ORIGINAL PAPER

Water distribution in wood after short term wetting

Mojca Zlahtic Zupanc . Ursa Mikac . Igor Sersa . Maks Merela .

Miha Humar

Received: 10 April 2018 / Accepted: 2 November 2018

� Springer Nature B.V. 2018

Abstract Water has a major influence on wood

properties, especially dynamic moisture cycles, which

affect the wood in outdoor applications. It is thus

important to understand the penetration and distribu-

tion of water in wood. In this study, rainfall events

were simulated to correspond to water immersion

periods of 1 h. Specimens were imaged by magnetic

resonance imaging (MRI) after 1 h of immersion.

These measurements were used to determine the water

distribution in the wood and to elucidate changes

during the drying of specimens of five wood species:

sweet chestnut heartwood (Castanea sativa), Euro-

pean larch heartwood (Larix decidua), Scots pine

heartwood and sapwood (Pinus sylvestris) and Nor-

way spruce (Picea abies). Both gravimetric and MRI

analysis showed that after 1 h of immersion, pine

sapwood took up the highest amount of water,

followed by spruce wood. Considerably lower mois-

ture contents were determined in pine heartwood,

chestnut and larch, which correlated with a lower

signal intensity. The outer parts of the specimens

exhibited similar patterns with all of the specimens.

The most variable results were the moisture content

time profiles in the middle part of the specimens.

Comparison of the MRI measurements and gravimet-

rically determined moisture contents during drying

validated the MRI measurements and confirmed the

method to be suitable for giving comprehensive

information about the water drying kinetic.

M. Zlahtic Zupanc � M. Merela � M. Humar (&)

Department of Wood Science and Technology,

Biotechnical Faculty, University of Ljubljana,

Jamnikarjeva 101, 1000 Ljubljana, Slovenia

e-mail: miha.humar@bf.uni-lj.si

U. Mikac � I. SersaJozef Stefan Institute, Jamova 39, 1000 Ljubljana,

Slovenia

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https://doi.org/10.1007/s10570-018-2102-y(0123456789().,-volV)(0123456789().,-volV)

Graphical abstract

Keywords Magnetic resonance imaging � MRI �Wood � Water � Moisture content � Drying

Introduction

Wood is one of the most important building materials.

Due to its positive environmental impact, good

properties and availability, the use of wood, specifi-

cally in use class 2 (outside, not in ground contact,

covered) and use class 3.1 (outside, not in ground

contact, not covered) applications, as defined by EN

335 (2013), has increased considerably in central

Europe in recent decades (Rametsteiner et al. 2007).

However, sufficient durability of wood is required to

meet users’ criteria for specific applications (Kutnik

et al. 2014). Since the majority of biocides are banned

because of environmental and health concerns, and

due to the negative public opinion on existing biocides

and the use of tropical timber, research philosophies

for improving the durability and prolongation of

service life of wood have focused on alternative

directions (Militz 2015; Humar et al. 2017). Recent

models clearly indicate that the service life of wood in

above ground applications is a function of inherent

durability (due to the presence of biocides and/or

biologically active extractives) and water exclusion

efficacy (Meyer et al. 2017). Increased moisture

content (MC) above a certain threshold increases the

possibility of fungal infestation (Schmidt 2006). It is

thus important to limit water uptake (Brischke and

Thelandersson 2014). In the work of Isaksson et al.

(2013), it was shown that the first signs of fungal decay

on spruce wood appeared after 325 days under

favorable conditions (with MC above 25% and

temperature suitable for fungal decay). In general, it

is accepted that wood destroying fungi need a moist

environment to grow, so the wood MC should be kept

below 25% for non-modified wood. However, some

recent findings indicate that fungi can degrade wood

even at a lower MC, as low as 16% (Meyer and

Brischke 2015). Regardless of the moisture limit for

fungal decay, it is of considerable importance to

control the wood MC. Water uptake can be controlled

with suitable design, proper detailing, modification

and an understanding of the material (Dietsch et al.

2014; Yao et al. 2018). It is therefore very important to

understand the moisture dynamics of wood, which is a

comprehensive parameter that reflects the drying and

wetting of wood.

Wood is a hygroscopic material, with the ability to

interact with water (adsorb or desorb) from humid air,

in common with other porous materials (Thybring

et al. 2017). Wood exchanges moisture with the

surrounding air, thus achieving a state of hygrothermal

equilibrium (Weise et al. 1996). The rate of this

exchange depends on the relative humidity and

temperature of the air and the current wood MC

(Chen and Wangaard 1968; Skaar 1972; Hartley et al.

1992; Vidal and Cloutier 2005; Tannert et al. 2011).

This affinity of wood for water is caused by accessible

hydroxyl groups within the wood cell walls. Cellulose

and hemicelluloses, being more hygroscopic than

lignin, are mainly responsible for moisture uptake

(Rowell and Banks 1985). The affinity between dry

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wood and water is so strong that it is impossible to

prevent moisture gain (Reeb 2009). Moisture changes

are, for example, responsible for shrinkage and

swelling, for moisture-induced stresses and for

mechanosorptive effects, which may ultimately lead

to cracking or loss of loadbearing capacity (Skaar

1988; Thelandersson and Larsen 2003; Hameury and

Sterley 2006). Just as wood is made of cells occurring

in two systems, any individual cell itself has twomajor

domains; the cell wall and the lumen. In the context of

moisture relations, the lumen is the space in which

liquid water accumulates when moisture is added after

the fiber saturation point (FSP) has been reached. At

higher moisture levels, wood moisture movement is

predominately characterized by capillary movement

of water through the wood cell lumina. Capillary water

uptake is the predominant mechanism for water

penetration during short rainfall events. At lower

MC, diffusion plays the key role. Diffusion of water

through wood depends on the wood density and

anatomical pattern (Fotsing and Tchagang 2005),

grain orientation (Mouchot et al. 2006), sap-

wood/heartwood (Rosenkilde and Glover 2002), wood

moisture and wood temperature, as well as environ-

mental parameters (Simpson 1993), growth conditions

(Cai 2005) or the presence of reaction wood (Tarmian

et al. 2012).

MC is defined as the ratio between the mass of

water (mw) in a moist wood sample and the mass of an

absolutely dry sample of wood (Merela.et al. 2009b).

There are two general approaches to determining

wood moisture content. In direct measurements, the

moisture content is determined by oven-drying or

water extraction, but both are destructive methods

with respect to timber members in situ. Indirect

measurement methods use the physical properties of

wood, which are correlated to the wood moisture

content (Dietsch et al. 2014). The most widely used

method for MC determination is the oven-drying

method (EN 13183-1 2002). It has the highest

accuracy or degree of precision for research purposes.

The method consists of cutting test pieces, measuring

their mass, and then oven-drying them. Several other

techniques have been developed from oven-based

methods (Thybring et al. 2018), such as Dynamic

Vapor Sorption (Engelund et al. 2010, 2011; Glass

et al. 2018; Thybring et al. 2018) or continuous

moisture monitoring (Van den Bulcke and Van Acker

2008; Humar et al. 2014). Unfortunately, this method

is destructive and relatively slow, and errors can occur

if the wood contains volatile material, other than

water, that evaporates during drying [e.g., resins

(Hartley and Marchant 1995)]. These issues can be

overcome if distillation or extraction methods are

applied instead of classical oven-drying methods

(Kollmann and Cote 1968; Niemz 2003). One of the

key drawbacks of direct methods forMC assessment is

their destructive nature. If MC is to be measured

during monitoring of an object, indirect methods have

to be applied (Brischke et al. 2008; Franke et al. 2013;

Krzisnik et al. 2018), process control (Simpson 1989;

Mitsui et al. 2008). In these applications, capacitive,

electrical resistance, microwave, radiometric, spectio-

metric, spectrometric or color reaction measurements

can be applied (Skaar 1988). Among the various

technologies, spectroscopy based methods have been

found to be particularly promising: near infra-red

spectroscopy (NIR) (Thygesen and Lundqvist 2000;

Tsuchikawa 2007) and nuclear magnetic resonance

(NMR) (Bucur 2003a, b; Morales et al. 2004; Merela

et al. 2009a, b). One of the key benefits of spectro-

scopic techniques is that they provide insights into

chemical wood–water interactions, as well as yielding

information on water distribution in the macro-void

wood structure (Thybring et al. 2018).

Nuclear magnetic resonance (NMR) enables

instantaneous determination of the proton density in

liquids and is thus convenient for determining the MC

of wood. It is a non-destructive, non-invasive and non-

contact technique already being successfully applied

in wood science (Callaghan 1991; Contreras et al.

2002; Bucur 2003a, b; Morales et al. 2004; Labbe et al.

2006; Oven et al. 2008, 2011; Thygesen and Elder

2008; Dvinskikh et al. 2011; Merela et al. 2009a, b;

Cox et al. 2010; Hernandez and Caceres 2010;

Kekkonen et al. 2014; Javed et al. 2015; Passarini

et al. 2015; Zlahtic et al. 2017; Mikac et al. 2018;

Gezici-Koc et al. 2017). In addition, an NMR modal-

ity, magnetic resonance imaging (MRI), is a versatile

tool widely used for investigating the spatial distribu-

tion of moisture in various specimens, including

modified wood and other porous materials (Kanazawa

et al. 2017; Thybring et al. 2018). Several studies have

used MRI to investigate wood–water interactions and

it has been shown that MRI is one of the most

appropriate methods for this purpose, given that it can

provide valuable information on the distribution and

concentration of water in wood (Brownstein 1980;

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Menon et al. 1987; Araujo et al. 1992, 1993; Hartley

et al. 1994; Robertson and Packer 1999, Rosenkilde

and Glover 2002; Casieri et al. 2004; Merela et al.

2005; Almeida et al. 2007; Kanazawa et al. 2017). It

has also been proven that MRI is effective in providing

information about the distribution and concentration

of water in wood during drying and absorption

processes (Hartley et al. 1994; Menon et al. 1987).

The majority of NMR/MRI studies on wood apply

methodologies normally associated with porous

media.Water can play various roles in the microscopic

structure of wood (Casieri et al. 2004).Wood therefore

has different 1HNMR signal sources: cell-wall water,

lumen water, and some hydrogen pertaining to wood

macromolecules. Predominately low field NMR can

distinguish between water-bound hydrogen located in

different physical and chemical environments (Araujo

et al. 1992). It is thus a good technique for determining

the distribution of water within different parts of the

wood structure. The spin–lattice (or longitudinal

relaxation, T1) and spin–spin relaxation (or transverse

relaxation, T2) times of water molecules are qualita-

tively different for compartmented water than for bulk

water (Almeida et al. 2007). In spite of these benefits,

MRI is not often used in the field of wood science,

mainly due to the expensive and relatively rare

equipment. In addition to cost related issues, the size

of the specimens is one of the limiting factors (since

better spatial resolution of MRI can be obtained with

smaller specimens). In addition, it is challenging,

although possible, to detect MC below the FSP in

wood with conventional imaging techniques because

of the short T2 times of bound water (Rosenkilde and

Glover 2002). The difficulty can be overcome by the

use the use of special MRI methods, such as the

SPRITE (Single-Point Ramped Imaging with T1

enhancement) method or by signal averaging (Wang

and Chang 1986).

Since water has a major influence on wood

properties, understanding the penetration and distri-

bution of water in wood is of great importance. The

majority of available techniques provide information

about the average MC of wood, not considering that

there might be pockets of water inside the wood, with

optimal conditions for fungal decay. In the present

study, we tried to elucidate changes in water distribu-

tion after dynamic moisture cycles simulating rain

events and to determine the time needed to dry the

central part of the specimens. For this purpose, the

MRI technique was employed to visualize the water

distribution in various wood species and to elucidate

the changes during drying. To the best of our

knowledge there are not many available methods

suitable for monitoring water distribution in porous

materials through time. Specimens in the research

were imaged after 1 h of soaking in distilled water in a

controlled climate. Understanding water distribution

is of great importance for the interpretation ofMC data

of wood exposed in outdoor conditions and to model

the effect of rain events on the wood moisture content.

Materials and methods

Wood material

The studywas performed on sweet chestnut heartwood

(Castanea sativa), European larch heartwood (Larix

decidua), Scots pine heartwood and sapwood (Pinus

sylvestris) and Norway spruce (Picea abies) wood.

Specimens were defect-free, without visible signs of

decay or blue staining, as prescribed by EN 113

(2006). The specimens were also xylotomically

oriented and had similar densities and ring widths.

The wood species were selected because they exhibit

varied water exclusion efficacies, as determined with

other tests (Zlahtic et al. 2017). In addition, these

wood species are of considerable commercial impor-

tance in Europe and are frequently used for a variety of

applications, including outdoor uses.

Specimens for MRI scanning were sawn from one

bigger specimen, as indicated in Fig. 1. The dimen-

sions of the specimens used for MRI scan were defined

by the size of the RF (radiofrequency) coil used, i.e.,

1.2 cm 9 1.2 cm 9 1.2 cm (longitudinal 9 radial 9

tangential direction). Specimens were not treated and

were kept under room conditions (T = 23 �C; RH =

65%) before the experiment.

High-resolution magnetic resonance imaging

Prior to the measurements, the specimens were

immersed in distilled water for 1 h, with sample

masses determined pre- and post-immersion. One-

hour immersion was used to simulate a rain event.

Although water penetration into wood during immer-

sion is not fully comparable to the mechanism of water

penetration during a rain event, this approach was used

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because it enables a standardized procedure that

reflects the properties of wood species and has been

found to be the closest method to rain events (Zlahtic

et al. 2015).

For the MRI scan, the immersed specimen was

placed at the top of a glass tube filled with freshly

activated silica gel (4.5460 g), inserted in a larger

glass tube and fixed with Teflon (polytetrafluo-

roethylene—PTFE) tape to prevent rotation during

the MRI scan. Silica gel enabled drying of wood that

had been immersed in water prior to the measure-

ments. If no silica gel was applied, the relative air

humidity (RH) in the chamber reached 100%, which

prevents drying almost completely.

After the MRI measurements, the specimens were

oven-dried at 103 ± 2 �C until their mass became

stable and they were then weighed. A gravimetrical

method according to EN 13183-1 (2002) was used to

determine MC before and after MRI scanning.

MRI measurements were performed on a TecMag

Redstone (Houston TX, USA) MRI spectrometer with

a superconducting 9.4 T Jastec magnet (Kobe, Hyogo,

Japan). The specimen in the glass tube was inserted in

a 20-mm diameter RF coil. A 1D MRI pulse sequence

was used to obtain the water distribution along the

longitudinal, tangential and radial directions. To

visualize the 3D distribution of water in the specimen

3D, MRI was performed using the gradient-echo (GE)

technique. The specimen was reoriented in the magnet

in such a way that it allowed 1D profiles to be taken

along tangential, radial and longitudinal directions.

Before the first 1D experiment, the orientation inside

the magnet was additionally checked by acquiring a

low-resolution 3D GE image.

Changes in moisture were monitored for 24 h in

four specimens and for 64 h in one specimen. In order

to determine the water distribution after soaking, 1D

MR signal intensity profiles were acquired in three

perpendicular orientations, with the following

parameters: field of view (FOV) of 20 mm, echo time

(TE) of 1.56 ms, and repetition time (TR) of 1 s were

each measured for the first 20 min. In the 24-h

experiments, the acquisition of 1D profiles was

followed by 3D GE imaging to visualize the 3D

distribution of the water in the specimen. The scan

parameters were: FOV 20 mm, imaging matrix

128 9 128 9 128 (isotropic resolution was

156 lm), excitation flip angle 30�, TE 1 ms, and total

imaging time 17 min. After that, 1D MR signal

intensity profiles were scanned for 22 h at identical

parameters to those of the first scan but with a lower

temporal resolution (TR of 120 s). The last measure-

ment was again 3D GE imaging. For one specimen of

each wood species, 3D GE images were acquired

every 4 h (after acquisition of the 1D profiles was

finished) to detect water migrations inside the

specimen.

Since the 64-h drying process was very long, it was

monitored in one specimen only. The monitoring

included 3D GE imaging using the same parameters as

described previously but with a higher spatial resolu-

tion-imaging matrix of 256 9 256 9 256 with iso-

tropic resolution of 78 lm, yielding a total imaging

time of 7 h. The drying process was monitored

initially by 20-min scanning with a sequence of 1D

profiles, which was followed by acquisition of the 3D

GE image. After 48 h of drying, another 3D GE image

was acquired and between acquisitions of the two 3D

images, the drying process was monitored by measur-

ing 1D profiles at 2-min intervals.

Data analysis

MRI datasets were analyzed by ImageJ (Schneider

et al. 2012) digital image processing software.

Because the settings for the MRI measurements were

not the same in all experiments (probe and coil tuning,

receiver gain etc.) normalization of the 1D MRI

Fig. 1 Specimens prepared

for magnetic resonance

imaging

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signals was performed. For each specimen, the time-

dependence of the integrated signal and the signal

values at both edges (lower and upper) and from the

middle of the specimen were obtained from 1D

profiles along the z direction (profiles in the longitu-

dinal direction). The integrated intensities were nor-

malized at 48 min after soaking in distilled water. For

signal normalization at the specified three points (both

edges and in the middle), the signal values were

divided by the signal value at the lower edge of the

specimen of the profile at 48 min after soaking.

Calibration of the MRI method for wood moisture

measurements

Wood specimen preparation

Additional experiments on parallel specimens were

performed to link the measured MR signal with the

corresponding MC. In total, 14 specimens were

prepared (two per each wood category) with the same

dimensions as for the previous experiment. One

specimen per species was used for the MRI scan and

one further specimen for equilibrium moisture content

(EMC) determination. The specimens were condi-

tioned in 7 different condition chambers equipped

with a fan and saturated salt solutions to regulate the

relative air humidity (RH = ± 1%), as can be seen in

Table 1. In order to prevent wetting of the samples in

the condensing environment, they were protected with

a shelter. Specimens were weighed (Sartorius, Ger-

many) after the equilibrium state was reached and

before each of the MRI experiments. The EMC was

then calculated according to the gravimetric method

from the difference between the equilibrium (me) and

the oven-dry mass (m0) of each specimen [Eq. (1)],

with an accuracy of the balance of 0.0001 g.

MC ð%Þ ¼ me � m0

m0

� 100 ð1Þ

1D profiles with the same parameters as were used in

for moisture distribution measurements were acquired

from specimens of knownMC to obtain the correlation

between the 1D profile signal intensity and MC for

each wood category. The specimens (within the glass

tube) were positioned and imaged in a 20-mm

diameter RF coil together with a phantom sample,

which was placed on top of the specimens and was

used for normalization among different experiments.

The glass tube was then closed, so as to prevent

changes in MC. Different signals were obtained

according to the different MCs in the different

materials.

The integrated signal intensities of 1D profiles were

used to determine the correlation between MC and

signal intensity. A linear relationship betweenMC and

integrated signal intensity was found in each material

(wood species):

S ¼ aMCþ b; ð2Þ

where S is the integrated signal intensity, MC is the

specimen‘s moisture content and a and b are constants

determined from the measured data for each wood

species and are listed in Table 2 together with the

coefficient of determination R2.

Normalization procedure

The obtained calibration curves (Table 2) were used to

determine MCs from the 1D profiles measured during

drying. Specimen MCs after 1 h soaking in distilled

water and at the end of the MRI experiments were

determined by the gravimetric method. The relation in

Eq. 2 was used to calculate the MC during MRI

measurements, from the measured 1D-signal intensity

profiles. After the first 1D profile was obtained

approximately 30 min after soaking (the time needed

to set the MRI experiment and determine the proper

specimen orientation in the magnet), the signal

intensity at time zero (t0) was determined by extrap-

olating the integrated signal intensity slope to zero

time (time when the specimen was taken out of the

water and the MC was determined gravimetrically) to

determine the obtained signal (Sobt) at t0. The

Table 1 Established atmosphere for the conditioning of

specimens prior to MRM calibration at 20 �C

Climate Relative air humidity (%) Saturated salt solution

1 20 CH3COOK

2 33 MgCl2

3 44 K2CO3

4 65 NaNO2

5 75 NaCl

6 87 ZnSO4

7 97–100 Distilled water

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theoretical signal (Stheo) was calculated from the

known relation between the signal intensity and the

MC (parameters a and b from Table 2) and knownMC

at t0:

Stheoðt0Þ ¼ a�MCðt0Þ þ b ð3Þ

MCs at different times after soaking were determined

from the integrated signal intensity of the longitudinal

1D profile as:

MCðtnÞ ¼StheoðtnÞ � b

að4Þ

where Stheo (tn) is determined from the measured

signal at tn as:

Stheo tnð Þ ¼ SobtðtnÞ �Stheo t0ð ÞSobt t0ð Þ ¼ SobtðtnÞ � rðt0Þ ð5Þ

The same procedure was performed for the upper,

middle and lower parts, as well by using the ratio r(t0)

from integrals.

Gravimetric method for moisture content

determination

Parallel to the MRI experiment, specimens made from

the same material were continuously weighed to an

accuracy of 0.0001 g (Sartorius, Germany). Speci-

mens were soaked in distilled water for 1 h and then

weighed every 120 s for 60 h, under constant labora-

tory conditions (20 �C/65% RH). After exposure,

specimens were oven-dried at 103 ± 2 �C to a

constant mass and weighed to determine the oven-

dry mass. The mass change was then calculated

(Eq. 1). These data were used for verification of the

MRI results.

Analysis of wood drying dynamics

The moisture content MC is proportional to the water

concentration C in wood (MC½%� ¼ 100m1w

q0C, where

m1w is the mass of a single water molecule and q0 is thedensity of the oven-dry wood). The diffusion equation

that describes the transport of water in the wood, and is

usually written as a function ofC, can therefore also be

written as a function of MC. In the case of one-

dimensional diffusion along the x direction, the

equation is:

oMC

ot¼ o

oxDoMC

ox

� �: ð6Þ

Here we consider a case in which the diffusion

coefficient D is constant and the sample along the

diffusion direction extends from - l to l (�l\x\l).

Wood dries due to surface water evaporation, which is

proportional to the difference between the MC at the

surface and the equilibrium moisture content MCeq.

The process can be described by the following

boundary condition at x ¼ � l and x ¼ l:

� DoMC

ox¼ aðMC �MCeqÞ; ð7Þ

where a is the surface evaporation rate. The wood

drying problem given by Eqs. 6, 7 can be solved

analytically for a case in which the sample has an

initially uniform moisture content MCiu greater than

MCeq (Crank 1975):

Table 2 Calibration curves of the equilibrium moisture content of wood as a function of the normalized nuclear magnetic resonance

signal intensity

Wood species

(Abbreviations)

Scots pine sapwood

(PsS)

Scots pine heartwood

(PsH)

Norway spruce

(Pa)

European larch

(Ld)

Sweet chestnut

(Cs)

y = ax ? b

a 0.7209 0.3471 0.4397 0.1614 0.6875

b - 5.3222 - 1.5604 - 2.8246 - 1.0387 - 5.1855

R2 0.9787 0.865 0.9633 0.8898 0.9738

The abbreviations of materials are used later in plots

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MC x; tð Þ ¼ MCiu �MCeq

� �X1n¼1

2L cosðbnx=lÞe�b2nDt=l2

ðb2n þ L2 þ LÞ cosðbnÞþMCeq

ð8Þ

Here bn s is the positive root of the equation

b tanðbÞ ¼ L and L is a dimensionless variable defined

as L ¼ al=D. When considering the average moisture

content in the sample, Eq. 8 is integrated over the

sample dimension, i.e., from – l to l, and divided by 2l,

thus obtaining:

MC tð Þ ¼ MCiu �MCeq

� �X1n¼1

2L2e�b2nDt=l2

b2nðb2n þ L2 þ LÞ

þMCeq ð9Þ

As proposed in Yuniarti et al. (2018), Eq. 9 can be

simplified by reducing the summation only to the first

term, for which decay with time is the slowest. This

approximation yields a simple model function for the

wood drying process:

MC tð Þ ¼ MCi �MCeq

� �e�t=s þMCeq: ð10Þ

whereMCi corresponds to the average initial moisture

content of the drying wood sample and s is the wooddrying characteristic time constant equal to:

s ¼ l2

b21D: ð11Þ

In the case of a small L, b tanðbÞ can be approximated

by b2 so that the characteristic time constant becomes:

s � l

a; L ! 0; ð12Þ

while in the case of a large L, b1 converges to p=2 so

that

s � 4l2

p2D; L ! 1; ð13Þ

Results and discussion

Since MRI measurements are challenging to interpret,

it is more convenient to present the results graphically,

with separate graphs for each species prepared.

Furthermore, MC data in different parts of specimens

and different times of drying are presented (Table 3):

MC0 corresponds to MC at the start of measurement;

MC10 corresponds to MC after 10 h of measurement

and the last point (MC20) corresponds toMC after 20 h

of measurement. MC after 60 h (MC60) can be

resolved from graphs only. In order to make these

complex plots easier to understand, details of the

graphs have been briefly described at the beginning of

the results. The relationship between MC and time of

drying for all five specimens can be seen in Fig. 2,

which comprises five curves per graph, numbered 0 to

4. Three measurements took 24 h, while one of them

was prolonged to between 58 and 60 h. The average

MC of the wood specimen is plotted on the vertical

axis, while the horizontal axis represents the drying

time. It can be seen from the graphs how the average

MC of wood changes during the drying of wet wood

above freshly activated silica gel inside the 20-mm

diameter RF coil, while MRI scanning was in

progress. In order to enable easier comparison of

typical curves recorded for each of the specimens, the

most representative curve for each material is plotted

in Fig. 2. Since the pattern of drying depends consid-

erably on the position on the specimen, the moisture

distribution in relation to drying time with individual

wood species is presented in Fig. 3, in which MC

changes in the upper (U), middle (M) and lower

(L) parts of the specimens are presented. The lower

part of the specimens is the part that was closest to the

freshly activated silica gel. The last graph in Fig. 4

shows the results of MC monitoring during laboratory

tests, in order to verify the relevant approach. The

curves in the graph are thus a result of continuous

weighing using a laboratory scale.

The shapes of the curves representing the drying of

PsH, Pa, Ld, Cs samples exhibited low variation

between each measurement, with the exception of PsS,

in which specimens 3 and 4 exhibited significant

deviation from the other three specimens. However,

the shape of the curves of all specimens was similar for

all the wood species monitored. Differences between

the specimens in the PsS specimen group can be linked

to anatomical differences and variability of the

specimens (Lesar et al. 2009; Zlahtic et al. 2017). In

addition, it should be noted that PsS had the highest

uptake of water; the variability was thus the most

noticeable. During 1 h of immersion, PsS took up

approximately 66% (MC0) water. This water was

released fairly fast, which was observed as a sharp

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decline in the linear part of the curve (Fig. 2, PsS).

High initial MC resulted in the most prominent

difference between the initial (MC0 = 66%) and final

(MC60 = 16%) MC. However, the MC determined

after 60 h of drying was still the highest compared to

other species: MC of Scots pine sapwood was 16%,

which was approximately twice the value determined

for other materials.

The second highest MC0 (46%) after 1 h of soaking

in distilled water was measured in spruce wood (Pa)

(Fig. 2, Table 3), with the shape and decline of the

curve similar to that of PsS. In the first 20 h of drying,

Table 3 Moisture content in different wood species [Scots

pine sapwood (PsS), Scots pine heartwood (PsH), Norway

spruce (Pa), European larch (Ld) and sweet chestnut (Cs)],

parts (T–total specimen, U–upper part, M—middle part and

L—lower part) and time [0—the start of measuring (MC0),

10 h (MC10) and 20 h (MC20)] of measurement

Wood species/specimens (Fig. 1) Time (h)

T Ua Ma La

MC0 MC10 MC20 MC0 MC10 MC20 MC0 MC10 MC20 MC0 MC10 MC20

PsS

0 66.0 52.1 40.8 66.0 46.0 36.4 40.1 46.9 37.6 87.4 54.6 40.9

1 65.6 52.3 41.0 66.4 44.1 34.6 35.8 37.6 30.3 74.4 42.4 32.4

2 66.7 52.3 40.9 67.8 42.9 33.6 34.1 35.8 28.8 71.3 41.1 32.2

3 64.8 56.3 48.7 64.2 54.6 44.9 37.5 41.3 37.9 77.6 50.4 40.6

4 62.2 44.3 33.8 64.8 35.3 24.8 27.7 26.8 21.6 48.1 25.0 20.2

PsH

0 21.3 10.8 8.9 22.5 7.5 6.6 8.1 8.6 7.6 28.1 8.7 6.8

1 20.1 10.1 8.3 21.9 6.9 6.1 7.5 7.4 6.5 20.8 7.3 6.1

2 18.3 9.9 8.5 19.9 7.5 6.7 8.6 8.4 7.6 22.0 8.2 6.8

3 19.2 10.2 9.0 21.0 8.6 7.7 11.5 10.4 9.4 32.0 9.9 8.3

4 19.2 10.3 8.6 20.9 6.8 6.0 6.7 7.6 6.8 18.7 7.4 6.3

Pa

0 46.0 28.6 20.5 58.2 16.1 13.9 14.0 17.1 14.1 46.0 18.1 13.6

1 42.4 24.4 18.8 52.6 13.6 12.2 13.2 15.7 13.2 42.4 15.7 12.4

2 44.9 28.1 20.3 52.8 15.6 13.4 14.6 18.0 15.5 55.0 22.0 15.1

3 43.5 24.3 18.5 50.5 14.2 12.9 15.9 16.7 14.3 62.4 19.2 14.1

4 51.6 28.1 18.1 60.1 14.9 11.9 14.1 14.9 12.3 51.6 14.4 10.1

Ld

0 19.5 11.5 9.4 21.8 7.8 7.4 10.0 7.4 7.2 22.3 7.7 7.3

1 16.5 10.1 8.4 21.5 9.2 8.0 10.2 8.6 7.8 19.4 10.5 8.5

2 15.8 10.0 8.6 18.4 9.4 8.3 10.4 9.0 8.1 19.7 10.8 8.7

3 17.2 10.0 8.6 21.3 8.9 8.1 9.9 8.8 7.9 24.4 10.8 8.7

4 18.9 11.0 8.9 25.4 9.5 8.1 9.7 8.9 8.0 20.9 10.1 8.4

Cs

0 21.3 12.0 11.5 25.5 8.8 8.6 8.1 8.8 8.7 31.7 8.9 8.8

1 21.0 12.9 11.7 25.2 10.0 9.1 8.6 9.1 8.7 31.2 9.4 9.1

2 20.0 12.2 11.0 21.8 9.3 8.6 8.4 8.7 8.4 23.2 8.9 8.7

3 21.1 12.0 11.0 23.1 8.4 8.1 8.0 8.4 8.2 21.6 8.7 8.5

4 25.1 11.6 11.2 27.4 8.6 8.4 8.2 8.4 8.4 25.5 9.1 8.4

aThe lower surface (L) was closer to the activated silica gel. The silica gel was beneath the sample. The upper surface was at the top

of the test tube, so the microclimates surrounding the samples were different. The middle part is midway between the upper and lower

surfaces

123

Cellulose

MC20 was reduced to 18–20% and, after 60 h, the MC

of spruce wood was further reduced by half (MC60-

= 9%), with the value being half that determined for

Scots pine sapwood. There are several reasons for this.

First, pine wood specimens take up considerably more

water and so a longer time is needed for drying.

Furthermore, the water holding capacity of the silica

gel is limited, so the relative humidity in the cell with

Scots pine specimens is likely to be higher than with

spruce wood specimens. During drying, the free water

from the cell cavities is first removed and, since this

water depends on weak capillary bonds for binding, it

can evaporate faster than bound water. Bound water

uses strong hydrogen bonds and cannot be removed

without modification of the chemical structure of the

wood. The wood MC changes are therefore faster in

the upper part of the hygroscopic region but, on

approaching a dry state, they slow down. This can be

seen in the curves representing the drying of PsS and

Pa, in which the first hours of drying show the highest

changes and the largest drop in MC occurs, whilst

smaller changes in MC are later observed.

In the remaining materials (PsH, Ld and Cs), the

lower MC after soaking corresponded to lower signal

intensities (Fig. 2 and 3). The lower water uptake was

a result of the refractory nature of these wood

specimens in comparison to Scots pine sapwood

specimens. The uptake of water by PsH, Ld and Cs

was approximately 20% during 1 h of immersion.

These values were less than half of those determined

with Pa and three times lower than with PsS. In the

later stages, the drying kinetics stabilized, and the MC

did not change considerably in the next 20–60 h. The

MC in PsH, Ld and Cs after 20 h of drying was similar

to that reported for spruce (8–11%).

In Fig. 2, typical drying curves for each wood

species are plotted, in order to enable easier compar-

ison between the most representative curves for each

of the materials used in this study. The graph clearly

shows the relationships between the wood species.

The highest MC0 (66%) was found with PsS, so it was

to be expected that the biggest difference between

initial and final MC during drying was found with PsS.

This material also had the highest MC60 (16%) at the

end of MRI scanning, indicating that the equilibrium

state was not reached. The highestMCwas determined

with Scots pine sapwood (PsS), while the MC of larch

(Ld), Scots pine heartwood (PsH) and sweet chestnut

(Cs) were found to be comparable. If all of the data of

the wood MC are normalized between 1 (highest MC)

and 0 (final MC), two types of curve appear (data not

shown), depending predominantly on the initial MC.

The drying curves of larch (Ld), Scots pine heartwood

(PsH) and sweet chestnut (Cs) are much steeper than

the drying curves of spruce (Pa) and Scots pine

sapwood (SpS), mainly because drying samples (SpS,

Pa) containing higher amounts of water (in relative

and absolute terms) takes longer. It was therefore to be

expected that larch (Ld), Scots pine heartwood (PsH)

and sweet chestnut (Cs) would reach the equilibrium

state faster, which is reflected in a steeper curve

(Fig. 2).

In each plot in Fig. 3, the three different curves

illustrate MC changes during drying in the upper (U),

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35 40 45 50 55 60

MC

(%)

Time (h)

PsS PsH Pa Ld Cs

Fig. 2 Moisture content

changes during drying

above freshly activated

silica gel. Typical curves

represent drying of Scots

pine sapwood (PsS), Scots

pine heartwood (PsH),

Norway spruce (Pa),

European larch (Ld) and

sweet chestnut (Cs)

123

Cellulose

0

20

40

60

80

MC

(%)

PsS U M L

0

20

40

60

80 PsH

U M L

0

20

40

60

80

MC

(%)

Pa

U M L

0

20

40

60

80 Ld

U M L

0

20

40

60

80

0 5 10 15 20 25 0 5 10 15 20 25

0 5 10 15 20 25 0 5 10 15 20 25

0 5 10 15 20 25

MC

(%)

Cs

U M L

Time (h)

Time (h)

Fig. 3 Moisture content

changes during drying

above freshly activated

silica gel. MC was

monitored in different parts

(U-upper part, M-middle

part and L-lower part) of the

specimens. Typical curves

represent the drying of Scots

pine sapwood (PsS), Scots

pine heartwood (PsH),

Norway spruce (Pa),

European larch (Ld) and

sweet chestnut (Cs)

Fig. 4 Moisture content changes of specimens during drying

determined by continuous weighing (a) and moisture content

changes during drying inside a magnet above freshly activated

silica gel (total MC) (b). Typical curves represent the drying of

Scots pine sapwood (PsS), Scots pine heartwood (PsH), Norway

spruce (Pa), European larch (Ld) and sweet chestnut (Cs)

123

Cellulose

lower (L) and middle parts of the relevant specimen. It

can be seen that drying of the upper and lower parts of

the specimens is similar, in spite of the fact that the

silica gel was positioned below the specimens only.

Because the specimens were not placed directly on the

silica gel, the humidity inside the glass tube did not

vary much and the impact of the silica gel on specimen

drying can be ignored. It can also be assumed that the

influence of gravity on drying can be ignored, due to

the small dimensions of the specimens.

The upper and lower curves showed a similar trend

to that seen in Fig. 2. The highest MC was thus

determined at the beginning, followed by a consider-

able MC decrease in the first hours of drying, and

stabilization thereafter. The MC of the outer and

middle parts of the specimen was very different with

short drying times, showing that water slowly pene-

trated into the specimen during soaking. With increas-

ing drying time, the differences became smaller and,

after 24 h of drying, the MC was uniform inside the

whole specimen. It should be noted that the MC of

Scots pine sapwood was considerably higher than with

the other wood species; water had thus also penetrated

into the middle part. It took a longer time to reduce the

MC of the middle parts.

Figure 3 provides an overview of the curves

representing the middle part of the specimens of the

various wood species. At the beginning of drying,

MC0 was lower than the MC determined after several

hours of drying, and the outer parts of the specimens

began to lose MC during drying. Water from the outer

parts evaporated, as well as migrating into the middle

part of specimens, which resulted in an increased MC

of the middle part of the specimens after a certain time.

However, with prolonged drying times, the MC of the

middle part also started to decrease and reached the

same MC as the upper and lower parts (Fig. 3).

As can be seen from Fig. 3, the curves correspond-

ing to the middle parts differ among the wood species.

PsS exhibited the highest MC, followed by Pa. Drying

of PsH, Ld and Cs resulted in similar curves. The

lowest MC was determined with those specimens. All

the specimens had MC0 values in the middle part

approximately half those in the outer parts of the

specimens (which was also influenced by the short

time of immersion in water; with longer times this

difference was negligible). MC0 in the middle of PsS

was around 35% (also see Table 3), which is consid-

erably less than that of the lower part (Fig. 3), in which

MC0 was around 70% (Table 3). After 20 h of drying,

the MC in the wood reached equilibrium, and was

comparable in all parts of the specimens (MC20-

= 30%), as seen from Table 3. A similar trend was

also observed with other specimens (Fig. 2, 3 and

Table 3).

Among other things, Fig. 3 shows the pattern of

MC changes during drying of the lower part of the

specimens. Those parts of the specimens take up

higher amounts of water during drying, so they

contribute most to the overall behavior of the speci-

mens. It is not surprising that the drying patterns of

MC shown in Fig. 3 were very similar to the drying

patterns of the overall specimens obtained from Fig. 2.

It should be noted that the specimens were fairly small,

so the influence of the surface was more prominent

than it would be on materials in use.

In order to verify the procedure, a similar exper-

iment was performed gravimetrically. The gravimetric

approach was used to validate the MRI method.

However, it should be noted that the gravimetric

method provides information about the overall aver-

age MC of wood, while MRI also provides informa-

tion about the water distribution in wood. The

gravimetric method is thus a considerably less com-

prehensive method than MRI measurements. MC

changes during drying that were determined with

continuous weighing using a laboratory scale can be

seen in Fig. 4a. A comparison of this graph to the

graph in Fig. 4b shows a similar shape and slope of the

curves in the two graphs, though some minor differ-

ences were noted. These were mainly the result of the

biological diversity of the material. This graph con-

firms that our MRI observations and the normalization

procedure in this research were correct.

One of the key benefits of the MRI method is that it

does not provide only information about average

(total) MC, but also the water distribution in each

layer. These measurements can be repeated at prede-

fined time periods (Mikac et al. 2018). The method is

based on the linear relationship between the amplitude

of the NMR signal and the mass of water in moist

wood samples. The relationship can be precisely

calibrated for a given RF probe and spectrometer setup

(Araujo et al. 1992). Once the system is calibrated, the

MC of any sample can be determined. The method is

robust, fast and non-invasive. The correlation between

the oven-dry and MRI method is 0.996 for the whole

MC range (Merela et al. 2009a, b). Furthermore, this

123

Cellulose

method provides a 3D presentation of the water

distribution. These micrographs are very informative.

In each MRI image, each cube is represented by more

than 2 million dots. On a linear scale, a centimeter is

represented by 10.6 dots. Every dot represents a

volume of approximately 0.000824 mm3. Unfortu-

nately, 2D and #Dmeasurements cannot be done at the

same time, which results in gaps in some of the plots

(Mikac et al. 2018). Figure 5 shows 3DMRI images of

all five materials tested in this study. The figures show

overall water distribution, considering both free and

bound water. However, separation of the free and

bound water signals would require additional mea-

surements, which were not possible in this study due to

time limitations, since single measurements take at

least 1 day. The first image was obtained after 1 h of

drying inside the magnet. The next images were

obtained after 5, 10 and 20 h of drying. These images

were added for better visualization of the water drying

kinetics in different specimens. With spruce wood

after 1 h of drying, most of the water can be seen at the

edges of the specimen.With time, this water emigrates

Fig. 5 MRI of different materials (the abbreviations of the materials are the same as in Table 2) obtained after different times of

drying. FOV was 20 mm, the imaging matrix was 128 9 128 9 128 (isotropic resolution 156 lm, with total imaging time 34 min)

123

Cellulose

to the central part of the sample, where it is only

distributed along the less dense early-wood. The wood

tissue in early-wood has bigger cell lumina, so it is

more permeable. There was also water accumulation

in the second and third growth rings, although the

reason for this was uncertain and more research with

microscopy should be undertaken to investigate this

phenomenon. The same pattern of water distribution in

early-wood can be seen in the drying images of pine

and larch. In sweet chestnut, the highest amounts of

water were in the upper and lower parts of the

specimen, while the middle part of specimen retained

less water. It seems that the vessels in chestnut are not

a good path for moisture transport, which may be

explained by the tyloses that are present in vessels.

From Fig. 5, it can be seen that the upper part of

specimens dried faster than the lower part. The same

feature can also be seen in Table 3, although these

differences were relatively small. The upper and lower

parts of the specimens are reported separately, since

the microclimates in the test tubes differ. The lower

parts of the samples were closer to the freshly

activated silica gel. Since we were not able to control

these micro conditions, we decided to address it in the

manuscript.

Analysis of MCs measured at different times after

drying with the model given by Eq. 10 enabled a

quantitative analysis of the drying dynamics of

different wood species. In Fig. 6, the best fits of the

model to the averaged measured MC data are shown

for all five examined wood species, while Table 4

contains the corresponding best fit parameters MCi,

MCeq, s and D. The latter was calculated from the best

fit parameter s using Eq. 13, assuming L is large

(L � 1). The half-dimension of the sample along the

direction with the fastest diffusion was equal to

l = 6 mm.

Despite the simplicity of the model, which does not

take into account the different water compartments in

wood, the dependence of the diffusion constant onMC

and temperature, and other non-diffusion processes of

drying, the model curves fit well to the experimental

MCs with all wood species except sweet chestnut (Cs),

for which the coefficient of determination was the

lowest (R2 = 0.996). As can be seen from the 3D MR

images of moisture distribution in Fig. 5, sweet

chestnut had the least uniform initial MC. The model

in Eq. 10, which was derived for the uniform initial

MC distribution, cannot therefore fit to the Cs data

well. Another possible explanation for the fit discrep-

ancy is incomplete MC data acquisition due to the

nature of the measurements, which also included 3D

MR scanning, during which drying profiles (2D) were

not recorded. This resulted in data gaps in the graphs in

Fig. 6. With some species, such as sweet chestnut

(Cs), Scots pine heartwood (PsH) and, to some extent,

also Norway spruce (Pa), the MC curves exhibited a

kink at approximately 10 h of drying. The kink may

also originate in a transition from a faster drying

regime to a slower drying one, possibly due to faster

drying of the free water compartment (Azzouz et al.

2018).

Drying dynamics can be characterized by the

characteristic time constant s. However, as can be

seen from Eqs. 11–13, s is not dependent only on the

intrinsic properties of the sample, such as the diffusion

constant D and the surface evaporation rate a. It

depends also on the sample size, in our case on the

linear sample dimension l. To determine both D and a,one would need two independent measurements of s,e.g., with two samples of the same wood species

having different dimensions. Such experiments were

not done in this study. Only one of the intrinsic

parameters, either D or a, can therefore be determined

from one value of s, provided that L converges on one

of the extremes: on 0 to determine a using Eq. 12 or on1 to determine D using Eq. 13. In Table 4, D values

are calculated using this approach. To test what the

corresponding L values are, a typical surface evapo-

ration rate of 1.4 9 10-7 m/s was selected from the

literature (Niklewski et al. 2016). This coefficient

yields values of L for the diffusion constants in

Table 4 in the range from 1.7 to 7.5 and the

corresponding b1 in the range from 1.03 to 1.39. This

could in principle result in underestimated diffusion

coefficients by 30% with (b1 = 1.39) and up to 130%

(b1 = 1.03). Values of D for Cs, Ld and PsS are

therefore totally unreliable and are not given in the

table. As the estimated values of L cannot be

considered low, Eq. 12 for calculation of the surface

evaporation rate a also cannot be applied. The only

reliable parameter of wood drying dynamic in our

study is therefore the characteristic time constant s.Comparison of s for different wood species in Table 2

shows that that drying was slowest with Scots pine

sapwood (PsS), was also slow with Norway spruce

(Pa), while it was almost equally fast with the

123

Cellulose

remaining three wood species (Cs, Ld and PsH). These

three species also had identical initial and equilibrium

MCs, while the initial MC of Norway spruce (Pa) was

considerably higher and was the highest with Scots

pine sapwood (PsS). Interestingly, the equilibriumMC

was lowest with PsS, which may also be a conse-

quence of too short a data acquisition window, which

mainly covered the faster drying regime and to a lesser

extent the slower drying regime.

The presented approach for analysis of the drying

dynamic is simple but efficient. It is important to note

that this is a quantitative approach. It describes the

drying dynamic with only three parameters, i.e., the

initial and equilibriumMCs and the characteristic time

constant of the drying process. In our study, MC data

were obtained by NMR/MRI. In principle, this method

can be used for any MC data, as long as the MC

measurements are not too scarce in time. For this

method, MCs corresponded to spatially averaged MC

values, meaning that the real potential of MRI, i.e., its

spatial resolution, was not exploited. For that, other

more sophisticated models that would take into

account possible different spatial MC profiles of the

drying front, need to be developed. However, NMR

provides another advantage over the standard gravi-

metric method for MC determination, namely, instan-

taneous MC measurement. This allows MC

acquisition with a high temporal resolution, which

can be important for monitoring fast drying processes.

Conclusion

MRI was demonstrated to be a suitable method for

monitoring drying kinetics in wood. The results

showed that the shape of the MC curves representing

0

10

20

30

40

50

60

70

MC

(%)

t (h)

PsS

0

10

20

30

40

50

MC

(%)

t (h)

Pa

0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 10 20 30 40 50 600

5

10

15

20

MC

(%)

t (h)

Cs

0

5

10

15

20

MC

(%)

t (h)

Ld

0 10 20 30 40 50 60 0 10 20 30 40 50 600

5

10

15

20

MC

(%)

t (h)

PsH

Fig. 6 Best fits between the

measured averagedMC time

courses (black) and their

model predictions (red/grey)

obtained as best fits of the

model in Eq. 10 to the data

Table 4 Best fit

parameters of the MC time-

dependence model (Eq. 10)

to the data in Fig. 6

Species MCi [%] MCeq [%] s [h] D [10-10 m2/s] R2

PsS 66.0 ± 0.3 4.4 ± 0.2 36.4 ± 0.2 1.11 ± 0.31 0.997

Pa 45.6 ± 0.1 9.7 ± 0.06 16.7 ± 0.1 2.43 ± 1.54 0.996

Cs 19.7 ± 0.1 9.1 ± 0.03 9.4 ± 0.1 / 0.965

Ld 18.3 ± 0.04 8.2 ± 0.03 8.8 ± 0.06 / 0.997

PsH 19.3 ± 0.02 7.6 ± 0.01 8.4 ± 0.04 / 0.997

123

Cellulose

the drying of PsH, Pa, Ld and Cs wood exhibited low

variation, while with PsS, significantly different

drying kinetics were observed due to anatomical

differences, variability of the specimens and the

highest amount of water uptake. One hour of immer-

sion of PsS resulted in the highest water uptake, 66%

(MC0). This water was released fairly fast, which

could be seen from a sharp decline in the linear part of

the MC curve, although the MC for PsS determined

after 60 h of drying was still the highest compared to

the other species, being twice that of the other samples.

The second highest MC0 (46%) was measured with

spruce wood and the lowest MC after 1 h of soaking in

distilled water was observed with pine heartwood,

sweet chestnut and larch. The highest changes in MC

occurred in the first hours of drying, followed by

slower drying until the equilibrium MC was reached.

In the specimens with the smallest water uptake (PsH,

Ld and Cs), of approximately 20% during 1 h of

immersion, a fast MC decrease was observed for the

first 5 h, whilst in the later stages, drying stabilized

and the MC did not change considerably in the next

20–60 h. The situation was different in Pa and PsS, in

which a significantly higher water uptake was

observed and, at 60 h of drying, the MC had still not

stabilized. The lower water uptake with pine heart-

wood, chestnut and larch is a result of the refractory

nature of these wood specimens.

MRI allowed the observation of spatially resolved

MC changes in the specimens. Time dependencies of

MC during drying in the upper, lower and middle parts

of the specimens were also determined. The results

showed that drying of the upper and lower parts of the

specimens was similar to the drying of the overall

specimens. The most interesting were the MC curves

corresponding to the middle part of the specimens. At

the beginning of drying, the initial MC0 was lower

than determined after several hours. At the end of the

drying experiment, the MC of the middle part of the

specimen reached the sameMC as the upper and lower

parts.

Similar experiments were also performed gravi-

metrically. These data indicated that the high-resolu-

tion MRI observations and the normalization used in

this research were correct and provided verification of

the results. What is more, the MRI measurements gave

more comprehensive information about the water

drying kinetics than the classic gravimetric method.

Acknowledgments The authors acknowledge the support of

the Slovenian Research Agency within the framework of project

L4-5517, L4-7547, program P4-0015 and the infrastructural

centre (IC LES PST 0481-09). Part of the research was also

supported by the project Tigr4smart.

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