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UBC Theses and Dissertations

Infiltration in water repellent soil Barrett, Gary Edward 1988

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INFILTRATION IN WATER REPELLENT SOIL by Gary Edward B a r r e t t B . S c , The U n i v e r s i t y of B r i t i s h Columbia, 1979 M.Sc, The U n i v e r s i t y of B r i t i s h Columbia, 1981 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Geography) We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1988 ®Gary Edward B a r r e t t , 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of G-(LQ(j (TJipbi^ The University of British Columbia Vancouver, Canada Date flfJfoW 10^ DE-6 (2/88) i i ABSTRACT Obse r v a t i o n s made at Goat Meadows - a s m a l l s u b - a l p i n e b a s i n l o c a t e d near Pemberton, B r i t i s h Columbia -demonstrated t h a t a l a y e r which i s e i t h e r water r e p e l l e n t or has only a l i m i t e d a f f i n i t y f o r water i s p r e s e n t at most v e g e t a t e d s i t e s . The l a y e r i s t y p i c a l l y a few ce n t i m e t r e s i n t h i c k n e s s , and i s u s u a l l y l o c a t e d at or near the top of the p r o f i l e : i t was prese n t o n l y i n the zone o f accumulation of o r g a n i c matter. The s p a t i a l d i s t r i b u t i o n o f the l a y e r d i d not appear t o be r e l a t e d t o the d i s t r i b u t i o n o f any p a r t i c u l a r s p e c i e s o f p l a n t . Sampling of s u b - a l p i n e s i t e s i n the Cascade, S e l k i r k , and P u r c e l l Mountains i n d i c a t e d t h a t such l a y e r s are common i n the a l p i n e - s u b - a l p i n e ecotone of southern B r i t i s h Columbia. The r e l a t i o n s h i p between ponding depth and i n f i l t r a t i o n r a t e was e x p l o r e d through experiments conducted on samples c o l l e c t e d near Ash Lake, i n Goat Meadows. These samples were chosen f o r a n a l y s i s because the r e p e l l e n t l a y e r was i n excess of t h i r t y c e n t i m e t r e s t h i c k at t h i s s i t e . I n f i l t r a t i o n r a t e s remained below 2xl0~ 9 m/s f o r a l l samples, even g i v e n ponding depths of up t o f o r t y c e n t i m e t r e s . Breakthrough of l i q u i d water was not observed, even a f t e r one month, which i m p l i e s t h a t most of i i i t h e i n f i l t r a t i o n o c c u r r e d as vapour t r a n s f e r . I n o r d e r t o observe t h e movement o f l i q u i d w a t e r t h r o u g h w a t e r r e p e l l e n t media, a p l e x i g l a s c e l l was c o n s t r u c t e d . A s y n t h e t i c water r e p e l l e n t sand w i t h u n i f o r m s u r f a c e p r o p e r t i e s was used as t h e medium. I t was found t h a t up t o some c r i t i c a l d e pth, t h e r e was no e n t r y o f wat e r i n t o t h e medium. As t h e p o n d i n g d e p t h was i n c r e a s e d i n s t e p s , t h e f r o n t would advance i n s t e p s : i t remained s t a t i o n a r y between t h e s e s t e p - i n c r e a s e s i n p o n d i n g d e p t h . As t h e f r o n t advanced, p r o t u b e r a n c e s o r " f i n g e r s " began t o d e v e l o p . A t some c r i t i c a l p o n d i n g d e p t h , a f i n g e r would grow w i t h o u t bound. These o b s e r v a t i o n s pose a c h a l l e n g e t o e x i s t i n g models o f i n f i l t r a t i o n , s i n c e i t appears t h a t h e t e r o g e n e i t y a t t h e s c a l e o f i n d i v i d u a l p o r e s must be i n v o k e d t o e x p l a i n them, b u t i t i s u s u a l l y assumed t h a t t h e p r o p e r t i e s o f a porous medium a r e c o n t i n u o u s a t t h i s s c a l e . The thermodynamics o f f i l l i n g and emptying o f p o r e s i s c o n s i d e r e d w i t h emphasis on t h e e f f e c t s o f p o r e shape and o f v a r i a t i o n s i n t h e p h y s i c o c h e m i c a l p r o p e r t i e s a t t h e s c a l e o f t h e p o r e . T h i s thermodynamic a n a l y s i s p r o v i d e s t h e c o n c e p t u a l b a s i s f o r development o f a model o f i n f i l t r a t i o n i n wh i c h p o r e - s c a l e h e t e r o g e n e i t y i s p r e s e r v e d . A l t h o u g h i t was not d e v e l o p e d as such, t h e i v model f o l l o w s t h e approach o f c e l l u l a r automata, i n w h i c h l o c a l r e l a t i o n s between p o r e s o r " c e l l s " g o v e r n t h e b e h a v i o u r o f t h e system. The model r e p l i c a t e d t h e o b s e r v a t i o n s o f i n f i l t r a t i o n i n t o s y n t h e t i c w a t e r r e p e l l e n t porous media w e l l : b o t h t h e h a l t i n g advance o f t h e f r o n t as t h e p o n d i n g d e p t h was i n c r e a s e d and t h e development o f f i n g e r s were s i m u l a t e d . The f a c t t h a t s uch complex b e h a v i o u r was p r e d i c t e d u s i n g o n l y a s i m p l e s e t o f p h y s i c a l l y b ased r u l e s c o n f i r m s t h e power o f t h e approach. V TABLE OF CONTENTS A b s t r a c t i i L i s t o f F i g u r e s v i i i L i s t o f P l a t e s x L i s t o f Symbols x i Acknowledgements x i i i C h a p t e r 1 - I n t r o d u c t i o n 1 A. The p h y s i c a l b a s i s o f wa t e r r e p e l l e n c y 5 -The d i s t r i b u t i o n o f wa t e r r e p e l l e n t s o i l s 6 B. M o d e l l i n g i n f i l t r a t i o n 12 C. O r g a n i z a t i o n o f t h e t h e s i s 15 Ch a p t e r 2 - F i e l d o b s e r v a t i o n s and l a b o r a t o r y 16 e x p e r i m e n t s A. Goat Meadows 17 B. Survey r e s u l t f o r s o u t h w e s t e r n B r i t i s h C olumbia 24 C. The r e l a t i o n s h i p between p o n d i n g d e p t h and 27 i n f i l t r a t i o n r a t e f o r Ash Lake samples D. O b s e r v a t i o n s o f i n f i l t r a t i o n i n a s y n t h e t i c 33 wa t e r r e p e l l e n t medium E. Summary 38 Ch a p t e r 3 - F i l l i n g and emptying o f p o r e s 41 A. W e t t i n g o f s o l i d s u r f a c e s 41 B. The e f f e c t o f geometry on f i l l i n g and emptying 47 o f p o r e s v i C. The e f f e c t of variati o n s of physicochemical 52 properties within pores on f i l l i n g and emptying - Spreading on s o l i d surfaces with 52 heterogeneous properties - Variations of properties within pores 55 - Experimental evidence 58 D. Summary 60 Chapter 4 - Modelling i n f i l t r a t i o n 62 A. The model 62 - Configuration of the flow f i e l d 64 - Constraints on the size of the model 66 - Gravity 67 - Boundary Conditions 68 - Assignment of c h a r a c t e r i s t i c s of 69 in d i v i d u a l pores - The f i l l i n g of pores 73 - Display of properties 79 B. Simulation of i n f i l t r a t i o n into a water 81 repellent medium - Review of the experimental r e s u l t s for 81 a synthetic water repellent medium - Validation of the model 83 C. S e n s i t i v i t y analysis 83 - Gravity 85 - Width of the d i s t r i b u t i o n of f i l l i n g 91 pressures - Contact angle 93 - Body radius 93 v i i D. Summary 95 Ch a p t e r 5 - Summary and D i s c u s s i o n 97 A. The d i s t r i b u t i o n o f wa t e r r e p e l l e n t s o i l s 97 B. I n f i l t r a t i o n i n wa t e r r e p e l l e n t media 100 C. The f i l l i n g and emptying o f p o r e s 101 D. M o d e l l i n g i n f i l t r a t i o n 102 E. I m p l i c a t i o n s f o r r u n o f f g e n e r a t i o n 104 R e f e r e n c e s 107 Appendix A - Methods f o r c o l l e c t i o n o f samples 111 Appe n d i x B - D e s c r i p t i o n o f t h e s u b - a l p i n e s u r v e y 113 s i t e s , s o u t h e r n B r i t i s h C o l u m b i a v i i i LIST OF FIGURES Figure T i t l e 1:1 Coating of a surface by amphophilic 7 molecules. 1:2 The contact angle. 8 2:1 Locations of sampling s i t e s . 18 2:2 Location of sampling s i t e s at Goat 20 Meadows. 2:3 C l a s s i f i c a t i o n of s o i l s by the water drop 21 penetration time test 2:4 Ch a r a c t e r i s t i c s of the Goat Meadows 23 samples. 2:5 Ch a r a c t e r i s t i c s of the sub-alpine survey 26 samples. 2:6 Location of the Ash Lake sampling s i t e s . 29 2:7 Apparatus for measurement of i n f i l t r a t i o n 30 rate. 2:8 Ch a r a c t e r i s t i c s of the Ash Lake samples. 32 2:9 Apparatus for observation of i n f i l t r a t i o n 36 in a synthetic water repellent medium. 2:10 I n f i l t r a t i o n i n synthetic water repellent 37 medium. 3:1 Wetting behavior as a function of the 4 6 contact angle. 3:2 C a p i l l a r y depression. 50 3:3 Hysteresis of the contact angle at 53 material boundaries. 3:4 F i l l i n g and draining of a c y l i n d r i c a l 56 pore within which the contact angle changes. IX 4:1 Diagram o f b o u n d a r i e s and p o r e 65 c o n n e c t i o n s . 4:2 D i s t r i b u t i o n o f neck r a d i i w i t h 72 body r a d i i . 4:3 F i l l i n g p o r e s by rows. 77 4:4 Comparison o f p o r e - f i l l i n g a l g o r i t h m s . 80 4:5 R e s u l t s o f m o d e l l i n g - growth o f a 84 f i n g e r . 4:6 R e s u l t s o f m o d e l l i n g - t h e e f f e c t o f 86 g r a v i t y . 4:7 R e s u l t s o f m o d e l l i n g - a second example 88 o f t h e e f f e c t o f g r a v i t y . 4:8 R e s u l t s o f m o d e l l i n g - t h e e f f e c t o f 90 g r a v i t y on m o i s t u r e c o n t e n t p r o f i l e s . 4:9 R e s u l t s o f m o d e l l i n g - t h e e f f e c t o f 92 t h e w i d t h o f t h e d i s t r i b u t i o n o f p o r e r a d i i . 4:10 Head a t " b r e a k t h r o u g h " v e r s u s c o s i n e o f 94 c o n t a c t a n g l e . 4:11 Head a t " b r e a k t h r o u g h " v e r s u s i n v e r s e o f 96 neck r a d i u s . X LIST OF PLATES P l a t e T i t l e 1 P h o t o m i c r o g r a p h o f s o i l s sample from 34 Ash Lake s i t e . 2 P h o t o m i c r o g r a p h o f w a t e r drop on sample 34 from Ash Lake s i t e . B : l Manning P a r k s i t e . 116 B:2 Manning Park samples. 117 B:3 Idaho Peak s i t e . 118 B:4 Idaho Peak samples. 1119 B:5 Kokanee Lake s i t e . 120 B:6 Kokanee Lake samples. 121 B:7 E l k Lake s i t e . 122 x i LIST OF SYMBOLS a c o n t a c t angle T s w s o l i d - w a t e r i n t e r f a c i a l energy T s a s o l i d - a i r i n t e r f a c i a l energy Tw a w a t e r - a i r i n t e r f a c i a l energy 0 v o l u m e t r i c water content p d e n s i t y a s w s o l i d - w a t e r i n t e r f a c i a l t e n s i o n a s a s o l i d - a i r i n t e r f a c i a l t e n s i o n a w a w a t e r - a i r i n t e r f a c i a l t e n s i o n (p p r e s s u r e p o t e n t i a l (pf p r e s s u r e p o t e n t i a l at which a pore w i l l f i l l cpe p r e s s u r e p o t e n t i a l at which a pore w i l l empty cpb p r e s s u r e p o t e n t i a l at upper boundary o f flow f i e l d Q the a f f i n i t y of a s o l i d f o r water A area o f an i n t e r f a c e g g r a v i t a t i o n a c c e l e r a t i o n h p r e s s u r e p o t e n t i a l expressed as a depth of water h b p r e s s u r e p o t e n t i a l at upper boundary expressed as a depth of water h f f i l l i n g p r e s s u r e f o r pore expressed as a head of water K h y d r a u l i c c o n d u c t i v i t y K[q>] h y d r a u l i c c o n d u c t i v i t y at a p r e s s u r e p o t e n t i a l of L depth t o w e t t i n g f r o n t from s u r f a c e P p r e s s u r e x i i r r a d i u s r b r a d i u s o f the body of a pore ( g r e a t e s t r a d i u s ) r n r a d i u s o f the neck of a pore ( s m a l l e s t r a d i u s ) t time W work x p o s i t i o n z h e i g h t above datum z b h e i g h t above datum of upper boundary o f flow f i e l d Symbols used i n d e s c r i p t i o n o f d i s t r i b u t i o n s o f pore p r o p e r t i e s rmean mean r a d i u s o f parent p o p u l a t i o n r s d s t a n d a r d d e v i a t i o n of r a d i u s of parent p o p u l a t i o n c t m e a n mean c o n t a c t angle o f parent p o p u l a t i o n o^in lower l i m i t f o r co n t a c t angle f o r r e c t a n g u l a r d i s t r i b u t i o n ot m a x upper l i m i t f o r co n t a c t angle f o r r e c t a n g u l a r d i s t r i b u t i o n x i i i ACKNOWLEDGEMENT S I t h a n k my t h e s i s s u p e r v i s o r , Dr. O l a v Slaymaker, f o r t h e academic g u i d a n c e p r o v i d e d and f o r t h e encouragement o f f e r e d t h r o u g h o u t t h i s p r o j e c t . I thank t h e o t h e r members o f t h e committee - Dr. M i c h a e l Church o f Geography, Dr. Jan D e V r i e s o f S o i l S c i e n c e , and Dr. R. A l l a n F r e e z e o f Geology - f o r t h e i r p a r t i c i p a t i o n i n a l l phases o f t h i s r e s e a r c h . I a l s o thank Dr. Thomas Dunne f o r making t h e arrangements w h i c h a l l o w e d me t o a t t e n d c l a s s e s i n Geology a t t h e U n i v e r s i t y o f Washington as a v i s i t i n g g r a d u a t e s t u d e n t . I am g r a t e f u l t o t h e N a t u r a l S c i e n c e s and E n g i n e e r i n g C o u n c i l o f Canada f o r p r o v i d i n g f i n a n c i a l s u p p o r t f o r two y e a r s . I thank t h e U n i v e r s i t y o f B r i t i s h C olumbia f o r a f u r t h e r y e a r o f s u p p o r t . I w o u l d a l s o l i k e t o acknowledge a number o f p e o p l e who c o n t r i b u t e d t o t h e r e s e a r c h . R i c h a r d L e s l i e d e s i g n e d and c o n s t r u c t e d much o f t h e equipment used i n t h e f i e l d and l a b o r a t o r y ; when problems a r o s e , he o f t e n gave g e n e r o u s l y o f h i s own t i m e . To Leonard S i e l e c k i , I e x t e n d my s i n c e r e t h a n k s f o r h i s c o n t r i b u t i o n t o t h e f i e l d r e s e a r c h , e s p e c i a l l y t h e s u r v e y o f t h e s u b - a l p i n e ecotone o f s o u t h e r n B r i t i s h C o lumbia. I thank A l i s t a i r McLean f o r h i s a s s i s t a n c e i n t h e l a b o r a t o r y and f o r p h o t o g r a p h i n g s o i l x i v samples. I am g r a t e f u l t o O l l i e Heggen, o f V i c t o r i a , f o r p r e p a r i n g a map o f t h e s u r v e y s i t e s . I owe a s p e c i a l debt t o Thorn G a l l i e f o r i n t r o d u c i n g me t o t h e s i t e , and f o r t h e a d v i c e and a s s i s t a n c e o f f e r e d as I began t h i s r e s e a r c h . I a l s o thank C a t h e r i n e Souch f o r h e l p i n t h e f i e l d , and f o r many u s e f u l d i s c u s s i o n s about the. r e s e a r c h . Ed L e v i n s o n and P e t e r C e l l i e r s a r e t h a n k e d f o r t a k i n g t i m e t o d i s c u s s a number o f i s s u e s w i t h me. I would a l s o l i k e t o e x t e n d t h a n k s t o t h o s e f r i e n d s w i t h whom I have s h a r e d an o f f i c e : C a r o l e R u t t l e , A r t h u r F a l l i c k , J u d i t h W r i g h t , and J o s e p h i n e K e l l y . I a l s o t h a n k my f o r m e r housemates, who a r e , i n f a c t , t o o numerous t o m e n t i o n . S p e c i a l t h a n k s a r e e x t e n d e d t o C a t h e r i n e Souch, Sue Grimmond, and P a t t i Luniw f o r t h e i r h e l p i n t h e f i n a l s t a g e s o f a s s e m b l i n g t h i s document. F i n a l l y , I would l i k e t o t h a n k my p a r e n t s , Edward and M u r i e l B a r r e t t , f o r a l i f e t i m e o f encouragement and s u p p o r t . 1 INTRODUCTION The i n f i l t r a t i o n p r o c e s s p l a y s a c e n t r a l r o l e i n r e g u l a t i o n o f t h e h y d r o l o g i c a l b e h a v i o u r o f d r a i n a g e b a s i n s , and has t h e r e f o r e r e c e i v e d a c o n s i d e r a b l e amount o f a t t e n t i o n . R i c h a r d s (1931) p r o v i d e d t h e b a s i s f o r our c u r r e n t u n d e r s t a n d i n g o f t h e i n f i l t r a t i o n p r o c e s s w i t h h i s t h e o r y o f " c a p i l l a r y c o n d u c t i o n " . R i c h a r d s assumed e x p l i c i t l y t h a t t h e s o l i d s u r f a c e s o f h i s h y p o t h e t i c a l p o r o u s medium a r e p e r f e c t l y w e t t a b l e . In t h i s t h e s i s , i n f i l t r a t i o n i s c o n s i d e r e d i n t o media i n w h i c h t h i s a s s u m p t i o n i s not met. The f o c u s i s upon i n f i l t r a t i o n i n t o w a t e r r e p e l l e n t s o i l s - w h i c h r e p r e s e n t an extreme d e p a r t u r e from t h e p e r f e c t l y w e t t a b l e medium c o n s i d e r e d by R i c h a r d s - but l e s s extreme c a s e s a r e a l s o examined. F i e l d i n v e s t i g a t i o n s o f t h e d i s t r i b u t i o n o f w a t e r r e p e l l e n t s o i l s i n t h e a l p i n e - s u b - a l p i n e ecotone o f B r i t i s h C o lumbia s e r v e d t o m o t i v a t e and d i r e c t t h e t h e o r e t i c a l work w h i c h c o n s t i t u t e s t h e c o r e o f t h i s t h e s i s . The i s s u e o f how water r e p e l l e n t l a y e r s might a f f e c t t h e p r o c e s s o f i n f i l t r a t i o n was prompted, i n p a r t , by B a r r e t t ' s (1981) o b s e r v a t i o n t h a t water r e p e l l e n t l a y e r s a r e an i m p o r t a n t f a c t o r i n t h e g e n e r a t i o n o f o v e r l a n d f l o w a t Goat Meadows, a s m a l l s u b - a l p i n e b a s i n n e a r Pemberton, B r i t i s h C o lumbia. The i m p o r t a n c e o f t h e phenomenon was 2 b r o u g h t i n t o c l e a r e r f o c u s by t h e work o f G a l l i e and Slaymaker (1984), who p r o p o s e d i n t h e i r i n t e r p r e t a t i o n o f s o l u t e s o u r c e s and t r a n s f e r s a t Goat Meadows t h a t w a t e r r e p e l l e n t l a y e r s might be r e s p o n s i b l e f o r w a t e r b y p a s s i n g t h e m a t r i x . As f a r as t h e a u t h o r i s aware, t h e s e s t u d i e s a r e t h e f i r s t t o suggest t h a t w a t e r r e p e l l e n t s o i l s a r e p r e s e n t i n t h e a l p i n e - s u b - a l p i n e ecotone o f B r i t i s h C o l u m b i a . The f i r s t phase o f t h e f i e l d i n v e s t i g a t i o n s was d i r e c t e d towards d e t e r m i n i n g t h e e x t e n t and n a t u r e o f wa t e r r e p e l l e n c y a t Goat Meadows. Samples were s t r a t i f i e d by s o i l - v e g e t a t i o n a s s o c i a t i o n s i d e n t i f i e d p r e v i o u s l y by G a l l i e (1983). The o b j e c t i v e o f t h e second phase o f t h e f i e l d work was t o d e t e r m i n e i f t h e r e s u l t s a t Goat Meadows are r e p r e s e n t a t i v e o f t h e a l p i n e - s u b - a l p i n e ecotone o f s o u t h e r n B r i t i s h C o lumbia: i t was c o n c l u d e d t h a t t h e y a r e . Of perhaps even g r e a t e r s i g n i f i c a n c e i s t h e d i s c o v e r y t h a t t h i n l a y e r s o f s o i l a r e common wh i c h , w h i l e n o t r e p e l l e n t , have a v e r y l i m i t e d a f f i n i t y f o r w a t e r . I n o r d e r t o u n d e r s t a n d b e t t e r t h e e f f e c t s o f w a t e r r e p e l l e n c y on i n f i l t r a t i o n , l a b o r a t o r y i n v e s t i g a t i o n s o f t h e p r o c e s s were c o n d u c t e d u s i n g samples c o l l e c t e d a t a s i t e where t h e r e p e l l e n t l a y e r was p a r t i c u l a r l y t h i c k and w e l l - d e f i n e d . The r e s u l t s s u g g e s t e d t h a t under c o n d i t i o n s 3 w h i c h might be met i n t h e f i e l d , t h e r e would be v i r t u a l l y no i n f i l t r a t i o n i n t h e s e most r e p e l l e n t o f l a y e r s , s i n c e t h e r e was no f l o w o f w a t e r even when wa t e r was ponded t o a d e p t h o f f o r t y c e n t i m e t r e s o r more. For e x t r e m e l y r e p e l l e n t s o i l s , t h e t r a n s p o r t o f w a t e r as vapour i s e x p e c t e d t o dominate under most c i r c u m s t a n c e s . T h i s r e s u l t i s i m p o r t a n t f o r u n d e r s t a n d i n g t h e h y d r o l o g i c a l b e h a v i o u r o f t h e b a s i n i n w h i c h t h e samples were c o l l e c t e d . U n d e r s t a n d i n g o f t h e p r o c e s s o f i n f i l t r a t i o n i n t o s o i l s w h i c h do not r e s i s t w e t t i n g so c o m p l e t e l y r e q u i r e d f u r t h e r i n v e s t i g a t i o n . The i n f i l t r a t i o n p r o c e s s i n water r e p e l l e n t s o i l s has r e c e i v e d l i t t l e a t t e n t i o n , a l t h o u g h i t has been s u g g e s t e d by P h i l i p (1975) t h a t i n f i l t r a t i o n i n w a t e r r e p e l l e n t s o i l s may be u n s t a b l e . I n such c a s e s , a p l a n a r w e t t i n g f r o n t does not form; i n s t e a d , s a t u r a t e d " f i n g e r s " grow. P h i l i p d i d not t e s t t h i s p r o p o s i t i o n d i r e c t l y , s i n c e i t a r o s e o n l y i n c o n n e c t i o n w i t h a more g e n e r a l a n a l y s i s o f u n s t a b l e i n f i l t r a t i o n based upon a c l a s s i c a l h y d r o d y n a m i c a l approach. In t h i s t h e s i s , t h e p r o p o s i t i o n was t e s t e d t h r o u g h o b s e r v a t i o n o f i n f i l t r a t i o n i n a s y n t h e t i c w a t e r r e p e l l e n t "sand" i n a c l e a r p l e x i g l a s c e l l . F i n g e r s d i d form, but t h e e a r l y s t a g e s o f t h e i n f i l t r a t i o n p r o c e s s and t h e development o f t h e f i n g e r s d i f f e r e d i n s i g n i f i c a n t ways from t h e p r e d i c t i o n s o f 4 P h i l i p . I n c o n v e n t i o n a l a n a l y s e s o f t h e i n f i l t r a t i o n p r o c e s s , t h e p r o p e r t i e s o f a porous medium a r e t r e a t e d as though t h e y a r e c o n t i n u o u s . I t i s argued i n t h i s t h e s i s t h a t t h e d i s c o n t i n u o u s n a t u r e o f t h e medium must be c o n s i d e r e d i n o r d e r t o d e s c r i b e a d e q u a t e l y t h e p r o c e s s o f i n f i l t r a t i o n as o b s e r v e d i n t h e s y n t h e t i c water r e p e l l e n t medium. T h i s p r o p o s i t i o n prompted development o f a model o f t h e i n f i l t r a t i o n p r o c e s s i n wh i c h t h e p r o p e r t i e s o f t h e medium a r e d i s c o n t i n u o u s . A l t h o u g h i t was not d e v e l o p e d as such, t h e model can be c o n s i d e r e d t o be an a p p l i c a t i o n o f t h e approach o f c e l l u l a r automata, i n t h a t l o c a l r e l a t i o n s g o v e r n t h e b e h a v i o u r o f t h e system (see T o f f o l i and M a r g o l u s , 1987). The approach t a k e n a l l o w e d t h e p r o c e s s o f f i n g e r f o r m a t i o n i n wa t e r r e p e l l e n t media t o be s i m u l a t e d u s i n g a s i m p l e s e t o f p h y s i c a l l y based r u l e s i n w h i c h t h e h e t e r o g e n e i t y o f pore p r o p e r t i e s i s r e c o g n i z e d . Not o n l y was f i n g e r f o r m a t i o n s i m u l a t e d , but t h e advance o f t h e w e t t i n g f r o n t from one p o s i t i o n o f s t a b i l i t y t o a n o t h e r , as o b s e r v e d i n t h e s y n t h e t i c water r e p e l l e n t medium, was a l s o r e p l i c a t e d . The f a c t t h a t a complex m a c r o s c o p i c p r o c e s s was p r e d i c t e d u s i n g o n l y r u l e s b a s e d upon m i c r o s c o p i c i n t e r a c t i o n s i s a s i g n i f i c a n t r e s u l t . The t e s t 5 o f t h e model was whether o r not t h e e v o l u t i o n o f t h e f i n g e r s was p r e d i c t e d , r a t h e r t h a n more c o n v e n t i o n a l c r i t e r i a b a sed upon i n f i l t r a t i o n r a t e s , o r some o t h e r q u a n t i t a t i v e t e s t . Such q u a n t i t a t i v e t e s t s might be a p p l i e d t o more complex v e r s i o n s o f t h e model, but t h e q u a l i t a t i v e t e s t s a p p l i e d , w h i c h c o n v e n t i o n a l approaches f a i l , a r e fundamental i n t h a t t h e y r e q u i r e t h e model t o r e p l i c a t e t h e p r o c e s s . I n t h i s t h e s i s , t h e f i e l d o b s e r v a t i o n s and l a b o r a t o r y e x p e r i m e n t s w h i c h prompted t h e a n a l y s i s a r e p r e s e n t e d a l o n g w i t h t h e t h e o r e t i c a l b a s i s o f t h e model, t h e development o f model, and t h e r e s u l t s o f t h e s i m u l a t i o n s . As b a c k g r o u n d f o r t h e s e d i s c u s s i o n s , t h e phenomenon o f w a t e r r e p e l l e n c y i s r e v i e w e d , and c o n v e n t i o n a l approaches t o m o d e l l i n g i n f i l t r a t i o n a r e c o n s i d e r e d . A. The p h y s i c a l b a s i s o f w a t e r r e p e l l e n c y I t i s t h o u g h t t h a t i n most c a s e s w a t e r r e p e l l e n c y i s c o n f e r r e d by a l a y e r o f o r g a n i c m a t t e r d e p o s i t e d on t h e s u r f a c e o f m i n e r a l g r a i n s . B o z e r , B r a n d t , and Hemwall (1969) have s u g g e s t e d t h a t such c o a t i n g s n o r m a l l y c o n s i s t o f a m p h o p h i l i c compounds; t h a t i s , compounds w h i c h have p o l a r o r i o n i z a b l e groups a t one end o f a c a r b o n c h a i n , and n o n p o l a r groups a t t h e o t h e r . The p o l a r o r i o n i z a b l e groups a r e a t t r a c t e d t o t h e s u r f a c e o f t h e m i n e r a l , and 6 t h e n o n p o l a r groups a r e d i r e c t e d outward, as i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e 1:1. I t i s t h e p r o p e r t i e s o f t h i s s u r f a c e c o a t i n g o f t h e m i n e r a l g r a i n w h i c h d e t e r m i n e whether o r not t h e m a t r i x i s h y d r o p h i l i c o r h y d r o p h o b i c . The c o n t a c t a n g l e i s o f t e n u sed t o c h a r a c t e r i z e t h e p h y s i c o c h e m i c a l p r o p e r t i e s o f a s u r f a c e . The c o n t a c t a n g l e i s t h e a n g l e formed by a w a t e r - a i r i n t e r f a c e w i t h a p l a n e h o r i z o n t a l s o l i d s u r f a c e , as i l l u s t r a t e d i n F i g u r e 1:2. The a n g l e o f c o n t a c t , a , i s g e n e r a l l y h e l d t o be governed by Young's e q u a t i o n (see Osipow, 1977): (°sa - <*sw>/°wa = C O S [a] (1) where a s a , a s w , and o w a a r e t h e s o l i d - a i r , s o l i d - w a t e r , and w a t e r - a i r i n t e r f a c i a l t e n s i o n s r e s p e c t i v e l y . A s u r f a c e i s h y d r o p h i l i c i f t h e i n t e r f a c i a l t e n s i o n a t t h e s o l i d s u r f a c e i s l e s s i f c o v e r e d by w a t e r t h a n by a i r , and h y d r o p h o b i c i f t h e c o n v e r s e i s t r u e . From Young's e q u a t i o n i t can be seen t h a t t h e c o n t a c t a n g l e w i l l be l e s s t h a n n i n e t y degrees f o r a h y d r o p h i l i c s u r f a c e , and g r e a t e r t h a n n i n e t y degrees f o r a h y d r o p h o b i c s u r f a c e . The d i s t r i b u t i o n of water repellent s o i l s A v a r i e t y o f m i c r o o r g a n i s m s and p l a n t s have been i m p l i c a t e d i n t h e p r o d u c t i o n o f s u b s t a n c e s w h i c h can c o n f e r w a t e r r e p e l l e n c y t o i n i t i a l l y n o n - r e p e l l e n t hydrophilic solid surface •m Molecule — @ hydrophilic hydrophobic Figure 1:1. Coating of a surface by amphophilic molecules. oo 9 m a t e r i a l s . I t was s u g g e s t e d by Bond and H a r r i s (1964) t h a t B a s i d o m y c e t e f u n g i produce a s u b s t a n c e w h i c h i s r e s p o n s i b l e f o r t h e r e p e l l e n c y o f an A u s t r a l i a n s o i l t h a t t h e y s t u d i e d . The r o l e o f m i c r o o r g a n i s m s i n c a u s i n g r e p e l l e n c y was i n v e s t i g a t e d f u r t h e r by Savage, M a r t i n , and L e t e y (1969), who t e s t e d e x t r a c t s from e i g h t s p e c i e s o f f u n g i . Two s p e c i e s o f f u n g i , Aspergillus sydotvi and Penicullum nigrans caused l i m i t e d r e p e l l e n c y i n an a r t i f i c i a l medium. In s o u t h e r n C a l i f o r n i a , w a t e r r e p e l l e n t s o i l s have been r e p o r t e d t o be a s s o c i a t e d w i t h C h a p a r r a l v e g e t a t i o n (Krammes and Debano, 1965). I n Utah, t h e r e i s e v i d e n c e t h a t l i t t e r from J u n i p e r t r e e s c o n t r i b u t e s t o t h e development o f water r e p e l l e n c y ( S c h o l l , 1971). R o b e r t s and Carbon (1972) found t h a t e x t r a c t s from a v a r i e t y o f m e s o p h y t i c and x e r o p h y t i c v e g e t a t i o n i n s o u t h w e s t e r n A u s t r a l i a c o u l d cause water r e p e l l e n c y , b u t t h e y a l s o s u g g e s t e d t h a t m i c r o o r g a n i s m s may p l a y a r o l e . The r e p e l l e n c y o f t h e s o i l s t h a t t h e y s t u d i e d appeared t o be due t o t h e p r e s e n c e o f a s t a b l e humic a c i d complex. M i l l e r and W i l k i n s o n (1977), i n a s t u d y o f water r e p e l l e n c y on g o l f g r e e n s , found t h a t r e p e l l e n c y appeared t o be caused by a " s k i n " o f o r g a n i c m a t t e r s i m i l a r i n c h a r a c t e r t o f u l v i c a c i d s . They s p e c u l a t e d t h a t t h e s e s u b s t a n c e s may have been produc e d by Basidomycete f u n g i , o r perhaps 10 d e r i v e d from decay p r o d u c t s o f t h e h y p h a l mat a f t e r d e a t h o f t h e fungus. I n w e s t e r n A u s t r a l i a , " l e a f d r i p " from M a l l e t t r e e s was found t o r e n d e r s o i l s w a t e r r e p e l l e n t (McGhie and Posner, 1980). The r e s u l t s r e p o r t e d above suggest t h a t w a t e r r e p e l l e n t s u b s t a n c e s a r e p r o d u c e d by a v a r i e t y o f o r g a n i s m s , i n c l u d i n g p l a n t s and some f u n g i , and may a l s o be d e r i v e d from t h e p r o d u c t s o f decay o f a v a r i e t y o f p l a n t s and m i c r o o r g a n i s m s . A l t h o u g h t h e c l i m a t e a s s o c i a t e d w i t h t h e s e s i t e s i s not r e p o r t e d i n a l l c a s e s , i t appears t h a t most o f t h e s e s i t e s a r e i n a r i d o r s e m i a r i d a r e a s , where t h e r e i s o n l y a s p a r s e v e g e t a t i v e c o v e r . I t i s not c l e a r whether t h e a s s o c i a t i o n w i t h c l i m a t e i s due t o g r e a t e r ease o f r e c o g n i t i o n o f t h e phenomenon because o f t h e l i m i t e d v e g e t a t i v e c o v e r , o r whether water r e p e l l e n c y i s i n f a c t more common i n t h e s e a r e a s . The same s u b s t a n c e s w h i c h p r o t e c t t h e s e organisms from d e s i c c a t i o n may a l s o be r e s p o n s i b l e f o r t h e water r e p e l l e n c y o f t h e s o i l , e i t h e r d i r e c t l y o r a f t e r a l t e r a t i o n by m i c r o o r g a n i s m s . Thus, t h e phenomenon may, i n f a c t , be c h a r a c t e r i s t i c o f some a r i d and s e m i a r i d e n v i r o n m e n t s . F i r e , whether a s s o c i a t e d w i t h f o r e s t f i r e s o r t h e c o n t r o l l e d b u r n i n g o f s l a s h , may produce o r i n t e n s i f y w a t e r r e p e l l e n c y (Debano, Mann, and H a m i l t o n , 1970; 11 Savage, Osborne, Letey, and Heaton, 1972; Debano and Rice, 1973; and Reeder and Jurgenson, 1979). It appears that the materials involved are altered by the heat of the f i r e , as well as being v o l a t i l i z e d and deposited on the surfaces of mineral grains. Savage, Martin, and Letey (1969) found that although only two of the eight species of fungi they tested conferred repellency to s o i l , heating the samples to between 200°C and 400°C produced repellency for a l l of the eight species of fungi. Giovannini and Lucchesi (1984), however, found that the water repellency of s o i l s at a s i t e at V i l l a s a l t o , i n Sardinia, decreased a f t e r a con t r o l l e d f i r e : presumably due to destruction of the compounds which normally confer repellency. Flow i n water repellent s o i l s has been discussed by Debano (1969), who pointed out that transport of water as a vapour i s l i k e l y to be of greater r e l a t i v e importance i n these s o i l s than i n a non-repellent s o i l because the flow of water as a l i q u i d i s i n h i b i t e d . Brandt (1969) conducted experiments on the flow of water as a l i q u i d i n water repellent s o i l s . In s o i l s which had been treated with a "waterproofing" agent, TBC, or 4-t-butyl catechol, i t was found that there was no flow up to some c r i t i c a l pressure: when pressures greater than t h i s were imposed, the rate of flow increased rapidly, then decreased to a constant, s l i g h t l y lower value. Brandt suggested that t h i s pattern-12 was due to reorientation of p a r t i c l e s as a r e s u l t of the imposition of high pressure gradients. P h i l i p (1975) has discussed flow i n water repellent media i n connection with his analysis of hydrodynamically unstable i n f i l t r a t i o n . He predicted that water repellency could lead to unstable i n f i l t r a t i o n , which manifests i t s e l f through formation of saturated fingers which outgrow the remainder of the front as i n f i l t r a t i o n proceeds. Fingering during i n f i l t r a t i o n was reported f i r s t by H i l l and Parlange (1972) for the case where a f i n e -textured layer o v e r l i e s a coarse-textured one. However, as P h i l i p (1975) has shown, fingering may be expected during v e r t i c a l flow whenever the " c a p i l l a r y gradient" opposes the g r a v i t a t i o n a l gradient. For i n f i l t r a t i o n into water repellent media, the c a p i l l a r y gradient w i l l oppose the g r a v i t a t i o n a l p o t e n t i a l gradient since water i s repell e d rather than attracted. While the c r i t e r i o n provided by P h i l i p appears to be a necessary condition, i t i s not clea r whether or not i t i s a s u f f i c i e n t condition for fin g e r i n g . B. Modelling i n f i l t r a t i o n As P h i l i p (1983) noted i n a b r i e f h i s t o r i c a l account of the development of the Green and Ampt equation, Buckingham (1907) l a i d the foundation for our present understanding 13 of the i n f i l t r a t i o n process through his d e f i n i t i o n of s o i l water p o t e n t i a l and unsaturated hydraulic conductivity. Four years a f t e r Buckingham, Green and Ampt (1911) published an equation for i n f i l t r a t i o n , which was v e r i f i e d experimentally for well-sorted media. In cases where the pressure at the upper surface of a sample i s maintained at zero - the just-ponding condition - the i n f i l t r a t i o n rate, i , i s given by: i = K (h + L) /L (2) where L i s the depth of penetration of the wetting front, h i s the c a p i l l a r y p o t e n t i a l expressed as a head of water, and K i s the hydraulic conductivity of the medium at saturation. In 1931, Richards proposed a more general equation for flow i n porous media, which for one-dimensional v e r t i c a l flow, may be written as: (80/8(p) 8<p/8t = 8/5z{K (8(p/8z + 1)} (3) where 0 i s the volumetric water content, <p i s the pressure p o t e n t i a l , t i s time, and K i s the hydraulic conductivity. This p a r t i a l d i f f e r e n t i a l equation i s solved for boundary and i n i t i a l conditions appropriate to the p a r t i c u l a r problem being considered. 14 The e q u a t i o n p r o p o s e d by R i c h a r d s i s s i m i l a r i n form t o e q u a t i o n s d e v e l o p e d t o d e s c r i b e t h e t r a n s f e r o f h e a t and e l e c t r i c i t y : a l l a r e based upon t h e p r i n c i p l e t h a t a f l u x i s d i r e c t e d from a r e a s o f h i g h e r p o t e n t i a l t o l o w e r p o t e n t i a l . By e x p e r i m e n t , a c o e f f i c i e n t can be found w h i c h r e l a t e s t h e magnitude o f t h e f l u x t o t h e s t r e n g t h o f t h e p o t e n t i a l g r a d i e n t . I n t h e case o f heat o r e l e c t r i c i t y , t h i s c o e f f i c i e n t o f t e n has o n l y a weak dependence upon t h e p o t e n t i a l i t s e l f , b u t i n t h e case o f t h e f l o w o f w a t e r i n u n s a t u r a t e d media t h e c o e f f i c i e n t - t h e u n s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y - depends upon b o t h t h e p r e s e n t p r e s s u r e p o t e n t i a l and t h e w e t t i n g h i s t o r y o f t h e medium. To f u r t h e r c o m p l i c a t e a p p l i c a t i o n o f t h i s e q u a t i o n , t h e r a t e o f change o f water c o n t e n t w i t h p o t e n t i a l i s a l s o a f u n c t i o n o f t h e p r e s s u r e p o t e n t i a l and t h e w e t t i n g h i s t o r y o f t h e medium. The complex b e h a v i o u r o f porous media i n r e s p o n s e t o changes i n t h e p r e s s u r e p o t e n t i a l confounds a n a l y t i c a l s o l u t i o n o f t h e R i c h a r d s e q u a t i o n , u n l e s s a number o f s i m p l i f y i n g a s sumptions a r e made. F o r example, P h i l i p ' s (1957) " d e l t a - f u n c t i o n model", i n w h i c h t h e r e l a t i o n s h i p between t h e d i f f u s i v i t y and t h e w a t e r c o n t e n t i s assumed t o be a d e l t a - f u n c t i o n , i s e q u i v a l e n t t o Green and Ampt's as s u m p t i o n t h a t t h e r e l a t i o n s h i p s between t h e w a t e r c o n t e n t and p r e s s u r e p o t e n t i a l and between t h e h y d r a u l i c 15 c o n d u c t i v i t y and p r e s s u r e p o t e n t i a l a r e s t e p - f u n c t i o n s ( P h i l i p , 1983). I t was not u n t i l n u m e r i c a l methods o f s o l u t i o n were b r o u g h t t o b e a r upon t h e pr o b l e m t h a t i n f i l t r a t i o n c o u l d be m o d e l l e d r e a l i s t i c a l l y f o r u n s a t u r a t e d s o i l s under a wide range o f c o n d i t i o n s . C. O r g a n i z a t i o n o f t h e t h e s i s The f i e l d o b s e r v a t i o n s and l a b o r a t o r y e x p e r i m e n t s w h i c h m o t i v a t e t h e t h e o r e t i c a l work p r e s e n t e d i n t h i s t h e s i s a r e r e v i e w e d i n C h a p t e r 2. I n Ch a p t e r 3, t h e r o l e o f v a r i a t i o n s i n t h e p h y s i c o c h e m i c a l p r o p e r t i e s o f s o i l s i n th e f i l l i n g and d r a i n i n g o f porous media i s c o n s i d e r e d . The m a t e r i a l d i s c u s s e d i n C h a p t e r 3 p r o v i d e s t h e t h e o r e t i c a l b a s i s f o r t h e model o f i n f i l t r a t i o n p r e s e n t e d i n C h a p t e r 4, w h i c h d e f i n e s t h e i n f i l t r a t i o n p r o c e s s e s i n terms o f l o c a l r e l a t i o n s between i n d i v i d u a l p o r e s , f o r wh i c h g e o m e t r i c and s u r f a c e p r o p e r t i e s a r e drawn randomly from p a r e n t p o p u l a t i o n s w i t h s p e c i f i e d p r o p e r t i e s . The t h e s i s c o n c l u d e s w i t h a summary o f t h e r e s u l t s and a d i s c u s s i o n o f some o f t h e i m p l i c a t i o n s f o r h y d r o l o g y i n Ch a p t e r 5. 16 CHAPTER 2 - FIELD OBSERVATIONS AND LABORATORY EXPERIMENTS I n t h i s c h a p t e r t h e r e s u l t s o f t h e f i e l d s t u d i e s and l a b o r a t o r y e x p e r i m e n t s a r e p r e s e n t e d . The f i e l d s t u d i e s were d e s i g n e d t o improve our u n d e r s t a n d i n g o f t h e d i s t r i b u t i o n o f wa t e r r e p e l l e n t s o i l s i n t h e a l p i n e - sub-a l p i n e e c o t o n e o f B r i t i s h C o lumbia. There were two phases o f t h e f i e l d r e s e a r c h . I n t h e f i r s t , t h e r e l a t i o n s h i p between s o i l - v e g e t a t i o n assemblages and wa t e r r e p e l l e n c y was examined a t Goat Meadows, a s u b - a l p i n e s i t e s t u d i e d p r e v i o u s l y by B a r r e t t (1981) and by G a l l i e and Slaymaker (1984, 1985). I n t h e second phase, t h e d i s t r i b u t i o n o f w a t e r r e p e l l e n c y a t o t h e r s u b - a l p i n e s i t e s i n s o u t h e r n B r i t i s h C olumbia was i n v e s t i g a t e d . The r e l a t i o n s h i p between i n f i l t r a t i o n r a t e and p o n d i n g d e p t h was i n v e s t i g a t e d f o r samples o f water r e p e l l e n t s o i l c o l l e c t e d n e a r Ash Lake, w h i c h i s l o c a t e d w i t h i n t h e Goat Meadows b a s i n . I n f i l t r a t i o n i n t o a s y n t h e t i c w a t e r r e p e l l e n t medium w i t h homogeneous s u r f a c e p r o p e r t i e s was a l s o i n v e s t i g a t e d : t h e p r i m a r y o b j e c t i v e was t o d e t e r m i n e whether i n f i l t r a t i o n would be u n s t a b l e , as p r e d i c t e d by P h i l i p (1975). The c h a p t e r opens w i t h a d i s c u s s i o n o f t h e f i e l d o b s e r v a t i o n s a t Goat Meadows. The r e s u l t s o f t h e s u r v e y o f 17 wat e r r e p e l l e n c y i n t h e a l p i n e - s u b - a l p i n e e c o t o n e o f B r i t i s h C o l u m b i a a r e r e p o r t e d n e x t . T h i s i s f o l l o w e d by a d i s c u s s i o n o f t h e i n v e s t i g a t i o n o f t h e r e l a t i o n s h i p between i n f i l t r a t i o n r a t e and p o n d i n g d e p t h f o r samples c o l l e c t e d a t Ash Lake. The e x p e r i m e n t s u s i n g s y n t h e t i c w a t e r r e p e l l e n t media a r e t h e n d e s c r i b e d . The c h a p t e r c o n c l u d e s w i t h a summary o f t h e r e s u l t s o f t h e s e f i e l d and l a b o r a t o r y i n v e s t i g a t i o n s . A. Goat Meadows Goat Meadows i s l o c a t e d near Pemberton, B r i t i s h C o l u m b i a , a t an e l e v a t i o n o f about 1800 metres above sea l e v e l ( F i g u r e 2:1). Bedrock i s composed p r i m a r i l y o f l a t e C r e t a c e o u s metasediments o f t h e Gambier Group, w h i c h forms a r o o f pendant on q u a r t z d i o r i t e o f t h e Coast P l u t o n i c Complex (Woodsworth, 1977; and R o d d i c k , 197 6 ) . O r t h i c and D y s t r i c B r u n i s o l s a r e d e v e l o p e d on l o e s s , w h i c h o v e r l i e s t i l l and b e d r o c k t o a d e p t h o f t e n t o t h i r t y c e n t i m e t r e s . Up t o t h r e e l a y e r s o f t e p h r a a r e found i n t h e p r o f i l e s , a l t h o u g h most c o n t a i n no more t h a n two; t h e l a y e r s a r e seldom more t h a n one c e n t i m e t r e t h i c k . The t h r e e -v e g e t a t i o n assemblages w h i c h G a l l i e and Slaymaker (1984, 1985) s u g g e s t e d might be a s s o c i a t e d w i t h w a t e r r e p e l l e n c y a r e a l l d e v e l o p e d on t h e l o e s s ; t h e o t h e r major s u r f a c e d e p o s i t s - t a l u s and c o l l u v i u m - a r e o n l y s p a r s e l y Figure 2:1. Location of sampling sites. 19 vegetated. P r e c i p i t a t i o n has been estimated by G a l l i e (1983) to be on the order of 1800 millimetres per year, of which 1500 millimetres accumulates as snow. Ten samples were c o l l e c t e d i n each of three s o i l -vegetation associations i d e n t i f i e d previously as being water repellent (Gallie, 1983): they are r e f e r r e d to here as the Luetkea, the Sedge, and the Heather associations. The methods used for c o l l e c t i o n of these samples are reported i n Appendix A. The d i s t r i b u t i o n of these associations and the locations of the sampling s i t e s are shown i n Figure 2:2. The water drop penetration time test was used to c l a s s i f y the s o i l layers (see Letey, 1969). Very long penetration times suggest water repellency, while very short penetration times indicate that the s o i l i s not water re p e l l e n t . For intermediate times, the i n t e r p r e t a t i o n i s less c l e a r . In these cases, i t i s possible that the s o i l simply has a very low a f f i n i t y for water; that i s , that the contact angle i s close to ninety degrees. A l t e r n a t i v e l y , the s o i l may exhibit transient repellency: a f t e r exposure to water the contact angle f a l l s gradually, ultimately dropping below ninety degrees. The c r i t e r i a used for c l a s s i f i c a t i o n are summarized i n Figure 2:3. The r e s u l t s of the water drop penetration time tests 20 Figure 2:2. Location of sampling sites at Goat Meadows. non-repellent Figure 2:3. Classification of soils by the water drop penetration time test. 22 a r e p r e s e n t e d i n F i g u r e 2:4. L a y e r s w h i c h meet t h e c r i t e r i o n f o r t r u e water r e p e l l e n c y were found i n p r o f i l e s from a l l t h r e e a s s o c i a t i o n s : f i v e from t h e Heat h e r , t h r e e from t h e Sedge, and two from t h e L u e t k e a . There i s , t h e r e f o r e , no c l e a r i n d i c a t i o n o f a s s o c i a t i o n between wa t e r r e p e l l e n c y and v e g e t a t i o n a s s o c i a t i o n . However, t h e r e a r e minor s p e c i e s w h i c h a r e common t o a l l a s s o c i a t i o n s ; one o r more o f t h e s e may c o n t r i b u t e t o t h e r e p e l l e n c y . I n t o t a l , t e n o f t h e t h i r t y p r o f i l e s had wat e r r e p e l l e n t l a y e r s . I n a d d i t i o n , a l l o f t h e r e m a i n i n g twenty samples had l a y e r s w i t h w a t e r drop p e n e t r a t i o n t i m e s w h i c h s u g g e s t e d t h a t t h e y had o n l y a l i m i t e d a f f i n i t y f o r w a t e r o r t h a t t h e r e p e l l e n c y was t r a n s i e n t . As i l l u s t r a t e d i n F i g u r e 2:4, t h e zones o f l i m i t e d a f f i n i t y o r wa t e r r e p e l l e n c y a r e g e n e r a l l y c o n f i n e d t o t h e t o p one t o f i v e c e n t i m e t r e s o f t h e s o i l p r o f i l e s . The upper one t o two c e n t i m e t r e s o f t h e p r o f i l e s a r e u s u a l l y r o o t - r i c h . I n most c a s e s , however, t h e zone o f l i m i t e d a f f i n i t y o r o f wat e r r e p e l l e n c y c o n t i n u e s below t h i s r o o t - r i c h zone. P o r t i o n s o f t h e p r o f i l e w h i c h do not show e v i d e n c e o f a c c u m u l a t i o n o f o r g a n i c m a t t e r a r e never r e p e l l e n t . T h i s o b s e r v a t i o n s u g g e s t s t h a t f o r m a t i o n o f wat e r r e p e l l e n t l a y e r s may be r e l a t e d t o t h e t r a n s l o c a t i o n o f o r g a n i c m a t t e r w i t h i n t h e p r o f i l e , and may t h e r e f o r e be a common f e a t u r e o f sub-23 o r E o Q . CD Q 10 L _ 0 E o Q . CD Q 10L 1 2 3 4 5 6 7 8 9 10 Sedge samples 1 2 3 4 5 6 7 8 9 10 Heather samples _ 0 E o Q . O a 10 1 3 4 5 6 7 8 Luetkea samples 9 10 Legend material | | root mat Q volcanic ash g loess affinity | water repellent g| reduced affinity [ ] non-repellent Figure 2:4. Characteristics of the Goat Meadows samples. 24 a l p i n e s o i l s . B. Survey r e s u l t s f o r s o u t h w e s t e r n B r i t i s h C olumbia The purpose o f t h e s u r v e y o f water r e p e l l e n c y a t sub-a l p i n e s i t e s i n s o u t h e r n B r i t i s h Columbia was t o d e t e r m i n e i f w a t e r r e p e l l e n t s o i l h o r i z o n s were p e c u l i a r t o t h e Goat Meadows s i t e , o r i f such l a y e r s e x i s t e d a t o t h e r sub-a l p i n e s i t e s . T h i s s u r v e y r e p r e s e n t s a modest s t e p towards a n s w e r i n g t h e more g e n e r a l q u e s t i o n o f how w i d e s p r e a d such l a y e r s a r e . S i x samples were c o l l e c t e d a t each o f t h e s i t e s ; t h e methods used a r e d e s c r i b e d i n Appendix A. The g o a l was t o e s t a b l i s h whether o r not water r e p e l l e n t l a y e r s were p r e s e n t a t each s i t e ; t h e r e f o r e i t was f e l t t h a t i t was not n e c e s s a r y t o d e f i n e r i g i d c r i t e r i a f o r t h e s e l e c t i o n o f s i t e s and samples. Indeed, s i n c e o n l y l i m i t e d i n f o r m a t i o n about t h e s i t e s was a v a i l a b l e i n advance, i t would have been d i f f i c u l t t o f o r m u l a t e such c r i t e r i a . The c h a r a c t e r i s t i c s o f each s i t e a r e d e s c r i b e d b r i e f l y h e r e : a more d e t a i l e d d e s c r i p t i o n i s s u p p l i e d i n Appendix B. The l o c a t i o n s o f t h e s i t e s s e l e c t e d a r e shown i n F i g u r e 2:1; t h e y a r e : Manning Park i n t h e Cascade M o u n t a i n s ; Idaho Peak i n t h e S e l k i r k M o u n t a i n s ; Kokanee Lake i n t h e S e l k i r k M o u n t a i n s ; and E l k Lake i n t h e Rocky 25 M o u n t a i n s . The i n t e n t i o n , i n i t i a l l y , was t o sample one s u b - a l p i n e s i t e i n each o f t h e Cascade, S e l k i r k , P u r c e l l , and Rocky M o u n t a i n s . The t h r e a t o f f o r e s t f i r e s i n t h e P u r c e l l s d u r i n g t h e summer o f 1984, t h e y e a r o f t h e s u r v e y , p r e v e n t e d s a m p l i n g i n t h a t range. The s i t e a t Kokanee G l a c i e r P a r k was added t o t h e s u r v e y t o compensate f o r t h e l o s s o f t h e s i t e i n t h e P u r c e l l s . A l l o f t h e s i t e s were c l e a r l y s u b - a l p i n e meadow, e x c e p t f o r E l k Lake P a r k , w h i c h had v e g e t a t i o n c h a r a c t e r i s t i c o f l o w e r e l e v a t i o n meadows. The r e s u l t s o f t h e wa t e r drop p e n e t r a t i o n t i m e t e s t s a r e summarized i n F i g u r e 2:5 f o r t h e samples c o l l e c t e d a t t h e f o u r s i t e s . A l l o f t h e p r o f i l e s have a l a y e r w h i c h has e i t h e r a l i m i t e d a f f i n i t y f o r wa t e r o r i s wa t e r r e p e l l e n t . F i v e o f t h e twenty samples have a l a y e r w h i c h i s c l a s s i f i e d as wa t e r r e p e l l e n t : f o u r were from Kokanee Lake, and one was from Idaho Peak. A l l o f r e m a i n i n g samples, e x c e p t t h e f o u r c o l l e c t e d a t E l k Lake P a r k , had a l a y e r o f l i m i t e d a f f i n i t y . V i s u a l i n s p e c t i o n o f t h e samples s u g g e s t s t h a t zones w h i c h e x h i b i t e i t h e r a l i m i t e d a f f i n i t y f o r wa t e r o r water r e p e l l e n c y a r e a s s o c i a t e d w i t h a c c u m u l a t i o n o f o r g a n i c m a t t e r i n t h e s o i l p r o f i l e . 26 o r E o Q . CD Q 20 E o a. CD Q 20 E o Q . CD Q 20 2 3 4 5 Manning Park samples 2 3 4 5 Kokanee Lake samples 1 2 3 4 Idaho Peak samples E o i SZ CL CD Q 20 Legend repellent • limited affinity non-repellent ' bottom of sample 1 2 3 4 Elk Lake Park samples Figure 2:5. Characteristics of the sub-alpine survey samples. 27 C.The r e l a t i o n s h i p between p o n d i n g d e p t h and i n f i l t r a t i o n r a t e f o r Ash Lake samples In t h i s s e c t i o n , t h e r e l a t i o n s h i p between p o n d i n g depth and i n f i l t r a t i o n r a t e i s e x p l o r e d . I f one a c c e p t s t h e arguments advanced by Debano (1969) r e g a r d i n g w a t e r f l o w i n w a t e r r e p e l l e n t s o i l s , t h e n i t i s e x p e c t e d t h a t up t o some c r i t i c a l p o n d i n g depth, t h e r e w i l l be no i n f i l t r a t i o n . Above t h a t d e p t h , w a t e r w i l l be f o r c e d i n t o p o r e s . Of c o u r s e , t h e r e w i l l be d i f f e r e n c e s between p o r e s w i t h r e s p e c t t o t h e p r e s s u r e r e q u i r e d t o cause them t o f i l l ; t h u s , t h e r e i s e x p e c t e d t o be a g r a d u a l t r a n s i t i o n from a c o n d i t i o n o f no f l o w t o s a t u r a t e d f l o w . The f a c t t h a t t h e p r o p e r t i e s o f s o i l samples v a r y r a p i d l y i n t h e v e r t i c a l makes t h e i r a n a l y s i s d i f f i c u l t . P r e l i m i n a r y f i e l d i n v e s t i g a t i o n s d e m o n s t r a t e d t h e p r e s e n c e o f a v e r y t h i c k w a t e r r e p e l l e n t l a y e r i n t h e s o i l s a t Ash Lake, w h i c h i s a d j a c e n t t o t h e Goat Meadows s i t e . The r e p e l l e n c y appeared t o e x t e n d t o depths i n e x c e s s o f t h i r t y c e n t i m e t r e s . The d e p t h t o t i l l may exceed one metre, w h i c h i s f a r g r e a t e r t h a n t h e t e n t o t h i r t y c e n t i m e t r e s o b s e r v e d a t t h e Goat Meadows s i t e . The ten d e n c y f o r g r e a t e r a c c u m u l a t i o n a t t h i s s i t e i s i l l u s t r a t e d by t h e t h i c k n e s s o f t e p h r a l a y e r s , w h i c h may exceed t e n c e n t i m e t r e s h e r e . Tephra l a y e r s a r e seldom more 28 than one centimetre thick at the Goat Meadows s i t e . Eleven samples, each t h i r t y centimetres i n length were c o l l e c t e d for analysis; the c o l l e c t i o n s i t e s are shown i n Figure 2:6. The samples were sealed immediately to prevent drying. The i n f i l t r a t i o n rate was determined at progressively greater ponding depths using the device i l l u s t r a t e d i n Figure 2:7. The rate was determined by timing the rate of f a l l of water i n a glass observation tube. The fact that the observation tube i s smaller i n diameter than the sample container e f f e c t i v e l y magnifies the i n f i l t r a t i o n rate: i n t h i s case by a factor of s i x t y - f o u r . The ponding depth was set by adding water to the observation tube. Evaporation from the tube was prevented by covering the top of the observation tube with p l a s t i c wrap, which was f i t t e d loosely, rather than being stretched across the top, so that i t could deform to accommodate the volume changes which accompany changes i n l e v e l of water i n the tube. Of course, the ponding depth decreases as the water i n f i l t r a t e s , but there was seldom more than a few centimetres drop between imposed increases i n the ponding depth. The design of the apparatus was suggested by Jan DeVries (personal communication, 1985). The ponding depth was increased i n steps from a l e v e l Figure 2:6. Location of sampling sites near Ash Lake. 30 Figure 2:7. Apparatus for measurement of infiltration rate. 31 o f l e s s t h a n t e n c e n t i m e t r e s , t o o v e r f o r t y c e n t i m e t r e s . As t h e p o n d i n g depth was i n c r e a s e d , t h e i n f i l t r a t i o n r a t e s r o s e s l i g h t l y i n some c a s e s , but remained below 2 x l 0 ~ 9 metres p e r second f o r a l l samples. Thus, t h e i n f i l t r a t i o n r a t e was l e s s t h a n 0.18 m i l l i m e t r e s p e r day, w h i c h i s l e s s t h a n 1.2 m i l l i m e t r e s p e r week. There was no e v i d e n c e o f s a t u r a t i o n a t t h e base o f most samples. I n f a c t , t h e base o f some samples d r i e d and c r a c k e d o v e r t h e c o u r s e o f t h e e x p e r i m e n t , i n d i c a t i n g t h a t vapour f l o w from t h e base exceeded t h e combined i n f l o w from above o f w a t e r as l i q u i d and as v a p o u r . T h i s was t r u e even f o r samples s u b j e c t e d t o p o n d i n g depths o f more t h a n twenty c e n t i m e t r e s f o r more t h a n one month. A f t e r t h e i n f i l t r a t i o n e x p e r i m e n t s were com p l e t e , t h e c o r e s were opened and t h e n c l a s s i f i e d u s i n g t h e w a t e r drop p e n e t r a t i o n t i m e t e s t . One sample was d i s r u p t e d d u r i n g o p e n i n g : t h e r e s u l t s o f t h e water drop p e n e t r a t i o n t i m e t e s t s f o r t h e t e n samples w h i c h remained a r e shown i n F i g u r e 2:8. I t i s apparent t h a t a l l o f t h e samples d i d , i n f a c t , have a w a t e r r e p e l l e n t zone. The r e p e l l e n t zone i n s i x o f t h e t e n samples t e s t e d appeared t o e x t e n d o v e r t h e e n t i r e t h i r t y c e n t i m e t r e d e p t h o f s a m p l i n g . I n t h e o t h e r f o u r samples, a zone, o r zones o f l i m i t e d a f f i n i t y were a l s o p r e s e n t . 32 Figure 2:8. Characteristics of the Ash Lake samples. 33 Several samples were examined using a stereo-microscope. Under magnification, i t appeared that i n d i v i d u a l grains were covered with a coating of material with a resinous l u s t r e . Water drops were placed upon the surfaces, and observed under the microscope. It was apparent that the contact angle of water with these resinous surfaces was greater than ninety degrees. In some cases, i t appeared that the angle was approximately one hundred and eighty degrees: air-water interfaces were v i s i b l e at the back surface of these drops. Samples of water repellent s o i l were ground i n a mortar, and then observed under a microscope. The constituent materials appeared to be s i l t s ized and f i n e r , except for some roots and larger pieces of wood. Most grains were coated by a material with a resinous l u s t r e . A microphotograph of a sample i s shown i n Plate 1. Water drops placed upon t h i s material assume a nearly spherical shape, with a contact angle which appears to be one hundred and eighty degrees. One such drop of water i s shown i n Plate 2. D. Observations of i n f i l t r a t i o n i n a synthetic water repellent medium The purpose of t h i s experiment was to observe the i n f i l t r a t i o n of water into a water repellent medium. A Plate 1. Photomicrograph of a soil sample from Ash Lake. Plate 2. Photomicrograph of a water drop on a soil sample from Ash Lake. 3 5 s y n t h e t i c p o r o u s medium was p l a c e d i n a c l e a r p l e x i g l a s c o n t a i n e r so t h a t t h e movement o f water c o u l d be o b s e r v e d . The p o n d i n g d e p t h was t h e n i n c r e a s e d i n s m a l l i n c r e m e n t s , u s i n g a c o n s t a n t head d e v i c e f o r c o n t r o l . The a p p a r a t u s used i s i l l u s t r a t e d i n F i g u r e 2:9. The w a t e r - a i r i n t e r f a c e a c t s as a s p e c u l a r s u r f a c e i f th e a n g l e o f i n c i d e n c e o f l i g h t s t r i k i n g t h e s u r f a c e i s low; t h u s , i t i s r e l a t i v e l y easy t o o b s e r v e t h e i n t e r f a c e . A t h i n f i l m o f a i r c o v e r s t h e i n d i v i d u a l g r a i n s i n t h e s y n t h e t i c medium, w h i c h s u g g e s t s t h a t a n g l e o f c o n t a c t i s one-hundred and e i g h t y d e g r e e s . D i s t o r t i o n o f t h e w a t e r -a i r i n t e r f a c e was o b s e r v e d as t h e p o n d i n g d e p t h i s i n c r e a s e d . Up t o some t h r e s h o l d p r e s s u r e t h e r e i s no e n t r y o f w a t e r i n t o t h e medium. As t h e p o n d i n g d e p t h i s i n c r e a s e d , some p o r e s n e a r t h e s u r f a c e w i l l wet. W i t h each i n c r e a s e i n p o n d i n g d e p t h , t h e r e i s advance o f a v e r y i r r e g u l a r f r o n t , w h i c h remains s t a t i o n a r y u n l e s s t h e p o n d i n g d e p t h changes. S m a l l " f i n g e r s " may form. These f i n g e r s t e n d t o grow as t h e p o n d i n g d e p t h i s i n c r e a s e d . A t some c r i t i c a l p r e s s u r e , one or more o f t h e s e f i n g e r s may grow u n t i l i t r e a c h e s t h e l o w e r boundary, w h i l e t h e r e s t o f t h e f r o n t remains s t a t i o n a r y . The advance o f t h e f r o n t i s i l l u s t r a t e d i n F i g u r e 2:10. 36 ' water synthetic water repellent medium gravel ; f head constant head reservoir Figure 2:9. Apparatus for observation of infiltration in a synthetic water repellent medium. 37 Depth 3 Depth 4 Figure 2:10. Infiltration in a synthetic water repellent medium. 38 The sequence described above i s observed only i f the ponding depth i s increased slowly. I f a ponding depth greater than some threshold value i s imposed suddenly, then a planar wetting front forms. The boundary condition imposed i n these experiments, where the ponding depth increases slowly, corresponds to a s i t u a t i o n which might be encountered, for example, i n a surface depression during a r a i n f a l l . E. Summary The f i e l d observations suggest that water repellent layers are not uncommon i n the alpine - sub-alpine ecotone of B r i t i s h Columbia. These layers grade into layers which are not repellent according to the res u l t s of the water drop penetration time t e s t ; instead they exhibit what i s interpreted to be either a l i m i t e d a f f i n i t y for water or, perhaps, transient repellency. Such layers would account for the observation by G a l l i e and Slaymaker (1984, 1985) that water tended to bypass the s o i l matrix, flowing instead over the surface and through macroscopic openings i n the s o i l . The r e l a t i o n between ponding depth and i n f i l t r a t i o n rate was explored for samples c o l l e c t e d at Ash Lake, where the repellent layer i s at least tens of centimetres thick. Even at ponding depths i n excess of forty centimetres, the 39 measurements o f i n f i l t r a t i o n r a t e s and changes i n s o i l m o i s t u r e s u g g e s t e d t h a t t r a n s p o r t o f wa t e r as a vapour dominated. Ponding depths c o u l d not be i n c r e a s e d t o t h e p o i n t where t h e r e was b r e a k t h r o u g h o f l i q u i d w a t e r from t h e samples b e f o r e b y p a s s i n g o f t h e sample a l o n g c o n t a i n e r w a l l s o c c u r r e d . Thus, i n o r d e r t o i n v e s t i g a t e t h e p r o c e s s f u r t h e r , e x p e r i m e n t s w i t h s y n t h e t i c w a t e r r e p e l l e n t media were c o n d u c t e d . The w e t t i n g f r o n t was found t o move from one p o s i t i o n o f s t a b i l i t y t o a n o t h e r as t h e p o n d i n g d e p t h was i n c r e a s e d , u n t i l one o r more f i n g e r s grows w i t h o u t bound. The o b s e r v a t i o n s o f i n f i l t r a t i o n i n t o a s y n t h e t i c w a t e r r e p e l l e n t media p r o v i d e a c h a l l e n g e f o r e x i s t i n g t h e o r y : i t i s not c l e a r t h a t approaches such a t t h a t t a k e n by R i c h a r d s (1931), w h i c h r e q u i r e t h e as s u m p t i o n t h a t t h e p r o p e r t i e s o f a porous medium a r e c o n t i n u o u s , can be used t o s i m u l a t e t h e b e h a v i o u r o b s e r v e d . I t seems p r o b a b l e t h a t d i s c o n t i n u i t i e s i n t h e medium a t t h e s c a l e o f t h e po r e a r e , u l t i m a t e l y , r e s p o n s i b l e f o r t h e f a c t t h a t t h e f r o n t advances i n d i s c r e t e s t e p s b e f o r e becoming u n s t a b l e a t some c r i t i c a l p o n d i n g d e p t h . I t i s f o r t h i s r e a s o n , t h a t an a l t e r n a t i v e approach t o m o d e l l i n g i n f i l t r a t i o n was sought - one i n w h i c h h e t e r o g e n e i t y a t t h e s c a l e o f t h e por e i s p r e s e r v e d , a t l e a s t i n p a r t . I n t h e f o l l o w i n g c h a p t e r , t h e e f f e c t s o f pore geometry and o f v a r i a t i o n s i n 40 t h e p h y s i c o c h e m i c a l p r o p e r t i e s o f p o r e s u r f a c e s on t h e f i l l i n g and emptying o f p o r e s a r e c o n s i d e r e d i n o r d e r t o p r o v i d e a f o u n d a t i o n f o r a new model o f i n f i l t r a t i o n , i n w h i c h t h i s p o r e - s c a l e v a r i a b i l i t y i s r e t a i n e d . 41 CHAPTER 3 - FILLING AND EMPTYING OF PORES In t h i s c h a p t e r , t h e e f f e c t s o f v a r i a t i o n s o f t h e c o n t a c t a n g l e on t h e f i l l i n g and emptying o f p o r e s a r e c o n s i d e r e d . The c h a p t e r b e g i n s w i t h a d i s c u s s i o n o f t h e w e t t i n g o f s o l i d s u r f a c e s , f o c u s i n g upon t h e c o n t a c t a n g l e as a measure o f t h e a f f i n i t y o f a s u r f a c e f o r w a t e r . The e f f e c t o f pore geometry on f i l l i n g and em p t y i n g i s t h e n r e v i e w e d b r i e f l y . T h i s i s f o l l o w e d by a d i s c u s s i o n o f t h e e f f e c t s o f v a r i a t i o n s o f p h y s i c o c h e m i c a l p r o p e r t i e s w i t h i n p o r e s on f i l l i n g and emptying. A. W e t t i n g o f s o l i d s u r f a c e s When a drop o f wa t e r i s p l a c e d upon a s o l i d s u r f a c e i t w i l l e i t h e r r e s t as a drop o r s p r e a d o v e r t h e s u r f a c e ; t h e outcome depends upon t h e r e l a t i v e v a l u e s o f t h e s p e c i f i c i n t e r f a c i a l f r e e e n e r g i e s f o r t h e s o l i d - w a t e r (xs w) , s o l i d - a i r (T s a) , and w a t e r - a i r (xwa) i n t e r f a c e s . The s p e c i f i c i n t e r f a c i a l f r e e energy may be c o n s i d e r e d t o be t h e work r e q u i r e d t o c r e a t e a u n i t a r e a o f i n t e r f a c e a t c o n s t a n t t e m p e r a t u r e and volume (see S p r a c k l i n g , 1985). The t e r m i s , t h e r e f o r e , e x p r e s s e d as energy p e r u n i t a r e a . An i n t e r f a c i a l t e n s i o n , however, i s e x p r e s s e d as f o r c e p e r u n i t l e n g t h , b u t t h i s i s d i m e n s i o n a l l y e q u i v a l e n t t o energy p e r u n i t a r e a . The two terms a r e n u m e r i c a l l y e q u i v a l e n t f o r a pure l i q u i d (Osipow, 1977), b u t i n o t h e r 42 ca s e s t h e y may not be. As S p r a c k l i n g (1985) n o t e s i n a d i s c u s s i o n o f an i s o t r o p i c one-component s o l i d w h i c h i s b e i n g s t r e t c h e d u n i f o r m l y i n a l l d i r e c t i o n s , t h e r e v e r s i b l e work, dW, r e q u i r e d t o i n c r e a s e t h e a r e a o f t h e s u r f a c e by dA i s g i v e n by: dW = d(xA) = Adx + XdA (1) where X i s t h e i n t e r f a c i a l f r e e energy. The work r e q u i r e d t o s t r e t c h t h e s u r f a c e by dA, g i v e n an i n t e r f a c i a l t e n s i o n o f a, i s g i v e n by: dW = adA (2) Thus, i t f o l l o w s t h a t : adA = Adx + xdA (3) From e q u a t i o n ( 3 ) , i t i s c l e a r t h a t t h e s u r f a c e t e n s i o n and s u r f a c e f r e e energy w i l l be i d e n t i c a l o n l y i f t h e term Adx i s z e r o . I n most s i t u a t i o n s - t h e e x c e p t i o n s a r e f o r e x t r e m e l y h y d r o p h i l i c and f o r e x t r e m e l y h y d r o p h o b i c s u r f a c e s - t h e r e l a t i o n between t h e s o l i d - w a t e r , s o l i d - a i r , and w a t e r - a i r i n t e r f a c e s i s d e s c r i b e d by Young's e q u a t i o n : (*sa - *sw) / *wa = COS [tt] (4) where a i s t h e c o n t a c t a n g l e (note t h a t Young's e q u a t i o n 43 may be e x p r e s s e d e i t h e r i n terms o f t h e t h r e e i n t e r f a c i a l f r e e e n e r g i e s o r t h e t h r e e s u r f a c e t e n s i o n s i n v o l v e d ) . F o r s e s s i l e d r ops on a p l a n a r , h o r i z o n t a l , homogeneous s u r f a c e , t h e a n g l e between t h e w a t e r - a i r i n t e r f a c e and t h e s o l i d s u r f a c e a t t h e p o i n t o f c o n t a c t i s e q u a l t o t h e c o n t a c t a n g l e as g i v e n i n e q u a t i o n (4) ( S p r a c k l i n g , 1985). A s u r f a c e i s c o n s i d e r e d t o be h y d r o p h i l i c i f t h e s p e c i f i c i n t e r f a c i a l f r e e energy o f t h e s o l i d - w a t e r i n t e r f a c e i s l e s s t h a n t h a t o f t h e s o l i d - a i r i n t e r f a c e . In such c a s e s , t h e l e f t - h a n d s i d e o f e q u a t i o n (4) i s p o s i t i v e ; i t f o l l o w s t h a t t h e c o n t a c t a n g l e i s l e s s t h a n n i n e t y degrees f o r a h y d r o p h i l i c s u r f a c e . A h y d r o p h o b i c s u r f a c e i s one f o r w h i c h t h e s o l i d - w a t e r i n t e r f a c i a l f r e e energy i s g r e a t e r t h a n t h e s o l i d - a i r i n t e r f a c i a l f r e e e n e r gy; f o r t h e s e s u r f a c e s t h e c o n t a c t a n g l e w i l l be g r e a t e r t h a n n i n e t y d e g r e e s . Water w i l l s p r e a d on a s o l i d s u r f a c e , c o m p l e t e l y e l i m i n a t i n g t h e s o l i d - a i r i n t e r f a c e , i f t h e s p e c i f i c s u r f a c e f r e e energy o f t h e s o l i d - a i r i n t e r f a c e i s g r e a t e r t h a n t h e sum o f t h e f r e e e n e r g i e s f o r t h e s o l i d - w a t e r and w a t e r - a i r i n t e r f a c e s w h i c h r e p l a c e i t . The c r i t e r i o n f o r s p r e a d i n g i s t h e r e f o r e : *sa > *sw + \,a (5) 44 The a r e a s o f i n t e r f a c e s i n v o l v e d a r e e q u a l i n t h i s c a s e ; t h e r e f o r e t h e y need not appear e x p l i c i t l y i n e q u a t i o n ( 5 ) . The c r i t e r i o n f o r s p r e a d i n g may be r e - e x p r e s s e d a s : <*sa " Xsw) / *wa > 1 (6) The l e f t - h a n d s i d e o f e q u a t i o n (6) i s s i m i l a r i n form t o t h a t o f t h e Young e q u a t i o n , but t h e r e i s no v a l u e o f t h e c o n t a c t a n g l e w h i c h s a t i s f i e s t h e r e l a t i o n . The a n g l e o f c o n t a c t i n t h i s case i s e f f e c t i v e l y z e r o . For h y d r o p h o b i c s u r f a c e s t h e s o l i d - w a t e r i n t e r f a c i a l f r e e energy i s g r e a t e r t h a n t h e s o l i d - a i r i n t e r f a c i a l f r e e e nergy. I f t h e d i f f e r e n c e between t h e two i s g r e a t e r t h a n t h e w a t e r - a i r i n t e r f a c i a l f r e e energy, t h e n l e s s energy i s r e q u i r e d t o produce new w a t e r - a i r i n t e r f a c e t h a n t o wet t h e s u r f a c e . Under t h e s e c o n d i t i o n s , a l a y e r o f a i r i s e x p e c t e d t o p e r s i s t on t h e s u r f a c e o f t h e s o l i d . That i s , a f i l m o f a i r i s e x p e c t e d t o be r e t a i n e d i f : <*sa - *sw) / *wa < "1 <7> The a n g l e o f c o n t a c t w i l l , e f f e c t i v e l y , be one hundred and e i g h t y degrees - t h e r e i s no v a l u e o f t h e c o n t a c t a n g l e w h i c h w i l l s a t i s f y Young's e q u a t i o n under t h e s e c o n d i t i o n s . 45 The l i m i t a t i o n s o f t h e c o n t a c t a n g l e as a measure o f t h e a f f i n i t y o f a s u r f a c e f o r wa t e r a r e o f t e n o v e r l o o k e d , even though t h e s e l i m i t s r e p r e s e n t s i g n i f i c a n t t h r e s h o l d s i n t h e way i n wh i c h w a t e r i n t e r a c t s w i t h a s u r f a c e . I n o r d e r t o f a c i l i t a t e d i s c u s s i o n o f t h e s e t h r e s h o l d s , a new te r m i s i n t r o d u c e d - t h e a f f i n i t y , CI - w h i c h i s d e f i n e d by: « = (*sa " t 8 W ) / x w a (8) The a f f i n i t y o f a s u r f a c e i s e q u a l t o t h e c o s i n e o f t h e c o n t a c t a n g l e f o r v a l u e s between n e g a t i v e one and one, but may f a l l o u t s i d e o f t h i s range. A s u r f a c e i s h y d r o p h i l i c i f t h e a f f i n i t y i s p o s i t i v e , and h y d r o p h o b i c i f i t i s n e g a t i v e . A f i l m o f water spreads s p o n t a n e o u s l y o v e r a s u r f a c e f o r v a l u e s o f t h e a f f i n i t y g r e a t e r t h a n one, w h i l e a f i l m o f a i r i s r e t a i n e d f o r v a l u e s l e s s t h a n n e g a t i v e one. The r e l a t i o n s between t h e a f f i n i t y and t h e w e t t i n g b e h a v i o u r o f a s u r f a c e a r e i l l u s t r a t e d i n F i g u r e 3:1, a l o n g w i t h t h e c o r r e s p o n d i n g a n g l e s o f c o n t a c t . The a f f i n i t y o f a s u r f a c e f o r water has been assumed i n t h i s d i s c u s s i o n t o be c o n s t a n t over t i m e , y e t t h e r e i s e v i d e n c e t h a t f o r some s o i l s , t h e wa t e r r e p e l l e n c y may be a t r a n s i e n t f e a t u r e . Some s o i l s w h i c h a r e i n i t i a l l y w a t e r r e p e l l e n t a p p a r e n t l y become n o n - r e p e l l e n t upon exposure t o wat e r (Wessel, 1986; J u n g e r i u s and van d e r Meulen, 1 9 8 8 ) . r a= 180 180 UBBBi -2 -1 contact angle 1 1 90 r . x ^ i M ] ] m j m Q a = 0 ; hydrophilic — coirrtadangle defined "' • ' film of water 0 1 I I affinity Figure 3:1. Wetting behavior as a function of the contact angle. 47 One p o s s i b l e e x p l a n a t i o n i s t h a t a m p h o p h i l i c compounds a d h e r i n g t o m i n e r a l g r a i n s may be d i s p l a c e d g r a d u a l l y from t h e s e s u r f a c e s , perhaps f o r m i n g m i c e l l e s i n t h e p r o c e s s . I t may a l s o be t h e case t h a t s l o w c h e m i c a l changes o c c u r i n m o l e c u l e s a t t h e s u r f a c e a f t e r w e t t i n g so t h a t t h e p h y s i c o c h e m i c a l p r o p e r t i e s o f t h e s u r f a c e do, i n f a c t , change. I n o t h e r c a s e s , secondary e f f e c t s such as t h e i n c o r p o r a t i o n o f s u r f a c e a c t i v e a g ents by t h e w a t e r may a c c o u n t f o r o b s e r v a t i o n s o f c h a n g i n g c o n t a c t a n g l e (Topp, 1966). I t i s a l s o well-known t h a t t h e c o n t a c t a n g l e i n d r y a i r may d i f f e r s i g n i f i c a n t l y from t h a t i n s a t u r a t e d a i r (Osipow, 1977). In t h e s e c t i o n s f o l l o w i n g , t h e e f f e c t s o f t h e shape and p h y s i c o c h e m i c a l p r o p e r t i e s o f p o r e s upon t h e i r f i l l i n g and e m p t y i n g a r e d i s c u s s e d . Only s i t u a t i o n s where t h e a f f i n i t y o f a s u r f a c e i s c o n s t a n t over t i m e a r e c o n s i d e r e d . A f u l l d i s c u s s i o n o f t h e e f f e c t s o f t r a n s i e n t p h y s i c o c h e m i c a l p r o p e r t i e s exceeds t h e scope o f t h i s t h e s i s . B. The e f f e c t o f p o r e geometry on f i l l i n g and emptying H y s t e r e s i s i n t h e r e l a t i o n between w a t e r c o n t e n t and p r e s s u r e p o t e n t i a l i s o f t e n e x p l a i n e d i n terms o f t h e geometry o f p o r e s . I n o r d e r t o i l l u s t r a t e t h e p r i n c i p l e s i n v o l v e d , a p o r e i s i d e a l i z e d as b e i n g c y l i n d r i c a l l y s y m m e t r i c a l w i t h narrow necks a t e i t h e r end o f a w i d e r 48 body. The p o r e f i l l s t h r o u g h one o f n e c k s , w h i l e a i r i s e x p e l l e d from t h e o t h e r . The r a d i u s o f t h e body o f t h e p o r e i s h e l d t o c o n t r o l t h e t e n s i o n a t w h i c h t h e p o r e w i l l f i l l , w h i l e t h e r a d i u s o f t h e neck i s h e l d t o c o n t r o l t h e t e n s i o n a t w h i c h t h e p o r e w i l l empty. S i n c e c a p i l l a r y f o r c e s a r e i n v e r s e l y p r o p o r t i o n a l t o t h e r a d i u s o f a c a p i l l a r y t u b e , t h e t e n s i o n a t w h i c h a h y d r o p h i l i c p o r e w i l l empty must be g r e a t e r t h a n t h e t e n s i o n a t w h i c h i t w i l l f i l l , s i n c e t h e r a d i u s o f t h e neck o f t h e p o r e i s l e s s t h a n t h a t o f t h e body. A porous medium i s , o f c o u r s e , much more complex t h a n t h i s , but t h i s s i m p l e example s e r v e s t o i l l u s t r a t e t h e b a s i c mechanism. H y s t e r e s i s i n t h e r e l a t i o n between w a t e r c o n t e n t and p r e s s u r e p o t e n t i a l i s a l s o e x p e c t e d f o r h y d r o p h o b i c porous media, b u t w i t h some i m p o r t a n t d i f f e r e n c e s . I n c o n t r a s t t o t h e s i t u a t i o n f o r h y d r o p h i l i c p o r e s , h y d r o p h o b i c ones r e q u i r e p o s i t i v e p r e s s u r e s i n o r d e r t o f i l l . T h i s p o i n t may be i l l u s t r a t e d t h r o u g h r e f e r e n c e t o t h e phenomenon o f c a p i l l a r y d e p r e s s i o n . I f a t h i n c y l i n d r i c a l t u b e composed o f h y d r o p h o b i c m a t e r i a l i s i n s e r t e d v e r t i c a l l y i n t o w a t e r , no w a t e r w i l l e n t e r t h e t u b e u n t i l some c r i t i c a l d e p t h has been r e a c h e d . F u r t h e r i n s e r t i o n w i l l not change t h e p o s i t i o n o f t h e w a t e r - a i r i n t e r f a c e w i t h i n t h e t u b e . The " c a p i l l a r y d e p r e s s i o n " i s g i v e n by t h e d e p t h o f t h e w a t e r -a i r i n t e r f a c e w i t h i n t h e tube r e l a t i v e t o t h e s u r f a c e o f 49 t h e w a t e r o u t s i d e o f t h e t u b e , as i l l u s t r a t e d i n F i g u r e 3:2. The h e i g h t o f c a p i l l a r y r i s e o r o f c a p i l l a r y d e p r e s s i o n i s g i v e n by: h = 2 a w a cos [a] / pgr (9) where a w a i s t h e w a t e r - a i r i n t e r f a c i a l t e n s i o n , p i s t h e d e n s i t y o f w a t e r , g i s t h e a c c e l e r a t i o n due t o g r a v i t y , and r i s t h e i n s i d e r a d i u s o f t h e t u b e . For h y d r o p h i l i c t u b e s , t h e " h e i g h t o f r i s e " , h, i s p o s i t i v e , b u t f o r h y d r o p h o b i c t u b e s i t w i l l be n e g a t i v e ; t h a t i s , c a p i l l a r y d e p r e s s i o n may be c h a r a c t e r i z e d as a n e g a t i v e h e i g h t o f r i s e . I t i s c l e a r t h a t a p o s i t i v e p r e s s u r e must be a p p l i e d i n o r d e r f o r h y d r o p h o b i c t u b e s o r p o r e s t o f i l l : t h e s m a l l e r t h e r a d i u s o f t h e tube o r p o r e , t h e g r e a t e r t h e p r e s s u r e r e q u i r e d f o r f i l l i n g . I t f o l l o w s from t h e arguments p r e s e n t e d above, t h a t i t i s t h e r a d i u s o f t h e neck o f a h y d r o p h o b i c p o r e w h i c h c o n t r o l s t h e p r e s s u r e s a t w h i c h i t w i l l f i l l , r a t h e r t h a n t h e r a d i u s o f t h e body o f t h e pore as i s t h e case f o r h y d r o p h i l i c p o r e s . W i t h r e s p e c t t o emptying, i t seems r e a s o n a b l e t o e x p e c t t h a t i t i s t h e r a d i u s o f t h e body o f t h e p ore w h i c h c o n t r o l s t h e p r e s s u r e a t w h i c h i t e m p t i e s . However, i n t h e case o f e x t r e m e l y h y d r o p h o b i c media, t h i s 50 Figure 3:2. Capillary depression. 51 may be not be t r u e . F o r p e r f e c t l y h y d r o p h o b i c m a t e r i a l (CI < - 1 ) , f o r w h i c h t h e c o n t a c t a n g l e i s one hundred and e i g h t y d e g r e e s , i t i s e x p e c t e d t h a t a f i l m o f a i r w i l l be r e t a i n e d a t t h e po r e s u r f a c e . I t i s p o s s i b l e t h a t a i r may move t h r o u g h t h i s f i l m t o t h e necks o f t h e p o r e s as t h e p r e s s u r e f a l l s below t h a t r e q u i r e d f o r f i l l i n g o f t h e n e c k s . I n such c a s e s , w a t e r may be s t r a n d e d w i t h i n t h e body o f a p o r e . U n l e s s t h e p r e s s u r e i s r a i s e d a g a i n t o a l e v e l a t w h i c h f i l l i n g t h e t h e neck o f t h e po r e can t a k e p l a c e , w a t e r may t r a n s f e r from t h e body o f t h e p o r e o n l y as v apour. In summary, t h e shape o f p o r e s i n d u c e s h y s t e r e s i s i n t h e f i l l i n g and emptying o f b o t h h y d r o p h i l i c and h y d r o p h o b i c p o r e s . I n h y d r o p h i l i c p o r e s , t h e r a d i u s o f t h e body o f a po r e c o n t r o l s t h e t e n s i o n a t w h i c h i t w i l l f i l l , w h i l e i n a h y d r o p h o b i c p o r e , i t i s t h e r a d i u s o f t h e neck w h i c h c o n t r o l s t h e p r e s s u r e a t w h i c h i t w i l l f i l l . S i m i l a r l y , i n h y d r o p h i l i c p o r e s , t h e r a d i u s o f t h e neck c o n t r o l s t h e t e n s i o n a t whi c h i t w i l l empty, w h i l e f o r h y d r o p h o b i c p o r e s i t i s t h e r a d i u s o f t h e body, e x c e p t , p e r h a p s , f o r v e r y h y d r o p h o b i c p o r e s , where a i r may move t h r o u g h a r e t a i n e d f i l m between necks t h e r e b y s t r a n d i n g w a t e r i n t h e body o f t h e p o r e . 52 C. The e f f e c t o f v a r i a t i o n s o f p h y s i c o c h e m i c a l p r o p e r t i e s w i t h i n p o r e s on f i l l i n g and emptying As d i s c u s s e d i n t h e p r e c e d i n g s e c t i o n , t h e r e l a t i o n s between w a t e r c o n t e n t and p r e s s u r e p o t e n t i a l f o r a porous medium a r e g e n e r a l l y h e l d t o be due p r i m a r i l y t o t h e complex shape o f p o r e s . In t h i s s e c t i o n , i t w i l l be shown t h a t v a r i a t i o n s o f p h y s i c o c h e m i c a l p r o p e r t i e s w i t h i n p o r e s can a l s o l e a d t o h y s t e r e s i s i n t h e r e l a t i o n between wa t e r c o n t e n t and p r e s s u r e p o t e n t i a l . The s p r e a d i n g o f w a t e r on a p l a n e s o l i d s u r f a c e w i t h heterogeneous p r o p e r t i e s i s e x p l o r e d i n p r e p a r a t i o n f o r a d i s c u s s i o n o f t h e e f f e c t o f v a r i a t i o n s i n t h e p h y s i c o c h e m i c a l p r o p e r t i e s on t h e f i l l i n g and emptying o f an i n d i v i d u a l p o r e . Spreading on s o l i d surfaces with heterogeneous properties C o n s i d e r t h e s i t u a t i o n i l l u s t r a t e d i n F i g u r e 3:3, i n w h i c h t h e w a t e r - a i r i n t e r f a c e meets t h e s o l i d s u r f a c e a t a boundary between m a t e r i a l s w h i c h have d i f f e r e n t c o n t a c t a n g l e s . A f i l m o f water i s assumed t o c o v e r m a t e r i a l 1. The p r e s s u r e p o t e n t i a l ( e x p r e s s e d i n terms o f t h e e q u i v a l e n t d e p t h o f water) a t t h e base o f t h i s f i l m w i l l be e q u a l t o t h e depth o f t h e f i l m e x c e p t n e a r i t s edge. I n t h i s example, t h e s o l i d s u r f a c e i s assumed t o be composed o f m a t e r i a l s w h i c h a r e h y d r o p h i l i c , but t h e same p r i n c i p l e s a p p l y f o r h y d r o p h o b i c s u r f a c e s . 53 water Material 1 Material 2 Material 1 Material 2 Figure 3:3. Hysteresis of the contact angle at material boundaries. 54 I n o r d e r f o r t h e w a t e r - a i r i n t e r f a c e t o move i n t o m a t e r i a l 2 from m a t e r i a l 1, t h e c o n t a c t a n g l e must i n c r e a s e t o t h e v a l u e c h a r a c t e r i s t i c o f m a t e r i a l 2. T h i s r e q u i r e s t h a t t h e depth o f t h e f i l m o f wa t e r must i n c r e a s e so t h a t t h e p r e s s u r e p o t e n t i a l w i t h i n t h e w a t e r i n c r e a s e s . F o r r e t r e a t o f t h e c o n t a c t from m a t e r i a l 2 t o m a t e r i a l 1, t h e d e p t h o f t h e f i l m must d e c r e a s e so t h a t t h e p r e s s u r e p o t e n t i a l w i t h i n t h e wa t e r f a l l s s u f f i c i e n t l y t o a l l o w t h e c o n t a c t a n g l e c h a r a c t e r i s t i c o f m a t e r i a l 1 t o be a c h i e v e d . F o r f i l m t h i c k n e s s , and t h e r e f o r e p r e s s u r e p o t e n t i a l , between t h e c r i t i c a l v a l u e s f o r advance and r e t r e a t , t h e edge o f t h e f i l m w i l l be i n e q u i l i b r i u m a t t h e c o n t a c t between t h e two s u r f a c e s . I f t h e m a t e r i a l p r o p e r t i e s were r e v e r s e d i n F i g u r e 3:3 so t h a t m a t e r i a l 2 had a s m a l l e r c o n t a c t a n g l e t h a n m a t e r i a l 1, t h e r e would be no f i l m t h i c k n e s s a t w h i c h t h e edge o f t h e f i l m would be i n e q u i l i b r i u m a t t h e c o n t a c t between m a t e r i a l s . F i l m t h i c k n e s s s u f f i c i e n t t o cause t h e wat e r t o s p r e a d on m a t e r i a l 1 would be more t h a n s u f f i c i e n t t o cause s p r e a d i n g on m a t e r i a l 2. S i m i l a r l y , a f i l m t h i c k n e s s s m a l l enough t o cause r e t r e a t o f w a t e r from m a t e r i a l 2, would be s m a l l e r t h a n t h a t r e q u i r e d f o r r e t r e a t on m a t e r i a l 1. Thus, t h e f i l m w i l l t e n d t o move away from t h e c o n t a c t between m a t e r i a l s i n b o t h c o n d i t i o n s o f advance and r e t r e a t . 55 I n c a s e s where t h e a f f i n i t y o f b o t h s u r f a c e s f o r w a t e r i s v e r y h i g h ( il > 1 ) , a f i l m o f water w i l l s p r e a d s p o n t a n e o u s l y over b o t h s u r f a c e s , so t h a t t h e c o n t a c t a n g l e i s e f f e c t i v e l y z e r o f o r b o t h . Thus, t h e v a r i a t i o n s i n t h e s u r f a c e p r o p e r t i e s w i l l not be e x p r e s s e d under t h e c o n d i t i o n s s p e c i f i e d h e r e : t h e r e i s no e q u i l i b r i u m p o s i t i o n f o r t h e edge o f t h e f i l m . S i m i l a r l y , f o r e x t r e m e l y h y d r o p h o b i c s u r f a c e s ( Q < - 1 ), a f i l m o f a i r w i l l be r e t a i n e d a t t h e s u r f a c e ; t h u s , t h e c o n t a c t a n g l e i s e f f e c t i v e l y one hundred and e i g h t y degrees f o r b o t h s u r f a c e s . Variations of properties within pores C o n s i d e r t h e c y l i n d r i c a l p o r e i l l u s t r a t e d i n F i g u r e 3:4. The p o r e i s assumed t o be c o n n e c t e d t o a r e s e r v o i r a t t h e "neck" o f t h e p o r e , w h i c h i s i n t h i s case s i m p l y a s e c t i o n o f t h e pore composed o f a m a t e r i a l w h i c h i s d i f f e r e n t t h a n t h a t o f t h e r e s t o f t h e p o r e , w h i c h i s r e f e r r e d t o h e r e as t h e "body" o f t h e p o r e . The r e s e r v o i r i s assumed t o be so l a r g e t h a t t h e r e w i l l be e s s e n t i a l l y no change i n t h e p r e s s u r e a s s o c i a t e d w i t h f i l l i n g and emptying o f t h e p o r e . Together, t h e r e s e r v o i r and p o r e c o n s t i t u t e a c l o s e d system. The p r e s s u r e o f w a t e r i n t h e r e s e r v o i r i s c o n t r o l l e d e x t e r n a l l y . A l l changes a r e assumed t o t a k e p l a c e i s o t h e r m a l l y . 56 ttl a 2 water —Hffl "neck" cylindrical pore CD c o o CD c5 5 pressure potential pressure potential Figure 3:4. Filling and draining of a cylindrical pore within which the contact angle changes. 57 C o n s i d e r t h e case where t h e pore i s i n i t i a l l y empty. As th e p r e s s u r e o f wa t e r i n t h e r e s e r v o i r i s i n c r e a s e d , some c r i t i c a l v a l u e w i l l e v e n t u a l l y be r e a c h e d w h i c h w i l l a l l o w w a t e r t o e n t e r t h e neck o f t h e p o r e . T h i s c r i t i c a l p r e s s u r e i s d e t e r m i n e d by t h e r a d i u s o f t h e t u b e and t h e c o n t a c t a n g l e . The w a t e r - a i r i n t e r f a c e w i l l move u n t i l t h e body o f t h e po r e i s re a c h e d , a t l e a s t . I f t h e c o n t a c t a n g l e a s s o c i a t e d w i t h t h e body o f t h e pore i s l e s s t h a n t h a t a s s o c i a t e d w i t h t h e neck, t h e pore w i l l f i l l s p o n t a n e o u s l y s i n c e t h e p r e s s u r e i s above t h e e q u i l i b r i u m v a l u e f o r t h e body o f t h e p o r e . I f t h e p r e s s u r e i s red u c e d , t h e f i l l e d c o n d i t i o n remains as a c o n d i t i o n o f e q u i l i b r i u m u n t i l some c r i t i c a l v a l u e i s r e a c h e d . Below t h a t p r e s s u r e , t h e pore may remain f i l l e d u n t i l t h e p r e s s u r e drops below t h e v a l u e t h a t would a l l o w e m ptying o f a c y l i n d r i c a l p o r e composed e n t i r e l y o f t h e m a t e r i a l o f w h i c h t h e body o f t h e po r e i s composed. The f i l l i n g and emp t y i n g o f t h e po r e i s e x p e c t e d t o p r o c e e d as i l l u s t r a t e d i n F i g u r e 3:4 ( f o r ax > a2) • I f t h e neck o f t h e pore has a s m a l l e r c o n t a c t a n g l e t h a n t h e body o f t h e po r e ( a x < oc2) , t h e f i l l i n g and emptying sequence i s somewhat d i f f e r e n t t h a n t h a t d e s c r i b e d above. I f t h e pore i s i n i t i a l l y empty, t h e n as 58 t h e p r e s s u r e i n t h e r e s e r v o i r i s i n c r e a s e d , some p r e s s u r e at w h i c h t h e neck f i l l s w i l l be r e a c h e d . The body o f t h e p o r e , however, w i l l not f i l l u n t i l some h i g h e r p r e s s u r e i s r e a c h e d . I n t h i s c a s e , t h e p r e s s u r e r e q u i r e d f o r f i l l i n g o f t h e body o f t h e pore i s t h e same as t h e p r e s s u r e a t wh i c h t h e po r e w i l l d r a i n . Thus, i f t h e volume o f wa t e r h e l d i n t h e neck o f t h e po r e i s assumed t o be n e g l i g i b l e , t h e n t h e p o r e w i l l f i l l and empty w i t h o u t h y s t e r e s i s . T h i s sequence i s i l l u s t r a t e d i n F i g u r e 3:4. Experimental evidence I t i s d i f f i c u l t t o demonstrate h e t e r o g e n e i t y o f t h e s u r f a c e p r o p e r t i e s o f a porous medium d i r e c t l y , g i v e n t h e complex geometry o f t h e po r e s u r f a c e and t h e problems i n h e r e n t i n d i r e c t o b s e r v a t i o n o f m i c r o s c o p i c f e a t u r e s i n an opaque m a t e r i a l . F o r t h e s e r e a s o n s , t h e phenomenon was i n v e s t i g a t e d t h r o u g h e x p e r i m e n t s w i t h g l a s s and p l a s t i c t u b i n g , w h i c h a r e s i m p l e g e o m e t r i c a l l y , and w h i c h a r e b o t h m a c r o s c o p i c and t r a n s p a r e n t . I f a c a p i l l a r y tube composed o f a s i n g l e s u b s t a n c e i s l o w e r e d s l o w l y i n t o a c o n t a i n e r o f w a t e r , i t i s e x p e c t e d t h a t w a t e r w i l l r i s e w i t h i n t h e tube t o a p a r t i c u l a r h e i g h t , w h i c h i s d e t e r m i n e d by t h e r a d i u s o f t h e tub e and th e c o n t a c t a n g l e . The h e i g h t o f r i s e i s not e x p e c t e d t o change as t h e tube i s l o w e r e d o r r a i s e d w i t h i n t h e 59 c o n t a i n e r . In some cases, however, the h e i g h t o f r i s e does change. As the h e i g h t changes, however, the p o s i t i o n o f the i n t e r f a c e w i t h i n the tube i s u s u a l l y observed t o remain f i x e d u n t i l some new h e i g h t o f r i s e i s ach i e v e d . In some cases, the i n t e r f a c e "jumps" from one p o s i t i o n t o another, w h i l e i n other cases the h e i g h t o f r i s e simply remains at the new v a l u e . In t r i a l s w i t h s e c t i o n s o f g l a s s t u b i n g w i t h an i n s i d e r a d i u s o f 0.05 c e n t i m e t e r s , the h e i g h t o f r i s e was observed t o vary from 2.9 c e n t i m e t e r s down t o 1.5 c e n t i m e t e r s , which corresponds t o c o n t a c t angles o f 12 and 60 degrees r e s p e c t i v e l y . These o b s e r v a t i o n s imply t h a t the s u r f a c e p r o p e r t i e s change a l o n g the l e n g t h o f the tube. T h i s p r e s e n t s a problem, however, s i n c e the tube i s composed e n t i r e l y o f g l a s s , and sh o u l d show only minor changes i n s u r f a c e p r o p e r t i e s , u n l e s s the s u r f a c e i s contaminated. To t e s t the p o s s i b i l i t y t h a t the tubes, which had not been used p r e v i o u s l y , were contaminated, they were c l e a n e d i n a t h r e e p e r c e n t s o l u t i o n o f hydrogen per o x i d e , and then r i n s e d t h o r o u g h l y w i t h i s o p r o p a n o l . When the t e s t s were repeated, the h e i g h t o f r i s e remained very c l o s e t o 2.9 ce n t i m e t e r s , which i s j u s t l e s s than the 2.96 ce n t i m e t e r s which would be expected f o r water i n a medium w i t h a co n t a c t angle of 0 degrees, at a temperature of 20°C. Thus, i t appears t h a t the h y s t e r e s i s i n the c o n t a c t angle 60 was due t o t h e p r e s e n c e o f u n e v e n l y a d s o r b e d c o n t a m i n a n t s . A s i m i l a r s e t o f e x p e r i m e n t s was c o n d u c t e d u s i n g p o l y e t h y l e n e t u b i n g , a g a i n w i t h an i n s i d e r a d i u s o f 0.05 c e n t i m e t e r s . I n t h e s e t r i a l s , b o t h c a p i l l a r y r i s e and d e p r e s s i o n were o b s e r v e d . The " t r a p p i n g " o f t h e meniscus at p a r t i c u l a r p o i n t s a l o n g t h e l e n g t h o f t h e t u b i n g was ob s e r v e d , as were o c c a s i o n a l jumps from one p o s i t i o n t o a n o t h e r . The maximum r i s e was 1.1 c e n t i m e t e r s , w h i l e t h e maximum d e p r e s s i o n was 0.9 c e n t i m e t e r s , w h i c h c o r r e s p o n d t o c o n t a c t a n g l e s o f 68 and 108 degrees r e s p e c t i v e l y . I n t h i s c a s e , t h e n , we have t h e most extreme case p o s s i b l e : h y d r o p h o b i c s u r f a c e s a d j o i n i n g h y d r o p h i l i c ones. The o b s e r v a t i o n s d e s c r i b e d above l e n d c r e d e n c e t o t h e p r o p o s i t i o n t h a t changes i n s u r f a c e p r o p e r t i e s a l o n e can l e a d t o h y s t e r e s i s i n t h e f i l l i n g and emptying o f i n d i v i d u a l p o r e s . Thus, v a r i a t i o n s i n t h e p h y s i c o c h e m i c a l p r o p e r t i e s o f s o i l s must be c o n s i d e r e d as a p o s s i b l e cause o f h y s t e r e s i s i n porous media, i n a d d i t i o n t o t h e g e o m e t r i c a l c h a r a c t e r i s t i c s o f p o r e s . D. Summary In t h i s c h a p t e r t h e i n f l u e n c e o f t h e p h y s i c o c h e m i c a l p r o p e r t i e s on t h e f i l l i n g and emptying o f p o r e s was r e v i e w e d . The e f f e c t o f pore geometry on f i l l i n g and 61 emptying of both hydrophilic and hydrophobic pores was considered. In addition, the role of v a r i a t i o n s of physicochemical properties within a pore i n producing hysteresis i n the r e l a t i o n between water content and pressure p o t e n t i a l was discussed. The concepts presented i n t h i s chapter provide the conceptual basis for the model of the behaviour of an assemblage of pores presented i n Chapter 4. 62 CHAPTER 4 - MODELLING INFILTRATION T h i s c h a p t e r b e g i n s w i t h a d e s c r i p t i o n o f t h e model. The r e s u l t s o f s i m u l a t i o n s o f i n f i l t r a t i o n i n t o a w a t e r r e p e l l e n t medium a r e t h e n p r e s e n t e d , and compared w i t h t h e o b s e r v a t i o n s o f i n f i l t r a t i o n i n t o a s y n t h e t i c w a t e r r e p e l l e n t medium r e p o r t e d i n C h a p t e r 2. F o l l o w i n g t h a t , t h e s e n s i t i v i t y o f t h e model i s d i s c u s s e d , w i t h r e f e r e n c e t o v a r i a t i o n s i n t h e g r a v i t a t i o n a l p o t e n t i a l , t h e w i d t h s o f d i s t r i b u t i o n s o f p o r e r a d i u s and c o n t a c t a n g l e , t h e mean p o r e s i z e , and t h e mean c o n t a c t a n g l e . The c h a p t e r c o n c l u d e s w i t h a b r i e f summary. A. The model The p r o b l e m o f d e a l i n g w i t h h e t e r o g e n e i t y a t t h e l e v e l o f t h e p o r e i s not t r i v i a l . However, f o r t h e p u r p o s e s o f t h e model, i t w i l l be assumed t h a t f o r each p o r e t h e r e i s a s i n g l e p r e s s u r e a t w h i c h i t w i l l f i l l and a s i n g l e p r e s s u r e a t w h i c h i t w i l l empty. Flow i s m o d e l l e d o n l y f o r a s i n g l e t w o - d i m e n s i o n a l " s h e e t " o f p o r e s c o n n e c t e d i n a r e g u l a r r e c t a n g u l a r g r i d . T h i s arrangement does n o t , o f c o u r s e , c o r r e s p o n d t o t h e geometry o f any r e a l p orous medium, b u t t h e memory and c o m p u t a t i o n a l r e q u i r e m e n t s f o r m o d e l l i n g i n t h r e e d i m e n s i o n s a r e much l a r g e r t h a n f o r two d i m e n s i o n s , and even " t r i v i a l " problems such as d i s p l a y i n g t h e r e s u l t s would become major programming p r o j e c t s . S i n c e 63 t h i s model appears t o be t h e f i r s t o f i t s t y p e , i t was d i f f i c u l t t o a n t i c i p a t e what t h e e f f e c t o f a p a r t i c u l a r "compromise" would be. An a m b i t i o u s g o a l was s e t f o r t h e model - i t must r e p l i c a t e q u a l i t a t i v e l y t h e sequence o f e v e n t s o b s e r v e d i n a s y n t h e t i c w a t e r r e p e l l e n t medium, as d e s c r i b e d i n C h a p t e r 2. Up t o t h e p o i n t where a t l e a s t a p o r t i o n o f t h e f r o n t b e g i n s t o advance w i t h o u t any a p p a r e n t bound, we a r e d e a l i n g w i t h p o s i t i o n s o f s t a t i c e q u i l i b r i u m f o r l i q u i d w a t e r w h i c h v a r y as t h e p r e s s u r e head a t t h e upper boundary i s i n c r e a s e d . Thus, t h e dynamics o f f l o w need not be i n c l u d e d , w h i c h s i m p l i f i e s t h e p r o b l e m c o n s i d e r a b l y . The model was coded i n T u r b o P a s c a l v e r s i o n 3 . 0 ( B o r l a n d I n t e r n a t i o n a l , 1985), a v a r i a n t o f P a s c a l d e v e l o p e d s p e c i f i c a l l y f o r use w i t h w i t h IBM ( I n t e r n a t i o n a l B u s i n e s s Machines) and IBM-compatible p e r s o n a l computers. I n t h i s c h a p t e r , o n l y t h e d e s i g n o f p o r t i o n s o f t h e model r e l e v a n t t o t h i s t h e s i s w i l l be d i s c u s s e d . I t s h o u l d be n o t e d , however, t h a t t h e computer program i t s e l f was d e s i g n e d t o be more g e n e r a l t h a n r e q u i r e d f o r t h e t h e s i s , but i t has not been t e s t e d f u l l y f o r uses o t h e r t h a n t h o s e r e p o r t e d h e r e . The program i s not documented, but i n t e r e s t e d r e a d e r s may c o n t a c t t h e a u t h o r f o r more i n f o r m a t i o n . The d i s c u s s i o n o f t h e model p r e s e n t e d i n t h i s s e c t i o n 64 i s d i v i d e d i n t o seven s u b s e c t i o n s : (1) c o n f i g u r a t i o n o f t h e f l o w f i e l d ; (2) c o n s t r a i n t s on t h e s i z e o f t h e model; (3) t h e g r a v i t a t i o n a l p o t e n t i a l ; (4) boundary c o n d i t i o n s ; (5) a ssignment o f p o r e p r o p e r t i e s ; (6) t h e f i l l i n g o f p o r e s ; and (7) t h e d i s p l a y o f t h e s t a t u s o f i n d i v i d u a l p o r e s . Configuration of the flow f i e l d The b a s i c c o n f i g u r a t i o n o f t h e f l o w f i e l d i s i l l u s t r a t e d i n F i g u r e 4:1. The p o r e s a r e a r r a n g e d on a g r i d s u ch t h a t each p o r e has f o u r c o n n e c t i o n s : (1) one t o t h e p o r e above i t o r t o t h e upper s a t u r a t e d boundary i f i t i s i n t h e f i r s t row; (2) one t o t h e pore t o t h e l e f t o r t o t h e l e f t n o - f l o w boundary; (3) one t o t h e p o r e t o t h e r i g h t o r t o t h e r i g h t n o - f l o w boundary; and (4) one t o t h e p o r e below i t o r t o t h e u n s a t u r a t e d l o w e r boundary. Water e n t e r s t h r o u g h t h e c o n n e c t i o n s a t t h e upper boundary a t a p r e s s u r e head s p e c i f i e d by t h e u s e r o f t h e model. The l o w e r boundary i s always u n s a t u r a t e d , no m a t t e r what p r e s s u r e head i s a p p l i e d a t t h e upper boundary; t h u s , w a t e r o r a i r may e x i t t h r o u g h t h i s boundary. S i n c e o n l y s t a t i c e q u i l i b r i u m i s c o n s i d e r e d i t i s not a p p r o p r i a t e t o s p e c i f y a p r e s s u r e f o r t h i s l o w e r boundary. saturated upper boundary at specified pressure potential unsaturated boundary Figure 4:1. Diagram of boundaries and pore connections. 66 Constraints on the s i z e of the model The major f a c t o r l i m i t i n g the s i z e o f the flow f i e l d i s the amount o f random access memory a v a i l a b l e . For many IBM and IBM-compatible p e r s o n a l computers, the maximum memory a v a i l a b l e i s 640 k i l o b y t e s . For the model, f o u r a t t r i b u t e s o f a pore must be s t o r e d i n memory; they a r e : (1) the p r e s s u r e head at which i t f i l l s ; (2) the p r e s s u r e head at which i t empties; (3) the volume of the pore; and (4) the " s t a t u s " o f the pore. Each of these a t t r i b u t e s i s d e f i n e d i n such a way t h a t i t can be s t o r e d as a s i n g l e byte o f i n f o r m a t i o n . Thus, g i v e n t h a t space i s r e q u i r e d t o s t o r e o t h e r v a r i a b l e s , and the program, t h i s i m p l i e s t h a t l e s s than 160,000 pores can be i n c l u d e d i n the f i e l d . The a t t r i b u t e s c o u l d be s t o r e d on magnetic media, but t h i s would slow e x e c u t i o n o f the programs c o n s i d e r a b l y . A second c o n s t r a i n t i s the amount of i n f o r m a t i o n which can be d i s p l a y e d on scr e e n . In the st a n d a r d g r a p h i c s mode f o r IBM and IBM-compatible p e r s o n a l computers, the scree n i s 320 p i x e l s wide by 200 p i x e l s deep, which means t h a t the a t t r i b u t e s o f onl y 64,000 pores can be d i s p l a y e d at one time. Screens c o u l d be d i s p l a y e d s e q u e n t i a l l y , but t h i s o p t i o n was not pursued. Some screen space was r e s e r v e d f o r d i s p l a y Of i n f o r m a t i o n , l e a v i n g a d i s p l a y area 316 p i x e l s wide by 184 p i x e l s deep. The flow f i e l d 67 was s e t t o t h e s e d i m e n s i o n s , w h i c h i n c l u d e s a t o t a l o f 58,144 p o r e s . Gravity The e f f e c t o f g r a v i t y i s i n c l u d e d i n t h e model. Only s t a t i c e q u i l i b r i u m i s c o n s i d e r e d ; hence, t h e sum o f t h e g r a v i t a t i o n a l and p r e s s u r e heads must be c o n s t a n t a t e q u i l i b r i u m . S i n c e t h e p r e s s u r e head a t e i t h e r t h e upper o r l o w e r boundary i s s p e c i f i e d , t h e f o l l o w i n g e q u a t i o n must h o l d : h + z = h b + z b (1) o r h = h b + z b - z (2) where h i s t h e e q u i l i b r i u m p r e s s u r e head a t h e i g h t z; h b i s t h e p r e s s u r e head a t t h e boundary; and z b i s t h e e l e v a t i o n o f t h e boundary. Thus, f o r a g i v e n boundary p r e s s u r e , t h e p r e s s u r e head i s s i m p l y a l i n e a r f u n c t i o n o f t h e e l e v a t i o n . I n t h i s model, t h e e l e v a t i o n change p e r row i s assumed t o e q u a l t h e average d i a m e t e r o f a p o r e . Thus, t h e p r e s s u r e . f o r any p o r e i s found by summing t h e e l e v a t i o n changes from t h e boundary. E i t h e r o f t h e two b o u n d a r i e s may be s p e c i f i e d as t h e t o p . 68 Boundary conditions Only t h e upper boundary c o n d i t i o n i s v a r i e d . The p r e s s u r e , w h i c h i s s p e c i f i e d as a head o f w a t e r , may be i n c r e a s e d o r d e c r e a s e d o v e r some s p e c i f i e d r ange. P o s i t i v e o r n e g a t i v e heads may be a p p l i e d a t t h e upper boundary, o v e r a range w h i c h i s d e f i n e d when t h e pr o b l e m i s f i r s t s p e c i f i e d . F o r t h e problems c o n s i d e r e d i n t h i s t h e s i s , however, o n l y p o s i t i v e p r e s s u r e heads a r e u s e d s i n c e t h e r e w i l l be no f l o w t h r o u g h a wa t e r r e p e l l e n t medium o t h e r w i s e . The o r i e n t a t i o n o f t h e sample can, i n e f f e c t , be v a r i e d by m a n i p u l a t i n g t h e g r a v i t a t i o n a l t e r m i n t h e model. The g r a v i t a t i o n a l component can be made t o be c o n s t a n t , w h i c h i s a p p r o x i m a t e l y e q u i v a l e n t t o s h i f t i n g t h e axes by 90 degrees such t h a t t h e "upper boundary" i s a s i d e boundary. The s i g n o f t h e g r a v i t a t i o n a l t e r m may a l s o be r e v e r s e d so t h a t t h e "upper boundary" i s now, i n e f f e c t , t h e l o w e r boundary. The term " i n e f f e c t " i s used h e r e , because t h e i n d e x i n g o f a l l o f t h e p o r e s and t h e o r i e n t a t i o n o f t h e d i s p l a y remains f i x e d f o r ease o f c o m p u t a t i o n . The image d i s p l a y e d i s 90 degrees from i t s t r u e o r i e n t a t i o n when no g r a v i t y t e r m i s i n c l u d e d and 180 degree from i t s t r u e o r i e n t a t i o n when t h e g r a v i t a t i o n a l f i e l d i s r e v e r s e d . The r e v e r s e d g r a v i t a t i o n a l f i e l d , as d e s c r i b e d above, 69 i s e q u i v a l e n t t o h a v i n g a l o w e r s a t u r a t e d boundary a t w h i c h a d e f i n e d p r e s s u r e head i s imposed, and a v e n t e d upper boundary. The model i s not used, however, t o s i m u l a t e t h e movement o f wa t e r up i n t o a w a t e r r e p e l l e n t medium from a s a t u r a t e d l o w e r boundary because a l i f t i n g f o r c e i s g e n e r a t e d a t t h e base o f t h e sample. I n a r e a l w a t e r r e p e l l e n t medium, t h i s i s o b s e r v e d t o cause r e -arrangement o f t h e m a t r i x and may even l i f t t h e sample from t h e base o f t h e c o n t a i n e r . These e f f e c t s can n o t , o f c o u r s e , be r e p l i c a t e d by t h i s s i m p l e model. R e v e r s i n g o r removing t h e g r a v i t a t i o n a l f i e l d can, however, be used t o e x p l o r e t h e e f f e c t s o f g r a v i t y on i n f i l t r a t i o n i n t h e po r o u s medium. Assignment of c h a r a c t e r i s t i c s of i n d i v i d u a l pores I n t h e model, i t i s t h e f i l l i n g p r e s s u r e o f a p o r e w h i c h i s c r u c i a l , b u t t h i s p r e s s u r e depends upon t h e geometry and t h e c o n t a c t a n g l e f o r i n d i v i d u a l p o r e s . F o r n o n - r e p e l l e n t p o r e s , t h e p r e s s u r e a t w h i c h a p o r e f i l l s i s assumed t o be governed by: h f = -2a cos [a] / (pgr b) (3) where r b i s t h e r a d i u s o f body o f t h e p o r e . For wa t e r r e p e l l e n t p o r e s , t h e r a d i u s o f t h e neck o f t h e p o r e , r n , 70 c o n t r o l s t h e p r e s s u r e a t w h i c h i t f i l l s ; t h u s : h f = -2(5 cos [a] / (pgr n) (4) The f i l l i n g p r e s s u r e i s , t h e r e f o r e , d e f i n e d by t h e c o n t a c t a n g l e and t h e r a d i u s o f e i t h e r t h e neck o f t h e p o r e o r t h e body o f t h e p o r e , depending upon whether t h e porous medium i s r e p e l l e n t o r n o n - r e p e l l e n t . The f i l l i n g p r e s s u r e f o r each pore i s a s s i g n e d u s i n g t h e r e l a t i o n s h i p s d e f i n e d by e q u a t i o n s (1) and ( 2 ) . The r a d i i and c o n t a c t a n g l e s f o r t h e p o r e s must be drawn from p o p u l a t i o n s s p e c i f i e d f o r each o f t h e l a y e r s p r e s e n t . There i s , i n p r i n c i p l e , no c o n s t r a i n t on t h e form o f t h e d i s t r i b u t i o n s s p e c i f i e d . However, f o r t h e p u r p o s e s o f t h e s i m u l a t i o n s p r e s e n t e d h e r e , i t seemed r e a s o n a b l e t o choose d i s t r i b u t i o n s f o r w h i c h r e a s o n a b l y e f f i c i e n t a l g o r i t h m s were a v a i l a b l e , such as t h e normal d i s t r i b u t i o n . I t seems r e a s o n a b l e t o assume t h a t i f a medium i s r e l a t i v e l y w e l l - s o r t e d , t h e pore s i z e d i s t r i b u t i o n may be c o n t r o l l e d by t h e dominant g r a i n s i z e . F o r such media, a t r u n c a t e d normal d i s t r i b u t i o n may a p p r o x i m a t e t h e a c t u a l p o r e s i z e d i s t r i b u t i o n r e a s o n a b l y w e l l . S i n c e t h e s y n t h e t i c w a t e r r e p e l l e n t medium used f o r t h e o b s e r v a t i o n s o f i n f i l t r a t i o n r e p o r t e d i n C h a p t e r 2 i s a r e l a t i v e l y w e l l - s o r t e d sand, i t was assumed f o r t h e p u r p o s e s o f 71 m o d e l l i n g t h a t the pore r a d i i be drawn randomly from a t r u n c a t e d normal d i s t r i b u t i o n : rmean ~ 2.66 r s d < r b < r m e a n + 2.66 r s d (5) or l i m i t < r b < r m e a n + 2.66 r s d (6) i f rmean " 2.66 r s d < l i m i t (7) The second form of the d i s t r i b u t i o n i s adopted i n cases i n which the f i r s t form of the d i s t r i b u t i o n would l e a d t o v e r y s m a l l , or n e g a t i v e v a l u e s f o r the r a d i u s . The v a l u e o f the " l i m i t " i s based upon the s c a l e s used, and the range of v a l u e s which can be r e p r e s e n t e d by the computer. The r a d i u s o f the "neck" of the pore must be l e s s than or equal t o the r a d i u s o f the "body" of the pore, hence i t i s a s s i g n e d a f t e r the r a d i u s o f the "body" i s s p e c i f i e d . The d i s t r i b u t i o n f o r an i n d i v i d u a l pore i s assumed t o be uniform on the range: l i m i t < r n < r b (8) The c o n s t r a i n t s on the r a d i u s of the neck are i l l u s t r a t e d i n F i g u r e 4:2. 72 Figure 4:2. Distribution of neck radii with body radii. 73 The c o n t a c t a n g l e s o f a pore a r e a s s i g n e d from d i s t r i b u t i o n s w h i c h a r e u n i f o r m between s p e c i f i e d l i m i t s . Thus, t h e range i s s i m p l y : <*min * « < 0t m a x (9) The mean v a l u e i s , t h e r e f o r e , g i v e n by: "mean = (Omin + Omax> /2 (10) T h i s d i s t r i b u t i o n a l l o w s f o r a c o n s i d e r a b l e amount o f f l e x i b i l i t y i n s e t t i n g t h e c o n t a c t a n g l e . I t may be s e t as a s i n g l e v a l u e r a n g i n g anywhere from z e r o t o one hundred and e i g h t y d e g r e e s , o r i t may be s e t so t h a t i t v a r i e s between any two v a l u e s . Thus, a l l p o r e s may be r e p e l l e n t , o r a l l may be n o n - r e p e l l e n t , o r t h e p o p u l a t i o n may c o n t a i n a m i x t u r e o f b o t h r e p e l l e n t and n o n - r e p e l l e n t p o r e s . The f i l l i n g of pores I n o r d e r f o r a po r e t o f i l l by t h e f l o w o f l i q u i d w a t e r , as opposed t o vapour f l o w , t h r e e c o n d i t i o n s must be met. The f i r s t c o n d i t i o n i s t h a t t h e f i l l i n g p r e s s u r e o f t h e p o r e must be l e s s t h a n t h e p r e s s u r e o f w a t e r imposed a t i t s c o n n e c t i o n p o i n t . Such p o r e s w i l l be r e f e r r e d t o as f i l l a b l e p o r e s . The second c o n d i t i o n i s t h a t t h e r e must be a c o n t i n u o u s t h r e a d o f water from t h e s a t u r a t e d boundary t o t h e p o r e , o t h e r w i s e t h e pore c o u l d f i l l o n l y t h r o u g h 74 t h e f l o w o f vapour. The t h i r d and f i n a l c o n d i t i o n i s t h a t t h e r e must be a c o n t i n u o u s p a t h t o t h e u n s a t u r a t e d boundary so t h a t a i r can be e x p e l l e d from t h e p o r e s . As f i l l i n g o f p o r e s p r o c e e d s , t h e c o n n e c t i o n s t o t h e s a t u r a t e d and u n s a t u r a t e d b o u n d a r i e s change. T e s t i n g t o see i f a l l o f t h e t h r e e c o n d i t i o n s s p e c i f i e d above a r e met, f i l l i n g a l l t h o s e p o r e s w h i c h c o u l d be f i l l e d , and t h e n t e s t i n g t h e e n t i r e system a g a i n t o see w h i c h c o u l d be f i l l e d can r e q u i r e a v e r y l a r g e number o f o p e r a t i o n s . F o r t u n a t e l y , t h e p r oblem can be r e f o r m u l a t e d so t h a t f a r fewer c a l c u l a t i o n s a r e r e q u i r e d t h a n f o r t h e " b r u t e f o r c e " method o u t l i n e d above. The p r oblem may be r e c a s t so t h a t t h e p o r e s w h i c h w i l l f i l l a r e d e f i n e d by t h e i n t e r s e c t i o n o f two s e t s o f p o r e s , w h i c h a r e d e f i n e d as f o l l o w s : Set 1 - a l l u n f i l l e d b u t p o t e n t i a l l y f i n a b l e p o r e s w h i c h a r e c o n n e c t e d t o t h e s a t u r a t e d boundary v i a a c o n t i n u o u s c h a i n o f u n f i l l e d b u t p o t e n t i a l l y f i l l a b l e p o r e s o r f i l l e d p o r e s ; and Set 2 - a l l u n f i l l e d but p o t e n t i a l l y f i l l a b l e p o r e s w h i c h a r e c o n n e c t e d t o t h e u n s a t u r a t e d boundary v i a a c o n t i n u o u s c h a i n o f empty p o r e s . E f f i c i e n t a l g o r i t h m s were d e v e l o p e d f o r d e f i n i n g Set 1 and Set 2 as d e f i n e d above. S i n c e t h e a l g o r i t h m s i n v o l v e d a r e 75 v i r t u a l l y i d e n t i c a l i n g e n e r a l form, o n l y t h e a l g o r i t h m f o r d e f i n i t i o n o f Set 1 w i l l be d i s c u s s e d . I n o r d e r t o d e t e r m i n e whether o r not a po r e can f i l l o r empty, i t i s n e c e s s a r y t o e s t a b l i s h t h e c o n n e c t i o n s between p o r e s and t h e b o u n d a r i e s . The f i r s t s t e p i n d o i n g t h i s must be t o d e t e r m i n e w h i c h p o r e s a r e e l i g i b l e t o be c o n n e c t e d . A po r e i s c o n s i d e r e d t o be e l i g i b l e t o be c o n n e c t e d t o t h e upper boundary o n l y i f i t i s f i l l a b l e a t i t s e q u i l i b r i u m p r e s s u r e head, as d e f i n e d i n e q u a t i o n ( 1 ) . I f a p o r e i s e l i g i b l e t o be co n n e c t e d , t h e n i t w i l l be c o n n e c t e d i f any o f t h e f o u r p o r e s a d j a c e n t t o i t a r e a l r e a d y c o n n e c t e d . The second s t e p , t h e r e f o r e , i n v o l v e s t e s t i n g t h e s t a t e o f s u r r o u n d i n g p o r e s i n o r d e r t o d e t e r m i n e i f any o f t h e s e a r e c o n n e c t e d . I n most s i t u a t i o n s , t h e s u r r o u n d i n g pore w h i c h i s c l o s e s t t o t h e boundary t o w h i c h c o n n e c t i o n s a r e b e i n g made i s t h e po r e w h i c h i s most l i k e l y t o be f i l l e d a l r e a d y . The two p o r e s t o e i t h e r s i d e o f t h e po r e a r e c o n s i d e r e d t o be e q u a l l y l i k e l y t o be f i l l e d , w h i l e t h e pore f u r t h e s t from t h e boundary i s l e a s t l i k e l y t o be f i l l e d . Thus, t h e sequence o f t e s t s i s : (1) t e s t t h e pore c l o s e s t t o t h e boundary; t h e n (2) t e s t t h e two p o r e s t o e i t h e r s i d e ; and (3) t e s t t h e s u r r o u n d i n g pore f u r t h e s t from t h e boundary. As c o n n e c t i o n s a r e made w i t h i n a row, p o r e s w h i c h a r e 76 c o n n e c t e d w i t h i n t h a t row can s e r v e as t h e c o n n e c t e d a d j a c e n t p o r e w h i c h must e x i s t i n o r d e r f o r a new c o n n e c t i o n t o be made. C o n s i d e r t h e p a t t e r n o f c o n n e c t i b l e and c o n n e c t e d p o r e s i l l u s t r a t e d i n F i g u r e 4:3. A f t e r a "sweep" t o t h e r i g h t , t h e r e a r e a number o f p o r e s w i t h i n t h e row w h i c h remain u n f i l l e d , but w h i c h c o u l d be f i l l e d by a "sweep" t o t h e r i g h t . Thus, r a t h e r t h a n advance by a row, a second sweep o f t h e row i s made, but t h i s t i m e i t i s t o t h e l e f t . The sequence o f p o r e s c o n n e c t e d a f t e r a sweep t o t h e l e f t , as shown i n F i g u r e 4:3, i l l u s t r a t e s how such a sweep would work. As a "sweep" i s made t o t h e r i g h t , t h e r e i s no advantage i n c h e c k i n g t h e s t a t u s o f p o r e s t o t h e r i g h t s i n c e t h e s e w i l l not be f i l l e d b e f o r e t h e sweep o c c u r s , e x c e p t i n r e l a t i v e l y r a r e s i t u a t i o n s w h i c h may a r i s e a f t e r t h e f i r s t i t e r a t i o n . Even t h e n , t h e r e i s no advantage i n c h e c k i n g f o r them s i n c e t h e i r c o n t r i b u t i o n t o f i l l i n g i s made more e f f i c i e n t l y by t h e "sweep" t o t h e l e f t . S i m i l a r l y , on t h e sweep t o t h e l e f t , t h e r e i s no r e a s o n t o check t h e s t a t u s o f p o r e s t o t h e l e f t . There w o u l d be some advantage t o c h e c k i n g t h e s t a t u s o f t h e a d j o i n i n g p o r e s f u r t h e s t from t h e boundary i n b o t h sweeps i n a few c a s e s , b u t on average t h i s w i l l y i e l d v e r y few e x t r a c o n n e c t i o n s p e r sweep. Thus, i t was d e c i d e d t h a t f o r t h e sweep t o t h e r i g h t , t h e c o n d i t i o n o f p o r e s c l o s e s t t o t h e r e l e v a n t 77 after "sweep" right after "sweep" left o r Legend unfillable tillable, but unfilled filled Figure 4:3. Filling pores by row. 78 boundary would be checked f i r s t , t h e n i f a c o n n e c t i o n was not made, t h e c o n d i t i o n o f p o r e s t o t h e l e f t w ould be checked. F o r t h e sweep t o t h e l e f t , t h e c o n d i t i o n o f p o r e s t o t h e r i g h t would be checked f i r s t , and t h e n t h e c o n d i t i o n o f n e i g h b o r p o r e s f u r t h e s t from t h e boundary, i f no c o n n e c t i o n had been made. Pores c l o s e s t t o t h e boundary a r e t h o s e w h i c h a r e most l i k e l y t o be f i l l e d , t h e r e f o r e , c o n n e c t i o n s a r e made on a row by row b a s i s , s t a r t i n g w i t h t h e row c l o s e s t t o t h e r e l e v a n t boundary. I f an e n t i r e row l a c k s a c o n n e c t i o n t o t h e boundary, t h e n t h e r e i s no p o i n t p r o c e e d i n g t o rows beyond s i n c e t h e r e i s no p o s s i b i l i t y o f making f u r t h e r c o n n e c t i o n s . A s i n g l e pass t h r o u g h t h e d a t a w i l l n o t , however, g u a r a n t e e t h a t a l l t h e p o r e s w h i c h can be c o n n e c t e d a r e c o n n e c t e d . Thus, i t i s n e c e s s a r y t o r e p e a t t h e p r o c e s s u n t i l a l l p o r e s w h i c h can be c o n n e c t e d a r e c o n n e c t e d . For some pore c o n f i g u r a t i o n s , i t i s most e f f i c i e n t t o change t h e o r d e r i n whi c h rows a r e c o n s i d e r e d w i t h each p a s s . The s e t o f p o r e s w h i c h can be c o n n e c t e d can be c o n s i d e r e d as b e i n g l i k e a t r e e , w i t h b r a n c h e s w h i c h may c u r l upwards o r downwards. E s t a b l i s h i n g c o n n e c t i o n s a l o n g a b r a n c h i s most e f f i c i e n t i f t h e e v a l u a t i o n p r o c e e d s i n t h e d i r e c t i o n o f t h e b r a n c h ; t h u s , b r a n c h e s w h i c h a r e 79 d i r e c t e d towards t h e boundary a r e f i l l e d more e f f i c i e n t l y i f t h e o r d e r o f e v a l u a t i o n o f rows i s i n t h a t d i r e c t i o n . T h i s p o i n t i s i l l u s t r a t e d w i t h a p o s s i b l e c o n f i g u r a t i o n o f p o r e s i n F i g u r e 4:4. Note t h a t t h e " a " sequence c o r r e s p o n d s t o t h e a l g o r i t h m used, w h i l e t h e "b" sequence i l l u s t r a t e s an a l g o r i t h m w h i c h i s s i m i l a r t o w a " i n e v e r y r e s p e c t e x c e p t t h a t t h e d i r e c t i o n o f " c o n n e c t i n g " does not r e v e r s e between i t e r a t i o n s . Display of properties The s t a t u s o f i n d i v i d u a l p o r e s - t h a t i s whether o r not t h e y a r e f u l l o r empty, f i l l a b l e o r not f i l l a b l e , c o n n e c t e d o r not c o n n e c t e d t o t h e upper boundary, and c o n n e c t e d o r not c o n n e c t e d t o t h e l o w e r boundary - can be d i s p l a y e d g r a p h i c a l l y u s i n g s e v e r a l r o u t i n e s d e s i g n e d f o r t h i s p u r p o s e . One r o u t i n e a l l o w s an i n d i v i d u a l s u b r e g i o n t o be vi e w e d , w h i l e a n o t h e r a l l o w s t h e e n t i r e r e g i o n t o be vi e w e d . The r e s u l t s may a l s o be p r i n t e d on some c o n v e n t i o n a l d o t - m a t r i x p r i n t e r s . The graphs r e p r o d u c e d i n t h i s t h e s i s were produc e d on an IBM i n k j e t p r i n t e r u s i n g a u t i l i t y program p r o d u c e d by IBM w h i c h can copy any image d i s p l a y e d on a s t a n d a r d IBM c o l o u r m o n i t o r . Sequence a alternating direction scheme start Sequenceb unidirectional scheme mmmm ummm ; - i start B83 3888 ' E •Dot BOOf / / B Mi: ^  Legend unfilled, unfillable pores unfilled, tillable pores filled pores mm mmm mmmm m m Figure 4:4. Comparison of pore-filling algorithms. 81 B. S i m u l a t i o n o f i n f i l t r a t i o n i n t o a w a t e r r e p e l l e n t medium The p o r e - b a s e d n u m e r i c a l model d e v e l o p e d h e r e i s used t o model i n f i l t r a t i o n i n w a t e r r e p e l l e n t media, and i n t o p r o f i l e s w i t h w a t e r r e p e l l e n t l a y e r s . The f l o w f i e l d f o r t h e model a p p r o x i m a t e s t h a t o f t h e e x p e r i m e n t s w i t h s y n t h e t i c w a t e r r e p e l l e n t medium. The s i m u l a t i o n s a l l i n v o l v e i m p o s i t i o n o f a p o s i t i v e p r e s s u r e head a t t h e upper boundary, w h i c h was i n c r e a s e d by s t e p s u n t i l no e q u i l i b r i u m p o s i t i o n f o r t h e complete f r o n t c o u l d be foun d . T h i s s e c t i o n b e g i n s w i t h a comparison o f a s i m u l a t i o n w i t h t h e e x p e r i m e n t a l r e s u l t s . The e f f e c t s o f g r a v i t y i n t h e p r o c e s s a r e t h e n e x p l o r e d by m a n i p u l a t i o n o f t h e g r a v i t a t i o n a l p o t e n t i a l t e r m . F o l l o w i n g t h a t , t h e s e n s i t i v i t y o f t h e model t o v a r i a t i o n s i n t h e w i d t h o f t h e d i s t r i b u t i o n o f t h e r a d i i and i n t h e w i d t h o f t h e d i s t r i b u t i o n o f t h e c o n t a c t a n g l e i s examined. Review of the experimental r e s u l t s for a synthetic water repellent medium The e x p e r i m e n t w i t h w a t e r r e p e l l e n t sand was v e r y s i m p l e . The d e p t h o f wa t e r ponded above t h e medium was i n c r e a s e d g r a d u a l l y by s t e p s u n t i l w a t e r p e n e t r a t e d t h e medium, t h u s f o l l o w i n g t h e change i n boundary c o n d i t i o n s w h i c h might o c c u r i n a d e p r e s s i o n s t o r a g e s i t e d u r i n g a 82 r a i n f a l l e v e n t , o r d u r i n g snowmelt. The sequence o f e v e n t s w h i c h o c c u r s a f t e r p o n d i n g b e g i n s may be d i v i d e d i n t o t h r e e d i s t i n c t p h a ses. The f i r s t phase i s c h a r a c t e r i z e d by t h e absence o f any i n f i l t r a t i o n : up t o some depth, t h e r e i s no p e n e t r a t i o n o f wat e r i n t o t h e medium, o n l y i n c r e a s i n g d i s t o r t i o n o f t h e w a t e r - a i r i n t e r f a c e a t t h e s u r f a c e o f t h e medium. The w e t t i n g " f r o n t " remains a t t h e s u r f a c e o f t h e medium d u r i n g t h i s phase. The second phase b e g i n s when w a t e r b e g i n s t o p e n e t r a t e some p o r e s , as a c r i t i c a l d e p t h o f p o n d i n g i s r e a c h e d . W i t h i n c r e a s i n g d e p t h o f p o n d i n g , s u b s e t s o f t h e po r e space b e g i n t o f i l l as c o n n e c t e d " c l u s t e r s " o f s a t u r a t e d p o r e s , w h i c h a r e c o n n e c t e d t o t h e f r o n t . The p e n e t r a t i o n o f wa t e r i n t o t h e medium does not assume t h e form o f a p l a n a r f r o n t , b u t o c c u r s i n a h i g h l y i r r e g u l a r p a t t e r n , w h i c h appears t o be a c h a r a c t e r i s t i c o f t h e p r o c e s s . Up t o t h i s p o i n t , i f t h e d e p t h o f p o n d i n g i s k e p t c o n s t a n t , t h e i r r e g u l a r p a t t e r n o f w e t t i n g becomes s t a b l e . That i s , t h e f r o n t becomes s t a t i o n a r y a t a p o s i t i o n o f m e c h a n i c a l e q u i l i b r i u m . The t h i r d phase i s c h a r a c t e r i z e d by c o n t i n u i n g advance o f some p o r t i o n s o f t h e f r o n t , w h i c h i s i n f e r r e d t o r e f l e c t t h e absence o f a p o s i t i o n o f e q u i l i b r i u m . 83 Validation of the model I n F i g u r e s 4:5a t h r o u g h 4:5d, t h e s i m u l a t e d p o s i t i o n s o f t h e w e t t i n g f r o n t i n a water r e p e l l e n t medium a r e shown f o r a sequence o f i n c r e a s i n g p r e s s u r e heads. The c h a r a c t e r i s t i c s o f t h e p o p u l a t i o n s from w h i c h t h e r a d i i and c o n t a c t a n g l e s a r e drawn a r e i n c l u d e d w i t h t h e f i g u r e s . I n F i g u r e 4:5a, a p r e s s u r e head o f o n l y 3.0 c e n t i m e t r e i s a p p l i e d a t t h e upper boundary. Note t h a t a t t h i s p r e s s u r e , t h e r e a r e v i r t u a l l y no f i l l e d p o r e s . I n F i g u r e 4:5b, an i r r e g u l a r f r o n t has formed a f t e r i m p o s i t i o n o f a p r e s s u r e head o f 4.0 c e n t i m e t r e s . A number o f s m a l l f i n g e r s , o r l o c a l e x t e n s i o n s o f t h e f r o n t have formed. I n F i g u r e 4:5c, a l a r g e f i n g e r has d e v e l o p e d i n r e s p o n s e t o t h e i m p o s i t i o n s o f a p r e s s u r e head o f 4.5 c e n t i m e t r e s . As shown i n F i g u r e 4:5d, t h e r e i s no p o s i t i o n o f e q u i l i b r i u m f o r some p a r t s o f t h e f r o n t . A t t h i s p o i n t , t h e s i m u l a t i o n i s no l o n g e r r e a l i s t i c i n t h e sense t h a t t h e dynamics o f f l o w w i t h i n t h e f i n g e r a r e not i n c l u d e d . However, t h e p r e d i c t i o n t h a t some p a r t s o f t h e f r o n t w i l l be s t a b l e w h i l e t h e f i n g e r grows does match t h e o b s e r v a t i o n s made f o r f l o w w i t h i n s y n t h e t i c w a t e r r e p e l l e n t medium. C. S e n s i t i v i t y a n a l y s i s The s i m u l a t e d sequence i s , q u a l i t a t i v e l y , v e r y s i m i l a r Figure 4:5. Results of modelling - growth of a finger. 00 85 t o t h a t a c t u a l l y observed. The development of f i n g e r s t u r n s out t o be a f e a t u r e common t o many of the sequences generated. Some of the f a c t o r s which i n f l u e n c e the forma t i o n o f such f i n g e r s w i l l be e x p l o r e d i n t h i s s e c t i o n ; these i n c l u d e the e f f e c t s o f g r a v i t y , o f the width o f d i s t r i b u t i o n o f f i l l i n g p r e s s u r e , o f the mean pore s i z e , and of the mean co n t a c t angle. Gravity The e f f e c t o f g r a v i t y upon the formation o f the f i n g e r s can be determined, i n p a r t , by e x p l o i t i n g the a b i l i t y o f the model t o si m u l a t e f i l l i n g from the bottom of the p r o f i l e . T h i s i s ac h i e v e d by r e v e r s i n g the d i r e c t i o n o f the g r a v i t a t i o n a l f i e l d r a t h e r than changing the o r i e n t a t i o n of pores w i t h i n the r e g i o n o f flow. Thus, only the d i r e c t i o n o f the p o t e n t i a l g r a d i e n t i s changed i n t h i s i n s t a n c e : the geometry and c o n t a c t angle remains the same f o r each pore. Using t h i s f e a t u r e o f the model, the r o l e of chance v a r i a t i o n s i n the p r o p e r t i e s o f the pores can be d i s e n t a n g l e d from the e f f e c t s o f g r a v i t y . In F i g u r e 4:6a, the p a t t e r n of w e t t i n g p r e d i c t e d f o r a porous medium wit h a "normal" g r a v i t a t i o n a l f i e l d i s i l l u s t r a t e d . In F i g u r e 4:6b, the p a t t e r n o f w e t t i n g f o r the same medium i n the presence of a " r e v e r s e d " g r a v i t a t i o n a l f i e l d i s shown. The r e v e r s a l o f the Figure 4:6. Results of modelling - the effect of gravity. 87 g r a v i t a t i o n a l f i e l d has, c l e a r l y , i n h i b i t e d t h e growth o f t h e f i n g e r . T h i s i s t o be e x p e c t e d , however, because t h e p r e s s u r e head i s now d e c r e a s i n g away from t h e boundary r a t h e r t h a n i n c r e a s i n g . I t might be e x p e c t e d , t h e n , t h a t i f t h e p r e s s u r e i s i n c r e a s e d f u r t h e r t o compensate f o r t h e d e c r e a s e i n t h e p r e s s u r e head away from t h e boundary, f i n g e r s w i l l form e v e n t u a l l y . I n F i g u r e s 4:6c and 4:6d, t h e e f f e c t s o f f u r t h e r i n c r e a s e o f t h e p r e s s u r e head a t t h e boundary f o r a r e v e r s e d g r a v i t a t i o n a l f i e l d a r e i l l u s t r a t e d . The f r o n t i s s t i l l uneven, b u t i t i s c o n s i d e r a b l y more even t h a n i f i t s growth had been a s s i s t e d by g r a v i t y . In F i g u r e 4:7a, t h e w e t t i n g p a t t e r n f o r a second medium under c o n d i t i o n s o f normal g r a v i t y i s i l l u s t r a t e d . The d i s t r i b u t i o n o f c o n t a c t a n g l e s , and t h e r e f o r e o f f i l l i n g p r e s s u r e s i s w i d e r i n t h i s example t h a n i n t h e p r e c e d i n g one. The f i n g e r i s , i n t h i s c a s e , e x t r e m e l y w e l l - d e f i n e d . In F i g u r e s 4:7b t h r o u g h 4:7d, t h e e v o l u t i o n o f t h e w e t t i n g f r o n t a g a i n s t a r e v e r s e d g r a v i t y g r a d i e n t i s i l l u s t r a t e d . I n t h i s c a s e , a f i n g e r w h i c h c r o s s e s t h e medium does emerge, b u t from a f r o n t w h i c h i s much c l o s e r t o t h a t boundary t h a n when g r a v i t y a s s i s t s t h e f o r m a t i o n o f a f i n g e r . We a l s o know t h a t a t some d i s t a n c e from t h a t boundary, t h e p r o b a b i l i t y o f t h e f r o n t a d v a n c i n g w i l l drop t o z e r o ; t h u s , t h i s f i n g e r w i l l not c o n t i n u e t o grow. T h i s Figure 4:7. Results of modelling - a second example of the effect of gravity 89 i s i n s h a r p c o n t r a s t t o t h e case where f i n g e r growth i s a s s i s t e d by g r a v i t y ; i n such c a s e s , t h e f i n g e r may e v e n t u a l l y r e a c h a p o i n t where a l l p o r e s a r e f i l l a b l e and no p o s i t i o n o f e q u i l i b r i u m w i l l be^ p o s s i b l e . One o f t h e l i m i t a t i o n s o f t h e v e r s i o n o f t h e model used i s t h a t t h e f l u c t u a t i o n s o f t h e f r o n t a r e r e l a t i v e l y l a r g e w i t h r e s p e c t t o t h e f l o w f i e l d . The f r o n t w h i c h d e v e l o p e d i n t h e r e v e r s e d g r a v i t a t i o n a l f i e l d and t h e one wh i c h d e v e l o p e d i n t h e normal f i e l d p r o d u c e d q u i t e d i f f e r e n t d i s t r i b u t i o n s o f t h e w a t e r c o n t e n t i n t h e v e r t i c a l , as i l l u s t r a t e d i n F i g u r e 4:8. The wat e r c o n t e n t f o r t h e r e v e r s e d f i e l d m a i n t a i n s a h i g h v a l u e up t o some d i s t a n c e from t h e boundary, t h e n drops r a p i d l y t o a v a l u e near z e r o . F o r t h e normal g r a v i t y f i e l d , t h e wa t e r c o n t e n t drops r a p i d l y a l m o s t i m m e d i a t e l y , b u t m a i n t a i n s a moderate, r e l a t i v e l y c o n s t a n t w a t e r c o n t e n t t h r o u g h t h e f l o w f i e l d . The r e s u l t s p r e s e n t e d here suggest t h a t i n a wa t e r r e p e l l e n t medium, f i n g e r s t e n d t o grow o n l y i f a s s i s t e d by g r a v i t y . The p r e s s u r e a t w h i c h a wa t e r r e p e l l e n t p o r e w i l l f i l l depends upon t h e r a d i u s o f t h e neck o f t h a t p o r e and upon i t s c o n t a c t a n g l e . F o r a g i v e n p r e s s u r e , t h e n , t h e p r o b a b i l i t y t h a t a pore i s f i l l a b l e i s governed by t h e d i s t r i b u t i o n s o f neck r a d i i and c o n t a c t a n g l e s f o r t h e "reverse" gravity a. Figure 4:8. Results of modelling -the effect of gravity on moisture content profiles. 91 medium. S i n c e t h e p r e s s u r e head a t e q u i l i b r i u m i n c r e a s e s w i t h d e p t h , t h e p r o b a b i l i t y t h a t a pore i s f i l l a b l e must a l s o i n c r e a s e w i t h d e p t h . I n o r d e r t o f i l l , however, a f i l l a b l e p o r e must be a d j a c e n t t o a n o t h e r f i l l e d p o r e w h i c h i s c o n n e c t e d v i a a c h a i n o f f i l l e d p o r e s t o t h e s a t u r a t e d boundary. Width of the d i s t r i b u t i o n of f i l l i n g pressures The w i d t h o f t h e d i s t r i b u t i o n o f p o r e s i z e s can be v a r i e d . I n F i g u r e s 4:9a t h r o u g h 4:9d, t h e p a t t e r n s o f w e t t i n g a s s o c i a t e d w i t h t h e l o w e s t p r e s s u r e a t w h i c h water i s c o n d u c t e d from t h e t o p o f t h e f l o w f i e l d t o t h e bottom a r e shown. These p a t t e r n s a r e f a i r l y s i m i l a r t o each o t h e r . I n t h e case o f t h e w i d e s t d i s t r i b u t i o n o f p o r e s i z e s , t h e d i s t r i b u t i o n o f p o r e r a d i i i s no l o n g e r n o r m a l , b e i n g t r u n c a t e d by t h e l i m i t i n g v a l u e s a t e i t h e r end. T h i s t r u n c a t i o n p r o b a b l y a c c o u n t s f o r t h e h i g h e r p r e s s u r e a s s o c i a t e d w i t h f i n g e r i n g i n t h i s c a s e : 7.8 c e n t i m e t r e s o f w a t e r v e r s u s no more t h a n 5.2 c e n t i m e t r e s o f w a t e r f o r t h e o t h e r examples. The e f f e c t o f v a r i a t i o n i n w i d t h o f d i s t r i b u t i o n o f c o n t a c t a n g l e s i s e x p e c t e d t o be s i m i l a r t o t h a t o f v a r i a t i o n s i n t h e d i s t r i b u t i o n o f p o r e s i z e s , s i n c e i t i s i n t h e f i n a l a n a l y s i s t h e d i s t r i b u t i o n o f f i l l i n g p r e s s u r e s w h i c h d e t e r m i n e s t h e p a t t e r n o f w e t t i n g . Figure 4:9. Results of modelling - the effect of the width of the distribution of pore radii. 93 Contact angle The p r e s s u r e a t w h i c h t h e r e i s " b r e a k t h r o u g h " - t h a t i s , where w a t e r r e a c h e s t h e lower boundary - i s e x p e c t e d t o be a f u n c t i o n o f t h e c o n t a c t a n g l e . The r e l a t i o n s h i p between f i l l i n g p r e s s u r e and t h e c o n t a c t a n g l e i s g i v e n by: h f = 2a c o s [ a ] / { p g r } (11) Thus, t h e p r e s s u r e a t t r a n s i t i o n from s t a b l e t o u n s t a b l e f l o w s h o u l d v a r y as t h e c o s i n e o f t h e c o n t a c t a n g l e . A sequence o f s i m u l a t i o n s was g e n e r a t e d i n w h i c h o n l y t h e c o n t a c t a n g l e was v a r i e d . The p r e s s u r e a t w h i c h f l o w was p r e d i c t e d t o b r e a k t h r o u g h i s p l o t t e d a g a i n s t t h e c o s i n e o f t h e c o n t a c t a n g l e i n F i g u r e 4:10. As e x p e c t e d t h e r e l a t i o n s h i p i s n e a r l y l i n e a r . Body radius The p r e s s u r e a t w h i c h b r e a k t h r o u g h o c c u r s i s e x p e c t e d t o v a r y w i t h t h e i n v e r s e o f t h e r a d i u s o f t h e neck o f t h e p o r e . I n t h e model, i t i s t h e mean r a d i u s o f t h e body o f t h e p o r e w h i c h i s s p e c i f i e d , but t h e neck r a d i u s i s c l o s e l y r e l a t e d t o i t . A sequence o f s i m u l a t i o n s was g e n e r a t e d i n wh i c h o n l y t h e mean r a d i u s was v a r i e d . The p r e s s u r e a t wh i c h f l o w was p r e d i c t e d t o b r e a k t h r o u g h i s 94 Figure 4:11. Head at "breakthrough" versus inverse of neck radius. 95 p l o t t e d against the inverse of the mean radius i n Figure 4:11. As expected the rel a t i o n s h i p i s nearly l i n e a r . D. Summary A model was developed for prediction of positions of s t a t i c equilibrium for fronts i n water repellent media. The sequence of front positions, t h e i r predicted shape, and the pattern of flow which re s u l t s when part of the front can no longer " f i n d " a p o s i t i o n of s t a t i c equilibrium conform to the general sequence observed for i n f i l t r a t i o n into water repellent synthetic porous media, as reported i n Chapter 2. The re l a t i o n s h i p between the e f f e c t of gravity and finger formation was explored. It was demonstrated that finger growth was favoured when assi s t e d by gravity. Although small fingers d i d appear when the front advanced upwards against gravity, i t was shown that the shape of the wetting front was fundamentally d i f f e r e n t . The s e n s i t i v i t y of the model to vari a t i o n s i n the widths of d i s t r i b u t i o n s of f i l l i n g pressures was explored. Over the range tested, the differences i n pattern appeared to be small: fingers formed i n a l l cases. The pressure at "breakthrough" - that i s , when a finger reaches the lower boundary - was found to be proportional to the cosine of the contact angle, and inversely proportional to the mean body radius of the 96 pores, as i s expected on t h e o r e t i c a l grounds. The r e s u l t s o f these s e n s i t i v i t y a n a l y s es p r o v i d e p a r t i a l c o n f i r m a t i o n t h a t the model i s o p e r a t i n g c o r r e c t l y . 97 CHAPTER 5 - SUMMARY AND DISCUSSION In t h i s c h a p t e r t h e r e s u l t s o f r e s e a r c h a r e summarized and d i s c u s s e d . The d i s t r i b u t i o n o f w a t e r r e p e l l e n t s o i l s i s d i s c u s s e d f i r s t . The f i n d i n g s w i t h r e s p e c t t o i n f i l t r a t i o n i n w a t e r r e p e l l e n t media a r e t h e n p r e s e n t e d . The thermodynamics o f t h e f i l l i n g and emptying o f p o r e s i s t h e n d i s c u s s e d . F o l l o w i n g t h a t , m o d e l l i n g o f i n f i l t r a t i o n i s r e v i e w e d . The c h a p t e r c l o s e s w i t h a d i s c u s s i o n o f t h e i m p l i c a t i o n s o f t h e r e s u l t s f o r r u n o f f g e n e r a t i o n . A. The d i s t r i b u t i o n o f w a t e r r e p e l l e n t s o i l s The f i e l d o b s e r v a t i o n s suggest t h a t w a t e r r e p e l l e n t l a y e r s a r e not uncommon i n t h e a l p i n e - s u b - a l p i n e ecotone o f s o u t h e r n B r i t i s h C o lumbia. These w a t e r r e p e l l e n t l a y e r s grade i n t o l a y e r s w h i c h have a l i m i t e d a f f i n i t y f o r w a t e r . B o t h t y p e s o f l a y e r appear t o be a s s o c i a t e d w i t h t h e a c c u m u l a t i o n o f o r g a n i c m a t t e r i n t h e p r o f i l e . I t appears t h a t t h e r e p e l l e n c y may be a consequence o f t h e normal t r a n s f o r m a t i o n and t r a n s l o c a t i o n o f o r g a n i c m a t t e r i n t h i s e n v i r o n m e n t . I t i s c l e a r t h a t f u r t h e r work on t h e v a r i a t i o n s i n t h e a f f i n i t y o f s o i l f o r w a t e r i n t h e s u b - a l p i n e and i n o t h e r e n v i r o n m e n t s i s r e q u i r e d . The a f f i n i t y o f s o i l f o r w a t e r can change v e r y r a p i d l y i n t h e v e r t i c a l , w i t h no 98 c o r r e s p o n d i n g change i n t e x t u r e , and thus may be missed i n r o u t i n e assessments o f the p r o p e r t i e s o f s o i l s . As w e l l , the methods used f o r sampling and f o r d e t e r m i n a t i o n o f h y d r a u l i c p r o p e r t i e s may not p r e s e r v e the o r i g i n a l l a y e r i n g , and i n some cases may d e s t r o y the n a t u r a l c o a t i n g s on g r a i n s which appear t o be r e s p o n s i b l e f o r the changes i n a f f i n i t y . Many of the standar d procedures recommend t h a t samples be o x i d i z e d w i t h a c o n c e n t r a t e d s o l u t i o n o f hydrogen peroxide, a f t e r g r i n d i n g and s e i v i n g o f the samples. T h i s treatment would almost c e r t a i n l y d e s t r o y any r e p e l l e n t coat on m i n e r a l g r a i n s . In o r d e r t o understand the h y d r o l o g i c behaviour o f s o i l s , methods of a n a l y s i s must be developed which p r e s e r v e the p r o p e r t i e s o f the i n t a c t s o i l s . The water drop p e n e t r a t i o n time t e s t can be used as a guide t o the changes, but p e n e t r a t i o n times do not bear any simple r e l a t i o n s h i p t o c o n t a c t angle, or t o any oth e r b a s i c p r o p e r t i e s . D etermination o f the i n f i l t r a b i l i t y o f samples as a f u n c t i o n o f the amount o f water which has i n f i l t r a t e d can be u s e f u l , as demonstrated i n t h i s study, but the e f f e c t s o f v a r i a t i o n s i n the c h a r a c t e r i s t i c g e o m e t r i c a l p r o p e r t i e s o f the pore space w i t h depth can not be r e a d i l y d i f f e r e n t i a t e d from the e f f e c t s o f v a r i a t i o n s i n the a f f i n i t y o f the s o i l f o r water. Even so, such i n f o r m a t i o n may be u s e f u l f o r understanding the movement of water 99 within the s o i l , and runoff generation. It i s also important to consider v a r i a t i o n s i n the ho r i z o n t a l , which was not done formally i n t h i s study. Observations i n the f i e l d , however, suggested that i n some areas, the horizons which are water r e p e l l e n t or which have a low a f f i n i t y for water may be breached by roots, and sometimes by de s i c c a t i o n cracks. The importance of flow i n "macropores" has been demonstrated i n connection with flow i n various s o i l s (see DeVries and Chow, 1978, and Bevan and Germann, 1982) . In s o i l s where there are horizons which are water repe l l e n t , or which have a low a f f i n i t y f o r water, the importance of macropores may be even greater than that documented already. It would be i n t e r e s t i n g to determine whether or not there are systematic v a r i a t i o n s i n the contact angle i n a d i r e c t i o n normal to the surfaces of these macropores. These v a r i a t i o n s would have important consequences for the hydrologic behaviour of such s o i l s . . In water r e p e l l e n t s o i l s , vapour flow can c o n s t i t u t e a s i g n i f i c a n t f r a c t i o n of the t o t a l flow. In the laboratory, the bottom of some samples dried over time when water was ponded on the surface. By removing the water from the surface, and weighing the sample, i t was determined that over time some samples were a c t u a l l y sustaining a net loss 100 of water, which i m p l i e s t h a t the r a t e o f vapour flow out o f the sample was g r e a t e r than the movement of water i n t o the sample. Development of t e c h n i q u e s f o r d e t e r m i n i n g r a t e s o f vapour flow under f i e l d c o n d i t i o n s i s r e q u i r e d i n o r d e r t o understand water movement i n such s o i l s . B. I n f i l t r a t i o n i n water r e p e l l e n t media O b s e r v a t i o n s o f i n f i l t r a t i o n i n t o a s y n t h e t i c water r e p e l l e n t medium suggest t h a t t h e r e i s no e n t r y o f water u n t i l some c r i t i c a l ponding depth i s reached. As p r e s s u r e i s i n c r e a s e d i n s t e p s , a w e t t i n g " f r o n t " advances from one p o s i t i o n o f s t a b i l i t y t o a new p o s i t i o n o f s t a b i l i t y . F i n g e r - s h a p e d i r r e g u l a r i t i e s i n the p o s i t i o n o f the f r o n t d e velop as the f r o n t advances. At some p r e s s u r e , one or more o f these f i n g e r s may b e g i n t o grow without any apparent l i m i t : t h e r e i s no e q u i l i b r i u m p o s i t i o n f o r t h i s p o r t i o n o f the f r o n t . I t was proposed t h a t the (unchecked) growth o f i n d i v i d u a l f i n g e r s i n d i c a t e s t h a t t h e r e i s no e q u i l i b r i u m p o s i t i o n f o r the f i n g e r beyond some p o i n t i n i t s growth. T h i s i s a d i f f e r e n t mechanism o f f i n g e r growth than t h a t proposed by P h i l i p (1975), where one p a r t o f an advancing f r o n t simply " o u t r a c e s " the remainder of the f r o n t . The r e s u l t s p r e s e n t e d here d i f f e r from t h a t model i n t h r e e important r e s p e c t s : (1) the remainder of the f r o n t 101 i s s t a t i o n a r y ; (2) the finger i s not n e c e s s a r i l y a t r a n s i e n t feature; and (3) the finger does not grow from a microscopic perturbation i n the wetting front which i s amplified as the front advances. These d i f f e r e n c e s suggest that re-evaluation of unstable i n f i l t r a t i o n i n non-r e p e l l e n t media i s required. C. The f i l l i n g and emptying of pores Hysteresis i n the r e l a t i o n between water content and pressure p o t e n t i a l i s usually considered to a r i s e as a r e s u l t of the geometrical c h a r a c t e r i s t i c s of pores. In t h i s t h e s i s , however, i t was argued that v a r i a t i o n s of the physicochemical properties within a porous medium can also cause h y s t e r e s i s . Analysis of water movement i n a hypothetical c y l i n d r i c a l pore i n which the physicochemical properties vary s p a t i a l l y indicated that such changes can lead to a d i f f e r e n c e between the pressure at which the c y l i n d e r w i l l f i l l and that at which i t w i l l empty, even i n the absence of any geometrical properties which would lead to h y s t e r e s i s i n the r e l a t i o n . These r e s u l t s were confirmed by simple experiments conducted with glass and polyethylene tubes. In the case of the glass tubes, i t was shown that the surface properties v a r i e d as a r e s u l t of 102 adsorbed contaminants, w h i l e i n the p o l y e t h y l e n e t u b i n g t h e r e were marked changes i n the p h y s i c o c h e m i c a l p r o p e r t i e s a l o n g t h e l e n g t h o f the tube. The i m p l i c a t i o n o f t h e s e f i n d i n g s i s t h a t v a r i a t i o n s o f the p h y s i c o c h e m i c a l p r o p e r t i e s o f a porous medium may l e a d t o h y s t e r e s i s i n t h e r e l a t i o n between water c o n t e n t and p r e s s u r e p o t e n t i a l . T h i s r e i n f o r c e s t h e more g e n e r a l p o i n t made i n t h i s t h e s i s t h a t t h e p h y s i c o c h e m i c a l p r o p e r t i e s o f s o i l s p l a y a c e n t r a l r o l e i n d e t e r m i n i n g t h e i r h y d r o l o g i c a l b e h a v i o u r . The i s s u e warrants f u r t h e r r e s e a r c h . D. M o d e l l i n g i n f i l t r a t i o n While t h e b e h a v i o u r of i n d i v i d u a l pores was r e l a t i v e l y easy t o a n a l y z e ; the b e h a v i o u r o f a connected s e t o f pores w i t h v a r y i n g g e o m e t r i c and c h e m i c a l p r o p e r t i e s p r e s e n t s a more d i f f i c u l t problem. In o r d e r t o address t h i s problem, a computer model was d e v e l o p e d o f a simple two-dimensional network o f i n t e r c o n n e c t e d pores w i t h g e o m e t r i c and s u r f a c e p r o p e r t i e s which a r e a s s i g n e d randomly from p r e d e f i n e d d i s t r i b u t i o n s . 103 I t was found t h a t the model c o u l d r e p l i c a t e the sequence o f even t s observed i n w e t t i n g o f t h e s y n t h e t i c water r e p e l l e n t medium. That i s , t h e r e was l i t t l e or no w e t t i n g up t o some c r i t i c a l s u r f a c e p r e s s u r e , f o l l o w e d by f o r m a t i o n o f an i r r e g u l a r f r o n t at h i g h e r p r e s s u r e s , then f o r m a t i o n o f i n c i p i e n t f i n g e r s and, f i n a l l y , unchecked growth o f f i n g e r s at s t i l l h i g h e r p r e s s u r e s . T h i s approach t o m o d e l l i n g , which i s based upon the p r o p e r t i e s o f i n d i v i d u a l pores, may prove u s e f u l i n a n a l y z i n g o t h e r p r o c e s s e s , such as t r a n s i t i o n s from e q u i l i b r i u m t o d i s e q u i l i b r i u m i n n o n - r e p e l l e n t media (that i s , some t y p e s o f f i n g e r i n g ) . I t s h o u l d a l s o be p o s s i b l e t o s i m u l a t e the dynamics o f systems o f i n t e r c o n n e c t e d p o r e s . I t may be worth n o t i n g t h a t many o f the computations i n v o l v e d are i n h e r e n t l y p a r a l l e l , which i m p l i e s t h a t a n a l y s i s of r e l a t e d , but more complex problems t h a n t h o s e c o n s i d e r e d here, may be f e a s i b l e on computers w i t h p a r a l l e l a r c h i t e c t u r e s . A l t h o u g h the model was developed as such, i t f o l l o w s the c e l l u l a r automata approach (see T o f f o l i and Margolus, 1987), i n which p u r e l y l o c a l r e l a t i o n s govern complex m a c r o s c o p i c phenomena. That the model d e v e l o p e d here can 104 s i m u l a t e t h e phenomenon o f f i n g e r i n g i n water r e p e l l e n t media, i n c l u d i n g t h e d i s c o n t i n u o u s advance o f t h e w e t t i n g f r o n t w i t h i n c r e a s i n g ponding depth, p r o v i d e s s t r o n g support f o r t h e . v a l i d i t y o f the u n d e r l y i n g assumptions. E. I m p l i c a t i o n s f o r r u n o f f g e n e r a t i o n In t h i s study, i t was found t h a t most o f t h e s o i l s sampled i n t h e s u b - a l p i n e s i t e s s e l e c t e d had a zone near the s u r f a c e o f t h e s o i l which had a l i m i t e d a f f i n i t y f o r water, and t h a t a t some s i t e s up t o o n e - t h i r d o f t h e s e zones were, i n f a c t , water r e p e l l e n t . Where the zone i s water r e p e l l e n t , a l l p r e c i p i t a t i o n w i l l be c o n v e r t e d i n t o o v e r l a n d flow, except i n s u r f a c e s t o r a g e s i t e s where water may pond t o a s u f f i c i e n t depth t o cause some i n f i l t r a t i o n t o o c c u r . Where the zone i s not a c t u a l l y w a t e r - r e p e l l e n t , but has a l i m i t e d a f f i n i t y f o r water, o v e r l a n d flow w i l l b e g i n e a r l i e r t han f o r h y d r o p h i l i c s o i l s f o r p r e c i p i t a t i o n events o f s u f f i c i e n t i n t e n s i t y t o cause o v e r l a n d flow; t h a t i s , t h o s e e v e n t s i n which the p r e c i p i t a t i o n r a t e exceeds the s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y o f t h e s o i l . The amount o f o v e r l a n d flow generated w i l l r i s e r a p i d l y t o a v a l u e e q u a l t o t h e d i f f e r e n c e between the p r e c i p i t a t i o n r a t e and the s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y . 105 The survey r e s u l t s at the v a r i o u s s i t e s suggest t h a t t r u l y r e p e l l e n t zones may be d i s t r i b u t e d i n " p a t c h e s " over the l a n d s c a p e . Thus, t h e r e may be patches where no i n f i l t r a t i o n i s o c c u r r i n g s i t u a t e d next t o patches i n which i n f i l t r a t i o n i s o c c u r r i n g . Water f l o w i n g from these water r e p e l l e n t patches may i n f i l t r a t e , at l e a s t i n p a r t , i n a d j a c e n t n o n - r e p e l l e n t a r e a s . S i m i l a r l y , o v e r l a n d flow generated i n areas where a l a y e r o f low a f f i n i t y e x i s t s may be absorbed i n areas where no such l a y e r e x i s t s . S i g n i f i c a n t l a t e r a l c o n t r a s t s i n both the amount o f o v e r l a n d flow generated and i n the amount o f water which i n f i l t r a t e s may e x i s t even i n the absence of s i g n i f i c a n t l a t e r a l c o n t r a s t s i n t e x t u r e . The presence of zones of l i m i t e d a f f i n i t y or o f water r e p e l l e n c y may decrease c o n s i d e r a b l y the moi s t u r e content of s o i l s . In the case of s o i l s w i t h a zone o f l i m i t e d a f f i n i t y , not o n l y w i l l t h e r e be l e s s i n f i l t r a t i o n than would be expe c t e d otherwise, but water w i l l d r a i n more e a s i l y s i n c e c a p i l l a r y f o r c e s are s m a l l or r e p u l s i v e . T h i s , then, f a v o u r s the development o f s u b s u r f a c e s a t u r a t e d zones. I t a l s o favours the movement o f water through macropores, s i n c e the c a p i l l a r y f o r c e s which n o r m a l l y b i n d water w i t h i n the ma t r i x are not important. Vapour flow w i l l not be impeded i n the s e s o i l s ; hence, moi s t u r e l o s s through e v a p o t r a n s p i r a t i o n w i l l not be 106 i n h i b i t e d ; i n d e e d , w a t e r may be e x t r a c t e d more e a s i l y t h a n from h y d r o p h i l i c s o i l s . Beneath t r u l y w a t e r r e p e l l e n t zones, where t h e r e i s no f l o w o f water as a l i q u i d from above, m o i s t u r e must move e i t h e r l a t e r a l l y o r from below, a l t h o u g h some vapour f l o w from t h e s u r f a c e t o t h e s u b s u r f a c e might o c c u r . The r e s u l t s o f t h e r e s e a r c h i m p l y t h a t i n o r d e r t o u n d e r s t a n d t h e h y d r o l o g y o f a p a r t i c u l a r b a s i n , i t i s n e c e s s a r y t o c o n s i d e r not o n l y t h e t e x t u r e and arrangement o f t h e m a t e r i a l s i n v o l v e d , i t i s a l s o n e c e s s a r y t o c o n s i d e r t h e v a r i a t i o n s i n t h e p h y s i c o c h e m i c a l p r o p e r t i e s o f t h e m a t e r i a l s i n v o l v e d . These v a r i a t i o n s have i m p o r t a n t i m p l i c a t i o n s b o t h f o r u n d e r s t a n d i n g t h e d e t a i l s o f t h e p r o c e s s e s i n v o l v e d , and f o r u n d e r s t a n d i n g t h e b e h a v i o u r o f e n t i r e b a s i n s . F u r t h e r m o r e , s i n c e t h e d i s t r i b u t i o n o f w a t e r w i t h i n t h e b a s i n w i l l be a f f e c t e d , t h e s e v a r i a t i o n s a r e e x p e c t e d t o have an impact on a wide range o f p r o c e s s e s l i n k e d t o t h e h y d r o l o g i c system. 107 REFERENCES B a r r e t t , G., 1981, Streamflow generation in a sub-alpine basin in the Coast Mountains of British Columbia, u n p u b l i s h e d M.Sc. t h e s i s , U n i v e r s i t y o f B r i t i s h Columbia, 89 p. Bevan, K. and P. Germann, 1982, Macropores and water flow i n s o i l s , Water Resources Research 18, 1311-1325. Bond, R.D. and J.R. H a r r i s , 1964, The i n f l u e n c e o f the m i c r o f l o r a on p h y s i c a l p r o p e r t i e s o f s o i l s I. E f f e c t s a s s o c i a t e d w i t h filamentous algae and f u n g i , Australian Journal of Soil Research 2, 111-122. B o r l a n d I n t e r n a t i o n a l , 1985, TurboPascal - v e r s i o n 3.0, S c o t t s V a l l e y , C a l i f o r n i a . Bozer, K.B., Brandt, G.H., and Hemwall, J.B., 1969, Chemistry of m a t e r i a l s t h a t make s o i l s hydrophobic, i n Water repellent soils - Proceedings of the symposium on water repellent soils, University of California, R i v e r s i d e , C a l i f o r n i a , May 6-10, 1968, 189-204. Brandt, G.H., 1969, The occurrence of w a t e r - r e p e l l e n t s o i l s i n A u s t r a l i a , i n Water repellent soils -Proceedings of the symposium on water repellent soils, U n i v e r s i t y o f C a l i f o r n i a , R i v e r s i d e , C a l i f o r n i a , May 6-10, 1968, 1-6. B r i t i s h Columbia M i n i s t r y o f Environment, 1985, Summary of snow survey measurements in British Columbia, 1935-1985, Water Management Branch, V i c t o r i a . Buckingham, E., 1907, S t u d i e s on the movement of s o i l m oisture, U.S. Department of Agriculture Soils Bulletin 38. Coates, J.A., 1974, Geology of the Manning Park area, B r i t i s h Columbia, Geological Society of Canada Bulletin 238, 177 p. Debano, L.F., 1969, Water movement i n w a t e r - r e p e l l e n t s o i l s , i n Water repellent soils - Proceedings of the symposium on water repellent soils, University of C a l i f o r n i a , R i v e r s i d e , C a l i f o r n i a , May 6-10, 1968, 189-204. 108 Debano, L.F, L.D. Mann, and D.A. Hamilton, 1970, T r a n s l o c a t i o n of hydrophobic substances i n t o s o i l by b u r n i n g o r g a n i c l i t t e r , Soil Science Society of America Proceedings 34, 130-133. Debano, L.F. and R.M. R i c e , 1973, W a t e r - r e p e l l e n t s o i l s : t h e i r i m p l i c a t i o n s i n f o r e s t r y , Journal of Forestry 7 1 , ( r e p r i n t ) . DeVries, J . and T.L. Chow, 1978, H y d r o l o g i c b e h a v i o r of a f o r e s t e d mountain s o i l i n c o a s t a l B r i t i s h Columbia, Water Resources Research 14, 935-942. G a l l i e , T.M., 1983, Chemical denudation and hydrology near tree limit, Coast Mountains, B r i t i s h Columbia. Ph.D. t h e s i s , U n i v e r s i t y of B r i t i s h Columbia, 262 p. G a l l i e , T.M. and 0.Slaymaker, 1984, V a r i a b l e s o l u t e sources i n a c o a s t a l s u b - a l p i n e environment, i n T.P. Burt and D.E. W a l l i n g ( e d i t o r s ) , Catchment experiments in f l u v i a l geomorphology, Geobooks, pp. 347-357. , 1985, H y d o l o g i c a l c o n t r o l s on stream che m i s t r y i n water q u a l i t y e v o l u t i o n w i t h i n the h y d r o l o g i c a l c y c l e of watersheds, Proceedings of the 15th hydrology symposium of the National Research Council of Canada, Quebec C i t y , pp. 288-306. G e o l o g i c a l Survey of Canada, Kananaskis Lakes, Open F i l e 634 (no d a t e ) . G i o v a n n i n i , G. and S. L u c c h e s i , 1984, D i f f e r e n t i a l thermal a n a l y s i s and i n f r a r e d i n v e s t i g a t i o n s on s o i l hydrophobic substances, Soil Science 137, 457-4 63. Green, W.H. and G.A. Ampt, 1911, S t u d i e s on s o i l p h y s i c s : I. Flow of a i r and water through s o i l s . Journal of Agricultural Science 4, 1-24. H i l l , D.E. and J.-Y. Parlange, 1972, Wetting f r o n t i n s t a b i l i t y i n l a y e r e d s o i l s . Soil Science Society of America Proceedings 36, 697-716. H i l l e l , D., 1980, Applications of soil physics, Academic Press, New York, 385 p. J u n g e r i u s , P.D. and F. van der Meulen, 1988, E r o s i o n p r o c e s s e s i n a dune landscape along the Dutch c o a s t . Catena. Accepted f o r p u b l i c a t i o n . 109 Krammes, J.S. and L.F. Debano, 1965, S o i l w e t t a b i l i t y : a n e g l e c t e d f a c t o r i n watershed management, Water Resources Research 1, 283-286. Letey, J . , 1969, Measurement of c o n t a c t angle, water drop p e n e t r a t i o n time, and c r i t i c a l s u r f a c e t e n s i o n , i n Water repellent soils - Proceedings of the symposium on water repellent soils, University of California, R i v e r s i d e , C a l i f o r n i a , May 6-10, 1968, 43-47. L i t t l e , H.W., 1960, Nelson map-area, west h a l f , B r i t i s h Columbia (82W1/2). Geological Survey of Canada Memoir 3 0 8 , 205 p. McGhie, D.A. and A.M. Posner, 1980, Water r e p e l l e n c e of a heavy- t e x t u r e d Western A u s t r a l i a Surface S o i l , Australian Journal of Soil Research 18, 309-323. M i l l e r , R.D. and J.F. W i l k i n s o n , 1977, Nature of the o r g a n i c c o a t i n g on sand g r a i n s of nonwettable g o l f greens. Soil Science Society of America Proceedings 4 1 , 1203-1204. Osipow, L . I . , 1977, Surface chemistry: theory and industrial applications, Robert E. K r i e g e r P u b l i s h i n g Company, New York, 473 p. P h i l i p , J.R., 1957, The th e o r y o f i n f i l t r a t i o n : 1. The i n f i l t r a t i o n e q u a t i o n and i t s s o l u t i o n . Soil Science 8 3 , 345-357. , 1975, The growth of d i s t u r b a n c e s i n u n s t a b l e i n f i l t r a t i o n flows, Soil Science Society of America Proceedings 39, 1049-1053. , 1983, I n f i l t r a t i o n i n one, two, and t h r e e dimensions, i n Advances in I n f i l t r a t i o n : Proceedings of the national conference on advances in i n f i l t r a t i o n , December 12-13, 1983, Chicago, I l l i n o i s 1-13. Reeder, C.J. and M.F. Jurgenson, 1979, F i r e - i n d u c e d water r e p e l l e n c y i n f o r e s t s o i l s o f upper Michigan, Canadian Journal of Forest Research 9, 369-373. Ri c h a r d s , L.A., 1931, C a p i l l a r y c o n d u c t i o n of f l u i d s through porous mediums. Physics 1, 318-333. 110 Roberts, F . J . and B.A. Carbon, 1972, Water r e p e l l e n c e i n sandy s o i l s o f South Western A u s t r a l i a I I . Some chemical c h a r a c t e r i s t i c s o f the hydrophobic s k i n s , Australian Journal of Soil Research 10, 35-42. Roddick, J.A., 1976, Summary o f the coast p l u t o n i c complex of B r i t i s h Columbia, Geological Society of America Abstracts 8, p. 405. Savage, S.M., J.P. M a r t i n , and J . Letey, 1969, C o n t r i b u t i o n o f some f u n g i i n n a t u r a l and heat induced water r e p e l l e n c y i n sand, Soil Science Society of America Proceedings 33, 14 9-150. Savage, S.M., J . Osborne, J . Letey, and C. Heaton, 1972, Substances c o n t r i b u t i n g t o f i r e - i n d u c e d water r e p e l l e n c y i n s o i l s , Soil Science Society of America Proceedings 35, 674-678. S c h o l l , D.G., 1971, S o i l w e t t a b i l i t y i n Utah j u n i p e r stands, Soil Science Society of America Proceedings 35, 344-345. S p r a c k l i n g , M.T., 1985, Liquids and solids. Routledge & Kegan Paul, Boston, 237 p. T o f f o l i , T. and N. Margolus, 1987, Cellular automata machines: a new modelling environment. The MIT Press, Cambridge, Massachusetts, 259 p. Topp, G.C., 1966, Surface t e n s i o n and water contamination r e l a t e d t o the s e l e c t i o n o f flow system components, Soil Science Society of America Proceedings 30, 128-129. Wessel, F., 1986, Water r e p e l l e n c y o f dune sand i n r e l a t i o n t o the v o l u m e t r i c moisture content and the o r g a n i c matter content. G e r e s e r v e e r d voor Supplement Band Catena. Woodsworth, G.J., 1977, Geology of the Pemberton (92J) map area, Geological Survey of Canada Open File Report 482, 1 map sheet. I l l APPENDIX A - METHODS FOR COLLECTION OF SAMPLES Two procedures f o r c o l l e c t i o n o f samples were used. One of these procedures was used where samples were a n a l y z e d at the f i e l d s i t e , and the other where the samples were c o l l e c t e d at the s i t e , but analyzed i n the l a b o r a t o r y . Both procedures are d e s c r i b e d i n t h i s s e c t i o n . C o l l e c t i o n of samples for analysis in the f i e l d In the case where samples were a n a l y z e d at the f i e l d s i t e , a sample was cut from a l a r g e r b l o c k o f m a t e r i a l i n order t o minimize d i s r u p t i o n o f the sample. The l a r g e r b l o c k o f m a t e r i a l was i s o l a t e d by c u t t i n g the edges w i t h a spade. The b l o c k was then l i f t e d from the ground as g e n t l y as p o s s i b l e . A sharp k n i f e was used t o cut a s m a l l e r r e c t a n g u l a r s l i c e from t h i s b l o c k . The samples were removed t o a s h e l t e r and a i r - d r i e d f o r one week p r i o r t o a n a l y s i s . C o l l e c t i o n of samples for analysis in the laboratory In s i t u a t i o n s where the samples were t o be t r a n s p o r t e d t o the l a b o r a t o r y f o r a n a l y s i s , cores were c o l l e c t e d by d r i v i n g PVC or ABS tubes i n t o the ground u s i n g a sledge hammer. These tubes were sharpened at one end w i t h a round f i l e . With sharpened tubes, compression of the sample was u s u a l l y l e s s than t e n percent, as determined by comparing 112 the l e n g t h o f the sample i n the tube w i t h the depth of p e n e t r a t i o n . The i n s i d e diameter o f both types o f p i p e i s 5.3 c e n t i m e t r e s . The t h i c k n e s s of w a l l of the PVC t u b i n g i s 0.3 c e n t i m e t r e s , w h i l e the t h i c k n e s s of the w a l l of the ABS t u b i n g i s 0.5 c e n t i m e t r e s . Both the PVC and ABS p i p e s proved t o be s a t i s f a c t o r y i f the s o i l was composed of l o e s s . The ABS p i p e was, however, c l e a r l y s u p e r i o r f o r s o i l s w i t h rocks, or f o r t i l l , or f o r cores l o n g e r than about t h i r t y c e n t i m e t r e s . The ends of the tube were covered w i t h c l e a r p l a s t i c wrap, then wrapped w i t h tape t o p r o v i d e support f o r the samples and t o prevent d r y i n g d u r i n g t r a n s p o r t t o the l a b o r a t o r y f o r a n a l y s i s . The samples were examined by removing a s t r i p from the p i p e p a r a l l e l t o the a x i s of the p i p e . The p i p e was s c o r e d u s i n g a t a b l e saw s e t t o produce a cut j u s t s l i g h t l y l e s s deep than the t h i c k n e s s of the w a l l of the p i p e . The p i p e was then r o t a t e d about n i n e t y degrees and s c o r e d a g a i n . The s t r i p s were s e p a r a t e d by completing the cut w i t h a sharp k n i f e . The s t r i p s c o u l d then be removed t o open a window on the s o i l . Spacing the c u t s n i n e t y degrees from each other allowed the s t r i p t o be removed wi t h a minimum of d i s r u p t i o n of the sample. 113 APPENDIX B - DESCRIPTION OF THE SUB-ALPINE SURVEY SITES, SOUTHERN BRITISH COLUMBIA The l o c a t i o n s of the s i t e s s e l e c t e d were shown i n F i g u r e 2:1. The s p e c i f i c s i t e s were s e l e c t e d on the b a s i s o f geographic l o c a t i o n and a c c e s s i b i l i t y . The c h a r a c t e r i s t i c s of the s i t e s are p r e s e n t e d here. Manning Park The samples were c o l l e c t e d at a s i t e near Three B r o t h e r s Mountain, i n Manning Park. The e l e v a t i o n o f the s i t e i s approximately 2150 metres, j u s t below t r e e - l i m i t . Bedrock i s mapped as b e i n g a Cretaceous arkose u n i t which i s p a r t of the Jackass Mountain Group (Coates, 1974) . There i s no c l i m a t e data a v a i l a b l e f o r the s i t e , but the May 1 snow packs at nearby B l a c k w e l l Peak, at an e l e v a t i o n of 1940 metres, average 922 m i l l i m e t r e s as a water e q u i v a l e n t depth ( B r i t i s h Columbia M i n i s t r y of Environment, 1985). The s i t e i s i n open s u b - a l p i n e meadow, as can be seen i n P l a t e B : l . The s o i l samples are shown i n P l a t e B:2. Idaho Peak Idaho Peak i s l o c a t e d i n the S e l k i r k Mountains of B r i t i s h Columbia, near New Denver. The s i t e i s l o c a t e d below t r e e - l i m i t , at an e l e v a t i o n of about 1800 metres. 114 Bedrock i s mapped by L i t t l e (1960) as Slocan Group, which i n c l u d e s T r i a s s i c s l a t e , a r g i l l i t e , q u a r t z i t e , limestone, conglomerate, and t u f f . There are no bedrock exposures i n the immediate v i c i n i t y o f the s i t e . There i s no c l i m a t e data a v a i l a b l e f o r Idaho Peak, but the water e q u i v a l e n t of the May 1 snowpack at nearby Sandon snowcourse, at 1007 metres, averages 361 m i l l i m e t r e s ( B r i t i s h Columbia M i n i s t r y o f Environment, 1985). The samples were c o l l e c t e d i n a a sm a l l s u b - a l p i n e meadow along Houston Creek, as shown i n P l a t e B:3. Only f o u r o f the s i x samples remained i n t a c t a f t e r c o l l e c t i o n and t r a n s p o r t ; these f o u r are shown i n P l a t e B:4. Kokanee Lake The Kokanee Lake s i t e i s l o c a t e d i n the S e l k i r k Mountains, w i t h i n Kokanee G l a c i e r Park. The s i t e i s l o c a t e d below t r e e - l i m i t , at an e l e v a t i o n o f approximately 194 0 metres. Bedrock i s mapped as a lower Cretaceous p o r p h y r i t i c g r a n i t e , which i s p a r t o f the Nelson B a t h o l i t h ( L i t t l e , 1960) . There i s no c l i m a t e data f o r the s i t e , but the water e q u i v a l e n t depth o f the May 1 snowpack at the Nelson snowcourse averages 353 m i l l i m e t r e s ( M i n i s t r y o f Environment, B r i t i s h Columbia, 1985). The samples were c o l l e c t e d i n a s u b - a l p i n e meadow, immediately upstream o f Kokanee Lake. The s i t e i s p i c t u r e d i n P l a t e B:5. The 115 c h a r a c t e r i s t i c s of the s o i l samples can be seen i n P l a t e B:6. Elk Lake Park The E l k Lake s i t e i s l o c a t e d i n Rocky Mountain Range, i n E l k Lake Park. The s i t e i s l o c a t e d below t r e e - l i m i t , at an e l e v a t i o n of approximately 2200 metres. The v e g e t a t i o n at the s i t e d i f f e r s markedly from t h a t at the o t h e r s i t e s . I t appears t h a t t r e e - l i m i t i s c o n t r o l l e d by the topography r a t h e r than c l i m a t e : steep bedrock s l o p e s r i s e nearby. Bedrock i s mapped as Rundle Group, a M i s s i s s i p p i a n l imestone (Kananaskis Lakes, G e o l o g i c a l Survey Canada Open F i l e 634, undated). There i s no c l i m a t e data f o r the s i t e , but the water e q u i v a l e n t of the May 1 snowpack at the Mount J o f f r e snowcourse, at an e l e v a t i o n o f 1750 metres, averages 396 m i l l i m e t r e s ( M i n i s t r y o f Environment, B r i t i s h Columbia, 1985). The sampling s i t e i s shown i n P l a t e B:7. The s o i l s were not cohesive, and no samples were r e t r i e v e d i n t a c t ; hence, a photograph of the cores c o u l d not be i n c l u d e d . Plate B:1. Manning Park site. i—1 Plate B:2. Manning Park samples. 4 5 6 Plate B:5. Kokanee Lake site. 121 Plate B:7. Elk Lake site. N 

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