determines the period of action of the above factors. This concept is also

related to the classification of soils in monogenetic and polygenetic: soils formed under a

defined set of factors (climate, relief, biota,) for a period of several thousand years with the

same climate or geologic stability (monogenetic), and soils generated by conditions (geological

and climatic) that varied along thousands of years (polygenetic).

b. Structure

Soils are three-dimensional structured heterogeneous objects, and the formation factors confer

the soil this 3D structural organisation. If we consider only the weathering of the parent material,

the soils will be constituted by particles evolving towards their minimum energy and maximum

entropy, with a structure inherited from the rocks and minerals of the parent material. However,

the organisation of soil constituents is much more complex. That complexity is acquired from

the interactions of all the forming factors. The individual particles are linked together and

become part of structural units of various sizes called aggregates (Figure 1.3).

Soil structure can be defined as the shape, size and arrangement of aggregates and voids. We

can distinguish between macro and micro-aggregates: the first ones are bigger than 250 µm and

are formed by roots and hyphae entangled to mineral materials, and the second ones are more

stable and result from the aggregation of fine particles (silt and clay) with the help of

polysaccharides produced by microbes (Ranjard and Richaume, 2001). An important concept

related to the soil structure is stability; this is the strength of the particle-to-particle forces that

preserve their arrangement against other potentially disruptive forces. The more common

binding agents that reinforce the structure are clay particles, oxy-hydroxide gels of Al and Fe,

organic polymers, roots, hyphae, cell walls residues, and humic materials (Singer and Munns,

1991). These have a crucial role in increasing soil stability.

Soil structure is closely related to scale, as seen in Figure 1.3. Soil scientists usually distinguish

two levels of structural organisation: on the one hand, the features associated with the

macrostructure, characteristics that can be observed in the field, and, on the other hand, the

detailed distribution, shape and size of aggregates and voids, which corresponds to the

microstructure. Moreover, if we study this small level of structure, some of the equations and

laws that explain the macroscopic behaviour become useless at larger scales. Therefore, the

connection of soil processes and properties across the scales is one of the questions of the soil

science that remain unsolved. In other words, the challenge is to understand how processes

19

occurring at small scales (i.e., core experiments) produce their effects a larger scales, e.g., at

field or landform (Pachepsky et al., 2003).

Figure 1.3. Model of the organisation of aggregates at different scales with the linking agents (from Tisdall and Oades, 1982).

c. Functions

Soil is the primary source of food and provides essential services in terrestrial environments. The

capacity of the soil to develop these functions is an indicator of its quality status (Blum, 2013).

Some of the critical roles of the soil are:

- Keep up the worlds more significant gene reserve, being the habitat of a vast number of

species.

- Preserve the paleontological and archaeological remains.

20

- Provide raw materials (minerals) and the physical base for the development of human

activities

- Filter contaminants and protect the food chain and the groundwater.

- Moreover, produce biomass through agriculture and forestry.

More specifically, the soil structure has a capital role in some soil functions: it regulates the

water budget and flow in hydrographic basins, controls the storage and the exchange of gases

with the atmosphere, controls the storage and release of nutrients and contaminants, and

determines the erosion and the penetration of roots. The present thesis is mostly focused on

the relation between the function of soil as a filter to retain particles and solutes, and the

morphology of the pore network. It has been shown that some properties of the soil, like the

macroporosity, the pore connectivity, and the pore orientation exert some control in the

transport of particles (Rabot et al., 2018). These findings and others brought in the present thesis

show that analysis of details of the soil structure can unveil processes that explain the transport

of nutrients and pollutants in soil.

A) Tillage

Increasing demand for food, raw materials and energy pushes the agriculture to exert a pressure

excess on the productive function of soil at the expense of other purposes. Agricultural pressure

threatens the soil functions that satisfy all the ecosystems services. Some of these functions

depend on the fragile soil structure, such as water holding capacity, nutrient storage, root

growth and gas exchange with the atmosphere. Tillage has been used for millennia to increase

crop productivity by decreasing the competency of weeds for water and nutrients and enhance

mineralisation of buried residues and weeds. Tillage exerts these effects via the modification of

the macro-structure.

Conventional management involves a sequence of agricultural operations aimed to increase the

production of a crop without considering the long-term effects on the ecosystem. These

operations are different depending on the type of crop and the geographic area (Simmons and

Nafziger, 2014). Typically, the method employed with this kind of agriculture is ploughing (Figure

1.4), which incorporates stubble to the soil, breaks up the soil surface and reorders the topsoil

structure. Also, the application of pesticides, herbicides and inorganic fertilisers in conventional

farming is often programmed based on calendar applications at prescribed doses (Womach,

2005). The main objective of these practices is to control weeds and pests, but they also affect

the nutrient redistribution and transform the soil structure, making it more suitable for seed

21

germination and root penetration in compacted soil. The counterpart of the conventional tillage

is the depletion of the soil organic matter content, which decreases the stability of the soil

structure. Loss of structure leads to soil erosion by water and wind, increases the compaction,

surface sealing and crusts, and the formation of plough pan. Use of agricultural chemicals results

in contamination by off-target dispersion of synthetic fertilisers and pesticides, with possible

harmful effects over beneficial fauna, flora and microorganisms in soil and environment.

Several management practices have been used for six thousand years to make agriculture more

sustainable and to preserve soil productivity (Pimentel and Burgess, 2014), but it was not until

the last fifty years that conservation tillage expanded in developed countries as a consequence

of changes in agricultural policies and laws that promote soil conservation. New management

procedures were developed both in conventional and conservative agriculture. These include

reduced tillage, mulching, ridge tillage and no-tillage practices (Figure 1.4), techniques that

decrease many problems derived from conventional tillage management. The objective of

conservation tillage is to get a short-term profitable crop production without long-term loss

productivity mostly due to depletion of the soil organic matter and degradation of structure and

subsequent erosion. Conservative soil use can be achieved by protecting the soil with crop

residues: to be considered conservation tillage at least 30% of the soil must be covered

(Womach, 2005). The soils resulting from this type of techniques have a greater macroporosity

(due to the increase in the earthworm activity), more microbial activity and carbon stored, less

tillage and fuel consumption, and less soil evaporation. These systems also show disadvantages,

like the higher pressure of the weeds and, risk of decreased nitrogen availability to plants by the

immobilisation of microbial flora. The effectiveness of this type of management can be increased

with rotation tillage and the control of the Carbon/Nitrogen and Carbon/Phosphorus ratios, both

in soil and in the organic amendments and fertilisers (Peigné et al., 2007).

Management practices can modify the soil structure and the pore network (Bronick and Lal,

2005). Tillage increases the compaction, breaks soil aggregates and pore continuity, lowers the

soil organic matter and nutrients, and disturbs the activity of plants and soil animals that

contribute to the aggregation. Consequently, soils under no-tillage conditions are more stable

than ploughed soils. The reduced tillage helps with the development of more complex pore

networks, with more bio-channels and macropores that increase the availability and movement

of water. However, these channels can also increase nutrient loss. The mulching also improves

the stability of soils through the incorporation of the organic matter, protecting against the

erosion, sealing and crusts, the evaporation, and by increasing the amount of organic carbon.

Application of manure and compost, either in surface or subsurface, also favours the

22

development of a structure, increase the amount of soil organic carbon and biological activity

by enhancing the stability of aggregates (Bronick and Lal, 2005). All these effects favour the

development of adequate habitats for soil fauna, whereby creates positive feedback to enhance

the formation of soil structure and biological activity.

Considering the above, it is clear that paradigmatic case examples of conventional or

conservation management have opposing effects on soil structure, habitat, biological activity,

chemical and physical properties (Andreini and Steenhuis, 1990).

Figure 1.4. Examples of the different techniques used in conventional and conservation tillage (FAO, 2000).

23

2. Soil physics: challenges and objectives of the present work

Soil physics studies the state and dynamics of substances and energy in the soil. Is the science

that deals with the structure and texture of the mineral constituents (matrix), the movement

and retention of substances (air, water, solutes and particles), and thermal flow (Campbell,

1985).

Before the decade of 1980, soil scientists and engineers used physical descriptions extracted

from macroscopic measurements: particle density and bulk density, particle size distribution,

water potential, water content, permeability, hydraulic functions, porosity, thermal properties

and mechanical behaviour of a whole soil specimen. Besides, the description of the structure

was qualitative, or, at best, semi-quantitative. However, those methods do not provide spatial

information and do not allow a topological nor morphological characterisation of the porous

space (Rabot et al., 2018).

For the last decades, some disruptive tools have been developed to visualise the three-

dimensional structure of the soil matrix and the pore network. These direct methods are based

on imaging techniques (X-Ray tomography, gamma-ray tomography or nuclear magnetic

resonance, among others), and allow direct visualisation and characterisation of individual soil

pores (Figure 2.1). The main advantage of these methods is their ability to extract the vast

complexity of the three-dimensional distribution structure of soil pores, constituents and their

interfaces. A considerable variety of descriptors of that complexity can be extracted from soil

samples without disruption of the soil structure.

Figure 2.1. Cross-sectional image of a soil sample scanned at a voxel size of 1 micron. Field of view: 4 x 4 mm.

24

These techniques constitute a real change in the methods of soil research because they bring a

quantitative description of structure and functions at a microscopic scale, i.e., at the pore-scale.

This change implies that fundamental physics laws governing processes at the pore-scale,

particle-scale or even molecular-scale, e.g., hydrodynamics, can be applied by computer model

calculations in mathematical representations of the actual pore space obtained from X-Ray CT

scans (Figure 2.2). Therefore, computer calculations can be used to predict soil processes and

properties at larger scales. For example, water retention curves and permeability are currently

calculated from individual pore-level information using X-Ray CT scans of soil cores. The

limitation of this up-scaling approach is the resolution of the images and scale of observation,

computing resources, identification of scale-dependent processes, and the occurrence of

chaotic behaviours.

Figure 2.2. Flow velocity contours and vectors calculated with Lattice-Boltzmann methods for a packed bed with contrasting flow velocities (Reynolds numbers): A) Re=0.02; B), Re=34 (adapted from Rong et al., 2013)

Through the methods mentioned, many authors tried to solve the problems of modern soil

physics. Jury et al. (2011) condensed those main unsolved problems (or main gaps) and divided

them into three goals or sections:

1. The first part is associated with the living organisms (the effect of plants and

microorganisms over the structure) and with the ecological function of the soil.

2. The second one includes the problems associated with flow instabilities and water

repellency.

3. And, the last one is related to the scale problem (upscaling), the properties that depend

on the scale and the relations between the structure of the soil and its functions.

25

In this PhD, we tried to contribute with the third section, and the main objective of the thesis is

to find descriptors and mechanisms linking soil transport with the properties of the structure.

For this aim, we performed tomographic analysis over soil samples followed by leaching

experiments using two types of tracers: particulate and solute. We also parametrised the

structure of the soil using percolation theory and multifractal analysis, studied the presence of

pressure jumps in soils with large earthworm pores and modelled the particle transport in the

most favourable scenario for the leaching (taking in account the size of pores and particles).

Figure 2.3. Soil sample scanned at a voxel size of 1 micron. Field of view: 4 x 4 x 2.5 mm. The scale indicates the centre of the pore-to-wall distance (in microns). The image processing and calculations for this figure were made with the SKYSCAN 3D.SUITE software.

26

3. Theoretical background

a. Colloidal filtration theory

The colloid filtration theory (CFT) was proposed by Yao et al. (1971) to model the attachment

and transport of particles in spherical collectors. This theory was used to develop models

(correlation equations) that estimate attachment dynamics of particles when a suspension flows

in a porous column of packed spherical collectors. Therefore, CFT allows us to estimate the

mobility, in porous media, of particulate contaminants and fertilisers, virus, bacteria, colloidal

plastics, among others, ranging from a few tens of nanometres to ten microns.

Following this model, the retention of colloids in the soil is determined by the porosity of the

column, the diameter of the particles, the pore water velocity (also named the fluid approach

velocity), the size of collector and particles, and their respective chemical composition.

Figure 3.1. Scheme of the attachment mechanisms of colloids according to the filtration theory model (from Tufenkji and Elimelech, 2004).

Thus, the correlation equations (Tufenkji and Elimelech, 2004) use the above variables to

calculate the single collision efficiency (η), which is the number of colloids contacting the surface

of a single collector divided by the number of potential collisions between the collector and

particles. The single collector efficiency can be calculated by summing the contributions of the

three major transport mechanisms of suspended colloids flowing towards a collector:

27

gravitational sedimentation (ηG), interception (ηI) and Brownian diffusion (ηD) (Figure 3.1). The

collector efficiency of the entire column can be calculated from η and its vertical length.

Using the correlation equations obtained by Yao et al. (1971) and Tufenkji and Elimelech, (2004),

we can model the theoretical single collector efficiency for spherical particles (Figure 3.2). The

most favourable scenario for the particle transport (from a size perspective) is for particles with

a diameter close to one micron. Despite the solutions of the correlation equations are valid only

for beds of packed spheres, the principles of the Yao’s CFT are valid to interpret the colloid

retention in liquid-solid interface of suspended particles flowing through porous media.

Figure 3.2. Representation of the single collector efficiency for each particle diameter calculated through the models proposed by Yao et al. (1971) and Tufenkji and Elimelech, (2004) (from Lin et al., 2008).

However, the CFT does not consider the influence of structure on the colloidal retention.

Colloids can be strained in junctions, throats or cracks. So, this theory cannot describe

experimental data of colloidal transport in structured porous media. Some authors proposed

methods to identify the straining and models to include this mechanism in the transport

(Bradford et al., 2006).

b. X-Ray scanning theory

X-Ray computed tomography (CT) is an analytical technique that allows the visualisation of the

interior of solid objects (Mooney et al., 2012). It is a non-invasive non-destructive tool based in

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the attenuation of the intensity of radiation caused by the sample. The X-rays are produced in a

tube with two electrodes: when a voltage is applied, the electrons strike the anode and produce

the X-rays (Figure 3.3). The beam of X-rays crosses the sample and, depending on the structure

and composition of the sample, a part of the X-rays is scattered or absorbed. The transmission

of X-rays through the sample can be explained by the Lambert-Beer law:

𝐼 = 𝐼0ⅇ−𝜇𝑥 (eq. 3.1)

Where I0 is the intensity before crossing the sample and I the intensity after passing the sample,

x is the thickness of the sample, and µ is the linear attenuation coefficient and depends on the

properties of the sample (bulk density and electron density) and on the energy of the radiation.

Figure 3.3. Operating principle of an X-Ray scanner (from Kyle and Ketcham, 2015).

The reduction in the intensity of the X-rays is the attenuation and is measured by a flat panel

formed by a two-dimensional matrix of detectors. The sample rotates in the scanner in

successive steps, and for each angle step, a two-dimensional image representing the intensity

attenuation map is stored as digital information in a computer. The digital maps of attenuation

from different angles are combined to obtain a 3D matrix using a computer procedure called

reconstruction. The solid object is represented as a stack of cross-sectional images whose pixels

(or voxels in 3D) have different values depending on the density of the material (Mooney et al.,

2012). The value of each pixel (voxel) is expressed in Hounsfield units (HU), so the density of the

air in the soil has a value of -1000 HU (black) and the water 0 HU (dark grey) (see Figure 2.1).

The denser the material, the clearer and the bigger the value in HU.

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c. Fractals and multifractals

Fractal is a theoretical tool used to describe and characterise complex systems with irregular

shapes. The irregularities and regularities of a fractal object (or system) are statistically similar

(or identical) over a vast range of scales (Mandelbrot, 1977). In soil science, fractal analysis is

used to describe, for example, porous networks extracted from CT images (Rezanezhad et al.,

2010). It is a potential tool that can be used for identifying scale relationships that could help

with the problem of the upscaling.

Figure 3.4. Three-dimensional representation of a Menger sponge. This object is a perfect fractal constructed theoretically by an iterative algorithm.

A fractal model assumes that the system is formed by small identical (or very similar) pieces that

are also identical (or very similar) to the whole system. An example of a fractal is the Menger

sponge (Figure 3.4), a perfect or deterministic fractal. In nature, we can find other types of

fractals: the stochastic fractals (Perrier and Bird, 2002). The branches of lightning or the flower

of the Romanesco broccoli are natural stochastic fractals: systems formed by a similar pattern

repeated at different scales. The pattern of a stochastic fractal is not perfect and has physical

limits. For example, a Romanesco broccoli has a growth limit. On the other hand, if we had an

infinite resolution and make zoom in a Menger sponge, we will always see the same pattern.

So, a fractal object has two characteristics: first, is formed by the same pattern repeated at

several scales, and second, has a fractal dimension (D). The fractal dimension is a property that

defines the complexity of a system and depends on its geometry. For example, the Menger

sponge (Figure 3.4) is an object with three dimensions with holes. So, this object does not

30

entirely occupy a 3D space. We can consider that the Menger sponge has a dimension between

2 (a plane) and 3 (a volume), a fractional or fractal dimension.

The box-counting is a method for the fractal dimension estimation, which has been widely used

because it can be automatically computable (Abram et al., 1995). In this method, the image is

covered by with a sequence of grids of different sizes (Figure 3.5), and the number of squares

needed to cover the structure, N(ε), is recorded. Then, the fractal dimension (D) is

N(ε) α εD (eq. 3.2)

Where ε is the scale (or the side length of the squares of the grid). It is usual to start with the

entire system (ε) and change the scale by a factor of two (ε/2, ε/4, ε/8…).

Figure 3.5. Example of the procedure used to calculate the fractal dimension (box-counting): the structure that we are evaluating is inscribed in a grid of different sizes, and we have to count the squares needed (blue squares) to describe the structure (from So et al., 2017).

The fractal dimension concept has its limitations. In our case, the soil pore network is a complex

system that cannot be fully characterised by a unique fractal dimension: the dimension changes

with the scale.

Two different soils can have the same (or a very similar) fractal dimension at full scale but may

differ in the distribution of the fractal dimension across scales. So, it is useful to perform a

multifractal analysis that measures the variations and characterises patterns at several scales

and describes the soil complexity into a multifractal spectrum (or singularity spectrum) (Posadas

et al., 2003).

The procedure to calculate the multifractal spectrum is similar to that used in the calculations

of the fractal dimension: we have to decompose our system in squares (or cubes in 3D). For 3D

objects such as soil CT scans, the calculations are based on the probability that a voxel belongs

to the porous space (number of pore voxels/ number of total voxels). To calculate the

multifractal spectrum, we also need to use a distortion factor or scaling exponent (q) that allows

us to do a separate analysis of the bigger and smaller structures and even zoom in and zoom out

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our structure. We used values of q between 5 and -5, with intervals of 0.2, a range wide enough

to obtain a well-developed multifractal spectrum. A complete explanation of the calculations

can be seen in Torre et al. (2018), and here we are going to summarise the procedure:

𝑃𝑖(𝜀) =𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑟𝑒 𝑣𝑜𝑥𝑒𝑙𝑠 𝑖𝑛 𝑖

𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑟𝑒 𝑣𝑜𝑥𝑒𝑙𝑠 (eq. 3.3)

Pi(ε) is the proportion of pore voxels in the ith box for a given scale (ε).

𝜇(𝑞, 𝜀) = ∑ 𝑃𝑖𝑞(𝜀)

𝑁(𝜀)

𝑖=1 (eq. 3.4)

µ(q, ε) is the partition function and depends on the distortion factor (q), and the scale (ε). The

slopes of the partition function (one for each value of q) are the mass exponents, τ, and are used

for the calculation of the generalised dimensions (Dq).

𝜏(𝑞) = (𝑞 − 1)𝐷𝑞 (eq. 3.5)

When plotting the generalised dimensions (Dq) versus the scaling exponent (q), we obtain the

Rényi spectrum (Figure 3.6). Each Dq is related to the variation of structures of different sizes

with the scale and, in general, the values of Dq increase with the pore network complexity (Ge

et al., 2015). The Rényi spectrum for multifractal objects has a sigmoidal shape (Figure 3.6).

Figure 3.6. Example of the Rényi spectrum of a soil sample. The orange arrows mark interesting points of the spectrum, namely, the values of the generalized dimensions when q = -5 (Dmin), q = 0 (D0), q = 1 (D1), and q = 2 (D2).

From this plot, we can extract several interesting variables:

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- D0, the value of Dq when q = 0, is the capacity dimension, also named the fractal

dimension of the entire object and gives a global vision of the system. In order to

calculate this number, each value of Pi is raised to 0, so it only takes into account if a

cube is empty or occupied (as in the case of the single fractal dimension).

- D1, the value of Dq when q = 1, is the entropy dimension, and measures the level of

disorder present in the sample and the probability of finding pores in a zone (Posadas

et al., 2002): the bigger the value of D1, the more uniform the distribution of pores and

the bigger the probability of finding pores in any area of the soil.

- D2, the value of Dq when q = 2, is the correlation dimension, that gives a measure of the

changes in complexity over consecutive scales.

- Dmin, the value of Dq for the minimum value of q (q = -5 in our case) is the dimension that

characterises the soil parts with fewer pores (or smaller ones), and is a susceptible

property (Ge et al., 2015).

Finally, to obtain the multifractal spectrum, the Legendre transformation is used:

𝑓(𝛼(𝑞)) = 𝑞 𝛼(𝑞) − 𝜏(𝑞) (eq. 3.6)

𝛼(𝑞) =ⅆ𝜏(𝑞)

ⅆ𝑞 (eq. 3.7)

The Holder exponent (α) characterises the scaling in each region, and if the porous network is

very complex, more values of α are required, and f(α), the Hausdorff dimension, is the fractal

dimension of the boxes with the same α. The f(α) is higher for values of α well distributed in the

soil column. The multifractal or singularity spectrum, is the representation of the values of α

versus the corresponding values of f(α), and, from this spectrum (Figure 3.7), we can extract

several properties:

- The aperture (Ap) of the spectrum indicates the range of fractal exponents.

𝐴𝑝 = 𝛼𝑚𝑎𝑥 − 𝛼𝑚𝑖𝑛 (eq. 3.8)

αmax and αmin are the maximum and minimum values of the Holder exponent,

respectively. Soils with complex networks and high porosities present wider spectra

than soils with low and simple porosities. In our case, we consider that the aperture is

the width calculated in the range q (-5 to 5), but we also calculated other apertures in

other ranges (q between -1 and +1, 0 and +1, -1 and 0).

- The symmetries of the spectrum are also interesting properties. We considered both

types: horizontal and vertical symmetries.

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The horizontal symmetry (Right-Left or R-L) is calculated with respect to a vertical line

that crosses the spectrum at α0 (when q = 0).

𝑅 − 𝐿 = (𝛼𝑚𝑎𝑥 − 𝛼0) − (𝛼0 − 𝛼𝑚𝑖𝑛) (eq. 3.9)

α0 is the value of α when q = 0. Considering (eq. 3.9), positive values of R-L indicate that

the right branch is wider. This means that the smaller pores are more complex (defined

by a large range of Holder exponents).

Finally, the vertical symmetry is the difference between the two extremes of the

spectrum expressed as

𝑉 = 𝑓(𝛼𝑚𝑖𝑛) − 𝑓(𝛼𝑚𝑎𝑥) (eq. 3.10)

f(αmin) is the value of f(α) when q = +5, and f(αmax) is the value of f(α) when q = -5. As in

the case of horizontal symmetry, a positive value indicates a larger right branch (in the

Y-axis). Values of α associated with high f(α) are better distributed in the soil column.

For example, if the right branch is larger in vertical, means that the bigger values of α,

the ones associated with small porosities, are worse distributed compared with the

values of the extreme left.

Figure 3.7. Example of the singularity spectrum of one sample and some of the properties that can be extracted: the general aperture (Ap), the aperture of the left (L) and the right (R) branches, and the vertical difference between the two branches (V).

Using both spectra and the properties mentioned is possible to put in numbers the complexity

of a pore network across the observation scales. The above quantitative descriptors allow

34

performing statistical inferences about the effects of any treatment factor on the complexity of

the soil structure.

d. Percolation theory

Percolation theory is a part of statistics that studies the properties of random systems, and

constitutes an interesting framework to study complex networks. Using the study methods

based on this theory, we can describe the transport and the structural properties of the porous

media (Berkowitz and Ewing, 1998).

The central point of the percolation theory is a single property, p, the percolation probability,

the probability of finding a portion of the volume that can conduct a fluid. In a system with

enough conducting spaces, it is probable to find a path that connects two or more edges (in a

2D lattice) or sides (3D lattice). If the system is a soil, a rise in the porosity increases the

possibility of finding a path that connects the extremes: an infinite path (also called infinite

cluster). So, percolation is a critical phenomenon: the properties of the system change suddenly

when the infinity cluster appears. We call percolation threshold (pc) to the proportion of empty

spaces necessary for the appearing of an infinite cluster. The value of pc depends on the

dimensions of the system (1D, 2D or 3D), the links allowed (sides, edges, borders) and the type

of the system: the pc of a random system is different from the pc of a structured soil pore network

(Berkowitz and Ewing, 1998).

Figure 3.8. 2D representation of the formation of a percolation backbone (in green) in two-dimensional square lattices with increasing probabilities (p) of finding a porous space (from left to right). The percolation threshold (pc) for a random 2D square lattice converges to 0.43. The white squares denote the regions available to flow, and the black ones are non-conducting.

35

For values of p > pc, there will be, at least, an infinite cluster that, considering a soil cube,

connects opposite sides allowing a flow to cross the cube. This cluster is formed by pores that

actually carry the flow (the backbone) and dangling branches (dangling ends) that do not carry

it. In Figure 3.8, an example of the backbone formation in 2D is proposed: from left to right; the

percolation probability increases until reaching a connection between the borders of the

system. So, the backbone is the core of the soil porosity when studying the flow, and it is

important to know its features and how it changes with soil management.

e. Pressure Jumps

The flow of water in soils controls the storage and transport of viruses, bacteria, nutrients,

contaminants and particles (Frimmel et al., 2007). It is essential to make an accurate description

of this water flow if we want to evaluate the contamination of groundwater and soil, for

example, to determine the risks derived of a spill, or if we want to develop efficient soil

remediation plans.

The water flow in unsaturated conditions is determined, in the majority of cases, through the

Richards equation, which assumes that moisture smoothly diffuses following a non-linear

function of a water potential gradient. Under this approach, determination of soil hydraulic

properties or, more precisely, the soil hydraulic functions, namely, water retention curve and

hydraulic conductivity, are crucial to describe the macroscopic hydraulic flow. These properties

can be obtained from dynamic outflow experiments, among other methods (van Dam et al.,

1994).

However, at the microscopic scale, the unsaturated water flow occurs as the contribution of

many sharp air-water displacements at pore-scale. So, the Richards equation cannot describe

water motion efficiently at the pore-scale (Hunt et al., 2013). These fast air-water displacements

produce quick pressure oscillations known as Haines jumps (Haines, 1930). The combination of

Haines jumps has a cooperative effect, and the small air-water displacements produced at pore-

scale (10−5 m) can generate larger pressure jumps (and displacements) at bigger scales (10−3 m)

(Armstrong et al., 2015).

The size of the Haines jumps is measured as a pressure oscillation, and the analysis of the size

distribution can help us to understand the nature of this process and to assess their potential

effects. The hierarchy of sizes has a distribution that can be modelled with a power law function

36

(Aker et al., 2000; Bultreys et al., 2015). Other authors pointed out that the distributions are

exponential in small scales (Moebius and Or, 2014). These differences can be attributed to the

scale considered. In this thesis, we studied the relationship between the soil structure and the

occurrence of the pressure jumps. The interest in this subject is because structure expands the

pressure oscillations from microscopic flow, i.e., from phase displacements at pore-scale, to

larger scales. In similar words, the occurrence of large pressure oscillations can be related to

phase displacements at structural pores. Research in deep on the mechanisms involved in the

generation of large jumps can be an important contribution to the issue of the upscaling of flow

in porous media. This contribution is useful to develop models of systems that will allow us to

extend local measurements to bigger soil volumes (Jury et al., 2011).

f. Transport models. Single porosity, dual porosity and preferential flow

Traditionally, to describe and predict solute and particle movement in soils, classical models

(equilibrium models) assume a uniform transport and flow (Köhne et al., 2006). The soil is

represented as a set of impermeable objects (soil particles or aggregates) separated by porous

space, the flow is described through Richard’s equation (Richards, 1931), and solute transport is

determined using the classical advection-dispersion equation (Kumar et al., 2010).

Transport in structured porous media, such soil, needs to deal with the problem of different

connectivities of pore regions across scales, which results in the physicochemical non-

equilibrium flow and transport that was reported in many fields and laboratory experiments

(Šimůnek et al., 2008). Those models are traditionally separated into two types: physical and

chemical (van Genuchten and Cleary, 1979). In Figure 3.9 are represented the most used physical

non-equilibrium models.

Figure 3.9. Schematic representation of the non-equilibrium models used to simplify the transport through the soil (from Šimůnek and van Genuchten, 2008).

37

On the basis of equilibrium models, a Mobile-Immobile Water model was developed considering

that the soil particles (or aggregates) have their own micro-porosity and contain a part of the

soil water (immobile water). So, there is water flow and transport through the pores and a

diffusion (and retention) of solutes and particles towards immobile water. In the Dual Porosity

models (Šimůnek et al., 2003) the same partition of water is assumed (mobile-immobile), but it

is considered that water also flows through the immobile part, so there is a change of the water

content in the micro-pores (immobile part). This exchange is produced only between the mobile

and immobile zones, and there is no exchange between the micro-porosities of two different

aggregates. In this case, the solutes and particles reach the immobile zone by diffusion and, also,

advection. The other two models of Figure 3.9 are the Dual Permeability models and are similar

to the Dual Porosity one, but allowing an inter-aggregate flow. In those models, it is assumed

that the soil has two porosities: macropores or inter-pores, with a high flow velocity but only

close to saturation, and matrix pores, with slower flow velocity. The exchange of water and

substances is possible between the two porosities. Moreover, the difference between both

models, Dual Permeability and Dual Permeability with MIM (Mobile-Immobile), is that in the last

one, the matrix porosity can have an immobile area that the solutes can reach through molecular

diffusion.

On the other hand, different chemical models exist depending on the water fractions considered

and the sorption (instantaneous or kinetic). From a chemical point of view, the simplest non-

equilibrium model considers the sorption as a first-order kinetic process with one type of

sorption sites and can be extended if two fractions of sorption sites are considered (Two-Site

Sorption). The models can get more and more complicated when considering mobile and

immobile zones, or matrix and fracture parts, with different sorption rates.

38

4. Materials & methods

a. Soil sampling and pre-characterisation

We sampled twenty undisturbed soil columns (100 mm in height × 84 mm in diameter) using

PVC cases (carcasses). The sampling was done in January 2013, from two adjacent experimental

plots (Figure 4.1). We took ten columns from a plot under organic management (O) that had a

prolonged historical use for cultivating root crops and vegetables, with the removal of the

stubble. In this plot, we are going to distinguish two types of samples: OA samples, that were

taken in parts where we observed a high presence of earthworm activity (deduced from the

distribution of earthworm casts on the soil surface), and OB samples, that were taken randomly.

We took five samples of each subtype. We considered that in these two groups of samples, the

type of pores is similar, whereas the difference lies in their number. We also took samples from

conventional zones devoted to spring cereal: five columns from a plot no-tilled after sowing with

the roots preserved (NT), and the last five were obtained from a plot shallow-tilled after sowing

(ST). Notice that not all the samples were suitable for all determinations; therefore, few samples

were excluded from some of the studies presented in this thesis. The soil cores were extracted

vertically (2-12 cm depth) and sealed with a plastic film immediately after sampling. All columns

were refrigerated at 4° C to prevent structure alteration. We determined basic chemical

properties and the texture in bulk samples from the same plots.

Figure 4.1. Sampling area and points of sampling. Centro de Desenvolvemento Agrogandeiro, Ourense, north-western Spain. Coordinates 42.099N, −7.726W WGS84.

39

The soil columns were slowly saturated upwards from the bottom, by applying suction to the

upper part with a peristaltic pump. The saturated weight was recorded. At the end of all the

experiments, we weighted the dry soil (after 24 hours in an oven at 105 ºC) and calculated the

saturated water content (θs) as the difference of weight of the saturated soil minus the weight

of the dry soil. We also calculated the dry bulk density with the volume enclosed in the carcass

(100 mm in height × 84 mm in diameter).

In the same area, we also collected two smaller undisturbed soil columns (50 mm in height × 50

mm in diameter) only used in the experiments to test the sepia ink as a colloidal tracer and to

model the colloidal attachment dynamics (section 4.h. Sepia ink). For the rest of the

experiments, we employed the bigger samples (Figure 4.2). So, we will refer the later as soil

columns, soil samples or “big samples” unless we specify otherwise.

b. Sand pre-characterisation

For experiments aimed to test methods and controls, we used quartz sand (SiO2) with a grain

diameter of 0.32 mm (Aldrich Chemical, Milwaukee, WI). The sand was cleaned with sodium

dithionite (0.1 M), hydrogen peroxide (5%), concentrated hydrochloric acid (12 M) and, finally,

with deionised water (Kuhnen et al., 2000). The sand reaches the isoelectric point at pH 2.0, so

that, in our work conditions, sand grains had a negatively charged surface.

Figure 4.2. Characteristics of the samples used for each experiment.

40

For the pressure jump tests (section 4.e. Pressure jumps) we packed the sand in the same PVC

carcasses used with soils (100 mm in height × 84 mm in diameter), with the bottom covered by

a porous plate Pyrex-P5 with a pore size of 10 µm. Moreover, in the experiments for testing the

transport of sepia ink (section 4.h. Sepia ink), we used glass columns (1.8 cm in diameter, 8 cm

length) with top and bottom covered by a nylon screen (0.1 mm mesh). In both types of

experiments made with sand, columns were wet-packed with deionised water. Figure 4.2 shows

photographs of the columns described above.

c. Computed tomography: image processing and morphologic properties

extraction.

All the undisturbed large soil columns were scanned with a dental scanner 3D Cone-beam i-CAT

(Imaging Sciences International LLC, PA, Hatfield, USA) with a cathode potential of 120 kV and

current intensity 5 mA. We obtained stacks of CT images with a resolution of 0.24 mm (i.e., the

voxel volume is 0.014 mm3). This length is the spatial resolution that indicates the size of the

smaller features, in our case the minimum size of pores that could be detected. To process the

CT images obtained, we employed the software ImageJ version 1.52a (Schindelin et al., 2012). It

is noteworthy that the precise identification of a pore requires identification of several adjacent

pore voxels. Therefore the minimum pore size that can be identified with the CT scanner used

is about 1 mm in diameter (Vogel et al., 2010).

We used the complete view of the soil samples and preserved their spatial orientations in the

field to analyse the transport. So, we considered the vertical component orientation of the

gravity-driven flow during the drainage experiments regarding the orientation of the biopores.

The procedure for obtaining the pore network involves the following steps:

- Straighten the tilted images and scaling. This step also involves the addition of a

coordinate reference system.

- Crop the image to delete the PVC casing and the outer parts of the tomography (the

black background).

- Discard the images that belong to gaps and lumps at the top and the bottom of the soil

column (≈ 0.5 cm in each extreme). These irregularities usually occur by the erosion of

surfaces by manipulation during sampling, transport, and scanning.

- Binarization, i.e., separation of the soils in two parts: pores and matrix. Image

binarization, also called segmentation, is one of the most critical steps, and, for this aim,

we used the Sauvola’s auto local thresholding analysis (Sauvola and Pietikäinen, 2000).

41

This binarization procedure is local, that means that it is based on the HU values of the

neighbourhood of each voxel. We used the same setting for every sample: radius of 50

pixels, parameter 1 (k value) of 0.3 and parameter 2 (r value) of 128 (default value).

Once obtained the binazised stack, we calculated several features of the pore network. The first

property obtained was the CT-Porosity, which is the proportion of voxels that belong to the

porous network. With the BoneJ Particle Analyzer plugin (Doube et al., 2010), we calculated the

pore volume, the surface area of the internal walls, the number of pores and the connectivity, a

property obtained through the Euler characteristic (Toriwaki and Yonekura, 2002). We also

determined the percolation clusters or infinite clusters, which are the CT pores connected from

top to bottom (this is a concept from the percolation theory already mentioned in the previous

section, 3.d. Percolation theory). The percolation clusters were extracted with the ImageJ plugin

3D object counter (Bolte and Cordelières, 2006): by knowing the bounding box features (the

smallest cube encompassing each pore), we identified the pores that started in the bottom side

and ended in the top surface.

From the 2D images, the circularity of the pores was calculated as:

𝐶ⅈ𝑟𝑐𝑢𝑙𝑎𝑟ⅈ𝑡𝑦 = 4𝜋 (𝐴𝑟𝑒𝑎

𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟2) (eq. 4.1)

The pore network was skeletonised in 3D, i.e. the pores were eroded until having the thinnest

diameter. At the end of the skeletonisation process, we obtained a set of voxel chains that

describe the longitudinal axis of the pores. In this way, computer algorithms used to extract

features from the network skeleton are easy to implement. The features relevant to the

transport in the soil are the number of branches, junctions, end-point voxels (or dangling ends),

and the real length of the branches and their Euclidean length. Also, we can calculate the

tortuosity of a pore segment by dividing the length of its skeleton path by the Euclidean distance

between their two endpoints (Wu et al., 2006).

Finally, we calculated the average optical (X-Ray) density of the materials that constitute the soil

matrix: the average CT number of the matrix (CTMatrix). This value represents the average density

of the soil matrix and pores below the spatial resolution of the X-Ray detector, i.e., smaller than

0.014 mm3. This density value is given in Hounsfield units (HU): the denser matrix, the higher

the HU value. We also measured the CT number for the pore walls (CTPore), the average HU values

of the one-voxel layer surrounding the pores, to examine the difference of density of the pore

walls regarding the density of the rest of the matrix. Note that both properties, CTMatrix and CTPore

42

were calculated from the non-binarized, but we used the binarized images as masks to identify

the interface between the porous part and the matrix.

A) Multifractals and percolation properties

The CT images were also used to measure the complexity of the pore network and its percolation

properties. These measurements are provided by the values that quantify the multifractality of

the soil pore network in the soil columns and the transport properties.

For the multifractal analysis, we extracted the Rényi and the multifractal spectra and measured

all the variables used to characterise these spectra, namely, D0, D1, D2, Dmin, R-L, Ap and V (see

Figure 3.6). These variables quantify the complexity across the spatial scales.

For the percolation theory, we calculated the percolation threshold (pc), the critical pore

thickness (CPT) and the coordination number (ZT), which is the average number of branches that

start in each junction. The pc is the fraction of empty space (porosity in this case) from which soil

starts percolating. In this work, we considered only the percolating paths between the top and

bottom faces of the soil column. To calculate the pc, we used the erosion method proposed by

Liu and Regenauer-Lieb (2011). Soil samples that already presented a pore connecting both

extremes were already above the percolation threshold (having a percolation cluster). In this

case, we eroded the digital image of the pore network until the narrowest throat was closed;

that disconnects the pore and the percolation cluster vanishes. Then, we considered that the pc

is the average porosity of the last two steps of the erosion process; these are just the porosity

values over and below the disconnection. For this part, we used only the samples with a

percolating cluster.

The above erosion method was also used to calculate the CPT, which is the minimum pore

diameter of the percolation cluster. By knowing the number of erosions performed until the

disconnection and the size of each erosion (0.24 mm x 2), it is easy to calculate the CPT.

Moreover, the coordination number (ZT) is calculated through the skeletonisation of the entire

network:

ZT = (2 x Number of branches – Number of end-points)/ Number of junctions (eq. 4.2)

The backbone was extracted from the percolation cluster, by erasing the dangling ends while

preserving the loops. We measured some of the characteristics from the backbone, the same

that we measured for the entire network (pore volume and pore wall surface, among others),

43

and we skeletonised it to extract the coordination number of the backbone (ZB). Is noteworthy

that, in this case, ZT depends only on the number of loops and the number of pores connected

to the top and bottom ends of the soil column.

d. Tensiometers and multi-step outflow

Macroscopic hydraulic properties and pressure jumps of the large soil samples were determined

with the multi-step outflow gravity-driven outflow method (van Dam et al., 1994). Identification

of pressure jumps in sand experiments were done with a single-step constant flow method.

The procedures used to perform these measurements were as follows. Soils were saturated

previously, as described above. After soil saturation and weighing, the next step was to drain

the soil and left to air-dry, until friable consistency was achieved. Then, we perforated two small

holes in each column: the first one at 2 cm from the surface (T1), and the second one at 7.5 cm

from the surface (T2). There is an angle of 90º between both holes (Figure 4.3). The soil extracted

from the perforations was dried and weighted to record the mass balance when calculating the

soil properties.

Figure 4.3. Left: example of the soil sample with the position of the tensiometers (separated by an angle of 90º). Right: valve with the porous cup that connected the soil water with the pressure sensor. The third entry of the valve was used to saturate the cup.

In each hole, we inserted a highly conductive tensiometer cup (6mm in diameter and 20 mm

length) made of porous polytetrafluoroethylene with a pore size of 10 μm. We used this material

because of its sensitivity and fast response. We coupled each cup to a three-way valve

connected to a tensiometer linked to the transducer. The third port of the valve was used to

prime the cup with a syringe before the beginning of the experiment. Using a water column, we

calibrated the tensiometers for a pressure range from 10 to -80 hPa (± 0.25%).

44

After tensiometer insertion, the holes were sealed with silicone gaskets, and the columns were

saturated again and fitted in the sintered glass porous plate Pyrex-P5. The porous plate was

connected to a vacuum tubing Tygon ID 4.8 mm that ended in the lower part of a glass T

connection. This connection was open to the atmosphere and allowed the water to flow to a

balance that registered the outflow volume (Figure 4.4). We made a loop in the tube to cancel

the influence of the occurrence of air bubbles on the pressure of the water column. This system

works like communicating vessels, with the water flowing due to a pressure difference. The

pressure at the bottom of the porous plate was controlled by sliding down the outflow level.

With the column saturated and the cups primed, the tensiometers measured positive pressures

close to +2 and +7.5 hPa (T1 and T2, respectively). The multistep experiment consists in applying

different suctions (negative pressures) to a saturated soil sample and examine the time course

of the matrix potential and the outflow rate. The amount of water lost in each step depends on

the applied pressure and on the diameter and shape of the pores.

Figure 4.4. Scheme of the assembly used for the multistep experiments.

Once the multistep outflow experiment begins, the outflow was slid in order to apply -9.8 hPa

of pressure (in the upper part of the sample) for one hour; secondly, the pressure was increased

to -19.8 hPa during another hour; thirdly, a pressure of -49 hPa was applied for four hours. These

pressures correspond to pores with diameters smaller than 0.29, 0.15 and 0.06 mm. To finish

the experiment, the pressure was increased to -88 hPa until the air entry potential of the

45

tensiometer was reached (when the capillary break occurs). The selected time between pressure

steps is variable and depends on the hydraulic properties of the soil sample. However, it is better

to start a new step when the water reaches or is close to a steady state (van Dam et al., 1994).

The sampling rate of the tensiometers during all the experiment was 1 Hz, with a pressure

resolution of ±0.02 hPa. With this method we obtained, for each sample, a part of the water

retention curve (from saturation to -80 hPa). Pressure data that will be analysed in section 5.b.

Pressure Jumps.

We also tested the accuracy of the tensiometers without applying suction. The sensors did not

measure a significant drift in a three-hour test, and with the sampling rate of 1 Hz, the noise was

less than 0.09% of full scale.

e. Pressure Jumps

In order to detect and describe the pressure jumps, we used the tensiometers showed in Figure

4.3 and two types of experiments: in packed sand columns and in structured soil columns.

A) Jumps in sand columns

In this assays, we used an assembly similar to the multistep outflow experiments (Figure 4.4),

with a difference: in this case, the flow was controlled by a pulseless pump to perform

imbibition-drainage cycles. We carried out two types of experiments using sand columns (100

mm in height × 84 mm in diameter) to test the tensiometers and the experimental setup.

In the first experiments, the sand was wet-packed with deionised water to have a homogeneous

column over the porous plate (Pyrex-P5). With a KDS-270-CE pulseless high-precision pump (KD

Scientific) connected to the bottom of the columns (below the plate) and two twin syringes of

20 mL, we performed cycles of infusion and withdrawal while recording the measurements of

the tensiometers (1 Hz).

The following experiments were similar, we used the same assembly and the same conditions,

but we injected an air bubble of 1mL at 5 cm from the surface. This bubble creates a structural

void and is maintained in the saturated sand column by capillary forces and by the water

viscosity. With this procedure, we introduced a pseudo-structural feature in a homogeneous

and isotropic porous media. Then we performed drainage-imbibition cycles. When the drainage

46

front intercepts the contour of the air bubble induces an irregular geometry on the capillary

front similar to the events that can occur in macroporous structured soil.

Through the assays performed with the sand, we were able to test the reliability of the

tensiometer readings in the experiments without air bubble, and the effect of the release of the

bubble enclosed in macropores over the pressure recording.

B) Jumps in soil

From the large soil columns sampled (100 mm in height × 84 mm in diameter), we selected six:

2 from the ST, 2 from the NT and 2 from the organic land plot. The pressure measurements were

done during the multistep, using the assembly shown in Figure 4.4. So, the initial conditions and

the suction steps applied are the ones that we used in the multistep (-9.8, -19.8, -49 and -88hPa).

C) Analysis of pressure jumps

The software used to extract and analyse the pressure fluctuations is the OpenElectrophy

package developed for spike analysis (Garcia and Fourcaud-Trocm, 2009). This method allows

the extraction of the jumps from the background noise without modifying their shape. The

median absolute deviation (MAD) of the noise was used to detects and select the jumps: we

considered as jumps the fluctuations bigger than five times the MAD. We calculated the jump

size by time integrating (the area under the curve), and we obtained jumps with the same units

as the dynamic viscosity (hPa s). After the jump extraction, we analysed the time between peaks

to determine if there is a relation between the occurrence time. For this aim, Ogata’s tests were

used (Ogata, 1988).

The pressure jump distributions were described as power-laws (Bultreys et al., 2015), and we

distinguished between two types of power laws: pure and truncated. For both types, the critical

property is the scaling exponent, α, that describes the slope of the distribution, the decay with

the size. In a pure power law (un-truncated), the xmin is the lower cutoff, the minimum size for

which the power law is maintained. In a pure power law there isn’t a maximum cutoff, so we

assume that it preserves the slope to infinity. In a truncated power law, we have, besides the

minimum cutoff, a maximum cutoff (xmax), that is equal to the largest pressure jump.

f. Breakthrough experiments with latex microspheres

47

In order to study the particle transport, we performed a series of breakthrough experiments

using undisturbed soil columns as described in the previous part of this section. We used two

tracers: microspheres (MS) as the particulate tracer, and bromide as the inert solute tracer.

To determine the most favourable conditions for particle transport, we used colloidal filtration

theory. The particles of 1 μm have an optimum size for transport: they are big enough so that

diffusion does not affect them much, and they are small enough to mitigate the effects of

interception and sedimentation (Figure 3.2). The MS used are made of red fluorescent

polystyrene latex (Magsphere Inc., Pasadena, California), have a diameter of 1 ± 0.11 μm and a

density of 1.05 g cm−3. The fluorophore is rhodamine, which has an excitation wavelength of

505-545 nm and an emission wavelength of 560-630 nm. Bromide solutions were prepared from

KBr analytical grade.

Both tracers (MS and Br−) were used at the same time: the MS, in a concentration of

2.28 × 108 microspheres mL−1, were suspended in a solution of KBr, with a concentration of Br−

of 0.025 M. During all the breakthrough experiment, the MS were kept suspended by using

pulses of ultrasounds (100 ms at 1 s intervals) with an ultrasonic homogenizer (Sonopuls HD

2200, Bandelin GmbH & Co. KG, Berlin, Germany).

In this experiment, we installed the samples on a stainless-steel mesh no.18 with a mesh size of

1 mm: enough to hold the soil and allow the pass of MS. The mesh was over a funnel connected

to a fraction collector. To distribute the suspension over the soil surface, we used a robotic arm

controlled through a computer. The software generated a set of random points that the arm has

to follow, so the drops over the soil surface were randomly distributed. To prevent the alteration

of the soil, the fall height of the drops was less than 3 mm. The flow applied over the surface

was constant (≈10 mL h−1 or 5.1 mm h−1). We varied this flow slightly to avoid surface ponding

(in a few samples).

Each breakthrough experiment can be divided into three phases: in the first part we stabilised

the flow through the soil with deionised water (DW), until reaching steady-state flow; secondly,

the pulse of MS and Br− was applied (≈2-3 pore volumes (PV)); and finally, a washing with DW

was performed (≈6–10 PV). In each fraction recovered with the funnel in the fraction collector

(4-6 mL) we measured the exact volume by weighting. The Br− concentration was determined

by automated colourimetry (van Staden et al., 2003), and the concentration of microspheres

with a fluorescence spectrometer (Jasco FP-750). We determined for both tracers, the

proportion of mass retained and recovered, as well as T5%, a property that indicates the arrival

time (in pore volumes) of the 5% of the mass of Br− (T5%Br) and MS (T5%MS).

48

In order to model the transport, we used a two-region physical non-equilibrium model that

simulates the effects of a dual porosity, which is typical of structured soils. This model divides

the soil between two zones: mobile (m) and immobile (im). We calculated the transport

parameters through the optimal inverse solution using the CXTFIT2.0 Code (STANMOD package,

Toride et al., 1995). This model assumes that the soil porosity can be divided into two different

regions: mobile and immobile. The transport is described with the following equations for the

mobile zone,

𝜃𝑚𝜕𝑐𝑚

𝜕𝑡= 𝜃𝑚 𝐷𝑚

𝜕2𝑐𝑚

𝜕𝑥2 − 𝐽𝑤 𝜕𝑐𝑚

𝜕𝑥− 𝛼(𝑐𝑚 − 𝑐𝑖𝑚) (eq. 4.3)

and for the immobile zone,

𝜃𝑖𝑚𝜕𝑐𝑖𝑚

𝜕𝑡= 𝛼(𝑐𝑚 − 𝑐𝑖𝑚) − 𝜃𝑖𝑚 𝜇𝑖𝑚 𝑐𝑖𝑚 (eq. 4.4)

Where: θ is the volumetric water content [L 3 L-3]; c is the concentration [ML-3]; D is the

dispersion coefficient [L2 T−1]; x and t are the distance [L] and time [T]; Jw is the volumetric

water flux density [L3 L−2 T−1]; α is the first-order kinetic coefficient between mobile and

immobile zones [T−1]; and µ is the first-order decay coefficient [T−1] that accounts for kinetical

trapping of colloids in the immobile zone. Jw is calculated through the pore water velocity (v),

Jw = v θ.

With dimensionless parameters, we can put the eq. 4.3 and 4.4 in a dimensionless form:

𝛽𝑅𝜕𝐶1

𝜕𝑇=

1 𝜕2𝐶1

𝑃 𝜕𝑍2 −𝜕𝐶1

𝜕𝑍− 𝜔(𝐶1 − 𝐶2) (eq. 4.5)

(1 − 𝛽)𝑅𝜕𝐶2

𝜕𝑇= 𝜔(𝐶1 − 𝐶2) − µ𝐶2 (eq. 4.6)

Where: 1 and 2 indicate mobile and immobile zone, respectively; R is the retardation factor; P

is the Peclet number, defined as P = vm L / Dm; C is the concentration; Z and T are the distance

and time, respectively; β is a partition coefficient between the mobile and immobile zone (β =

θm/θ); and ω is the dimensionless mass transfer coefficient (ω = αL /θv).

In summary, to model the transport of Br− and MS, we used the pore-water velocity, a

retardation factor of 1, and the BTC points (concentration and time) to determine, through

inverse modelling, D, β, ω and µ. The last parameter was only added for the MS modelling.

A) Soil sectioning and microsphere counting

49

After the breakthrough experiments, we sliced the columns in 0.5 cm sections with a spatula, a

nylon string and a piston jack to push the sample from below. We took fluorescence

macrophotographs (16 Mpixel resolution) from the upper part of each slice with a camera

(Canon EOS 400D, Tokyo, Japan) in a dark room. The camera had a dichroic filter attached with

a bandwidth of 43 nm (592-635 nm) (Edmund Optics Inc. serial No #67-048), and the fluorescent

microparticles were excited with a green laser (Edmund Optics. Inc. Stock No #84-929,

Barrington, NJ) attached to a beam expander (Edmund Optics Inc. Stock No #58-272) (Figure

4.5). So, using this method, we located the places were the microspheres stained the pore walls.

Figure 4.5. Scheme of the assembly used to take the fluorescence macrophotographs, with an example of the result in the right part.

After taking the picture, each slice was placed in a Petri dish where we identified the stained

pores with the help of the pictures and the laser. In order to estimate the contribution of the

preferential pathways separately from the matrix, we extracted the stained pores with

perforating punches and stored them apart. To determine the profile concentration and the

number of particles retained in each part (preferential paths and the rest of the soil), we

measured the number of microspheres using the procedure described below. The soil and the

pore walls (separated in previous steps) were suspended in a solution of Tween 20 (in distilled

water, 0.02%): 20 mL for the matrix and 10 mL for the pathways. We used vortex followed by a

10 seconds ultrasonication (to avoid heating) to homogenise the suspension, and we filtered

three aliquots in nitrocellulose membranes of 47 mm in diameter with a pore size of 0.45 μm.

50

We took digital pictures of several parts of each filter with a camera, a dichroic filter coupled to

a binocular magnifier and a green laser. Particle counting was carried out with an automatic

supervised procedure using ImageJ.

Finally, the samples were dried (24 hours in an oven at 105 ºC) to determine the number of

particles per gram of dry soil, as well as the bulk density.

g. Preferential pathways extraction

Some authors use the results of the breakthrough experiments combined with mathematical

models to predict the behaviour of nutrients and pollutants in the soil (Magga et al., 2012).

However, the development of imaging techniques like X-ray CT that allows the visualisation and

characterisation of the pore network can improve our predictions regarding the fate of materials

(Akin and Kovscek, 2003). So, it is possible to identify the paths of a tracer with CT if its

attenuation factor is high enough to be detected by the CT panel sensors (Grayling et al., 2018).

Therefore, to carry out this method is necessary to use a specific tracer, with an attenuation

factor that makes it visible in the tomography image, and is necessary to make several

tomographic analyses, which have a considerable economic cost and require the processing of

a vast amount of data.

Figure 4.6. Overlapped images of a soil section with and without a filter to detect the stained pores that the particles used to cross the soil samples (preferential paths).

51

In view of these drawbacks, we proposed a novel method to describe the shape of the

preferential paths by combining fluorescence photography with just one computed

tomography. Since it is not possible to describe the features of the preferential paths from the

fluorescence images only (≈ 20 images), we proposed a procedure that combines CT with

fluorescence photography to select the pores that carry the particles.

The procedure comprises the following steps: the first step is the alignment of both sets of

images, CT images binarized (CT-stack) and fluorescence macrophotographs (MS-stack) (Figure

4.6). This was made with the marking notches of the column casing. Then, the MS preferential

paths were determined with the Simple Neurite Tracer (Longair et al., 2011), a plugin

implemented in ImageJ that is able to trace linear structures in a 3D grey-scale tomography. The

tracing of the MS paths started at the bottom of the sample, in the MS-stack. By starting from

the bottom, we ensure that the MS entering the soil surface crossed all the sample and reached

the bottom end. We selected the centre of the fluorescence spots, and we located the same

place as that spot in the CT-stack: the path started only if that point belonged to a CT-macropore.

The following step was to repeat the procedure in the immediately above fluorescence image

of the MS-Stack and the corresponding image of the CT-Stack: if the spot is in the same

macropore, the software links both extremes by choosing a path with a similar HU value (pore

tone). This process is repeated until the upper end of the sample is reached. The overall process

is repeated for each MS path. In this way, we obtained the skeleton of the MS Paths (Figure

4.7A). The information of the skeleton was analysed in the same way as the skeleton of the

entire network: branches, junctions, tortuosity, etc., as described in more detail above.

Figure 4.7. A) Skeleton of the preferential paths of a soil sample, and B) Preferential paths obtained by adapting the skeleton to the real shape of the pores.

52

In order to obtain the actual shape of the walls of the MS paths and their volume, we dilated the

path skeleton and then overlapped it with the CT-stack (Figure 4.7B). So, we obtained the

proportion of the porosity used by the MS to travel through the samples (% MS paths), and also

the proportion of pore volume connected from top to bottom used by the MS (% MS connected

paths) and the disconnected ones (% MS disconnected paths).

h. Sepia ink

Sepia ink was characterised, and we examined its suitability as a surrogate of protein-based

nano-sized colloids for transport experiments. We used the colloidal filtration theory (CFT) to

calculate the collector efficiency (η) for the soil and sand during transport. The sand experiments

were performed in small packed sand columns and small undisturbed soil cores (5 cm in

diameter x 5 cm height).

A) Ink characterisation

The sepia used in the experiments was obtained frozen and stabilised with sodium

carboxymethyl cellulose (Nortidal Sea Products Ltd., Gipúzcoa, Spain). The price of the ink is

0.05-0.08 € g−1, about 850 times cheaper than polystyrene particles of a similar size.

The commercial ink was washed with the procedure explained below. First, 4 g of ink were

suspended in 250 mL of deionised water. The suspension was centrifuged at 20000 g for 30min

(Beckmann, rotor JA-24.50). The supernatant was discarded, and we used vortex-stirring and

sonication to suspend the ink particles in deionised water again. The washing was repeated five

times.

The ink size was determined with two methods: using a Philips XL30 scanning electron

microscope (SEM), through the analysis of the images obtained, and with a qNano (Izon, Oxford,

UK), using the Tunable Resistive Pulse Sensing (TRPS) technology. The first method allowed us

to visualise the shape and make sure that the ink particles had a spherical shape, and the second

(TRPS) allowed us to determine the concentration.

To assess the stability of the ink suspension, we measured the Zeta potential (ξ) with a dynamic

laser light scattering (DLS) apparatus (ZetaSizer NANO, Malvern Inc.). Measurements were made

in water and in three electrolyte concentrations (0.1, 0.01 and 0.001M NaCl), varying the pH

from 2 to 9 to examine the influence of variable charge and ionic strength on ξ.

53

B) Breakthrough experiments with ink

The transport experiments with ink were similar to the ones with MS, but in this case, we first

used sand columns to determine parameters of the colloid filtration, and then we tried with

undisturbed soils samples. The ink concentration was the same in all experiments (0.24 mg mL−1,

or 1.07 x 1011 particles mL−1).

We conducted the experiments in water saturated conditions with a wet-packed sand column

of 1.8 cm in diameter and 8 cm length. The bottom of the column was connected to a flow cell

in a spectrophotometer (Jenway 6310) to determine the ink concentration (320 nm) at 30 s

intervals. The flow rate was 15 mL h−1, we used DW and three electrolytes, and we made steady

state and stopped flow experiments to identify attachment kinetics (see Table 4.1). The flow

was stopped when 1.2 PV had crossed the soil sample. At the end of the experiment, sand

columns were sliced to determine the profile concentration of ink.

The ink transport experiments in soil were done in duplicated undisturbed cores. Soil had pH in

water of 4.44 and 3.71 in KCl 1:2.5 (soil/liquid ratio) which indicates protonated acidic chemical

functional groups on the variable charge surfaces, and presence of potential acidic cations likely,

(H2O)nAl(OH)2+, (H2O)nAl(OH)3+and (H2O)6Al3+), in the exchange complex of negatively charged

surfaces. Soil texture was clay-loam, with an average collector diameter of 0.043 mm inferred

from texture, and a flow of 10 m h−1 with moisture close to saturation. We used the same robotic

arm as in the experiments with MS to distribute the suspension over the soil surface.

The experiments with both soil samples consisted of the following steps: flow stabilisation with

water, a pulse of Br− (≈3 PV, 8.4 × 10− 5 M Br−), water washing (≈9 PV), ink pulse (≈3PV,

0.24 mg mL− 1), water washing (≈9 PV), a second pulse of Br− (≈3 PV, 8.4 × 10− 5 M Br−) and the

last water washing (≈9 PV). As can be seen, we applied one Br− pulse before the ink pulse and a

second one after, to detect changes in the BTCs induced by the passage of the ink particles

through the soil.

We used the correlation equation developed by Tufenkji and Elimelech (2004) for predicting

single-collector efficiency (η) in the filtration of colloidal particles in saturated porous media.

The correlation equation uses the porosity of the column, the flow velocity, the size of the soil

particles and the Hamaker interaction parameter for the silica-protein pair (10−20 J). For the

transport of sepia ink in soil, we used the median of the particle size distribution (d50 = 0.043

mm) as the collector diameter, the ink particle size of 154 nm, and a flow rate of 10 mL h−1.

54

Table 4.1. Summary of the transport experiments performed in the sand with ink

Flow Rate

(mL h−1)

Pulse duration

(Pore Volumes) Pulse Composition

Time

stopped

(min)

15

10 0.24 mg L− 1 ink/distilled water 0

2

0.24 mg L− 1 ink/distilled water

0

15

120

0.24 mg L− 1 ink/ 0.1M NaCl 0

15

0.24 mg L− 1 ink/ 0.01M NaCl 0

15

0.24 mg L− 1 ink/ 0.001M NaCl 0

15

Therefore, in the soil we found η = 0.66. Considering the small size of the ink particles, the value

of η is due to the diffusion component, ηD = 0.66 (ηG =6.2 10−4 and ηI = 7.1 10−4). The sand

presented a much smaller value of η = 3.6 10−2 because in this case, the size of the collector was

bigger (d50 of the sand = 0.32 mm).

The modelling part in these experiments is similar to the employed for the modelling of MS and

Br− (section 4.f Breakthrough experiments with latex microspheres). Actually, the Br− was

modelled using the Eq. 4.3 and 4.4 (considering µ = 0). The transport of ink was modelled in a

slightly different way. We did not consider the ink exchange between the mobile and immobile

parts in sand and soil columns, but the kinetic attachment of the ink to the collector surfaces.

𝜃𝜕𝑐

𝜕𝑡= 𝜃 𝐷

𝜕2𝑐

𝜕𝑥2 − 𝐽𝑤 𝜕𝑐

𝜕𝑥− ρ𝑏

𝜕𝑆𝑎𝑡𝑡

𝜕𝑡 (eq. 4.7)

Where ρb is the bulk density of the porous matrix; and Satt is the concentration of ink particles

attached to soil or sand grains. The attachment is calculated through:

ρ𝑏𝜕𝑆𝑎𝑡𝑡

𝜕𝑡= θ𝐾𝑎𝑡𝑡𝜓𝑎𝑡𝑡𝑐 − ρ𝑏 𝐾ⅆ𝑒𝑡𝑆𝑎𝑡𝑡 (eq. 4.8)

Where Katt and Kdet are the first-order attachment and detachment coefficients for ink

particles, respectively, and ψatt is the dimensionless attachment function. The model that

55

provided better results when adjusting the BTCs was the depth-dependent colloid straining

model (Bradford et al., 2003).

𝛹𝑎𝑡𝑡 = (ⅆ50+𝑥−𝑥0

ⅆ50)

−𝛽 (eq. 4.9)

Where d50 is the collector diameter, x0 the depth distance from which the straining begins, and

β is an empirical factor (β = 0.43 or 0.479). Through inverse modelling, we determined D, Satt,

Kaat, and Kdet.

i. Statistics

Assessment of the influence of soil management on the pore network structure and their

derived properties and the correlations between the variables related to the structure and

transport are crucial in the present thesis. In order to test these influences and correlations,

first, we tested the distributions of the variables for normality through the Kolmogorov-Smirnov

test (Corder and Foreman, 2011). Non-normal distributed data were transformed with the

natural logarithm or with the square root. The influence of soil management on the soil variables

was evaluated with the one-factor analysis of variance ANOVA (Sthle and Wold, 1989). Finally,

in order to determine the correlations between different properties, we employed the

correlation coefficient (Pearson's r). All the statistical analysis were done with the software R (R

Development Core Team, 2011).

56

5. Results & Discussion

Figure 5.1 summarises the studies carried out in this thesis: it shows the results obtained from

each part, with the exception of the colloidal transport experiments using sepia ink which are

discussed apart. First of all, we obtained a quick characterisation of the basic properties of soil

samples as well as the pore network structure from CT analysis, from which we calculated

multifractal and percolation-derived characteristics in the structured soil (Results 1). Then we

performed multistep outflow experiments in the same samples, whose results were used to

analyse the pressure jumps (Results 5). These soils also were used to perform transport

experiments with fluorescent microspheres and bromide, and through modelling and

sectioning, we determined transport and retention parameters (Results 2). Modelling and

retention characteristics (Results 2) were then compared with CT derived properties (Results 1)

to find relations between both types of data (Results 3). Moreover, fluorescence photographs

took during the sectioning were combined with X-ray tomography to determine the

preferential paths (Results 4).

Figure 5.1. A schematic roadmap that summarises the main results carried out in this thesis and the results obtained (MTO, multi-step outflow experiments; BTC, breakthrough experiments).

The results obtained from the transport of sepia ink are excluded from Figure 5.1 because those

experiments were preliminary studies addressed to test several techniques that were developed

57

later in the main body of this thesis. These were carried out in other soil samples different from

the large columns used in the systematic studies. Despite that, these experiments were an

interesting approach to the study, and we believe that these results have enough interest to be

discussed in this thesis.

a. Soil and sand pre-characterisation

The soils presented a pH in a 1:10 soil:water ratio of 5.9 ±0.05, and a sandy loam texture

according to the USDA (Table 5.1). The soils had a similar content of sand, but the organic field

presented less organic matter and a larger content of silt and clay.

Table 5.1. Sieve analysis results.

Zone Coarse Sand Fine Sand Silt Clay Organic Matter

NT 46.2 ±0.5 26.1 ±0.9 5.7 ±2.9 10.9 ±1.2 11.1 ±2.6

ST 42.9 ±2.4 28.3 ±1.7 5.3 ±4.1 11 ±0.6 12.5 ±4.6

O. 44.5 ±0.2 29 ±0.4 8.1 ±0.3 9.2 ±0.7 8.5 ±0.5

The soils presented an average bulk density (ρb) of 1.46 ± 0.05, and an average saturated

volumetric water content (θs) of 0.47 ± 0.04 (Figure 5.2). Neither of these two properties showed

significant differences regarding soil management. The soil from the ST plot presented the

greatest ρb variability because most of the samples have a large compacted layer and/or large

cracks produced by tillage. These features compensate each other, resulting in a θs average, in

the ST soil, similar to the obtained for other managements. The samples from the NT plot

presented the greater ρb and the lower θs. The density is conditioned by the time that has passed

between the last tillage and the sampling, and the presence of roots in the pores. The former

determines the degree of evolution of the structure and the latter can explain the lower θs: a

compacted matrix and macropores occupied with roots leave less space for water storage.

Samples from the organic plot have an intermediate ρb because of the presence of biopores

combined with a massive structure of the matrix. The difference between both sample types

(OA and OB) is only the amount of biopores: OA samples have larger pores that increase the θs

and produce a slight decrease of the ρb when compared with the OB soil.

58

A)

B)

Figure 5.2. Box plot diagram of the A) Bulk density and B) Saturated water content of the soils studied.

Looking at the pore size distribution extracted from the multi-step outflow, the soils did not

show significant differences: the pores with a diameter larger than 0.29 mm represented the 2.1

± 0.5 % of the soil volume, the pores with a diameter larger than 0.145 mm represented the 2.9

± 0.5 %, and the pores with a diameter larger than 0.058 mm were the 3.6 ± 0.5 %.

b. Pressure jumps

Through the assembly showed in Figure 4.4, we measured the matric pressure oscillations

produced in the soils during the drainage. To begin with, the experimental setup and the first

part of the hypothesis were examined with imbibition-drainage experiments in sand columns.

Then, the same examination was conducted in drainage experiments with the soil columns.

A) Jumps in sand

In the inflow-outflow experiments made with sand without injected air, we could not find large

(detectable) pressure jumps (Figure 5.3A) in any of the flow rates between 1 and 100 mL h−1.

However, when injecting air bubbles, the tensiometers always showed large pressure jumps

(Figure 5.3B) in any flow rate used. As can be seen in Figure 5.3B, jumps were detected at the

59

same time in both tensiometers (T1 and T2), a feature that confirms that the pressure wave is

so fast (>30 cm s−1) that we cannot measure a delay between both pressure sensors.

During our experiments with sand, we injected different amounts of air, and we were able to

identify one, two and, in some cases, a series of jumps. This also happens with the same bubble

in different cycles of drainage/injection: the air is partially released, but we keep detecting small

jumps in consecutive cycles (Figure 5.3B). Despite the difference in occurrence and size, the

shape is always very similar: a fast increase of the pressure followed by a slow relaxation. It is

important to mention that, in all experiments, the jumps occurred mostly when the suction

reached the air-entry potential for the sand (-17 hPa).

A)

B)

Figure 5.3. Pressure data from the infusion-withdrawal experiments performed with sand: A) Without injected air bubbles, and B) With an injected air bubble.

B) Jumps in soil

Pressure jumps were observed in all the soil samples. Figure 5.4 illustrates the traces of pressure

records of six soils during their respective multi-step outflow experiment. To characterise the

jumps in some samples we used a higher sampling frequency of 10 Hz with the samples number

5 (C5, NT) and 14 (C14, ST). The number of jumps and the mean time between jumps registered

in samples 5 and 14 are summarized in Table 5.2. As can be seen, the sample C5 has more jumps

than C14. Moreover, the C5 jumps are separated by shorter intervals. This larger amount of

jumps in the C5 can be caused by the variety of pore sizes present in this sample, and by the

higher X-ray density of the pore walls. The density of pore walls is inversely correlated with the

porosity, so that the denser the walls the larger the bubble pressure. From these relations, we

inferred that dense pore walls increase the pressure necessary to trigger the jumps so that the

amplitude of oscillations can be larger. The C14 has a larger porosity, but in this sample, the

60

pores are huge or very small, and their walls have a low density, so the water potential may

reach the equilibrium with smaller jumps or even by much smoother moisture waves. The larger

jumps occurred more often just after the suction increase, and appear isolated or forming more

complex structures (Figure 5.4).

The jumps in soil have sizes between 0.1 and 5 hPa, and durations from 20 to 120 s: the increase

of the pressure is produced quickly (1 - 5 s), but the relaxation occurs at a slower rate. The time

scale of the jumps found in our studies is much greater than the reported in the literature for

Haines jumps in sand experiments (DiCarlo et al., 2003) or porous models (Moebius and Or,

2014).

We developed a hypothesis for the occurrence of large jumps during drainage in the presence

of structural pores or bubbles injected in sand. Haines jumps occur as a consequence of phase

displacements at a single pore scale. We propose that our jumps occur involve dual permeability

phenomena. This means that the excess of pressure can be equilibrated by flow along the

macropore itself and flow across the macropore walls. Thus, the slow rate of relaxation

produced after the jumps in macropores can be explained by flow across the walls. And the fast

rise of pressure can occur as a consequence of by the rupture of the capillary shield both at the

macropore throats and at the porous walls.

Table 5.2. Summary of pressure record obtained in the two samples in which we collected the data with a frequency of 10 Hz (C5 and C15).

Sample Tensiometer Jumps Mean Inter-jump

interval (s)

C5 T1 1086 31 ± 51

T2 1029 32 ± 53

C14 T1 673 110 ± 263

T2 660 112 ± 250

61

Figure 5.4. Pressure records for the multi-steps of the six samples considered: T1 in red and T2 in blue.

This hypothesis describes consistently the behaviour of the pressure oscillations in our

experiments and their dynamics. Let's assume the presence of air-filled pores surrounded by

capillary shields, for example, the injected air bubble in the saturated packed sand column. At

some point, the drainage front reaches the top of the air bubble and the capillary tension

reaches the bubble pressure and breaks the capillary shield on the top of the bubble and the air

enters into the pore. That produces a quick rise of the pressure followed by a slow reorganisation

of the air and water interfaces, with the excess of water flowing slowly into the matrix (Figure

5.5). This hypothesis is supported by the fact that, in the sand, the jumps are produced once the

air-entry potential is reached.

This hypothesis can be a valuable starting point to study scale flow processes in the soil and

other structured porous media since it evidences a mechanism connecting two different scales:

62

the break in the capillary shield (at pore-scale) and the redistribution of air and water (at core-

scale).

Figure 5.5. Scheme of the hypothesis of jump occurrence in a macropore. The capillary shield maintains the air in the pore (a); the suction increases until breaking the shield and the air enters in the pore producing a rise in the pressure (b); and finally, the water is slowly redistributed in the wetting front (c).

We see that jumps appear in the soil as rather complex structures, which suggests additive

effects, superposition of several pressure jumps leading to interference phenomena of pressure

waves, or multiplicative effects which lead to synergistic cascade effects that may trigger

avalanches. The size distribution of the jumps can shed some light about the nature of the

process. Therefore, we analysed the type of distribution of the jump sizes using the peak area

of the jump, that has units of viscosity (hPa s−1). Synergistic behaviour leads to scale-less

distribution, i.e., power law. However, the scale can be limited by the size of the support, i.e.,

the size of the soil sample, so that the distribution may become truncated. We examined both

truncated and un-truncated power-law distributions. Statistical tests cannot reject the null

hypotheses that the distribution is a power-law or a truncated power-law, so that tests on the

type of distribution are inconclusive. That means that we cannot discard that the pressure jumps

result from a collaborative process.

63

Consequently, we analysed both types of distributions: in the first case, we considered that the

larger value of the truncated distribution (xmax) is the size of the larger jump; in the second case

there is no size limit. The minimum value (xmin) was determined by the procedure developed by

Deluca and Corral (2013). Some of the results obtained are shown in Tables 5.3 and 5.4.

Table 5.3. Results of the truncated fitting for each of the two tensiometers of the cores C5 and C14. α is the exponent of the power law, xmin is the minimum size of the jumps, and xmax is the

size of the larger jump.

Column# Tensiometer. α xmin

(hPa s) xmax

(hPa s)

C5 T1 1.73 ±0.07 0.069 4.41

C5 T2 1.90 ±0.09 0.048 4.36

C14 T1 2.15 ±0.10 0.832 10.7

C14 T2 2.83 ±0.28 1.660 10.3

The exponents for the power law distribution in C5 are similar to the obtained in the literature:

α = 1.7 (DiCarlo et al., 2003) and α = 1.9 (Aker et al., 2000) which seems to suggest that the

pressure jumps in structured soil are of the same nature that Haines jumps, but operating at

larger scale. However, in the case of C14, the exponent is much larger, a feature that can be

explained by the huge pores present in this soil.

In conclusion, there are strong evidence of the occurrence of large pressure jumps during

drainage in the presence of macropores, but the scaling relations of these jumps with the pore-

scale Haines jumps are not clear.

Table 5.4. Results of the un-truncated fitting for each of the two tensiometers of the cores C5 and C14. α is the exponent of the power law, and xmin is the minimum size of the jumps.

Column# Tensiometer. α xmin

(hPa s)

C5 T1 2.92 ±0.29 0.479

C5 T2 1.97 ±0.08 0.048

C14 T1 2.64 ±0.16 1.820

C14 T2 3.13 ±0.28 1.738

64

c. MS Breakthrough results

A) Recovering and retention of Br− and MS

This subsection shows the influence of the soil structure on transport by examining the relations

between solute and colloid breakthrough curves and the features of the pore network of

undisturbed soil columns. Mass balance at the end of the breakthrough experiment showed that

only 85 ± 5% of bromide was recovered. It can be assumed that 15 % of this tracer was physically

retained, i.e., transferred to stagnant regions of the soil matrix. The amount of retained Br− was

independent of the soil management.

In the case of microspheres (MS), the retention was larger than Br− (43 ± 19%). Colloids have

additional physical retention mechanisms regarding unreactive soluble tracers (Bradford and

Torkzaban, 2008). However, there are no significant differences in mass retention between soils.

We attribute the lack of significance to the large intragroup variation and the presence of big

bio-pores that connect both extremes of the samples. Notice the correlation between the

retention percentages of the MS and the Br− (Figure 5.6, R2 = 0.597), that indicates that the

magnitude of the retention varies monotonically for both tracers in all the soil samples. The

regression line in Figure 5.6 also shows a linear relationship that points an MS retention about

2.26 times higher than the Br− retention.

Figure 5.6. The relation between the percentage of bromide and microspheres retained in soil samples, colours indicate the soil management.

65

Figure 5.7. A) Epifluorescence macrophotograph showing the fluorescence spots surrounding macropores; B) Close view of a pore wall region inscribed in a dashed circle with the particle accumulation, revealed by the epifluorescence microscopy, in green (x10 magnification); C) Epifluorescence microphotograph (x 1000 magnification) showing individual microspheres attached to mineral grains of soil in a pore wall; D) Concentration profile in number of particles by gram of dry soil corresponding to one representative soil column. The blue line represents the concentration of particles by gram of dry matrix, and the red one the concentration in the pore wall.

Examination of the fluorescent stains (Figure 5.7A), selective sampling and MS quantification in

deposition spots (Figure 5.7B) showed that retention occurs in the dangling end pores, i.e., dead-

66

end pores that end in the matrix, and also in the walls of the particle conducting pores (Fig.5.7C).

That retention is four times larger in the upper half of the samples, and, in proportion, the

retention of MS is three times larger in the macroporous walls than in the matrix (Figure 5.7D).

Only two samples from the conventionally tilled soil had a larger concentration of particles in

the matrix than in the pore walls (by gram of dry soil). Notice that the tillage breaks the clods

and disrupts the natural pore network, enhancing the exchange with the matrix (Figure 5.8A),

while the earthworm burrows have lined walls. Lining is a feature that hinders the transport

between the pore space and the matrix (Figure 5.8B).

Figure 5.8. Scheme of the transport of particles across the soil. A) There may be an exchange of particles between the macroporous part and the matrix if the pore walls are light enough. B) Lined pore walls hinder the exchange of particles, enhancing the preferential flow of particles through the soil.

B) Modelling transport of Br− and MS

The dual porosity transport model fitted fairly well the bromide data obtained (R ≥ 0.95) (Figure

5.9). The calculated parameters for each sample were quite similar, and only the dispersion

coefficient (D) and the 5% solute arrival time (T5%Br) showed significant differences between

zones. However, the differences in D resulted from differences in pore water velocities of the

soil columns during the breakthrough experiments, and there were no significant differences in

the solute dispersivity. Conventionally tilled soils showed the biggest T5%Br: ST 0.32 ± 0.08 PV,

and NT 0.33 ± 0.03 PV. The ST soil had a lot of cracks and a denser matrix layer in the bottom

half, facts that could produce a delay in the transport. NT soil had many interconnected root

pores that increased the complexity of the network, a fact that could contribute to a delay in

67

the bromide transport. In the organic samples, the bromide could flow along lined earthworm

pores to cross the samples quickly (OA T5%Br = 0.23 ± 0.06 PV, and OB T5%Mr = 0.21 ± 0.05 PV).

The transport between mobile and immobile zones is very similar among soils, i.e., we could not

find significant differences when considering the βBr and ωBr parameters. The ST soil showed a

slightly greater fraction of immobile zones (βBr = 0.13 ± 0.8, compared to the obtained for the

rest 0.09 ± 0.05). This could be an effect of the denser lower layer that induced solute stagnation,

which also caused a delay in the T5%Br. Also, the ωBr coefficient of ST was slightly higher than the

rest of soils, an effect that suggests that the presence of the denser lower half increased the

mass transfer of the soluble tracer to the soil matrix. The OA soil, unless having a low βBr,

presented a slightly high ωBr (0.16 ± 0.12). As can be appreciated, the standard deviation is huge,

and this value was caused by one core (no 10) poorly connected. The MS breakthrough of this

core was impossible to model using the CDE equation.

Figure 5.9. Examples of the bromide transport modelling (one sample of each soil). Orange dots represent the real data obtained, and the blue line is the fitted dual porosity model.

Modelling transport of MS required the incorporation of a soil-colloid interaction. Therefore, we

added a 1st order retention parameter (μ) that quantified the kinetic microsphere entrapment.

Also, we could not model the BTC of the samples no. 10 and 19. The first one (no. 10) showed

the biggest entrapment of MS and the lowest density, an indicator of a high content of soil

organic matter. The relation between particle retention and bulk density was also reported by

68

Jacobsen et al. (1997). Sample 19 has a pore network without connections between the upper

and the lower part, and the BTC showed several concentration peaks that never reached half of

the input concentration. So, the highest retention of MS occurred in poorly connected CT-pore

networks.

The rest of the samples did not show significant differences because of the intragroup variability.

If we compare the results with the obtained for the bromide, the values of dMS, βMS and ωMS are

quite larger, indicating that (in general) the MS travelled slower than the bromide, and with

more interaction with the soil particles, as expected. However, there is one exception: the NT

plot presented an average dMS lower 4.63 ± 2.84 (dBr = 14.11 ± 3.17). In this case, seems that the

particles that crossed the samples used only a few semi-occupied very straight root pores.

d. Ink experiment results

A) Sepia ink properties

A priori, sepia ink particles present interesting properties for the assessment of colloidal particle

transport in soil. As can be seen in Figure 5.10A, the ink particles present a semi-spherical shape,

they are cheaper than the other tracers used, and are completely innocuous. The experiments

performed with the TRPS technology showed particle populations with low poly-dispersivity

(Figure 5.10B), with a size of 130 ± 20 nm.

Moreover, the zeta potential (ζ) of the suspension used in the experiment (0.24 mg mL−1, or 1.07

x 1011 particles mL−1), was below -20 mV in a wide range of pH (4-9) and in a solution of NaCl 0.1

M (Figure 5.10C). So, the particles presented high mobility in acid soils that make them suitable

for their use as tracers in Galician soils.

69

A)

B)

C)

Figure 5.10. A) Image of an ink aggregate obtained through scanning electron microscopy (x 40000), B) Overlapped distributions of two samples of ink measured with the qNano, and C) Zeta potential of ink suspensions in three concentrations of NaCl and in deionised water at different pH. The ink concentration was the same in each measurement.

B) Ink transport in packed sand columns

The steady-state BTCs in sand showed a decrease in the efficiency of the collector with time,

caused by the blocking of the attachment sites were the ink was adsorbed. The concentration

profile of the ink was hyper-exponential, so the number of particles retained in the lower part

of the column was very low. The models based on the colloidal filtration theory (CFT) and kinetic

blocking described precisely the BTCs but not the hyper-exponential concentration profiles

(Bradford et al., 2009). The shape factor for the depth-dependent blocking model proposed by

Bradford et al. (2003) β has an optimal value of 0.43. The best fitting parameters were: a

maximum solid phase particle concentration (Smax) of 0.51 mg g−1, a first-order attachment

coefficient of 8.74 h−1, a solute exchange between mobile and immobile regions of α = 0.58, and

a shape factor (β) of 0.479 ± 0.026. These results are similar to those obtained, in similar

experiments, with Rhodococcus rhodochrous, Escherichia coli, Commamonas and

70

hydroxyapatite nanoparticles (Gargiulo et al., 2007; Tong et al., 2005; Wang et al., 2011), so the

ink particles can be used as surrogates of those microorganisms.

Figure 5.11. Data obtained from the nine breakthrough experiments performed with ink in sand.

The breakthrough with stopped flow showed an increase of the retention: 21, 30 and 31 % of

retention for continuous flow, 15 min and 120 min stop, respectively (Figure 5.11A). During the

stopped flow, the particles have more time to reach adsorption sites and the attachment

strength to the quartz particles increases (Torkzaban et al., 2007). Moreover, in those stops, the

collision efficiency increases, as reported by other researchers (Tufenkji and Elimelech, 2004).

The small salt concentrations (1mM NaCl) produced a dramatic increase in the retention (from

21 % with DW, to 96 % with 1mM NaCl), that can be caused by the retention in the secondary

energy minimum (Litton and Olson, 1996). More concentrated electrolyte concentrations (10

mM and 100 mM) resulted in similar retention percentages (Figure 5.11B, C and D).

71

C) Ink transport in undisturbed soil

Breakthrough experiments were performed in duplicate using two soil cores. These consisted of

three breakthrough tests: the first one was a pulse of Br−, then a pulse of ink suspension, and

followed by a second pulse of Br−. We observed a decrease in the retention of Br− after the ink

pulse in both samples. In the Core #1, the 0.6% of Br− was retained before the ink pulse, and

0.2% after it; and in the Core #2 the Br− retention was reduced from 5.6% to 2.3%. This decrease

can be caused by the saturation of retention zones by the first pulse of Br− and by the ink

particles attached (with a negative zeta potential).

The ink retention was higher than Br−: 13 and 11 % for cores #1 and #2, respectively, but is almost

two times smaller than the retention in sand (with DW). The shape of the BTCs and the inverse

modelling indicate that the blocking effect of the adsorption sites is similar in soil and in sand. If

we compare the results from the modelling of ink pulses in sand and in soil, we can conclude

that the attachment and the detachment rates are larger in sand, as well as the pore water

velocity. Also, the dispersion coefficient is larger in the sand.

The smaller retention in soil regarding the sand was an unexpected result. We hypothesized that

the lower retention of bromide can be caused by the dominant macropore flow produced by

the biopores. The bypass flow in the soil may contribute to descend the collision efficiency and

enhance the transport through the soil.

The main drawback of the ink as a tracer is the difficulty in determining the concentration profile.

However, one possibility is to use the TRPS technology to quantify the particles in a polydisperse

suspension in a precise range of sizes, for example, in the range of sepia ink particle size

(between 80 and 150 nm).

e. Soil CT Properties

The CT allowed us to extract properties of the three-dimensional soil pore network and to

quantify them. All variables describing the network were normally distributed, with the

exception of the Average Branch Length that was log-normal distributed and normalised in

consequence. Differences in the porous networks regarding the soil management were tested

with the one-factor ANOVA. A summary of some results is shown in Table 5.5.

72

Table 5.5. Summary of mean values and standard deviations of some of the characteristics extracted from the CT analysis. Different superscript means that there are significant

differences between different managements at a probability value P < 0.05.

Tillage Pore volume

(cm3

)

Pore Wall

Surface (dm2

)

Fractal

Dimension Tortuosity

Average Branch

Length (mm)

CT-Matrix density

value (HU)

CT-Pore Walls

density value (HU)

ST 52.94 ± 13.28b

14.17 ± 2.06b

2.67 ± 0.12b

1.23 ± 0.01b

2.04 ± 0.18a

1098 ± 32ab

136 ± 6a

NT 25.44 ± 11.75a

10.76 ± 2.10ab

2.70 ± 0.03b

1.18 ± 0.02a

2.98 ± 0.46b

1075 ± 32a

144 ± 4ab

OA 55.01 ± 7.29b

14.22 ± 3.93b

2.71 ± 0.17b

1.22 ± 0.01b

2.18 ± 0.08a

1114 ± 28ab

146 ± 6ab

OB 19.91 ± 11.75a

6.98 ± 3.43a

2.34 ± 0.13a

1.19 ± 0.01a

1.86 ± 0.30a

1149 ± 30b

148 ± 6b

As can be seen, there are similarities between the ST soil and the OA: both soils have a great

Pore Volume and Pore Wall surface, features caused by the tillage in the first case and by the

earthworms in the second one; the soil porosities are well distributed as can be inferred by the

value of the fractal dimension (closer to 3); and their pores are more tortuous than in other

samples. Tortuosity may be caused by the disrupting effect of the tillage (in the ST samples) and

by the presence of biopores (in the OA soil), as it has been proved that the tortuosity can

increase by 56% after tillage (Bramorski et al., 2012). However, if we take a look at the shade of

the CT-Pore Walls (their HU value), we can see that both soils have different density: the shade

of the ST samples is lower, indicating less dense pore walls. The shape of the ST porosity shows

that it is a mixture of few biopores and many cracks. The biopores in OA have their walls lined

by a denser layer, as reported earlier for earthworm burrows (Rogasik et al., 2014; Schneider et

al., 2018). Something similar happens with the root pores: the roots, in some way increases the

density on their surrounding soil matrix. We hypothesize that roots exert some pressure in the

surrounding soil and can reorder the soil particles towards an increased bulk density.

NT and OB soils have lower porosities, but their porous networks are slightly different. For

example, the pores the OB plot are unevenly distributed in space. The pores of both NT and OB

are quite straight when compared with soils from the other two plots, but, while the pore roots

of the NT are larger and regularly cross the samples from one extreme to another, the pores of

the OB are short and, mostly, generated by buried remains of stubble. Moreover, the NT soil

had the lightest CT-Matrix.

73

A) Linking features of CT-pore network with transport

We found correlations between the values obtained from the transport experiments (modelling

and mass balance) and the properties of the pore network extracted from the CT images. A

summary of the most interesting ones is showed in Table 5.6.

Table 5.6. Summary of the correlations existing between the transport experiment results (modelling and mass balance) and the properties of the pore network extracted from the CT images. Sample no. 19 was excluded from some regressions because their properties were

outliers.

The properties that showed significant relations are the ones related with the modelling of Br−

and with the retention of both tracers. For example, the dBr increases with the pore wall surface

and with the number of branch slabs, which is basically the total length of the pores. So, the

span of velocities of bromide transport increases in soils with large pores and high surface. The

larger surface can be produced by the roughness, a feature that increases the exchange between

the pore network and the matrix. Moreover, the pores with less surface are those with the walls

lined by the earthworms or compressed by roots, which hinder the transport of Br− between the

pore and the matrix and enhance the macropore flow. The dMS is related to the number of

Transport property CT property Pearson's R After discarding

sample nº 19

dBr Pore wall surface 0.691

dBr Number of pore branches 0.575

dMS Number of pore junctions 0.524

T5%Br CTMatrix − 0.556

T5%Br Total number of slab voxels 0.524

T5%MS CTMatrix − 0.696

% of MS Retained in the

Upper half CTMatrix − 0.498 R= -0.589

% of MS Retained in the

Matrix CTMatrix − 0.439 R = − 0.643

% Br− recovered CTMatrix 0.367 R = 0.687

74

junctions and also with the number of slabs, indicating that large interconnected pores enhance

the development of different flow velocities.

The CTMatrix is an interesting property since is inversely related with the delay times of Br− (T5%Br)

and MS (T5%MS), which indicates that the tracers travel faster in soils with denser matrices. We

conjectured that this correlation happens because the denser matrix prevents Br− from

penetrating the matrix in the same way as the lined walls. This hypothesis is supported by the

inverse correlation that exists between the CTMatrix and the retention of MS in the matrix, and by

the direct relation between the CTMatrix and the recovering of bromide. These last relations

became significant when discarding the core number 19 that presents a unique earthworm pore

that ends at the midpoint of the PVC casing wall. Therefore, MS particles cannot cross the

sample and are maintained in the porous network, a fact that enhances the exchange between

the porous part and the matrix.

f. Multifractal analysis results

As can be seen in Figure 5.12, all the plots presented the Rényi spectrum with the typical sigmoid

shape of a multifractal object. The Dq shows a decrease with q, which indicates that the fractal

dimension increases with the scale (Lafond et al., 2012), and the scaling distribution is more

heterogeneous if the distribution of Dq is wider (Marinho et al., 2016). In our case, three soils

(OA, ST and NT) showed similar spectra, but the samples from the OB plot presented more flat

spectra due to the less complexity at larger scales.

Figure 5.12. Average Rényi spectrum for the samples of each tillage management.

75

We found that D0 and Dmin, which are the values of the generalized dimensions when q = 0 and

q = -5, respectively, are sensible indicators describing the complexity of the pore networks. By

plotting D0 vs Dmin (Figure 5.13), we can separate the networks by the levels of complexity as

reported from Ge et al. (2015): the more complex the porous network, the larger the values of

D0 and Dmin. In our soils, the simpler pores are from the OB plot, and the more complex are from

NT and some samples of OA and ST. This agrees with the type of pores and the conclusions

obtained with other properties, as well as with the visual inspection of the shape of the pore

networks.

Figure 5.13. Relation between D0 and Dmin. This distributes the soil pore networks in order of increasing complexity.

From the multifractal spectrum (Figure 5.14), we draw similar findings to the ones obtained for

the Rényi spectrum. The NT samples have significantly (F-test, P < 0.05) wider spectra (3.19 ±

0.41), which means that the pore network is more complex. This complexity is due to the

presence of inter-connected pore roots. The OA samples also have wider spectra (3.02 ± 0.45)

caused by the earthworm pores, but the other samples of the organic plot (OB, with lower

biopore density) have the narrowest spectra (2.01 ± 0.22) because the porosity is low and only

a few biopores contribute to the network complexity. The aperture of the ST soil is under the

average (2.68 ± 0.14) due to a dense lower part of the soil that tends to monofractality.

76

Figure 5.14. The characteristic multifractal spectrum of each tillage management.

Looking at the symmetries, we can distinguish between four types of spectra. The majority of

the samples have a larger right branch both in horizontal and in vertical. This is the case of most

of the samples from OA, and the majority of the samples from ST and NT, and means that the

small pores are more complex but they are unevenly distributed regarding the larger pores

(simpler and homogeneously distributed in space). Two samples (one from NT and two from OB)

showed the opposite behaviour, shorter right branch, which indicates poorly distributed and

complex large pores. Another two samples (from ST and OB) have large complex pores evenly

distributed. The rest of the samples from NT have porosities dominated by complex small pores.

A) Linking multifractals with CT, transport and soil properties

In Table 5.7, we included a few examples of correlations between some fractal characteristics

and CT properties. The fractal dimension (D), the aperture and the symmetries are correlated

with almost all the descriptors of the soil network morphology determined in this thesis.

The total CT-porosity correlates quite well with the R-L symmetry, but the correlation is not

significant with the Ap. We hypothesize that this can be caused by the limiting support to

develop the complexity: to have a complex network defined by a huge span of Holder exponents,

i.e., a large Ap, it is necessary to have an adequate support (soil) to hold this variety of features.

In this case, the support is the porosity. However, if the support goes to extreme values of

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porosity, high and low, the Ap decreases at these extremes. This hypothesis is supported by the

correlation between the pore wall surface and the Ap (R = 0.678).

Another interesting correlation was found between the bulk density and the V: high bulk density

causes populations of small pores to be unevenly distributed compared to the large ones (cracks

and root pores), that still appear under compaction thorough all soil volume. The correlation

between the density and the aperture is negative, which means that denser soils reduce the

degree of multifractality, or, in other words, denser soils are less complex (Paz-Ferreiro et al.,

2013).

Table 5.7. Correlations between multifractal and CT properties (and the bulk density).

αmax αmin Ap R – L V

CT-porosity (%) 0,635** 0,835*** 0,395 0,822*** 0.792***

Pore wall surface (mm2) 0,798*** 0,780*** 0,678** 0,582** 0.455

Average pore surface (mm2) 0,767*** 0,810*** 0,611** 0,630** 0.434

Bulk Density (g cm-3) -0,306 -0,548* -0,091 -0,730*** -0,802***

Multifractal characteristics are poorly correlated with the transport properties. We only found

a significant correlation between the dispersivity of Br− and the aperture of the MF spectrum (R

= 0.628). This correlation indicates that in complex networks, which need more Holder

exponents to define their characteristics, the solute dispersivity is higher. In other words,

complex media generate a larger span of pore water velocities than simple systems. This

correlation can be explained by the total pore wall surface, which is also correlated with the

aperture of the MF spectrum (complex pores have more irregular shapes that increase their wall

area surface). We showed above that the average pore wall surface is directly related to the DBr.

The relation between the attachment and the surface roughness was already pointed by

Bradford and Torkzaban (2008).

g. Percolation and backbone properties

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The pc, i.e., the point where the soil starts to percolate (over the resolution of the CT images),

has an average of 0.014 ± 0.014. This is much lower than the obtained for random media (0.097

± 0.001), and for other porous materials such rocks (mylonite samples, pc = 0.067), or bread, pc

= 0.2448 (Liu and Regenauer-Lieb, 2011). The soil porosity is a quite anisotropic system and has

an organised structure. These features can explain its low pc value so that few pores can connect

the top to the bottom end of the soil sample. In other experiments with soils, the values

obtained range from 0.04 and 0.06 (Jarvis et al., 2017). The differences can be caused by the

lower resolution of our images or by the soil used, with a porosity developed after months

without tillage in the best case (ST). Comparing the soils used, we can see that the NT samples

presented the lower pc values (0.004 ± 0.003) generated by thinly elongated roots with a low

tortuosity. In the other extreme, we have the samples of the OB plot, with the highest pc and

more intra-group variability (0.024 ± 0.026). This plot has more variability in general (considering

other CT properties), and the pc is conditioned by the pore volume and the irregularities of the

pore network: narrow pore throats could be accounted as an interruption of the pore continuity.

The other two plots (ST and OA) have medium values because of the huge CT-porosities (Figure

5.15A).

A)

B)

Figure 5.15. Box plot of the A) Percolation threshold and B) Critical pore thickness of the samples of each tillage management.

Figure 5.15B represents the critical pore thickness (CPT) for each soil plot. The conventional soils

(ST and NT) showed the same average, but the intra-group variability is greater in NT (2.74 ±

2.57 mm) than in ST (2.74 ± 1.24 mm). The NT has, mainly, thin root pores with a CTP between

0.72 and 1.2 mm, but a couple of samples present large biopores that cross almost vertically the

soil. This biopores showed the biggest CTP (between 5.2 and 6 mm). The CTP (1.84 ± 1.21 mm)

of the OB, like the pc, can be explained by narrow throats closed after few erosions of the pore

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volume. Large values of CTP imply robustness of the connectivity of CT-porosity. On the contrary,

soils with a small CTP tend to disconnection, which leads to changes in the transport pathways.

The average value of the coordination number (ZT = 2.91 ± 0.19), indicates that in each junction

converge about three branches. There are significant differences among plots: samples from NT

and OB had ZT values of 2.88 ± 0.16 and 2.69 ± 0.19 respectively, lower values when compared

with ST (3.07 ± 0.05) and OA (3.01 ± 0.05). All the samples have values between the extremes

for natural soils (2 < ZT < 5) defined by Yanuka et al. (1986).

A)

B)

C)

D)

Figure 5.16. Images in 3D of the backbone skeletons of the different plots sampled: A) ST (nº 14), B) NT (nº 2), C) OA (nº 3), and D) OB (nº 19).

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Figure 5.16 shows the 3D projections of the backbone skeletons from representative samples of

all the soil managements. As can be appreciated, the soil with the simpler backbone is the OB:

the lower porosity of this area combined with the short length of the pores contributed to

establishing few connections between the extremes of the system. The volume and the pore

wall surface of the backbones in OB, 10.9 ± 5.3 cm3and 2.5 ± 1.9 dm2, respectively, are four times

smaller when compared with the ST or OA backbones. The uneven distribution of pores also

gives to the OB plot a backbone's fractal dimension significantly lower (D = 1.98 ± 0.13). But, the

few large pores join the small ones to conform more tortuous backbones (1.52 ± 0.08) than

those present in the rest of the treatments. Tortuosity is increased by the low presence of large

biopores that makes more visible the twisted pores created by harvest residues, small roots and

little biopores.

The backbones of the NT soils are also easy to distinguish: very straight pores (tortuosity = 1.41

± 0.05), with low volume but a great specific surface area, very ramified, with high circularity

(0.85 ± 0.02). These backbones, with a fractal dimension of 2.18 ± 0.06, are evenly distributed

than the OB backbones, but poorly distributed compared to the other two plots (ST, D = 2.35 ±

0.05, and OA, D = 2.30). This, apparently, contradictory feature (soils very ramified and

connected with a low fractal dimension) is due to the volume of the backbone: comparing the

NT with the ST soil, for example, the NT backbone's volume is almost three times smaller (15.9

± 8.1 cm3 for the NT and 43.0 ± 15.7 cm3 for the ST).

h. Microsphere pathway characterisation

The method proposed to extract the microsphere pathways is reproducible and can be used to

identify the pores which the MS went through to cross the soil column from top to bottom.

The volume of preferential MS pathways represents only the 1.25 ± 0.9 % of the total soil

volume, one-fifth of the porosity volume extracted from the CT images. This can be visualised in

the Figure 5.17, where the different parts of the network studied are displayed as follows: the

complete network, the pores connected from top to bottom, the backbone and the MS

pathways. It is noteworthy that the MS also circulated along disconnected paths from top to

bottom. Therefore, particles travelled through the matrix via pores smaller than the limit of

detection of the CT.

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A)

B)

C)

D)

Figure 5.17. Example of the networks studied for each sample. A) Complete porous network, B) Pores connected from top to bottom, C) Backbone, and D) Preferential pathways of the microspheres.

The absence of differences between the pathways of different tillage managements suggests

that particles crossed the samples through pores with similar morphology or that the paths were

independent of the morphology.

A) Features of the microsphere pathways

We found an interesting characteristic from the images used to identify the MS pathways: the

average proportion of soil surface covered by fluorescence stains (%Stained). This feature was

quantified by measuring the mean surface area of soil covered by MS (fluorescent stains) on the

cross-section of soil slices (Figures 5.7a and 5.7b). This magnitude depends on the penetration

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of MS both into the matrix (in 2D) and into the soil (in depth). The %Stained is correlated to the

CT-porosity (R = 0.72), the tortuosity (R = 0.51), and most of the descriptors of the pore network.

Moreover, it is even better correlated with the volume and surface of the backbone (R = 0.77,

and R = 0.72, respectively). It is also inversely correlated with the bulk density of the soil (R = -

0.75), and with the density of the pore walls, CTPore (R = -0.53). The last correlation indicates that

denser walls difficult the entrance of MS into the matrix.

The proportion of MS paths is related to the CT porosity of the soil (R = 0.745) and with the pores

connected from top to bottom (R = 0.772). Those relations are quite obvious because, in most

of the cases, a larger porosity means more biopores or root pores, which connect the extremes

of the soil, and constitute the preferential paths for the MS.

The ratio of Disconnected Paths/MS Paths is inversely correlated with the ratio of pores

connected from top to bottom (R = -0.511), with the retention of MS (-0.525) and with the

retention of Br− (-0.660). The first correlation is easy to explain: MS can cross samples through

connected pores from top to bottom, and also cross through the matrix out of the disconnected

pores. The ratio Disconnected Paths /MS Paths is also inversely correlated with the retention,

which can be traduced in a less presence of MS in disconnected pores. That happens in soils with

low dry bulk densities, where the MS can use the matrix to travel through the soils (Lehmann et

al. 2018).

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6. Summary and general discussion

Computed tomography (CT) is a non-invasive technique that can be used to explore the

complexity of the soil structure in a quantitative way. There is a growing development of this

technology with increasing resolution, spatial accuracy, and sensitivity. New developments of

analysis of the pore space using mathematical concepts and computer analysis, such as the

multifractal analysis and percolation theory, open new perspectives on the understanding of the

role of complexity in the soil processes and functions (Köhne et al., 2011). CT analysis can be

used to extract physical key variables that control the water flow and transport.

In the present work, we used CT to determine the network properties of soils under different

tillage management. With this technique, we calculated, without altering the samples, the pore

volume, the pore wall surface, and the tortuosity of the network, among other properties. We

concluded the first part of the work describing the differences and similitudes between the

different soils. For example, the soil from a plot devoted to conventional management with

shallow tillage (ST) presented similar values, of the above descriptors, to those of a plot devoted

to organic management with no-till but with a great presence of earthworms (OA). The pore

networks of both soils had large volumes constituted by large pores. The pores were very

tortuous but short, and their soil matrices presented an intermediate density regarding the rest

of the soil treatments. The soil under conventional management with no-till (NT) preserved the

pores formed by roots of the precedent crop. The NT soil had small CT porosity, with straight

pores, large branches and a high circularity in their pore cross-sections. The last type of soil

studied, is the organic plot randomly sampled (OB), and was also different from the other

groups. This plot presented the lowest CT porosity, with circular and straight pores as in the case

of NT, but shorter in size and unevenly distributed throughout the soil profile.

The study of the CT porosity under the light of the multifractal analysis and the percolation

theory increased our knowledge about the soil properties related to the complexity of the soil

pore network and the influence of management.

Soil pore networks presented a multifractal spectrum typical of the self-similar objects with very

complex features varying with scale, so we concluded that they cannot be described by a unique

fractal dimension, i.e., the scaling relations of the soils sampled need to be described using

different scaling factors. This was already pointed in several studies that compared the

multifractal spectrum of soils tilled with different tools (Torre et al., 2018b). When comparing

the soils that we used, the spectra of the OB samples is quite different from the others: OB soil

has a narrow spectrum associated with simpler structures at smaller scales. This soil has a low

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CT porosity constituted mostly by small pores well distributed, and few large complex pores. The

other soils are quite close to each other, with large pores simpler and evenly distributed in

depth, but a small difference in the spectrum of NT can be noticed: is more symmetrical. This

means that both large and small pores have similar complexity and are equally distributed in the

soil volume.

On the other hand, the percolation approach allowed the extraction and characterisation of the

backbone, which is the pore (or pore set) that connects the top and bottom ends and allows the

faster flow of water, solutes and suspended particles in near saturated conditions. The OB soil

had the simplest and smaller backbones, concretely, four times smaller in volume fraction than

the backbone of the ST or OA plots. The crop roots of the NT soil generated pores with

backbones less tortuous with a larger proportion of surface/volume, and a circular perimeter.

ST and OA backbones presented similar characteristics: had a greater volume and surface, were

evenly distributed (as shown by the multifractal spectrum), and had large tortuosity. The soils

studied presented differences because of the management and the time elapsed after tillage.

The time passed between tillage and sampling was enough for developing the features of the

pore network and its backbone. In similar studies, the authors could not find differences in the

soil network since the short time after tillage was not enough for the evolution of structure

(Jarvis et al., 2017).

Moreover, since CT is a non-destructive method, we could combine the results from the

quantification of the network structure properties with the transport. Therefore, we explored

the links between structure and transport by the joint use of CT and leaching experiments, using

solute and colloidal tracers to model the transport and to extract the preferential paths. The

leaching experiments were performed in conditions close to saturation, using a pulse of

microspheres suspended in a bromide solution (to examine both, solute and colloid transport).

The modelling was performed by fitting a double porosity model to the breakthrough curves

(BTC). We used this model because of the large pores present in the soils used. The

segmentation of the CT images yielded two regions of the pore space referred above, namely,

structural macropores (CT porosity) and matrix. So, the double porosity model allowed us to

consider the effects of transport between the two zones: matrix (immobile) and CT pores

(mobile). The bromide was adjusted first to fit the transport parameters for unreactive solutes.

Once these parameters were well established, they were set as fixed points to fit other specific

parameters of the colloidal transport model. The values of the parameters obtained from the

bromide modelling (D, βBr and ωBr) were quite similar among soils, and we only found differences

85

in D due to the different pore water velocities set to obtain near-saturation conditions in each

experiment. So, the dispersivity did not show significant differences.

The modelling of the transport of MS included another parameter for the kinetic attachment to

soil particles (µ). In general, the model parameters were bigger in the case of MS modelling,

including the dispersivity. That indicates that colloid particles crossed the soils with a larger span

of pore water velocities than solute tracers and MS were more retained in soil surfaces.

The preferential pathways are the ones used by the particles to travel through the soil and cover

large distances in a few seconds, controlling the transport of materials in conditions near

saturation (Luo et al., 2008). With the method developed in the present thesis, we could

measure several characteristics of those paths and determine the influence of management in

these characteristics. The extraction of preferential pathways was made by taking fluorescence

macrophotographs of the soil sections after the transport experiments with the fluorescent MS.

In those photos, the MS left traces in the pore walls that appeared as fluorescent stains. That

trace results from the attachment of MS to soil surfaces. However, the resolution of the vertical

paths is very low: in 10 cm soil samples, we only obtained 20 macrophotographs (the soil slices

had ≈ 0.5 cm). So, we used those photos as landmarks to locate the preferential paths in the CT

images and define the passage of the MS along the CT pores accurately. As a result, we obtained

a digital 3D representation of the pores that conducted microspheres at the resolution achieved

by the CT scanner. Statistical analysis of the features of these paths in samples from different

plots revealed that the morphology of preferential paths is indistinguishable with regard to the

soil management.

The leaching experiments performed have a problem related with the pollution that does not

exist in the laboratory but is crucial at field scale: the latex particles used as particulate tracer

are not “eco-friendly”, not very recommendable in open systems, and even less considering the

current hot topic of microplastics. In order to get rid of these problems, we studied the ink

eumelanins as an alternative colloid tracer.

We used eumelanin particles from the ink bag of Sepia officinalis, L. These are protein-based,

non-toxic particles (from 80 to 150 nm in diameter), and very stable in suspension. Eumelanins

showed low retention in 5 cm depth soil samples, are easy to measure by spectrometry and

present a high negative zeta potential in a wide range of pH. The main problem of that tracer is

the difficulty to quantify it in soil extracts.

One of the main problems of modern soil physics is the upscaling of imbibition and drainage

mechanisms, from the discontinuous nature of the phase displacement at pore-scale (Haines

86

jumps) to the smooth appearance of the moisture redistribution at core-scale. Haines jumps

result from displacements of air-water interfaces along the successive pores bodies and pore

throats of the micro- and mesopore network. In the present thesis, we also tried to shed some

light on the role of soil structure in water flow by exploring the fine structure of the pressure

curve during drainage of structured soil, measured with high sensitivity tensiometers.

We reported for the first time the existence of pressure jumps at core-scale during the drainage.

These pressure jumps have similar dynamics than the Haines jumps but with a much larger

pressure change and duration. These large jumps demonstrate that discontinuities during the

passage of the drainage front also occurred at core-scale, in the macropores. The hypothesis is

that the jumps are caused by the presence of a capillary shield surrounding macropores or

macropore throats. When the tension during drainage increases enough, the capillary shield

breaks and allows a fast entrance of the air in the pore. So, the water retained in the pore and

in the capillary shield is redistributed in the soil and produces a quick relaxation of the pressure.

The upscaling from pore-scale to core-scale can be explained by this mechanism since the

displacement causes a quick rise in pressure, and the redistribution of water is produced in the

entire core. Therefore, our findings can relate the soil architecture with the water movement,

and help to understand the unsaturated flow and transport.

The last part of the thesis consisted of comparing the results obtained across all the sections

with the aim to find links between different properties. That could improve our understanding

of the relations existing between the pore network and the transport, allowing us to predict

some aspects of the soil functioning.

The properties extracted directly from the CT images (before multifractal and percolation

analysis), showed good correlations with the results obtained from the leaching experiments.

For example, 5% of bromide arrival time is inversely correlated with the CTMatrix. Thus, this tracer

can cross quickly those soils with denser matrices that conduct the solute flow mainly through

the large pores. This hypothesis is supported by the fact that the amount of bromide retained is

lower in those samples with a dense matrix. We found that the optical density of the soil matrix

(CTMatrix) is one of the most interesting CT properties, since is also related with the retention of

MS: lighter matrices favour the exchange of particles and increase the retention. Other authors

also found that, in a soil with a lighter matrix (high CTMatrix), the transport of solutes is more

homogeneous (Katuwal et al., 2015).

Considering the multifractal features obtained from each soil, we found an interesting inverse

correlation between the vertical symmetry of the spectra (V) and the dry bulk density of the soil.

87

The positive values of V indicate that the small pore populations are unevenly distributed

compared to the larger ones, so the correlation points that, in denser soils, the small pores are

homogeneously distributed and the larger ones are present in all the sample. In view of the

above, the soil density has not a strong influence on the occurrence of pores generated by

earthworms and roots, but influences the occurrence of the smaller CT pores. The aperture of

the multifractal spectrum is also directly correlated with the dispersivity of bromide (dBr). This is

a very interesting finding since this high correlation reports for the first time the relation

between the complexity of the soil porous network with the solute transport. This correlation

also indicates that soils with richer scale relationships and more complex structures produce a

larger span of transport velocities for the bromide. And this correlation is supported by another

link between the aperture and the average pore wall surface: pores with rough walls are more

complex and enhance the exchange of bromide with the matrix.

The percolation analysis highlights the correlations between the backbone features and some

macroscopic physical magnitudes of soil and transport. For example, some backbone properties

as the volume, pore wall surface, fractal dimension and number of loops are inversely correlated

with the dry soil bulk density, indicating that the compaction impedes the development of large

and complex backbones. The surface area of the backbone walls and the total number of

branches are very interesting properties since are directly related with the dispersivity of

bromide: pores with a larger surface and many ramifications produce a larger variety of Br−

velocities. Furthermore, the number of endpoints of the backbone (pores that enter and leave

the soil) is correlated with other descriptors of the transport: is directly correlated with the delay

in the transport of bromide and microspheres, with the β e ω of Br−, and is inversely correlated

with the proportion of particles retained in the pore walls with respect to the particles retained

in the matrix. That correlation indicates that the number of inputs and outputs connected to the

backbone determine the extent of solute transfer between mobile and immobile regions of the

dual-porosity model. The endpoints of the backbone also have a strong influence in the ratio of

the distribution of retained particles in the pore walls and the matrix.

To conclude the correlation analyses, we also found significant relations between the

microsphere pathway descriptors and other soil properties. For example, the %Stained, a

feature related to the penetration distance of colloidal particles into the pore walls, is correlated

with the tortuosity of the pores. That correlation is consistent with the hypothesis that twisted

shapes favour the exchange of substances with the matrix across the pore walls. Moreover, a

more significant correlation between the %Stained and the backbone volume supports the role

of the backbone in the transport of particles. The %Stained is inversely correlated with the dry

88

bulk density of the entire soil and with the density of the pore walls calculated with the CT

images (CTPore). Denser soil matrices and denser soil walls difficult the exchange of particles with

the matrix and force them to be retained in the pore walls without entering in the matrix. In

consequence, the optical density of the pore walls is a soil property that should be taken into

account when devising studies to address the colloidal transport via preferential pathways.

89

7. Conclusions and future perspectives

- The mass balance of both soluble (Br−) and colloidal (latex microspheres) tracers in

transport experiments on intact structured soil columns was not influenced by the type

of tillage management.

- The two-region physical non-equilibrium model fitted the data quite accurately. We

were able to model all the results obtained for the bromide transport and almost all the

microsphere transport experiments. The results indicated that the particulate tracer, in

general, travels through the soil with a wider range of velocities than the soluble one.

Moreover, the exchange of microspheres with the matrix was also larger than the

exchange of bromide, causing an increase in microsphere retention.

- Some of the characteristics of the best fitting transport models (like the solute

dispersivity, the delay time of the 5% of the mass, or the partition between the porous

part and the matrix) were neatly influenced by the pore architecture generated by

different soil managements.

- X-ray computed tomography provides information about the soil pore network

architecture that is relevant for transport. Tomographic analysis along with computer

tools for image processing allowed us to find differences between the properties of soil

networks developed under different tillage managements. Obtaining tomography

images is becoming more accessible and its accuracy is increasing, so there is a growing

interest as a non-destructive technique for soil exploration. However, it is important to

develop standardized methods to process the images in order to compare the results

obtained with other soils and in scanners with other characteristics.

- The application of multifractal analysis and percolation tools to CT images allowed a

more precise characterisation of the pore complexity of the soil. On the one hand, the

multifractal spectra of the soils provided several descriptors of the complexity of the

pore network that were used to compare different soil management. On the other hand,

X-ray tomography allowed the parametrisation of the percolation backbone, that has a

major role in the preferential flow.

- Matrix and pore wall opacity to X-rays are strongly correlated with solute dispersivity,

with the retention of bromide and microspheres, and with the delay in the bromide

transport. We also obtained significant correlations between complexity and transport.

It is remarkable the correlation between the solute dispersivity and the aperture of the

multifractal spectrum. Analysis of the CT images provides valuable information about

90

the pore network properties that enhances the current knowledge of the soil filtering

function.

- The combination of CT images and transport experiments with fluorescence

photography allowed the isolation and characterisation of the preferential pathways of

colloid transport. We found that the preferential pathways were independent of the

management and led to similar a mass balance. This highlights the importance of the

exchange with the matrix and the matrix density in the transport.

- For the first time, we characterised pressure jumps, detected during soil drainage,

produced by fast air-water displacements in structural large pores. Our findings reveal

the occurrence of fast fluid displacements at core-scale, similar to the Haines jumps

resulting from displacements at pore-scale. The analysis of their properties, the

frequency of their appearance, and the underlying fluid dynamics open a promising field

of scaling unsaturated flow in soil.

- And finally, we found that sepia ink particles are adequate for colloid transport studies.

The particles are protein-based, with similar size and density to some virus capsids. They

form stable aqueous suspensions, are non-toxic and cheaper than plastic tracers. So,

they are promising particulate tracers that can be used as virus surrogates in colloid

transport studies in the laboratory or in the field.

91

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9. Supporting papers

Paper I:

Soto-Gómez, D., Pérez-Rodríguez, P., López-Periago, J. E. & Paradelo, M. Sepia ink as a

surrogate for colloid transport tests in porous media. J. Contam. Hydrol. 191, 88–98 (2016).

Paper II:

Soto-Gómez, D., Paradelo, M., Corral, Á. & López Periago, J. E. Pressure Jumps during Drainage

in Macroporous Soils. Vadose Zo. J. 16, 12 (2017).

Paper III:

Soto-Gómez, D., Pérez-Rodríguez, P., Vázquez-Juiz, L., López-Periago, J. E. & Paradelo, M.

Linking pore network characteristics extracted from CT images to the transport of solute and

colloid tracers in soils under different tillage managements. Soil Tillage Res. 177, 145–154

(2018).

Paper IV:

Soto‐Gómez, D., Pérez‐Rodríguez, P., Vázquez Juíz, L., López‐Periago, J. E. & Paradelo Pérez, M.

A new method to trace colloid transport pathways in macroporous soils using X‐ray computed

tomography and fluorescence macrophotography. Eur. J. Soil Sci. 70, 431–442 (2019).

Paper V:

Soto‐Gómez, D., Pérez‐Rodríguez, P., Vázquez Juíz, L., López‐Periago, J. E., Paradelo Pérez, M.

& Koestel, J. Percolation theory applied to soil tomography.

Submitted to Geoderma.

Paper VI:

Soto-Gómez, D., Pérez-Rodríguez, P., Vázquez-Juiz, L., Paradelo, M., & López-Periago, J. E. 3D

Multifractal characterization of computed tomography images of soils under different tillage

management: linking multifractal parameters to physical properties.

Submitted to Geoderma.

102

Sepia ink as a surrogate for colloid transport tests inporous media

Diego Soto-Gómez a,⁎, Paula Pérez-Rodríguez a, J. Eugenio López-Periago a, Marcos Paradelo a,b

a Soil Science and Agricultural Chemistry Group, Department of Plant Biology and Soil Science, Faculty of Sciences, University of Vigo, E-32004 Ourense, Spainb Department of Agroecology, Faculty of Sciences and Technology, Aarhus University, Blichers Allé 20, P.O. Box 50, DK-8830 Tjele, Denmark

a r t i c l e i n f o a b s t r a c t

Article history:Received 30 September 2015Received in revised form 16 May 2016Accepted 30 May 2016Available online 6 June 2016

We examined the suitability of the ink of Sepia officinalis as a surrogate for transport studies ofmicroorganisms andmicroparticles in porousmedia. Sepia ink is an organic pigment consisted ona suspension of eumelanin, and that has several advantages for its use as a promising material forintroducing the frugal-innovation in the fields of public health and environmental research: verylow cost, non-toxic, spherical shape, moderate polydispersivity, size near large viruses, non-anomalous electrokinetic behavior, low retention in the soil, and high stability.Electrokinetic determinations and transport experiments in quartz sand columns and soilcolumns were done with purified suspensions of sepia ink. Influence of ionic strength on theelectrophoretic mobility of ink particles showed the typical behavior of polystyrene latex spheres.Breakthrough curve (BTC) and retention profile (RP) in quartz sand columns showed a depthdependent and blocking adsorption model with an increase in adsorption rates with the ionicstrength. Partially saturated transport through undisturbed soil showed less retention than inquartz sand, andmatrix exclusionwas also observed. Quantification of ink in leachate fractions bylight absorbance is direct, but quantification in the soil profile with moderate to high organicmatter content was rather cumbersome.We concluded that sepia ink is a suitable cheap surrogate for exploring transport of pathogenicviruses, bacteria and particulate contaminants in groundwater, and could be used for developingfrugal-innovation related with the assessment of soil and aquifer filtration function, andmonitoring of water filtration systems in low-income regions.

© 2016 Elsevier B.V. All rights reserved.

Keywords:Colloid transportSepia inkSoilFrugal-innovationWastewater reclamationVirus

1. Introduction

There is a great variety of engineered nanoparticles, colloidfacilitated chemicals and virus families relevant to humandisease that can contaminate the surface water or groundwa-ter. The spread of these substances, especially human viralpathogens and bacteria, in natural waters relies on theeffectiveness of soil as a natural filter (Perrier et al., 2010).Soil can reduce the presence of this kind of particles by a factor

of 10−4. Knowledge of colloid filtration in porous media hasbeen developed during the past years to estimate theeffectiveness of filtration of pathogenic microorganisms fromdrinking water (Bradford et al., 2014).

Bacteria transport studies time consuming in bacterialquantification (Hornberger et al., 1992), large uncertaintiesregarding the theory.

Surrogates for viruses and micro or nano-sized contami-nants can be used to facilitate the study of transport in porousmedia (Gitis et al., 2002; Harvey et al., 2011; Knappett et al.,2008; Schijven et al., 2003). Particle surrogates should be easyto obtain and quantify, with constant composition and

Journal of Contaminant Hydrology 191 (2016) 88–98

⁎ Corresponding author.E-mail address: disoto@uvigo.es (D. Soto-Gómez).

http://dx.doi.org/10.1016/j.jconhyd.2016.05.0050169-7722/© 2016 Elsevier B.V. All rights reserved.

Contents lists available at ScienceDirect

Journal of Contaminant Hydrology

j ourna l homepage: www.e lsev ie r .com/ locate / jconhyd

properties, and safe for humans and the environment (Cheng etal., 1994a,b). These can be used to study the interactionsbetween colloidal particles and soil, and to test hypothesesabout their fate in the environment, including facilitatedtransport of contaminants and spreading of bacteria andviruses in soil and aquifers (Dongdem et al., 2009).

Reliable surrogates for pathogenic microorganisms can beused in testing and monitoring of water purification systems,especially in developing countries with very limited technicalresources (Xagoraraki et al., 2014), or in research of newmaterials for virus purification (Gutierrez et al., 2009). Inaddition, surrogates can be used to identify technical andmanagement deficiencies in wastewater treatment systemswhich may lead to human exposure and disease. Also can beused for potable reuse of reclaimed wastewater via artificialrecharge (Verbyla and Mihelcic, 2014), especially to examineremoval of bacteria and viruses.

An important number of the studies of colloid transport inporous media use fluorescent or radio-labeled polystyrenelatex microspheres (Frimmel et al., 2007) with differentfunctional groups attached to their surface. However, carbox-ylated latex microspheres (20 and 200 nm) show differentresponses to changes in solution chemistry compared to viralpathogens and bacteriophages (Mondal and Sleep, 2013).Besides, these materials are costly: 100 mL of this particlescost between 460 and 2000 €. Sharma et al. (2012) proposedthe use of DNA-tagged polylactic microspheres for tracking ofthe paths of colloids in natural media. DNA-labeled, protein-coated silica nanoparticles were used to mimic filtration andtransport of rotavirus and adenovirus in sand media (Pang etal., 2014).

Particle deposition in porous media is complex. In the caseof saturated water flow three mechanisms have commonlybeen identified (McDowell-Boyer et al., 1986): attachment,mechanical filtration (i.e. which occurs at the top of the filter),and mechanical retention into the matrix (straining)(Torkzaban et al., 2008). Briefly, attachment is referred to theretention of particles in the matrix by adsorption to the porousmatrix (Bradford et al., 2002). Attachment of particles ingranular porous media can be described in part by modelsbased on the capture of colloids by spherical collectors,formulated for first time by Yao et al. (Yao et al., 1971). Thus,small spherical particles with large negative charge will havesmall deposition rates in soil. In addition, adsorption rate can betime dependent, either decreasing rate by progressive occupa-tion of available adsorption sites (blocking) or increasing rateby cooperative adsorption of new arriving particles by the firstadsorbed ones (ripening) (Bradford et al., 2003).

Many laboratory experiments have demonstrated that thecolloidal filtration is less effective in structured soils. Particlescan travel faster throughmacropores, and several models weredeveloped to differentiate between the transport inmacropores and in the matrix (Jarvis et al., 1999). Additionally,in unsaturated porousmedia, colloids can bedeposited throughcapillary force interactions in soil-water interface (SWI) andair-water interface (AWI) found in pendular rings, triple pointsand water films (DeNovio et al., 2004).

Sepia ink is considered to be pure eumelanin and is used asa standard for natural eumelanins. A comprehensive descrip-tion of these compounds can be found in other works (Liu andSimon, 2003a). Sepia ink is formed by an almost pure colloidal

suspension of eumelanin. All melanins are generated from theoxidation of molecules of tyrosine, forming DOPA-quinone,which polymerizes to different types of melanins. The firstaggregation level cell comprises two or three of thesemolecules or nanoclusters forming a core (Zajac et al., 1994).These stacks of oligomers are joined by edges and formfilaments that aggregate to form spheres with a size ~154 ±10 nm. Sepia ink has a total metal content of 4.7%, being 2.4%Mg and 1.7% Ca the most abundant and 170 mg kg−1 Fe, thatcontribute to the conformational structure during biosynthesisbut are not required to sustain the morphology once thegranule is assembled (Liu and Simon, 2005). The sphericalshape and size of sepia ink particles can mimic the colloidalproperties of some families of viruses such as Adenoviridae andRetroviridae.

Sepia ink eumelanin is insoluble and stable in water,absorbs ultraviolet and visible radiation, and can relax photo-excited states without emitting radiation (Meredith and Sarna,2006).These properties are optimal for optical shielding inseawaterwhich serves to protect sepias from predators (Derby,2014).The stability of this substance in saline environmentssuggests that sepia ink could be a good candidate for colloidaltransport studies.

In this work, we examine the colloidal properties of dilutedsepia ink suspensions for their potential use as a surrogate tostudy of the transport of bacteria, viral pathogens andnanoparticles in packed quartz sand and undisturbed soil.Firstly, we determined the electrokinetic properties of sepiaink; then, transport of sepia ink in water-saturated quartz sandcolumn was examined to identify the attachment model, byusing steady-state breakthroughs and stopped flow tests; andfinally, transport experiments in partially-saturated undis-turbed soil cores were done to examine the influence of thesoil physical properties in the movement of suspended sepiaink particles.

2. Material and methods

2.1. Materials

2.1.1. Sepia inkSepia inkwas obtained as frozen ink stabilized with sodium

carboxy methyl cellulose (Nortidal Sea Products Ltd.,Guipúzcoa, Spain). The price of this material (buying smallamounts) is about 0.05–0.08 € g−1, around 700–1000 timescheaper than polystyrene particles of the same size. A stocksuspension of purified eumelanins was obtained by washing asuspension of 4 g of commercial ink in 250 mL of deionizedwater (DW). The washing process was performed as follows:centrifugation at 20,000 g for 30 min (Beckmann, using a rotorJA-24.50) and resuspension by vortex-stirring inwarmDWandsonication (Bandelin electronic sonoplus HD 2200, Berlin,Germany). This washing was repeated five times. Aliquots ofdiluted stock suspension were analyzed to determine size andshape by using Scanning Electron Microscopy (SEM). Particlecounts in purified suspensions in DW, with a qNano (Izon,Oxfod, UK), were used in conjunction with the particlediameter in order to calculate the concentration of suspendedparticles. Particle density measured with a He pycnometer onfreeze-dried samples was 1.27 g cm−3 which is lighter thanrotavirus, 1.36–1.4 g cm−3 (Vonderfecht et al., 1984) and

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Hepatitis-B, 1.32–1.35 g cm−3 (Sprinzl et al., 2001), but heavierthan polystyrene particles used as surrogates, of 1.05, 1.07, and1.05 g cm−3 (Passmore et al., 2010).

Zeta potential (ξ, mV)measurements are commonly used toassess the stability of colloidal suspensions and adsorption ofcolloid particles onto charged surfaces. Electrophoretic mobil-ity UE (μm s−1 cm mV−1) and ξ were determined in DW andthree concentrations of electrolyte (0.1, 0.01 and 0.001MNaCl)with the Zetasizer NANO (ZetaSizer NANO, Malvern Inc.). Thistechnique calculates ξ by measuring electrophoretic mobilitywith a combination of laser Doppler velocimetry and phaseanalysis light scattering (PALS) in a patented technique calledM3-PALS. Zeta potential is calculated from the UE using theSmoluchowsky-Henry equation (Hunter, 1981). The popula-tion of sepia ink particles was examined by flow cytometryusing a Beckman Coulter FC500 (Beckman Coulter, Inc.).

2.1.2. SandQuartz sand (SiO2) was used as the column packing

material. The quartz grains were well sorted, with a graindiameter of 0.32 mm (Aldrich Chemical, Milwaukee, WI). Thesand was thoroughly cleaned by following a proceduredescribed elsewhere (Kuhnen et al., 2000) prior to use. Theisoelectric point of quartz is at pH 2.0, which provided negativesurface charge in all the experiments. Clean quartz sand waswet-packed in columns (1.8 cm in diameter, 8 cm length) withdegassed DW. The top and bottom were covered with a nylonscreen, 0.1 mm mesh, to retain the sand grains. The watercontent and the bulk density were identical for each test.

Table 2 shows the properties of the packed quartz sandcolumn related with the colloid filtration theory (CFT). Thelarge diameter of the sand related to sepia ink, made thetheoretical mechanical filtration very low. This behavior isascribed in the scientific literature to heterogeneity of surfacecharge, double layer interaction dynamics, deposition insecondary DLVO minima potential, other non-DLVO interac-tions and the roughness of the quartz sand (Treumann et al.,2014).

The single-collector contact efficiency from the Tufenkji-Elimelech (Tufenkji and Elimelech, 2004) correlation function(Table 2) was η =3.59 10−2 due to the diffusional componentηD = 3.58 × 10−2.

2.1.3. SoilTwo undisturbed soil cores (5 cm diameter and 5 cm long)

were sampled from 2 to 7 cm soil depth in a homogeneousexperimental plot (Xinzo de Limia, Ourense). The pH value ofthe soil, in water, was 4.44, and 3.71 in 0.1 M KCl 1:2.5 (soil/liquid ratio). This difference between the twomeasurements isdue to the exchangeable aluminum. Organic carbon contentwas 2.73 g per 100 g−1 soil, determined by elemental analysison a Thermo-Finnigan 1112 series NC instrument. Wemeasured exchangeable cations in ammonium chloride ex-tracts (1 M pH 7): Na 1.84, K 0.69, Ca 0.31, Mg0.13 cmol charge kg−1 dry soil. Soil texture (USDA classifica-tion system) was clay-loam, with 43% sand, 24% silt and 33%clay, determined by the wet sieving and pipette methods. Thegeometric mean particle diameter was 0.043 mm and ageometric standard deviation of 20 μm.

2.2. Breakthrough experiments

2.2.1. Transport in saturated quartz sandThe inlet suspensions used in the column tests were

prepared by mixing the purified sepia ink with DW or selectedNaCl concentrations (viz., 0.1, 0.01 and 0.001M). Concentrationof ink was 0.24 mg mL−1 (~1.07 × 1011 particles mL−1,calculated from particle density and average size) in alltransport experiments. The ink-suspensions were sonicated(cycles 1 s sonication 10 s silence) while they were applied atthe top end of the column for all the experiments with aperistaltic pump (Gilson Minipuls III, Gilson Inc.).

Concentration of ink in the effluent fractions was measuredby light absorption in an 80 μL flow-through cell from HellmaGmbH (Müllheim, Germany); measurements were made at awavelength of 320 nm at 30 s intervals on a Jenway 6310spectrophotometer. The linear correlation (r2 N 0.999) be-tween light absorption of diluted standards of ink was used tocalibrate the photometric readings. The cumulated volume ofthe percolatewas recorded and expressed as pore volume units(PV). Breakthrough curves (BTCs)were plotted by representingthe relative concentration of ink in the outflow in function ofthe number of PV percolated. Outflow samples were alsocollected with a fraction collector to measure pH and EC.

Each breakthrough experiment consisted in three steps,namely: (1) pore water stabilization by washing the quartzsand column with ink-free DW or NaCl solution (1, 10 and100 mM); (2) application of the ink suspension at the samepH 6.4 ± 0.2 and ionic strength as the outflow (sameelectrolyte) used in the step 1; (3) elution by washing thequartz sand column with an ink-free solution at the same pHand ionic strength (same electrolyte) as previous steps. Twotypes of experiments were done: steady state flow saturatedtransport and saturated stopped-flow. The experimental designis shown in the Table 1.

Table 1Experimental design: electrolyte concentrations, pulse duration and stoppedflow times. The pH in all influents was 6.4.

Pulse duration(PV)

Pulse composition:ink/electrolyte

Time stopped(min)

Quartzsand

10 0.24 mg L−1 ink/distilledwater

0

2 0.24 mg L−1 ink/distilledwater

015120

0.24 mg L−1 ink/0.1 MNaCl M

015

0.24 mg L−1 ink/0.01 NaCl M

015

0.24 mg L−1 ink/0.001NaCl M

015

Soilcoresa

3 0 mg L−1

ink/8.4 × 10−5 Br− M0

9 0 mg L−1 ink/distilledwater

0

3 0.24 mg L−1 ink/distilledwater

0

9 0 mg L−1 ink/distilledwater

0

3 0 mg L−1

ink/8.4 × 10−5 Br− M0

a The same for both cores.

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2.2.1.1. Steady flow. First, a steady-state breakthrough experi-ment with a long pulse (10 PV) was performed as explainedpreviously, without interruption. Concentration profile ofretained particles (RP) was determined at the end of thebreakthrough.

2.2.1.2. Stopped flow. In order to test if the deposition of inkcolloids is time dependent, we performed stopped flowexperiments.

In this case, each pulse durationwas about 2 PV of duration,but the flow was stopped when 1.2 PV had passed through thecolumn, and resumed after 15 min or 120 min.

Steady and stopped flow tests were made during thebreakthrough, in the same conditions, in order to check if theattachment of ink colloids is time-dependent. We employedthree NaCl concentrations in order to examine the influence ofionic strength on the filtration during the stopped flow. Alsoweused sand under saturated conditions in order to have ahomogeneous material that could be modeled easily andcompared with other works.

2.2.2. Transport in soil

2.2.2.1. Breakthrough setup. Each soil core was placed on astainless steel mesh No. 18 attached to a polypropylene funnelthat conducted the outflow from the bottom to the automatedfraction collector. Flow boundary conditions in all break-through experiments were: constant flow rate at the upperboundary and free drainage at the bottom. All the pulses andDW were distributed dropwise at random points thoroughlythe top soil surface by a robotic arm attached to the dripper at aflow rate of 10 mL h−1 (5.1 mm h−1). This ensured a uniformdistribution of the ink on the soil surface because colloids donot diffuse as fast as solutes. The fall height of drops was lessthan 3 mm to prevent disruption of the soil structure.

The experiment consisted in three steps: First, a 10 h pulseof KBr− used as unreactive tracer (100 mL, 8.4 × 10−5 M Br−)was applied followed by 30 h washing (300 mL DW). Then asingle pulse of ink of 10 h duration (100mL of suspension witha concentration 0.24 mg mL−1, equivalent to ~1.07 × 1012

particles) was applied. Suspensions were kept stirred byrepeated sonication pulses (1 s duration each 10 s) whiledistributed on the top of the soil, to prevent any eventualaggregation of particles before entering the soil. The ink pulsewas followed by 30 h washing with DW. Finally, a second Br−

pulse was applied in the same way as the first one. The twotracer pulses, before and after the ink pulse, were performed tocheck any change in the core produced by the particles ofeumelanin.

The effluent fraction volume (~5 mL per tube) wasdetermined byweighing. pH, CE, ξ and Br−were alsomeasuredin aliquots. Ink concentration in the outflow fractions wasdetermined photometrically by calibrating the absorbance inink standards diluted in the ink-free soil outflow percolates.

After the transport experiments, the cores were segmentedin 0.25 cm slices and dried at 115 °C, in order to get the RP.Experiment was repeated using two cores extracted from closelocations.

We carried out this kind of experiments, with an inksuspension in soils, in order to test the retention of the particlesalong the soil profile.

2.3. Modeling tracer in soil columns

We worked with the hypotheses that our data could befitted by a two-region solute transport model (van GenuchtenandWagenet 1989). This means that our cores had preferentialflow paths, and the bromide could have used this paths totravel faster. In thismodel, the soil solution is treated as dividedbetween immobile and mobile regions. It is assumed thatsolutes infiltrate the soil from the surface by diffusion andconvection in the mobile region and by a first-order process oftransfer from the mobile to the immobile region. Theseassumptions lead to the equations

θm ∂cm=∂tð Þ ¼ θm Dm∂2cm=∂x

2–vm∂cm=∂x� �

−α cm–cimð Þ ð1Þ

θim ∂cim=∂tð Þ ¼ α cm–cimð Þ ð2Þ

where x is distance down the column (cm); t is time (h); thesubscripts m and im indicate quantities describing the mobileand immobile liquid regions, respectively; c is concentration ofsolute (mg L−1); θm and θim are the volumetric water contentsof the soil in the mobile and immobile regions, respectively(cm3 cm−3) θm + θim = θ, where θ is porosity or void fraction(cm3); vm is the average velocity of water through pores in themobile region (cm/h; vm = vθ/θm); Dm is the hydrodynamiccoefficient of dispersion of the solute in the soil solution in themobile region (cm2 h−1); and α (h−1) is the first-order masstransfer coefficient for solute exchange between the mobileand immobile regions.

Eqs. (1) and (2)may be expressed in termsof dimensionlessquantities in the form

βR∂cm=∂T ¼ 1=Pð Þ∂2cm=∂Z2–∂cm=∂Z−ω cm–cimð Þ ð3Þ

1−βð ÞR∂cim=∂T ¼ ω cm–cimð Þ ð4Þ

where Z = x/L (L being the depth of the sampling tube, thebreakthrough data for which are being fitted with the model);T = vt/L; P = vmL/Dm is the Peclet number; R = 1 + ρbKd/θreflects retardation due to adsorption; β = (θm + fρbKd)/(θ+ ρbKd) is the fraction of solute “sites” (water volume plusadsorption sites) in the mobile region; ω= αL/θv is the scaledmass transfer coefficient; f is the fraction of adsorption sitesexposed to themobile liquid phase; ρb is the bulk density of thesolid phase; and Kd is the partition coefficient (mL g−1). In thiswork, the program CXTFIT v.2.1 (Toride et al. 1995), a softwarepackage included in HYDRUS 1D, was used to fit theseequations to breakthrough data obtained in experimentsdesigned to approximate the following initial and boundaryconditions:

1Þcm Z;0ð Þ ¼ cim Z;0ð Þ ¼ 0 for all Z; ð5Þ

2Þcm 0; Tð Þ– 1=Pð Þ∂cm 0; Tð Þ=∂Z ¼ ci Tð Þ ¼ ci; ð6Þ

3Þ∂cm=∂Z 1; Tð Þ ¼ 0 ð7Þ

where the input function ci(T) represents the duration of a

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pulse (min) of constant concentration ci dropped randomlyonto the top of the column. For the relationship betweencondition 2 andmass balance, and the assumptions involved incondition 3, see Parker and van Genuchten (1984).

2.4. Particle transport model

The model of the particle transport has been derived fromthe classical convection-dispersion equation (CDE) and particlecapture models in porous media. We assume that particles donot enter into the immobile water. Therefore, for an aqueoussuspension of monodisperse particles flowing verticallythrough a porous media, the one-dimensional form of theCDE with kinetic attachment may be written:

θ ∂c=∂tð Þ ¼ θ D∂2c=∂x2–v∂c=∂x� �

–ρb ∂ Sattð Þ=∂tð Þ ð8Þ

where D is the hydrodynamic dispersion coefficient (cm2 h−1),v is the average pore-water velocity (cm/h), ρb is the bulkdensity of the porous matrix (g cm−3), and Satt (g g−1) is theconcentration of particles attached to sand grains. The

attachment rate is given by

ρb ∂ SAttð Þ=∂tð Þ ¼ θkAttψAttc−ρbkDetSAtt ð9Þ

where kAtt and kDet are the first-order particle attachment anddetachment coefficients, respectively (h−1), and ψAtt is adimensionless attachment function.

The depth-dependent colloid straining model provided thebest results fittings to the experimental BTCs (Bradford et al.,2003).

ψAtt ¼ dc þ x–x0ð Þ=dcð Þ−β ð10Þ

where dc is the mean particle diameter (cm), x0 depthwhere the straining starts (cm) (here is the soil surface, so x0=0), and β is an empirical factor with an optimal value of 0.43(Bradford et al., 2003). The kAtt was obtained from inversemodeling of the of sepia ink BTCs.

Fig. 1. Scanning electron microphotographs of purified sepia ink eumelanins: a) ×40,000 and b) ×180,000 magnification. Similar photographs were used fordetermination of the particle size and the description of the shape. c) Density plot of flow cytometry intensities in log-log scale of front scattering (FS), side scattering(SS). d) Histogram of relative density event counts in the two gated clusters enclosed in the outer contours in panel c.

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3. Results and discussion

3.1. Sepia ink properties

SEM photographs showed that purification removed small-er fractions and other impurities. Purified sepia eumelaninparticles were quasi-spherical (Fig. 1a, b) with size close to100 ± 10 nm in diameter smaller than the 154 ± 10 nm (Liuand Simon, 2003b).

The flow cytometry analysis of the ink suspension in DWshowed a scattering map with a typical pattern of a polydis-perse population of single particles and aggregates. Two mainclusters appeared when we represent the front scattering (FS)and the side scattering (SS) data, one with a huge amount ofparticles, and a largest one, with bigger particles (Fig. 1c, d).Larger and complex clusters also appeared in the scatteringplots but to a lesser extent (b 0.05% of all events).

Dynamic light scattering (DLS) showed that the hydrody-namic diameter of particles was from 164 to 170 nm. That was10 nm larger than the reported by Liu & Simon (Liu and Simon,2003b) and 70 nm larger than measured by SEM. Thatdifference can be due to polydispersivity that causes a dramaticinfluence of a few large particles on the intensity of scattering.

The ξ reached amaximum of−45± 6.6mV in DW at pH of6.5 and EC 0.046 mS cm−1. Zeta potential was below−20 mVin the range of pH from 4 to 9 with concentrations of NaCl lessthan 0.1 M (Fig. 2). Therefore, particles have a high electro-phoretic mobility in moderately acid soil water and ground-water (pH ~ 6.5), which is very common in the vadoseenvironment. Zeta potential was similar to the viruses, andthe isoelectric point (pH ~2) was near the typical values forenterobacteria phagues (Michen and Graule, 2010). Thefunctional groups of the melanin –COOH, − NH and –OH arethe same of viruses and the responsible of the pH-dependentsurface charge (Hong and Simon, 2006).

3.2. Transport in quartz sand

3.2.1. Steady flowBreakthrough curve in quartz sand (Fig. 3) clearly showed

that collector efficiency decreased with time, which agreed

with a blocking effect of the adsorption sites. Mass balanceindicates a 20% of mass retention at the end of the experiment.The RP was hyperexponential (Fig. 3b), which has beenreported for latex microspheres, bacteria, viruses, hydroxyap-atite nanoparticles, and functionalized nanotubes in conditionsof electrochemical repulsion (Bradford and Bettahar, 2006;Bradford and Toride, 2007; Gargiulo et al., 2008, Gargiulo et al.,2007). Hyperexponential profiles indicate a decrease inretained concentrations with distance of transport, which canbe ascribed to straining (Bradford et al., 2005), impurities andthe roughness of the quartz sand or polydispersivity of particles(Tong and Johnson, 2007).

The models based on the CFT with and kinetic blocking,namely, Langmuirian and Random sequential adsorptiondescribed well all the BTCs but were unable to reproduce thehyperexponential RP (not shown). The best fitting results wereobtained with the approach based on the effects of straining,blocking and attachment with a depth-dependent coefficientfor the straining (see Table 4). The parameter Smax (themaximum solid phase particle concentration, mg g−1) = 0.51(Eq. (8)) and kAtt (the first order attachment coefficient) =8.74 h−1 (Eq. (9)), andη=3.59 10−2 (Table 2), gives a stickingefficiency α = 0.58 (Eqs. (1), (2)). The best description of theconcentration profile was obtained with β = 0.479 ± 0.026(Eq. (10)), and indicated that depth-dependent straining wasthe most likely model. We also used the reference value of thecoefficient β= 0.431 (Eq. (10)), found by other authors for thetransport of spherical latex beads in sand columns (Bradfordet al., 2003). This coefficient reproduced reasonably the BTC inFig. 3a, and the concentration profile in Fig. 3b.

Few works reported depth-dependent blocking andstraining models for viruses and bacteria. For 0.33 mm quartzsand 0.8 water saturation Rhodococcus rhodochrous, gram-positive bacteria 1 μm size, showed straining with a depth-dependent blocking factor β = 0.37; obtaining large valuesSmax = 19.2 , kAtt = 15 h−1, and kDet (the first-orderdetachment coefficient) = 3.6 h−1 (Gargiulo et al., 2007).Mean values for the distributed attachment coefficient for theCommamonas bacterial strain DA001 with dimensions 1.1 x0.3 μm were in the range from 0.75 to 3.56 h−1 (Tong et al.,2005). Bacteria Escherichia coli 0157:H7 in 0.36 mm saturated

Fig. 2. pH-ξ titration curves of sepia ink eumelanins in deionized water and different electrolyte (NaCl) concentrations.

93D. Soto-Gómez et al. / Journal of Contaminant Hydrology 191 (2016) 88–98

quartz sand was slower Smax = 0.306, kAtt = 1.26 h−1 withoutdepth-dependent straining. Transport of denser 3.2 g cm−3

hydroxyapatite nanoparticles 0.1 μm was also modeled withtwo sites depth-dependent blocking usingβ= 0.432 (Wang etal., 2011). Parameters for the fast sites in DWwere quite similarto ours with lower kAtt = 0.43 h−1 and Smax = 2.4 and for fastsites.

Above references indicate that transport of sepia ink insaturated quartz filters is similar to some bacteria. Thisindicates that sepia eumelanin is a good surrogate for thiskind of microorganisms in transport experiments.

The desorption tail of the BTC had smaller concentrationsthan the best fittingmodel. It can be reproducedwith a smallerdetachment rate, viz. kDet from 0.7 to 0.9 h−1 (Eq. (9)), byincreasing the weights associated with the desorption data inthe inverse solution HYDRUS-1D. However, with this proce-dure the overall performance fitting decreased and poorerpredictions of the ascending part of the BTCwere obtained. Thisbehavior suggested that detachment rate decreased by hyster-etic mechanisms, such as particle straining in small pores,

reinforcement of ink-soil bounds or irreversible capture ininterfaces.

3.2.2. Stopped flowStopped flow using ink in DW (Fig. 4a) increased retention

in the column. After completion of the pulse, desorption tailsindicate the release of excess retained ink particles. Massbalance showed 21%, 30% and 31% retention for continuousflow, 15 min and 120 min stopped flow respectively (Fig. 4a)accordingly with colloid filtration theory. When the flow ratedecreases or stops the colloid-sphere collision efficiencyincreases (Tufenkji and Elimelech, 2004). In addition, byincreasing the residence time the particles have more time toaccess into less favorable adsorption sites and reinforce theinter-particle and particle-quartz bonds (Torkzaban et al.,2007). Breakthrough experiments involving variable NaClconcentrations (Fig. 4b-d) revealed that the increased concen-tration of the electrolyte from DW to 1 mM NaCl caused adramatic retention, from 21% tomore than 96% (Fig. 4a, b). Theinfluence of electrolyte can be ascribed to its influence on the

Fig. 3. Transport experiment of sepia ink suspensions in quartz sand. a) BTC and b) the profile of retained particles at the end of the BTC. Points represent theexperimental BTC and lines are the numerical calculations with the two best fitting colloid transport models, using two values of the shape factor for the depth-dependent blocking model β. Pulse input of particle suspensions on the column lasted 5–10 pore volumes.

Table 2Physical properties of the quart sand filtration column used and the single-collector removal efficiency for sepia ink particles η using the Tufenkji-Elimelech correlationbased on the colloid filtration theory. ηD, η G, ηI indicate the individual removal efficiencies due to diffusion, sedimentation and interception, for saturated quartz sandand soil cores with two pore flow velocities.

Parameters Sand Soil 5 mL h−1 Soil 10 mL h−1 Units

Column diameter 1.76 4.8 4.8 cmFlow rate 15 5 10 cm3 h−1

Particle size 0.154 0.154 0.154 μmCollector diameter (d50) 0.32 0.043 0.043 mmFluid approach velocity (v) 1.4 × 10−5 1.2 × 10−6 2.4 × 10−6 m s−1

Particle density (ρp) 1.27 1.27 1.27 kg dm−3

Fluid density (ρf) 103 103 103 kg dm−3

Fluid viscosity (μ) 1.0 × 10−3 1.0 × 10−3 1.0 × 10−3 kg m−1 s−1

Temperature (T) 293 293 293 KHamaker constant (A) 1.0 × 10−20 1.0 × 10−20 1.0 × 10−20 JPorosity (ϕ) 0.41 0.63 0.63 –Happel model parameter (As) 35.7 11.2 11.2 –ηD 3.6 × 10−2 1.1 × 10−0 6.6 × 10−1 –ηI 5.5 × 10−5 7.7 × 10−4 7.1 × 10−4 –ηG 4.3 × 10−5 1.3 × 10−3 6.2 × 10−4 –η = ηD + ηI + ηG 3.6 × 10−2 1.1 × 10−0 6.6 × 10−1 –

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Fig. 4. Experimental BTCs for sepia ink particles in saturated quartz sand columns with a pulse duration of 2 pore volumes. a) Steady flow of ink suspension in distilledwater (blue dots), response to 15min stopped flow (reddots) and 120min stopped flow (greendots); b), c), d) show the influence of electrolytewith 1, 10 and 100mMNaCl respectively with steady flow (blue) and 15 min stopped flow (red). Flow was stopped after 1.2 pore volumes of ink pulse.

Fig. 5.BTCs for Br− and sepia ink from transport in partially saturated experiments in two structured soil cores. Pulse durationwas 2.5 pore volumes. Br− BTCs inCores #1 and #2 a, b) colors indicate the BTC of Br− before the ink pulse (red) and after the ink pulse (red). c, d) BTC for the sepia ink in the respective cores #1 and#2. Symbolsindicate the experimental data and dashed lines the best fitting model.

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adsorption at the secondary energy minimum (Litton andOlson, 1996). Further increase in the electrolyte concentration(Fig. 4c, d) increased retention from 96% to 98%. Stopped flowfor 15 min in presence of electrolyte increased the massretained in the same proportion as the DW experiments.Behavior of sepia ink in quartz sand was consistent with thesimilar experiments conducted by other researchers withsurrogates and microorganisms (Bradford et al., 2014).

3.3. Transport in soil

Transport of Br− in the Core #1 (Fig. 5a, b) showed a smallretention (0.6% mass ratio) in the clean soil, viz. after the inkpulse, and decreased to a negligible after the ink passage (0.2%equals the mass balance error determination); the figures forthe Core #2 were mass balance 5.6% in clean soil and 2.3% afterthe ink passage (Fig. 5a, b). Physical retention of Br− iscommonly ascribed to transport from mobile regions toimmobile regions into the soil matrix (MIM) (van Genuchtenand Wierenga, 1976). Decreased retention of Br− in theimmobile regions at the second Br− pulse can be due to coatingthe MIM transfer paths by the adsorbed ink.

Solute transport modeling of the unreactive Br− (Table 3)showed that the pore water velocities increased accordinglywith the fraction of mobile pore water. Accordingwith the Eqs.(1) and (2), core #1 had θim 0.23 to 0.26 immobile water with afirst order transfer coefficient αmim ~ 0.1 h−1, for the Core #2transfer was about three times slower αmim ~0.027 h−1. Ingeneral, transfer rate to immobile regions was small.

Ink BTCs are shown in the Fig. 5c, d. Mass balance indicateretention of 13 and 11%, respectively, which was higher thanBr− but about two times smaller than the retention in the cleanquartz sandwith DW. Unfortunately, ink concentration profilesin soil were erratic (data not shown) so the particle retentionmodel could not be identified. Similarity of the BTC shapessuggested that sand and soil had similar blocking effect ofadsorption sites.

The theoretical attachment efficiency was calculated for thegeometric mean particle diameter of d50 = 0.043 mm andaverage pore water velocities (Table 2). This was calculated inorder to compare with transport in sand, giving η from 0.6 to1.1, that were about 20 to 30 times larger than sand values.

For comparison with the quartz sand columns, we modeledthe transport parameters under the assumption that the depth-dependent blocking model was valid for soil. The summary ofthe best fitting (Table 4) indicates that the parameter Smax =0.35 ± 0.32 (Eq. (8)) was slightly smaller than in sand.Attachment and detachment rates were about 9 to 20 times

lower than in sand. The theoretical sticking efficiencies were inthe interval α = 2 × 10−3 to 7 × 10−3(Eqs. (1), (2)), aboutthree orders of magnitude lower than sand. These comparisonsshould be regardedwith caution because flow in structured soilis different from the packed homogeneous sand column.Furthermore, the theoretical analysis of colloid collectorinteractions is adequate for homogeneous granular beds forwhich it was developed.

The lower retention of ink in soil than in quartz sand can beexplained by exclusion from regions of the soil matrix anddominant macropore flow regime in undisturbed soil cores.Therefore, ink had less interaction with the soil matrix thanwith the sand. This was already reported for experiments withE. coli and tracers (Martins et al., 2013). Macropores and soilchemistry in this acidic soil contribute repulsion of ink out ofthe soil matrix and are important factors that decrease thecolloid sticking efficiency.

4. Summary

Purified sepia ink obtained from Sepia officinalis is com-posed of spherical proteins that forms polydisperse stablecolloidal suspensions over a broad range of pH (4–8) and saltconcentrations. Filtration in quartz sand also shows adsorptionunder electrical repulsive conditions with a response to theelectrolyte effects similar to the manufactured microspheresand microorganisms with similar size. The electrophoreticmobility is very sensitive to the electrolyte concentration withan electrophoretic behavior similar to surface functionalizedlatex spheres with negative charge groups.

The retention model identified in saturated sand break-through is attachmentwith a depth-dependent blockingwhichwas reported in the scientific literature as very common for theviruses, bacteria, colloids and nanoparticles in similarexperiments.

Exclusion, preferential flow through macropores, soil poreconnectivity and the chemistry of the soil solution were therelevant factors on the high mobility of sepia ink into soil.

The main drawback of using sepia ink in colloid transportstudies is the difficulty to determine the retained concentra-tions in soil. Using RMI techniques, quantum dots, or DNA-labeling are sophisticated techniques that may overcome thisdifficulty.

Sepia ink is organic and stable, environmental friendly, non-toxic with metal-complexing properties; and can be used as acheap biotic surrogate for exploring transport of pathogenicviruses, bacteria and particulate contaminants in groundwater.These features make sepia ink as suitable material for

Table 3Transport parameters and goodness-of-fit indicators for the Br− in the undisturbed soil cores using the physicalmobile-immobile transfermodel. Twopulses KBr pulseswere applied, the first before the ink pulse and the second after the ink pulse.

Core # Run aρb aϕ v D θim αmim r2 MAE RMSE

1 Before ink 0.71 0.68 0.90 ± 0.08 0.18 ± 0.017 0.23 ± 0.009 0.086 ± 0.016 0.985 0.011 0.0181 After ink 0.71 0.68 1.6 ± 0.18 0.26 ± 0.10 0.26 ± 0.023 0.098 ± 0.023 0.993 0.012 0.0152 Before ink 0.90 0.63 0.59 ± 0.05 0.11 ± 0.016 0.122 ± 0.007 0.0265 ± 0.005 0.996 0.016 0.0272 After ink 0.90 0.63 0.65 ± 0.05 0.17 ± 0.04 0.07 ± 0.02 0.028 ± 0.02 0.995 0.022 0.036

ρb: bulk density (g cm−3); ϕ : porosity (cm3 cm−3); v: pore water velocity (cm/h); D: coefficient of hydrodynamic dispersion (cm2 h−1); θim: fraction pore volumefilled with immobile water (cm3 cm−3);αmim: first order solute transfer rate between mobile immobile pores (h−1); r2 for regression of predicted vs observed; MAE:mean weighted absolute error; RMSE: root mean square weighted error. Superscripts indicate a data from gravimetry.(Eqs. (1), (2)).

96 D. Soto-Gómez et al. / Journal of Contaminant Hydrology 191 (2016) 88–98

developing frugal-innovation related with the assessment ofsoil and aquifer filtration function, monitoring of waterfiltration systems in low-income regions, and potentiallyeffective for remediation of metal-contaminated groundwater.

Acknowledgments

Authors want to acknowledge their fund sources: P.P.R. isfunded by Pre-doctoral Fellowship Program (FPU) of Spain'sMinistry of Education (AP2010-5250) and M.P. is funded by apost-doctoral fellowship awarded by Xunta de Galicia (PlanI2C) (POS-A/2013/171). D.S.G. was additionally funded by CIA(GRC2014/017) and AA1 research contracts (FEDER, Xunta deGalicia). Authors thank CACTI services from theUniversidade deVigo for the SEM photographs, and Almudena and BastianComesaña for the particle density determinations at FlowCytometry.

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Table 4Non-linear least-squares analysis fitting for the one site depth dependent blocking coefficient model for quartz sand and the two soil cores.

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Sand 8.5a 1.29 ± 0.24 0.00 0.32 0.479 ± 0.026 0.51 ± 0.055 8.74 ± 0.08 0.91 ± 0.077 0.975 0.0099 0.016Sand 8.5a 2.3 ± 0.48 0.00 0.32 0.431 0.51 ± 0.055 8.74 ± 0.08 0.74 ± 0.028 0.975 0.014 0.022Core #1 1.3 ± 0.2 1.2 ± 0.18 0.27a 0.0043 0.431b 0.21 ± 0.05 0.67 ± 0.01 0.067 ± 0.004 0.993 0.0196 0.033Core #2 0.62 ± 0.05 0.39 ± 0.03 0.10a 0.0043 0.431b 0.32 ± 0.008 0.49 ± 0.01 0.10 ± 0.007 0.993 0.0196 0.003

D: coefficient of hydrodynamic dispersion (cm2 h−1); v: porewater velocity (cm/h); θim: fraction pore volume filledwith immobile water (cm3 cm−3); d50: geometricmean particle diameter (mm); β : shape factor for the depth-dependent blocking model; Smax: is the maximum solid phase particle concentration (mg g−1); ka: firstorder attachment rate (h−1); kd: first order detachment rate (h−1); r2 for regression of predicted vs observed; mean weighted absolute error, MAE root mean squareweighted error, RMSE. Superscripts indicate a values were set from the optimummodel for the Br− transport; b assumed from sand experiments.(Eqs. (1), (2), (8), (9), (10)).

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Pressure Jumps during Drainage in Macroporous Soils Diego Soto, Marcos Paradelo, Álvaro Corral, and José Eugenio López Periago To cite this article: Soto, D., M. Paradelo, Á. Cor-ral, and J.E.L. Periago. 2017. Pressure jumps

during drainage in macro-porous soils. Vadose Zone J. 16(13). doi:10.2136/vzj2017.04.0088

The final authenticated version is available online at: https://doi.org/10.2136/vzj2017.04.0088

Abstract

Discontinuous air–water displacement at the pore scale (from 10−5 to 10−3 m) affects fluid

invasion in porous media at the core scale (10−3 to 1 m). Understanding of this effect is essential

to upscale flow processes. In this study we used the analysis of pressure jumps to propose an

upscaling mechanism. Large pressure jumps occur during drainage in macroporous structured

soils; we suggest a hypothesis for their occurrence. Drainage experiments in packed sand and

structured soils enclosing large pores showed large jumps (?5-hPa peak pressure). Large jumps

resulted from a pressure relax-ation process that first initiates from pore-scale air–water

displacements and then expands to larger scales. We found that the power-law exponents for

the distribution of the size of large jumps found in structured soil are greater than the typical

values reported for Haines jumps in packed granular porous media. The difference in the

exponent suggests that the magnitude of dis-placements occurring in structured soil has

different scaling factors than in simple media. A mechanism for this change of scale is proposed

on the basis of the large contrast between pore throat and matrix in macroporous soil. The

mechanism consists of a fast pressure relaxation in the macropores triggered by a break in the

capillary shield at the pore throat. These findings contribute to an explanation of the scaling

relations of air–water displace-ments in complex porous media and unveil links between the soil

structure and flow of fluids.

Contents lists available at ScienceDirect

Soil & Tillage Research

journal homepage: www.elsevier.com/locate/still

Linking pore network characteristics extracted from CT images to thetransport of solute and colloid tracers in soils under different tillagemanagements

Diego Soto-Gómeza,b,⁎, Paula Pérez-Rodrígueza,b,c, Laura Vázquez-Juiza,b,J. Eugenio López-Periagoa,b, Marcos Paradeloa,b,d

a Soil Science and Agricultural Chemistry Group, Department of Plant Biology and Soil Science, Faculty of Sciences, University of Vigo, E-32004, Ourense, SpainbHydraulics Laboratory, Campus da Auga, Facultade de Ciencias, Campus da Auga, University of Vigo, Spainc Laboratory of Hydrology and Geochemistry of Strasbourg (LHyGeS), Université de Strasbourg, Strasbourg, Franced Department of Agroecology, Faculty of Sciences and Technology, Aarhus University, Blichers Allé 20, P.O. Box 5 Box 50, DK-8830, Tjele, Denmark

A R T I C L E I N F O

Keywords:Colloid transportMacroporosityModelingOrganic farmingSoil structureSoil managementSoil tomography

A B S T R A C T

The understanding of relations between quantitative information of soil structure from X-ray computed tomo-graphy (CT) and soil functions is an important topic in agronomy and soil science. The influence of tillage onmacroporosity (i.e., pores measured by CT >240 μm in all directions) could be manifested in their effects onsolute and colloid transport properties. Tillage will also have crucial importance on preferential flow; i.e., adirect flow through root and earthworm channels. Increasing knowledge of the relationships between soil tillage,structure, and transport contributes to a deeper insight into the key factors of soil management influencingproductivity, environmental quality and crop health. The aim of this work is the identification of relationshipsbetween soil management of the pore network and the influence of the characteristics of the paths identified byCT on the transport of solute and colloidal tracers. In this work, we used CT to characterize the macroporenetwork ( > 0.24 mm) of sixteen columns (100 height× 84 diameter, mm) of adjacent plots under different soilmanagement as follows: conventional management with shallow tillage after sowing (4 samples), conventionalmanagement with no tillage after sowing (4 samples), and organic vegetables (8 samples). The soil samples wereinstalled in columns under a dripper, and the transport behavior was examined during breakthrough of Br− and1-μm latex microspheres in samples near saturation. Transport of Br− and latex microspheres was modeled usinga two-region physical non-equilibrium model (dual porosity). Preferential flow was higher under organicmanagement, although the pore water velocities were, in general, lower. The preferential flow of Br− wascorrelated with the total volume of macropores extracted from each tomography, and the local increase in theHounsfield value (i.e., CT matrix density, CTMatrix) surrounding the macropores. The denser lining, produced bythe earthworms in the inner walls of the pores, was inversely correlated with the kinetic exchange coefficientbetween mobile and immobile zones of the dual-porosity model. The macropore roughness indicated by the CT-macropore surface area was correlated with the solute dispersion coefficient and with the solute travel time.Finally, we found that the overall CTMatrix density is inversely related to the preferential flow. The importance ofthis work lies in the improvement of the accuracy of predictions related to flow and transport through soils,especially those processes that include particles traveling through the soil.

1. Introduction

Tillage modifies the natural soil structure by changing the bulkdensity, the size of the aggregates, the soil penetration resistance andthe water holding capacity. The objective of tillage is to eliminateweeds and mix the soil, thus temporarily increasing the oxygenationand the soil water holding capacity (Coolman and Hoyt, 1993).

However, repeated tillage activities for several years have led to lessaggregated and easily erodible soils (Hevia et al., 2007). No-tillage orother soil conservation methods aim to decrease the biopore disruptionand to preserve the natural soil pore network.

The pore network has strong effects on the ability of soil to allow themovement of water downwards and to transport soluble and particulatesubstances. Furthermore, the water availability and flow are of great

https://doi.org/10.1016/j.still.2017.12.007Received 7 March 2017; Received in revised form 6 November 2017; Accepted 3 December 2017

⁎ Corresponding author.E-mail addresses: disoto@uvigo.es, diego.cerreda@gmail.com (D. Soto-Gómez).

Soil & Tillage Research 177 (2018) 145–154

0167-1987/ © 2017 Elsevier B.V. All rights reserved.

T

importance for the crops, i.e., in the seedling emergence, in the size andnumber of roots, and in the plant density (Rashidi and Keshavarzpour,2007).

Conventional and conservation tillage may produce differences inthe number, shape, size, and continuity of the soil pores. No-tillageand minimum tillage techniques allow the soil to develop a complexand well-connected pore network because they do not disrupt earth-worm activity, root channels and cracks (Cannell, 1985). The mac-ropores and cracks represent only a small percentage of the soil pores,but they have a huge influence on the transport of water, solutes andsuspended colloids. These pores can be used by the water to bypassthe upper layers of the soil. Moreover, colloidal particles with at-tached substances (facilitated transport) can travel faster throughthese channels, increasing the nutrient loss by leaching (de Jongeet al., 2004). Particulate organic matter, labile colloidal nutrients,viruses, bacteria, and protozoa have limited mobility through the soilmatrix but can travel several meters in the soil by using preferentialpathways (macropores), such as earthworm and root pores(McDowell-Boyer et al., 1986).

Usually, the role of macropores in solute and colloidal transport isstudied by tracer experiments in soil columns or in the field, using so-luble substances or colloids (Paradelo et al., 2013; Soto-Gómez et al.,2016), or measuring some of the macroscopic soil characteristics suchas the hydraulic conductivity and the air permeability (Kjaergaardet al., 2004). However, in the last years, X-ray CT has proved to offerimportant information on structural parameters of the soil pore net-work system, such as pore topology and morphology, without alteringthe sample (Katuwal et al., 2015a). This method has been successfullyused to study the effects of soil management (conventional tillage andno-tillage) on the soil pore structure and analyze the changes in themacroporosity with depth and pore size distributions (Pires et al.,2017). Other works used CT images to analyze the compaction con-sequences and their effects on the soil atmosphere and to determine thebulk density without altering the sample (Lipiec and Hatano, 2003). CTcan be used for visualization and description of the root distribution(Perret et al., 2007). In this case, there are some discrepancies betweenthis method and a destructive one; the CT underestimates the length ofthe roots due to the spatial resolution of the scan.

Furthermore, CT techniques have been used successfully to estimatesolute transport parameters (Anderson et al., 2015, 2014). Solutebreakthrough studies with a continuous CT monitoring showed thatmost of the solute transport occurred throughout the highly continuousbiogenetic pores (Luo et al., 2008). Naveed et al. (2013) found goodcorrelations between soil air permeability and the equivalent porediameter divided by the tortuosity (both calculated from CT images).

In this work, we hypothesized that differences in soil structurecreated by different soil tillage managements, inferred from the X-rayCT derived characteristics, would influence the transport of solutes andcolloids.

The objectives of the present study are as follows: (i) to characterizethe structure of soil under different tillage managements and with dif-ferent degrees of earthworm activity (deducted from the signs of surfacealterations observed); (ii) to model the transport of Br− and fluores-cence microspheres; and (iii) to relate transport characteristics to CT-derived characteristics to estimate the dynamic behavior of colloidalparticles in the soil.

2. Material & methods

2.1. Soil sampling

Sixteen undisturbed columns (100mm in height× 84mm in dia-meter) were collected using PVC cases in January 2013 from two ad-jacent experimental parcels (Centro de Desenvolvemento Agrogandeiro,Ourense, northwestern Spain, coordinates 42.099N, −7.726WWGS84). Eight undisturbed soil columns were sampled from a plotunder organic management (Org) with a long historical use devoted toroot crops and vegetables, with the removal of the stubble. Two sub-zones with different earthworm activity were identified, namely, high(Org. A) and low (Org. B) activity (we took 4 samples of each subzone).We consider that in these two subzones, the type of pores is similar,whereas the difference lies in their number and shape. This con-sideration was deducted in the field from signs of surface alteration. In aconventional zone, four columns were taken from a plot devoted tospring cereal with no-till (Conv. NT) after sowing, so the roots werepreserved, and the other four columns were from a plot that wasshallow-tilled (Conv. ST) after sowing.

The columns were extracted vertically (2–12 cm depth). They weresealed immediately and refrigerated at 4 °C to prevent structure al-teration before CT scanning and transport experiments. Chemicalproperties and texture were almost identical in bulk samples adjacent toeach soil column with a pH, in a 1:10 soil:water ratio, of 5.9 ± 0.05.The soil texture class was sandy loam according to the USDA soilclassification (Table 1).

The soil columns were mounted with a mesh in the bottom and theweight was recorded. Then, columns were slowly saturated upwardsfrom the bottom by applying suction to the upper part of the flow cellwith a peristaltic pump. Saturated water content (θs) was calculated asthe difference of weight of the saturated soil minus the weight of thedry soil. After saturation, we let the columns drain for 1 h. After that,moisture (θ) was measured as above. Since we tried to perform thetransport experiments close to saturation (flow rate ≈10mL h−1), weconsidered this value as the lower limit of the actual water contentduring the transport experiments (Table 2).

2.2. Macropore characterization with CT

The CT images were acquired with a dental 3D Cone-beam i-CATscanner (Imaging Sciences International LLC, PA, Hatfield, USA), using120 kV, 5mA current and a voxel size of 0.24mm.

The raw data were processed with the free software ImageJ version1.52a (Schindelin et al., 2012). Images were cropped to fit the soilenclosed into the column and then converted to binary values usingSauvola’s auto local thresholding analysis (Sauvola and Pietikäinen,2000) to segment the soil matrix and macropores (samples of thissegmentation appear in Fig. 1). To apply this method, the followingsettings were used: radius of 50 pixels, parameter 1 (k value) of 0.3 andparameter 2 (r value) of 128 (default value). The value of each pixelwas:

Pixel= (pixel > mean * (1+ k+(standard deviation/r− 1))) (1)

The CT-macroporosity was defined as the soil volume fraction

Table 1Soil texture results for the three plots with standard deviations.

Management % Coarse Sand (> 0.5 mm) % Fine Sand (0.5− 0.05mm) % Silt (0.05− 0.002mm) % Clay (< 0.002mm) % Organic Matter

Conv. NT (n= 4) 46.2 ± 0.5 26.1 ± 0.9 5.7 ± 2.9 10.9 ± 1.2 11.1 ± 2.6Conv. ST (n= 4) 42.9 ± 2.4 28.3 ± 1.7 5.3 ± 4.1 11 ± 0.6 12.5 ± 4.6Org. (n= 8) 44.5 ± 0.2 29 ± 0.4 8.1 ± 0.3 9.2 ± 0.7 8.5 ± 0.5

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occupied by macropores larger than 0.24mm in any dimension, and itwas calculated by dividing the sum of the pore voxels by the number ofall voxels. The number of pores, the surface area of pore walls and theirvolume were calculated using the Bone-J Particle Analyzer plugin inImageJ (Doube et al., 2010). The binary images were purified by dis-carding the noise (using the Despeckle noise plugin), and the con-nectivity was also calculated with Bone-J. The skeleton of the porenetwork was analyzed, obtaining the number of paths and branches,slab voxels, end-point voxels (dangling ends), and the real length (LR)and Euclidean length (LE) of each one. With these two parameters, wecalculated the tortuosity (τ) (Wu et al., 2006)

τ=LR/LE (2)

Note that this tortuosity corresponds to macropores identified byimage analysis. Henceforth, we will refer to this parameter as CT-tor-tuosity. We used the average value of all the pores larger than 10mm.

The circularity of each pore (for each slice of the stack) was cal-culated using the following formula

= ⎛⎝

⎞⎠

Circularity π AreaPerimeter

4 2 (3)

The average CT number of the matrix (CTMatrix) represents thedensity of the matrix measured by the X-ray absorbance using theHounsfield scale (HU). CTMatrix was calculated by excluding the mac-ropores and the stones and considering the gray shade of each voxelusing the criteria of Katuwal et al. (2015b). We also separated theCTMatrix values of the layer of voxels corresponding to the pore walls. Inthis layer, the HU was used to examine the density of the pore walls.

2.3. Breakthrough experiments

Red fluorescent polystyrene latex microspheres (Magsphere Inc.,Pasadena, California) were used as colloidal tracers. The particles havea diameter of 1 ± 0.11 μm with a density of 1.05 g cm−3. The excita-tion and emission wavelengths of the fluorochrome were 505–545 and560–630 nm, respectively.

The stock suspension, which contains 4.55×1010 microspheresmL−1, was diluted 1:200 in a solution of 0.025M of Br− (KBr) to obtaina suspension 2.28×108 microspheres mL−1. Bromide was used as an

unreactive solute tracer for comparison with the colloid tracer.The microspheres were kept in suspension during the experiment by

the application of 100ms duration ultrasound pulses at the colloid re-servoir at 1 s intervals, using an ultrasonic homogenizer (Sonopuls HD2200, Bandelin GmbH & Co. KG, Berlin, Germany).

Each soil sample was mounted in a column on a stainless-steel meshno.18 (sieve opening=1mm) attached to a polypropylene funnel thatconducted the outflow from the bottom to an automated fraction col-lector. Water and microsphere suspensions were distributed dropwise atrandom points on the top soil surface by a robotic arm attached to thedripper. Flow boundary conditions in all breakthrough experimentswere as follows: constant flux at the upper boundary with flow rates of≈10mL h−1 (5.1 mmh−1) (when it was possible considering the per-meability of the soil) and seepage face at the bottom. The infiltrationrate varied in some columns, so the flow rate was occasionally reducedto avoid surface ponding. The fall height of the drops was less than3mm to prevent the disruption of the soil structure.

Before the breakthrough curve (BTC) experiments, flow was stabi-lized with deionized water (DW), and when a steady state flow wasreached, a pulse of microspheres suspended in the KBr solution wasapplied (≈2–3 PV). Pulses were followed by washing with DW (≈6–10PV). The effluent fraction volume (≈4–6mL per tube) was determinedby weighing, the Br− concentration was measured by automated col-orimetry (van Staden et al., 2003), and the microsphere concentrationwas determined by fluorescence (Jasco Fluorescence Spectrometer,Jasco FP-750). Photometric readings were calibrated with the countingof microspheres trapped in 0.45-μm filters using fluorescence micro-scopy and image analysis. The correlation between the two methodswas linear (R > 0.997).

After the transport experiments, the columns were carefully slicedin sections ≈5mm using a nylon string and a spatula. A piston jack anda precision vernier caliper were used to extract the soil from the ring in5-mm steps. The slices were placed in Petri dishes to identify micro-sphere spots under a fluorescence laboratory magnifier. Then, soil porewalls stained with microsphere aggregates were removed from theslices with perforating punches and saved in Eppendorf tubes. The restof the soil slices were stored separately in bottles. Therefore, the mi-crospheres retained in the contour of the macropores were quantifiedseparately from the soil matrix as follows. The contents of the tubes and

Table 2Transport parameters of each column obtained from the Br− modeling.

Zone Column number t (h) v (cm h−1) θs θ D (cm2 h−1) d (cm) β ω

Conv. ST 6 6.39 2.71 0.51 0.47 45 16.62 0.15 0.18012 6.45 3.48 0.43 0.40 28 8.05 0.09 0.27014 6.27 2.60 0.49 0.44 70 26.94 0.05 0.01916 5.7 2.67 0.43 0.37 18 6.75 0.23 0.150

Average 6.20 ± 0.34 2.86 ± 0.41 0.46 ± 0.04 0.42 ± 0.04 40.25 ± 22.75 14.59 ± 9.32 0.13 ± 0.08 0.15 ± 0.10

Conv. NT 2 6.05 3.41 0.41 0.4 37.2 10.91 0.10 0.0564 6.69 2.67 0.45 0.4 35 13.11 0.05 0.0835 7.81 2.51 0.42 0.4 35 13.94 0.08 0.0777 6.78 2.6 0.47 0.45 48 18.46 0.19 0.170

Average 6.83 ± 0.73 2.80 ± 0.41 0.44 ± 0.03 0.41 ± 0.03 38.80 ± 6.22 14.11 ± 3.17 0.11 ± 0.06 0.10 ± 0.05

Org. A 3 5.78 2.01 0.50 0.47 20.55 10.20 0.14 0.1918 4.43 2.81 0.47 0.43 12 4.26 0.15 0.1309 31.21 0.36 0.51 0.47 12.3 34.39 0.02 0.00410 20.88 0.36 0.57 0.52 4 11.2 0.05 0.300

Average 15.57 ± 12.82 1.39 ± 1.23 0.51 ± 0.04 0.47 ± 0.04 12.21 ± 6.76 15.01 ± 13.27 0.09 ± 0.06 0.16 ± 0.12

Org. B 13 5.52 2.83 0.48 0.46 10 3.54 0.08 0.13015 8.75 1.27 0.50 0.48 30 23.59 0.10 0.10019 14.02 0.73 0.47 0.44 8 10.89 0.06 0.00120 4.78 3.03 0.45 0.42 12 3.96 0.15 0.100

Average 8.27 ± 4.20 1.97 ± 1.14 0.47 ± 0.02 0.45 ± 0.03 15.00 ± 10.13 10.49 ± 9.36 0.10 ± 0.04 0.08 ± 0.06

t [T] is the duration of the pulse; v [L T−1] is the pore water velocity; θs is the saturated water content; θ is the volumetric water content after saturation and a drainage of 1 h; D is thedispersion coefficient for the bromide [L2 T−1]; d is the dispersivity [L]; β, is a dimensionless parameter for the partitioning of bromide in the two-region transport model; and ω is thedimensionless mass transfer coefficient of bromide.

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bottles were weighed and suspended in 10mL (pore walls) and 20mL(matrix) of a non-ionic surfactant solution (Tween 20 in distilled water,0.02%). Suspensions were shaken and homogenized for 10 s with anultrasonic homogenizer. Aliquots (0.5 mL each, 3 replicates) were im-mediately pipetted and diluted in appropriate volumes of 0.02% Tween20 and were filtered through nitrocellulose membranes (pore size0.45 μm, diam. 47mm). Particle counting in the membranes was madeusing digital images obtained with a fluorescence laboratory magnifierand a digital camera. Bulk density ρb and the volumetric water contentθ were determined at the end, after drying each slice at 105 °C.

The average pore-water velocity v (Table 2) was calculated from theirrigation rate q and the average soil water content θavg:

v= q/θavg (4)

The two-region physical non-equilibrium model was fitted to theexperimental BTCs using the software STANMOD (CXTFIT Code). Theoptimal inverse solution was used to calculate the transport parameters.This model assumes that the soil porosity can be divided into two dif-ferent regions as follows: mobile and immobile (Toride et al., 1995).The transport model is given by the following equation:

∂∂

= ∂∂

− ∂∂

− −θ ct

θ D cx

J cx

α c c( )mm

mm

wm

m im2

2 (5)

∂∂

= − −θ ct

α c c θ μ c( )imim

m im im im im (6)

Fig. 1. 3D representation of the columns from eachplot. A) ST (column number 6); B) NT (columnnumber 7); C) Org. A (column number 8); and D)Org. B (column number 19).

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where θ is the volumetric water content [L3 L−3]; c is the concentration[ML−3]; D is the dispersion coefficient [L2 T−1]; x and t are the distance[L] and time [T]; Jw is the volumetric water flux density [LT−1]; αis thefirst-order kinetic coefficient between mobile and immobile zones[T−1]; and μ is the first-order decay coefficient [T−1]. The subscripts mand im indicate the mobile and immobile liquid regions, respectively.The dispersivity for the Br− and MS (d and dMS) was calculated bydividing the dispersion coefficient by the pore-water velocity.

We adjusted the following parameters: β, a dimensionless parameterfor partitioning in the two-region transport model

=β θθm

(7)

;ω, the dimensionless mass transfer coefficient

=ω αLθv (8)

; and μ, the dimensionless first order decay coefficient for the im-mobile region

=μLθ μ

θvim im

(9)

The μ was adjusted only for the microspheres to model irreversibletrapping in the immobile regions; μ was set to zero (no irreversibletrapping) for the transport of Br−.

The dimensionless 5%-arrival time of Br− (T5%) was used to esti-mate the degree of preferential transport in the BTC. T5% was calculatedby considering the period of time (in pore volumes) it took for 5% of thebromide to reach the bottom of the column. See details in Koestel et al.(2013).

3. Results & discussion

3.1. Soil structure differences from image analysis

The CT parameters were analyzed with the Shapiro-Wilk test tocheck that the data of each variable were normally distributed, and theone exception was the branch length average (cm). Consequently, toexamine the differences among the soil managements, we used a singlefactor ANOVA with all the variables but with the average branchlength. With branch length average, the test employed was the Kruskal-Wallis test. Through these tests, we observed and corroborated sig-nificant differences between the CT features of the plots studied(Table 3).

The CT-macropores in the ST plot presented the shortest branchlengths on average and the most tortuous branches, while NT had largeand straight branches mostly generated by undisturbed decaying rootsfrom the past crop. Bramorski et al. (2012) proved that tortuosity in-creased 56% after tillage, improving the water and sediment storage.The pores of the NT zone had, in general, the largest wall surface area,but they were not significantly different from the ST plot. The CT-macropores in the Org. plot and NT had similar average branch length

and tortuosity, but the Org. A subzone had the largest CT-macroporesbecause of the higher number of earthworm burrows. The lower valuesof the wall surface area in the two Org. zones, A and B, could be due tothe type of pores; the walls of these pores were lined by earthworm cast,making the pores smooth and reducing their surface (Pagenkemperet al., 2015). Root pores are responsible for high circularity in the NTcolumns. The ST plot showed a slightly lower circularity than the or-ganic plots and that is because the Org. samples had, to some degree,earthworm pores, which are more circular than the pores produced bythe shallow tillage, a feature already noted by Gantzer and Anderson(2002). Nevertheless, the organic plots (A and B) could not reach thelevel of circularity of the NT plot, which can be explained by the type ofvegetation; that is, cultures have more circularity than grass and per-manent vegetation (Rachman et al., 2005; Udawatta et al., 2006). It isimportant to note that the values shown in Table 3 are average values ofall pores bigger than 0.24mm in diameter, not only root or earthwormpores.

In the CT images, the tone of the pore walls of the plots with rootand earthworm pores was slightly clearer than pore walls of the ST plot(HU values were as follows: Conv. ST, 136.4 ± 7.21; Conv. NT,143.55 ± 3.69; Org. A, 142.65 ± 2.62; Org. B, 146.74 ± 6.2), butthere were no significant differences between the plots. However, thisincrease in the density of the soil in the areas surrounding the earth-worm burrows was already described by Rogasik et al. (2014).

3.2. Solute and colloid transport and modeling

Pulses of a suspension of microspheres in KBr (500mL,≈ 2.5 porevolumes, PV) were applied in the NT and ST columns. For the Org.columns, we used shorter pulses (350mL≈ 1.5 PV) to avoid the surfaceponding observed in the first experiments. The pulse durations are inTable 2. The mass balance of Br− in the transport experiments indicatedthat 15 ± 5% was not eluted after 10 PV. This imbalance is commonlyfound in tracer experiments in structured soil and is typically ascribedto solute transfer between mobile and immobile water regions of soil(van Genuchten and Wierenga, 1976), and suggests physical retentionof bromide in immobile zones. High organic matter content may alsocontribute to increasing retention (Larsbo et al., 2016). The similarity inthe mass balance between treatment plots indicated that the soilmanagement had no influence on the non-reactive transport. Poor re-lationships between soil macropore features and tracer transport werealready reported for cracked paddy soils (Zhang et al., 2015).

The transport models fitted fairly well for most of the Br− in thecolumns (R2 > 0.95, P < 0.001; between observed and predicted BTCdata), as seen in Fig. 2. The poorest fittings were obtained for threecolumns of the Org. plot considering the R2: columns no. 10, 15 and 20,with an R of 0.948, 0.943 and 0.946, respectively.

Table 2 summarizes the parameters of non-reactive transport. Thezones had similar transport parameters for Br−, and only the solutedispersion coefficient (D) and the 5%-solute arrival time showed sig-nificant differences between zones.

Table 3CT macroporosity descriptors (with standard deviation) influenced by the management type, after a single factor ANOVA or a Kruskal-Wallis test (for the average branch length).

Conv. ST Conv. NT Org. A Org. B

CT Macroporosity (%) 7.56 ± 3.38ab 4.65 ± 1.4b 9.52 ± 2.55a 4.34 ± 2.36b

Total Volume (cm3) 39.71 ± 13.98 ab 26.57 ± 8.98 b 55.73 ± 11.71a 25.62 ± 15.67b

Average Pore Surface (cm2) 2.15 ± 1.00ab 2.19 ± 0.48a 1.68 ± 0.12a 0.98 ± 0.37b

Total Slab Voxels 65669 ± 18217ab 89604 ± 13468b 88333 ± 23452a 45467 ± 25580b

Total Branch Length (m) 20.7 ± 5.99ab 26.35 ± 4.1a 27.52 ± 7.53a 13.95 ± 8.13b

Average Branch Length (cm) 0.29 ± 0.009a 0.45 ± 0.063b 0.3 ± 0.022a 0.3 ± 0.019a

Circularity 0.51 ± 0.015a 0.65 ± 0.045b 0.55 ± 0.027a 0.62 ± 0.019b

Average Tortuosity 1.291 ± 0.008b 1.252 ± 0.017a 1.287 ± 0.009ab 1.279 ± 0.013ab

Average Tortuosity (pores larger than 10mm) 1.48 ± 0.16b 1.24 ± 0.061a 1.65 ± 0.24b 1.37 ± 0.09ab

a,bdifferent superscript showed significant differences between groups with different management at a probability value P < 0.05.

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The ST columns presented the largest D, 40.3 ± 22.8 cm2 h−1 butalso had the largest deviations. Transport in ST may be influenced bythe sharp density increase with depth and the associated pore network,namely, a massive structure at the bottom crossed by few cracks. Thispore network feature may expand the range of the pore water velo-cities, which can explain the large dispersion of Br−. The NT also had alarge D, 38.8 ± 6.2 cm2 h−1, and this was due to the large wall surfacearea of the pores; i.e., many root channels with different lengths andgeometries that also increase the span of pore water velocities. On theother hand, organic soil columns had a smaller mean D than the NT(Student’s t-test, P < 0.05); with 12.2 ± 6.8 cm2 h−1 for the Org. A,and 15.0 ± 10.1 cm2 h−1 for the Org. B.

The T5% showed a very small variation inside the groups. Values ofthis parameter were identical for the NT and ST soils (0.322 ± 0.001PV and 0.325 ± 0.007 PV, respectively). The means of these datashowed significant differences between organic and conventional (t-test, P < 0.001). For the Org. A and Org. B, the values were smaller(0.235 ± 0.003 and 0.207 ± 0.002 PV, respectively) (Fig. 3). Thevalues obtained were very similar to the ones reported by Koestel et al.(2012), with a T5% for the arable soils between 0.35 and 0.1. In thiswork, they also found a reduction of the T5% in the arable soils with

minimum tillage in the same way as in our work.There was a good correlation between D and the 5%-arrival time

(Fig. 4B) (R= 0.545, P < 0.02). That positive relation differed fromthe general negative relationship found by Koestel et al. (2012). How-ever, there has to be consideration for the scale of our 5%-arrival time-dispersion parameter defining a small subset of the region shown inKoestel et al. (2012). Our data covers a rounded-shaped point cloud inthe above reference and does not present a neat negative slope. Thepositive correlation may suggest that the larger the dispersion, theweaker the preferential flow. Furthermore, these soils have a largeamount of organic matter that has a strong influence over the disper-sion and the 5%-solute arrival. In addition, the 5%-arrival is also relatedto the pore-water velocity (R=0.620, P < 0.02) and has no significantcorrelation with the dispersivity (R= 0.057). These relationships in-dicate that the correlation between D and the 5%-arrival time in ourexperiments can be spurious, and the variation in the pore water ve-locity is the factor that determines the preferential flow.

The smaller dispersion and the shorter T5% in the organic plots canbe explained by the bypass flow, which, in turn, is favored by theearthworm pores. The effect of this type of pore over the increase inpreferential flow, nutrient losses and tracer leachate was already de-monstrated by many authors (Edwards et al., 1989; Shipitalo et al.,2000, 1994), and it is responsible for the shorter time required by theBr− for traveling along the soil. The preferential flow can also explainthe lower dispersion. However, in this case, we consider the earthwormlining that covered the walls was the main factor. The lined walls seemto increase the pore water velocities and decrease their range of var-iation (Pagenkemper et al., 2015).

Inverse modeling of the microsphere BTCs (Fig. 5) was carried out,starting with the optimal set of parameters obtained for the Br− dualporosity model. In this case, the addition of the coefficient of decay, μ,accounts for the irreversible retention of MS in the immobile zone. TheBTCs of two columns (no. 10 and 19) had a complex shape that couldnot be used to fit the model (Fig. 5E). On the one hand, the column no.19 has a single large macropore that connects vertically the bottomwith the top. Its BTC shows a very early peak, then a sudden decrease inthe breakthrough, followed by a second sharp peak. That behavioursuggests changes in the preferential flow paths during the break-through. Our hypothesis is that the particle suspension went throughthe sample using a unique pathway that was blocked (by accumulationof MS or soil particles) during the experiment, and then the particleswere accumulated until the path was available again. On the otherhand, the column no. 10 presents the lowest bulk density from all the

Fig. 2. Observed and modeled Br− breakthroughbehavior for one column of each zone. The two-re-gion physical non-equilibrium model (dual porosity)was used.

Fig. 3. T5% (in pore volumes) results for the column averages of each zone. a,b,c Factorswith the same superscript in the key labels were not different (P < 0.05) using a singlefactor ANOVA.

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samples, an indicator of high organic matter content (Adams, 1973),with many macropores distributed evenly in all the soil volume. Thissuggests that this architecture is more efficient in adsorbing micro-spheres (Jacobsen et al., 1997).

Transport parameters of MS were not different between zones, butthe extreme values of the dispersion coefficient appear in the non-

organic management; the highest values were between 88 and100 cm2 h−1 in ST and the lowest were 5 cm2 h−1 in NT. The largestdispersion of MS in the ST was the same as in the Br− case, suggestingthat the underlying factors we conjectured for the large dispersion ofBr− could be valid for the MS. In contrast, in the NT soil, straight rootpores that contribute to a large dispersion of Br− did not have the sameinfluence on the MS transport. This occurred even though these twozones had similar pore-water velocities.

3.3. Structure-transport relationships

When comparing the best-fitting transport parameters and the dataobtained from the X-ray CT images, we observed some significantcorrelations. For example, the dispersion coefficient for Br− and theaverage pore surface were linearly correlated (R=0.803, P < 0.001)(Fig. 4C). In general, this trend was preserved for each zone. The non-organic soils had pores with the largest wall surface area(217 ± 72mm2) and dispersion coefficient (39.5 ± 15.5 cm2 h−1).Note the smaller averages for the organic field (133 ± 45mm2 and13.6 ± 8.1 cm2 h−1). The dispersion of Br− was also correlated withthe average number of slab voxels per branch (R=0.728, P < 0.001),which means that the pores with larger branches had a larger dispersioncoefficient. On the other hand, the walls of the earthworm burrows inthe organic field appeared to be lined by a dense matrix. The liningtends to reduce the exchange of solute between mobile and immobileregions (Jarvis, 2007), which hinders the transport across the porewalls and decreases the spatial variation of distribution of transportvelocities in the soil column. Consequently, in the plots with moreearthworm pores, we obtained smaller dispersion coefficients.

Best fitting model parameters can help to identify the dominantmechanisms of the transport of MS. We observed several good corre-lations between dual porosity model parameters and percentages ofretention of MS and Br− in the columns (Table 4). These correlationsindicated that the model is consistent across most of the BTC experi-ments and soil management types. For example, the retention of mi-crospheres is well described by the dimensionless MS transfer coeffi-cient between the matrix and macropores (ωMS). Therefore, with highvalues of ωMS, more particles may enter into the matrix in which a firstorder kinetic coefficient of particle removal, μMS, accounts for thetrapping of the MS in the immobile region. Recall that the transport ofBr− was also well explained by the transfer between the matrix andmacropores. The significance of fitting the two-region model supportsthe hypothesis that the dual-porosity model describes the variability inthe unsaturated transport of solutes and colloids reasonably well.

The T5% in the overall columns is slightly correlated with theaverage pore surface area of the walls (is more a trend than a correla-tion since the significance is quite lower), suggesting a relation betweenpreferential solute transport and the average pore surface (Fig. 4A).That relation could be interpreted as the pores with a larger wall sur-face area (i.e., more roughness and no lining) produce a physical re-tention in the transport of the Br−. The greater preferential flow ve-locity in the lined pores agreed with the well-known role of theearthworms in the fast transport along preferential pathways (Kautzet al., 2013). However, the relationship between T5% and the pore wallsurface area in the ST columns was inverse to the rest of the zones (seeFig. 4A). The reason for that inverse correlation was the scale of arrivaltimes in ST was compressed in a narrow interval (0.29 to 0.37 PV), andwe could not conclude anything with certainty with only four similarsamples. However, if we discard these columns, the correlation is stillvalid.

The total end-point voxels and the size of the tails of the bromideBTC were also correlated (R= 0.54). End-point voxels represent dan-gling paths that end in the matrix; their presence could enhance solutetransport between the mobile and immobile regions of the soil. Thereversible mobile-immobile transfer is typically associated with solutetailing in the BTC. The interesting point here is that the macroscopic

Fig. 4. Relation between the following: A) the average pore surface and the T5% (in porevolumes); B) the dispersion of Br− and the T5% (in pore volumes); and C) the average poresurface and the dispersion of Br−.

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behavior of the dual-porosity transport was related to the description ofthe structure. The CTMatrix shows a negative correlation with T5%(R=− 0.56; P < 0.02), which indicates that the denser the matrix,the faster the Br− transport across macropores. This relation suggeststhat a dense matrix makes it difficult for the solute to transfer intoimmobile regions and for the solute flux to channel through the mac-ropores.

The data reported by Safadoust et al. (2015) support the resultsobtained in this study. The bromide transport parameters were relatedto the porosity; the larger the percentage of macropores, the larger thedispersion and the mass exchange rate between the mobile and im-mobile zones.

The CTMatrix of the entire column presents a negative correlationwith the percent of MS retained in the upper half, i.e., from 0 to 5 cmdepth, with R=− 0.498; P < 0.05. There is a similar correlation(R=−0.439, P < 0.08) between the CTMatrix and the percent of MS

Fig. 5. Observed and modeled microsphere break-through behavior for the following: A), B), C) and D)one column of each zone; and E) two columns thatwe could not model: n° 10 (Org. A) and n° 19 (Org.B). C/C0 is the relative concentration.

Table 4Pearson’s correlation coefficient for the relationship between some parameters of mi-crosphere modeling and retention.

DMS(cm2 h−1) βMS ωMS μMS

% MS Recovered 0.054 −0.553* −0.673** −0.796**% MS Retained −0.488 0.505 0.797** 0.803a

Up_Retention (Retention inthe upper half of thecolumn)

−0.470 0.514 0.816** 0.839a

Matrix_Retention −0.410 0.637* 0.832* 0.847a

Pore_Retention −0.560* −0.535 −0.073 −0.093Br− (%) 0.290 −0.540* −0.628* –

DMS is the dispersion coefficient for the MS [L]; βMS, is a dimensionless parameter for thepartitioning of MS in a two-region transport model; ωMS is the dimensionless mass transfercoefficient of MS; and μMS is the first-order decay coefficient [T−1] for the MS.

a High correlation results of the leverage influence from one single observation.

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retained in the matrix regarding the total MS retention in the column(matrix and pore walls). We suggest that, in columns with a lighterCTMatrix, the MS enter easily into the matrix, where it is retained and, onthe contrary, a denser matrix favors the transport of the MS into mac-ropores and decreases their capture into the matrix. It is noteworthythat this correlation becomes statistically significant (Fig. 6) after dis-carding the column number 19 (R=−0.643; P < 0.02). The columnno. 19 of the Org. B plot had huge macropores ending in the PVC ring(i.e., walls of the column) (Fig. 1D). That configuration enhanced thetransfer of MS into the matrix. Similarly, the correlation between theBr− recovery and CTMatrix increased after removing column no. 19 (i.e.,from R=0.367 to R=0.687; P < 0.02). We concluded that dead-endmacropores and a lighter matrix favor the retention of solute andtransfer of colloids into the matrix.

4. Conclusion

The influence of soil management on the soil structure and on thesolute and colloid transport properties was studied by analysis of CTimages of intact soil columns, followed by breakthrough experiments ofBr− and microspheres. On the one hand, the CT characterization al-lowed us to find significant differences between the studied manage-ments. On the other hand, the two-region physical non-equilibriumtransport model fitted the breakthrough of bromide and polystyrenelatex microspheres well. Organic management showed the highestpreferential transport, which was related to the type of macropores, i.e.,earthworm burrows with lined walls. The presence of lined walls andpreferential transport were related to the small mass transfer coefficientbetween the matrix and macropores in the dual-porosity model.

Indicators of the macropore network and matrix density obtainedfrom CT and image analysis explained solute and colloid transport. Theresults showed a clear influence of the soil management on the mor-phological descriptors of the soil structure and transport properties.Correlations found in this work provide some experimental evidence oflinks between the geometry of the soil pore network and the transport.

Acknowledgements

The authors want to acknowledge the following funding sources:D.S.G. is funded by the Pre-doctoral Fellowship Program (FPU) ofSpain’s Ministry of Education FPU14/00681, and M.P. and P.P.R. arefunded by a post-doctoral fellowship awarded by Xunta de Galicia(POS-A/2013/171 Plan I2C and Gain program ED481B-2017/31, re-spectively). L.V.J. was additionally funded by CIA and BV1 researchcontracts (FEDER, Xunta de Galicia). Authors thank to the Centro deDesenvolvemento Agrogandeiro (Xinzo, Ourense) for allowing the sam-pling in their plots, and Oscar Lantes at the archaeometry unit RIADT-

CACTUS services USC for the CT image acquisition with their dental 3DCone-beam i-CAT scanner.

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A new method to trace colloid transport pathways in macroporous soils using X‐ray computed tomography and fluorescence macrophotography Diego Soto-Gómez, Paula Pérez-Rodríguez, Laura Vázquez Juíz, José E. López-Periago, Marcos Paradelo Pérez

To cite this article: Soto-Gómez D, Pérez-Rodríguez P, Vázquez Juíz L, López-Periago JE, Par-adelo Pérez M. A new method to trace colloid trans-port pathways in macroporous soils using X-raycomputed tomography and fluorescence macropho-tography.Eur J Soil Sci. 2019;70:431–442.https://doi.org/10.1111/ejss.12783 Diego Soto‐Gómez The final authenticated version is available online at: https://doi.org/10.1111/ejss.12783 Abstract

The fast and deep percolation of particles through soil is attributed to preferential flow

pathways, and their extent can be critical in the filtering of particulate pollutants in soil. Particle

deposition on the pore walls and transport between the pores and matrix modulate the

preferential flow of particulate pollutants. In the present research, we developed a novel

method of combining fluorescence macrophotography and X‐ray computed tomography (CT) to

track preferential pathways of colloidal fluorescent microspheres (MS) in breakthrough

experiments. We located accumulations of MS by fluorescence imaging and used them to

delimit the deposition structures along the preferential colloid pathways by superimposing

these images on the 3‐D pore network obtained from CT. Advection–diffusion with transport

parameters from the dual‐porosity equation correlated with preferential pathway features

across different soil management techniques. However, management did not influence the

morphology of the MS preferential pathways. Preferential flow occurred in only a small fraction

of the total pore network and was controlled by pores connected to the soil surface and by

matrix density.

1

Percolation theory applied to soil tomography 1

*Diego Soto-Gómez1,2, Laura Vázquez Juíz1,2, Paula Pérez-Rodríguez1,2,3, J. Eugenio 2

López-Periago1,2, Marcos Paradelo4, and John Koestel5 3

1Soil Science and Agricultural Chemistry Group, Department of Plant Biology and 4

Soil Science, Faculty of Sciences, University of Vigo, E-32004 Ourense, Spain. 5

2 Hydraulics Laboratory, Campus da Auga, University of Vigo, E-32004 Ourense, 6

Spain. 7

3Laboratory of Hydrology and Geochemistry of Strasbourg (LHyGeS) 8

Université de Strasbourg, Strasbourg, France. 9

10

4Department of Sustainable Agriculture Sciences, Rothamsted Research, Harpenden, 11

Herts, United Kingdom 12

5Department of Soil and Environment, Swedish University of Agricultural Sciences, Box 13

7014, 750 07 Uppsala, Sweden 14

*Corresponding author Phone: +34 988 387 090; fax: +34 988 387 001, mail: disoto@uvigo.es 15

16

ABSTRACT 17

This study provides insights on the significance of network features of soil macropores on the 18

transport of solutes and colloids, and in the filtrating capacity of the soil. We applied percolation 19

theory and network analysis to the pore network extracted from X-ray computed tomography 20

(imaged porosity) in intact columns sampled from topsoils with different tillage treatments. 21

Moreover, we developed a procedure to extract the backbone, which is the part of the percolation 22

2

cluster that controls the direct flow between two boundaries in near saturated conditions, using 23

the ImageJ open source imaging software. We also calculated the percolation threshold of each 24

soil, the probability at which the soil starts to percolate (for the resolution considered). 25

Some backbone characteristics (pore volume, wall surface, circularity, fractal dimension, number 26

of loops and tortuosity) showed significant differences between the treatments. Tilled 27

conventional and organic with high earthworm activity exhibited more complex backbones than 28

no-till soil. Backbone volume, surface, fractal dimension and number of loops are correlated with 29

the surface area of pore walls stained by fluorescent microspheres (MS) used as a colloidal tracer. 30

We also found good correlations between the tortuosity and the number of end-points of the 31

backbone and the transport model parameters for the microspheres and bromide. These findings 32

reinforce the phenomenology between transport in porous media and percolation theory. 33

Moreover, the properties based on percolation theory allow a more complete characterization of 34

the complex soil structure and the development of more accurate transport models. 35

36

Keywords: Tomography; percolation theory; backbone; network analysis; colloidal transport; 37

fluorescence microspheres. 38

39

Introduction 40

Many of the soil functions that support the life on the earth are governed by interactions of solutes 41

and colloids with active soil interfaces. Accessibility of these substances to every active site of 42

the soil may depend on their transport along a hierarchy of interconnected pores with variable 43

diameters and lengths. For example, pores larger than c. 0.3 mm in equivalent cylindrical diameter 44

(henceforth macropores) allow water, solutes, and suspended particles to rapidly bypass the soil 45

matrix (Jarvis, 2007). This fast transport of water and other substances that takes place near 46

saturation in well-connected pore networks is called preferential flow. The occurrence of vertical 47

macropores in soil promotes the fast movement of contaminants through the preferential flow 48

3

paths away from the active interfaces towards the vulnerable sites. For example, preferential flow 49

may decrease the filtering function of microbial pathogens which constitutes a serious threat to 50

groundwater quality (Flury, 1996). 51

Understanding preferential flow impacts requires refinement in the identification methods of the 52

actual transport pathways in soil. X-ray computed tomography is frequently used to infer the 53

potential pathways form a 3D representation of the pore network (Helliwell et al., 2013). 54

Technological progress that allows establishing quantitative relations between macropore 55

connectivity and preferential flow paths is only emerging. In recent years we can find some 56

achievements regarding the subject: Jarvis et al. (2017) applied percolation concepts to describe 57

the connectivity of the soil macropore network, and they found a significant correlation between 58

the imaged fraction of the soil porosity that percolates and the porosity extracted from X-ray CT 59

images (imaged porosity). In this work, the authors investigated the percolation clusters but not 60

the backbones, since the dead-end pores were not cut off. More recently, Soto-Gómez et al. (2018) 61

identified the traces of colloid pathways after transport experiments in soil columns. 62

The significance of the transport and accessibility to sites in a soil pore network can be understood 63

from percolation theory which quantifies connectivity characteristics of disordered complex 64

networks of paths (Berkowitz and Ewing, 1998). In general terms, percolation theory simplifies 65

a complex structure consisting in conductive and non-conductive regions and describes the 66

transmission of certain property between their bounds (Stauffer et al., 2003) . It also provides a 67

framework to understand transport in complex pore networks through scales (Muhammad, 1995). 68

Meanwhile, it is an important tool for upscaling (Liu and Regenauer-Lieb, 2011). In short, 69

percolation theory considers the probability (p) of a small portion of soil volume randomly chosen 70

is occupied by a fluid (in this case, air or water). The core point of the percolation problem in 71

random porous media is to identify the critical probability at which a connecting pore links two 72

boundaries of a Eulerian type volume. This is called the percolation threshold (pc), and is the limit 73

of a critical phenomenon. In soils, for example, pc at a given scale determines the preferential 74

transport of particles bigger than the resolution of the scale considered. The present work is 75

4

focused on the preferential flow along macropores in the root zone in which biota or tillage may 76

create hierarchized structures. In these cases, the measured values of pc for macropores may differ 77

from the theoretical pc of randomly packed media. 78

Percolation theory was used to model permeability of saturated rocks (Katz and Thompson, 79

1986), permeability and water retention curves in fractal soil models (Hunt, 2004), and, in a lesser 80

extent, in natural soils (Ghanbarian and Hunt, 2017; Hunt and Gee, 2002). Moreover, percolation 81

theory is usually used in the form of critical path analysis, to extract the percolation cluster (the 82

pore that connects the extremes, upper and lower, of the system), and to characterize the 83

percolation backbone (Hunt, 2005). The backbone refers to the subset of the percolation cluster 84

without dangling ends that control the flow between two boundaries (Clemo and Smith, 1997). 85

The importance of the backbone properties on the percolation phenomena in porous media has 86

been recognized for decades (Barthélémy et al., 1999; Stanley and Coniglio, 1984). Computer 87

models of 2D networks show the conductance is related to the size and volume of the backbone 88

(Paul et al., 2000). The fractal dimensionality of the percolation backbone controls the time-scale 89

of fluid flow and transport in geologic media (Hunt and Ghanbarian, 2016). So far, there are no 90

available studies on the characteristics of the backbone in structured soils, and their relations with 91

transport properties. 92

Network analysis contributes to finding relations between topology and transport via quantitative 93

descriptors, namely, tortuosity, continuity, number of junctions, number of loops and Euler 94

characteristic, among others. This analysis may also be applied to the backbone, since this part of 95

the porosity has an important role in the transport in near saturation conditions. So, knowledge 96

about the backbone can improve the predictions about the fate of water and other materials. One 97

of the characteristics of the backbone that can be considered is, for example, the amount of loops 98

since each loop potentially contributes to preferential flow (Sahimi and Islam, 1996). 99

Based on the above, we determined the percolation threshold of several soil samples to determine 100

the critical porosity at which they start to percolate (for the tomography resolution employed). 101

5

Moreover, we hypothesize that the properties of the percolation backbone are better correlated 102

with the near saturation transport in structured soils than the quantitative descriptors of the 103

complete imaged pore network. The present work compares some characteristics extracted from 104

the modeling of particles and bromide and the properties that describe the backbone obtained 105

from imaged CT porosity (volume, surface, tortuosity, etc). 106

107

Materials & Methods 108

Sampling sites and soil samples 109

We used 20 undisturbed soil columns from three adjacent experimental plots (Centro de 110

Desenvolvemento Agrogandeiro, Ourense, northern Spain, 42.099N -7.726W WGS84). 111

Cylindrical PVC cases with 100 mm height and 84 mm inner diameter were pushed into the soil 112

(2-12 cm soil depth) and carefully extracted. Five replicates were taken in each of two treatments, 113

both from plots under a conventional management: a plot with spring cereals that was not tilled 114

after sowing (NT) and a plot that was shallow-tilled (ST). The remaining ten samples were 115

acquired from an organic plot used for root crops and vegetables. Each five were collected from 116

an area with high (OA) and with low (OB) earthworm activity. The soil properties at the four 117

sampling locations were very similar. The mean pH as measured in a 1:10 soil-water suspension 118

was 5.9 ±0.05 with no differences between treatment plots. The soil texture was classified as a 119

sandy loam (USDA soil classification) (Table 1) (Soto Gomez et al., 2018). 120

121

Transport experiments and sample sectioning 122

The soil columns were placed at field capacity in a stainless-steel mesh attached to a funnel that 123

conducted the outflow to a fraction collector. We performed transport experiments using red 124

fluorescent polystyrene carboxylate latex microspheres (MS) with a diameter of 1 ± 0.11μm 125

(Magsphere Inc., Pasadena, California), suspended in a bromide solution (0.025 M of KBr, ionic 126

6

strength 25 mM) that behaves as an unreactive solute tracer for comparison with the colloidal 127

tracer. The top boundary condition was set to a constant flux of ~10 mL h-1 (5.1 mm h-1). The 128

average infiltration velocity in all experiments was 2 ±1 cm h-1, reaching a near-saturated flow. 129

Variation among columns depends on the permeability of each column. Therefore, flowrate on 130

the top was adjusted to prevent overflow. Volumetric water content during the breakthrough was 131

0.43 ±0.04 cm3 cm-3, very near to saturation (0.47 ±0.04 cm3 cm-3). The bottom of the columns 132

was left open to the atmosphere, invoking a seepage-face. Before starting the tracer application, 133

deionized water was applied until steady-state flow was reached, then the MS suspension was 134

evenly distributed dropwise over the soil surface. The MS concentration in the effluent was 135

determined by fluorescence (Jasco Fluorescence Spectrometer, Jasco FP-750) and the Br- by 136

automated colorimetry (van Staden et al., 2003). 137

Following the transport experiments, the columns were sliced in 0.5 cm sections. We took 138

fluorescence macrophotographs from the upper end of each soil slice, in a dark room. The 139

fluorescence images were segmented using Otsu’s (Otsu, 1979), separating the stained regions 140

with the MS from unstained ones. Moreover, we quantified the MS trapped in soil by measuring 141

the concentration within each of the sliced soil sections. The soil was suspended by vortex 142

followed by sonication for 10 s each in a solution of Tween 20 (0.02 %) in distilled water just 143

before filtering. Here, we filtered three aliquots of a suspension of each soil slice and took images 144

of the fluorescent glow of particles reflected in the membrane filters through a magnifying glass. 145

We counted the individual glow spots in the images as described in Soto-Gómez et al. (2018b). 146

After the transport experiments, the soil columns were saturated and weighed. Then they were 147

oven dried at 105 ºC and weighed again to calculate the bulk density (ρd) and the saturated 148

volumetric content (θ). 149

150

Transport modeling 151

7

Inverse modeling to the experimental BTCs was carried by nonlinear fitting using the CXTFIT 152

model (Toride et al., 1995). This model assumes that the soil porosity divides into two different 153

regions, a mobile and an immobile one (Coats and Smith, 2007): 154

𝜃𝑚𝜕𝑐𝑚

𝜕𝑡= 𝜃𝑚 𝐷𝑚

𝜕2𝑐𝑚

𝜕𝑥2 − 𝐽𝑤 𝜕𝑐𝑚

𝜕𝑥− 𝛼(𝑐𝑚 − 𝑐𝑖𝑚) (eq. 1) 155

156

𝜃𝑖𝑚𝜕𝑐𝑖𝑚

𝜕𝑡= 𝛼(𝑐𝑚 − 𝑐𝑖𝑚) − 𝜃𝑖𝑚 𝜇𝑖𝑚 𝑐𝑖𝑚 (eq. 2) 157

θ is the volumetric water content [L3 L-3]; c is the concentration [ML-3]; Dm is the dispersion 158

coefficient in the mobile flow domain [L2 T-1]; x and t are the distance [L] and time [T]; Jw is the 159

volumetric water flux density [LT-1]; α is the first-order kinetic coefficient between mobile and 160

immobile zones [T-1]; and µ is the first-order decay coefficient [T-1] that in our case is used to 161

model the irreversible trapping of MS in the soil. The subscripts ‘m’ and ‘im’ refer to the mobile 162

and immobile liquid regions. The inverse solution yielded the dispersion coefficient of the 163

Bromide (DmBr) and microspheres (DmMS), α, µ and β, a dimensionless parameter for partitioning 164

that indicates the proportion of water content in the mobile zone: β = θm / θ. We first fitted the 165

two-region solute transport model to the BTCs of Br-, and then used the fitted parameters (α, µ 166

and β) as initial values for fitting the BTCs of MS. 167

168

Image acquisition, processing and image analyses 169

The columns were scanned with a 3D Cone-beam i-CAT scanner (Imaging Sciences International 170

LLC, PA, Hatfield, USA), using a tube voltage of 120 kV, an electrical current of 5 mA current 171

and a voxel size of 0.24 mm. The reconstructed 3-D images were processed with the free software 172

ImageJ version 1.52a (Schindelin et al., 2012). Pretreatment of the images consisted in removing 173

all the non-soil objects, namely, the PVC casing and the upper and the lower headspaces. The 174

Sauvola’s auto local thresholding was employed to obtain binary images representing the pore 175

network and the solid fraction (Sauvola and Pietikäinen, 2000). The value of each pixel is 176

8

determined individually, considering a surrounding window of pixels (50 pixels in our case). The 177

thresholding is calculated in each window using the mean intensity (µi) and the local standard 178

deviation (σi), by: 179

Pixel tresholding = µi * ( 1 + k * (σi/ r - 1 )) (eq. 3) 180

Where k and r values are constants decided depending on the kind of sample and on the 181

característics of the scanner. We used a k value (parameter 1) of 0.3 and a r value (parameter 2) 182

of 128 (the maximum standard deviation). 183

The CT-porosity thus obtained to that of the resolvable macropores, ≥1.2 mm in diameter(Vogel 184

et al., 2010). We measured the pore volume and the pore wall surface. Moreover, we obtained the 185

connectivity calculated as one minus the Euler number, and the fractal dimension for the pore 186

structures. The skeleton of the pore network (Thovert et al., 1993) was obtained and analyzed 187

using the plugin Skeletonize 3D (Doube et al., 2010). From this, we received the number of 188

branches, junctions (places where branches join), end-points (ends of the pores), and the average 189

branch length. Using these parameters, we calculated the tortuosity of each branch by dividing 190

the real branch length that separates two consecutive junctions by the Euclidean distance existing 191

between them (Wu et al., 2006). To present the results, we made the average tortuosity 192

considering all branches. We also calculated the coordination number, ZT: 193

ZT = (2 x Number of branches – Number of end-points)/ Number of junctions (eq. 4) 194

195

Calculation of the percolation threshold and critical pore diameter (pc and CPT) 196

Soil pore networks cannot be regarded as a random structure (Jarvis et al., 2017), so we used the 197

method for structured pore networks suggested by Liu and Regenauer-Lieb (2011). Considering 198

the probability of a unit soil volume being occupied by a pore, p, is equivalent to the imaged 199

porosity, we calculate the percolation threshold, pc, which is the probability for the first time the 200

soil pore network percolates (i.e., the pore network is connected from the top to the bottom of the 201

9

soil column). The imaged pores were eroded or dilated by stepwise removal or addition of voxels 202

until reaching the percolation threshold using the Image-J plugin 3-D (Figure 1B), i.e., until the 203

percolation cluster of the pore network became disconnected for the first time (Liu and 204

Regenauer-Lieb, 2011). We consider that two voxel pores are connected if they share a side, an 205

edge or a border (Rubik neighborhood or 26NN). Each erosion step removed the outermost voxel 206

layer from the imaged pores. We defined the percolation threshold as the average of the imaged 207

porosity before and after the last erosion step. This method was validated in a computed random 208

3D cube obtaining a pc of 0.0969 ± 0.0009 very close to the reported value of 0.0976 for the 26NN 209

neighborhood with computer simulations (Kurzawski and Malarz, 2012). 210

With the erosion method, we also calculated the critical pore diameter (CPT), i.e., the diameter 211

of the biggest sphere that could pass through the soil column from top to bottom (Jarvis et al., 212

2017). This parameter was calculated by considering the number of erosion steps needed to reach 213

the pc and the voxel size. 214

215

Backbone extraction 216

The backbone extraction procedure is not trivial because the pruning of dangling ends must be 217

done on the skeleton of the percolation cluster and later the backbone must be reconstructed from 218

the pruned skeleton and the imaged porosity as follows. The first step was to extract the 219

percolation cluster with Image-J. Then, the cluster was transformed into the skeleton as indicated 220

above, preserving the length of the segments of the backbone. Notice that the Image-J pruning 221

algorithm erases all the ending voxels of the cluster. Thus, before skeletonization, two slices 222

occupied entirely by void voxels were added to the top and the bottom of the image stack to 223

protect them from pruning (Luo et al., 2010). Then, the pruning process deleted the ends of the 224

branches bigger than one voxel size, here 0.24mm, resulting in a row of connected voxels. Then, 225

the two void slices were removed to get the skeleton of the backbone (Figure 1C). Finally, the 226

backbone was reconstructed from its skeleton by adding void voxels layer-by-layer around their 227

10

main axes. Once the thickness of the dilated skeleton reached the one of the imaged percolation 228

cluster which the skeleton originates was combined with the imaged pore in such a way that the 229

added voxels exceeding the boundaries of the percolation cluster were removed and the imaged 230

backbone was obtained (Figure 1D). 231

From the imaged backbone and its skeleton we calculated the same morphological measures as 232

for the entire pore network and its skeleton, including the coordination number of the backbone, 233

ZB. Moreover, for the backbone, we also calculated the number of loops and some features of the 234

2D horizontal slices, like the average roundness (4*π*Area/ Perimeter2) and circularity (4*Area/ 235

(π*Major Axis2)). 236

The backbone properties were compared with the complete network features and with the 237

transport experiment characteristics. The samples without percolating imaged pores (17 and 20) 238

were not included in the analysis. 239

240

Results and Discussion 241

Transport 242

The average mass balance after transport showed significant retention of Br-, in the range from 243

10 to 20 %. This retention is physical because of the low chemical adsorption of Br- to soil (Klute 244

et al., 1986). It is typical of the transport in variably saturated structured soil, in which solutes 245

diffuse to stagnant regions separated from the main flow. In accordance, the BTCs were modeled 246

by the dual porosity mobile-immobile model. Inverse modeling of BTCs in all columns resulted 247

in acceptable fitting with a R2 > 0.9420. Fitted dispersion coefficient (Dm = 26 ±18 cm2 h-1) was 248

very high due to a spread of the BTCs that result of the variance of transport velocities developed 249

along preferential flow paths. Also, the variance of Dm between column experiments was very 250

high with a coefficient of variation 67%. The fraction of mobile water regions in the model was 251

β = 0.105 ±0.06, and the first order transfer coefficient between mobile and immobile zones α = 252

0.12 ± 0.09 h-1. 253

11

The presence of percolation clusters influenced transport of the MS. Retention of the MS after the 254

breakthrough was 40 ±18%; this figure is more than three times the average retention for the Br-. 255

Transport of MS was modeled using the same parameters describing the Br- transport but fitting 256

the dispersion coefficient Dm = 40 ±35 cm2 h-1 (Figure 2) and a decay coefficient µ = 0.6 ±1.0 h-257

1 (half-life time 1 ±0.7 h) that simulates the kinetic trapping of MS in the immobile region. The 258

fitted Dm for the MS was 1.5 times larger than the Br- and showed even a larger standard error 259

due to the differences in arrival times of the MS and the increased differences in their BTC 260

between the column experiments. Kinetic trapping is a typical behavior colloid retention rate in 261

porous media (Bradford et al., 2015); it was already reported the best-fitted model in previous 262

experiments (Soto-Gómez et al., 2018b). The above results show a large variation in the transport 263

features with similar texture; that can be related to differences in the organization of the pore 264

network properties. 265

266

Percolation threshold and network parameters of the imaged porosity: CPT and Z 267

The average pc was smaller (0.014 ± 0.014) (Figure 3) than the percolation threshold of a random 268

structure (0.097 ± 0.001). It was also smaller when compared to other natural samples like a 269

mylonite sample or bread (pc = 0.0671 and 0.2448 respectively) (Liu and Regenauer-Lieb, 2011). 270

This difference indicates that the soil pore networks are correlated structures which causes them 271

to percolate at lower porosities. Jarvis et al. (2017), using soil samples from recently harrowed 272

arable topsoil, obtained also larger percolation thresholds (0.04 to 0.06) in imaged CT porosity at 273

0.065 mm resolution. The difference to our study can be due: the larger amount of long biopores 274

present in our samples that cross the column vertically top to bottom, the method used to extract 275

the pc or the 0.24 mm resolution that underestimates the porosity. So, comparison of the 276

percolation threshold values between different studies must be taken with care because these also 277

depend on the minimum pore size resolvable by CT and the segmentation process. 278

12

We could not find significant differences in the percolation threshold between the four sampling 279

locations (Figure 3A). Nevertheless, we want to point out some trends. The NT samples exhibited 280

a smaller pc (0.004 ± 0.003) since it contained many elongated, thin and straight root pores. The 281

ST samples showed slightly larger values for pc due to an important proportion of cracks and 282

some biopores. The OA samples represented the highest pc due to thicker and more tortuous 283

orientation of the earthworm burrows. The OB plot samples were a special case since this plot 284

included the only two samples (nº 17 and 20) without a connected path from top to bottom. The 285

remaining samples of the OB showed low pc values related to the presence of a few biopores 286

together with generally low porosity. 287

The critical pore diameter (CPT) had an average value of 2.44 ± 1.52 mm, and there were no 288

significant differences among the different plots. Note that the large standard error (2.74 ± 2.57) 289

in the NT zone occurred by the uneven distribution of earthworm pores within the NT group of 290

samples. The CPT raised from 0.88 ± 0.28 mm in three NT samples without earthworm burrows 291

to 5.04 and 6.00 mm with earthworm burrows in the samples #5 and #7. 292

The coordination number for the skeleton of the complete network (ZT) has an average value of 293

2.91 ± 0.19, a similar value to the obtained for the Berea sandstone, Z = 2.8 (Yanuka et al., 1986). 294

This means that in each junction of the network converge about three branches, similar than the 295

Z of a Bethe lattice (Z = 3). There are significant differences among plots. samples from NT and 296

OB had lower ZT (2.88 ± 0.016 and 2.69 ± 0.19 respectively) when compared with ST (3.07 ± 297

0.05) and OA (3.01 ± 0.05). 298

299

Backbone properties 300

The representative backbone skeletons for each zone (Figure 4) illustrate the influence of the 301

management on the backbone shape. The ST plot (Figure 4A) produced very complex backbones 302

in the upper half because of the disruption of soil matrix increased the number of segments, loops 303

and tortuosity. The NT plot backbones (Figure 4B) were a bundle of vertical tubes that matches 304

13

the pattern generated by the fasciculate root systems of monocotyledonous grass and cereal. The 305

OA plot (Figure 4C) with the highest earthworm activity showed complex backbones that extend 306

along all the space directions. These were mostly generated by earthworm burrows. Conversely, 307

the low activity organic zone (OB, Figure 4D) had much simpler backbones than the former. 308

Table 2 shows the average quantitative characteristics of the backbones also grouped by plots. 309

The volume of the backbone was larger for ST and OA, which have the largest cracks and 310

earthworm pores. In contrast, NT presented smaller backbone volume because the porosity 311

captured by CT was generated by the channels from mineralized dead roots and a few earthworm 312

burrows. Consequently, the small diameter and uniformity of roots confer the largest pore wall 313

surface area. The NT backbones also have higher circularity and roundness than the other plots. 314

The number of junctions, branches and loops are quantitative indicators of the complexity, being 315

the soil from the ST and OA zones the most complex (Table 2). The loops in the backbone are 316

preserved from the pruning of the percolation cluster because, unlike the dangling ends, they 317

participate in the water flow and transport through the backbone as redundant pathways. The OB 318

samples had the lowest number of loops but presented the higher tortuosity (Table 2). These 319

columns had the smallests number of big pores, which coincides with the occurrence of small 320

twisted pores that increased tortuosity. This twisting resulted from the combined morphologies of 321

pores with different genesis: buried crop residues, small cracks, roots, and burrows. 322

The coordination number of the backbone (ZB) averages the number of branches and junctions 323

per backbone. These numbers depend on the number of loops in the backbone and its branches 324

that connect the top and bottom ends of the soil column. The coordination number of the backbone 325

(ZB = 3.43 ± 0.07), was slightly higher than the coordination number of the entire image pore 326

network, ZT. Both coordination numbers, ZB = 3.43 and ZT = 2.91 are similar. Differences in ZB 327

between treatments were not significant; this means that ZB is independent of the soil 328

management. 329

330

14

Correlations between percolation theory-derived characteristics with soil physical 331

properties and transport 332

Correlations with soil properties 333

The percolation threshold of the porous network was poorly correlated with the rest of the physical 334

parameters of the soil (dry bulk density, tortuosity, connectivity and pore surface, among others). 335

It was slightly correlated with the CT-Porosity (R = 0.476). 336

We found that ZT (the coordination number for the entire network) is correlated with most of the 337

parameters extracted from the pore network, for example, CT-Porosity (R = 0.82), fractal 338

dimension (R = 0.81) and tortuosity (R = 0.86). The correlation with the CT-Porosity showed the 339

same behavior to that described by other authors (Yanuka et al., 1986). 340

The dry bulk density of the soil was correlated with the backbone characteristics: denser samples 341

present backbones with less volume, surface, fractal dimension, and loops. We also observed a 342

positive correlation between bulk density and roundness (and circularity). This correlation 343

increases in the NT soil columns, having dense and well connected by root pores with high 344

circularity. Correlation in the other zones is due to the presence of earthworm pores with high 345

circularity belonging to the backbone, even in denser samples. 346

347

Correlations with transport 348

We found particularly interesting the correlations that involve parameters extracted from the 349

modeling of Br- and MS transport and the characteristics of the backbone (Table 2). The tortuosity 350

of the backbone was positively correlated with the dispersion coefficient of MS. We conjectured 351

that the twisted pore shapes enhanced the transport of MS between the pore walls and the matrix 352

since the MIM transfer is often correlated with the dispersion. The dispersion of Br- was 353

positively correlated with the pore surface, end-points and slab voxels. It is likely that those three 354

physical parameters increase the exchange of Br- with the matrix and hence, similarly to the 355

15

tortuosity, the dispersion. The number of end-points was also correlated with the β coefficients, 356

both for Br- and MS. The backbone only has end-points in the upper and lower extremes, so is 357

logical to think that the samples with more input and output paths connected will have more 358

mobile water (β = θm / θ). The first-order kinetic coefficient between mobile and immobile zones 359

rate transfer coefficient was not correlated with any percolation characteristic. 360

Finally, the average surface stained by the MS showed the best correlations with the backbone 361

properties. It was positively correlated with the backbone’s volume, surface, fractal dimension, 362

and the number of branches, junctions, loops and connectivity. Thus, the more complex the 363

backbone, the bigger the surface stained. This relationship can be explained by the moisture 364

conditions: all the experiments were carried out close to saturation, with the backbone presumably 365

conducting the tracer suspension. Such near-saturated conditions make it necessary to consider 366

the colloid retention induced by the flow between mobile and immobile zones across the backbone 367

wall. Therefore, the colloid concentration would be greater in backbones with larger volume, 368

surface and complexity. Considering that we could not find significant differences between the 369

mass balance of MS in different soils, in the samples with smaller backbones the particles were 370

better distributed between the pore walls and the matrix, while in the samples with bigger 371

backbones the particles were mostly retained in the wall of the backbone. This happens because 372

of the sandy loam texture of our soils. However, in soils with a finer texture, the colloids have 373

more difficulties to reach the matrix and the contribution of the backbone to the preferential 374

transport is bigger, a fact already pointed by Jarvis et al. (2007). 375

376

Conclusion 377

The properties of the backbone appear to be highly important for understanding the macropore 378

flow and the preferential transport of solutes and colloids. The principal channels of transport are 379

included in the backbone, and its features will determine the fate of most of the substances. Most 380

16

of the descriptors of the backbone studied showed significant correlations to the applied tillage. 381

This is an indication that preferential transport is influenced by the agricultural management. 382

We found significant correlations between the dispersive transport of solute and colloidal tracers 383

and the backbone properties, and between the average stained surface and the volume of the 384

backbone. The significance of our results can be limited by the resolution in the acquisition of the 385

imaged porosity. These correlations should be studied more in depth in future research increasing 386

the size and resolution of the CT images from larger soil samples. 387

Percolation theory can provide promising tools to assess the filter function of soil under different 388

management practices. The connectivity of macropores is critical in preferential flow, facilitating 389

solutes and colloids to bypass the soil matrix. Concepts from percolation theory and network 390

analysis are candidates for describing pore morphology and inferring its correspondence on 391

transport. 392

393

Acknowledgments 394

The authors acknowledge the following funding sources: D.S.G. is funded by the Predoctoral 395

Fellowship Program (FPU) of Spain’s Ministry of Education FPU14/00681, P.P.R is funded by a 396

postdoctoral fellowship awarded by Xunta de Galicia (Gain program ED481B-2017/31), L.V.J. 397

is funded by CITACA ED431/07 and BV1 research contracts (FEDER, Xunta de Galicia) and 398

M.P is supported by the BBSRC-funded Soil to Nutrition strategic program (BBS/E/C/000I0310). 399

The authors thank the Centro de Desenvolvemento Agrogandeiro (Ourense) for allowing the 400

sampling in their plots and Oscar Lantes at the archeometry unit RIADT-CACTUS services USC 401

for the CT image acquisition with their dental 3-D Cone-beam i-CAT scanner. 402

403

17

Figures 404

405

Figure 1: Sequence of 3d representation images illustrating the stages of extraction of the 406

backbone from the imaged CT porosity of the column number 13 (in the organic management 407

zone OB): A) In binary, after applying the Sauvola’s Auto Local Thresholding method, with the 408

porous part in grey; B) After several erosions of the porous part, until reaching the percolation 409

threshold; C) Skeleton of the backbone; and D) Backbone filled. 410

411

Figure 2: Box-plot that illustrate the differences in the distribution between zones of: A) 412

dispersion coefficient for the microspheres (DmMS), and B) β coefficient for the microspheres 413

(βMS). (NT, soil no-tilled after sowing; ST, soil shallow tilled; OA, organic soil with high 414

earthworm alteration; and OB, organic soil with low earthworm alteration) 415

416

Figure 3: Box-plot that illustrate the differences in the distribution between zones of: A) 417

percolation threshold (pc), B) critical pore diameter (CPT), C) coordination number for the entire 418

network (ZT), and D) coordination number for the backbone (ZB). Note that two of the samples 419

of the Organic B field (OB) did not have a backbone, so they do not appear in the Figures B) and 420

D). (NT, soil no-tilled after sowing; ST, soil shallow tilled; OA, organic soil with high earthworm 421

alteration; and OB, organic soil with low earthworm alteration) 422

423

Figure 4: 3D representations of the backbone skeletons of samples with different managements: 424

A) ST (nº 14), B) NT (nº 2), C) OA (nº 3), and D) OB (nº 19). (NT, soil no-tilled after sowing; 425

ST, soil shallow tilled; OA, organic soil with high earthworm alteration; and OB, organic soil 426

with low earthworm alteration) 427

428

18

429

A)

B)

C)

D)

Figure 1. 430

431

19

432

433

434

20

435

436

437

438

21

439

A)

B)

C)

D)

Figure 4. 440

441

22

Tables 442

Table 1: Texture and organic matter of the soils studied with standard deviations. 443

Management % Coarse Sand

( > 0.5 mm)

% Fine Sand

(0.5 – 0.05

mm)

% Silt

(0.05 – 0.002

mm)

% Clay

( < 0.002 mm) % Organic Matter

Conventional

Non-tilled 46.2 ± 0.5 26.1 ± 0.9 5.7 ± 2.9 10.9 ± 1.2 11.1 ± 2.6

Conventional

Shallow Tilled 42.9 ± 2.4 28.3 ± 1.7 5.3 ± 4.1 11 ± 0.6 12.5 ± 4.6

Organic 44.5 ± 0.2 29 ± 0.4 8.1 ± 0.3 9.2 ± 0.7 8.5 ± 0.5

444

445

23

Table 2. Average results of the backbone properties per zone. 446

Zone

Pore

Volume

(cm3)

Pore Wall

Surface

(dm2)

Circularity Roundness Fractal

Dimension

ST 43.0 ± 15.7 b 10.5 ± 3.1c 0.71 ± 0.01b 0.56 ± 0.01a 2.35 ± 0.05c

NT 15.9 ± 8.1a 6.2 ± 1.0ab 0.85 ± 0.02a 0.65 ± 0.01b 2.18 ± 0.06b

OA 38.7 ± 7.4b 9.1 ± 1.0bc 0.69 ± 0.01b 0.57 ± 0.00a 2.30 ± 0.03bc

OB 10.9 ± 5.3a 2.5 ± 1.9a 0.71 ± 0.02b 0.60 ± 0.03a 1.98 ± 0.13a

Zone Branches Junctions Loops Tortuosity

ST 6147 ± 1794c 3538 ± 851c 57.0 ± 6.0c 1.47 ± 0.04ab

NT 2974 ± 1929ab 1720 ± 1064ab 25.0 ± 9.6ab 1.41 ± 0.05a

OA 4484 ± 1565bc 2602 ± 935bc 46.4 ± 4.7bc 1.46 ± 0.04ab

OB 926 ± 1120a 533 ± 656a 15.3 ± 12.7a 1.52 ± 0.08b a, b, c different superscript showed significant differences between groups with different 447

management (at a probability value P < 0.05). 448

24

Table 3. Correlations between backbone properties and coordination number (of the complete network), and the pore volume of the complete network, some

characteristics of the soils and parameters from the transport experiments.

Volume (mm3)

Surface (mm2) Circularity Fractal

Dimension Nº of

Branches Nº of

Junctions

Nº of End-

Points

Nº of Loops Tortuosity ZT

Pore volume of the entire

network (mm3) 0.94*** 0.88*** -0.65** 0.83*** 0.77*** 0.77*** 0.87*** 0.82***

ρd (g cm-3) -0.76*** -0.60** 0.68** -0.57* -0.55* -0.61**

% of Stained surface 0.77*** 0.72*** 0.74*** 0.53* 0.53* 0.62** 0.65**

Br- dispersion coefficient

(Dm) 0.47* 0.64**

MS dispersion coefficient

(Dm) 0.53*

β coefficient (Br-) 0.47*

β coefficient (MS) 0.57*

Linear for a level of significance of: * 0.05, ** 0.01, and *** 0.001.

25

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1

3D Multifractal characterization of computed tomography images 1

of soils under different tillage management: linking 2

multifractal parameters to physical properties 3

*Diego Soto-Gómez1, 2, Paula Pérez-Rodríguez1, 2, 3, Laura Vázquez Juíz1, 2, 4

Marcos Paradelo4, and J. Eugenio López-Periago1, 2 5

1Soil Science and Agricultural Chemistry Group, Department of Plant Biology and 6

Soil Science, Faculty of Sciences, University of Vigo, E-32004 Ourense, Spain. 7

2Hydraulics Laboratory, Campus da Auga, Facultade de Ciencias, Campus da Auga, 8

University of Vigo. 9

3Laboratory of Hydrology and Geochemistry of Strasbourg (LHyGeS) 10

Université de Strasbourg, Strasbourg, France. 11

4Department of Sustainable Agriculture Sciences, Rothamsted Research, Harpenden, 12

Hertfordshire, United Kingdom 13

*Corresponding author Phone: +34 988 387 070; fax: +34 988 387 001, mail: 14

disoto@uvigo.es 15

16

ABSTRACT 17

Multifractal analysis of pore images obtained from X-ray computed tomography (CT) was used 18

to characterize the scaling properties of macropores in soils with different managements and 19

their correspondence with macroscopic physical properties related with the soil functions. 20

2

We used CT images of twenty undisturbed soil columns to examine the multifractal properties 21

of the pores identified by X-ray computed tomography (CT-porosity). Multifractal spectra 22

successfully describe the scaling of the pore network in all soil columns. The dimensions and 23

scaling parameters of these spectra correlate with macroscopic magnitudes, namely, CT-24

porosity, surface area of the pore walls, tortuosity, and bulk density. We also found strong 25

correlations between the singularity spectra and the topological descriptors of the pore network 26

skeleton: total slab voxels, number of branches per path, number of endpoints and sum of 27

branch length, among others. These correlations show that the complexity of the CT-porosity 28

can be related quantitatively with physical properties, the organization of the pore skeleton and 29

solute transport. 30

31

Keywords: multifractal analysis, soil management, soil structure, pore network, organic 32

farming. 33

34

1 Introduction 35

Soil porosity is an evolving and complex three-dimensional network that governs the transport 36

of gases, water, solutes, colloids, and particles. At the same time, the transport of these 37

substances along the soil pore network takes part in key processes and functions in terrestrial 38

environments such as water balance, plant growth, nutrient cycles (Young and Crawford, 2004), 39

and gas exchange, that includes release and capture of greenhouse gasses (Quigley et al., 2018; 40

Steffens et al., 2017). For a few decades, CT imaging provided a non-destructive method to 41

extract the porous network and allowed to measure the shape and the size of the soil pores, as 42

well as their connectivity, number of paths, junctions, branches and loops (Helliwell et al., 43

2013; Horgan, 1998; I. G. Torre et al., 2018). The importance of the spatial organization of the 44

soil pore network is increasingly recognized because determines phenomena close related to 45

water flow and transport, such as entrapped air, irreducible water saturation and hysteresis (Jury 46

3

et al., 2011). Biopores usually constitute a small proportion of the soil pores, but due to 47

hierarchical network structure (Elliott et al., 1999), have a critical effect on percolation and 48

leaching water, solutes, and suspended particles (Heuvelink and Webster, 2001; Larsbo et al., 49

2014). Furthermore, hierarchical organization of biopores influences the preferential transport 50

because favours the occurrence of large continuous paths (Marcus et al., 2013; Paradelo et al., 51

2013; Rabbi et al., 2018). More recently, it was shown that biopore organization is related to the 52

occurrence of low-frequency pressure jumps during drainage (Soto et al., 2017). 53

Changes in the soil pore network across scales can be explained by their scaling relations by 54

using fractal analysis. Fractal techniques were used in the assessment of the variability of soil 55

properties and scaling (Pachepsky et al., 1996). Interestingly, fractal analysis can account for the 56

rare occurrences in hierarchical networks such as very large pores that have a dramatic effect on 57

the hydraulic conductivity and preferential transport in depth (Alvarez-Benedi and Munoz-58

Carpena, 2004). The inherent complexity of pore networks is best described with multifractal 59

analysis that accounts for the rich scaling properties of the soil structure. Multifractal analysis 60

on two dimensional (2D) thin slices was used to describe the fractal behavior of soil pore space 61

with several thresholdings (Bird et al., 2006; Giménez et al., 2002; Tarquis et al., 2009). Lately, 62

multifractal analysis on 2D images of soil porosity is evolving and 3D analysis gained 63

importance (Piñuela et al., 2010; Torre et al., 2018). Pore networks reconstructed from CT 64

images were used to characterize the scaling of pores in peat and to estimate the hydraulic 65

properties (Rezanezhad et al., 2010). Recently, Wang et al. (2018) reported changes in the 66

indicators of the multifractal spectra in 3D of soils sampled around opencast coal mining upon 67

restoration actions, but no relation of physical magnitudes with fractal parameters or topologic 68

measures were reported. 69

Percolation and conductivity related properties of pore networks were derived for some 70

mathematic fractal objects used to model the soil structure (Hunt, 2004; Perrier et al., 2010). 71

Worth noting the studies using computer simulations on idealized porous media such as 72

Jiménez-Hornero et al. (2009), and, more recently, Lafond et al. (2012), who compared 73

4

multifractal properties of porosity inferred from CT images with gas diffusion and physical 74

properties. However, these relations are far from being achieved in disordered porous media. 75

Linking multiscale descriptors of disordered natural porous objects with macroscopic properties 76

and transport functions is in the early stage of its development. Indeed, advances will require 77

combined (multi)fractal analysis and experimental measures of soil physical parameters. 78

Despite that, some authors found correlations between features of the preferential flow and the 79

multifractal spectrum, very little studies are available about the correlations between 80

multifractal descriptors of the soil porosity and their transport properties (Posadas et al., 2009). 81

This work is focused on the analysis of the relations between the scaling of the soil pores, the 82

topology of the pore network, and the macroscopic descriptors of transport in soils with 83

structure a dominated by biopores. To this aim, we performed a multifractal analysis of CT-84

porosity images and compared the results with parameters of transport. We present results of (1) 85

the comparison of multifractal properties of the CT-porosities of soils under three different 86

types of tillage management; (2) changes in the multifractal characteristics of 2D soil sections 87

with depth; and (3) correlations between multifractal descriptors and other soil properties, such 88

us statistical descriptors of the pore network topology and parameters describing transport. 89

90

2 Materials and methods 91

2.1 Soil sampling and leaching experiments 92

The sampling strategy was conducted for obtaining a variety of structural pores in the same soil 93

with small variations in texture and chemical properties. The texture is sandy loam according to 94

the USDA texture classification, with pH in water of 5.9 ± 0.05. The study was done on twenty 95

unaltered columns (100x84 mm, height by diameter). The first 10 columns were sampled from a 96

plot in which tests of organic farming are performed (Org.): five from subplots that showed 97

higher earthworm activity deduced by surface alteration (Org. A), and the other five were 98

randomly taken in the plot (Org. B). Another five columns were sampled from a conventional 99

5

cereal-potato rotation plot with disrupted root channels by shallow tillage up to 10 cm depth, 100

presenting a denser layer at the bottom of the columns (ST). The last five columns were 101

sampled from a no-till (NT) treatment where roots were preserved. The sieve and organic matter 102

analysis results (Table 1) showed that all managements were quite similar, but the Org. 103

treatment presented the smallest amount of organic matter because of its historical use for root 104

crops with the removal of stubble. 105

The columns were carefully extracted (2-12 cm depth) in a friable mechanical condition and 106

were sealed immediately after extraction. Finally, they all were stored in darkness at 4° C. Data 107

of solute and colloidal breakthrough experiments and preferential flow paths were collected 108

from previous work (see Soto-Gómez et al., 2018b). 109

110

2.2 CT Images acquisition, filtering, and treatment 111

The samples were scanned with a cone-beam X-ray computed scanner apparatus (i-CAT 3D, 112

Imaging Sciences International) with the X-ray tube set to 120 kV and 5 mA current. We 113

obtained a 2D image sequence (stack) of each column with a voxel size of 0.24 mm using the 114

ImageJ-Fiji software (Schindelin et al., 2012). 115

Segmentation of images was conducted to separate the pores from the matrix obtaining a set of 116

binarized images. This is a critical step of the analysis. The appropriate segmentation method 117

depends on the image quality, resolution, distribution of X-ray attenuation data, and, finally, the 118

objective of the study (Pagenkemper et al., 2015). In our case, the best segmentation method for 119

the separation of pores from the soil matrix was the Sauvola’s auto local thresholding (Sauvola 120

and Pietikäinen, 2000). This procedure gave the most consistent shape and structure of pores. 121

The CT-porosity (cm3) was calculated over the processed binary images, considering the 122

number of voxels occupied by pores. The number of pores, and the surface and volume of 123

every single pore were also calculated and recorded. The binary images were processed to 124

obtain the skeleton of the pores (Doube et al., 2010). The topologic parameters extracted from 125

6

the pore network skeleton were: number of branches and junctions, end-point voxels (voxels 126

where the branches end, in the matrix or in the extremes of the sample), slab voxels, and triple 127

and quadruple points (junctions that link three or four branches respectively). The path length 128

(LR) and Euclidean length (LE) of each path of the skeleton were used to calculate the average 129

CT tortuosity (τ) (Wu et al., 2006) 130

𝜏 =𝐿𝑅

𝐿𝐸 (eq. 1) 131

The tortuosity has important implications for the transport of substances throughout soil 132

(Roberts et al., 1987). Then, we calculated parameters describing the pore network namely the 133

Euler characteristic and the connectivity (Ragan and Hinkle, 1975). In our case, these two 134

characteristics are quite related to the number of connections or junctions of the skeleton (R2 = 135

0.889 and R2 = 0.851 respectively). 136

137

138

2.3 Multifractal analysis 139

The multifractal calculations were carried out for both 2D slices (X-Y, plane) and 3D cubes. 140

The multifractal analysis in the 2D slices was done using the ImageJ-Fiji Fraclac plugging 141

(Karperien, 2013) that provides the vertical distribution of parameters of the multifractal 142

spectra. 143

The computer program used in the 3D multifractal calculations was written from the software 144

ImageJ-Fiji BoneJ (Doube et al., 2010), but was limited to cubes. Therefore, two 3D cubes 145

were extracted from two depths (Z axis) in the centre of the images (in the X-Y plane): the 146

upper part (0 to -4.8 cm Z axis) and the lower part (from -4.8 to -9.6 cm, approximately). The 147

edge of all cubes was 200 voxels (≈ 4.8 cm length). Thus, the 3D multifractal calculations for 148

each column were done on those two depths. The method used for the calculations of the 149

multifractal spectra, namely, Rényi spectrum and singularity spectrum, is summarized in the 150

7

Supplementary Information. The multifractal parameters obtained from the above spectra were 151

the fractal dimension in 3D (D0), the correlation dimension (D1), the entropy dimension (D2), 152

the aperture of the spectrum (Ap), the right to left symmetry of the spectrum (R-L), and the 153

vertical symmetry of the spectrum (V). We also calculated the aperture and slope of several 154

ranges: q (-1 to 1); q (0 to 1); q (-1 to 0), and so on. 155

Graphical meaning of those parameters can be visualized in Figures 1 and 2. Moreover, a 156

complete example of the multifractal calculations for one cube is shown in the Supplementary 157

Information. 158

159

2.4 Statistical analysis 160

Normality of all the sets of multifractal indicators and soil variables was assessed with the 161

Kolmogorov–Smirnov test. The influence of soil management on multifractal indicators was 162

tested either with F-test for normally distributed values or the non-parametric Kruskal-Wallis on 163

the non-parametric ones. Correlation between parameters was tested with the Pearson’s 164

correlation coefficient (R). 165

166

3 Results and discussion 167

A summary of the porosity data is shown below. The size of the pores that were identified with 168

the CT and image analysis ranged from 1.4 10-2 mm3 to 3.5 104 mm3. The latter one corresponds 169

to the volume of a large multi-branched earthworm burrow. This range covers almost six orders 170

of magnitude in volume. The average number of individual pores was 2365 per soil column, 171

with a range from 1285 to 3930. Detailed information of the characteristics of each soil obtained 172

through the CT analysis, as well as other soil properties such as bulk density and saturated water 173

content, are shown in the Supplementary Information in Tables S1, S2, S3, and S4. 174

8

All soil columns were examined in order to determine the parameters of the Rényi spectrum, the 175

multifractal singularity spectrum and the vertical distribution of the fractal dimensions of 2D 176

slices. 177

Management practices influenced the parameters that are displayed in Table 2. In 2D we found 178

differences between the average fractal dimension (D). In the 3D cubes, the significant effects 179

of the management were found in the multifractal dimension in 3D (D0), the correlation 180

dimension (D1), the entropy dimension (D2), the aperture of the spectrum (Ap), the right to left 181

symmetry of the spectrum (R-L), and the vertical symmetry of the spectrum (V). The 182

consistency of the multifractal calculations was assessed by checking the relation D0 ≥ D1 ≥ D2. 183

It is important to recall that the parameters showed in Table 2 extracted from 3D cubes are 184

average values from the two parts (upper and lower) of the soil column. 185

186

Multifractal analysis of 3D porosity: Rényi spectrum 187

The Rényi spectrum of all columns draws a sigmoid (Figure 3), the typical shape of the systems 188

with multifractal behavior. In all cases, the Dq decreased with the value of q (Lafond et al., 189

2012). As have been pointed by Marinho et al. (2016), the wider (in the vertical axis) the Dq 190

spectrum, the more heterogeneous the scaling distribution. 191

On the one hand, we have the soils from the Conv. NT and Org. A, with amplitudes of 2.42 ± 192

0.12 (Figure 3A) and 2.35 ± 0.15(Figure 3B), respectively. The presence of a broad range of 193

pore root sizes in NT increases the heterogeneity in both sides of the spectrum, and even the 194

positive part (related with the bigger pores) presents a slight drop (San José Martínez et al., 195

2010). In Org. A samples, the shape indicates multifractality, but the bigger pores (right part of 196

the spectrum) do not present many changes with scale (Dq is almost constant). On the other 197

hand, Org B. samples are significantly less heterogeneous with an amplitude of the Rényi 198

spectrum of 1.52 ± 0.13 (Figure 3C). Conv. ST samples present a medium value of the spectrum 199

width (2.10 ± 0.05), and have the minimum standard error. Tillage techniques create pore 200

9

populations more homogenous. This can be appreciated comparing the standard errors and by 201

taking a look at Figure 3D and 3B, the ones that belong to soils without tillage. 202

The value of the D0 follows the decreasing order Org. A > Conv. NT > Conv. ST > Org. B, with 203

values of 2.71 ± 0.08, 2.70 ± 0.01, 2.67 ± 0.05 and 2.34 ± 0.06, respectively. However, only the 204

Org. B shows significant differences with the other zones. The 2.34 is far from the topological 205

dimension, 3, which means that the pore distribution range is narrow (Wang et al., 2016). The 206

results of this parameter are similar to the corresponding one in 2D (Figure 4), and the 207

differences with the Org. B zone are maintained in other generalized dimensions (D1, D2 and 208

Dmin). Considering the tomography porosities (CT-Porosity) of the four zones (Tables S1, S2, S3 209

and S4), it is possible to conclude that the generalized dimensions are determined mainly by the 210

distribution of the pores, since the Conv. NT zone presents a low CT-Porosity (23.07 ± 4.68 211

cm3) compared to the Org. A (43.21 ± 4.98 cm3) and the Conv. ST (40.78 ± 6.92 cm3) zones. Of 212

course, the porosity would also condition the generalized dimensions, and that can explain the 213

significantly different values of the Org. B, a plot with an average CT-Porosity of 15.56 ± 214

3.61cm3. 215

216

Multifractal analysis of 3D porosity: singularity spectrum 217

Multifractal characteristics of the singularity spectrum also showed some significant differences 218

when comparing management techniques. However, the differences are caused by the extreme 219

values of the Org. B zone (Table 2), as happened with the parameters of the Rényi spectrum. 220

Despite that, a comparison of some multifractal features across the management practices can be 221

illustrative. 222

The columns from no-tilled soil (NT) presented a wider spectrum (3.19 ± 0.18) than other 223

treatments, and this means that the pore structure is more complex due to the variety of pores 224

generated by roots. It is important to note that some of these columns presented big earthworm 225

pores, like the column nº 7. This sample has a huge CT-Porosity (Table S2) when compared 226

10

with the samples of the same plot, but the presence of a giant pore fills the space that could be 227

occupied by small complex populations. Moreover, this core is a good example for the 228

understanding of the value of multifractals since de single fractal dimension in 3D (D0) is fairly 229

big because of the porosity, but the pores are not so complex when compared with the samples 230

of the same plot. In the NT plot, we found the only two examples (nº2 and 11) of spectrums 231

with a positive value of R-L (horizontal symmetry) and a negative V (Vertical symmetry) 232

(Figure 5). This means that the small populations of these two samples are more complex and 233

common in the soil profile. That is caused by the low presence of earthworm pores. Moreover, 234

when plotting the Aperture of the spectrum versus the Dmin (Figure 6), the NT cores are in the 235

zone of high pore complexity (excluding the core 7). This relation is based in the works of Ge et 236

al. (2015), where plotted D0 in front of Dmin to determine the complexity of the network. 237

However, we substituted D0 by the aperture, since we consider it a sensitive parameter that 238

approximates more closely to the observed. 239

In the organic field (Org. A), the presence of earthworm pores (in some columns) increased the 240

width of the spectra as expected (3.02 ± 0.20). It is important to remember that the Org. A 241

columns were sampled in zones where the presence of earthworms was more evident, while the 242

Org. B columns were randomly taken in the same plot. Since the presence of earthworm pores 243

in the soil is not homogeneous, we observed a great variation (like in the case of NT samples). 244

The main difference is caused by sample nº 10, the one with the lower CT-Porosity (Table S3). 245

Samples of the Org. A plot have, in general, complex structures according to the Dmin Vs 246

Aperture plot (Figure 6). The singularity spectrum of all of the samples has the shape of the core 247

nº8 (Figure 5): positive values for the two symmetries. That means that the small pores are more 248

complex but less common, and the bigger pores are well distributed in the samples but they are 249

also simpler. 250

Conv. ST soil samples have an average aperture of 2.68 ± 0.06, a value halfway between the 251

complex spectra of Conv. NT and Org. A samples, and the simple one of the Org. B zone, as 252

can be appreciated in Figure 6. Most of the cores of this plot presents a spectrum similar to the 253

11

obtained with Org. A samples, with positive values for both symmetries, indicating the presence 254

of simple big pores well distributed in all the sample. Those pore populations were caused by 255

tillage, some earthworms and crop residues. The only sample that shows a different behavior is 256

number 12, a core that has relatively big pores poorly distributed. It is important to consider that 257

the parameters showed in Table 2 are average values from the two parts (upper and lower) of 258

the sample, a feature that will be considered in the next section of this article. 259

The Org. B samples are significantly different from the others. For example, the apertures of the 260

singularity spectra are quite low (2.01 ± 0.10). The pores of this soil are caused by some 261

earthworms and remains of roots and vegetal residues. However, the average CT-Porosity is 262

quite low and the pores are poorly distributed. When comparing the morphological features 263

obtained from the tomography, this zone is significantly different, with fewer junctions and 264

branches, and a lower connectivity. The lack of complexity can be appreciated in Figure 6. The 265

spectra of these samples are inverse to the ones of the Org. A, with negative values for both 266

symmetries: they have complex big pores concentrated in some parts, and simple smaller pores 267

well distributed. A similar result has already reported by Posadas et al. (2003). The exception is 268

the number 19, a sample that shows a unique behavior with a negative R-L and a positive V: 269

complex big pores better distributed than smaller ones. However, the vertical symmetry is too 270

close to 0 that we can consider that the distribution of pore populations in the sample is fairly 271

similar. 272

273

Vertical variation of fractal properties and influence of the soil management 274

The porosity of the CT-pore network and 2D fractal dimension in the X-Y slices (D) decrease 275

with depth. Correlation between porosity and D is reported, as it was already pointed by other 276

authors (Hatano et al., 1992; Oleschko et al., 2000). The mutual decrease of porosity and D, and 277

its correlation can be related to the decreasing in the pore network complexity with the depth 278

12

that was reported by Yang et al. (2018). Moreover, the fractal dimension peaked in some narrow 279

depth intervals that also showed a local increase in the CT-porosity. 280

The vertical variation of the Rényi and singularity spectra in 3D cubes was assessed by the 281

calculation of the difference between the features of the spectrum of the cube in the top of the 282

column minus those features of the lower cube (these characteristics are shown in Table 2). The 283

D0 (the fractal dimension in 3D) decreases in the lower half of the column an average of 0.12 ± 284

0.03 for almost all samples (Figures 3B and 3C). This decrease in D0 also correlates with the 285

decrease in the CT-porosity in agreement with the 2D fractal dimension. The drop in D0 is not 286

so strong in the cores of the Conv. NT zone (0.07 ± 0.01) since the roots are well distributed in 287

the entire sample. In the Org. B zone, the decrease is also small (0.10 ± 0.10), but this plot has 288

more error and the initial values of D0 are also lower. Moreover, the pore populations are poorly 289

distributed in all the sample (not only in the lower part). Org. A and Conv. ST samples showed 290

a pronounced drop in almost all samples (0.13 ± 0.07 and 0.17 ± 0.08, respectively), caused by a 291

compacted lower half in the case of Conv. ST, and by a bigger presence of earthworm pores and 292

vegetal rests in the upper part in the case of Org. A. 293

Something similar happens with the values of D1, a parameter related to the disorder. Again, the 294

Conv. NT samples have a fairly constant value of uniformity in both halves. In Org. B the value 295

of D1 is quite low, and the decrease is not so evident as in the case of Org. A and Conv. ST, 296

plots where the drop is very strong, indicating that the pore populations of the lower part are 297

quite disordered. This can be related to the decrease in the values of connectivity with depth, a 298

fact pointed by Muñoz-Ortega et al. (2015) for uncultivated and tilled soils. 299

In the case of the singularity spectrum, when considering the aperture, there is a decrease, in 300

almost all samples, in the range of values of the Holder exponent needed to describe the pore 301

network (Figure 7). So, the complexity of the pore network is reduced with depth. If we 302

compare the reduction with the value near the surface (from 0 to -4.8 cm), the lower part (from -303

4.8 to -9.6) is 9.19 ± 0.06% less complex. However, the change is not so drastic in the Conv. NT 304

and Org. A zones. The Conv. ST presents the higher variations: the number 14, a sample 305

13

extremely compacted near the lower extreme, presents a reduction in the complexity of 45.98 306

%, but the number 18, a compacted sample with a big multi-branched earthworm pore located 307

near the bottom, presents a spectrum 71.21 % wider in the lower part. Finally, the case of the 308

Org. B is the simplest one: the reduction in complexity happens in all the samples (21.87 ± 309

5.54%). 310

Considering the symmetries, both values (R-L and V) tend to 0 with the depth, i.e., in general, 311

the spectrum tends to symmetry: R-L is reduced from 0.43 ± 0.14 to 0.19 ± 0.13 and V from 312

0.09 ± 0.15 to 0.06 ± 0.11. This indicates more equilibrated pore populations in the lower parts 313

of the samples: big and small pores equally distributed with similar complexity. However, we 314

found some exceptions. The left part (big pores) of the singularity spectra of the cores 18 (Conv. 315

ST) and 1 (Org. A) does not change with depth, while the small pores are better distributed and 316

less complex in the upper part. 317

318

Correlations between multifractality and descriptors of the pore network and 319

macroscopic soil physical properties. 320

In the Table 3 are shown some of the correlations found between the average multifractal 321

parameters in 3D (in this part we are not considering the fractal dimension in 2D), and some soil 322

physical properties and topological descriptors of the pore network skeleton. 323

First, to understand the relations of Table 3 we need to consider that large structures are 324

represented by a large number of pixels with a large number of different pixel configurations, 325

i.e., freedom degrees. It can be inferred that large pore structures with many degrees of freedom 326

can cover wide ranges of scale factors. A small 2D region represented by a lattice of 2 x 2 pixels 327

(0.23 mm2) has 24 different configurations. However, to represent a larger pore structure we 328

need a larger region e.g., with 2 x 2 mm2, we have ~2 1069 different configurations. That huge 329

number can support very complex fractal structures. Dependency on the support size can 330

explain why most of the macroscopic magnitudes derived from the CT images (volume and 331

14

surface) and topological descriptors of the skeleton (slab voxels, branches and junctions per 332

path, among others) showed good correlations with the multifractal parameters. Values of all 333

these descriptors depend on the size and complexity of the pore network. So that the discrete 334

representation of junctions, branches, etc. needs a larger support (i.e., a larger area with many 335

pixels) than objects with small Hausdorff exponents, e.g., a straight pore represented by an 336

alignment of a few pixels, or a small circular pore (one single pixel). 337

Starting with the descriptors extracted from the Rényi spectrum (D0 and D2), they are correlated 338

with almost all the parameters considered in Table 3. Those two multifractal characteristics are 339

related with the distribution of the pores in the soil, so the bigger the CT-Porosity, pore volume 340

and surface, the bigger the probability of having a better distribution of pores, and the bigger the 341

value of D0 and D2. And with the parameters related to the skeleton, the same happens: more 342

complexity (junctions, branches, slab voxels, connectivity…), bigger the values of those two 343

parameters. Tortuosity is a characteristic of the pore network with important implications for the 344

transport of substances throughout soil (Roberts et al., 1987). The positive correlation with the 345

tortuosity can be explained through the CT-Porosity: this feature is extremely correlated with 346

the tortuosity (R =0.89), and indicates that big pores (earthworm pores, for example) increase 347

the average tortuosity. So, the big pores increase the tortuosity and improve the distribution of 348

pores along the soil profile. Finally, the parameters of the Rényi spectrum are also related to the 349

bromide dispersion, which suggests a link between the complexity across scales and transport. 350

This can be explained by the hypothesis that complex pore networks may favour the occurrence 351

of solute transport pathways at several scales, and that will increase the range of travel times 352

and power-water velocities, which leads to a bigger dispersion. 353

When considering the correlations with the parameters of the multifractal spectrum, the total 354

aperture and the aperture between q=1 and q=-1 (Ap (-1, 1)), showed similar values, but the Ap 355

(-1, 1) seems to be more sensitive. This feature is positively correlated with the CT-Porosity, the 356

volume and surface of pores and the skeleton parameters, as expected. The bigger the number of 357

pores, the complex they can be. It is also interesting the correlation existing between the Ap, D0, 358

15

D2, R-L, V and the surface area of the preferential colloidal paths described in the colloid 359

transport experiments reported by Soto-Gómez et al. (2018a). Figures 8A, B and C show that 360

the complexity pointed by the broad range of scales of the singularity spectrum correlates with 361

the surface stained by the fluorescent colloid tracer. This indicates that the soils with complex 362

and well distributed small pores enhance de distribution of microspheres. 363

364

4 Conclusions 365

In this article we have presented the fractal and multifractal analysis of the soil pore network 366

using CT images of intact soil columns sampled from plots devoted to different agricultural 367

management practices. Spatial distribution of macroporosity showed multifractal properties 368

represented by a sigmoidal Rényi spectrum and a wide singularity spectrum. 369

Characteristics defining the average shape of the Rényi and singularity spectra of soil columns 370

were influenced by management, but only one study plot showed significant differences (Org. 371

B). Presence of compacted layers in tilled soil, the abundance of root channels in not-tilled soil 372

and earthworm burrows in organic management produced significant changes in the 373

multifractality. Moreover, it is possible to establish different levels of the complexity of soil 374

pore networks considering the Dmin and the aperture of the multifractal spectrum. We also 375

concluded that the fractal dimension (in 2D), multifractal parameters and, consequently, the 376

pore complexity, decrease with depth. 377

Is noteworthy that the multifractal parameters are correlated with macroscopic soil variables, 378

such as bulk density and tortuosity, as well as with some topological descriptors of the pore 379

network skeleton. These correlations suggest the existence of links between the spatial 380

distribution of the pore network and the multiplicity of scale factors. Besides, the parameters 381

studied also present correlations with the bromide dispersion and with the surface of soil stained 382

by a particulate tracer. 383

16

The above results are interesting from the point of view of the parameterization of the 384

complexity of the porous networks of soils, and can help to link the physical properties of the 385

soil porosity, the pore network topology and the transport. This is quite helpful when making 386

more precise predictions regarding the fate of substances in the environment. 387

388

5 Acknowledgments 389

The authors want to acknowledge the following funding sources: D.S.G. is funded by the Pre-390

Doctoral Fellowship Program (FPU) of Spain’s Ministry of Education FPU14/00681, and P.P.R 391

is funded by a post-doctoral fellowship awarded by Xunta de Galicia (Gain program ED481B-392

2017/31). L.V.J. was additionally funded by CIA and BV1 research contracts (FEDER, Xunta 393

de Galicia). This work is partially founded by the INOU program K840. Authors thank the 394

Centro de Desenvolvemento Agrogandeiro (Ourense) for allowing the sampling in their plots. 395

396

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551

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7 Figures 552

Figure 1. Representation of an example of the Rényi spectrum (q Vs Dq). This example belongs 553

to the sample number 16 (Conv. ST). Orange arrows indicate interesting values of the 554

generalized dimensions: D0 (Dq when q=0), D1 (Dq when q = 1), D2 (Dq when q = 2), and Dmin 555

(Dq when q = -5). 556

Figure 2. Representation of an example of the Singularity spectrum (α Vs f(α)). This example 557

belongs to the sample number 16 (Conv. ST). Orange arrows indicate some interesting values of 558

α: α0 (α when q = 0), αmin (α when q = +5), and αmax (α when q = -5). The green line represents 559

the total aperture of the spectrum (Ap), the yellow lines are the apertures for the right (R) and 560

left (L) branches of the spectrum, and the vertical grey line points the vertical symmetry of the 561

spectrum (V). V is the difference between the f(αmin) (the value of f(α) when q = +5), and f(αmax) 562

(the value of f(α) when q = -5). 563

Figure 3. Rényi spectra for all columns organized by tillage managements: A) Conv. NT; B) 564

Org. A; C) Conv. ST; and D) Org. B. 565

Figure 4. A) Average fractal dimension (in 2D) for the four treatments. B) and C) Variation of 566

the fractal dimension of each image with the depth: Column nº7, Conv. NT treatment (B) and 567

Column nº6, Conv. ST treatment (C). (It is important to note that the scale is different). 568

Figure 5. Singularity spectrum of four columns representing the four shape classes that were 569

identified in this study. Classes were established considering horizontal (L-R) and vertical (V) 570

symmetries. 571

Figure 6. Crossplot representing average Aperture and Dmin of all the columns. The complexity 572

of the pore network increases from the bottom left to the top right. 573

Figure 7. Plots illustrating the influence of depth in the multifractal spectrum of the soil pore 574

network (left) and 3D representations of the columns (right). The plots show the average 575

spectrum of the upper half of the column (orange squares) and the lower part (blue circles) from 576

24

two different soil columns. In the A) (ST plot, column no. 6) the Aperture decreases from 3.4 in 577

the upper half to 2.3, and the drop of D0 has a value of 0.3. That means a remarkable decrease of 578

both number and diversity of pore structures in the bottom half. B) The same effect, but to a 579

much lesser extent, was observed in the other columns (e.g., in column no. 8 in Org. A). 580

Figure 8. Relation between the average stained surface by a particulate fluorescent tracer and 581

some parameters of the multifractal spectrum: A) Aperture, B) R-L (horizontal symmetry) and 582

C) V (vertical symmetry). 583

25

584 Figure 1 585

586

26

587

588

Figure 2 589

27

590

28

591

592

29

593

594

595

30

596

Figure 6 597

31

598

A)

B)

Figure 7. 599

600

601

32

A)

B)

C)

Figure 8. 602

603

33

8 Tables 604

Table 1. Sieve analysis results. 605

Treatment Coarse Sand Fine Sand Silt Clay Organic Matter

Conv. NT 46.2 ±0.5 26.1 ±0.9 5.7 ±2.9 10.9 ±1.2 11.1 ±2.6

Conv. ST 42.9 ±2.4 28.3 ±1.7 5.3 ±4.1 11 ±0.6 12.5 ±4.6

Org. 44.5 ±0.2 29 ±0.4 8.1 ±0.3 9.2 ±0.7 8.5 ±0.5

606

607

34

Table 2. Mean values of the features of the multifractal spectra of 2D slices and 3D cubes that 608

showed significant differences between treatments: D, fractal dimension in 2D; D0, generalized 609

dimension for q = 0; D1, generalized dimension for q = 1; D2, generalized dimension for q = 2; 610

Ap, aperture of the multifractal spectrum; R-l, horizontal symmetry of the multifractal spectrum; 611

and V, vertical symmetry of the multifractal spectrum. 612

613

614

Sample number

Average profile of 2D slices

Parameters of the Rényi and the multifractal spectrum of 3D pores

D D0 D1 D2 Ap R-L V ST

6 0.94 ± 0.04 2.70 ± 0.16 2.36 ± 0.20 2.26 ± 0.19 2.85 ± 0.57 0.43 ± 0.71 0.15 ± 0.34 12 1.07 ± 0.02 2.49 ± 0.04 2.06 ± 0.08 1.96 ± 0.10 2.47 ± 0.13 -0.32 ± 0.37 -0.07 ± 0.51 14 1.15 ± 0.03 2.77 ± 0.07 2.48 ± 0.05 2.40 ± 0.04 2.65 ± 0.79 0.70 ± 0.66 0.67 ± 0.46 16 0.97 ± 0.05 2.60 ± 0.10 2.30 ± 0.10 2.21 ± 0.12 2.69 ± 0.13 0.59 ± 0.20 0.51 ± 0.26 18 1.20 ± 0.03 2.76 ± 0.05 2.50 ± 0.02 2.44 ± 0.00 2.74 ± 0.72 0.95 ± 0.43 0.83 ± 0.34

NT 2 1.22 ± 0.01 2.67 ± 0.05 2.33 ± 0.02 2.18 ± 0.01 3.16 ± 0.45 0.11 ± 0.05 -0.87 ± 0.22 4 1.47 ± 0.00 2.69 ± 0.02 2.34 ± 0.02 2.16 ± 0.03 3.39 ± 0.37 0.57 ± 0.06 0.02 ± 0.01 5 1.42 ± 0.01 2.73 ± 0.02 2.39 ± 0.04 2.21 ± 0.04 3.57 ± 0.13 0.66 ± 0.00 0.02 ± 0.26 7 1.38 ± 0.01 2.72 ± 0.05 2.46 ± 0.05 2.40 ± 0.05 2.52 ± 0.05 0.75 ± 0.04 0.60 ± 0.04

11 0.92 ± 0.03 2.67 ± 0.04 2.36 ± 0.03 2.23 ± 0.02 3.31 ± 0.15 0.56 ± 0.04 -0.25 ± 0.21 Org. A

1 1.25 ± 0.02 2.87 ±0.02 2.47 ± 0.01 2.35 ±0.01 3.57 ± 0.50 0.65 ± 0.31 0.31 ± 0.59 3 1.27 ± 0.03 2.71 ± 0.07 2.38 ± 0.07 2.29 ± 0.06 2.97 ± 0.36 0.76 ± 0.31 0.51 ± 0.08 8 0.99 ± 0.03 2.75 ± 0.11 2.45 ± 0.19 2.37 ± 0.23 2.94 ± 0.23 0.88 ± 0.83 0.65 ± 0.78 9 1.03 ± 0.03 2.78 ± 0.05 2.43 ± 0.02 2.29 ± 0.00 3.28 ± 0.00 0.70 ± 0.07 0.26 ± 0.06

10 1.00 ± 0.03 2.41 ± 0.21 2.12 ± 0.16 2.03 ± 0.13 2.35 ± 0.30 0.25 ± 0.08 0.11 ± 0.14 Org. B

13 0.94 ± 0.01 2.28 ± 0.20 1.99 ± 0.19 1.92 ± 0.17 1.95 ± 0.19 -0.09 ± 0.03 -0.05 ± 0.08 15 1.10 ± 0.01 2.48 ± 0.09 2.08 ± 0.07 1.94 ± 0.05 2.34 ± 0.30 -0.44 ± 0.30 -0.56 ± 0.02 17 0.78 ± 0.02 2.35 ± 0.07 1.98 ± 0.06 1.86 ± 0.05 2.01 ± 0.03 -0.52 ± 0.10 -0.76 ± 0.11 19 0.94 ± 0.01 2.42 ± 0.04 2.03 ± 0.05 1.97 ± 0.09 2.03 ± 0.34 -0.32 ± 0.12 0.04 ± 0.18 20 0.97 ± 0.01 2.15 ± 0.10 1.84 ± 0.05 1.71 ± 0.00 1.73 ± 0.34 -0.61 ± 0.07 -0.67 ± 0.11

35

615

Table 3. Correlation between the average values of some multifractal properties and other soil 616

characteristics such as bulk density and CT-parameters. 617

D0 D2 Ap R-L V Ap(-1,1)

CT-porosity (cm3) 0.707*** 0.797*** 0.383 0.746*** 0.846*** 0.677** Total pore volume (mm3) 0.717*** 0.798*** 0.401 0.763*** 0.861*** 0.697*** Total pore surface (mm2) 0.811*** 0.806*** 0.642** 0.820*** 0.668** 0.774***

Average pore volume (mm3) 0.528* 0.704*** 0.040 0.655** 0.755*** 0.390 Average pore surface (mm2) 0.613** 0.714*** 0.283 0.757*** 0.733*** 0.487*

Number of Branches 0.752*** 0.731*** 0.535* 0.680*** 0.575** 0.690*** Number of Junctions 0.744*** 0.786*** 0.464* 0.746*** 0.700*** 0.659**

End-point voxels 0.627** 0.476* 0.573** 0.406 0.205 0.625** Slab Voxels 0.801*** 0.735*** 0.790*** 0.771*** 0.421 0.751*** Triple Points 0.750*** 0.788*** 0.477* 0.750*** 0.698*** 0.669**

Quadruple Points 0.723*** 0.775*** 0.441 0.734*** 0.696*** 0.622** Average CT tortuosity 0.522** 0.651** 0.184 0.628** 0.822*** 0.472*

Connectivity 0.720*** 0.794*** 0.398 0.778*** 0.735*** 0.591** Bulk Density (g cm-3) -0.277 -0.450* 0.058 -0.436 -0.674** -0.199

DBr (Dispersion) 0.494* 0.545* 0.278 0.422 0.311 0.308

Average Stained Area (%) 0.802*** 0.842*** 0.614** 0.823*** 0.776*** 0.807***

Probability values for the Pearson’s correlation coefficient: * P ≤ 0.05; ** P ≤ 0.01; *** P ≤ 618

0.001 619

620

36

9 Supplementary information 621

9.1. Fractal and Multifractal Theory 622

In a homogeneous system, the probability (P) that a magnitude changes with the scale (ε) is 623

𝑃(𝜀) ∝ 𝜀−𝐷 (eq. S1) 624

where ∝ means proportionality. The fractal dimension (D) describes how a pattern varies with 625

the scale. In heterogeneous systems, we need to define the probability in different regions (i), 626

and the probability in the ith region (Pi) is 627

𝑃𝑖(𝜀) ∝ 𝜀𝛼𝑖 (eq. S2) 628

The Holder exponent ( i) characterizes the scaling in the ith region. If there are different scaling 629

relationships because of the complexity of the pore network, more values of i are required. 630

To obtain the fractal dimensions at different scales, the box-counting method is used. This 631

consists of covering the surface with a grid of squares of a size (ε) and count the number of 632

squares that contain a part of the structure with the same Holder exponent N(). A fractal set 633

satisfies the following relation 634

𝑁(𝛼) ∝ 𝜀−𝑓(𝛼) (eq. S3) 635

Where f(), also named the Hausdorff dimension, is the fractal dimension of the boxes with the 636

same . If that value of is well distributed in the soil column, the f() will be higher. In other 637

words, if a type of pore appears homogeneously in the soil, the f() associated with that type of 638

pores will be bigger. The multifractal spectrum, also called singularity spectrum, is the 639

representation of versus f(). This method is easily understood, however, is not very used 640

because usually yields to inaccurate answers. Therefore, we used the calculation method 641

proposed by Chhabra et al. (1989). The multifractal spectrum can also be described with the 642

generalized dimensions of the qth moment distribution, Dq 643

37

𝐷𝑞 =1

𝑞−1𝑙𝑖𝑚𝜀→0

log(µ (𝑞,ε))

log 𝜀 (eq. S4) 644

When q ≠ 1, and for q = 1 645

𝐷1 = 𝑙𝑖𝑚𝜀→0

µ( 𝑞,𝜀) 𝑙𝑜𝑔(µ(𝑞,𝜀))

𝑙𝑜𝑔 𝜀 (eq. S5) 646

Where µ(q, ε) is a partition function that normalizes the distribution 647

𝜇(𝑞, 𝜀) = ∑ 𝑃𝑖𝑞(𝜀)

𝑁(𝜀)

𝑖=1 (eq. S6) 648

and q is an arbitrary scaling exponent used to distort µ, and see how it behaves with the scale ε: 649

positive q values accentuate denser regions, and negative q accentuates the lighter ones. 650

Usually, q value is set from -10 to 10 (Paz Ferreiro and Vidal Vázquez, 2010), but in this work 651

we obtained better results between -5 and 5. This is not unusual and in the literature is easy to 652

find different ranges, for example -4 to 4 (Caniego et al., 2003) or -8 to 8 (San José Martínez et 653

al., 2010). We used 0.2 intervals between -5 and 5, but we decided to use smaller intervals 654

(0.04) in the values close to 0 (from -1 to 1) in order to increase the accuracy in that part. 655

To scale, the partition function is used 656

𝜇(𝑞, 𝜀) ∝ 𝜀𝜏(𝑞) (eq. S7) 657

Where τ is the correlation exponent of the qth order 658

𝜏(𝑞) = (𝑞 − 1)𝐷𝑞 (eq. S8) 659

Finally, the Legendre transformation is used to calculate f(α) and α through τ(q), 660

𝑓(𝛼(𝑞)) = 𝑞 𝛼(𝑞) − 𝜏(𝑞) (eq. S9) 661

𝛼(𝑞) =ⅆ𝜏(𝑞)

ⅆ𝑞 (eq. S10) 662

38

The variation of the Dq with q is called the Rényi spectrum (Figure 1), and was calculated to 663

evaluate the multifractal behaviour of the data: if multifractal behaviour exists then Dq shouldn’t 664

be equal for all the measures and has to decrease with q (Lafond et al., 2012). In general, the 665

values of Dq increase with the pore network complexity (Ge et al., 2015). 666

Moreover, other indicators were used to compare the multifractal characteristics of the different 667

soil treatments: 668

- The fractal dimension of each slice of the column. This parameter was calculated in 2D 669

through the box counting method, using the Fraclac plugging (Karperien, 2013). It is important 670

to consider that this fractal dimension, D, was calculated using each slice to see the effect of the 671

depth. For the rest of the features studied in the article, cubes of soil were employed. 672

- D0 (Dq=0; ), is the capacity dimension (eq. S4), a parameter that provides a global vision of the 673

system. When calculating D0 each Pi is elevated to 0, so only the cubes that contain pores are 674

taken into account. That means that D0 is the fractal dimension of the entire system. 675

- D1 (Dq=1) is the entropy dimension (eq. S5), quantifies the degree of disorder present and the 676

probability of find pores in a region (Posadas et al., 2002): higher values of D1 indicate that the 677

magnitude of features are uniformly distributed through all scales. 678

- D2 (Dq=2) is the correlation dimension, and is related to the correlation of measures in intervals 679

of size ε. 680

- Dmin (Dq for the lowest value of q) is the generalized dimension that characterizes the lighter 681

regions (less porous) and is very sensitive. This parameter represented in a crossplot with the D0 682

offers valuable information about the soil pore architecture (Ge et al., 2015). 683

-Aperture (Ap) of the singularity spectrum, which measures the length of the range of fractal 684

exponents (α) (Figure 2). 685

𝐴𝑝 = 𝛼𝑚𝑎𝑥 − 𝛼𝑚𝑖𝑛 (eq. S11) 686

39

where αmax and αmin are the maximum and minimum values of the Holder exponent, 687

respectively. If the structure has many exponents (i.e., large Ap) is a rich structure, complex, 688

with different scaling factors. Aperture and slope of several ranges q (-1 to 1); q (0 to 1); q (-1 to 689

0), and so on, were also calculated. 690

- Horizontal symmetry with respect to the vertical line that crosses the maximum point of the 691

spectrum, α0. The Right – Left (R-L) symmetry is given by 692

𝑅 − 𝐿 = (𝛼𝑚𝑎𝑥 − 𝛼0) − (𝛼0 − 𝛼𝑚𝑖𝑛) (eq. S12) 693

where α represents the Holder exponents for: α0, the value of α when q = 0, which is the point 694

where f(α) reaches the maximum value; the maximum value of α (αmax), and the minimum value 695

of α (αmin). So, we consider that positive values represent spectra with a wider right branch, 696

which means that smaller pores are more complex. If the spectrum has a wider left branch, we 697

need more Holder exponents to characterize this part (denser, i.e., bigger pores) because is more 698

complex. 699

- Another type of symmetry is referred to the vertical difference between the two extreme points 700

of the branches of the spectrum 701

𝑉 = 𝑓(𝛼𝑚𝑖𝑛) − 𝑓(𝛼𝑚𝑎𝑥) (eq. S13) 702

As it happened with the R-L, positive values of V indicate that the right branch is larger, but in 703

this case in the y axis. The values of α that show a high f(α) are better distributed in the soil 704

column. So, if the right branch is larger in vertical, the α associated with that part has lower f(α) 705

values, which means that are worse distributed in the soil when compared with the values of the 706

left. 707

708

9.2 Multifractal calculation example 709

710

40

We present an example of the calculations of the multifractal spectrum for the upper part of a 711

soil sample (nº 5), a cube of 200x200x200 pixels (≈ 4.8 cm). A 3D representation of the pore 712

network can be seen in Figure S1. 713

First of all, the probability that a pixel belongs to the porous space needs to be defined. The 714

number of pixels of the system is 2003 (8 106), and 3.34 105 belong to porous space. So, the 715

probability of finding a pore (P) for the entire system (scale = ε) is 0.0417 (4.17 %). At this 716

scale, Pi is equal to one. 717

The next step is to consider a smaller scale. For this aim, we just divided the side by a factor of 718

two and obtained 8 cubes of 100x100x100 pixels (Figure S2). So, at this scale (ε / 2), we 719

obtained 8 values for Pi by dividing the probability of find a pore in each cube by P. Then, we 720

have to consider smaller scales and calculate Pi: 50x50x50 (64 values of Pi), 25x25x25 (512 721

values for Pi), 12x12x12 (4096 values for Pi) and 6x6x6 (32768 values for Pi). 722

Then, we need to choose the scale of q, a mathematical tool used to simulate a zoom in and a 723

zoom out. This value will help us to examine the characteristics of treatments with more and 724

less pores. We are going to use values between 5 and -5, using intervals of 0.2, because is a 725

wide range and the singularity spectrum is well developed. Sometimes, inconsistencies can 726

appear in the edges of the spectrum when using extreme values for q. Once the range of q has 727

been chosen, it is time to apply eq. S6 and S7 to calculate µ and τ. With these formulas, Figure 728

S3 is obtained, and we can see how Pi behaves for different values of q when ε tends to 0. The 729

slope of each representation of q is τ, but we observe a problem with smaller scales and negative 730

values for q: the behaviour is only linear between ε = 200 and ε = 25. This happens in other 731

articles (Mendoza et al., 2010; Paz Ferreiro and Vidal Vázquez, 2010), and, in order to avoid 732

bigger errors, we discarded smaller scales (ε < 25). 733

Finally, with τ (the slope of each partition function) and the values of q, it is possible to 734

calculate the generalized dimensions Dq, the Holder exponent α and the Hausdorff dimension f 735

(α), through the equations S8, S9 and S10. By plotting Dq versus q, we obtained the Rényi 736

spectrum (Figure S4A), and α versus f(α) is the singularity spectrum (Figure S4B). The data of 737

all the parameters is showed in Table S5. 738

41

10 Supplementary information: Figures and Tables 739

740

741

Figure S1. 3D representation of the pore network of the upper part of the sample nº 5. This cube 742

has 4.8 cm (200 pixels) in each axis. 743

744

42

745

(0, 0, 0)

(100, 0, 0)

(0, 100, 0)

(100, 100, 0)

(100, 100, 100)

(100, 0, 100)

(0, 100, 100)

(100, 100, 100)

Figure S2: 3D representation of the cubes obtained for the scale ε/2. The three coordinates 746

represent the point where each cube starts, considering that the 0, 0, 0 position is in the left front 747

upper corner of the core. 748

749

43

750 751

752

753

754

44

4A)

4B)

Figure S4: Representations of the A) Rényi spectrum, and B) Singularity spectrum. 755

45

Table S1. Properties of the columns from the Conv. ST field. 756

757

Management Conv. ST Average

Column Number 6 12 14 16 18 -

CT-porosity (cm3) 37.98 27.33 53.03 25.31 60.24 40.78 ± 6.92

Total pore volume (mm3) 26763 18814 29613 17388 34824 25480 ± 3286

Total pore surface (mm2) 77691 46565 77036 56860 74712 66573 ± 6301

Average pore volume (mm3) 9.20 6.78 18.19 9.91 18.22 12.46 ± 2.40

Average pore surface (mm2) 26.72 16.78 47.32 32.42 39.10 32.74 ± 5.21

Number of Branches 6644 3714 5481 4242 5005 5017 ± 508

Number of Junctions 2394 950 2219 1533 1902 1780 ± 258

End-point voxels 6228 5014 4154 3896 4368 4732 ± 417

Slab Voxels 40642 21196 37871 29118 35632 32892 ± 3489

Triple Points 1993 810 1844 1269 1603 1504 ± 212

Quadruple Points 302 109 301 218 234 233 ± 35

Average CT 3D tortuosity 1.22 1.18 1.23 1.21 1.22 1.21 ± 0.01

Connectivity 468.5 54.4 515.9 297.8 367.5 340.6 ± 81.0

Bulk Density (g cm-3) 1.43 1.53 1.36 1.44 1.37 1.43 ± 0.03

DBr (Dispersion) 45 28 70 18 55 43.2 ± 9.3

Average Stained Area (%) 13.06 14.29 15.45 13.20 15.61 14.32 ± 0.54

46

Table S2. Properties of the columns from the Conv. NT field. 758

759

760

Management Conv. NT Average

Column Number 2 4 5 7 11 -

CT-porosity (cm3) 13.43 24.13 25.31 38.88 13.60 23.07 ± 4.68

Total pore volume (mm3) 7658 17047 17759 26621 7845 15385 ± 3544

Total pore surface (mm2) 47116 74292 76017 78062 49927 65083 ± 6802

Average pore volume (mm3) 2.98 7.75 6.91 11.59 3.01 6.45 ± 1.61

Average pore surface (mm2) 18.35 33.77 29.59 33.98 19.18 26.97 ± 3.44

Number of Branches 3412 4433 4442 5894 3679 4372 ± 432

Number of Junctions 801 1433 1316 2233 905 1338 ± 254

End-point voxels 4806 4678 5175 5010 4760 4886 ± 91

Slab Voxels 36063 58225 58870 57266 32091 48503 ± 5928

Triple Points 694 1227 1157 1859 1138 1215 ± 186

Quadruple Points 90 182 134 285 163 171 ± 32

Average CT 3D tortuosity 1.15 1.17 1.17 1.20 1.16 1.17 ± 0.01

Connectivity 72.25 281.13 227.50 647.50 86.38 262.95 ± 104.17

Bulk Density (g cm-3) 1.54 1.50 1.49 1.45 1.56 1.51 ± 0.02

DBr (Dispersion) 37.2 35 35 48 34.84 38 ± 2.54

Average Stained Area (%) 112.39 12.03 12.90 13.71 12.31 12.67 ± 0.30

47

Table S3. Properties of the columns from the Org. A plot. 761

762

Management Org. A Average

Column Number 1 3 8 9 10 -

CT-porosity (cm3) 50.44 53.92 45.11 41.33 25.27 43.21 ± 4.98

Total pore volume (mm3) 28351 31358 32422 28978 17456 27713 ± 2671

Total pore surface (mm2) 53082 79652 80580 100541 54016 73574 ± 8988

Average pore volume (mm3) 9.71 13.80 12.07 7.37 8.44 8.60 ± 1.04

Average pore surface (mm2) 18.19 35.04 29.99 25.58 26.13 25.86± 2.12

Number of Branches 4291 4944 5841 8522 4020 5524 ± 813

Number of Junctions 1240 1728 2013 2896 1273 1850 ± 294

End-point voxels 4760 4901 5740 8446 4348 5639 ± 737

Slab Voxels 28493 34094 42214 51128 25934 35644 ± 3847

Triple Points 1153 1497 1693 2423 1084 1540 ± 199

Quadruple Points 143 187 250 396 146 221 ± 39

Average CT 3D tortuosity 1.21 1.22 1.21 1.22 1.21 1.21 ± 0.004

Connectivity 163.87 245.63 389.25 423.38 131.75 270.77 ± 58.61

Bulk Density (g cm-3) 1.42 1.44 1.43 1.47 1.41 1.43 ± 0.01

DBr (Dispersion) 8.7 20.55 12 12.3 4 11.51 ± 2.71

Average Stained Area (%) 15.87 17.27 16.18 14.55 11.71 15.11 ± 0.96

48

Table S4. Properties of the columns from the Org. B plot. 763

764

Management Org. B Average

Column Number 13 15 17 19 20 -

CT-porosity (cm3) 22.99 24.07 6.86 15.88 7.99 15.56 ± 3.61

Total pore volume (mm3) 13889 16485 4455 9848 4841 9904 ± 2393

Total pore surface (mm2) 33600 58987 23650 32461 19507 33641 ± 6868

Average pore volume (mm3) 10.73 5.53 1.95 4.17 3.77 5.23 ± 1.49

Average pore surface (mm2) 25.97 19.79 10.35 13.74 15.18 17.01 ± 2.70

Number of Branches 1925 4719 2558 2786 1426 2683 ± 562

Number of Junctions 497 1350 492 582 283 641 ± 184

End-point voxels 2522 5740 4020 4215 2234 3746 ± 635

Slab Voxels 13077 27243 12160 15189 8646 15263 ± 3176

Triple Points 430 1166 427 507 256 557 ± 158

Quadruple Points 58 145 54 60 21 68 ± 21

Average CT 3D tortuosity 1.18 1.19 1.15 1.17 1.16 1.17 ± 0.01

Connectivity -4.38 106.25 -4.63 -40.13 -57.25 -0.025 ± 28.48

Bulk Density (g cm-3) 1.45 1.43 1.52 1.51 1.48 1.48 ± 0.02

DBr (Dispersion) 10 30 2.65 8 12 12.53 ± 4.64

Average Stained Area (%) 9.89 9.03 7.56 10.02 9.15 9.13 ± 0.44

49

Table S5: Example of the calculation of the multifractal parameters. 765

q τ Dq α f(α) q τ Dq α f(α) -5.0 -26.651 4.442 - - 0.2 -2.072 2.590 2.915 1.770 -4.8 -25.632 4.419 5.092 0.793 0.4 -1.512 2.521 2.726 1.735 -4.6 -24.613 4.395 5.093 0.789 0.6 -0.985 2.463 2.581 1.689 -4.4 -23.595 4.369 5.094 0.787 0.8 -0.483 2.415 2.469 1.639 -4.2 -22.576 4.341 5.095 0.784 1.0 0.000 2.381 2.397 1.610 -4.0 -21.556 4.311 5.096 0.783 1.2 0.467 2.337 2.337 1.558 -3.8 -20.537 4.279 5.096 0.782 1.4 0.922 2.305 2.273 1.507 -3.6 -19.518 4.243 5.096 0.782 1.6 1.366 2.276 2.219 1.456 -3.4 -18.499 4.204 5.095 0.783 1.8 1.800 2.250 2.172 1.406 -3.2 -17.480 4.162 5.094 0.786 2.0 2.226 2.226 2.130 1.356 -3.0 -16.462 4.115 5.091 0.792 2.2 2.645 2.204 2.092 1.305 -2.8 -15.444 4.064 5.087 0.800 2.4 3.056 2.183 2.057 1.254 -2.6 -14.428 4.008 5.081 0.812 2.6 3.461 2.163 2.025 1.202 -2.4 -13.414 3.945 5.070 0.830 2.8 3.860 2.144 1.994 1.150 -2.2 -12.403 3.876 5.055 0.855 3.0 4.253 2.127 1.966 1.097 -2.0 -11.397 3.799 5.032 0.889 3.2 4.641 2.110 1.940 1.045 -1.8 -10.397 3.713 4.998 0.933 3.4 5.024 2.093 1.916 0.992 -1.6 -9.407 3.618 4.950 0.991 3.6 5.403 2.078 1.893 0.941 -1.4 -8.431 3.513 4.880 1.066 3.8 5.777 2.063 1.872 0.891 -1.2 -7.475 3.398 4.781 1.158 4.0 6.148 2.049 1.852 0.842 -1.0 -6.547 3.273 4.640 1.271 4.2 6.514 2.036 1.835 0.794 -0.8 -5.658 3.143 4.353 1.450 4.4 6.878 2.023 1.819 0.749 -0.6 -4.819 3.012 4.077 1.582 4.6 7.239 2.011 1.804 0.706 -0.4 -4.041 2.887 3.763 1.691 4.8 7.597 1.999 1.791 0.665 -0.2 -3.327 2.773 3.445 1.759 5.0 7.953 1.988 1.778 0.626 0.0 -2.674 2.674 3.156 1.782

766