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ABSTRACT

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Abaza, Mohamed M.

10;

1936; Streaming

Current and Streaming Potential

Induced by

Water Flow Through Porous

Media;

Department

of

Civil

Engineering; Dr. Calvin

G. Clyde, major professor.

This

study was conducted to inves t igate analyt ica l ly and experi-

mentally the re la t ionship between the rate of flow of water through

porous materia l

and the streaming current and streaming potential

in-

duced by

this

flow.

The effect

of dissolved

s l t s

in

the

permeating

solution and the size

of the

so i l

p r t ic les

was also investigated.

Results and conclusions

of

th is

study are

summarized as

follows:

1.

A modified procedure using

the

appropriate delay to

.insure

stead

s t te

conditions

was used for the measurements of both stream-


3/142

waters

and NaCl and KCl solut ions provided

that

the conductance

of

the solution was taken

as

a parameter.

5 decrease

in

current and potential was observed with in-

crease of

soi l

par t ic le diameter.

6.

a

Relationships

~ the form o l bN and ~

Clog

N da re

suggested to express the effec ts

of

part ic le s ize and sa l t concen-

t ra t ion on the

streaming

current and the

streaming

potential

induced

by the flow.

7. Induced

streaming potential

was

found to

increase

with

the

decrease in temperature.

8. The analyt ical relationships

developed

together with the

experimental work

could probably be used as the basis of a

method

for

measuring

the rate of

flow

through

porous material .


4/142

ACKNOWLEDGMENTS

am indebted to Dr.

Calvin

G. Clyde

major p rofessor

and

thesis di rec to r for his continuous encouragement deep in teres t

valuable advice guidance throughout this work and finally for his

active in teres t

in providing

an environment conducive

to

research by

acquir ing nece s sa

ry

equipment

in shor t t ime.

Special

thanks

are

due

to

Dr.

S.

A.

Taylor

m e m be r

of

the

doctoral

commit tee who introduced m e to i r rever s ible

thermodynamic s

for

his painstaking

review

of

that

part

of

the dis

sertat ion.

am

also grateful

to

Dr. V. E. Hansen Dr. G. Z.

Watters

and

Dr.

D.

V. Sisson for serv ing as memb ers

of

m y

doctoral comm it tee .


5/142

TABLE OF CONTENTS

Chapter

I

INTRODUCTION

Objectives

I I

ELECTROKINETIC PHENOMENA

Historical

Recent Theories

and

Modifications

to

He1moho1tz •

Factors Affecting Streaming Potential in

Porous

Media

Utilization

of Streaming Potential for the

Determination of Flow

Parameters

I I I DERIVATION OF THE

ANALYTICAL EQUATIONS

Streaming Current

Streaming Potential •

Limitations

and

Assumptions

•

Page

5

6

6

8

10

14

14

19

21


6/142

Table

1

2.

3.

4.

5.

6.

7 •

LIST

OF TABLES

Conversion factors •

Phenomenological

coefficients and electrokinet ic

couplings equation

20

Phenomenological coefficients and electrokinet ic

couplings

equation

21

Calculated , values

for

different concentra-

t ions of

KC

for Sl

and

S2 •

Cell

constant

measurements,

Sample

1

Cell

constant measurements,

Sample

2

Chemical

analysis of

simulated

natural waters

Page

80

81

8

83

8

85

86


7/142

LIST OF FIGURES

Figure

1.

2.

4.

5.

6.

The

structure

of the

double

layer

and

the

cor

responding

potent ia ls .

is

a t

the

wall,

is

a t

the beginning

of the

diffuse double

layer ,

a t the hydrodynamic plane of shear

o

In

the

diffuse

double

layer the potential decays by a

factor of

l o v e r a

distance

of 6

= }

for

low

p o t e n t i a l s ~ a f t e r Mysels, 1959

•

Experimental apparatus--general view

A general view

of

the

instrumentation

set

Schematic sketch for

the

apparatus showing the

flow system

.

Block diagram of the electrodes and

associated

electronic instrumentation

Details

of

the

cel l

•

Page

87

88

89

90

91

92


8/142

Figure

13. Discharge q

in

cm

3

/sec versus

streaming

potent ia l

E

x

10

3

in volts with NaC permeating through

S2

confined in

ce l l s

f i t ted with

Ag-AgCl

and p1atinized

p l

electrodes

0

14

D

o

h . 3/ °

. SC

arge

1n cm sec versus stream1ng

current

I

x 10

9

in ampers

with 5 x 10-

4

NaCl permeating

through

S2

confined

in

ce l l s

f i t ted

with

Ag-AgC1

and

plat inized p l electrodes

15. Slope of discharge versus

streaming

potent ial

in mill ivol ts

x

sec versus normality of KCl

2

solutions

~ ~ r m e a t i n g through

~

confined in cel ls

f i t ted with

Ag-AgCl

and

platin1zed plo electrodes

16.

Normality

of

permeating

solution

versus the

resistance

for 8

1

and

8

2

17.

The

slope

versus NaCl

normality for 8

1

and S2

18. Slope S versus

NaCl

normality for Sl

and

8

2

19.

The slope versus KCl normality for Sl and 8

2

.

Page

99

100

101

102

103

104

105


9/142

Figure

27.

Discharge in cm

3

/ sec

vs. applied

di f feren t ia l

pressure H in

cms

of

water for potassium

chlor ide

so lu t ion with different sa l t concen

t ra t ions

permeating through 8

1

and 8

2

28.

Discharge

q versus

streaming potential E

for

conductance water

permeating through

8

1

and 8

2

29.

Discharge

q

versus streaming potent ia l

E

for

NaGl

permeating through

8

1

a t different

sa l t concentra-

t i o n s • • • • • • •

30. Discharge q versus streaming potent ia l E for NaGl

permeating through

8

2

a t different

sa l t concentra-

t

ions

•

31.

Discharge q

versus streaming potent ia l

E for

KGl

permeating through

8

1

at d i f ferent

sa l t concentra-

t ions

• •

32. Discharge

q versus streaming

potent ia l

E for

KGl

permeating through

8

2

a t

di f ferent sa l t concentra-

t ions •

33.

Discharge

q

versus

streaming

potent ia l

E

for

WI

Page

113

114

115

116

117

118


10/142

Figure

Page

40

Discharge q versus

streaming

current

I

for

WI

W

2

and

W

permeating through

8

1

126

41 Discharge q versus

streaming

current I for

W

permeating through

8

2

127

42

art ic le size

dis t r ibut ion

for

both

sand samples

128

43

Cell

constant

for

8

1

and

8

2

•

129


11/142

Symbol

A

0

a

mp

C

C

s

C

l

,

C

2

D

d

E .

s

t r

i

s t r

E

Notations

Cross sectional area perpendicular to the

direct ion

of the flow

Average

radius of

pore

Ampers

Cell constant

Specific

conductance

Proportionali ty

constants

Dielectric

constant

Effective sample

diameter

d

lO

Streaming potent ia l

elect r ical potential

difference

across the system

Charge carr ied per

second

per l iquid per unit

surface

length


12/142

Symbol

L

11

L

P

L12

L21

L

22

L

e

m

moa.

moVe

N

p

P

s

q

qp

Notations

Represent hydrodynamic

conductance

Represent elec t ro

osmosis

Represent streaming

potential

Represent elect r ic l conductance

Effective area of pores;

superf ic ia l

porosi ty

Mi11iampers

Mill ivolts

Normality of s l t solution

Pressure difference

across the

system

Total perimeter of l iquid sol id interface in a

cross section area

of the

sample

Discharge; volume r te

of flow

Rate

of

flow that would

exist

in absence

of

coupling


13/142

Symbol

}

rt

Notations

Kozeny

coeff ic ient

Laplacian

operator

Elect rosta t ic potent ia l

Potential t the surface of the wall

Potential

a t the two layer

interface

Dynamic viscosi ty

Electronic charge

Porosity

Elect r ica l charge density

Zeta potential potential at the hydrodynamic

plane

of

shear


14/142

CH PTER

INTRODUCTION

The problem of developing suff ic ient water

suppl ies

for in-

dustry,

agriculture

and

domestic

use

is

rapidly

growing

more

serious

and may well become of basic worldwide

concern

i f the

present

rate

of population growth

and economic

development

is maintained.

In developing ground water

supplies there

is

often

a

need for

deta i led information concerning the

ra te

and direct ion of ground

water movement

in

order to

evaluate

the

ult imate safe

yield

of ground

water reservoirs .

Measurements

of

the velocity of f luid

flow

throu.gh

porous media have been of concern to

the

hydrologis t ,

soi l

mechani-

cian, petroleum

engineer

and sanitary

engineer

for

more than

half

a


15/142

2

and heterogeneous

charac ter i s t ics of

the medium.

Most

equations

relat ing

head

to discharge,

time, space

and

hydrologic

propert ies have

been

derived through

applicat ion of

Darcy s law

to

the

continuity

equation. Thus, determination

of

the

hydraulic constants of an aquifer requires not only measurement

of

the

head

dis t r ibut ion

in

space

and

time

but

also

measurements

of

dis

charge from or

recharge

to

the aquifer a t

the

same locat ion

where

the

shape of the f low-field boundary

is knowno

Thus, a t

most

loca

tions

in

an

aquifer ,

i t

is not pract ical

to obtain

by direct m e s u r e ~

ments the data needed

for

applicat ion

of

the available

analytic

equations.

I f some

method

for

measuring ground water velocity

can

be found,

the

u t i l i ty of

the tes ts

to

determine the hydraulic

constants

of the

aquifer can be

greatly

extendedo

The obvious approach is

to include,


16/142

The simultaneous

t ransfer

of heat and

the

flow of water u n e r ~

ground

resul t

in

head

and

temperature

distr ibutions

which

can be

ex

pressed by different ia l

equations.

Some

of

these

qual i ta t ive re la-

t ions have been published. Some quant i ta t ive experiments

re la t ing

temperature and veloci ty

changes

have yet to be conducted

before

valid

conclusions

can

be

derived. Therefore,

a new

approach

is

sug

gested

in this work. That is to

ut i l ize

electrokinet ic phenomena,

known and

extensively

used in co l lo idal and biological

science,

for

the

evaluat ion

of discharge and velocity for

flow

of

f luids

through

porous materials .

When

a solid comes

in

contact

with

l iquid,

an e lec t r ic pot,ential

difference between

the two comes

into existance a t

the

interface.

Consequently, the l iquid will be

charged

opposite to

the

solid (wall).

Ions of the

l iquid

accumulate

near

the

solid

surface

and cause .an


17/142

4

to

flow. This

phenomena

is ow

well

understood for uniform c p i l ~

1aries

and

has

been

shown

also to

exist when

flow

occurs

through

porous

plugs and diaphragms see Abramson, 1934; Kraemer, 1942;

G1asstone, 1946; Overbeek

and

Wigga, 1946; Partington, 1949; Butler,

1951; Overbeek, 1953a

and

b;

Rutgers,

1954;

Bikerrnan, 1958; Bier,

1959;

Mysels,

1959;

Adamson

1960; Schulman and

Parriera ,

1963;

and

Davies

and

Ridea1, 1963).

Many measurements

of streaming potent ial

have been ut i l i zed

in studying

the

s t ructural

and

electrochemi.cal

properties of sol id surfaces in contact with l iquids Neale

and

Peters , 1945;

Buchanan and

Heyman 1948 and 1949a

and b;

Goring and

Mason

1950; Dulin

and Elton, 1952

and

1953; Fuerstenau,

1953; Gaudin

and Fuerstenau,

1955; Biefer

and Mason,

1959; Martinez, 1960; Par-

r i e ra

and

Schulman, 1961).

I t

is

well known

that ,

when

l iquid

flows

through porous materi-


18/142

5

needed experimental procedures th is study has been

undertaken.

Experimental

procedures

developed

and

equipment used

in

th is

work

have

proved

to

be r e l iab le

enough

to

investigate the approach sug-

gested.

Analyt ical

relationships developed

together

with the experi-

mental

work could probably be

used

as the basis of a rel iable method

for

measuring

the

rate

of

flow

through

porous

materials .

Objectives

The object ives

of

th is

study

are:

1. o develop

the analyt ical relationship

between

the

ra te

of

flow

of

f luid

through porous

material

and

streaming

current

I

and

streaming

potent ia l

E induced

by

th is flow.

2. o

establish

a rel iable

experimental

procedure for

the

me.a-

surement

of

E

and

I

developed by

flow of

water

through porous materi -

al .


19/142

CHAPTER

I I

ELECTROKINETIC

PHENOMENA

Histor ica l

Elect rok inet ic phenomena

were

observed as

far

back as

the

begin-

ning

of the

19th

century. In 1808 Reuss discovered that flow through

a capi l lary

element

can be induced by the applicat ion of an e lec t r ic

f ie ld . About hal f

a century

l a t e r in 1852,

iedmann

performed

a

number of

quanti tat ive. experiments

and

promulgated

one

of the funda-

mental theories of elec t rokine t ics .

His

theory,

which

has been ver i -

fied

many t imes,

sta tes that

the volumetric

flow t ransported through

porous material by galvanic current i s d i rec t ly proport ional to the

in tens i ty

of the applied

current.

In

1859

Quinke

discovered

the


20/142

7

In 879

Helmoholtz developed the double layer

theory

which re

lated

analyt ical ly

the

elect r ic l and

f luid

flow

parameters

of

elec

t rokinet ic

t ranspor t .

Although subsequently modified,

his develop

ment stood the t es t

of time and

s t i l l represents

an acceptable

formu

l t ion

of the electroosmosis phenomena in most capil lary mater ial .

Actuated

by an

in teres t

in

the nature of

s t b i l i ty

of

s u s p e n s i o n s ~

Smoluchowski (1921) reinvestigated the theory

of Helmoholtz.

F:reund

l ich (1909) published and discussed the

resul t s

of some prior compre

hensive experiments performed by other

inves t iga tors .

His d e m o n s t r a ~

t ion--based on Saxen s experimental

resul t s 1 8 9 2 ) ~ s h o w e d that i f

both

electroosmosis and

streaming potent ial

are

measured in the

same

system,

then

the proportionali ty

constant

in electroosmosis re l t ing

volumetric flow

to e lec t r ic

current was ident ical with that

rel t ing

streaming potent ial and applied pressure. From tha t

time

on thE: f ie ld


21/142

Recent

Theories and Modifications

to

Helmoho1tz

He1moholtz theory

The

basic premise of Helmoholtz development is that

when a

l iquid and solid come

into contact ,

there is usual ly an accumulation

of

ions of the l iquid near the surface of the solid to produce a

double layer. Helmoho1tz envisaged the double layer as

two

para l le l

planes of opposi tely

charged

ions. The fixed layer adheres to the

surface

and

a

neutra l iz ing counter ion layer tha t

exis ts

in

a

single

plane para l le l to the surface

a t

a

distance

x

into

the l iquid e

considered the

mutual

act ion

between

the

ions

to

be

negligible .

Gouy theory

In 1910 Gouy introduced a more rea l i s t i c concept of

the

poten-

t i a l and charge dist r ibut ion

in the

f luid

adjacent to

the sol id wall .


22/142

Stern

theory

In

1924

Stern

suggested

a

type

of

double

layer

which

is

a com-

bination of the

simple

Helmoholtz fixed layer

with

the

Gouy

diffuse

layer. Roughly

the potent ia l

is assumed

to

vary with dis tance as

shown

in

Figure

I . In Stern s picture of

the

double

layer , he

con

sidered the possibi l i ty of

specif ic

adsorption

of ions and assumed

that these ions were also located in the plane x. This

layer

of

adsorbed ions is called the Stern

layer.

The

to tal

potential drop

is accordingly divided

into

a potential

drop over

the diffuse part

of the

double layer

and

that over

the

molecular

condenser.

Present

theory

9

With

a l l these modifications the theory ow reaches acceptable

status that could be summarized

as

follows:

The charge on

the solid

wall of

the

part ic le)

at t racts

counter

ions

and

repels s imilar

ions.


23/142

10

equi l ibrium condi t ions a re destroyed

and a

se r ie s of e lec t r ok ine t i c

e f f ec t s

may

be

observed.

Each

may

be

dis t inguished

pr imar i ly

by

the

nature of

the

dis turb ing

force , which

may

be

mechanical or e l e c t r i c a l .

One

of

these e f f ec t s i s the s t reaming po ten t ia l . In

t h i s

case

the

dis turb ing

force is mechanical movement

which crea tes an

e l e c t r i c

cu r ren t .

When

the

l i qu id

i s

forced to

f low

through

the

charged

c a p i l l a r y ~ cur ren t

flows with the l iqu id

and i s known as

the

s t ream-

ing

cur ren t see

Chapter

IV). This cur ren t can bui ld up

a

po ten t ia l

d i f f e r ence

between

two

e lec t rodes s i tua ted a t the ends

of

the

cap

i l -

l a ry

known as s t reaming po ten t i a l .

Factors Affect ing Streaming Po ten t ia l

in

Porous

Media

As

may be

s e e n ~

the s t reaming po ten t ia l

i s

dependent upon three

majo "

fac tors :

the

composi t ion

of the

l i qu id

phase (permeant

so lu-


24/142

11

contact with pure water or di lu te solutions. This charge ar ises

ei ther

from

the adsorption of

hydroxyl ions

or

dissocia t ion

of

H

ions) or the

adsorption

of

negative

ions from

elec t rolyte

solutions.

For example,

with

potassium or sodium chloride solutions

tested, the

negative

potent ial

of sand could

be

as

shown

in Figure 1, Appendix.

Effect of the composition of l iquid phase

The effect

of the

composition

of

the l iquid is

detected in

the

electrokinet ic behavior of streaming potent ial

for

l iquids

contain-

ing dissolved elec t rolyte

That

effec t

wil l

be recognized

through

i t s effec t

on the

double layer thickness and the conductivity of the

system. The

nature of the elec t rolyte

is as important

as i t s

concen-

t ra t ion The

resul t s

found

for

the

influence of

ions on potent ial

consequently

on streaming potent ial) may

be

summarized

as:

1.

The

nature

of

the counter

ions

is

more

effect ive

than

tha t


25/142

12

streaming

potential . Investigations of

the

re la t ion between turbu-

lence and streaming potential with

an

objective being

the

use of

e1ectrokinetics as a tool for turbulence

measurements

in pipe flow

have

been conducted Cermak

and

Baldwin, 1963). The research accom-

plished

by Binder 1960) showed

that


might be

a

valuable tool

in

the study

of

turbulence

and

unsteady water

flows.

Chaung

and Duckstein 1962) ci ted by

Cermak

and Baldwin, 1963) s u ~

ceeded in adapting the electrokinet ic electrode to

the

study of ful ly

developed

pipe flow see also

Binder and

Cermak, 1963).

Some thoughts

have

been

given

also

by Bocquet 1952)

at

the

University

of

Michigan

regarding

the

measurement

of

blood flow in veins

by streaming poten-

t i a l techniques.

In

the f ie ld

of soils

porous

media), not much work has

been

done

on the

usage

of


for

fluid

flow measurements


26/142

3

account for the

non-Darcy

behavior of flow through

Kaolini te .

Olsen

1966) conducted an experimental investigation

to

study values of

the induced

hydraulic

and potential difference across Kaolinite sam-

ple

as affected

by the form of the externally

imposed

inducing

force.

These forces were in the

form

of

l iquid flow,

current and Na l

con

centra t ion difference

across the

sample.

The research work reported

in

here,

however, is

intended

to

develop

an

analyt ical

re la t ionship

between

streaming

potential and

streaming

current induced

through

sand

beds by

flowing solut ions and

the

r te

of

flow

of

these

solutions.

The

experimental

investigations

were conducted to tes t

this analyt ical relat ionship;

also to deter

mine

how

this

re la t ionship

wil l

be

affected

by

electro ly te concen

t r t ion in the percolat ing solut ions and the

size

of the p r t ic les

forming

those beds.

These

relationships

are

then

discussed

in order


27/142

CHAPTER

I I I

DERIVATION OF THE ANALYTICAL EQUATIONS

Streaming Current

Assume that Poiseul l s theory for velocity

dis t r ibut ion

(para-

bolic veloci ty

distribution)

in

a capi l lary

is valid

for

each

inf in i -

tesimal length of the flow channels. Then

in

a

length

oL of the

flow

channel

of

average

radius a, the

axial veloci ty

of flow of

l iquid

(of viscos i ty 11

at

a point any dis tance from the center under a d

i f -

ferent ia l pressure p (where Op = h as the flow channels are

horizontal with oz =

0).

= ~

V(r)

4110

L

2 2

(a

- r

1)


28/142

15

p

3)

I f , as

is usually the case, the ionic atmosphere

a t the

wall

the

diffuse double layer) is extremely thin in comparison with

the

pore diameter, then the gradient

of

the velocity, :; can be assumed

to

be

constant

inside

the

layer,

and

the

velocity,

v x)

at

any

dis-

tance,

x x

= a-r , from

the wall

is

given

by

x

S

dv

v x)

dx) x=o

dx 4)

0

as

dv

dx)x=o

2 T)L

5)

therefore

x

v x)

=

dv)

dx

pax

o dx x=o

2T}L

6)


29/142

16

r-a

i

_paD

[

(xd f)x=a

d'i'

dx

]

s t r

- 81)rrL

dx X=X

o

dx

x=xo

~

[

(xd' ')x=a


30/142


31/142


32/142

9

Streaming

Potential

This streaming current (convective current)

is responsible

for

the streaming potent ia l

E

t

As a

consequence

of the streaming

cur

s r

rent ,

a

potential difference will

be

set

up

between the

ends

of the

bed which in turn wil l cause an elect r ic

conduction

current I oppo

c

s i te

in

sense with the

streaming

current.

At

steady

s ta te ,

I

s t r

will

be balanced

by

I and

the potential difference, streaming

c

potent ial , wil l remain steady as

I - I

c s t r

and

the

to ta l

current

wil l

be

I + I = 0

c s t r

The conducting of the charge back wil l be through the l iquid and

solid

surface so,

16)


33/142

20

1940;

Jones and

Wood 1945; Gaudin

and

Feurestenau,

1955)

showed that

the

contr ibution of

surface

conductance

to

the conductance of

the

electrolyte in

the

plug

could be

appreciable. This contr ibution is

usually

compensated

by the use of a ce l l constant. In

such

case

k = where R is

the

no-flow resistance between

electrodes

and

C is

the

cel l

constant

and

So,

I

s t r

E

s t r

I

c

C

E

s t r R

R

I

s t r

x C

= TT

(l-ct).'

2

~

tr .

R

(18a)

C . q

R

under

the previously

mentioned conditions and as C is

constant ,

then

E = Constant • q = C q

(18b)


34/142

2

or current) increases nonlinearly

with

p While th is effect

is

not important

for aqueous solutions under pract ical conditions, i t is

signif icant for non-aqueous solutions where the ionic double layer

is

much

more

diffuse and may extend

into the region

of

turbulent

flow.

d) Darcy

Law

is

valid and

the

media

is

homogeneous

and

iso-

t ropic .

Limitations

and

Assumptions

The

previous conditions are

to be

sat i s f ied

for the val id i ty of

equations

15) and

18). The

following

is a discussion for

those

l imitat ions

in general and

degree

of

approximation in

cases where

any

of these

conditions is

no

longer sat i s f ied

Laminar flow condition. The condition

that

the flow of the


35/142

22

concluded no effect

in their work.

However,

Rutger,

Desmet

and

Myer

1957) established

such an effect for diffuse

double

layer

as in

the

case of

benzene

in

contact with

glass) in

capi l lar ies and were

able

to develop

a

re la t ionship between

streaming

current

and the average

veloci ty

V V =

discharge/cross

sectional area) for

turbulent

flow

as

follows:

~

s

t r

- 20

v

where I ,D , are

as

defined before, 0

is

the thickness of dif -

s t r

fuse part of

double

layer

and

a is the radius of the capi l la ry .

Similar equations were obtained

by

Davis and

Ridel 1963).

Bournans

cited by Davies

and

Rideal, 1963) developed

the

analysis for the

case where

some

of the

ions from

the ionic sphere near the wall will

extend into

the turbulent core. His terms should be

added

to ei ther


36/142

3

large with

respect

to the thickness of the double layer . Burgreen

and Nakache 1964)

developed

another

analyt ical

solution

for the case

of the ul t ra f ine s l i t

Rice

and

Whitehead

1965) developed a solu-

t ion

for the case of f ine cylindrical

capi l lar ies

In

both

i t was

shown that the electrokinet ic potent ial i s dependent upon electro-

kinet ic

radius

which

is

direct ly

proportional

to the

capil lary

radius.

They ~ u g g e s t e d that

their function be used

in the case

of

ul t raf ine

pores

instead of the c lass ica l Helmoholtz

equations

in which the

potent ial

is

considered

to be

independent

of the capil lary pore)

s ize

Dielectr ic constant D

and

dynamic viscosity, lJ factors. In

the previous

derivat ion,

the

dielect r ic constant,

D

and

the

dynamic

viscosity, ~ o f the

l iquid

in the double layer were taken, as usual,

the same as for bulk solutions.

Some

authors have pointed out that


37/142

24

influence

both

and D. However,

comparison

of theoretical results

with experiment

showed

that

both

effects

are

rather

small

under

most

conditions

Hunter, 1966).

Chattoraj and Bull 1959) and Hoydon

1960) have previously shown that .for

l iquid surface having

adsorbed

films

giving

charge densit ies less than

30,000 esu/cm

2

, a good agree-

ment

with the

true potential

may

be

obtained

by

assuming

a

bulk

value

for

D and

in the double layer.

Surface

charge

densit ies

are

calculated from , potential by

means of Gouy

theory, for uni-univalent electrolyte

a t 25

0

C i t

is

Parriera and Schulman, 1961)

c ~

I

v ::::

134

Sinh 51.5

19)

where

cr is the electrokinetic

charge,

in electron charge/angstrom,

c

is

the sa l t

concentration

in mole/ l i t re , and , is

zeta

potential


38/142

25

experimentally

using

resonance method and Linton and Maoss have formu-

1ated those results

as

D

= 79.80 [

-

4.28

x

10-

3

t - 25) + 2.12 x

10-

5

t

-

25)2

- 4.1 x

10-

7

t - 25)3 ]

Partington

(1954)

has developed

the

following

formula

D

=

78.54 [ - .0046 t - 25) + 88 x 10-

5

t -

25)2

J

He

also

reported measured values for water at

25

0

C

to be 80.37

and

7902. Buchman and Heymann (1949c)

reported

D =

85.5,

80.8 and 76.5

o

for

6,

18 and 30 C

respectively.

Our experiments were conducted in the constant temperature room

where the temperatures were kept a t

a fa ir ly

constant temperature of

80 .5

0

F. At such controlled temperature, the temperature of water

and

solutions

was generally

kept at

25

0

C

.2

0

C.

So,

D

values

in


39/142

Thermodynamics of

Irreversible

Processes

Streaming current and streaming

potent ials

6

Since

a l l electrokinet ic processes are i r revers ib le the thermo-

dynamics

of

i r revers ib le

(non-equilibrium) processes

can be applied

to

derive

general

relat ionships

between

different

electrokinet ic

processes

including

streaming potential and streaming current

(Staverman, 1952; DeGroot, Mazur

and Overbeek,

1952;

Overbeek,

1953b;

Guggenheim,

1957; Taylor, 1960, 1963

and

1964; Zaslavsky and

Ravina, 1965).

When t ransport of l iquid and t ransport of electr ic charge take

place

by

simultaneous

e lec t r ica l

and

hydrodynamic processes, the

e lec t r ica l

and

viscous flows in terfere with each other giving r i se

to i r revers ib le processes (coupling phenomena) known as

e l e t r o ~


40/142

27

conductance, L2l represents e lectrohydraulic conductance, and L12

represents

the

hydroelectr ic

conductance

or

in

view

of

Onsager

re la

t ions,

both

are water-electr ic in teract ion coefficients and equal

each other .

Using another

form

of phenomenological

coefficients we

can write

q

J

L

LI

I

21a)

w p

I =

J

L q L

E

:2

e q e

As we have

sa l t moving in the system, we should include another equa-

t ion and another factor in

each equation.

In

di lu te

solution,

how-

ever, such

as

we

used, i t has

been shown

that the

flow of

sal ts

may

have

negligible

influence on

water flow Michaeli and Kedem, 1961).

The

coefficients in equations 21)

are

related to those

in

equa-

t ion 20) as follows


41/142


42/142

29

because

of

thei r

part icu lar

concern

with the

system under study:

a)

Fluxes

are

l inear ly related

to

driving forces;

i f they are

not, then equations 20), 21) and 22) need to be expanded

to

the non-

l inear case.

b)

Only

hydraulic

and elect r ical

gradients

cause flows;

i f

other

forms

are

acting,

then

addit ional

terms

must

be

included in

the above derivations.

The

requirements

that the forces and fluxes

be

l inear were

checked for

each

run

and

substantiated Figures

25, 26 and

27). In

each case the re la t ion between the discharge q and pressure was

shown

to be

l inear the same as for

the discharge

and streaming poten-

t ia1.

The requirement that

only

hydraulic

and elect r ical gradients

cause the flow was

met

by the experimental conditions. The two side


43/142

30

one of

these

two could be used as a check on calculat ions Tables

and 3 show a summary

of

these

coefficients

with

their

calculated

values

and

their

dimensions Conversion factors between experimental

resul ts and the

quanti t ies required

for computations

of

these coef-

f ic ients

are

shown in Table 1


44/142

CH PTER

IV

EXPERIMENT L PP R TUS

ND PROCEDURE

Apparatus

The experimental

apparatus

is

shown

in Figures

2 and 3.

Details

of

dif ferent

parts are

shown

in Figures

4

and

5. The

paratus

consists

of

three main parts: streaming ce l l s

flow system

and pressure manometers

and

the

e lec t r ica l

ci rcui t and elec t ronic

equipment

for

measurement

and

recording

of

the streaming

potent ia l .

Streaming

cel l

Two ident ical streaming ce l l s were used, one f i t ted with s i lver -

s i lver chloride electrodes and the other with pla t in ized

platinum


45/142

3

Flow system

Deionized conductance)

water

and

sa l t

solut ions

were

stored

in

an elevated pyrex reservoir . The l iquid then flowed to the s ide

tank which was

kept

a t a

desired

constant posit ion on the stand by

bolting i t s support

into

the corresponding holes at equal dis tances

into

the

stand.

To

keep

the

head

constant

in

the tank, the

flow

was

approximately control led by the screw clamp and the outflow was

wasted

through an

outflow system

near the

top

of

the tank. The tanks

have provisions

so

that thermometers and

conduct ivi ty

ce l l electrodes

can be

fixed

through the top

of

the tank. The flow connections are

also

arranged

such as

to

allow

for

spot

samples

to

be

drawn during

flow into or

out

of

those

tanks. Spot samples could be

obtained

also

from the outflow

system. Solutions

from the

tank were

conveyed

to

the two side

compartments

of

ei ther

cel l through

the flow control


46/142

output

from

the electrometer was fed into the y

axis

of a time

base

recorder

Model HR-96

where

the

x

axis

was

an

adjustable

time

of

sweep. The

recorder has

a range

from

.05

in/sec

to 20

in/sec in

steps

with a chart

that

provides 7 x 10 inches

of

plot t ing

area.

Resistance

and

conductivity

of

the

porous plug column

were

measured

with

a

general radio

impedance

bridge

model 16S0-A)e

The

specif ic resistance and conductivity

of the

permeant solution were

measured

by dip

in

a

conductivity

ce l l

model R

16B2.

Details of Procedures

Preparation of sample

water and

solutes

Ottowa sand C109

and

C190

grain size

dis t r ibut ion

curves

shown

in Figure 42, was

leached

repeatedly in boil ing concentrated

hydro-


47/142

34

through the

porous

plate . Also, no t race of a i r

would

be

formed on

the

electrode

which

might cause

change

in

the

electrode

potential .

Very

few workers Goring and

Mason, 1950) concerned themselves

with

the deaerat ion of water, yet proper deaerat ion is essential in ob-

taining reproducible resul ts

and

i t s

importance

cannot be too strongly

emphasized. Chemical reagents used were

purif ied

crys ta l reagents.

Electrodes

Silver-s i lver

chloride

electrode. Silver-s i lver

chloride

elec-

trodes

were prepared from

a perforated

l ight platinum disc

two

inches

in

diameter

and one

mill imeter

thick.

The

disc

had

144

per-

forations

per

square

inch, each .032 inch

in

size. The face of the

disc was

covered with

80 mesh

platinum

gauze spot welded to

i t .

A

platinum wire

was

elect r ical ly spot

welded

to

the back

of the

per-


48/142

35

10 gm K Ag (CN)2) potassium s i lver cyanide per l i t re The

sa l t

was

prepared

af te r

the procedure of Basset

and

Corbette:

add

41

gm

of

s i lver cyanide to an aqueous solution of 20

gm

potassium cyanide.

When the

s i lver

plating solution was used

for

more than one time,

t

was freed from

the

free cyanide by adding di lu te s i lver ni t ra te

solu-

t ion unt i l no

discolora t ion

was

observed.

Silver deposition was

coo-

2

t inued

for

six hours a t 004 rna

cm

) 81 rna. When the pla t ing was

f inished, the electrodes were soaked in concentrated ammonium hydrox-

ide NH

4

0H)

for

three hours and washed with water

for

two days. The

same ce l l vessels were used in chlor idiz ing the electrode

with

the

electrode as

anode

in

the ci rcui t and electrodeposit ion. This process

was performed in the dark

by

turning

the

l ight off and covering the

anode

vessel

with

black.

2

The

current

densi ty was the same .4 m.a/em )

for about 30 minutes using 0.1 N

hydrochloric acid

(HCI)

as

electro-


49/142

36

The gauze was brief ly immersed in a di lu te aqua

regia

cleaning mix-

ture

made

of

three

volumes

of

12 N

Hel,

one

volume

of

16 N

ni t r ic

acid and four volumes of water).

The

electrode

was

then treated with

warm

concentrated

ni t r ic

acid

and

washed in conductance water.

Im-

mediately before plat in izat ion, the electrodes were cathodical ly

electrol ized

in

di lu te

0.01 N

sul fur ic

acid for

10

minutes

and 30

m.a.

The electrodes

were then

washed with double

dis t i l l ed

water

and then plat in ized in the

previously

discussed elect r ic cel l f i l led

with

a two per cent solution of commercial

platinum

chloride in 2 N

hydrochloric acid.

The

current density

was 300

m.a. ~ 1 5

ma/cm

2

for 15

minutes.

The

whole procedure

was

then

repeated while the

electrometer was positioned to the current measurement. The deposi-

t ion

was

hardly

vis ib le

grey and the

no

flow potential

was

about

2

m.v. in

conductance

water.


50/142

7

and

the

chart

cal ibra ted

by

adjust ing the vernier control located in

the

center of

the

attenuator control.

The

mult iple pole

multiple

throw e lec t r ic

switch was then switched

to the desired

cel l Ag-AgCI

and platinum electrode cel ls simultaneously. The

flow

switch board

was then switched to l e t the solution flow from

r ight

to l e f t through

the sample.

The

streaming potent ia l recorded

continuously

on

the

recorder chart . When the

steady s ta te

condi t ion for

both

the

poten·

t i a l

and

pressure head

was reached

the

manometer readings were r e ~

corded and

the

flow

stopped.

The

flow

was then reversed to

flow

from l e f t to r ight and the previous process repeated. This whole

procedure was then repeated at s ix to eight

dif ferent

pressures

yielding several

se ts

of data a t dif ferent values of streaming poten-

t i a l .

In

the f i r s t preliminary runs the ce l l resistance was measured

for

each

pressure

and

found

to be

fai r ly constant

over the period


51/142

39


52/142

Figure

43.

For

dis t i l l ed

water

and

di luted solut ions

of

KCl the

specif ic

conductivity

of

the plug

was

compared

to

that

of the bulk

l iquid thus

indicat ing

a large surface conductance. With

increasing

concentration

of

electrolyte surface conductance effect becomes less

and the greater part

of

the conductivity becomes due to bulk

l iquide

The ce l l

constant ,

C C

=

conductivity of the l iquid x bulk

resis tance of

the

plug) therefore

decreased

unt i l the normality

reached such a

value

that surface conductance was no longer s ign i f i -

cant; C then remained almost constant . From Figure 43 i t

is

evident

that for the

plug, the

ce l l

constant ,

C i s e f fec t ive ly

constant

-5 -2

for

the range

of

normality

= 5 x 10

through

2 x 10 • So a value

for C 0.85 was taken as a representative

constant

for

the f i r s t

sample 1 and C

= 0.510

for sample 2.


53/142

40

with

the

electrodes.

He

also

concluded tha t th is extraneous potent ia l

is

made

up

of

two

phenomenons, one

associated with

the

flow

and

the

other

with polar iza t ion. However, polar iza t ion could be in turn

con-

nected

to

the

flow condi t ions.

The fact tha t polar iza t ion potent ia l

may

stay constant during flow

but may

change once flow has stopped

indicates

that connection. Thus one

can conclude tha t

the

electrode

contr ibutes an arbi t rary EMF to the streaming potent ia l

which

con-

t inues for a period af te r the

flow has

stopped.

Previous methods

of obtaining

streaming

potent ia l

Although

electrode potent ia ls (flow,

polarizat ion)

had

been

noticed some

time

ago,

i t

was not unt i l recently (Zuker, 1959;

Korpi,

1960) tha t thorough

invest igat ions

have

been

made. Most of the pre-

vious

workers

t r ied to eliminate the electrode effects or

render

41


54/142

under

a known almost constant

pressure

and the streaming potent ial

was

read, then the

flow

was

stopped

and

readings

were

taken

af te r

sixty seconds. Next

with

the

flow in

the opposite direct ion the

streaming potent ial was

measured.

The no

flow

potent ial (reading

af te r

s ix ty seconds from the flow stoppage) was added

or

subtracted

as correction to the reading depending

on the

direct ion of the l o w ~

This

procedure produced

a

s t raight l ine re la t ionship between

E and the

pressure, P,

for

solut ions of very low concentrations.

s t r

Yet i t

produced anomalous curves for

solut ions

with concentration

-3

greater

than 10 N.

Also,

the corrected streaming potent ials in

both direc t ions do not seem to

agree

and produce two separate l ines

for E P

relat ionships

not

passing

through the origin, a

case which

is

not

supported

by

the electrokinet ic phenomena.

Korpi

used

a procedure--which was

the primary object of his

42


55/142

condition that the convection current , I t is

balanced

by the con

s r

duction

current

(counter

current) ,

Ie

and

then

the

to ta l

flow

of

e lec t r i c i ty

wil l

be zero; I

s t r

+

Ie

O

I t

is when this condition

prevai ls that one

should stop or s ta r t

the flow

and

record the

read-

ings

which wil l

be the

actual

streaming

potent ia l .

Secondly,

the

electrode contribution

to the


is embodied in the streaming potential readings and prevails

for

a

period

af ter

the

flow

is stopped (Zuker, 1959). That contribution

is

related

to the flow and

proved

to

be

direct ional . So when

the

flow is suddenly

stopped or s tar ted , the sudden increasing or de-

creasing

ordinate is not only the streaming

potential but will also

be the flow potential added or subtracted to the

streaming

potent ial

depending on the flow direct ion.

Modifications the

procedure

43


56/142

=

a. The actual

streaming potential

wi l l

then

be a ; b Korpi s

method

when

used

wil l

give

an

erroneous

value

ei ther Eb E )

or

c

E

f

- E

g

.

Those

two

values wil l algebraically

include,

rather

than

the electrode potent ia l , the effect of

the

response of the recorder.

This factor was

observed by Korpi

and suggested

as

a source of error

in his recorded values.

s

i t could be seen from Figures

10 and

-4

-3

for

10 N

KGl

and

10 N

KGl

i f

Korpi s

method

were used, then

streaming potential

in one

direct ion wil l be

25

per cent to

100

per

cent

more

than

that

in

the other direct ion (compare ordinate

1

and

2

of the f igures) . The eff iciency of our procedure is appreciated for

the cases of relat ively

high

concentration

and

low

pressure

(rate of

flow).

In these cases

the

error effec t

using

the

Korpi method

may

be

more than

the

actual

readings,

and the ordinate considered by

Korpi may

give

negative values .


57/142

45


58/142

streaming current induced due to the

same

different i l pressure head.

Most

of

the

resul ts

obtained

produced

a s t ra ight l ine relat ion-

ship

between both

E

and

I

and the effect ive different i l pressure or

discharge.

These

l ines passed

by

the origin in agreement with the

electrokinet ic

phenomena and

the analyt ical developments.

Flow and pressure

measurements

were found

to

be suff ic ient ly

consistent

for

repeated runs t steady

s t te

conditions. Errors

from

these

sources

i f

any

are within the precision of the tes t

measurements.

Experimental

Results

8unnnary of the

complete

resul

ts from

the

experimental

investi·-

gations

is given in

Figures 5 to

41. Only concluding

results

are

presented

here which i l lus t r t e the principal

features of

the stream-

46


59/142

Experimental resul ts are presented here under the

following

headings:

a) Plug

resistance,

b)

Rate

of

flow

and

applied

differ-

ent ia l

pressure,

c) Phenomenological coefficients and electrokinet ic

couplings,

d) Rate of

flow and developed

streaming potential and

streaming

current,

e) Salt concentration and

par t ic le

s ize effects

f)

Temperature

effects

g) Zeta potent ia l ,

h)

Pract ical

considera-

t ions.

Plug

resistance

The

plug resistance

of

the

cel l

was

measured

for

each run and

results

are

shown

in

Figure

16.

In

th is

figure

log plug

resistance

is plotted against log electro ly te concentration

normality)

in the

permeating

solution are tabulated. From the graph i t

can

be seen

that a l l resistances

are

below 10

5

ohms for concentrations greater

than 10-

4

N

47


60/142

Rate

of

flow and applied di f fe ren t ia l pressure

3

Flow

ra te

means

flow

ra te

per

uni t

time,

i e

ern per

second.

For

calcula t ion of seepage veloci ty in

ern/sec,

i t must be divided by

a factor equal to

the

cross-sectional area mult ipl ied by the porosi ty .

For Sl th is factor wil l be equal

to 19.06

and for S

i t

is equal to

17.20. The applied di f fe ren t ia l

pressure

here

is

the pressure be-

tween

the ends

of

the

sample in centimeters

of

water, for pressure

per uni t length i t

has

to be divided by 7.70. Each

point on

the

graphs shown is the

average

of two readings, one

with

solut ions

flow-

ing l e f t to

r ight

and the

other

with solut ions passing r ight to l e f t

through

the plug

for

a l l values

measured.

Values

for the ra te

of flow

in cm

3

/ sec

are

plot ted as

a funct ion

of applied pressure in ern

of

water on Figures 25, 6 and 7 for con-

ductance

water, sodium

chlor ide and

potassium

chlor ide solut ions

48


61/142

The discharge

ra te

q

will

then

be

P

A

=

K L.

ld

2

3

a

A

E

T

I-a )2

.

.

L

23)

d

0.023

centimeters,

a

=

31 and

\

= 5.50,

and

d

0.0575

centimeters,

a

=

28

and

e

=

6.12

and

(.9..)

for

Sl

p

= 0.20

for S2

From

the previous

experimental resul ts

reported

in

this

study

Fig-

ures 25, 26 and 27),

or

Sl

is on the

average

= 0.485, and

for

S2 =

2.20.

then

49


62/142

clear that there

was no

significant difference in the

p vs q

re la-

.

h

d

tt

. Th1 s means

that

10ns

1p

ue

0

coun

ere

ec

ro-osmOS1S.

q E=o

will

be

the same as g)

q

1=

The

effect

of

sa l t concentration

of

the pore

f luid on the

ra te of

flow showed in

general

that

there

was no

effect

on

the pressure

discharge

relat ionship due

to change

in

elect ro ly te

concentration for

both samples and

solutions

tested.

Phenomenological

coefficients and electrokinet ic

couplings

Phenomenological coefficients were determined from experimental

results

together with

equations (20)

and

(21)

and calculated

values

are

summarized

in

Tables 2 and

3. s these equations involved

both

e lec t r ica l

and

mechanical

units

i t

was

necessary to convert

the

ex-

perimental resul ts into cgs uni ts . These

required

conversion factors

are tabulated in Table 1.

After

having determined those coefficients ,

50


63/142

Also, as

w

have sa l t moving with the system,

then

i t

is

expected

that

the

flux of

sa l t

would

affec t

the

rate

of

flow

Taylor,

1964). The

experimental resul t ,

however, has shown

neither . This

is

due

to

the fact that ,

in

case of saturated coarse

sand,

the linkage

t ransfer coefficients

are

very

small

with

respect

to the direct ones.

Also,

in di lute

solution

such

as the ones

used,

i t has been shown

that Michaeli and

Kedem

1961)

the flow of

sal ts

has negligible

influence.

This

means that

the

flow of

solution

is

determined only

by the

effect ive

pressure, and

this is what

was actu-

al ly

observed.

Rate of flow and developed

streaming

potential

and

streaming current

The values for

streaming

potent ia l , E for different samples

-6 -3

considered

ranged

from

30 x 10 to 240 x 10 vol ts . Streaming cur-


64/142


65/142

53


66/142

concentration. Similar relat ionship in the form of S c l og

N d

where

d is

another constant

value

for

each

size and

c

related

also

to the

sa l t

concentrat ion.

This

could be

seen from

Figures 18

and

20.

In th is

case

the

two

l ines approach

each

other in

a

similar

man-

nero

The

conveyance

of

charges

is l imited

only

to the

diffuse

part

of the double layer , i . e . to the l iquid that can flow with

respect

to the surface.

The

potent ial within such

layer

decreases

pract ical -

ly

in

exponential manner

see

Figure 1).

This diffuse double

layer

has no sharply defined

end

point

but slowly

becomes negligible. I t

is nevertheless convenient

to

assign to i t a thickness designed

usually by 6 This thickness changes

great ly with the normality of

the solution. Hence, when the

sa l t

concentration in the permeating

solution increases i t suppresses

the

double layer , especially

i t s

54


67/142

by both v and then one would

expect

i t to vary l inear ly with log

sa l t concentration. The reason

for

more

rapid

decrease

of

streaming

potent ial E (than

streaming

current

I) due

to

increase in

sa l t con-

centra t ion may be

due

to the fac t tha t E

is

proportional to

both

I

and the conductivity

of

the bulk solution. Hence, rather than being

proportional only

to and the

conveyance, i t

is

also affected

by

change in the conductivity. The l a t t e r is found also to be propor-

t ional

to

log sa l t

concentration. Therefore, one would expect log

E

i Ci= - )

to be

proportional to log normality

of

the bulk solution.

q

According to class ical derivat ions He1moho1tz and Smow10wsky)

the size and shape does

not

affec t

streaming

potent ia l . The o n v e n ~

t iona1 equation

(25)


68/142

6


69/142

were multiplied

by

~

and the resul ted

values were plotted on Figure

19 together with the

experimental resul ts

a

close

agreement was

ob-

tained. The

difference

between

calculated and

observed values, how-

Rl R

thought to

be

due

to the

difference between and -1

c

l

c

2

ever,

is

This difference was

actual ly

about

10

per cent.

Temperature

effects

By temperature effects

i t

is

meant the

effects of

change

in t e m ~

perature

of the sample

and

the

percolating solutions

on the

resul t-

ing streaming potential provided that al l

other

factors are kept con-

s tant .

All the experimental

resul ts

reported

in

these

have

been

ob-

tained by keeping

the

whole apparatus in the constant

temperature

room with the l iquid solutions always l e f t

in

the room unt i l

their

temperature

was

the

same

as that of the room, i . e . at

80

lOF. How

ever, two special runs were made with

the temperature in the

room

57


70/142

order

of

-0.20

millivolt/oC.

Variations due

to temperature

effects

may

be related to the increasing thickness of

the double

layer with

the

increase in

temperature.

I t also could be

due

to changes in

die lec tr ic ,

D, and

viscosity with

change in

temperature.

As

. dD ,

I

hown previously Chapter I I I , dT .30 was

reported

for conduc-

tance water.

Zeta potential

Of

paramount importance

in

the quanti ta t ive study represented

here is the evaluation of

the

zeta

potential ,

As mentioned be-

fore,

C

is

the

potential

at

the

plane

of shear

(Figure

1), that

is

the potential at the

boundary between

the solvent adhering to the

particles at rest and

that

which moves with respect to i t .

Streaming current is given previously as

58


71/142

Calculated values for

1 and 2 for

KCl are tabulated

in Table 4

and

were

plotted

as

a

function of KCl concentrations Figure

22 _

s

shown

in this f i gu r e , decreased l inearly with the logarithm of

the sa l t concentrations wi t h values higher for

S2-

Two separate

l ines f i t ted the calculated

values for

1 and 2

These two l ines

are not paral le l but

approach

each

other as

sa l t concentration de-

creases.

Helmoholtz-Smowluchowski

class ical formula

is

usually used in

ca. lculat ing,

potential from streaming potential

measurements_

This

equation

has been amended by several

authors Briggs, 1928; Rutgers,

1940 and

there is

a general

agreement now Buchanan and

Heymann,

1949c) to

use

the equation

JTT}

= D

Ek

P

29)

59


72/142

considered

to

avoid

surface

conductance problems.

Buchanan and Hey-

man

suggested the function

where l l variables as defined

before.

The equation s t i l l includes

c, which would affect the precision of calculation. The Davis and

Ridea1

re la t ion

is

applicable

only

for

capil lar ies

and

needs

to

be

adjusted

to

be

used

for porous materials .

In

our procedure we

use

TT

= ))

30)

This

is believed to constitute

a

satisfactory

method

of finding

.

Besides

avoiding conduction

problems,

i t pOints out the effect of

both size

and shape

of

the media on

.

Our calculated

values

for

for

10.

4

N KC

is

190 m.v. This is in close agreement

with

the

60


73/142

material .

Sedimentary

rocks

are

more soluble than igneous rocks.

Because of

the ir

high

solubi l i ty

combined

with the ir

abundance in

the

ear th s crust , they furnish a major portion

of the soluble con-

st i tuents

to ground water. Out of the commonly added cations due to

sediment rocks

sodium,

Na, and calcium, K, have the highest

possibi l i -

t ies .

Bicarbonates, carbonates and sulfates are the corresponding

anions. Chloride,

CI,

also occurs to a certain amount, with sewage.

connate waters

and

intruded sea water

as i t s

major

contributing

source

Foster, 1942; Todd, 1960).

For the experimental resul ts reported in this study, two sal ts

NaCl and KGI were used as solute in

the

test solutions. For each

run,

one at a time each of the two sal ts at a specified concentra-

t ion was used. The normality of the solutions was used

to express

their sa l t

concentrations.

Therefore, i t was fel t

necessary

to test

61


74/142

solut ions. This

suggests

the feasibi l i ty

of the

use

of this proce-

dure

for

natural ly exist ing

ground water with dissolved combined

sal ts as

well

as solutions

with

one soluble sa l t

Considering the di f f icul t ies

connected

with

the determination

of the normality of these natural waters, an alternative method to

the

normality was

thought

to be used to express the

concentration of

solutions. This

is done

by

measuring

the electr ical conductance

of

the solutions. When the experimental resul ts for E, I and q for

these simulated

natural

ground waters

were

compared

to

those

for

NaCl

and K l

solutions

tested

before, comparable results were obtained

provided

that

conductance of the

solutions

was taken

as

a parameter

Figure 24).


75/142

CH PTER

VI

CONCLUSIONS ND SUGGESTIONS FOR FURTHER RESE RCH

Conclusions

Analytical derivations

and

analysis of

the

experimental

inves-

t igations, together

with

the subsequent interpretation

and

discus-

sions

of the

results from

this study,

suggest the following conclu-

sions with respect to streaming

current and

streaming

potential

in-

duced by

water

flow through porous media.

1. The flow through samples

tested

followed Darcy s law and

the ratio

of

petmeability

coefficients

of

different samples agreed

with

Kozeny Carreman equation,

2. There

was no significant

difference in flow

versus pressure

6


76/142

in the form

of

I = Clq and E = c

2

q are suggested

in

which C

I

and C

2

are dependent

upon

sa l t concentration and

par t ic le

size diameter.

5. Both streaming current , I and streaming potential , E, were

affected

by

sa l t concentration

normality and

less affected

by

the

type

of

ions

in

the solut ion.

An increase of

soluble

sa l t

con-

centrat ion resul ted

in a

decrease in

both E and

I .

A

sharp

decrease

was observed in case of streaming

potential whereas

a

gradual

de-

crease was

observed

in the case of streaming current .

6.

Increase in soi l particles

effective

diameter,

a t

a con-

stant sa l t concentration, caused a

decrease

in both a and S

where

I

S

= - •

q

This

decrease was more for dilute

solu-

tions.

These

relat ionships may be expressed

by

log a

= a

long

N b

and S = c

long

N a where a and c related to sa l t

concentration,

band d related to part ic le size.

6


77/142

easy

procedure for cases

where such

effect is of a significant amount.

11.

Analytical relat ionships

developed together with the

experi-

mental

work could probably be used as the

basis of re l iable

method

for

measuring

the rate

of flow

through

porous

materials.

Suggestion for Further Research

Experimental investigations in

this

study

were

limited only to

sand samples

of

effective diameters

of

0.230 and

0.575 millimeters.

Permeating

solutions

tested

were conductance water sodium

chloride

and potassium chloride solut ions.

Combination

of

sal ts as

solutes

in

the

permeating

solutions

were

tested in order to determine the

pract ical i ty of the proposed procedure

for naturally

exist ing waters.

In view of these experimental l imitat ions complete

information

on

the

practical aspects

of

the

flow streaming

potential and streaming


78/142

66


79/142

electrokinetic coupling

effect

was

negligible.

5. Some

studies

should

be

devoted to different problems that

will be

encountered

in

the

field

use

of the suggested

procedure,

Two

of these

problems

will be:

a)

To develop

a rel iable

procedure

for

placing

electrodes

in si tes without disturbing the media through which rate of flow

is to be

determined;

b)

To

isolate

part icular s trata f i t ted to these elec-

trodes

without disturbing the

general flow

pattern

of

the

flow.

6.

Util izat ion of the suggested

procedure

for

determining the

direction

of

the

flow

should be

experimentally evaluated. This

could

be done by placing

similar

electrodes

at

different positions in a

sample through which liquid is flowing. t is expected that the

highest induced E

or I would be recorded

between

the two electrodes


80/142

68


81/142

Buchanan,

A S.,

and E. Heyman. 1949a. The

electrokinetic potential

of barium sulphate.

Proceeding

of

the Royal

Society of

London

195A:152.

Buchanan, A S. , and E. Heyman. 1949b. Electrokinetic potential of

sparingly soluble sulfa tes . Journal

of

Colloidal Science,

Part I I I 4:137, 151.

Buchanan, A S.,

and E. Heyman. 1949c.

Determination of electro

kinetic potential

in concentrated s o l u t o n ~ by

the

streaming

current

method.

Journal of Colloidal Science

4 : l 5 7 ~

Bull, H B., and R. A Gortner. 1932. The effect of part ic le size

on

the

zeta

potential . Journal of Physical Chemistry

36:111.

Burgreen,

D.,

and F. R Nakache.

1963.

Electrokinetic flow in

capillary elements. Aeronautic System

Division

Technical

Documents Report 63-243.

Burgreen,

D.,

and

F.

R

Nakache. 1964.

Electrokinetic

flow

in

ul t raf ine capillary

s l i t s . Journal

of Physical Chemistry

68:

1084.

Butler, J . A V 1951. Electr ical phenomena at

interfaces.

The

Macmillan Company New

York, p. 30.

Cermak J.

E.,

and L. V Baldwin. 1963. Measurements of

Turbulence


82/142

70


83/142

Gurney,

R. W. 1953. Ionic processes in

solution.

McGraw-Hill,

New

York.

Haggis, H.,

J .

B.

Hasted,

and

A.

S.

Buchanan.

1952.

Dielectr ic

depression caused

in water by

addit ion of elect ro ly te . Journal

of

Chemical Physics 24:575.

Ham A. J . and E. D. M. Dean. 1940. An examination

of

elec trokinet ic

charge

as a function of the thickness of

the double layer.

Transaction

of the Faraday Society 36:53.

Harr,

M.

E.

1962.

Ground

Water

and

Seepage.

McGraw-Hill

Company,

New

York, p. 4.

Hasted, J . B., D. M. Robinson,

and

C.

H.

Collie.

1948.

Dielect r ic

propert ies of

aqueous

ionic

solut ions

pat 1 Part 11.

Journal of

Chemical Physics 16:1.

Helmoholtz,

H.

1879. Ann.

Physik

Vol. 7, Part 3,

p.

337; Gesamrnte

Abhanglungen,

Vol.