Electro-kinetic phenomena and their application to soil mechanics

Publisher’s version / Version de l'éditeur:

Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.

Questions? Contact the NRC Publications Archive team at

PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.

https://publications-cnrc.canada.ca/fra/droits

L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.

Technical Translation (National Research Council of Canada), 1948-02-25

READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.

https://nrc-publications.canada.ca/eng/copyright

NRC Publications Archive Record / Notice des Archives des publications du CNRC :

https://nrc-publications.canada.ca/eng/view/object/?id=20397384-42ac-47a2-be2c-8ee92712be88 https://publications-cnrc.canada.ca/fra/voir/objet/?id=20397384-42ac-47a2-be2c-8ee92712be88

NRC Publications Archive

Archives des publications du CNRC

For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien DOI ci-dessous.

https://doi.org/10.4224/20331591

Access and use of this website and the material on it are subject to the Terms and Conditions set forth at

Electro-kinetic phenomena and their application to soil mechanics

~ * * n , Q n n * c . * c . i . , . - , r*" *.-,,. .i..--.l--r."* ,..l".mi.%-.V. r .. .,r-

I

i

NATION& RESURCH COUNCIL OF CANADA

AND THEIR APPLICATIOLV TO SOIL i6ECHANICS (Elektrokinetische Erscheinungen und ihre

Anwendung i n der ~odenmechanik)

Dip. Ing.

W.

Schaad and

Ing. Dr. Sc. Techn. Re Haefeli.

translated by

D.A. Sinclair

This i s the F i r s t o f the Series of Translations Prepared for the Division of Building Research.

T n i s i s a r e p r t f r o ~ n t h e V e r s u c n s a n s t a l t f& Yiasser- bau und iirdbau (Fiesearch I n s t i t u t e f c r a y u r a u l i c s and Eartnworks) a t t n e Eidgcnossische Technische iiocLischule

( F e d e r a l I n s t i t u t e o f Technology), Zuricil, Switzerland. The paper has appeareu i n t h e Sciiweizerische k u z e i t u n g , 6 5 t h year, Wo. 16 t o I d , 1948. The t r a n s l a t i o n i s p u b l i s h e d w i t h t h e kind a p p r o v a l o f t h e a u t h o r s .

The N a t i c n a l Research Council through i t s 3 i v i s i o n o f a u i l d i n g Research has a c l o s e l i n k w i t h t h i s I n s t i t u t e which h a s been v i s i t e d by ti^:' w r i t e r and by Jr. G. J. K l e i n

o f t h e 3 i v i s i o n o f kleciianical hngineering,

The S o i l idechanics S e c t i t m o f t h e Divisicl~l o f j u i l d i n g Research l o o k s formard t o developing *.or:; i n t n e f i e l d o f e l e c t r o - k i n e t i c piieno,nena i n connection w i t h s ,il p r o p e r t i e s , The su'3ject i s a s p e c i a l i z e d one b u t a p p e a r s t u nave s p e c i a l i n p o r t a n c e i n r e l a t i ~ n t o some o f t h e f i n e grained s o i l s which a r e so comnonly found i n Canada. L i t e r a t u r e on t h e s u b j e c t i s s c a r c e and f o r t h i s r e a s o n t h e p u b l i c a t i ~ a o f

t h i s t r a n s l ~ t i o n i s e s p e c i a l l y welcome,

Robert E', Legket, D i r e c t o r ,

Page

-

1

Tech, Trans. TT-61 ELECTRO-KImTIC PHENO?vEGNA A I D THEIR

APPLICATION TO SOIL MECHANICS

I INTRODUCTION

S i n c e 1935 a new branch of s o i l mechanics h a s come i n t o e x i s t e n c e t h r o u g h t h e a p p l i c a t i o n of a new p h y s i c a l dimension ( i n a d d i t i o n t o t h e u s u a l liicchanical o b s e r v a t i o n , t r e a t m e n t and v a l u a t i o n of s o i l t y p e s ) , namely, e l e c t r i c i t y . I t i s obvious, o f c o u r s e , t h a t t h e chemical p r o p e r t i e s of t h e s o i l types must a l s o be t a k e n i n t o c o n s i d e r a t i o n , s i n c e t h e e f f e c t s o f e l e c t r i c a l c u r r e n t s on porous ground forma- t i o n s a r e accompanied by chemical r e a c t i o n s .

One of t h e f i r s t f i e l d s of a p p l i c a t i o n was the a t t e m p t t o s t r e n g t h e n s o i l s by e l e c t r o - c h e m i c a l means and by t h e a s s o c i a t e d c o n v e r s i o n of c e r t a i n i o n groups, and t h u s t o s t a b i l i z e t h e i r chemical g r a i n s t r u c t u r e s permanently by accu u l a t i o n o f i n s o l u b l e o r o n l y s l i g h t l y s o l u b l e substances1)

'y.

Another p o s s i b l e a p p l i c a t i o n i s t h e u s e o f d i r e c t e l e c t r i c a l c u r r a n t s t o e f f e c t t h e d r a i n a g e o f f i n e - g r a i n e d s o i l s . H e r e a f t e r t h i s method w i l l be r e f e r r e d t o a s " e l e c t r o - d r a i n a g e w 8 ) to 1 6 ) The p r a c t i c a l d i f f i c u l t i e s e n c o u n t e r e d i n t h e d r a i n a g e of f i n e - g r a i n e d s o i l t y p e s , t o g e t h e r w i t h t h e a t t e m p t s made i n Germany t o o b v i a t e t h e s e d i f f i c u l t i e s by e l e c t r o - k i n e t i c p r o c e d u r e s , l e d t h e s o i l d i v i s i o n o f . t h e Hesea ch I n - s t i t u t e f o r H y d r a u l i c s and Earthworks a t t h e E. T o Hexf t o u n d e r t a k e a s y s t e r r a t i c c o n s i d e r a t i o n o f t h e problem i n a l l

i t s r a m i f i c a t i o n s , The c o n v i c t i o n t h a t the s t u d y was one o f p r o c e s s e s and methods of g e n e r a l s i g n i f i c a n c e r e s u l t e d i n a r e q u e s t f o r f i n a n c i a l s u p p o r t o f t h e s e p r o j e c t s by t h e Confederate Foundation f o r t h e A vancoment o f t h e Swiss

P

Economy by S c i e n t i f i c ResearchXJf

.

A f t e r a c o n s i d e r a b l e sum had been g r a n t e d t o c a r r y o u t a d e f i n i t e program ( f o r which we w u l d l i k e t o e x p r e s s o u r thanks t o t h e Foundation a t t h i s t i m e ) t h e work was s t a r t e d w i t h t h e s t u d y o f e l e c t r o - d r a i n a g e . h

x )

TransX'ator I s Note: E i d g e n o s s i s c h e

-

_-

Technische- Hochschule

-

Confederate Technical U n i v e r s i t y .

u)

~ r m s l a t o r Is Note: E i d g e n o s s i s c h e S t i f t u n g z u r Foerderung d e r

S c h w e i z e r i s c h e n V o l k s w i r t s c h a f t durch w i s s e n s c l l a f t l i c h e Forschung.

Page

T e u r ' a :'I-61

A t the b e g i n n i n g o f f n v e s t i g a t i o n s i n t o c i v i l

e l : , , i L ~ e ~ r 3 i i i g l i t e r a t u r e

,

i t

was found t h a t t h e t h e o r e t i c a l p r i n c i p l e s of e l e c t r o - k i n e t i c s were h a r d t o f i n d , o r , i n some c a s e s , were j u s t n o t a v a i l a b l e , The r e s e a r c h program s e t up i n 1943

-

b e g i n n i n g w i t h e l e m e n t a r y experiments on c a p i l l a r i e s

-

aimed a t c l a r i f y i n g a11 problems I n t h i s f i e l d , Some examples o f t h e s e problerns a r e : t h e e f f e c t of e l e c t - r i c i t y on t h e v i s c o s i t y of w a t e r ; t h e v a l i d i t y o f Darcyos

law; t h e e f f e c t s of e l e c t r i c a l and a t m o s p h e r i c p r o c e s s e s on c a p i l l a r y t e n s i o n s t o g e t h e r w i t h t h e i r s i g n i f i c a n c e i n s o i l mechanics; the mechanics o f the d r a i n a g e p r o c e s s ; t h e e f f e c t

of e l e c t r l c i t y on flow o f w a t e r t h r o u g h p o r e s and t h e r e - s u l t i n : ~ , a c c e l e r a t i o n of s e t t l e m e n t s , C l o s e l y r e l a t e d t o t h i s i n v e s t i y ; a t i o n was a n e x h a u s t i v 2 s t u d y of p r e v i o u s e a r c h e s i n t h e f i e l d of e l e c t r o - o s m o s i s , which r e p r e c c . t h e d e c i s i v e cause of t h e e l e c t r o - d r a i n a g e e f f e c t ,

Thc

t h e o r e t i c a l problzrns i n t h i s l a t t e r a f i e l d were c l a r i f i e u t o a c o n s i d e r a b l e e x t e n t by t h e p r e v i o u s work and

w f l P

t h e r e f o r e be d e a l t w i t h f i r s t t h e p r e s e n t p u b l i c a t i o n ,

Our thanks a r e p a r t i c u l a r l y due t o the Z e l l

A,G, L i g n i t e Company and i t s e n g i n e e r ,

Mr,

C,

B a e s s l o r , and

also t o t h e f i r m of S w i s s b o r i n g , a l l of wI-lorn displaynvd a l i v e l y i n t e r e s t i n t h e problem, 'Ille former company made i t

p o s s i b l e f o r p r a c t i c a l experiments t o b e c a r r i e d o u t i n an a r e a s u i t a b l e f o r t h e a p p l f c a t i o n of t h e e l e c t r o - drainage

t e c h n i q u e , These e x p e r i t n e ~ l t s were s u p e r v i s e d b y D i p ,

C,

B l a t t e r of S w i s s b o r i n g i n c o - o p e r a t i o n w i t h t h e s o i l I Y . ~ .l ,lc=s

l a b o r a t o r y , The S w i s s b o r i n g

f i r m

i s the patent, h o l d e r i ; , ' a s p e c i a l e l e c t r o - d r a i n a g e ,.,t tiled,

I1 PRINCIPLES ---- OF

---

ELECTRO-DRAINA-GE

The p r i n c i p l s of a c t i v a t i n g t h e s:r:wr,3

water by a d i r e c t e l g c t r i c a l c u r r e n t I s i l l u s t r a t e d

In

F i g u r e l o Suppose t h a t

an

e l e c t r o d e , f o r example, a gas p i p e i s frnrnepsed i n a f i l t e r w e l l , t h a t

a

second e l e c t r o d e i s d r i v e n i n t o the ground, and t h a t t h e two e l e c t s o d s s a r e connect3d t o a d i r e c t c u r r e n t s o u r c e , An e l e c t r i c a l f i e l d

w f l l t h e n be produced i n the ground, A p a r t of t h e e l e c t r i c a l . c u r r e n t w i l l now flow from the p o s i t i v e t o .the negatf-ve

e:lzetrode t h r o u i ~ h th e ground water" o r through t h e s o i l be-

ii'23.t;h the ground water t a b l e . I n f i n e - g r a i n e d s o i - I s , from which

gsouxzd :.:step e i t h e r cannot b e d r a i n e d a t a l l by t h e s r d f n a r y

,.,,,.:

;;Itii13.~a.l

methods, o r car1 b e d r a i n e d orlly w i t h d i f f i c u l t y g

e l e c t r 6 - o s m o s i s t a k e s p l a c e i n thz c a ~ i l l a r i a s . This

phenomenon w f l X b e e x p l a i n e d l a t e r , For t h i s r e a s o n , If s h e d i r e c . t l . o n of t h e c u r r e n t i s s u i t a L l , ,liur?.n, tho w a t e r mole-

Page

-

3 Tech, Trans,. . TT-61 of t h e e l e c t r i c f i e l d l i n e s t o t h e w e l l , . Consequently a much g r e a t e r movemant o f w a t e r t a k e s p l a c e t h a n t h a t b r o u g h t about b y t h e n a t u r a l h y d r a u l i c g r a d i e n t , The e x p l a n a t i o n of t h , i s movement i s t o be found i n the p r i n c i p l e of c o n t a c t p o t e n t i a l d i f f e r e n c e ( F i g , 2 ) . When two b o d i e s o f d i f f e r e n t m a t e r i a l come t o g e t h e r e l e c t r i c a l f o r c e s a r e g c n e r a t e d between t h e i r r e s p e c t i v e e l e c t r o n s o r i o n s which a r e j o i n e d , b u t which, n e v e r t l - l e l e s s , a r e s t i l l mobile t o some e x t e l t , A d i f f e r e n c e of e l e c t r i c a l p o t e n t i a l o c c u r s a t t h e d i v i d i n g s u r f a c e , making the con- t i g u o u s b o d i e s c o n p a r a b l e t o a p l a t e c o n d e n s e r , analogous phenomenon i s c l e a r l y r e c o g n i z a b l e when two m e t a l s w i t h a

r e l a t i v e l y l a r g e d i f f e r e n c e o f o t e r l t i a l a r e c o n n e c t e d by

an e l e c t r o l y t e ( e , g , , t a p w a t e r

7

which c o n d u c t s t h e c u r r e n t from one m e t a l t o t h e o t h e r , Owing t o t h e d i f f e r e n c e o f po- t e n t i a l a n e l e c t r o l y t i c p r o c e s s t a k e s p l a c e r e s u l t i n g i n t h e f a r a i l t a r c o r r o s i o n t h a t o c c u r s a t t h e c o n t a c t p o i n t s of t h e d i f f e r e n t m e t a l s 1 7 ) , Table T i n whjch t h e s o - c a l l e d n o r -

mal p o t e n t i a l s of s e v e r a l m e t a l s a r e l i s t e d w i t h r e f e r e n c e t o hydrogen, shows t h a t t h e s e p r o c e s s e s ' a r e a s s o c i a t e d with c o n s i d e r a b l e d i f f e r e n c e s of p o t e n t i a l , The b a s e r m e t a l s show a g r e a t e r tendency t o d i s s o l v e i n t h e prc?s&ce o f e l e c t r o l y t e s t h a n t h e p r e c i o u s o n e s , . When two d i f f e r e n t m e t a l s a r e brou:$>ht simultaneously i n t o c o n t a c t w i t h an e l e c t r o l y t e t h e m e t a l of lower p o t e n t i a l w i l l d i s s o l v e ,

An analogous phenomenon a l s o t a k e s p l a c e on c o n t a c t of two non-me t a l s , Thus, f o r example, when w a t e r com3s i n t o c o n t a c t with a n o t h e r s u b s t a n c e , t h e s o i l i n o u r c a s e , a d i f f e r e n c e of p o t e r l t i a l a r i s e s i n t h e s o - c a l l e d boundary l a y e r , I n p h y s i c a l c h e m i s t r y t h i s d l f f e r e n c e i s d e - s i g n a t e d a s t h e e l e c t r i c a l p a r t i c l e p o t e n t i a l The sub-

2

s t a n c e h a v i n g t h e h i g h e r d i e l e c t r i c c o n s t a n t becomes p o s i t i v e l y cl a r g e d i n e l a t i o n t o the s u b s t a n c e w i t h t h e lower d i e l e c t r i c c o n s t a n t 18f S i n c e w a t e r , a s compared with.many o t h e r s u b s t a n c e s , h a s a r a t h e r h i g h d i e l e c t r i c c o n s t a n t o f a p p r o x i m a t e l y 80, i t u s u a l l y becomes p o s i t i v e l y charged i n r e l a t i o n t o t h e s o i l , I f t h e c o n d i t i o n s i n an i d e a l i z e d c a p i l l a r y ( F i g , 3 ) a r e now c o n s i d e r e d , t h e n a t t h e v e r y t h i n "boundary l a y e r f ' ( i n c a p i l l a r y p h y s i c s , i n c o n t r a s t t o hydrau- l i c s , t h e t e r m ''boundary l a y e r r 1 means t h e zone o f c o n t a c t be- tween a f l u i d and a s o l i d m a t e r i a l ) between t h e f l u i d .in t h e c a p i l l a r y and t h e w a l l m a t e r i a l , a double l a y e r o f e l e c t r i c a l c h a r g e s i s formed which a c t s a s a condenskr and produces t h e c o n t a c t p o t e n t i a l ( o r e l e c t r i c a l p a r t i c l e p o t e n t i a l )

5

a l - r e a d y r e f e r r e d t o ,

Page

-

4

Tech, T r a n s , TT-61

I f

an

electrical p o t e n t i a l i s now s e t u p a % t h e ends of t h e c a p i l l a r i g s by e l e c t r o d e a c t i o n , t h e n t h e p o s i t i v e boundary l a y e r c h a r g e s i n t h e w a t e r , f o r example, w i l l be d r i v e n away from t h e p o s i t i v e e l e c t r o t i e towards t h e n e g a t i v e by t h e e l e c t r i c a l f i e l d p r o d u c e d be tween them, T h i s 1s t h e c a u s e of t h a t movement o f w a t e r p a r t i c l e s i n f i n e c a p i l l a r i e s u n d e r t h e i n f l u e n c e o f e l e c t r i c i t y \ v h f c h i s known a s " e l e c t r o - o s m o s i s "

.

The w a t e r m o l e c u l e s j u s t e n t e r i n g thl3 c a p i l l a r i e s a r e c o n t i n u a l l y b e i n g y e c h a r g e d i n t h e p r o x i m i t y o f t h e wa1.i f: thus p r o d u c f n g a c o n t i n u o u s movement of w a t e r , A m o l e c u l a r p r o c e s s o f t h i s n a t u r e i s

a l s o completed i n t h e m o l e c u l e s which occupy p o r e s J and i t

c a n a l s o be a p p l i e d , t h e r e f o r e , t o t h e e l e c t r o d r a i n a g e o f r e l a t i v e l y f i n e - g r a i n e d , p o r o u s s o i l f o r m a t i o n s ( F i g o

1 1 ,

T h i s t y p e o f movemmt m u s t S e c l e a r l y d i s t i n g u i s h e d f r o m t h e t r a n s f e r o f i o n s i n e l e c t r o l y t e s , I.,klich l i k e w i s e t a k e s p l a c e u n d e r t h e i n f l u e n c e o f a n e l e c t r i c a l c u r r e n t i n f i n e diaphrae;ms i n c o n j u n c t i o n w i t h e l e c t r o - o s m o s i s C l o s e l y r e l a t e d t o t h e phenomenon o f e l e c t r o - osmosis i s t h a t o f " e l e c t r o - c a t a p k i o r e s i s " , , by which i s meant t h e t r a v e l o f p a r t i c l e s s u s p e n d e d i n a f l u i d due t o t h e e f f e c t o f an e l e c t r i c a l c u r r e n t , Another r e l a t e d p r o c e s s

fe

t h a t o f " e l e c t r o d i a l y s i s " , i n which e l e c t r o l y t e s p a s s t h r o u g h membranes t h a t a r e i m p e r v i o u s t o c o l l o i d s , T h i s i s u s e f u l i n t h e s e p a r a t i o n o f m i x t u r o s o f e l e c t r o l y t e s and c o l l o i d s o S t i l l a n o t h e r d i v i s i o n i n t h e s a m e c a t e g o r y i s found i n t h s i n v e r s e phenomena t o t h o s e o f e l e c t r o - o s m o s i s and c a t a p h o r e s i s , t h e s o - c a l l e d " f l o w c u r r e r l t s " ( S t r o e m u n g s s t r o e m e ) , i , e o , e l e c t r i c a l c u r r e n t s p r o d u c e d by h y d r a u l i c c a p i l l a r y f l o w s , When w a t e r i s f o r c e d thlaough a d i a p h ~ a g r n w i t h f i n e p o r e s an e l e c t r i c a l c u r r e n t i s g e n e r a t e d t o g e t h e r w i t h a n e l e c t r l c a Y f i e l d , due t o t h e a s s o c i a t e d t r a v e l o f t h e f l u i d p a r t i c l e s c h a r g e d by t h e c o n t a c t p o t e n t i a l a t t h o b o u n d a r y l a y e r , Such f l o w p o t e n t i a l s a l s o o c c u r when t h e p a r l i i ! P -: s u s p e n d e d i n a f l u i d a r e t r a n s p o r t e d , A 1 1 t h e phenomena m e n t i o n e d h e r e a r e comprehended i n t h e g e n e r a l t e r n " e l e c t ~ o c - k i n e t i c p r o c e s s e s " , P e r h a p s t h e e x p l a n a t i o n o f t h e vepy c o n t r o - v e r s l a l p r o b l e m o f t h e " d i v i n i n g r o d n i s t o be f o u n i n t h e 1 9 8 e l e c t r i c a l f i e l d s p r o d u c e d b y t h e s e f l o w c u r r e n t s

.

It i s c o n c e i v a b l e t h a t t h e n e r v o u s s y s t e m s o f s e n s i t i v e p e o p l e r e a c t t o such f i e l d s o f low i n t e n s i t y , j u s t as s e n s i t i v e n a t u r e s r e s p o n d u n d e r c e r t a i n a t m o s p h e r i c c o n d i t i o n s t o i n - f l u e n c e s t h a t c a n n o t y e t be d e m o n s t r a t e d b y p h y s i c a l means,

The f i , ? l c i s produced b y f l o w c u r r e n t s would a l s o e x p l a i n why t h e a c t i v a t i o n o f t h e d i v i n i n g r o d d o e s n o t o c c u r i n t h e p r e s 3 n c e of w a t e r f l o w i n g i n o p e n c h a n n e l s o r i n p i p e s , The

Page

-

5

Te ch

.

T ~ a n s . TT- 61

flow c u r r e n t s =ld t h e i r f i e l d s a r e o n l y produced when w a t e r o r f l u i d s p a s s through masses c o n t a i n i n g f i n e p o r e s , uvhereas no such p r o c e s s can a r i s e i n homogeneous masses of w a t e r

owins t o tl e l a c k o f numerous s u r f a c e s with c o n t a c t p o t e n t i a l s . The d i s c o v e r y of e l e c t ~ o - o s m o s i s d a t e s back

t o t h e beginning of the n i n e t e e n t h c e n t u r y , A b r i e f summary of' f t s d i s c o v e r y and de elopmznt i s gfven i n t h e works of I l l i g and Schoenfeldte0Y. The phenomenon was observed by

Reus i n the y e a r 1807 b u t he was s t i l l u n s b l s t o e x p l a i n i t 2 1 j 0 The dl s c o v e r y was followed by r e s e a r c h e s of many famous p h y s i c i s t s and chemis s who s t u d i e d the problem

in-

5

t e n s i v e l y , Thus \qiedemanne2

,

f o r example, e s t a b l i s h e d t h e s o - c a l l e d Viiedemann number from t h e knowledge t h a t t h e m o u n t of f l u i d t r a n s m i t t e d through a porous diaphragm by e l e c t r o - osmosis i s p r o p o r t i o n a l t o the s t r e n g t h o f the e l e c t r i c cur- r e n t , The ~liedemann number r s p r e s e n t s t h e r a t i o o f the amount of t r a n s m i t t e d S l u f d t o t h e s t r e n g t h of c u r r e n t , Numerous i n v e s t i g a t ons follorved by famous r e s e a r c h workers s u c h a s H i t t o r f

23i,

~ u i n c k e 2 4 ) ~ r e u n d 2 5 1 , ~a;c:~.?fi), F'errinz?),

ruse^^),

ernan ant^^

f D 38), and o t h e r s . I n Ciuincke 4s o b i t u a r y ( d o 1924) ~ a l a e h n e 3 1 ) mentioned t h a t t h e d i s c o v e r y o f the e l e c t r o - k i n e t i c p r o c e s s e s , t o g e t h e r w i t h t h e e a r l i e s t e x p e r i - ments i n t h a t f i e l d , caused t h e same e x c i t e m e n t a s t h e Zaterc

d i s c o v e r y o f t h e B e c q u e ~ e l r a y s , which r e s u l t e d i n t h e 1so- l a t i o n o f radium b y the C u r i e s ,

The m a t h e m a t i c a l - p h y s i c a l f o m u a t f o o f t h e

5

phenomenon was f i r s t u n d e r t a k e n by ~ e l m h o l t z ~ ~ a

337

who succeeded i n g r a s p i n g the p r o c e s s i n i t s e s s e n t i . a l s b y ob-

s e r v a t i o n of t h e e l e c t r i c a l f o r c e s , A s l i g h t omissfon on h i s p a r t , the f a i l u r e t o take the d i e l e c t r i c co s t a n t s i n t o

account, was 1 t e r c o r r e c t e d , f i r s t by Perrfne7Y, t h e n by

S r n o l u ~ h o w s k i ~ ~ ~ . This l a t t e r s t e p was a l s o a r e s u l t of a

f u r t h e development of t h e t h e o r y and i t s c r i t i c a l e l u c i d a t i o n . L ~ r n b ~ ~ f developed a t h e o r y which d e v i a t e d somewhat from

H e l m h o l t z ~ s , b u t which l e d e s s e n t i a l l y t o the same c o n c l u s i o n a s t h a t of He1rLilloA tz-Perrin-Smoluchowskf. F i n a l l y t h e l a t t e ~ t h e o r y , althoui;,h t h e r e was s t i l l no e x p l a n a t i o n o f p a r t i c u l a r a s p e c t s of t h e d i f f e r e n t fews, was t a k e n up by such r e -

s e a r c h e r s a s F r e u n d l i c h 3 ? j , f o r example, whf l e Lamb 's con- c e p t i o n d i d n o t t a k e h o l d , The modiffed HelmhoBtzian t h e o r y i s r e g a r d e d as s tandard today, a1 though t h e p o f n t s of con- t r o v e r a y between t h e e a r l i e r i n v e s t i g a t o r s s t i l l e x f s t , It should be mentioned, h o w ~ v e r , t h a t t h e s e d i f f e r e n t p o i n t s o f view i n no way h i n d e r e d p r a c t i c a l a p p l i c a t i o n i n p h y s i c a l c h e m i s t r y , and f o r t h a t r e a s o n , probably, they were n o t pursued f ' u r t h e r o

Page

-

6 Tech, T r a n s , TT-6%

I n

he r e l a t e d f i e l d o f c a t a p h o r o s i s Debye and I3ueckelJ6),

39j

d e v e l o p e d t h e l a w s f o r t h e r a t e o f e l e c t r o - c a t a p h o r e t i c removal o f s u s p e n d e d p a r t i c l e s on t h e b a s i s o f p h y s i c a l o b s e r v a t i o n , These l a w s h a d a l r e dy b e e n e s t a b 1 i s h e d

in

t h e i r fundament n l s by S m o l u ' c h ~ w s k i ~ ~ ~ .

The

e l e c t ~ o - k i n e t i c e f f e c t s whfch have been d e s c r i b e d were m a i n l y employed i n p h y s i c a l c h e m i s t r y f o r s e p a r a t i n g mixed p h a s e s a n d , among o t h e r t h i n g s , f o r t h e d r y i n g of p e a t ; i n m e d i c i n e and p h y s i o l o g y t h e y were u s e d t o i n t r o d u c e medicaments i n t o t h e c h a n n e l s o f t h e t i s s u e s

-

f o r example, t h e s k i n and t h e r o o t s o f t h e t e e t h

-

t o men- t i o n j u s t a few of' t h e a p p l i c a t i o n s ,

I n

Gelarnany c e r t a i n in--, d u s t r i e s were d e v e l o p e d f o r t h e a p p l i c a t i o n o f t h e e l e c t r o - k i n e t i c p r o c e s s e s , e , g , , t h e i l e c t r o -osmosis Coo.? ~ t d , ~ ) ,

founded by Coudt S c h ~ v e r i n , Thore a r e numerous p a t e n t s

c o v e r i n g t h e a p p l i c a t i o n s , most of wi- i c h a r e d i s c u s s e d i n a 4 1

3

work by P r a u a p i t z and R e i t s t o e t t e r "

,

I11 FUNDAMENTAL LAWS, DEFIWITIONS

-

AND

APPLICATIONS

The f o r m u l a deduced b y H e l m h o l t z - P e r r i n - Smoluchowskf f o r t h e q u a n t i t y t r a n s m i t t e d b y e l e c t r s - - - c s n o s f s

is

b a s e d on a n o n - c o n d u c t i n g c a p i l l a r y ( ~ f g , 4 ) u n d e r a h y d r a u l i c s u p e r p r e s s u r e p

-

yw h , A t e i t h e r end thel-e i s a n e f f e c t i v e p o t e n t i a l U, p r o d u c i n g an e l e c t r i c c u r r e n t o f s t r e n g t h I, The v e l o c i t y o f t h e f l u i d p a s s i n g t h r o u g h t h e c a p i l l a r y i s a c c o r d i n g l y ' ThSs i s t h e e q u a t i o n n o r m a l l y a p p l i e d i n t h e c,goso s y s t e m

(celltfmetre-gram-second s y s tern o f e l e c t r o s t a t 1 c measurement.)

,

The n o m e n c l a t u r e i s a s f o l l o w s :

u =

mean v e l o c i t y of t h e i m p e l l e d f l u i d d

=

d i a m e t e r o f t h e c a p i l l a ~ y

7

-

v i s c o s i t y o f t h e f l u i d p

=

e f f e c t i v e p r e s s u r e d i f f e r e n c e a t t h e c a p i l l a r y y, h

=

s p e c i f i c w e i g h t o f t h e ' f l u i d o r w a t e r .

-

--

Gom,b.Ho

Page

-

7 Tech, T r a n s , TT-6l h = p r e s s u r e head

1

=

l e n g t h o f t h e c a p f l l a r i e s

4

=

e l e c t r o - k i n e t i c p a r t i c l e p o t e n t i a l p,

=

s p e c i f i c r e s i s t a n c e o f t h e f l u i d D

=

d i e l e c t r i c c o n s t z n t of t h e _fluid j

=

e l e c t r i c c u r r e n t d e n s i t y I n t h e c a p i l l a r y It i s i n m e d i a t e l y a p p a r e n t from e x a m i n a t i o n o f e q u a t i o n (1) t h a t i t s f i r s t t e r n r e p r e s e r l t s t h e l a Y u o f l a m i n a r f l o w v e l o c l t y uo o f a f l u i d a s deduced b y P o i s e u i l l e f o r a h y d r a u l i c p r e s s u r e d i f f e r e n c e , w h i l e t h e s e c o n d t e r n d e n o t e s t h e v e l o c i t y component u l p r o d u c e d b y t h e e l e c t r i c c u r r e n t , so t h a t , t h e two conlponents m e r e l y s u p e r p o s e e a c h o t h e r o T h i s f a c t i s v e r y p e r t i n e n t t o t h e a p p l i c a t i o n o f e l e c t r o - d r a i n a g e , s i n c e t h e above s u p e r p o s i t i o n l a w a l s o a p p l i e s f o r f l o w s t h r o l ~ r g k ~ p o r o u s m a s s e s ,

The c , , i , > l l z a l form o f t h e law a s g i v e n b y H e l m h o l t z , P e r r i n anci 5moluchowski n e g l e c t s c e r t a i n i n - f l u e n c e s , t h e dependence o f t h e p r o c e s s on t h e c a p i l l a r y r a d i u s , f o r example, a ~ d t h e c o n d u c t i s n o f t h e c u r r e n t

t h r o u g h t h e capf l h a r y w a l l s t o & t -L.:~

wf

t h t h e c)r*dinary g a l -

v a n i c c u r r e n t c o n d u c t i o n which a l w a y s t a k e s p l a c e s i m u l - t a n e o u s l y w i t h t h i s p r o c e s s as a p a r a l l e l . . p h e n o m e n o n , The l a w s t i l l b r l n g s o u t t h e f u n d a m e n t a l f a c t , however, t h a t t h e v e l o c i t y o f t h e f l o w is p r o p o r t i o n a l t o t h e c u r r e n t d e n s i t y j and f o r t h e s a k e of simplicity, t h e r e f o r e , It w i l l be r e - t a i n e d h e r e a f t e r a s a b a s r s , The a c t u a l r e l a t i r n s h % p s , due t o t h e above-ment i o n e d i n f l u e n c e s , a r e c o n s i d e r a b l y more c o m p l i c a t e d , The e x a c t d e d u c t i o n o f t h e l a w , whlch h a s s i n c e been a c c o r r ~ p l i s h e d ~ w % l l a p p e a r f n a s p e c i a l work o f t h e f i r s t named a u t h o r , I n o r d e r t o make t h e above r e l a t i o n s h i p s a p p l i c a b l e t o f l o w s i n f i n e l y d i s p e r s e d s g s t e n i s a c o n v e r s i o n must be made from t h e mean v e l o c i t y u f n t h z c a p i l l a r y t o

t h e " f i l t e r v e l o c i t y s v v ~ r e l a t i v e to t h e e n t i r e c r o s s - s e c t i o n o f t h e p o r o u s m a s s , T h i s s t e p 1 s n e c e s s a r y f o r t h e s i m p l e r e a s o n t h a t o n l y t h e f f l t e r v e l o c f t , y c a n b e m e a s u r e d

Page

-

8

Tech-, T r a n s , TT-61

a c c u r a t e l y enough, I f , i n a d d i t i o n . , t h e magnitudes which c h a ~ a c t e r f ze t h e r r l a t e r i a l a r e b r o u g h t t o g s t h e r i n t o a s i n g l e f a c t o r , Dalacyl:s l a w i s o b t a i n e d from P o i s e u i l l e Gs e q u a t i o n i n t h e e f f e c t i v e f i e l d o f g r a v i t y f o r c e , w h i l e i n t h e e f f e c t i v e f i e l d o f e l e c t r i c a l f o r c e a s i m i l a r s i n i p l i - f l . c a t i o n may b e c a r r i e d . o u t , The r e l a t i o n s h i p f o r t h e l a m i n a r f i l t e r v e l o c i t y which c o r r e s p o n d s t o t h e He1mholt.z- Perrin-Smoluchowski law 1 s : i n whfch VF

=

t o t a l f i l t e r v e l o c i t y VD

=

f i l t e r v e l o c i t y a c c o r d i n g t o Darcy VE

=

e l e c t r o - o s m o t i c f i l t e r v e l o c i t y k = p e r m e a b i l i t y c o e f f i c i e n t ( a c c o r d i n g t o Darcy] J

=

g r a d i e n t o f t h e h y c i ~ a u l i c p r e s s u r e a x i s

kE

=

e l e c t r o - o s m o t i c f l o w c o e f f i c i e n t E

=

e l e c t r i c a l f i e l d ~ t r e n g t . h ,

In

t h i s form e q u a t i o n ( 3 ) may b e r e g a s d e d as t h e e x t e n d e d " g e n e r a l f I P t e s Pawtv f o r m u l a t i n g t h e super-, p o s e d e f f e c t s o f p ; r a v i t y on t h e one hand, and t h e e l e c t r o - m o t i v e power on t h e o t h e r , The a n a l o g y between t h e two

s u p p l e m e n t a r y e f f e c t s a l s o a p p e a r s i n t h e f a c t t h a t t h e d5-fs, f e r e r ~ c e i n e l e c t r i c a h p o t e n t i a l ( e l e c t r i c a l f i e l d s t p e n g t h ]

E = - -

fh

on t h e one h a n d , c o r r e s p o n d s t o t h e g r a d i e n f 2 s o f t h e h y d r a u l i c a x i s o f p r e s s u r e

J

7

-

-L

*

on t h e o t h e r Y,

(6-

zz e l e c t r i c a l p o t e n t i a l and s t= d f s t a n c e o f t r a y j A l , 1 I Whereas k r e p r e s e n t s t h e f f l t e p v e l o c i t y which a d j u s t s i t s e l f t o t h e g r a d i s n t J9 ~ - g k e @ t r o ~ m o t i c C$low c o e f f i c i e n t kE s i g n i f i e s t h e f i l t e r veBu:ity which o c c u ~ s at. an e l ~ c t r i c a l f i e l d s t r = t h _ % - a t k m .

--

- C o n t r a r y tc t h e f i l t e r v e l o c i t y v~ c;;o t h e per:.wakIGPtg c o e f f i c i e n t

k,

whfch a r e e x p r e s s e d i n mi,; s e c ,, kg has t h e dfmensi on

0

cm:

-.--

,

s o t h a t when m u l t i p l i e d agaln b y E

Page

-

9

Tech, Trans,

TT-61

t h e dimension i n c l u d e s a v e l o c i t y , Moreover, t h e e l e c t p o - osmotic f l o w . c o e f f i c f e n t f s dependent on e n t i r e l y d i f f e r e n t c h a r a c t e r i s t i c s of t h e whole pore s t r u c t u r e : , f o r example, t h e d i e l e c t r i c c o n s t a n t s of t h e f l u i d and t h e s p e c i f i c e l e c t r i c a l r e s i s t a n c e s of t h e s o l i d and f l u f d p h a s e s , t h e r a t f o of' g a l -

-C l.-, _C

v a n i c t o e l e c t r o - o s n o t i c cl~.rl-eni; condu~:;l;in..; ,,,$ po-.?s '.

ty

r a t i o s a ~ r : t h e v l z c o s i t y and temperature of' t h e f l u l d phase.

The m a t e r i a l c l : ~ ; ~ , c , c t . z ~ ' i s t ; i c i n q ~ ~ e s t i o : . ~ is a ;rc:rj.'. ~(Xiipli:;i one s t r u c t u r c i l l y , b u t i t s t o t a l e f f e c t can be d e t e m l i n o d e x p e r i m e n t a l l y w i t h o u t t h e n e c e s s i t y of knowing t h e e l e m e n t a l magnitudes

,

By u s i n g t h e e l e c t r o - o s m o t i c flow c o e f f i c i e n t

k~

t h e d i f f e r e n t m a t e r i a l s can be c h a r a c t e r i z e d w i t h r e s p e c t t o t h e i r e l e c t r o - o s m o t i c behavioup i n a manner s i m i l a r t o t h a t i n which t h i s i s done w i t h t h e p e r m e a b i l i t y c o e f f i c i e n t k f o r t h e c a s e o f s i m p l e h y d r a u l i c p e r m e a b i l i t y , I t h a s t h e d i s a d v a n t a g e , however, t h a t no v i s u a l p h y s i c a l . r e p r e s e n t a t i o n i s p o s s i b l e w i t h i t s dimension, This c o n s i d e r a t i o n l e d t o t h e s e a r c h f o r a n o t h e r method o f e x p r e s s i n g q u a n t i t a t i v e l y the e l e c t r o - o s m o t i c e f f e c t of a p o ~ o u s m a t e r i a l , One pos- s i b i l i t y i s t o d e t e r m i n e t h e " e l e c t r o - o s m o t i c h e i g h t of r i s e "

HE

o r t h e " s p e c i f i c e l e c t r o - o s m o t i c h e i g h t s f r i s e "

k ,

With r e f e r e n c e t o F i g u r e '7,

HE

s i g n i f i e s the d i f f e r e n c e

i n

f l u i d s u r f a c e l e v e l , e x p r e s s e d i n c e n t i m e t r e s , which o c c u r s i n t h e two v e r t i c a l s e c t i o n s o f a U-tube when a t e s t sample o f s o i l m a t e r i a l l o d g e d i n t h e h o r i z o n t a l s e c t i o n i s s u b j e c t e d t o a t e n s i o n U

= 1

V o l t , When t h i s h e i g h t of r i s e i s r e a c h e d a complete s t a t e o f r e s t i s i n t r o d u c e d . cue t o t h e f a c t t h a t t h e e l e c t r j c a l t e n s i o n J u s t b a l a n c e s t h e hydro- s t , a t i c p r e s - s u r e , I f t h e f i l t e r v e l o c i t y vF = 0 i s used t o e x p p e s s t h i s s t a t e o f e q u i l i b r i u m i n e q u ~ t i o n ( 3 ) , f t f o l l o w s t h a t

(L

=

l e n g t h of s a n p l e , F i g , 7 ) k~

HE

=

-

U

=

hE U

=

e l e c t r o - o s m o t i c h e i g h t o f r i s e k produced by t h e t e n s i o n

U,

( 4 1 where t h e f a c t o r hE

-

kE now s i g n i f i e s t h e z ~ l f i c e l e c t r o - o s m o t i c h e i g h t o f r i s e and h a s t h e dimension c m , / ~ o l t , For U

=

1 V o l t t h e v a l u e

Page

-

18 Tech, T r a n s , T T - 6 1 is o b t a i n e d from e q u a t i o n ( 4 ) f o r t h e s p e c i f i c ele@tx8o~-oamot:ic h e f g h t o f r i s e hE,

The

s p e c i f i c h e i g h t o f xai.se

hE

i s t h e r e f o r e d i r e c t l y p r o p o r t i o n a l t o t h e e l e c t r o - a s m o t i c c o e f f i c i e n t - and. i n d f r e c t l y p r o p o r t i o n , f l t o t h e hydraulic p e r m e a b i l i t y ks-: e f f i c i e n t , E x p r e s s e d i n c r n , , / ~ o l t f t fs nwnelhically P d e r l t i c a l With t h e r a t i o o f the e l e c t ~ o ~ s s m o t f c f k ~ w c o e f f i c i e n t to t h e p o m e a b i l . i t y c o e f f i c i e n t , On t h e o+,ier hand If' a f l o w p r o c e s s i s i n i t i a t e d , , u n d e r o t h e r w i s e i d e n t i c a l c o n d f t i o n s . . f f r s t h y d ~ a u P i c a 2 B y w i t h g r a t l . i e n t

J

= 1, t h e n e l e c - t ~ a ~ . V o l t o s m o t i c a l b y w i t h the f i e l d s t r e n g t h E

-

I

---

,, t h e s e c o n d cra , t e s t w i l l g i v e a f i l t e r v e l o c f t.y ( t i m e s g r e a t s r t h a n t h e f l r s t . S u p p l e m e n t i n g the v a l u e

Inn,

t h z hlowled;-;e o f t h e " s p e c i f i c e l e c t r o - o s m o t i c h e i g h t of laisetf !lErnakes i t 'pos-

s i b l e t o a s s e s s an f r n p o r t ~ ~ t p r o s l e m -, t o what e x t e n t a g i v e n f l o w p r o c e s s can be i n f l u e n c e d by nloarls o f e l e c t y o - osmosis ,, t h e r e f o r e b e t a k e n a s a

_--

measure o f t h e _--

--

e l e c t r o - o s n o t i c e.f&, I n

t h i s

c o n n e c t i o n i t shou1.d h e -.c::n Lion.ed t h a t t h e f u r t h e l a developnient o f t h e b a s i c l a w c :ylressed i n e q u a t i o n

f a )

l e a d s t o t h e d i f f e ~ ~ e n t l a l . e q u a t l o n o f t h e hy,=z d r a u l i c e l e c t r c c - - o s m o t i c f i l t e r f l a w where k

-

p e r m e a b i l i t y c o e f f i c i e n t ( ~ a r ; c g ) A

-

L a p l a c i m o p e r a t o r

aH

=

h y d r a u l i c p o t e n t i a l of t h e ground w a t e r flow

DB

=

d i e l e c t r i c c o n s t a n t o f tihe s a t u r a t e d soL1

$

=

e l e c t r i c a l p o t e n t i a l

6

=

e l e c t r i c a l c h a r g e d e n s i t y o f t h e s p a c e u n l t , The v e c t o r e q u a t f o n o f t h e c o r r e s p o n d f n g f i l - t e r f l o w i s t h e r e f o r e _---=

--ITS

e x 2 r

e'6

~ 6 h - . p ~ e ~ 3 ; 1 ~ r

t h e c , & , s , syster,i., whereas a l l h e o t h e r e q u a t i o n s , o f coupse, have [;enern1 v a l i d i t . y ,

Page

-

11 Tech, Trans, TT-361

-

_VF

-

_-

-

_vD

₊

_TE

₌

_-

_{k g r a d}

_dH

_-

_{kE g r a d}

_$

=

-

_{g r a d (kdH}

₊

_kE

4 )

I f g r a d

dH

i s c o n s i d e r e d a s c o r r e s p o n d i n g t o t h e g r a d i e n t of t h e h y d r a u l i c p r e s s u r e a x i s ,

J,

and g r a d

&

t o t h e e l e c t - r i c a l f i e l d s t r e n g t h

E,

then e x p r e s s i o n ( 7 ) i s i d e n t i c a l w i t h e q u a t i o n ( 3 ) . F i n a l l y t h e q u a n t i t y o f f l u i d t r a n s f e r r e d by osmosis i n an e l e c t r i c a l f i e l d i s where

p

i s t h e s p e c i f i c r e s i s t a n c e of t h e s a t u r a t e d s o i l m a t e r i a l and I i s t h e s t r e n e t h o f t h e c u r r e n t . As an example of an a p p l i c a t i o n , approximate c a l c u l a t i o n p r i n c i p l e s f o r f i l t e r w e l l systenls may b e g i v e n i n o r d e r t o complete t h e p i c t u r e , Owing t o t h e h e t e r o - g e n e i t y o f t h e s o i l , even t ! ~ c o r e t i c a l l y e x a c t e x p r e s s f o n s , a s i n t h e c a l c u l a t i o n o f nomlcl I ' i l t e r w e l l s y s terns, p e r m i t o n l y an e s t i m a t i o n of t h e o r d e r of' magnitude, which can a l s o b e o b t a i n e d from h i g h l y s i m p l i f i 2 d e x p r e s s i o n s , For the simple f i l t e r w e l l w i t h o n l y two e l e c t r o d e s , t h e n e a r l y f l a t s e c t i o n o f the flow f i e l d down t o t h e lower edge o f t h e e l e c t r o d e s was c o n s i d e r e d ( ~ i g , 1)

,

n e g l e c t i n g t h a t p a r t of t h e f i e l d l y i n g below t h e e l e c t r o d e s , The t r a n s i t f o n a l r e s i s t a n c e t o conduction a t t h e e l e c t r o d e s was a l s o n e g l e c t e d , By a p p l i c a t i o n of e q u a t i o n s ( 4 ) t o ( 8 ) , o m i t t i n g t h e terms of lower o r d e r , t h e d e s l r e d v a l u e s f o r t h e f i l t e r w e l l ( F i g , 1) a r e a s f o l l o w s : E l e c t r i c a l r e s i s t a n c e Currenf; s t r e n g t h Output ( w a t t ) (11)

Page

-

12 Tech, T r a n s , TT-6% Q u a n t i t y I m p e l l e d by e l e c t r o - o s m o s i s where ( c f , a l s o F i g ,

1.1

p = s p e c i f i c r e s i s t a n c e o f t h e s a t u r a t e d s o i l m a t e p i ai

t

= l e n p ; ~ li .;f e l e c t r o d e s u b m e ~ g e d i n t h e ground w a t e ~ s

=

e l e c t r o d e i n t e r v a l r

-

r a d i u s o f e l e c t r o d e . U = v o l t a g e For t h e . c a l c u l a t i o n o f a f f l t e r w e l l o p e ~ a t e d w i t h more t h a n two e l e c t r o d e s K f r c h h o f f t s l a w o f c u r p e n t d i a - t r i b u t i o n can b e ap:)l.ied a s a rough q ? p ~ o x i m a t i o 1 1 , F o r t h e c o m b i n a t i o n ~ f a w e l l electlaode wf th two a u x i l i a r y e l e c t r o d e a t h e f o l l o w i n g e l e c t r i c a l r e s i s t a n c e i s o b t a i n e d rillen t h e

l a t t e r a r e e q u a l d i s t a n c e s f ~ o m t h e well:

wklfPe t h e r e m a i n i n g e x p r e s s i o n s may t j e c a l c u l a t e d b y analogy w f t h e q u a t i o n s ( 1 0 ) t o 912),

I n t h e g e n e r a l c a s e o f seepage Induced by e l e c t r o - o s m o s i s , e n t i r e l y d i f f e r e n t l i m i t i n [ . ; c o n d i t i ons may

p r e v a i l f o r t h e Tlou I n t h e g r a v i t y f i e l d and i n t h e e l e c t - r i c a l f i e l d , Here t h e v e l o c i t y v e c t o r s of t h e two compenent~s o f m o t i o n have d i f f e ~ e n t , d i r e c t i o n s ( F i g , 5 1 0 The f S e l d o f g r a v i t y , with I t s p a r t i c u l a r l i m f t i n g c o n d i t i o n s i s overr- l a p p e d by a n e l e c t r i c a l i ' l e l d w i t h o t h e ~ boundary s u s f a c e s , The essential p o f n t i s t h a t b m o s s

-

e s s.---=- a v e l o c f

-

tg - &entcLaL, s o t k ~ a t c a l c u l a t i o n o f t h e 6 > ' r o c e g s a c c o r d i n g t o t h e r u l e s o f t h e p o t e n t i a l t h e o r y 4 &

ft0Z37~

441 can be c a r r i e d o u t s e p a r a t e l y w i t h t h e a i d of s o l u t f o n s f o r b o t h f i e l d e f f e c t s whfch m i ~ h t a l r e a d y be a v a f l a b l e , S h o u l d Che two v e l o c i t y v e c t o r s r e s u l t i n g from t h e f o r c e s f g r a v i t y on t h e one hand, a n d t h e e l e c t r i c a l f o r c e on t h e o t h e r , be

Page

-

13

Tech, Trans, TT-61 known a t any p a r t i c u l a r p o i n t of t h e system through which

t h e flow t a k e s p l a c e , t h e n t h e r e s u l t i n g v e l o c i t y w i l l be o b t a i n e d by geometric a d d i t i o n of t h e r e s p e c t i v e v e c t o r s

( F i g . 5 ) . Moreover, s h c e b o t h c o n s t i t u e n t motions a r e f r e e from v o r t i c e s , t h z L a c s u l t i n g seepage w i l l a l s o be f r e e from v o r t i c e s and, witrlin ~ i v e n boundary s u r f a c e s , w i l l t a k e p l a c e i n such a way t h a t t h e energy used i n f r i c t i o n w i l l

be a t a minimum, Thk8)was proven f o r t h e movement of ground w a t e r by Lord Kelvin

EXPERIMENTS

The aim of the p r e s e n t experiments i s f i r s t l y t o prove t h e v a l i d i t y of t h e g e n e r a l f i l t e r law f o r f i n e l y d i s p e r s e d pore s t r u c t u r e s , and s e c o n d l y t o d i s c o v e r the methods by which t h e e l e c t r o - o s m o t i c flow c o e f f i c i e n t kE

and the s p e c i f i c e l e c t r o - o s m o t i c h e i ~ l l t of r i s e h~ may be most simply measured f o r a g i v e n m a t e r i a l , If c y f i n d r i c a l

s a m p l ~ s of m a t e r i a l a r e t o be used the a p p a r a t u s t o be de- veloped must f u l f i l t h e b a s i c reqlxiremerlts of p e r m i t t i n g floci passage through t h e sample, f i r s t , under the i n f l u e n c e of g r a v i t y a l o n e , second, under t h e i n f l u e n c e of' an e l e c t - r i c a l f i e l d a l o n e , and f i n a l 1

,

under t h e combined e f f e c t of b o t h f i e l d s ( c f . Sec.

IV

cy. The two c o e f f i c i e n t s , on t h e o t h e r hand, may be determined e i t h e r by measuring the s e e p a g e . q u a n t i t y f o r a given e l e c t r i c a l v o l t a g e ( q u a n t i t y measurement), o r by d e t e r m i n i n g the a s s o c i a t e d h e i g h t of r i s e ( h e i g h t - o f - r i s e measurement),

a ) Q u a n t i t y Measurement ( F i e . 6 )

When t h e h y d r o s t a t i c p r e s s u r e d i f f e r e n c e be- tween Lhe two ends o f t h e sample h a s been overcome

(J

= 0 ) by means of' th13 s p e c i a l t e s t arrangement t h e measurement of q u a n t l t y f o r the d e t e r m i n a t i o n of k~ t a k e s p l a c e by analogy with t h e d e t e r m i n a t i o n of k on t h e b a s i s of the r e l a t i o n s h f p

( c f , e q u a t i o n ( 3 ) )

S i n c e t h e boundary c o n d i t i o n s h e r e a r e so chosen t h a t a u n i - a x i a l flow through t h e c y l i n d r i c a l sample r e s u l t s , t h e

d 6 E

u

e l e c t r i c a l ' f i e l d s t r e n g t h E

=

-

-

-

-

ds

-

L i s c o n s t a n t over the e n t i r e l e n g t h of t h e sample. Hence

Page 14

Tech, Tpans, T T - 6 1

vE

=

measured e l e c t ~ o - o s m o t i c f l i t e l - . volcjci ir.y

%

= measured q u a n t i t y t ~ a n s p o r t e d by e l e c t . r o , - osni~ss i s L

=

l e n g t h o f sample F

-

c r o s s - = s e c t t o n o f a m p l e U

-

v o l t a g e a p p l i e d I

=

c u r r e n t s t ~ e n g t h R

-

e l e c t r i c a l r e s i s t a n c e o f t h e sample, b ) H e i g h t - o f - R i s e Measurement [ F i g ,

--

7 )

The e l e c t r o - o s m o t i c h e i g h t o f r f s e HE, which c a n be d e t e r m i n e d w i t h r e l a t i v e eam,-,e by t h e a r r a n g e m e n t i l l u s t r a t e d d i a g r a r m a t i c a l l y I n F i g u r e 7 a s w e l l a s by t h e t h e o r e t i c a l . e x p r e s s i o n s g i d e n i n S e c t i o n 111, c o r r e s p o n d s t o t h e c a p i l l a r y h e i g h t o f r i s e H c a u s e d b y t h e s u r f a c e t e n s f on o f t h e w a t e r , I f the p e r n l s a b i l i t y c o e f f i c i e n t k i s a l s o known, t h e n , a c c o r d i n g t o e q u n t i o n s ( 4 ) and (51, t h e e l e c t r o o s m o t i c flow c o e f f i c i e n t can a l s o be c a l c u l a t e i l from t h e h e i g h t o f r i s e

HE

o r from t h e s p e c i f i c h e i g h t o f r i s e

%,

S o t h a t t h e e l e c t p o - o s m o t f c problem m i g h t be s t u d i e d on th:: b a s i s of s o i l mecklanfcs p r i n c i p l e s , t h e r e g u l a r odome te1.s o f t h e s? f'L rrtechanf c s l a b o r a t o r y were

f i r s t c o n v e r t e d t c r n p o r a ~ 5 l y ( F i g , 8 and 9 ) t o e n a b l e f n f t f a X c r i e n t a t . i o n e x p e r i m e n t s t o be c a k r i e d c u t o I n t h e c o u r s e of i n v s s t f g a t i o r l s t h e desi;,n o f a n e l e c t r " o ' - o d o r n e t e ~ ~ an

a p p a r a t u s e s p e c l a;ly s u i t o e d f o r t h f s r e s e a r c h , was a c h i e v e d , A s c h e m a t i c pictu1.e of t h i s i n s t r u m e n t fs g f v e n In F i g u r e 1 0 , and t h e c o m p l e t e d a p p a r h a t u s i s shown i n Figure

11,

The o u t e r cylfncier c a s i n g was made o f glass s o t h a t t k e p r o c e s s c o u l d b e w a t c h e d ,

Page

-

1 5

Tech,, T r a n s , TT-61 The sample i s e n c l o s e d between a f i l t e r p l a t e and a p i s t o n which a l s o s e r v e s as a f i l t e r p l a t e , Both p l a t e s a r e made of an a r t i f i c i a l r e s i n s u p p l i e d by L i c a f i l A e G o ,

Z u r i c h , This m a t e r i a l i s h i g h l y r e s i s t a n t t o chemical pro- c e s s e s and does n o t s w e l l , P l a t i n u m f o i l s were chosen a s e l e c t r o d e s i n o r d e r t o avoid c o r r o s i o n due t o t h e e l e c t r o - l y t i c p r o c e s s e s which always o c c u r d u r i n g t h e experiments a s

a secondary phenomenon, These p r o c e s s e s would have had a d i s t u r b i n g e f f e c t on t h 5 r e s u l t , n i e p a r t s of t h e a p p a r a t u s were manufactured by t h e

A,

Dumas Glassworks, Z u r i c h , and

t h e S o K r i e g P r e c i s i o n ivlechanical Workshop, Z u r i c h , The

e l e c t r o - o d o m e t e r can be used b o t h f o r q u a n t i t y and. heig$t t - o f - r i s e mehsurement

For q u a n t i t y measurement t h e w a t e r s u r f a c e l e v e l i n t h e odometer i s k e p t t h e same a s i n t h e i n t a k e o r o v e r f l o w t u b e s i n o r d e r t o e l i m i n a t e a h y d r a u l i c s u p e r p r e s - s u r e ( F i g , l O a ) , So t h a t t h e g a s e s which always r e s u l t from e l e c t r o l y s i s may be l e d o f f , , t h e l o w e r f i l t e r p l a t e i s c u t d i a g o n a l l y and a gas e s c a p e tube w i t h s t o p c o c k was a t t a c h e d , The s t o p c o c k may be opened p e r i o d i c a l l y o r a s t a n d p i p e may be provided. By means of t h e l r t t e r arrangement t h e con-

t i n u o u s e l i m i n a t i o n of t h e g a s e s i s made p o s ~ i b l e , With t h i s arrangement, t o o , t h e lower w a t e r compartrrient can be c o n s t a n t l y f l u s h e d w i t h f r e s h w a t e r whenever s t r o n g a c i d i f i c a t i o n o r

enrichment of t h e b a s i c s u b s t a n c e s o c c u r s , and a c i i s t u r b f n g c o n c e n t r a t i o n of e l e c t r o l y t e s i s t h u s p r e v e n t e d * The chosen e l e c t r o - o s m o t i c flow d i r e c t i o n i a upward and t h e p o l e s a r e connected a s shown i n F i g u r e 10a,

The scurie arrangement c a n be employed f o r measuring 8- i f t h e w a t e r I n t a k e i s c u t o f f and

t h e d r o p of t h e w a t e r l e v e l i n t h e o v e r f l o w tube i s observed ( n e g a t i v e heii;ht of r i s e ) . The e l e c t r o - o s m o t i c h e i g h t of' r i s e can t h e n be c L d c u l a t e d from measurement of t h e w a t e r v e l o c i t y a t a ~ i v e n p o f n t .

A l t e r n a t i v e l y , t h e p o l a r i t y of t h e e l e c t r o d e s may be s w i t c h e d > c ) t h a t t h e d i r e c t i o n o f flow o f w a t e r

3

i s

r e v e r s e d (downwards). The w a t e r i n t a k e tube i s then r e - p l a c e d by a s u f f i c i e n t l y t a l l , c a l i b r a t e d s t a n d p i p e , and a

s i m i l a r s t a n d p i p e i s a l s o a t t a c h e d t o t h e g a s escape tube

t o

p e r m i t escape of t h e g a s b u b b l e s w i t h o u t l o s s of' w a t e r ( F i g , l o b ) . I n t h i s c a s e , t o o , t h e f i n a l h e i g h t can be c a l c u l a t e d from a measwement o f t h e r a t e o f c l i m b ,

An experiment w i t h s i l t y sand (E'ig, 1 2 ) niay be u s e d

t o

shorv t h a t a v e r y c o n s i d e r a b l e h e i g h t o f r i s e i s

Page

-

1 6

Tech, Transo TTc.61

i n v o l v e d i n t h e e i e c t r o - , o s m o t i c

climb

of t h e w a t e ~ , A t f i r s t a r i s e of' a b o u t 1 0 5 0 m e t r e s was o b s e r v e d , However, s i n c e t h e s t a n d p i p e was riot t a l l enough t o permi

t

a t t a i n m e n t of t h e f i n a l s t a t e , t h e h e i e l l t of' r i s e w.as c a l c u l a t e d from t h e measured v e l o c i t y and $/as found t o be from 1 2 t o 1 3 m e t r e s ,

whfch ap,rees with t h e h e i g h t of r i s e d e t e r m i n e d from t h e co-J e f f i c i e n t s k and k~ ( F i g , 12) f o r t h e mean v o l t a g e employed o f 1 4 , 7 V 0 [ ~ i t h t h i s r n a t e r i n l ~ f s 8 b o u t 8 ? t i m e s k , , i o e , ,

%

N 87 c m , / ~ o l t ) ~

For t h e s c l e n t i f i c exporimen t s , which have not, y e t b e e n concludedd t h e sample m a t e r f a% bein?; u s e d i s a f i n e q u a r t z powder a s c h e m l c s l l g i r l s e n s i t i v e a s p o s s i b l e , I t s g r ~ i n s i z e d i s t r i b u t i o r l curve i s g i v e n i n Fill;ure 13,

The

p e r m e a b i l i t y c o e f f i c i e n t of t h i s m a t e r i a l i s r o u g h l y k = 3 , 7 x

10-6

cmo/sec,, t h e e l e c t r a - o s m o t i c flow c o e f f i c i e n t / F cm,, s e e . a p p r o x i m a t e l y kE

=

4 0 5

x

1 0 "

m G

0 t h e s p e c i f i c e l e c t r o - o s m o t i c h e i g h t of r i s e hs

=

1 2 c m o / ~ o l % ,

Regarded from t h e p u r e l y mechanical v i e w p o i n t , f t might be e x p e c t e d t h a t an i n t e n s i f f c a t i o n o f s e e p a g e , s u c h a s t h a t caused by e l e c t r o - ~ o s m o s i s , would l e a d t o v e r y rnapked s o i l movements i n a m a t e r i a l t h a t had no c,ohesiono, However, e x p e ~ i m e n t s which wepe e s p e c i a l l y u n d e r t a k e n t o i n v e s t i g a t e t % l i s m a t t e r r e v e a l e d t h a t no such p r o c e s s o c c u r ~ e d duping t h e e l e ctro- osmotically induced seepage. From o v e r - - a l l c o n s i d e r a ~ t Lion of t h e e l . e c t r i c a l f o ~ c e s p r e s e n t i n b o t h s o l f d and f l i ~ f d m a t e r i a l i t i s found i n c o n f o r m i t y w i t h the t e s t r e s u l t s t h a %

t h e r e i s a s t a t i c e q u i l i b r i u m of' the t w o - p h a s e s.yst.ern s u b j e c t e d t o e l e c t r o - o s m o t i c f l o e , A t . t h e same time t h i s agreement

r e p r e s e n t s a confirBma.tion of the hypo t h e t i c a l view that, b o t h p o s i t i v e and n e g a t i v e c h a r g e s , a.nd herlcc a df f f e r e n c e i n p o t e n t i a l , ( e l ~ c t r o = = ~ k f n e t i c p a r t . i c l e p o t e n t i a l ) , o c c u r s 9 . t

t.he boundary l a y e s &

I n a d d i t i o n t o the l a b o r a t o r y experiment.^ t h l ~ s f a r d e s c r f b e d i t was p o s s i b l e , through t h e c o - o p e r a t f o n of t h e Z e l l P e a t F a c t o r y and t h e filam of S w i s s b o r i n g i n Z u r i c h p tr)

s e t up a s p e c i a l t e s t i n a s u i t a b l e s i l t y sand t e r r a i n , b ' i ~ u r ~ e 1 4 shows a p l a n of t h e a p p a r a t u s d e s i ~ n e d f o r t h e

f i l t e r w e l l . O r d i n a r y gas p i p e s were employed as e l e c t r o d e s , A welding t r a n s f o r m e r w i t h a d j u s t a b l e v o l t a r e p r o v i d e d the d i r e c t c u r r e n t ,

F i g u r e 1 5 g i v e s t h e c , r a p h i c a % r e p r e s e n t a t i o n of a n e l e c t r o - d r a i n a g e t e s t u s i n g a v o l t a g e o f 64 V and a x 1

p. 1;:. 1 7

I ' c c l ~ . T r a n s , TT-61 w a t e r l e v e l i n t h e w e l l i s g i v e n w i t h no curar3snt; a p p l i e d and

t h e n , f o p comparison, ~ i f i t h c u r r e ~ i t , I t i s b l o l - t l l noting: t h a t

h e r e , t o o , t h e w a t e r i n t h e w e l l c o u l d be rXrlil s e d cbove t h e normal ground w a t e r l e v e l , I n agreement

1!i

tl: t;le l a b o r a t o r y

t e s t s i t t h u s a p p e a r s p o s s i b l e t o pump ground w a t e r i n f i n e g r a i n e d r n a t e r 5 a l s b y means of A: d i r e c t c u r r e n t , b u t t h i s i s

d e p e n d e n t on a c h e m i c a l chan,r;e i n t h e w a t e r clue t o e l e c t r o - l y t i c i n f l u e n c e s , The lops o f t h e c u r v e of r i s e , ifhick1 i n t h e p r e s e n t c a s e :~mountscl t o a b o u t 4x1, s u g g e s t s a prot;able i n c r e a s e i n tlle p e r m e a b i l i t y c o e f f i c i e n t due t o t h e eff'eci; of t h e c u r r e n t , I t must be remembered t h a t t h e e l e c t r i c is

r e n t d o e s n o t a c t u a l l y i n c r e a s e t h e p e r r n e a b i l l t y o f t h e sc I

b u t o n l y t e m p o r a r i l y i n c r e a s e s t h e o u ~ r l t i t y o f s e e p a g e o Tile

e f f e c t comiences when t h e c u r r e n t i s t u r n e d on and ends i m - m e d i a t e l y a s soon a s i t i s t u r n e d o f f , I t i s w h o l l y depen-

d e n t on t h e e l e c t r o - o s m o t i c t r a n s f e r o f w a t e r , P ' i n a l l g

i t

must k:e m e n t i o n e d t h a t t h e e l e c t r i c a l r e s i s t a n c e of t h e s o i l w i t h t h i s s e t - u p amounted t o a p p r o x i m a t e l y 40 ohms, t h e c u r - r . ; n t s t r e n g t h was ~ o u , o k l y 1.6 t o 1 , 7 amperes, and t h e o u t - 1)ut employed was a p p r o x i m a t e l y f r o m 1 0 0 t o 1 1 0 w a t t s , i , e , , no rnore t h a n t h n t r e q u i r e d i'oua a s t r o n g i n c a n d e s c a n t lamp

( c f , F i g , 1 6 ) , These f i g u r e s i n d i c a t e t h e s i m p l i c i t y and economy o f t h e method,

Table I1 c o n t a i n s t h e d a t a from two q u a n t i t y rneasl.lrement t e s t s made a t one and t h e sarne f j l t e r w e l l u s i n g

d i f f e r e n t e l e c t r o d e i n t e r v a l s , For p u r p o s e s o f c o m p a r i s o n t h e c a l c u l a t e d r e s u l t s a c c o r d i n g t o e q u a t i o n s ( 9 ) t o ( 1 2 )

a r e a l s o g i v e n , These show t h a t t h e t h e o r y p e r m i t s e s t i m a - t i o n b o t h of t h e amount o f t h e e n e r g y r e q u i r e d and o f t h e e f f e c t which may be e x p e c t e d from a g i v e n e l e c t r o - d r c , i n a t . ; e s y s t e m , on t h e b a s i s o f r e l a t i v e l y few l a b o r a t o r y t e s t s , F o r t h i s r e a s o n o n l y t h e z l e c t r o - o s m o t i c f ' l ow c o e f f L C i 5 n t a n d t h e s p e c i f i c e l e c t r i c a l r e s i s t a n c e i n t h e s o i l m a t - r i a l n e e d be d e t e r m i n e d f n t h e l u b o r a t o ~ y , A s t i l l Creacerl n c c u r a c y i s a t t a i n a b l e by means o f d i r e c t measurBements of r e s i s t a n c e i n t h e r i e l d end b y c o n s t r u c t i o n of t e s t w e l l s , S i n c e t h e t ; ~ e o r e t i c a l developms.nts deduced i n S e c t i o n s I1 and I11 depend on t h e z t p p l i c a b i l i t y of Ohxi's

law, t h i s was a l s o t e s t e d u n d e r g r o u n ~ w i t h t h e a i d of t h e e x p e r i ~ l e a t ~ l i.'eld s e t - u p , The r e s u l t s a r e g i v e n g r a p h i c a l l y i n F i g u r e 16. I t i s c l e a r t h a t t h e r e q u i r e d p r o p o r t i o n a l i t y be tmeen m p > r q - , c v o l t a p ; ~ i s v e r y w e l l f u l f i l l e d , A p o s s i b l e a p p l i c a t i o n o f t h e p r i n c i p l e o f i n d u c i n g t h e f l o w of w a t e r tflrouell p o r e s by means o f e l o c b - r i c a l d i r e c t c u r r e n t Is t h e a c c e l e r a t i o n o f s e t t l e m e n t pro-

Page

-

18

Tech, T r a n s , TT-61

c e s s e s I n f i n e - & r a i n e d _ s o i l s d a Under cer.L.ain c i r c u m s t a n c e s .

--->. -

t h i s c a n b e o f practical s i g n i f i c a n c e , F i g u r e 17 f l l u s t z a a t e s

an s x p e ~ i r n e n t of t h f s n a t u r e u s i n g two samples o f . t h e same m a t e r i a l . I n one c a s e t h e sample o f s i l t y s a n d was k e p t i n

t h e o d o r n ? t 1 3 ~ u n d e r a d e f i n i t e l o a d i n c r e m e n t l ~ i t h no c u r r e n t a p p l i e d ; i n t h e o t h e r c a s e t h e c o n d i t i o n s were i c i e n t j c a l e x c e p t t h a t t h e sarnpls was p e r i o d i c a l l y s u b j e c t e d t o a d i r e c t c u r r e n t , The a c c e l e r a t i o n o f t h e s e t t l e m e n t s and t h e i r i n - c r e a s e i n s i z e aue t o t h e e f f e c t o f t h e c u r r e n t d u r i n g t h e s e p e r i o d s are s t r i k i n g l y r e p r e s e n t e d i n F i g u r e 1 7 , I t h a s n o t y e t b e e n p o s s i b l e t o explz.ln on what t h f s e f f e c t d e p e n d s , The o b v i o u s p r e s u m p t i o n , t h a t whenever a f l o w t a k e s p l a c e t h r o u g h a f i n e l y d i s p e r s e d s y s t e m t h e f r i c t i o n f o r c e s g e n e r a t e d between t h e s o l i d and f l u i d p h a s e s c a u s e the i n c r e a s e of s e t t l e m e n t s , d i d n o t l e a d t o any p o s i t i v e r e s u l . t , I t i s much more l i k e l y t h a t t h e s e f r i c t i o n f o r c e s a r e compensated

by e l e c t r i c a l f i e l d f o r c e s working i n t h e o p p o s i t e d i r e c t i o l . , s o t h a t p r s s u m a b l y no a d d i t i o n a l g r a i n - t o - g r a i n p r e s s u r e s i n

t h e form o f o r d i n a r y f l o w p r e s s u r e s a r i s e , Thus flow p r e s - s u r e s o f t h i s n a t u r e a r e s c a r c e l y t o be c o n s i d e r e d a s t h e causc: o f t h e e l e c t r o s - o s m o t i c a l l y i n d u c e d c o n c e n t r a t i o n o f t h e m a t e r i a l , which a l s o o c c u r r e d i n a p u r e c l a y , V FUTURE OUTLOOK The a b o v e - d e s c r i b e d i n v e s t i g a t i o n s and p r e - l i m i n a r y r e s u l t s a r e Fntended above a l l t o b r i n g t h e p r o b l e m s , p r i n c i 2 1 e s and p o s s i b l e a p p l i c a t i o n s o f e l e c t r o - k f n e t i c

phenomena, vrith p a r t i c u l a r r e f e r e n c e t o t h e method o f e l e c t r o ,

d r a i n a g e , c l o s e r t o t h e r e a l m o f practice, Tklfs method o f e l e c t r o c d r a i n a g e dep3nds on e l e c t r o o s m o s i s , and a t t h f s p o i n t i t s h o u l d b e emphasfzed, i n o r d e r t o f i l l o u t t h e

e x ,

p o s i t f o n t h u s f a r made, t h a t t h e e f f e c t i n q u e s t i o n i s one which o n l y o c c u r s i n p o r o u s s t r u c t u r e s which have s u f f i c i e n t l y

f i n e d i s p e r s i o n , A s t h e s i z e of t h e p o r e s i n c r e a s e s , t h e g a l v a n i c c u r r e n t p r ~ d u c f n ~ ~ t h e e l e c t r o l y s i s f o m s a c o ~ ~ s t . a n t + l y L a c r e a s i n k perce.ltai,a o f t h e whole p r o c e s s i n r e l a t i o n t o t h e e l e c t r o ~ o s m o t i r : c u r r e n t . Faaorn t h e p o i n t o f view c f e l e c t x o , d r a i n a g e , t h i s g a l v a n i c c u r r e n t i s a l o s s , Presumably t h e a p p l i c a t i o n o f t h e method of e l e c t ~ o - o s m o s i s t o s e e p a g e s l a l i m i t e d t o pope d i a m e t e r s of a p p r o x i m a t e l y 0,1 t o

P

m i l l f m e t r e i n d f a m e t e ~ . The l a b o r a t - o r y e z i m s n t s c a r r i e d o u t t o d a t e w i t h t h e odometer ( F i g , 10 and 11) have sho-m t h a t i n con-

s i d e r a t i o n of t h e s e p a l l a t i o n o f t h e g a s e s a t t h e e l e c t r o d e s

i t was more a d v a n t a g e o u s , f ~ o m t h e p o i n t o f view o f t e c h n i q u e , t o have t h e s e e p a g e t h r o u g h t h e matezaf

al

t a k e p l a c e h o ~ f z o n -