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UBC Theses and Dissertations

An experimental investigation of dry patch formation and stability in thin liquid films McAdam, Donald 1974

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AN EXPERIMENTAL INVESTIGATION OF DRY PATCH FORMATION AND STABILITY IN THIN LIQUID FILMS BY DONALD WILLIAM THORNTON McADAM B. Sc., Un i v e r s i t y of Alberta, 1961 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of Mechanical Engineering We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November, 1974 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h C o lumbia, I agree t h a t t he L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my De-partment o r by h i s r e p r e s e n t a t i v e s . I t i s un d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . 1 DONAED WILLIAM THORNTON McADAM Department o f M e c h a n i c a l E n g i n e e r i n g The U n i v e r s i t y of B r i t i s h Columbia Vancouver, B r i t i s h Columbia V6T 1W5 Date i i ABSTRACT -An e x p e r i m e n t a l s t u d y was conducted on t h e f o r m a -t i o n and s t a b i l i t y o f d r y p a t c h e s i n a t h i n l i q u i d f i l m f l o w -i n g down a h e a t e d p l a t e . The o c c u r r e n c e o f such a d r y p a t c h i s o f g r e a t p r a c t i c a l s i g n i f i c a n c e s i n c e , i n some c a s e s , t h e l o s s o f l i q u i d c o o l i n g e f f e c t a l l o w s t h e t e m p e r a t u r e o f t h e he a t e d s u r f a c e t o exceed i t s m e l t i n g p o i n t . T h i s i s p a r t i c -u l a r l y dangerous i n a h i g h heat f l u x , two-phase system such as t h e c o r e o f a b o i l i n g - w a t e r - c o o l e d r e a c t o r . P r e v i o u s t h e o r e t i c a l a n a l y s e s i n d i c a t e t h a t d r y p a t c h s t a b i l i t y and p o s s i b l e r e w e t t i n g depends on a b a l a n c e between i n e r t i a f o r c e s a t t h e upstream edge t e n d i n g t o rewet t h e d r y p a t c h and s u r f a c e t e n s i o n and t h e r m o c a p i l l a r y ' f o r c e s which cause i t t o s p r e a d . Dynamic c o n t a c t a n g l e i s p a r t i c -u l a r l y s i g n i f i c a n t i n t h e s e a n a l y s e s . D i r e c t e x p e r i m e n t a l c o n f i r m a t i o n o f t h e s e a n a l y s e s was not p r e v i o u s l y p o s s i b l e because measurements o f dynamic c o n t a c t a n g l e under f i l m b reak up c o n d i t i o n s have never b e f o r e been made. F i l m break up was o b s e r v e d i n a t h i n l i q u i d f i l m o f c a r b o n d i o x i d e a t b u l k c o n d i t i o n s f r o m 2°C and 3.62 MPa (megapascals) t o 18°C and 5.5 MPa by h i g h - s p e e d (2500 frames per second) p h o t o g r a p h y . R e y n o l d s numbers based on f i l m t h i c k n e s s ranged from 185 t o 1000. Dynamic c o n t a c t a n g l e was measured u s i n g a s p e c i -i i i a l l y d e v e l o p e d . s c h l i e r e n system and p h o t o d e n s i t o m e t e r meas-urements of t h e r e c o r d i n g f i l m . The t e c h n i q u e i s b ased on t h e a n g l e of r e f r a c t i o n of. l i g h t by t h e c u r v e d l i q u i d s u r -f a c e upstream of t h e d r y p a t c h . The a n g l e o f r e f r a c t i o n i s r e l a t e d t o t h e s l o p e o f t h e l i q u i d s u r f a c e and i s t r a n s -formed t o an o p t i c a l d e n s i t y f i e l d by a g r aded f i l t e r . S u r f a c e p r o f i l e a n d . f i l m t h i c k n e s s were c a l c u l a t e d knowing the s l o p e s upstream of t h e d r y p a t c h . C o n t a c t a n g l e and s u r f a c e p r o f i l e as a f u n c t i o n o f t i m e were f o u n d by a n a l y s -i n g s u c c e s s i v e frames o f movie f i l m . A q u a s i - s t a b l e d r y p a t c h i s e s t a b l i s h e d by a b a l a n c e o f ' t h e f o r c e s a c t i n g ' a t .the s t a g n a t i o n p o i n t . . ; C o n t a c t a n g l e i n c r e a s e s as t h e s t a g n a t i o n p o i n t advances u n t i l t h e s u r f a c e t e n s i o n f o r c e b a l a n c e s t h e i n e r t i a f o r c e . The s t a g n a t i o n p o i n t then becomes s t a t i o n a r y and b e g i n s t o recede, due t o t h e s u r f a c e t e n s i o n f o r c e . C o n t a c t a n g l e de-c r e a s e s as t h e s t a g n a t i o n p o i n t r e c e d e s u n t i l s u r f a c e t e n -s i o n f o r c e i s a g a i n b a l a n c e d by i n e r t i a f o r c e and t h e c y c l e i s t h e n r e p e a t e d u n t i l t h e d r y p a t c h r e w e t s . R e w e t t i n g o c c u r s when l a r g e waves h i t t h e d r y p a t c h . The p r e s e n t e x p e r i m e n t s i n d i c a t e t h a t one c r i t e r -i o n f o r a s t a b l e d r y p a t c h i s a b a l a n c e o f body f o r c e s by s u r f a c e t e n s i o n f o r c e s and t h i s i s c h a r a c t e r i z e d by the Bond number. T h i s i s a p p r o x i m a t e l y e q u a l t o one,bas- . ed oh measured f i l m t h i c k n e s s . Measured r e s u l t s compare w e l l w i t h t h e o r e t i c a l analyses in laminar films a t Reynolds numbers l e s s than 250. At higher Reynolds numbers t h e o r e t i c a l r e s u l t s do not agree with measured r e s u l t s . Further models are r e -quired which consider the three-dimensional nature of the stagnation point, the dynamic e f f e c t of surface waves on contact angle and which give good predictions of mini-, mum thickness in turbulent f i l m s . TABLE OF CONTENTS Chap t e r Page 1 INTRODUCTION 1 1.1 G e n e r a l 1 1.2 B o i l i n g . C l a s s i f i c a t i o n s 4 1.2.1 P o o l B o i l i n g . . 5 1.2.2 Flow B o i l i n g 6 1.3 Scope o f Work 8 2 PREVIOUS WORK 11 2.1 G e n e r a l . . 11 2.2 E x p e r i m e n t a l S t u d i e s o f F i l m Breakup . . 1 2 2.3 A n a l y t i c a l S t u d i e s o f F i l m Breakup . . . . 1 6 2.4 C o n t a c t A n g l e • 23 2.5 Flow i n T h i n F i l m s 26 3 EXPERIMENTAL EQUIPMENT 31 3.1 G e n e r a l 31 3.2 Flow Loop . . . 32 3.3 T e s t S e c t i o n 33 3.4 O p t i c a l System 35 3.5 A n a l y s i n g Equipment 36 4 EXPERIMENTAL PROCEDURE 39 4.1 G e n e r a l . 39 4.2 System O p e r a t i o n 39 4.3 O p t i c a l Measurements 41 4.4 C a l i b r a t i o n o f the O p t i c a l System 47 C h a p t e r Page 5 EXPERIMENTAL RESULTS . 50 5.1 G e n e r a l . . . . 50 5.2 Low Reynolds Number R e s u l t s 54 5.3 High R e y n o l d s Number R e s u l t s 58 6 DISCUSSION . . . 62 6.1 G e n e r a l 62 6.2 Low Reyn o l d s Number 66 6.3 High Reynolds Number 77 6.4 R e w e t t i n g o f Dry P a t c h e s . . . . . . . . . 80 7 SUMMARY AND CONCLUSIONS 83 REFERENCES . . . . . . 158 APPENDIX A - P r o p e r t i e s of Carbon D i o x i d e . . . . . . . 162 APPENDIX B - C a l i b r a t i o n o f Flow C o n t r o l V a l v e 166 T APPENDIX C - R e l a t i o n s h i p Between A n g l e of R e f r a c t i o n and I n t e n s i t y V a r i a t i o n 169 APPENDIX D - E f f e c t o f Heat T r a n s f e r Through The P l a t e . 175 v i i LIST OF TABLES Page Table 6.1 Comparison of Predicted and Measured Minimum Film Thickness T = 2°C, Re = 185, 6 = 48o(Average) 69 Table 6.2 Comparison of Predicted a'nd Measured Minimum Film Thickness T = 2°C, Re .= 310, 9 =• 42° 73 Table .6.3 Evaluation of Bond Number, at Low Reynolds Number 74 Table 6.4 Comparison of Predicted and Measured Minimum Film Thickness ~ T = 18°C, Re = 1055, Q = 65 600 W/m 79 Table 6.5 • Evaluation of Bond Number at High Reynolds Number 79 Table A l Properties of C0 2 165 v i i i LIST OF FIGURES FIGURE TITLE PAGE 1 Flow B o i l i n g Regimes, Upward Flow 8*7 2 Dry P a t c h on a S o l i d S u r f a c e 88 3 P o o l B o i l i n g Regimes 89 4 Flow B o i l i n g i n a Tube Showing th e B e g i n -n i n g of the S l u g Elow Regime. C0„ a t 1.7 MPa, Q = 5700 W / m , - I n l e t Temp. - 30°C 90 5 Some V a r i a b l e s I n v o l v e d i n Flow B o i l i n g and F i l m Breakup. 91 6 L a t e r a l M o t i o n Due t o S u r f a c e T e n s i o n V a r i -a t i o n 92 7 F o r c e s A c t i n g a t a Dry P a t c h (Ref. 13) 93 8 L i q u i d Drop on a S o l i d S u r f a c e 94 9 V a r i a t i o n o f Apparent C o n t a c t A n g l e Due t o S u r f a c e Roughness 95 10 P r e d i c t i o n of C r i t i c a l Heat F l u x i n Water at,6.9 MPa U s i n g C 0 2 a t 1.96 MPa 96 11 Loop F l o w s h e e t 97 12 T e s t S e c t i o n 98 13 T e s t S e c t i o n H o l d e r 99 14 S c h l i e r e n System w i t h a Graded F i l t e r , Show-i n g E f f e c t o f I n c o r r e c t Camera P o s i t i o n i n g 100 15 O p t i c a l Set-up a t T e s t S e c t i o n 101 16 M i c r o d e n s i t o m e t e r and A n a l y s i n g Equipment 102 17 T y p i c a l M i c r o d e n s i t o m e t e r T r a c e 103 18 R e f r a c t i o n o f L i g h t a t Curved L i q u i d S u r f a c e 104 19 C a l i b r a t i o n Lens and Set-up 105 20 M i c r o d e n s i t o m e t e r Scan P o s i t i o n 106 21 M i c r o d e n s i t o m e t e r T r a c e at 50:1 107 22 . Comparison of C a l c u l a t e d and A c t u a l . L e n s P r o f i l e 108 23 B o i l i n g Number vs Re y n o l d s Number, T = 2 C 109 FIGURE TITLE PAGE 24 B o i l i n g Number T = 9°C vs Re y n o l d s Number, 110 25 B o i l i n g Number T = 13^C vs Reynolds Number, 111 26 B o i l i n g Number T = 18°C vs Reynolds Number, 112 27 F o r m a t i o n o f a . Dry P a t c h Re = = 700, T = 9°C 113 28 . F i l m P r o f i l e s , T = 2°C, Re = ' 185 . 120 .29 C o n t a c t A n g l e T • 2°C, Re = V a r i a t i o n 185 w i t h ' .Time, 121 .  30 F i l m P r o f i l e , T ' = • 2°C, Re = : 310 122 31 C o n t a c t A n g l e T = 2°C, Re = V a r i a t i o n 310 w i t h Time,... .123 32 F i l m P r o f i l e , T = 9°C, Re = . 420 " . '124 33 ' C o n t a c t A n g l e T = 9°C, Re = V a r i a t i o n 420 w i t h Time, .1.25 34 F o r m a t i o n o f a Dry Patch ' , T ' = 2°C, Re = 185 126 35 F i l m P r o f i l e , 1 1 = 2°C, Re = 940 128 36 C o n t a c t A n g l e T = 2°C, Re = V a r i a t i o n 940 w i t h Time, 129 37 F i l m P r o f i l e , T - 9°C, Re = 700 130 38 C o n t a c t A n g l e T = 9°C , Re = V a r i a t i o n 700 w i t h Time., 131 39 F i l m P r o f i l e , T = 9°C , Re = 1080 132 40 C o n t a c t A n g l e T = 9 C , Re ='. V a r i a t i o n 1080. w i t h Time , 133 • 41 . F i l m P r o f i l e , T = 13°C,: Re = 750 134 42 C o n t a c t A n g l e .T = 13 C, Re = V a r i a t i o n = 75.0 w i t h Time, 135 43 F i l m P r o f i l e , T = 13°C, Re = 885 . 136 44 .' C o n t a c t A n g l e T = 13 C, Re = V a r i a t i o n = 885 w i t h Time,' 137 45'.' F i l m P r o f i l e , T = 18°C, Re = 750 ' 138 46 C o n t a c t A n g l e . ' T = 18°C, Re = V a r i a t i o n = 750 w i t h Time, 139 47 F i l m P r o f i l e , T = 19°C, Re = 1055 140 48 C o n t a c t A n g l e T = 18°C, Re = V a r i a t i o n , 1055 w i t h Time, 141 FIGURE TITLE PAGE 49 F i l m C o n t o u r s . a t S t a g n a t i o n P o i n t , T = 9°C, Re = 700 142 50 Vapor P r e s s u r e of CC>2 143 51 D e n s i t y o f S a t u r a t e d CO^ Vapor 144 52 D e n s i t y o f L i q u i d C 0 2 .. 145 53.. Dynamic V i s c o s i t y of CC>2 146 54 L a t e n t Heat of C 0 2 147 55 Thermal C o n d u c t i v i t y of C 0 2 148 56 S u r f a c e T e n s i o n o f L i q u i d C 0 2 149 57 L o r e n z - L o r e n t z E q u a t i o n f o r C 0 2 150 58 V a l v e C a l i b r a t i o n I n s e r t 151 . 59 L i q u i d J e t Used f o r C a l i b r a t i o n .152 60 V a l v e C a l i b r a t i o n , T = 2°C 153 61 V a l v e C a l i b r a t i o n , . T = 9°C 154 62 - V a l v e C a l i b r a t i o n , T = 13°C 155 63 V a l v e C a l i b r a t i o n , T = 18°C 156 64 System Geometry 157 SYMBOLS v e l o c i t y , m/s p l a t e R e y n o l d s number, T/yx > d i m e n s i o n l e s s 2 Weber number, pu .6Va , d i m e n s i o n l e s s Bond number pgo /cr , d i m e n s i o n l e s s m o d i f i e d Bond number d e f i n e d by E q u a t i o n . ( 6 . 5 ) L o r e r i z - L o r e n t z c o n s t a n t , m /kg c o n s t a n t depending on o p t i c a l s e t - u p r e f r a c t i v e i n d e x o f l i q u i d C ^ , d i m e n s i o n l e s s r e f r a c t i v e i n d e x of COg va p o r , d i m e n s i o n l e s s p l a t e w i d t h , m p l a t e l e n g t h , m p e r p e n d i c u l a r d i s t a n c e from p l a t e , mm d i s t a n c e a l o n g p l a t e , mm d i s t a n c e a c r o s s p l a t e , mm 2 a c c e l e r a t i o n due t o g r a v i t y , m/s te m p e r a t u r e , °C 2 heat f l u x , W/m 2 a r e a , m t h e r m a l c o n d u c t i v i t y , W/m.K t i m e , s tube d i a m e t e r , m s p e c i f i c h e a t , J/kg.k i n t e n s i t y c o r r e s p o n d i n g t o r e f r a c t e d l i g h t i n t e n s i t y c o r r e s p o n d i n g t o u n r e f r a c t e d l i g h t heat t r a n s f e r c o e f f i c i e n t , W/m^  °C. p l a t e t h i c k n e s s , m x i i X l l l Symbols (Cont'd) f f l u i d L . l i q u i d A a i r S s o l i d ACKNOWLEDGEMENTS I would l i k e t o e x p r e s s my g r a t i t u d e t o my s u p e r v i s o r , Dr. E. G. Hauptmann, f o r h i s a d v i c e and c o u n c i l d u r i n g the v a r i o u s s t a g e s o f t h i s work. In p a r t i c u l a r , h i s a d v i c e and s u g g e s t i o n s d u r i n g the p r e -p a r a t i o n of my t h e s i s a r e v e r y much a p p r e c i a t e d . A l s o s i n c e r e thanks and a p p r e c i a t i o n a r e due t o my f r i e n d , V i c t o r Lee, f o r drawing a l l the f i g u r e s and f o r our many d i s c u s s i o n s , b o t h t e c h n i c a l and o t h e r w i s e . The s t a f f of. t h e . M e c h a n i c a l E n g i n e e r i n g Department h e l p e d me i n many ways and t o them I am v e r y g r a t e f u l . Thanks and a p p r e c i a t i o n a r e due t o my Mother who ty p e d t h i s t h e s i s and t o Mary W i l l i a m s who t y p e d the f o r m u l a e . And f i n a l l y t o my c h i l d r e n , who were p a t i e n t and under s t a n d i n g , a t times when I was n o t . The K i l l a m P r e d o c t o r a l F e l l o w s h i p which a s s i s t e d me f i n a n c i a l l y d u r i n g t h r e e y e a r s o f my work was v e r y much a p p r e c i a t e d as was f i n a n c i a l a s s i s t a n c e from The N a t i o n a l Research C o u n c i l o f Canada. INTRODUCTION 1.1 G e n e r a l The f l o w of l i q u i d i n t h i n f i l m s has many im-p o r t a n t a p p l i c a t i o n s . A t h i n f i l m o f l i q u i d f l o w i n g over a s o l i d s u r f a c e w i t h i t s f r e e s u r f a c e i n c o n t a c t w i t h a gas can be obser v e d i n such everyday examples as r a i n f l o w i n g down a windowpane o r o f f a r o a d . T y p i c a l i n d u s t r i a l examples i n v o l v i n g heat and mass t r a n s f e r are c o o l i n g t o w e r s , w e t t e d w a l l towers f o r a b s o r p t i o n o r d e s o r p t i o n , condensers and e v a p o r a t o r s . I f t h e l i q u i d f i l m b r e a k s up i n a heat t r a n s f e r a p p l i c a t i o n , l e a v i n g a d r y p a t c h , s u r f a c e t e m p e r a t u r e at t h e d r y patc h may r i s e h i g h enough t o p r e v e n t r e w e t t i n g ( L e i d -e n f r o s t phenomenon) o r melt the s u r f a c e . I n a mass t r a n s f e r o p e r a t i o n the t o t a l l i q u i d s u r f a c e a r e a i s reduced thus r e d u c i n g o p e r a t i n g e f f i c i e n c y . I t i s im-p o r t a n t t o un d e r s t a n d the mechanism o f f i l m breakup and r e w e t t i n g so t h a t t h e s e e f f e c t s can be p r e v e n t e d . The p r e s e n t e x p e r i m e n t s were i n t e n d e d t o g a i n an un-d e r s t a n d i n g o f the breakup of t h i n f i l m s and t h e s t a -b i l i t y of the d r y p a t c h e s formed. The i n t e n t was t o make measurements a t d r y patc h e s formed on a heated f l a t p l a t e and f i n d a c t u a l v a l u e s of t h e d i f f e r e n t f o r c e s a c t i n g . E x i s t i n g t h e o r e t i c a l a n a l y s e s o f d r y pa t c h s t a b i l i t y can then be checked w i t h t h e s e meas-ured v a l u e s . The advent of b o i l i n g water c o o l e d n u c l e a r r e a c t o r s f o r e l e c t r i c power g e n e r a t i o n has i n c r e a s e d e f -f o r t s t o u n d e r s t a n d the break up of t h i n f i l m s . B o i l i n g o c c u r s i n the c o r e of a b o i l i n g water c o o l e d r e a c t o r and at some p o i n t i n the f u e l c h a n n e l f u e l i s c o o l e d by a t h i n l i q u i d f i l m . ( T h i s i s d i s c u s s e d i n more d e t a i l i n S e c t . ( 1 . 2 . 2 ) ) . D i s r u p t i o n of t h i s f i l m r e s u l t s i n a l a r g e r e d u c t i o n o f the heat t r a n s f e r c o e f f i c i e n t ( 1 ) * and c o n s e q u e n t l y a l a r g e i n c r e a s e i n f u e l s u r f a c e temp-e r a t u r e s i n c e heat f l u x i s c o n s t a n t . The phenomenon i s c a l l e d d r y o u t and t h e heat f l u x a t which i t o c c u r s i s the c r i t i c a l heat f l u x . Temperature r i s e a t d r y o u t can be l a r g e enough t o cause f u e l s heath f a i l u r e and r e l e a s e o f f i s s i o n p r o d u c t s t o the c o o l a n t . The power o u t p u t o f Canada's b o i l i n g water c o o l e d r e a c t o r s i s l i m i t e d by the f a c t t h a t d r y o u t must be p r e v e n t e d . Design p r a c t i c e f o r b o i l i n g water c o o l e d r e - • a c t o r s has been l a r g e l y based on c o r r e l a t i o n s o f c r i t i - ' c a l heat f l u x w i t h parameters such as p r e s s u r e , mass v e l o c i t y and i n l e t s u b c o o l i n g . C o r r e l a t i o n s , w h i l e use-f u l and n e c e s s a r y f o r d e s i g n p u r p o s e s , t e l l l i t t l e about the fundamental n a t u r e o f t h e phenomenon. F o r example, c r i t i c a l heat f l u x v a r i e s l i n e a r l y w i t h i n l e t s u b - c o o l -i n g and t h i s would seem t o i n d i c a t e something s i m p l e and b a s i c t o t h e burnout phenomenon but an adequate e x p l a n -a t i o n o f t h i s l i n e a r i t y has not been found ( 2 ) . * Numbers i n p a r e n t h e s i s r e f e r t o r e f e r e n c e s . There i s ho g e n e r a l agreement on t h e d r y o u t mechanism o r ' w h i c h parameters a r e i m p o r t a n t so dimen-s i o n a l - a n a l y s i s cannot be used e f f e c t i v e l y . Dimension-' l e s s g r o u p i n g o f • p a r a m e t e r s has been t r i e d (3) but exper imental'. v e r i f i c a t i o n o f the s e " s c a l i n g laws" has met w i t h l i m i t e d s u c c e s s (4). Most s t u d i e s on f o r c e d c o n v e c t i o n b o i l i n g have been w i t h s i m p l e g e o m e t r i e s such as round tubes (5) and f l o w regimes o c c u r r i n g i n a tube are shown i n F i g u r e (1) The tube at some p o i n t i s c o o l e d by a t h i n a n n u l a r f i l m of l i q u i d c l i m b i n g t h e w a l l under t h e i n f l u e n c e o f the vapor c o r e . ( B o i l i n g regimes are d i s c u s s e d i n more de-t a i l i n S e c t i o n 1.2.2). Dryout r e s u l t s from the breakup of t h i s t h i n f i l m and r e a s o n s f o r t h i s breakup a r e not c l e a r l y u n d e r s t o o d . E a r l y workers (6) t r i e d t o e x p l a i n f i l m b r e a k -up on t h e b a s i s o f a hydrodynamic i n s t a b i l i t y r e s u l t i n g from t h e a c t i o n of t h e vapor on t h e l i q u i d f i l m . Ex-p e r i m e n t a l s t u d i e s o f f i l m breakup w i t h and w i t h o u t heat-i n g ( 7 , 8,. 9, 10) i n d i c a t e t h a t s u r f a c e t e n s i o n p l a y s an i m p o r t a n t p a r t . Recent a n a l y s e s ( 1 1 , 12, .13) a l s o i n d i -c a t e t h a t s u r f a c e t e n s i o n i s i m p o r t a n t i n the s t a b i l i t y of d r y p a t c h e s formed on heated, and unheated s u r f a c e s . These a n a l y s e s attempt t o e x p l a i n d r y p a t c h s t a b i l i t y by b a l a n c i n g f o r c e s a c t i n g on the l i q u i d f i l m a t the up-stream edge o f the dry p a t c h . One f o r c e i s s u r f a c e t e n -s i o n , which a c t s a t some' a n g l e t o t h e s o l i d s u r f a c e . T h i s c o n t a c t a n g l e i s shown i n F i g u r e ( 2 ) . A s s u m p t i o n s have been made as t o f o r c e s a c t i n g and t h e i r r e l a t i v e v a l u e s but t h e s e depend h e a v i l y on t h e dynamic c o n t a c t a n g l e and t h i s had not p r e v i o u s l y been measured. S t a t i c c o n t a c t a n g l e v a l u e s d i d not g i v e good agreement w i t h measured r e s u l t s ( 1 4 ) . Measurement of dynamic c o n t a c t a n g l e i s of g r e a t importance i n the u n d e r s t a n d i n g o f the r e l a t i v e magnitudes of the f o r c e s assumed t o be a c t i n g a t t h e up-stream edge of a dry p a t c h ( F i g u r e 2 ) . Dynamic c o n t a c t a n g l e has been measured i n the p r e s e n t e x p e r i m e n t s un-der breakup c o n d i t i o n s of a f i l m f a l l i n g on a heated p l a t e . . A c t u a l measurements on a f a l l i n g f i l m w i l l g i v e , a b e t t e r u n d e r s t a n d i n g o f i m p o r t a n t f o r c e s and p r o v i d e a means of c h e c k i n g e x i s t i n g t h e o r e t i c a l a n a l y s e s . 1.2 B o i l i n g C l a s s i f i c a t i o n s B o i l i n g phenomenon has been e x t e n s i v e l y s t u d i e d and s t u d i e s have been grouped under two c l a s s i -f i c a t i o n s ; p o o l b o i l i n g and f l o w b o i l i n g . P o o l b o i l i n g o c c u r s when a h e a t e r i s submerged in an i n i t i a l l y s t a g -nant p o o l of l i q u i d . Flow b o i l i n g r e f e r s t o b o i l i n g o c c u r r i n g i n f o r c e d c o n v e c t i o n . There are some s i m i l -a r i t i e s between t h e s e c l a s s i f i c a t i o n s but the r e s u l t s o f p o o l b o i l i n g cannot be a p p l i e d t o f l o w b o i l i n g be-cause .the b a s i c mechanism appears t o be d i f f e r e n t ( 2 ) . P o o l b o i l i n g w i l l be d e a l t w i t h o n l y where s i m i l a r i t i e s e x i s t between i t and f l o w b o i l i n g . 1.2.1 P o o l B o i l i n g There a r e s e v e r a l regimes i n p o o l b o i l i n g and th e s e a r e shown i n F i g u r e ( 3 ) .When h e a t e r t emperature exceeds s a t u r a t i o n by o n l y a few degrees no b u b b l e s form on t h e h e a t e r s u r f a c e and heat i s t r a n s f e r r e d by n a t u r a l c o n v e c t i o n . T h i s i s t h e c o n v e c t i o n heat t r a n s f e r regime i n F i g u r e ( 3 ) . N u c l e a t i o n b e g i n s when the l i q u i d i n con-t a c t w i t h the s u r f a c e i s s u p e r h e a t e d . L i q u i d next t o the s u r f a c e can be superh e a t e d as much as 9°C ( 1 5 ) . Heat f l u x r e a c h e s a maximum a t p o i n t C ( F i g -ure 3) and i f an e l e c t r i c h e a t e r i s used ( i . e . , c o n s t a n t heat f l u x ) a s h i f t t o t h e s t a b l e f i l m b o i l i n g regime ( p o i n t E) o c c u r s w i t h a l a r g e i n c r e a s e i n t e m p e r a t u r e . The h e a t e r may melt i f heat f l u x i s f u r t h e r i n c r e a s e d . In t h i s regime the h e a t e r s u r f a c e i s b l a n k e t e d by a v a -por f i l m and heat i s t r a n s f e r r e d by r a d i a t i o n and con-d u c t i o n . F i l m b o i l i n g can be ob s e r v e d when a drop o f water i s p l a c e d on a.very hot s u r f a c e . I t w i l l not wet the s u r f a c e but becomes surrounded by a vapor f i l m and bounces on the s u r f a c e u n t i l t he water i s e v a p o r a t e d . T h i s i s c a l l e d t h e L i e d e n f r o s t phenomenon and can be ob-serv e d i n f l o w b o i l i n g under c o n d i t i o n s of d r y p a t c h f o r -m a t i o n . 1.2.2 Flow B o i l i n g There a re s e v e r a l regimes a s s o c i a t e d w i t h f l o w b o i l i n g and an i d e a l i z e d p i c t u r e of t h e s e regimes i n a heated tube i s shown i n F i g u r e ( 1 ) . Subcooled l i q u i d e n t -e r s the bottom of the tube and i s heated as i t f l o w s up-ward. A t some p o i n t i n the tube l i q u i d n e x t t o the w a l l r e a c h e s a degree of superheat h i g h enough f o r b u b b l e s t o form. S i n c e b u l k f l u i d t e m perature i s below s a t u r a t i o n b u b b l e s condense as t h e y l e a v e the w a l l . When b u l k tem-p e r a t u r e r e a c h e s s a t u r a t i o n , b u b b l e s c o v e r t h e tube c r o s s -s e c t i o n and c o a l e s e i n t o l a r g e vapor s l u g s . The tube i s then c o o l e d by a t h i n f i l m o f l i q u i d i n c o n t a c t w i t h the w a l l . ( F i g u r e (4) shows the b e g i n n i n g of t h e s l u g f l o w regime f o r CO^ b o i l i n g i n an e l e c t r i c a l l y heated g l a s s tube.) F u r t h e r up t h e tube vapor s l u g s break down and the a n n u l a r f l o w regime b e g i n s . An a n n u l a r l i q u i d f i l m c l i m b s the w a l l because of shear due t o t h e v a p o r - l i q u i d c o r e . T h i s f i l m i s c o n t i n u a l l y t h i n n e d by e v a p o r a t i o n and en t r a i n m e n t and l i q u i d i s added by d e p o s i t i o n from the c o r e . I t i s i n t h i s a n n u l a r f l o w regime which d r y o u t oc-c u r s . At some p o i n t , assuming heat f l u x i s h i g h enough, the f i l m b r e a k s up and tube i s c o o l e d by the v a p o r - l i q u i d c o r e . Tube tem p e r a t u r e i n c r e a s e s a t t h i s p o i n t because o f the l a r g e r e d u c t i o n i n heat t r a n s f e r c o e f f i c i e n t . Heat t r a n s f e r c o e f f i c i e n t can reduce by a f a c t o r of 10 when the w a l l becomes d r y ( 1 ) . F u r t h e r up t h e tube, assuming i t w i l l o p e r a t e i n t h i s c o n d i t i o n , c o o l i n g i s due t o wet vapor and when q u a l i t y r e a c h e s 100%, s u p e r h e a t e d steam. F o r t h e h i g h heat f l u x e s e n c o u n t e r e d i n n u c l e a r r e a c t o r s i t has not been p o s s i b l e t o o p e r a t e i n t h i s c o n d i t i o n w i t h e x i s t -i n g f u e l d e s i g n s . The a n n u l a r f i l m b r e a k s up i n t o r i v u l e t s f l o w -i n g around d r y p a t c h e s (16, 1 7 ) . N u c l e a t i o n does not cause t h e s e d r y p a t c h e s s i n c e i t does not o c c u r i n t h i n f i l m s because degree of superheat n e c e s s a r y t o a c t i v a t e n u c l e a t i o n s i t e s i s not r e a c h e d . Dry p a t c h e s can rewet, grow upstream o r remain s t a t i o n a r y and a n a l y t i c a l s t u d i e s (11, 12, 13) i n d i c a t e t h a t r e w e t t i n g depends on a b a l a n c e of s u r f a c e t e n s i o n , shear and o t h e r f o r c e s at t h e top edge of the d r y p a t c h . I f the d r y p a t c h does not rewet s u r f a c e t e m p e r a t u r e can exceed the L e i d e n f r o s t tempera-t u r e and i t becomes d i f f i c u l t t o rewet. When r e w e t t i n g o c c u r s under t h e s e c o n d i t i o n s t h e r e i s a s p u t t e r i n g r e -g i o n w i t h , h i g h t u r b u l e n c e and h i g h b o i l i n g heat t r a n s f e r c o e f f i c i e n t at t h e edge o f t h e d r y p a t c h ( 1 8 ) . Break up o f an a n n u l a r f i l m has been a t t r i b u t -ed t o hydrodynamic i n s t a b i l i t y due t o waves caused by the v a p o r - l i q u i d c o r e ( 6 ) , s u r f a c e t e n s i o n g r a d i e n t s caused by unequal h e a t i n g o f t h e f i l m ( 7 , 1 9 ) , e b u l -l i t i o n ( 7 , 13) and l o s s o f l i q u i d due t o e v a p o r a t i o n and e n t r a i n m e h t ( 1 6 ) . A l l a n a l y s e s of dry p a t c h s t a b i l i t y i n d i c a t e dependence on t h e dynamic c o n t a c t a n g l e ( F i g u r e 2 ) , which had not been measured under b o i l i n g c o n d i t i o n s . 1.4 Scope o f Work T h e o r e t i c a l a n a l y s e s ( 1 1 , 12, 13) i n d i c a t e t h a t f o r c e s i n v o l v e d i n d r y p a t c h s t a b i l i t y , a r e s u r f a c e t e n s i o n , momentum, shear f o r c e , drag over t h e s m a l l s t e p i n the f i l m a t t h e d r y p a t c h , vapor t h r u s t due t o e v a p o r a t i o n and body f o r c e s . The aim of the e x p e r i m e n t a l s t u d y was t o g a i n an u n d e r s t a n d i n g of t h e f o r c e s i n v o l v e d i n f i l m breakup and s t a b i l i t y i n o r d e r t o de t e r m i n e which o f the above, o r any a d d i t i o n a l , f o r c e s a re i m p o r t a n t . A c t u a l measurement o f dynamic c o n t a c t a n g l e and l i q u i d f i l m p r o f i l e upstream o f a d r y p a t c h i s r e q u i r e d t o c o n f i r m o r negate t h e a n a l y t -i c a l models (12, 13) of f i l m break up i n two phase f l o w . E x p eriments were done t o .measure dynamic c o n t a c t a n g l e and c a l c u l a t e f i l m p r o f i l e upstream o f a d r y p a t c h under d i f -f e r e n t o p e r a t i n g c o n d i t i o n s . Dry p a t c h e s were formed i n a f i l m o f l i q u i d CG^ r u n n i n g down a heated g l a s s p l a t e under t h e i n f l u e n c e of g r a v i t y . I t was o r i g i n a l l y i n t e n d e d t o st u d y breakup . of an a n n u l a r f i l m i n a tube and a g l a s s tube 9 mm OD X 6 mm ID and about 1000 mm l o n g ^ w i t h a t r a n s p a r e n t h e a t i n g f i l m de-p o s i t e d on t h e o u t s i d e was used. There were s e v e r e phy-s i c a l problems a s s o c i a t e d w i t h making measurements i n -s i d e t h e tube and t h i s set-up was abandoned. A few o b s e r v -a t i o n s o f f l o w b o i l i n g were made and t h e photograph i n F i g -ure (4) showing t h e b e g i n n i n g of the s l u g f l o w regime i n b o i l i n g Cc>2 was ta k e n d u r i n g t h e s e t e s t s . A n n u l a r f l o w was not obser v e d because t h e g l a s s tube e x p l o d e d a t a low heat f l u x and t h e experiment was not r e p e a t e d . I f t h e a n n u l a r f i l m i s t h i n r e l a t i v e t o tube r a d i u s t h e e f f e c t o f tube c u r v a t u r e can be n e g l e c t e d and s i n c e t h i s i s the case i n a n n u l a r f l o w a f l a t p l a t e can be used i n s t e a d o f a t u b e . McPherson (13) s t a t e s t h a t f i l m t h i c k n e s s upstream o f a dry-p a t c h i n ah e l e c t r i c a l l y heated t u b e , 12.6 mm OD x 1.6 mm w a l l o p e r a t i n g i n two phase a n n u l a r f l o w a t 85% q u a l i t y i s 0.005 mm. Heat f l u x was 630 x 1 0 3 W/m2 (200 x 1 0 3 B/h f t 2 and mass f l u x 2.44 x 1 0 6 kg/h.m 2 (0.5 x 1 0 6 l b / h f t 2 ) . The use o f a heated g l a s s p l a t e s i m p l i f i e s c o n t a c t a n g l e meas-urement and o b s e r v a t i o n o f t h e f i l m . Dynamic c o n t a c t a n g l e was measured u s i n g an o p t i c a l t e c h n i q u e which d i d not d i s t u r b t h e f i l m i n any way. L i g h t p a s s i n g through t h e c u r v e d l i q u i d s u r f a c e of t h e f i l m i s r e f r a c t e d because of t h e d e n s i t y d i f f e r -ence between l i q u i d and vapor and t h e a n g l e o f r e f r a c t i o n depends on t h e s l o p e o f t h e l i q u i d s u r f a c e . A. s c h l i e r e n system c o u p l e d w i t h o p t i c a l d e n s i t y measurement was used t o measure r e f r a c t i o n . The method i s d e s c r i b e d i n Sec-t i o n ( 3 . 4 ) . "The v a r i a t i o n i n o p t i c a l d e n s i t y c o r r e s p o n d e d t o d i f f e r e n t s l o p e s of the l i q u i d s u r f a c e and t h i s was r e c o r d e d on movie f i l m . O p t i c a l d e n s i t y was measured w i t h a m i c r o d e n s i t o m e t e r ( S e c t i o n 3 . 5 ) . C r i t i c a l heat f l u x was measured a t d i f f e r e n t f l o w r a t e s at a f i x e d p r e s s u r e and d r y p a t c h f o r m a t i o n was r e c o r d e d on movie n e g a t i v e s a t d i f f e r e n t f l o w c o n d i t i o n s . (Note: To a v o i d c o n f u s i o n between t h e l i q u i d f i l m on the p l a t e and movie f i l m , movie f i l m w i l l be r e f e r r e d t o as a n e g a t i v e . ) The aim was t o r e c o r d t h e h i s t o r y o f a d r y p a t c h as i t moved o r remained s t a t i o n a r y and t o measure the v a r i a t i o n of c o n t a c t a n g l e w i t h t i m e and t h i s was r e -l a t e d t o the d i r e c t i o n the edge o f the dry p a t c h was mov-i n g . PREVIOUS WORK 2.1 G e n e r a l B o i l i n g heat t r a n s f e r i s a complex p r o c e s s i n -v o l v i n g many v a r i a b l e s and F i g u r e (5) shows some o f t h e v a r i a b l e s i n v o l v e d i n f l o w b o i l i n g and f i l m , b r eakup. A t - "•, tempts t o group v a r i a b l e s i n t o d i m e n s i o n l e s s groups has met w i t h l i m i t e d s u c c e s s because i t i s not known e x a c t -l y which ones are i m p o r t a n t . B a r n e t t (3) grouped p^, p^, 'X, Cp k f , a and 6 i n t o t h r e e d i f f e r e n t d i m e n s i o n -l e s s s e t s ( c o n t a i n i n g d i f f e r e n t v a r i a b l e s ) t o form s c a l i n g laws. I f t h e v a l u e s of t h e s e groups a r e the same over a range o f o p e r a t i n g c o n d i t i o n s f o r two systems u s i n g d i f -f e r e n t f l u i d s the s c a l i n g law can be c o n s i d e r e d v a l i d . I f a s e t o f d i m e n s i o n l e s s g r o u p i n g s i s v a l i d i t c o u l d a i d i n i d e n t i f y i n g the i m p o r t a n t v a r i a b l e s and en a b l e t h e d r y o u t mechanism t o be u n d e r s t o o d . One of B a r n e t t ' s s c a l i n g laws c o n t a i n e d s u r f a c e t e n s i o n but he does not c o n s i d e r t h i s s e t t o be c o r r e c t . T h i s i s based on d r y o u t c o r r e l a t i o n s i n n a t u r a l convec-t i o n p o o l b o i l i n g and i t i s suggested t h a t s i n c e cr and g are l i n k e d i n p o o l b o i l i n g and s i n c e g r a v i t y appears t o have l i t t l e e f f e c t i n f l o w b o i l i n g then a w i l l have l i t -t l e e f f e c t i n f l o w b o i l i n g . T h i s seems u n r e a s o n a b l e s i n c e the d r y o u t mechanism i n p o o l b o i l i n g and f l o w b o i l -i n g i s d i f f e r e n t and r e s u l t s of one cannot be e x t r a p o l -ated from the o t h e r ( 2 ) . In a l a t e r paper (4) B a r n e t t suggests 14 p o s s i b l e s e t s of s c a l i n g laws u s i n g d i f f e r -ent p r o p e r t i e s and t e s t e d f i v e o f t h e s e e x p e r i m e n t a l l y by comparing c r i t i c a l heat f l u x and water at 6.9 MPa (1000 ps w i t h t h o s e from a Freon-12 system a t 1.07 (155 p s i a ) . A t these p r e s s u r e s P^/Py ^ s t h e same f o r b o t h systems and vo i d a g e (volume o c c u p i e d by vapor) i s s c a l e d ( 3 ) . B e s t agreement was o b t a i n e d w i t h a s c a l i n g law which d i d not i n el u d e s u r f a c e t e n s i o n but. B a r n e t t p o i n t s out t h a t s u r f a c e t e n s i o n c o u l d be i m p o r t a n t s i n c e combining i t w i t h p r o - . p e r t i e s o t h e r than C and k, c o u l d be s a t i s f a c t o r y . p i V i s c o s i t y , f o r example, was not i n c l u d e d i n t h i s s e t o f d i m e n s i o n l e s s g r o u p i n g s . B a r n e t t c o n s i d e r s t h a t even h i s b e s t s c a l i n g law has some p r o p e r t y m i s s i n g but he does not c o n s i d e r t h i s t o be s u r f a c e t e n s i o n . 2.2 E x p e r i m e n t a l S t u d i e s of F i l m Breakup S t u d i e s of f i l m breakup i n a n n u l a r f l o w and ove r heated s u r f a c e s have r e s u l t e d i n s e v e r a l proposed mechanisms o f f i l m breakup ( 7 - 1 0 ) . The s t a b i l i t y of the r e s u l t i n g - d r y p a t c h e s has been a n a l y s e d (11-14) but ex-p e r i m e n t a l v e r i f i c a t i o n has not p r e v i o u s l y been p o s s i b l e because t h e r e were no measured v a l u e s o f dynamic c o n t a c t a n g l e . T i p p e t s (6.) i n an e a r l y a n a l y s i s of c r i t i c a l heat f l u x c o n d i t i o n s . s u g g e s t e d t h a t d r y o u t was caused by hydrodynamic i n s t a b i l i t y due t o t h e vapor c o r e f l o w i n g over t h e l i q u i d - v a p o r i n t e r f a c e . Dryout o c c u r r e d when 13 t h e s e dynamic f o r c e s become g r e a t e r t h a n s t a b i l i z i n g s u r f a c e t e n s i o n f o r c e s and t h e f i l m was c o m p l e t e l y e n t r a i n e d by t h e v a p o r - l i q u i d c o r e . T h i s was p o s t u l a t e d t o o c c u r a t some c r i t i c a l q u a l i t y . (Steam q u a l i t y , a t c r i t i c a l heat f l u x c o n d i t i o n s ) . Tong and H e w i t t ( 2 0 ) p o i n t out t h a t t h e c r i t i c a l q u a l i t y can be v a r i e d a r b i t r a r i l y by v a r y i n g t h e mode of e n t r y of the phases ( i . e . , by h a v i n g a m i x t u r e o f steam and water a t t h e i n l e t ) and t h u s t h e r e i s no c r i t i c a l q u a l i t y a t which th e f i l m i s c o m p l e t e l y e n t r a i n e d . E n t r a i n -ment of t h e f i l m due t o hydrodynamic i n s t a b i l i t y of t h i s s o r t o c c u r s o v e r most of t h e range of a n n u l a r f l o w but i t i s a g r a d u a l p r o c e s s and i t i s compensated f o r by d e p o s i -t i o n o f e n t r a i n e d d r o p l e t s . E q u i l i b r i u m c o n d i t i o n s can be r e a c h e d i f t h e c h a n n e l i s long, enough. A l t h o u g h t h e f i l m i s d i s r u p t e d by t h e vapor c o r e t h i s i s not the s p e c i f -i c cause o f f i l m breakup ( 2 0 ) . ' ' .. Hsu, Simon and Lad (7) d i d an e x p e r i m e n t a l and a n a l y t i c a l s t u d y on t h i n f i l m breakup a n d ' a t t r i b u t e d i t t o t h e c o m p e t i t i v e p r o c e s s e s o f n u c l e a t i o n , ' v a p o r i z a t i o n at t h e i n t e r f a c e and t h e r m o c a p i l l a r y e f f e c t s caused by t e m p e r a t u r e v a r i a t i o n s i n t h e f i l m . N u c l e a t i o n i s sup-p r e s s e d i f t h e f i l m i s t h i n and then t h e r m o c a p i l l a r y e f -f e c t s dominate (7).. These a r e caused by an unequal h e a t -i n g due t o l o n g i t u d i n a l waves i n t h e f i l m . T h i n r e g i o n s become h o t t e r than t h i c k r e g i o n s and l i q u i d i s drawn from t h e s e due t o a s u r f a c e t e n s i o n d i f f e r e n c e . T h i s i s i l l u s -t r a t e d i n F i g u r e (6). I f t h e f i l m i s t h i c k and n u c l e a t i o n o c c u r s , the m i x i n g a c t i o n o f t h e b u b b l e s e l i m i n a t e s tem-p e r a t u r e v a r i a t i o n s and t h e r m o c a p i l l a r y e f f e c t s do not o c c u r . Hsu e t a l emphasize t h a t t h e t e m p e r a t u r e v a r i a t i o n o f t h e f r e e s u r f a c e i s due t o a r e l a t i v e l y s t a b l e wave p a t -t e r n and i f the f i l m i s smooth o r t u r b u l e n t , t h e r m o c a p i l -l a r y motion w i l l not cause break up. Simon and Hsu i n a l a t e r paper (19) c o n c l u d e d t h a t h e a t i n g caused l a t e r a l s u r f a c e t e n s i o n g r a d i e n t s which l e a d t o the breakup of the t h i n f i l m . They sug-gest t h a t the f i l m b r e a k s up when a minimum t h i c k n e s s i s reached no m a t t e r how t h i s t h i c k n e s s i s r e a c h e d . They suggest t h a t t h e Weber number i s t h e c o n t r o l l i n g quant-i t y and c a l c u l a t e Weber numbers c o r r e s p o n d i n g t o t h e m i n i -mum . t h i c k n e s s f o r water and a g l y c e r o l - w a t e r s o l u t i o n . The Weber numbers a r e s u f f i c i e n t l y c l o s e t h a t t hey assume a c o n s t a n t Weber number c r i t e r i o n f o r minimum f i l m t h i c k -ness. The major assumption i n t h i s work i s t h a t f i l m break up o c c u r s when a minimum t h i c k n e s s i s reached no.matter what t h e mechanism causes i t t o r e a c h t h a t t h i c k n e s s . They d i d not measure f i l m t h i c k n e s s e s but c a l c u l a t e d an i n i t i a l t h i c k n e s s ( a t the top of a heated rod) based on l a m i n a r f l o w and p l o t t e d t h i s a g a i n s t heat f l u x a t break up. T h i s was e x t r a p o l a t e d t o z e r o heat f l u x t o f i n d the minimum t h i c k n e s s . T h i s may be t h e case where no b o i l i n g o c c u r s anywhere i n t h e f i l m but Hsu e t a l (7) and o t h e r s (8) r e p o r t e d g r e a t l y reduced minimum' w e t t i n g r a t e s when b o i l i n g o c c u r r e d . Heat f l u x e s used by Simon and Hsu (19) were low enough so t h a t e v a p o r a t i o n c o u l d be n e g l e c t e d . Norman and B i n n s (10) a l s o c o n c l u d e d t h a t f i l m , breakup was due.to s u r f a c e t e n s i o n d i f f e r e n c e s ' caused by unequal h e a t i n g of the f i l m due t o r i p p l e s . R e s u l t s o f minimum f i l m t h i c k n e s s ( c o r r e s p o n d i n g t o minimum w e t t i n g r a t e ) were c o r r e l a t e d w i t h s u r f a c e t e n s i o n . The d i f f e r e n c e between t h e s e e x p e r i m e n t s and t h o s e o f (7) i s t h a t l a t e r a l r i p p l e s c a u s e - t h e s u r f a c e t e n s i o n v a r i a t i o n s , whereas w i t h (7) the same r e s u l t o c c u r s because of l o n g i t u d i n a l r i p p l e s . Norman and B i n n s p o i n t out t h a t t h e break up p o i n t was d i f f i c u l t t o see because of t h e absence of r i p -p l e s . H e w i t t (16) a l s o noted a smoothing of t h e f i l m n e a r the break up p o i n t . H e w i t t e t a l (16) s t a t e t h a t d r y o u t o c c u r s simp-l y because of 'a l o s s o f l i q u i d due t o e v a p o r a t i o n and en- -t r a i n m e n t . A r e c e n t model (21) proposed by W h a l l e y , H u t c h -i n s o n and H e w i t t c a l c u l a t e s the d r y o u t p o i n t . a s t h a t a t which the f i l m f l o w r a t e becomes e q u a l t o z e r o . However, i n p r e v i o u s work (16) H e w i t t o b s e r v e d t h a t f i l m break up o c c u r r e d c l o s e t o t h e p o i n t of z e r o f i l m f l o w r a t e but a t a f i n i t e f l o w r a t e d r y p a t c h e s formed w i t h r i v u l e t s r u n -n i n g around them. N u c l e a t i o n was o b s e r v e d i n t h e s e r i v u -l e t s however i t d i d not cause d r y p a t c h f o r m a t i o n . Hew-i t t (16) o b s e r v e d t h a t b ubble f o r m a t i o n caused l i q u i d l o s s by e h t r a i n m e n t but does n o t , s a y i t causes d r y p a t c h e s . I t appears t h a t a model based on t h e d r y o u t o c c u r r i n g when f i l m f l o w r a t e r e a c h e s ze r o i s not c o m p l e t e l y c o r r e c t s i n c e dry p a t c h e s o c c u r - b e f o r e f i l m f l o w becomes z e r o . Mac-b e t h ' ( 5 ) p o i n t s put t h a t even s m a l l d r y p a t c h e s can re-, s u i t i n h i g h t e m p e r a t u r e s o c c u r r i n g on t h e heated s u r -f a c e . Berenson and Stone (17) from a p h o t o g r a p h i c s t u d y of b o i l i n g F r eon 113 noted n u c l e a t i o n s i g h t s i n a n n u l a r f l o w and say t h a t n u c l e a t i o n may produce the i n i t i a l d r y spot but o f f e r no e x p e r i m e n t a l e v i d e n c e t o prove t h i s . They o b s e r v e d t h a t a l t h o u g h n u c l e a t i o n s i t e s e x i s t v a -por i s p r i m a r i l y g e n e r a t e d at the l i q u i d - v a p o r i n t e r f a c e and not by b u b b l e s . 2.3 A n a l y t i c a l S t u d i e s of F i l m S t a b i l i t y A d r y p a t c h may form and rewet. Norman and M c l n t y r e (8) obser v e d t h i s at f l o w s s l i g h t l y h i g h e r than t h e i r minimum w e t t i n g r a t e . When a d r y p a t c h forms a s t a g n a t i o n p o i n t forms a t the l i q u i d - v a p o r - s o l i d i n t e r -f a c e and r e w e t t i n g depends on a b a l a n c e of f o r c e s a c t i n g at t h i s p o i n t . •• H a r t l e y and Murgatroyd (11) were the f i r s t t o a n a l y s e d r y p a t c h s t a b i l i t y b ut d i d not d i s c u s s the mech-anism o f dry p a t c h f o r m a t i o n . . T h e i r ; a n a l y s i s i s based on a f o r c e b a l a n c e a t the l i q u i d - v a p b ' r - s o l i d i n t e r f a c e , on an unheated s u r f a c e as shown i n F i g u r e ( 2 ) . The i n e r t i a f o r c e , due t o " l i q u i d a p p r o a c h i n g the s t a g n a t i o n p o i n t b e i n g brought t o r e s t i s 17 F u 6 2 •p(U(y ) - r dy (2.1) 0 f o r some width A.z . The s u r f a c e t e n s i o n f o r c e opposing t h i s i n e r t i a f o r c e and i s , F ' = • ' c ( l - c o s e ) (2.2) a The c r i t e r i o n . f o r a s t a b l e dry patch i s F = F„ u a 6 P p(U(y)-) dy - a ( l - c o s e ) . (2.3) 0 H a r t l e y and Murgatroyd e v a l u a t e d t h i s equation f o r a laminar f i l m with a p a r a b o l i c v e l o c i t y p r o f i l e to f i n d a minimum t h i c k n e s s , given by 6 1.72 (a ( l - c o s e )/oV (y/pg P (2.4) c The c r i t e r i o n f o r a s t a b l e - d r y patch i s then ^ c A & i t ^ o where ^ e i s the c r i t i c a l t h i c k n e s s given b y Equation (2.4) . and i s the t h i c k n e s s at a wave c r e s t . For each con-t a c t angle t h i s c r i t i c a l t h i c k n e s s can be supported and i f the f i l m becomes t h i c k e r than &• • the p a t c h r e w e t s . c T h i s s i m p l e a n a l y s i s shows the s t r o n g dependency on c o n t a c t ' a n g l e . S u r f a c e t e n s i o n f o r c e can, t h e o r e t i c a l l y , v a r y from 0 t o 2a. (A c o n t a c t a n g l e o f 180° i s never r e a c h -ed i n p r a c t i c e a l t h o u g h mercury on - s t e e l g i v e s 6 = 154° (22) )' I t was not p o s s i b l e f o r H a r t l e y and M u r g a t r o y d t o compare t h e i r r e s u l t s w i t h e x p e r i m e n t a l data, s i n c e measurements o f dynamic c o n t a c t a n g l e were not a v a i l a b l e , however,.they d i d • c a l c u l a t e c o n t a c t a n g l e s which would g i v e agreement w i t h . e x p e r i m e n t a l d a t a . A change i n c o n t a c t a n g l e from 45° t o 20° d e c r e a s e s minimum w e t t i n g r a t e by a f a c t o r of about 10. No s p e c i a l s i g n i f i c a n c e i s a t t a c h e d t o t h e s e r e s u l t s but they do show the s t r o n g dependence on c o n t a c t a n g l e . H e w i t t and Lacey (9) found a l a r g e d i s c r e p a n c y when they compared s t a t i c c o n t a c t a n g l e s . w i t h . a n g l e s c a l -c u l a t e d t o g i v e agreement w i t h t h e i r r e s u l t s . The s u r f a c e , t e n s i o n f o r c e based on s t a t i c c o n t a c t a n g l e was a f a c t o r o f 7.8 l a r g e r than t h a t r e q u i r e d t o g i v e agreement w i t h t h e i r r e s u l t s . These r e s u l t s show t h a t s t a t i c c o n t a c t a n g l e s are not a p p l i c a b l e t o t h i s dynamic s i t u a t i o n . H e w i t t and Lacey suggest t h a t t h e r e i s an e x t r a f o r c e t e n d i n g t o rewet th e d r y p a t c h and t h i s may be an aerodynamic f o r c e on t h e b u l g e o c c u r r i n g i m m e d i a t e l y upstream of the. d r y p a t c h . Zuber and Staub (12) extended H a r t l e y and Murgat-r o y d ' s a n a l y s i s t o i n c l u d e t h e r m a l e f f e c t s but d i d not c o n -s i d e r d r y p a t c h f o r m a t i o n . Thermal a f f e c t s cause a non-u n i f o r m t e m p e r a t u r e a t t h e . i n t e r f a c e r e s u l t i n g i n a thermo-19 c a p i l l a r y f o r c e and e v a p o r a t i o n a t t h e i n t e r f a c e causes a vapor t h r u s t f o r c e on the i n t e r f a c e . A b a l a n c e of t h e s e f o r c e s a t t h e s t a g n a t i o n p o i n t d e t e r m i n e s c o n d i t i o n s f o r which t h e dry p a t c h w i l l remain s t a t i o n a r y . T h i s o c c u r s i f , I n e r t i a f o r c e = S u r f a c e T e n s i o n F o r c e + . T h e r m o c a p i l l a r y F o r c e + Vapor T h r u s t . ! Zuber & Staub assume a l i n e a r ' t e m p e r a t u r e p r o f i l e and a wedge shaped l i q u i d s u r f a c e t o e s t i m a t e t h e s e f o r c e s r e l a t i v e t o each o t h e r . The c o n d i t i o n f o r a s t a t i o n a r y d r y p a t c h i s 15 g_Ap P f v j S1* c O ( 1 - C O S 0 ) + 9a Q r- cos0 • + p k K v £P cos 2( (2.5) The e f f e c t of the i n e r t i a f o r c e ( l e f t hand s i d e of E q u a t i o n 2.5) i s t o rewet t h e dry. :patch and the e f f e c t of s u r f a c e t e n s i o n , t h e r m o c a p i l l a r y and vapor t h r u s t terms ( r i g h t hand s i d e ) i s t o spread i t . The dependence on t h e c o n t a c t a n g l e i s o b v i o u s . Zuber and Staub grouped t h e s e terms i n t o t h r e e d i m e n s i o n l e s s terms t o i n d i c a t e t h e i r r e l a t i v e magnitudes; S u r f a c e w e t t i n g I n e r t i a TT = I a(1-cose) 15 f A p. IP? v 5e (2.6) 20 T h e r m o c a p i l l a r y I n e r t i a = T T 2 = 3T k a C O S 9 15 g Ap Pf v. 6 5 c (2.7) v l P v A J AF- 6 c o s 2 9 P* e I n e r t i a " 7 7 3 p f g Ap 2 15 . c (2.8) The r e l a t i v e i m p o r t a n c e o f o t h e r f o r c e s , f o r ex-ample s u r f a c e w e t t i n g t o t h e r m o c a p i l l a r i t y can be seen by d i v i d i n g e q u a t i o n (2.6) by e q u a t i o n ( 2 . 7 ) . Zuber and Staub c o u l d not v e r i f y t h e i r r e l a t i o n s h i p s w i t h e x p e r i m e n t a l v a l -ues but they d i d c a l c u l a t e the magnitudes of t h e i r d i m e n s i o n -l e s s groups f o r d i f f e r e n t l i q u i d s w i t h assumed c o n t a c t a n g l e s T h e i r v a l u e s show the s t r o n g e f f e c t of c o n t a c t a n g l e . F o r example, f o r a water f i l m the r a t i o o f t h e r m o c a p i l l a r y f o r c e t o s u r f a c e t e n s i o n f o r c e i s 0.55, a t 8 = 10° and 0.01 a t 9 = 60°. The r a t i o o f vapor t h r u s t t o s u r f a c e , t e n s i o n i s 0.017 a t 6 = 10° and 0.001 a t 9 = 60°. The r e l a t i v e im-p o r t a n c e of vapor t h r u s t and t h e r m o c a p i l l a r y f o r c e s depends on f l u i d p r o p e r t i e s and heat f l u x . • Vapor t h r u s t i s more i m p o r t a n t than t h e r m o c a p i l l a r y f o r c e f o r l i q u i d m e t a l s , whereas the o p p o s i t e i s t r u e f o r w a t e r . G e n e r a l l y , an i n -c r e a s e i n the c o n t a c t a n g l e causes a s u b s t a n t i a l i n c r e a s e i n the s u r f a c e t e n s i o n f o r c e , r e l a t i v e t o t h e o t h e r f o r c e s a c t -i n g . ... 21 The a n a l y s i s o f d r y p a t c h s t a b i l i t y was extended f u r t h e r by'McPherson (1.3) who i n c l u d e d shear due t o . vapor at the l i q u i d - v a p o r i n t e r f a c e , h y d r o s t a t i c head of t h e l i -q u i d f i l m and a d r ag f o r c e due t o t h e s m a l l s t e p i n the f i l m i n a d d i t i o n t o f o r c e s c o n s i d e r e d by o t h e r s . He s u g g e s t s t h a t d r y o u t i s i n i t i a t e d by n u c l e a t i o n , t h e r m o c a p i l l a r y f o r c e s , or by f i l m s t a r v a t i o n (At h i g h q u a l i t i e s t h e r e may be i n -s u f f i c i e n t l i q u i d t o r e p l e n i s h t h e e v a p o r a t i n g f i l m ) . The dry p a t c h can grow upstream, rewet, o r remain s t a t i o n a r y , depending on t h e magnitude of t h e f o r c e s a c t i n g . McPherson's f o r c e b a l a n c e at t h e edge of the d r y p a t c h was s i m i l a r t o Zuber and S t a u b 1 s e x c e p t t h a t he i n - , e l u d e d a d d i t i o n a l f o r c e s and an i n c r e a s e i n heat f l u x due t o i n c r e a s e d t e m p e r a t u r e at t h e d r y p a t c h and consequent con-d u c t i o n a l o n g t h e p l a t e t o t h e wet r e g i o n s s u r r o u n d i n g the. p l a t e . T h i s i n c r e a s e s the e v a p o r a t i o n r a t e i n t h e wet r e - , g i o n a d j a c e n t t o the d r y p a t c h , and a l s o causes a change i n s u r f a c e t e n s i o n a t t h e s t a g n a t i o n p o i n t . The r e s u l t a n t f o r c e a c t i n g on the s t a g n a t i o n p o i n t i s t h e sum.of the vapor t h r u s t , s t a g n a t i o n f o r c e , shear f o r c e , s u r f a c e f o r c e , body f o r c e and drag f o r c e and t h e s e are i l l u s t r a t e d i n F i g u r e ( 7 ) . McPherson's i n c l u s i o n of a body f o r c e i s i n c o r r e c t s i n c e he assumes a h o r i z o n t a l p l a t e , however, t h i s does not a f f e c t h i s r e s u l t s , s i n c e body f o r c e i s s e v e r a l o r d e r s o f magnitude l e s s than s u r f a c e f o r c e . The main f o r c e s a c t i n g on t h e f i l m are s u r f a c e f o r c e , . F. , shear f o r c e , F , and s t a g n a t i o n f o r c e , cr s F and t h e r e s u l t a n t i s g i v e n by F = F. + F + F , cr s m' (2.9) o r - a ( 0 ) ) - x.f£±5l) l -i 2 U le F = ( a(Q)cos9 U looJ 2pp S (• + (2.10) oo Note t h a t c o n t a c t a n g l e appears i n o n l y one o f thes e terms.-The c o n d i t i o n f o r a q u a s i - s t a b l e d r y p a t c h i s a b a l a n c e between s u r f a c e f o r c e and shear and s t a g n a t i o n f o r c -e s . When a d r y p a t c h i s formed t h e upstream s u r f a c e f o r c e d e c e l e r a t e s the f i l m c a u s i n g a downstream shear f o r c e . Shear f o r c e and p o s s i b l y s t a g n a t i o n f o r c e w i l l i n c r e a s e un-t i l t hey b a l a n c e t h e s u r f a c e f o r c e and t h e d r y p a t c h w i l l become q u a s i - s t a b l e . The dry p a t c h w i l l be s t a t i o n a r y i f the sum o f t h e s e f o r c e s i s eq u a l t o z e r o however because o f v a r i a t i o n i n c o n t a c t a n g l e t h i s c o n d i t i o n i s not g e n e r a l l y s a t i s f i e d and the s t a g n a t i o n p o i n t w i l l o s c i l l a t e . ed i t can o n l y be r e w e t t e d by some p e r t u r b a t i o n o f the s y s -tem, such as i n c r e a s e d f i l m f l o w r a t e o r d r o p l e t d e p o s i t i o n r a t e . He su g g e s t s t h a t mid-patch temperature w i l l ex-ceed t h e L e i d e n f r o s t p o i n t and ad v a n c i n g f i l m w i l l be thrown o f f the h e a t e r . Sun e t a l (18) have a n a l y s e d a McPherson s u g g e s t s t h a t when a d r y p a t c h i s form-23 s i m i l a r case o f a v e r y hot p l a t e b e i n g c o o l e d by a l i q u i d f i l m and c o n c l u d e t h a t the advancing l i q u i d f i l m w i l l have a s p u t t e r i n g r e g i o n a t the a d v a n c i n g edge, which d i s r u p t s the f i l m . An a n a l y s i s of f o r c e s s i m i l a r t o t h o s e above would not a p p l y under t h e s e c o n d i t i o n s . 2.4 C o n t a c t A n g l e C o n t a c t a n g l e i s the a n g l e a l i q u i d makes w i t h a s o l i d s u r f a c e . I n t h e p r e s e n t e x p e r i m e n t s t h e c o n t a c t a n g l e i s the a n g l e the l i q u i d f i l m makes w i t h t h e heated p l a t e a t the s t a g n a t i o n p o i n t ( F i g u r e 2 ) . C o n t a c t a n g l e i s d e t e r m i n e d by t h e r e l a t i v e mag-n i t u d e s o f the a t t r a c t i o n o f the s o l i d f o r the l i q u i d and the a t t r a c t i o n o f t h e l i q u i d f o r i t s e l f ( s e l f - c o h e s i o n ) ( 2 2 ) . S u r f a c e t e n s i o n f o r c e s a c t i n g oh a l i q u i d on a s o l i d s u r f a c e a r e shown i n F i g u r e ( 8 ) . A b a l a n c e of •forces a t t h e edge of the l i q u i d g i v e s °S/A = a S / L + a L / A C O S 9 ' ( 2 - a i ) A more u s e f u l r e l a t i o n s h i p i s found by s u b s t i t u t i n g . W S / L = aS/A + a L / A " a S / L • ( 2 * 1 2 ) where Wc i s t h e work of a d h e s i o n , i . e., the work r e q u i r -O / L i ed t o s e p a r a t e the s o l i d and t h e l i q u i d . E q u a t i o n (2.11) becomes W S / L = a L / A ( 1 + C O S 9 ) (2.13) and i s c a l l e d Young's e q u a t i o n . I t shows t h a t t h e con-t a c t a n g l e i s governed by t h e magnitude of t h e a t t r a c -t i o n o f t h e s o l i d f o r the l i q u i d ^ W s / L ^ a n c J t h e s u r ~ f a c e t e n s i o n of the l i q u i d . F o r any g i v e n 0 c o n t a c t L/A a n g l e , 9, i n c r e a s e s as a d h e s i o n between s o l i d and l i q u i d d e c r e a s e s and a c o n t a c t a n g l e o f 180° i n d i c a t e s z e r o ad-h e s i o n . S u r f a c e t e n s i o n r e s u l t s from the f a c t t h a t mole-c u l e s a t the s u r f a c e are a t t r a c t e d by o t h e r m o l e c u l e s on o n l y t h r e e s i d e s whereas m o l e c u l e s away from th e s u r f a c e are a t t r a c t e d on f o u r s i d e s . S u r f a c e t e n s i o n p r o v i d e s t h i s " e x t r a f o r c e " on the m o l e c u l e s a t t h e s u r f a c e . There seems t o be no r e a s o n why s t a t i c c o n t a c t a n g l e s h o u l d be any d i f f e r e n t from dynamic c o n t a c t a n g l e however i t has been shown t h a t t h e r e i s a d i f f e r e n c e ( 2 2 ) . C o n t a c t a n g l e can be a f f e c t e d by s u r f a c e rough-ness, a b s o r p t i o n o f i m p u r i t i e s by the s u r f a c e and, f o r c o n t a c t a n g l e s at the i n t e r f a c e between s o l i d , l i q u i d and gas, r e p r o d u c i b i l i t y can be a f f e c t e d by any o f t h e s e phases ( 2 3 ) . C o n t a c t a n g l e i s a l s o a f f e c t e d by whether th e edge of t h e l i q u i d i s a d v a n c i n g o r r e c e d i n g . A n g l e s measured when t h e s o l i d s u r f a c e i s a d v a n c i n g i n t o the l i q u i d may be g r e a t e r than when the p l a t e i s wi t h d r a w n . (One method o f measuring c o n t a c t a n g l e s i s t o move a t i l t e d p l a t e i n t o o r out of a l i q u i d . The p l a t e . i s t i l t ed so t h a t the l i q u i d on one s i d e i s h o r i z o n t a l , and the angle a t which the p l a t e i s t i l t e d i s t h e c o n t a c t a n g l e ) I t i s suggested (22) t h a t t h e l a r g e r a d v a n c i n g c o n t a c t a n g l e may be due t o a f i l m o f some m a t e r i a l which p r e -v e n t s the l i q u i d a d h e r i n g t o the s o l i d . T h i s f i l m may be w h o l l y o r p a r t i a l l y removed a f t e r c o n t a c t w i t h t h e l i q u i d so t h a t a d h e s i o n between the l i q u i d and s o l i d i s i n c r e a s e d ^ s / L i n c r e a s e s ) and c o n t a c t a n g l e i s r e -duced. Davi e s and R i d e a l (22) suggest t h a t c o n t a c t an-g l e h y s t e r e s i s i s reduced i f t h e s u r f a c e i s c l e a n . Bikerman (23) p o i n t s o u t t h a t t h e d i f f e r e n c e between adv a n c i n g and r e c e d i n g , c o n t a c t a n g l e s can exceed 90° i f t h e s u r f a c e i s not c l e a n . Dynamic c o n t a c t a n g l e was measured by A b l e t t (24) by r o t a t i n g a wax c o a t e d drum i n w a t e r . I t was found t h a t a d v a n c i n g c o n t a c t a n g l e s (drum r o t a t i n g . i n t o the l i q u i d ) were g r e a t e r than r e c e d i n g c o n t a c t a n g l e s (drum r o t a t i n g out o f the l i q u i d ) by about 17°. The average v a l u e o f t h e s e a n g l e s was almost e q u a l t o t h e s t a t i c c o n t a c t a n g l e . C o n t a c t a n g l e s were independent of v e l o c i t y a t v e l o c i t i e s from 0.6 mm/s t o 4.0 mm/s f o r a w a t e r , wax, a i r system. A t speeds l e s s than 0.6 mm/s c o n t a c t a n g l e v a r i e d w i t h v e l o c i t y . The d i f -f e r e n c e i n advancing and r e c e d i n g c o n t a c t a n g l e s was a t t r i b u t e d t o t h e f a c t t h a t f o r an a d v a n c i n g a n g l e the s o l i d had not p r e v i o u s l y been wetted and f o r a r e c e d i n g a n g l e i t had been w e t t e d . S u r f a c e roughness a l s o a f f e c t s c o n t a c t a n g l e by making i t f u r t h e r from 90°; i f a smooth m a t e r i a l g i v e s a c o n t a c t a n g l e g r e a t e r than 90° r o u g h e n i n g the s u r f a c e i n -c r e a s e s i t s t i l l f u r t h e r . S h u t t l e w o r t h and B a i l e y (25) suggest t h a t c o n t a c t a n g l e h y s t e r e s i s can be e x p l a i n e d by the i n e v i t a b l e roughness of s o l i d s u r f a c e s and i t i s not n e c e s s a r y t o i n v o k e any s p e c i a l mechanism of a b s o r p t i o n a l t h o u g h they p o i n t out t h a t a b s o r p t i o n p r o b a b l y c o n t r i -b u t e s t o h y s t e r e s i s . T h e i r a n a l y s i s a p p l i e s t o s p r e a d i n g drops when the l i q u i d a t t a i n s an e q u i l i b r i u m p o s i t i o n , however i t shows how apparent c o n t a c t a n g l e can v a r y be-cause o f s u r f a c e , roughness. F i g u r e (9) shows a l i q u i d on a rough s u r f a c e and the v a r i a t i o n i n c o n t a c t a n g l e due t o s u r f a c e roughness. S h u t t l e w o r t h and B a i l e y s t a t e t h a t even the s m o o t h e s t . s o l i d s u r f a c e s have p r o j e c t i o n s h i g h e r than 100S and t h e s e would be s u f f i c i e n t t o e x p l a i n t h e o b s e r v -ed e f f e c t s of c o n t a c t a n g l e h y s t e r e s i s . 2.5 Flow i n T h i n F i l m s Dryout t e s t s i n tubes i n d i c a t e t h a t t h e r e are two f a i r l y d i s t i n c t d r y o u t regimes. Macbeth (2) has c a l -l e d , t h e s e the low and h i g h v e l o c i t y burnout r e g i m e s . In the low v e l o c i t y regime c r i t i c a l heat f l u x i s s t r o n g l y dependent on mass v e l o c i t y but i n t h e h i g h v e l o c i t y regime i t may be o n l y weakly dependent on mass v e l o c i t y . T h i s depends on t h e L/d r a t i o f o r a t low r a t i o s t h e r e i s not a g r e a t change between the low and h i g h v e l o c i t y regimes ( 5 ) . F i g u r e (10) i l l u s t r a t e s the. two regimes f o r F r e o n -12 and CO^ d r y o u t t e s t s . The aim o f t h e p r e s e n t e x p e r i -ments was. t o s t u d y f i l m breakup on a f l a t p l a t e i n l a m i -nar and- t u r b u l e n t f i l m s and f i l m f l o w w i l l be d e a l t w i t h o n l y b r i e f l y as a background t o t h e s t u d y o f break up. There has been a l a r g e amount of work done on t h i n l i q u i d f i l m s because o f t h e i r many a p p l i c a t i o n s and F u l f o r d (26) g i v e s a p a r t i c u l a r l y good summary. Flow i n t h i n f i l m s i s u s u a l l y accompanied by waves a t the f r e e s u r f a c e which c o m p l i c a t e t h e o r e t i c a l a n a l y s i s however t h e presence of waves i s not an i n d i c a t i o n .that the f l o w i s t u r b u l e n t . Under s u i t a b l e c o n d i t i o n s i t i s p o s s i b l e t o have smooth l a m i n a r f l o w , wavy l a m i n a r o r t u r b u l e n t f l o w s . G e n e r a l l y a c c e p t e d regimes o f f i l m f l o w are ( 2 7 ) : Laminar f l o w without' r i p p l i n g ' Re . < 1 t o 6.' Laminar f l o w w i t h r i p p l i n g 6 < Re < 250 t o 5 T u r b u l e n t f l o w Re > 250 t o 500. The f u l l y d e v e l o p e d v e l o c i t y p r o f i l e f o r a Newtonian f l u i d d r a i n i n g down a v e r t i c a l p l a t e has been found t o be, u pg (2y6 - y ) " 2u (2.14) w i t h t h e assumptions o f no shear at the i n t e r f a c e , a smooth f r e e s u r f a c e and g r a v i t y f o r c e b a l a n c e d by shear f o r c e . T h i s r e l a t i o n s h i p h o l d s up t o Re=250 ( 2 8 ) . H a r t l e y and M u r g a t r o y d (11) used t h i s e x p r e s s i o n t o c a l c u l a t e minimum f i l m t h i c k n e s s . A s i m i l a r e q u a t i o n was used by Zuber and Staub (12) e x c e p t t h a t p^ - p y was used i n p l a c e o f p^ . I f t h e f i l m i s l a m i n a r t h i c k n e s s can be p r e -d i c t e d from b a l a n c e assuming no shear o r wave motion a t the l i q u i d -vapor i n t e r f a c e . D u k l e r and B e r g e l i n (29) have shown t h a t r e s u l t s b e g i n t o d e v i a t e from t h o s e p r e d i c t e d by N u s s e l t ' s e q u a t i o n at Re=270. They d e v e l o p e q u a t i o n s u s i n g the von t h i c k n e s s t o f l o w r a t e and p h y s i c a l p r o p e r t i e s o ver v i s -cous and t u r b u l e n t f l o w r a n g e s . These e q u a t i o n s do not a p p l y i n t h e p r e s e n t e x p e r i m e n t s s i n c e e v a p o r a t i o n o c c u r s but t h e y can. be used t o g i v e an i n d i c a t i o n o f f i l m t h i c k -ness a t h i g h Reynolds numbers. U s i n g a u n i v e r s a l v e l o -c i t y p r o f i l e and i n t e g r a t i n g o v er t h e f i l m t h i c k n e s s g i v e s r = (2.15) T h i s was d e v e l o p e d by N u s s e l t from a f o r c e Karman v e l o c i t y d i s t r i b u t i o n t h e o r y r e l a t i n g mean f i l m Re + 64 = 3.On + 2.5nlnn (2.16) where r\ i s t h e d i m e n s i o n l e s s t h i c k n e s s at t h e f i l m s u r - . . f a c e . F o r f l o w w i t h no shear a t the i n t e r f a c e n • P l 9 6 . (2.17) I f the w i d t h of the f l o w c h a n n e l i s f i n i t e , as i t was w i t h t h e p r e s e n t e x p e r i m e n t s , f l o w i s no l o n g e r two d i m e n s i o n a l and edge e f f e c t s o c c u r . Two t y p e s of edge e f f e c t s o c c u r ; v i s c o u s edge e f f e c t s due t o drag a t the s i d e w a l l s and c a p i l l a r y e f f e c t s . F u l f o r d (26) g i v e s s o l u t i o n s f o r v e l o c i t y d i s t r i b u t i o n and f l o w r a t e con-s i d e r i n g o n l y v i s c o u s e f f e c t s and shows t h a t i f p l a t e w i d t h i s c o n s i d e r a b l y l a r g e r than f i l m t h i c k n e s s , as i t u s u a l l y i s , t h e e x p r e s s i o n f o r mass v e l o c i t y i s P/9<$3 ( l _ 1.27A) (2.18) 3U f o r smooth l a m i n a r f l o w on a. v e r t i c a l s u r f a c e . The f a c t o r 1.27 /^w i s a c o r r e c t i o n f o r v i s c o u s edge e f f e c t s . T h i s f a c t o r was not c o n s i d e r e d i n t h e p r e s e n t e x p e r i m e n t s and i s d i s c u s s e d f u r t h e r i n S e c t i o n . 6. S u r f a c e t e n s i o n causes an i n c r e a s e i n f i l m t h i c k n e s s a t the edge and t h i s r e s u l t s i n a l o c a l i n -c r e a s e i n f i l m v e l o c i t y near t h e w a l l . E q u a t i o n (2.14) shows t h a t v e l o c i t y a t the s u r f a c e v a r i e s as 6*" and be-cause f i l m t h i c k n e s s i n c r e a s e s due t o c a p i l l a r i t y e f f e c t s s u r f a c e v e l o c i t y i n c r e a s e s near the edge o f t h e p l a t e and f a l l s t o ze r o v e r y c l o s e t o the s i d e w a l l where v i s c o u s e f f e c t s become dominant. I f t h e r a t i o o f f i l m t h i c k n e s s t o p l a t e w i d t h i s s m a l l edge e f f e c t s can be n e g l e c t e d . O b s e r v a t i o n s i n t h e p r e s e n t e x p e r i m e n t s showed no s i g n o f e d g e . e f f e c t s . Flow i n t h i n f i l m s can have s e v e r a l d i f f e r e n t forms and s u r f a c e waves a r e not an i n d i c a t i o n o f t u r b u -l e n c e . Much work has gone' i n t o f i n d i n g , t h e c r i t i c a l R eynolds number f o r wave i n c e p t i o n . T a i l b y and P o r t a l s k i (30) o b s e r v e d s u r f a c e waves i n water f i l m s a t Re = 1.7 but n o t e d , t h a t t h e r e was a smooth r e g i o n b e f o r e w a v e • i n -c e p t i o n s • The c r i t i c a l R eynolds number for.wave i n c e p t i o n was found to-be z e r o f o r a v e r t i c a l p l a t e by C a s t e l l a n a and B o n i l l a ( 3 1 ) . There w i l l always be s u r f a c e waves on the f l o w s e n c ountered i n the p r e s e n t e x p e r i m e n t s . T h i s i s i m p o r t a n t f o r t h e r m o c a p i l l a r y breakup because w i t h o u t s u r f a c e waves t h e r e can be no unequal h e a t i n g of the f i l m due t o t h i c k n e s s v a r i a t i o n . EXPERIMENTAL EQUIPMENT 3.1 G e n e r a l A f i l m of l i q u i d CO^ d r a i n i n g by g r a v i t y down a heated p l a t e was used t o study t h i n f i l m break up under b o i l i n g c o n d i t i o n s . The t e s t s e c t i o n was d e s i g n e d so t h a t the bottom 25 mm o f t h e heated p l a t e c o u l d be o b s e r v e d . A s c h l i e r e n system w i t h a graded f i l t e r was used t o o b t a i n q u a n t i t a t i v e measurements. Photographs o f f i l m break up were t a k e n w i t h a movie camera. L i q u i d f l o w r a t e over the p l a t e was c o n t r o l l e d . by a c a l i b r a t e d m e t e r i n g v a l v e . A g l a s s p l a t e w i t h a t r a n s p a r e n t h e a t i n g f i l m , d e p o s i t e d on. one s i d e ( t h e s i d e i n c o n t a c t w i t h the l i q u i d ) was used t o heat t h e f i l m and heat f l u x was c o n t r o l l e d by v a r y i n g v o l t a g e a p p l i e d to the p l a t e . System p r e s s u r e and t e m p e r a t u r e was c o n t r o l l e d by a Freon r e f r i g e r a t i o n system o p e r a t e d as r e q u i r e d t o m a i n t a i n t emperature (and p r e s s u r e ) a t t h e r e q u i r e d v a l u e . The system was c a p a b l e of o p e r a t i n g o v e r a p r e s s u r e range of about 2 MPa (300 p s i a ) t o '6 MPa (900 p s i a ) and a tem-p e r a t u r e range from about 20°C t o - 40°C. Based•on r e -s u l t s o f m o d e l l i n g s t u d i e s (32, 3 3 ) . i t was f e l t t h a t CO^ c o u l d be used f o r a more fundamental s t u d y of l i q u i d f i l m break up. . F i g u r e (10) shows some r e s u l t s from t h e s e s t u d i e s . C r i t i c a l ' h e a t f l u x e s i n a water system a t 6.9 MPa (1000 p s i a ) were p r e d i c t e d from r e s u l t s i n C0„ a t 1.96 MPa ( 2 8 5 ' p s i a ) w i t h good agreement. Based on t h e s e t e s t s i t was f e l t t h a t the mechanism of f i l m b r eak up i n COg was s i m i l a r t o t h a t i n a water system .and t h a t CO^ c o u l d be used f o r t h e p r e s e n t s t u d y . 3.2 Flow Loop The f l o w l o o p i s shown s c h e m a t i c a l l y i n F i g -ure ( 1 1 ) . It-was c o n s t r u c t e d o f s t a i n l e s s s t e e l t u b -i n g and f i t t i n g s t o e l i m i n a t e c o r r o s i o n and co n t a m i n -a t i o n o f t h e w o r k i n g f l u i d . A l a r g e f l o w was c i r c u l a t e d through the main l o o p by a canned r o t o r pump and the g l a s s p l a t e t e s t s e c t i o n was o p e r a t e d as a bypass o f f the main system. Heat added i n t h e t e s t s e c t i o n had l i t -t l e e f f e c t on b u l k c o n d i t i o n s i n t h e system but heat was added by t h e pump and t h i s was removed by the r e f r i g e r -a t o r . The r e f r i g e r a t o r was run as r e q u i r e d t o m a i n t a i n t e s t s e c t i o n t e m p e r a t u r e w i t h i n i3°C o f the d e s i r e d tem-p e r a t u r e . A t low te m p e r a t u r e s i t r a n f u l l t i m e and a t h i g h e r t e m p e r a t u r e s i n t e r m i t t e n t l y . A bypass around t h e r e f r i g e r a t o r was a l s o used f o r t e m p e r a t u r e c o n t r o l . Main l o o p f l o w was m o n i t e r e d w i t h a s t a n d a r d ASME v e n t u r i and a d i f f e r e n t i a l p r e s s u r e meter. T h i s was done o n l y as an i n d i c a t i o n t h a t t h e system was op-e r a t i n g p r o p e r l y . F o r example, a low d i f f e r e n t i a l p r e s -sur e i n d i c a t e d i n s u f f i c i e n t CC^ i n t h e system. Temperature of l i q u i d c i r c u l a t i n g i n t h e main p o r t i o n of the l o o p was measured w i t h a s t a i n l e s s s t e e l sheathed c o p p e r - c o n s t a n t a n thermocouple. T h i s r e a d i n g was compared w i t h t e s t s e c t i o n i n l e t t e m p e r a t u r e as an i n d i c a t i o n t h a t t h e system was o p e r a t i n g s a t i s f a c t o r i l y . .Main l o o p t e m p e r a t u r e was s l i g h t l y l o w e r because of heat g a i n e d i n u n i n s u l a t e d t u b i n g a t the i n l e t t o t h e t e s t s e c t i o n and a l a r g e d i f f e r e n c e i n t e m p e r a t u r e (about 1 0 ° C ) i n d i c a t e d t h a t t h e system was not o p e r a t i n g p r o p e r l y . F o r example a broken thermocouple a t t h e t e s t s e c t i o n i n l e t was i n d i c a t e d by comparing b o t h r e a d i n g s . Carbon d i o x i d e t emperature a t the t e s t s e c t i o n i n l e t was measured w i t h a sheathed thermocouple and t h i s t e m perature was used t o d e t e r m i n e t e s t s e c t i o n p r e s s u r e s i n c e i t o p e r a t e d a t s a t u r a t e d c o n d i t i o n s . 3.3 T e s t S e c t i o n The t e s t s e c t i o n arrangement i s shown i n F i g -ure ( 1 2 ) . Flow passed over a w e i r and d r a i n e d down the f r o n t s u r f a c e o f a g l a s s p l a t e . The.; p l a t e was h e l d i n an aluminum tube w i t h h o l e s c u t so t h a t the bottom p o r -t i o n c o u l d be o b s e r v e d . L i q u i d CC^ e n t e r e d the t e s t s e c t i o n t h r ough a tube e x t e n d i n g t o t h e bottom o f t h e r e s e r v o i r and f l o w e d upwards through copper 'wool' used t o smooth f l o w . A g l a s s p l a t e w i t h i t s top edge sharpened was used as a w e i r . T h i s was g l u e d t o the heated p l a t e and t h u s form-ed "the t o p 25. mm o f t h e f l o w c h a n n e l . T h i s s e c t i o n was not hea t e d . The heated p o r t i o n o f t h e c h a n n e l .was 163.mm l o n g and 16 mm wide. Aluminum s t r i p s were a t t a c h e d t o the,edges, of the p l a t e t o p r o v i d e a f l o w - c h a n n e l and form an e l e c t r i c -a l c o n t a c t w i t h t h e c o n d u c t i n g s u r f a c e . They were a t t a c h e d w i t h an e l e c t r i c a l l y c o n d u c t i n g cement (Eccobond S o l d e r 58C) and p r e s s e d a g a i n s t t h e p l a t e w i t h T e f l o n s p a c e r s . . See F i g -ure ( 1 2 ) . Copper l e a d s were plugged i n t o t h e s e b u s b a r s t o p r o v i d e e l e c t r i c a l c o n n e c t i o n s . P l a t e r e s i s t a n c e was meas-ured b e f o r e assembly w i t h the b u s b a r s and l e a d s and a f t e r assembly i n the system and was t h e same i n b o t h c a s e s (3.4 ohms). The t e s t s e c t i o n was h e l d i n a s t a i n l e s s s t e e l . , b l o c k 76 mm by 100 mm by 180 mm h i g h w i t h v i e w i n g p o r t s on each s i d e . ' A s e c t i o n view i s shown i n .Figure ( 1 3 ) . View-.-i n g p o r t s were o p t i c a l q u a l i t y tempered g l a s s , 19 mm t h i c k , and 25 mm minimum d i a m e t e r . The view p o r t on one s i d e was e n l a r g e d t o e l i m i n a t e any c u t - o f f due.to l a r g e d e f l e c t i o n s . E n l a r g i n g t h e p o r t i n t h i s way meant t h a t an a n g l e of r e -f r a c t i o n a s . l a r g e as 37° c o u l d be o b s e r v e d , however t h i s d e f l e c t i o n c o r r e s p o n d s t o a s u r f a c e s l o p e g r e a t e r than t h e c r i t i c a l a n g l e . More d e t a i l s of the t e s t s e c t i o n b l o c k a r e g i v e n i n ( 3 4 ) . E l e c t r i c a l l e a d . p a s s e d through Conax t r a n s d u c e r 'glands w i t h T e f l o n s e a l s . T h i s method o f c o n n e c t i n g l e a d s t o t h e t e s t s e c t i o n proved v e r y - c o n v e n i e n t s i n c e i t f a c i l i t -a t e d easy assembly and removal o f t h e t e s t s e c t i o n . 3.4 O p t i c a l System A s c h l i e r e n o p t i c a l system u s i n g l e n s e s and a l i n e a r l y graded f i l t e r was used t o o b t a i n q u a n t i t a t i v e measurements. The o p t i c a l system i s shown i n F i g u r e (14) The graded f i l t e r was mounted v e r t i c a l l y so t h a t i t was not s e n s i t i v e t o d e f l e c t i o n s i n a h o r i z o n t a l p l a n e . A f i l t e r w i t h a l a r g e d e n s i t y change per u n i t l e n g t h was used t o g i v e maximum s e n s i t i v i t y even though t h i s r e q u i r -ed a dark f i l t e r w i t h a l a r g e a t t e n u a t i o n . . - The f i l t e r , was mounted w i t h the d.ark end up f o r m o s t ' t e s t s . T h e . r e g i o n n e x t t o t h e wet p a t c h then showed as a l i g h t e r r e g i o n on t h e n e g a t i v e s i n c e t h e de-f l e c t e d beam was a t t e n u a t e d t o a g r e a t e r degree than t h e u n d e f l e c t e d beam. ( F i g u r e 1 4 ) . When t h e f i l t e r was r e v -e r s e d and t h e dark end was down t h e wet r e g i o n upstream of the d r y p a t c h was d a r k e r than the d r y r e g i o n s i n c e the d e f l e c t e d beam passed through a r e g i o n o f l e s s a t -t e n u a t i o n and more l i g h t a r r i v e d a t t h e n e g a t i v e . I n i t i a l l y a m i c r o s c o p e i l l u m i n a t i o n lamp was used as a l i g h t s o u r c e and a c o n d e n s i n g . l e n s f o c u s e d the l i g h t on a p i n h o l e (about 1 mm d i a ) l o c a t e d a t the f o c a l l e n g t h o f . the f i r s t c o l l i m a t i n g l e n s (an A e r o -E k t a r f / 2 . 5 , 178 mm f o c a l l e n g t h l e n s ) . A s i m i l a r l e n s was used on t h e o p p o s i t e s i d e o f t h e t e s t s e c t i o n how-ever t h e e f f e c t i v e f o c a l l e n g t h was s h o r t e n e d by p u t -t i n g a s m a l l l e n s b e h i n d i t . T h i s made the image s m a l l enough so t h a t a r e a s o n a b l e amount of t h e p l a t e c o u l d be seen when the camera 1 was l o c a t e d a t t h e f i l m p l a n e . F i g -ure (15) shows the o p t i c a l arrangement. A helium-neon l a s e r was used as a l i g h t s o u r c e when h i g h speed movies (about 2500 frames/second)were tak en because the i n c a n d e s c e n t l i g h t was i n a d e q u a t e . The o p t i c a l s e t up was s i m i l a r t o t h a t a l r e a d y d e s c r i b e d except t h a t no: c o n d e n s i n g l e n s was r e q u i r e d . A beam ex-pander was a t t a c h e d d i r e c t l y t o the l a s e r and t h i s was l o c a t e d a t the f o c a l l e n g t h of the f i r s t c o l l i m a t i n g l e n s A B o l e x 16 mm camera r u n n i n g a t 64 frames per second was used w i t h the m i c r o s c o p e i l l u m i n a t i o n lamp as the l i g h t s o u r c e f o r i n i t i a l t e s t s . Some r e s u l t s were o b t a i n e d but i t appeared t h a t t h i s camera.speed was too slow t o o b s e r v e what was happening. E x a m i n a t i o n of the r e s u l t s showed a p e r i o d i c v a r i a t i o n i n f i l m t h i c k n e s s caused by waves on the l i q u i d s u r f a c e . A Hycam r o t a t i n g p r i s m camera c a p a b l e o f o p e r a t i n g up t o 8000 frames per second was used i n s t e a d o f a B o l e x camera f o r a l l o t h e r t e s t s . 3.5 A n a l y s i n g Equipment O p t i c a l d e n s i t y on the n e g a t i v e was measured w i t h a J o y c e - L o e b l A u t o m a t i c R e c o r d i n g M i c r o d e n s i t o m e t -e r , Model Mk I I I CS., F i g u r e (16) shows t h i s machine. The m i c r o d e n s i t o m e t e r (MDM) e s s e n t i a l l y measures i n -tensity of a l i g h t beam passing through a specimen .(in this case the negative) and compares i t with a reference beam. Differences in int e n s i t y are indicated on a re-cording chart. The operation of the MDM w i l l be des-cribed b r i e f l y . Light.from a source i s s p l i t into two beams, one passes through•the specimen and the other i s a. reference beam. These beams are alternately switched to a photomultiplier and i f the two beams have different, i n t e n s i t i e s a signal i s produced causing an o p t i c a l at-tenuater (a lin e a r wedge) to move and reduce i n t e n s i t y difference to zero. A continuous null-balance i s ob-tained and the distance the wedge moves i s proportioned to the difference in o p t i c a l density.between the r e f e r -ence beam and the beam passing through the specimen. A pen attached to the wedge carriage draws a chart re- . cord whose v e r t i c a l distance i s proportional to t h i s i n t e n s i t y • d i f f e r e n c e . A t y p i c a l MDM chart i s shown-in Figure (17). Because of the large amount of data, i n -t e n s i t i e s were not read from the recording charts. A voltage proportional to int e n s i t y was produced and re-corded on paper tape. The recording chart was driven in the x-d i -rection as'the pen moved in the y - d i r e c t i o n . The speci-men table was connected to the chart table by variable r a t i o arm so that a very small distance on the negative could be expanded on the chart. Ratios of 1:1 to 2000:1 ( c h a r t d i s t a n c e : specimen d i s t a n c e ) were a v a i l a b l e and 500:1 was used. C h a r t d i s t a n c e was r e l a t e d t o d i s t a n c e on the p l a t e knowing t h e m a g n i f i c a t i o n on t h e n e g a t i v e . T h i s i s d e s c r i b e d f u r t h e r i n S e c t . 4."4. V o l t a g e r e a d i n g s were ta k e n a t a known time i n t e r v a l (1 r e a d i n g per second) and t h e MDM r e c o r d i n g t a b l e was d r i v e n a t a c o n s t a n t speed (1.86 mm/s). The d i s t a n c e between r e a d i n g s was r e l a t e d t o d i s t a n c e on t h e p l a t e by knowing the m a g n i f i c a t i o n on t h e n e g a t i v e . T h i s i s d i s c u s s e d f u r t h e r i n S e c t i o n 4.4. EXPERIMENTAL PROCEDURE 4.1 G e n e r a l Experiments were run t o get d r y o u t d a t a over a range of f l o w r a t e s a t d i f f e r e n t p r e s s u r e s and h i g h speed movies were taken a t d i f f e r e n t f l o w c o n d i t i o n s . These n e g a t i v e s were a n a l y s e d t o measure dynamic c o n t a c t a n g l e and c a l c u l a t e l i q u i d f i l m p r o f i l e s upstream of a d r y p a t c h . The method of t a k i n g and a n a l y s i n g d a t a i s des-c r i b e d . 4.2 System O p e r a t i o n The. t e s t s e c t i o n was o p e r a t e d as a bypass o f f the main l o o p : a n d a l a r g e amount of l i q u i d was c i r c u l a t -ed by a canned motor pump but o n l y a., s m a l l p o r t i o n passed through t h e t e s t s e c t i o n . Temperature was lowered w i t h t h e F r e o n r e f r i g -e r a t o r u n t i l t e s t s e c t i o n i n l e t t e m p e r a t u r e was a t the d e s i r e d v a l u e and t h e r e f r i g e r a t o r was then e i t h e r shut o f f o r bypassed. I t was s t a r t e d a g a i n when temp e r a t u r e ,rose beyond 3°C above, t h e d e s i r e d v a l u e . There was no d i f f i c u l t y i n m a i n t a i n i n g t e m p e r a t u r e w i t h i n i3°C of t h e d e s i r e d v a l u e . T e s t s were run a t 2°C, 9°C, 13°C and 18°C c o r r e s p o n d i n g t o 3.62 MPa(525 p s i a ) , -4.3 MPa(625.• p s i a ) , 4.83 MPa(700 p s i a ) and 5.52 MPa(800 p s i a ) . Dryout d a t a was o b t a i n e d by s e t t i n g t h e .flow r a t e and r a i s i n g v o l t a g e s l o w l y u n t i l a ste a d y d r y p a t c h was o b t a i n e d . A t r a n s f o r m e r was used t o v a r y • v o l t a g e . The f i l m was ob s e r v e d by p l a c i n g an opaque s c r e e n i n f r o n t o f t h e camera. When s t e a d y d r y p a t c h e s were ob-serv e d v o l t a g e was r e c o r d e d and reduced t o z e r o . Flow was changed and t h e pr o c e d u r e r e p e a t e d . A n e e d l e v a l v e c a l i b r a t e d t o r e l a t e v a l v e open i n g t o Reynolds number was used t o c o n t r o l f l o w . . Valve- • c a l i b r a t i o n i s d i s c u s s e d i n Appendix B. • T e s t s were s t a r t e d a t about Re' = 700 f l o w was i n c r e a s e d u n t i l v o l t a g e l e v e l l e d o f f or i n c r e a s e d slow-l y c o r r e s p o n d i n g t o t h e c r i t i c a l heat f l u x c u r v e vs mass v e l o c i t y o b s e r v e d i n t u b e s . F o r i n d i v i d u a l r u n s v o l t -age r e q u i r e d t o produce d r y pa t c h e s d i d l e v e l o f f at Re 800 depending on temp e r a t u r e a l t h o u g h t h i s i s not e v i -dent when r e s u l t s of a l l runs a re p l o t t e d t o g e t h e r . Flow was then reduced i n eq u a l i n c r e m e n t s t o .the l o w e s t p o s s i b l e f l o w r a t e . At v e r y low f l o w s (Re = 200) t h e f i l m was. d i f f i c u l t t o see and i t was d i f f i c u l t t o t e l l a t which v o l t a g e a d r y p a t c h formed and i n ca s e s o f doubt, .read-i n g s were r e p e a t e d s e v e r a l t i m e s . •• A f t e r v o l t a g e was r e c o r d e d i t was. q u i c k l y . reduced t o z e r o so t h a t t h e d r y p a t c h d i d not.'heat up The f i l m was a l l o w e d t o f l o w down t h e p l a t e f o r a s h o r t p e r i o d of time b e f o r e another r e a d i n g was ta k e n so t h a t p l a t e t e m p e r a t u r e c o u l d r e t u r n t o a s t a b l e v a l u e . When photographs were d e s i r e d the o b s e r v a t i o n s c r e e n was r e -moved and the f i l m o b s e r v e d through t h e camera v i e w f i n d - ' e r . 4.3 O p t i c a l Measurements A l l a n a l y s e s ( 1 1 , 12, 13) on d r y p a t c h f o r -mation and s t a b i l i t y have shown a heavy dependence on the dynamic c o n t a c t a n g l e which must be measured t o check t h e s e t h e o r i e s . The b a s i s of the method of f i n d i n g s u r f a c e s l o p e i s S n e l l ' s Law which g i v e s the r e l a t i o n s h i p be-tween i n c i d e n t and r e f r a c t e d l i g h t a t a d e n s i t y i n t e r -f a c e . F i g u r e ( 1 8 ) . shows r e f r a c t i o n of a l i g h t beam at the c u r v e d s u r f a c e of t h e f i l m upstream of a d r y p a t c h . A p p l y i n g S n e l l ' s Law g i v e s n 1 s i n 0 = n 2 s i n (0 + a ) . ( 4 . 1 ) S i n c e 0 = 6, the an g l e made by t h e s u r f a c e , E q u a t i o n ( 4 . 1 ) becomes n n s i n e = n 9 s i n (Q + A ) . (4.2') Expanding g i v e s 42 n, sin 6 = n 9 sin 6' cos .a + n 0 cos 9 sin a . Dividing by n, sin 6 and rearranging, n 2 sin a tan 6 = ( 4 - 3 ) 1 - n 2 cos a and, since tan 9 = dy_ dx n 2 sin a n dy_ = _1 . (4.4) dx 1 - n 2 cos a Surface slope can be found by measuring the angle of r e f r a c t i o n , a , which i s related to o p t i c a l density at the f i l m plane by d = tan B(I - I ), (4.5) B = a c o n s t a n t depending on t h e set-up (see Appendix C), I = i n t e n s i t y c o r r e s p o n d i n g t o t h e d e f l e c t e d beam ( F i g u r e 17), .1 = i n t e n s i t y c o r r e s p o n d i n g t o t h e u n d e f l e c t -° ed beam ( F i g u r e 17). ( T h i s e q u a t i o n i s developed i n Appendix C ) . S u b s t i t u t i n g E q u a t i o n (4.4) g i v e s , s i n ( t a n - 1 B( A l ) ) dy. ' (4.6) d x 1 - ^ 2 cos ( t a n - 1 B ( A I ) ) • n l S i n c e i n t e n s i t y v a l u e s at d i f f e r e n t l o c a t i o n s a l o n g t h e l i q u i d s u r f a c e were - c o n v e r t e d d i r e c t l y t o v o l t -age r e a d i n g s (see S e c t i o n 3.5), E q u a t i o n (4.6) becomes, ^2 s i n ( t a n - 1 B( ijE) ) n l (4.7) <_ =  dx A n 2 ^ „ c ^ ^ - 1 1 1 - 2 cos ( t a n B( AlE)) n. where A:E = E - E o E = v o l t a g e c o r r e s p o n d i n g t o d e f l e c t e d beam E = v o l t a g e c o r r e s p o n d i n g t o u n d e f l e c t e d beam. Note t h a t t h e c o n s t a n t B, used i n E q u a t i o n (4.7) has a d i f f e r e n t v a l u e than t h a t i n E q u a t i o n (4.6) s i n c e i n -t e n s i t y has been c o n v e r t e d t o v o l t a g e . V o l t a g e i s d i -r e c t l y p r o p o r t i o n a l t o i n t e n s i t y . T h i s method i s r e s t r i c t e d t o s u r f a c e a n g l e s be-low t h e c r i t i c a l a n g l e f o r t o t a l i n t e r n a l r e f l e c t i o n . I f s u r f a c e a n g l e i s e q u a l t o , or g r e a t e r than t h e c r i t i c a l -a n g l e , i n c i d e n t l i g h t i s i n t e r n a l l y r e f l e c t e d and t h e c o r r e s p o n d i n g r e g i o n on t h e n e g a t i v e w i l l be unexposed. The s l o p e at any p o i n t on t h e l i q u i d s u r f a c e can be found w i t h e q u a t i o n (4.7) i f t h e v o l t a g e c o r -r e s p o n d i n g t o t h a t p o i n t and t o the u n d e f l e c t e d beam ( i . e . , t h e d r y ar e a of the p l a t e ) a re known. I f t he graded f i l t e r i s i n s t a l l e d w i t h t h e dark end up, l i g h t d e f l e c t e d upward a t t h e l i q u i d s u r f a c e ( F i g u r e 18) passes t h r o u g h a d a r k e r r e g i o n o f t h e f i l -t e r and i s a t t e n u a t e d t o a g r e a t e r degree than u n d e f l e c t -ed l i g h t which p a s s e s through t h e d r y a r e a o f t h e p l a t e . T h i s r e s u l t s i n r e g i o n at the edge o f the wet r e g i o n b e i n g l i g h t e r on t h e n e g a t i v e than t h e d r y r e g i o n where l i g h t has been u n d e f l e c t e d . An MDM t r a c e c o r r e s p o n d i n g t o t h i s s i t u a t i o n i s shown i n F i g u r e ( 1 7 ) . O p t i c a l d e n s i t y on the n e g a t i v e i s a f u n c t i o n of the a n g l e o f r e f r a c t i o n which i s a f u n c t i o n o f s u r f a c e s l o p e . Camera p o s i t i o n was det e r m i n e d by p l a c i n g a l e n s on t h e g l a s s p l a t e i n such a way t h a t a p o r t i o n o f t h e l i g h t , beam passed be-low the lens and a portion passed through i t and was de-fle c t e d (Figure 19). The camera was positioned so that the edges of the deflected and undeflected beams lined up. This ensured that the camera was at the f i l m plane. ' A microdensitometer (MDM) was used to measure variation in o p t i c a l density across the region at the edge o f a dry patch. Figure (20) shows the region of the MDM scan. The operation of the machine was such that the negative moved under the measuring beam and care was taken that the scan crossed the middle of the U-shape. although t h i s was not always possible because of d i s t o r t i o n of the top of the dry patch. A l l scans were made .from.the dry region to the wet region and voltage corresponding to the dry region was used as the reference voltage i n Equation (4.7). Frames ana-lysed were selected at d i f f e r e n t time in t e r v a l s depend-ing on how the l i q u i d edge was moving. An MDM trace was made for every frame of negative analysed but these traces were not used to read i n t e n s i t y . Figure (17) shows a t y p i c a l trace at a 500:1 r a t i o . The frame was scanned and a chart drawn and the chart was examined to check the reference l e v e l and locate the edge of the dry patch. If examination of the chart showed an unsatisfactory scan (for example incorrect positioning, of the negative) necessary changes were made and an-other trace-drawn. When a sat i s f a c t o r y trace was obtained the frame was rescanned w i t h t h e tape punch o p e r a t i n g and v o l t a g e c o r r e s p o n d i n g t o i n t e n s i t y was r e c o r d e d . The edge of the d r y p a t c h c o u l d e a s i l y be l o c a t e d by wa t c h i n g the t r a c e and. o b s e r v i n g the v i e w i n g s c r e e n i n t he MDM. When t h e edge was reached the pen moved toward the bottom of the c h a r t . When t h e edge of t h e dry p a t c h was rea c h e d o p t i c a l d e n s i t y reduced and t h e pen began moving toward the bottom of the c h a r t but because t h e specimen d i d not s t o p moving the t r a c e i n -d i c a t e d a g r a d u a l movement. F i g u r e (17) shows t h i s r e -g i o n . No r e a d i n g s were taken i n t h i s r e g i o n . Examina-t i o n o f the v i e w i n g s c r e e n over t h i s r e g i o n showed no a p p r e c i a b l e motion a c r o s s t h i s r e g i o n and i t i s f e l t t h a t no e r r o r was introduced.. The g r a d u a l downward motion of the MDM t r a c e a t a 500:1 r a t i o , was s i m p l y due t o the f a c t t h a t t h e specimen never stopped moving. When t h e same d r y p a t c h was measured u s i n g a low r a t i o (50:1) ( i . e . , 50 mm on t h e MDM.chart e q u a l s 1 mm on the n e g a t i v e ) . The edge o f the d r y p a t c h was i n d i c a t e d by an almost v e r t i c a l drop i n the t r a c e . F i g u r e (21) shows an MDM t r a c e a t 50:1. S i n c e i t w a s . r e q u i r e d t o know i n t e n s i t y o r v o l t a g e a t d i f f e r e n t . p o s i t i o n s from t h e edge o f t h e dry p a t c h i t . was n e c e s s a r y t o know the x - p o s i t i o n o f each r e a d i n g . T h i s was done by d r i v i n g t he MDM c h a r t t a b l e a t a c o n s t a n t speed and t a k i n g v o l t a g e r e a d i n g s a known time i n t e r v a l s . The time i n t e r v a l between r e a d i n was c o n t r o l l e d by a f u n c t i o n g e n e r a t o r s e n d i n g a p u l s e to the tape punch c o n t r o l u n i t and g e n e r a l l y 1 r e a d i n g per second was t a k e n . S i g n a l s from t h e f u n c t i o n gener-a t o r were d i s p l a y e d on.an o s c i l l i s c o p e t o ensure t h a t the t i m e i n t e r v a l was c o r r e c t . The MDM c h a r t t a b l e moved 1.86 mm/s which g i v e s a r e a d i n g e v e r y .1.86 mm on t h e c h a r t i f one r e a d -i n g i s t a k e n each second. The r e l a t i o n s h i p between c h a r t d i s t a n c e s and d i s t a n c e on t h e heated p l a t e was determined by s c a n n i n g a n e g a t i v e of a known d i s t a n c e , (on t h e p l a t e ) . M a g n i f i c a t i o n on t h e n e g a t i v e was then a u t o m a t i c a l l y i n c l u d e d . The r a t i o o f c h a r t d i s t a n c e t o p l a t e d i s t a n c e was 620:1 w i t h a 500:1 r a t i o arm. V o l t a g e r e a d i n g s were t a k e n a t i n t e r v a l s c o r r e s p o n d i n g t o x = 0.003 mm on t h e f i l m under t h e s e c o n d i t i o n s . Paper tape was r e a d by a computer and r e a d -i n g s were t r a n s f e r r e d t o punched c a r d s . .The s l o p e at p o s i t i o n s a l o n g t h e l i q u i d s u r f a c e was c a l c u l a t e d w i t h E q u a t i o n (4.7) and t h i s was i n t e g r a t e d by a computer to g i v e t h e s u r f a c e p r o f i l e . C o n t a c t a n g l e was found from t h e c a l c u l a t e d s l o p e a t t h e edge of the d r y p a t c h . 4.5 C a l i b r a t i o n o f t h e O p t i c a l System The s c h l i e r e n o p t i c a l system r e q u i r e d o n l y the u s u a l c a r e i n p o s i t i o n i n g and a l i g n i n g t h e com-ponents and camera p o s i t i o n i n g was d i s c u s s e d i n Sec-t i o n 4.3. The system c o n s t a n t B i s s e t by t h e f o c a l l e n g t h of the second s c h l i e r e n l e n s , i n t e n s i t y of t h e l i g h t s o u r c e , t h e f i l t e r used and t h e d i s t a n c e between components. T h i s i s d i s c u s s e d i n Appendix C. The s y s -tem i s s e l f - c a l i b r a t i n g i n t h a t t h e system c o n s t a n t i s d e termined from the system i t s e l f and a u t o m a t i c a l l y i n -c l u d e s e f f e c t s of r e f r a c t i o n a t t h e v a r i o u s s u r f a c e s . >.'• The system c o n s t a n t was found from E q u a t i o n . (4.7) knowing.the v o l t a g e d i f f e r e n c e (E - E ) c o r r e s -ponding t o a known s l o p e ( d y / d x ) . A l e n s of known- p r o -f i l e was a t t a c h e d t o t h e p l a t e i n such a way t h a t a p o r -t i o n of the i n c i d e n t l i g h t passed below the l e n s and was u n d e f l e c t e d and a p o r t i o n passed through i t and was d e f l e c t e d . F i g u r e (19) shows the c a l i b r a t i o n s e t up. The camera was p o s i t i o n e d so t h a t - t h e edges of the s p l i t beam l i n e d up and a movie was taken t o r e c o r d op-t i c a l d e n s i t y c o r r e s p o n d i n g t o t h e d e f l e c t i o n by the known s l o p e . S e v e r a l frames of n e g a t i v e were scanned w i t h t h e MDM and v o l t a g e d i f f e r e n c e c o r r e s p o n d i n g t o d i f f e r e n t p o i n t s on t h e l e n s were d e t e r m i n e d . S i n c e the s l o p e o f t h e l e n s was a l s o known as a f u n c t i o n of p o s i t i o n t h e system c o n s t a n t , B, c o u l d be c a l c u l a t e d a l o n g the l e n s . Ah average v a l u e of B was then used t o c a l c u l a t e the l e n s p r o f i l e from v o l t a g e r e a d i n g s and the l e n s p r o f i l e was p l o t t e d by a computer. A compar-i s o n o f t h e computed p r o f i l e , p l o t t e d from th e c a l c u -l a t e d v a l u e o f B and measured i n t e n s i t y v a l u e s a l o n g the l e n s and the a c t u a l p r o f i l e i s shown i n F i g u r e ( 2 2 ) . The camera and a l l o t h e r components remained i n the same p o s i t i o n s a f t e r the l e n s was removed from the g l a s s p l a t e . The c a l c u l a t e d system c o n s t a n t can then be used i n E q u a t i o n (4.7) w i t h t h e r a t i o o f r e -f r a c t i v e i n d i c e s f o r C0 2 t o f i n d s l o p e s and p r o f i l e s a t a d r y p a t c h i n a CO^ f i l m . EXPERIMENTAL RESULTS 5.1 G e n e r a l Dynamic c o n t a c t a n g l e and f i l m p r o f i l e upstream of a d r y p a t c h were measured a t p r e s s u r e s v a r y i n g from 3.6 MPa (525 p s i a ) t o 5.5 MPa (800 p s i a ) c o r r e s p o n d i n g to a t e m p e r a t u r e range of 2°C t o 18°C. F i l m f l o w r a t e s v a r i e d from Re = 185 t o about Re = 1000. T h i s i s the Reynolds number at the top of the p l a t e and not Reynolds number c o r r e s p o n d i n g t o the f l o w a t t h e break.up p o i n t . The heated g l a s s p l a t e was s e t up so t h a t t h e bottom 25 mm c o u l d be o b s e r v e d and heat f l u x was i n c r e a s -ed u n t i l d r y p a t c h e s formed. P a t c h e s formed randomly on the p l a t e and i t was d i f f i c u l t t o get p a t c h e s which c o u l d be photographed a t a l l f l o w c o n d i t i o n s . About 40 r o l l s of movie f i l m were taken but not a l l of t h e s e c o n t a i n e d i n f o r m a t i o n which c o u l d be a n a l y s e d . When the h i g h speed camera was used i t took about 2. seconds t o expose 30.5 metres of n e g a t i v e and i f no d r y p a t c h o c c u r r e d on the p l a t e d u r i n g t h i s i n t e r v a l o n l y f i l m f l o w c o n d i t i o n s were r e c o r d e d . The number of frames c o n t a i n i n g d ry p a t c h -es v a r i e d from 50 t o 400 a l t h o u g h some n e g a t i v e s showed s e v e r a l sequences o f p a t c h e s f o r m i n g and r e w e t t i n g . C r i t i c a l heat f l u x i s p l o t t e d a g a i n s t Reynolds number i n n o n - d i m e n s i o n a l form i n F i g u r e s (23 t o 2 6 ) . The t r e n d i s the same as t h a t f o r tube d a t a (see F i g u r e 10) i n t h a t c r i t i c a l heat f l u x i n c r e a s e s w i t h Reynolds number up t o some p o i n t and then l e v e l s o f f . When r e s u l t s a r e p l o t t e d i n n o n - d i m e n s i o n a l form the l e v e l l i n g o f f of t h e heat f l u x r e s u l t s i n a r e d u c t i o n o f t h e b o i l i n g number (= QL/rx) as Reynolds number i n c r e a s e s . T h i s i s s i m i -l a r t o r e s u l t s o b s e r v e d i n d r y o u t t e s t s i n round t u b e s . Macbeth (2,5) p o i n t e d out two a p p a r e n t l y d i f f e r e n t regimes of f l o w b o i l i n g i d e n t i f i e d by him as t h e low and h i g h v e l o c i t y r e g i m e s . C r i t i c a l heat f l u x i n . t h e low. v e l o c i t y regime i s s t r o n g l y dependent on mass v e l o c i t y whereas i n t h e h i g h v e l o c i t y regime i t may be o n l y weakly dependent. Tubes w i t h a s m a l l l e n g t h t o d i a m e t e r r a t i o show l i t t l e change i n the dependence o f c r i t i c a l heat f l u x on mass v e l o c i t y ( 5 ) . F i g u r e (10) shows t h e two regimes f o r Freon-12 and CC^ d r y o u t t e s t s and t h e g r a d -u a l change between the r e g i m e s . The e f f e c t of p r e s s u r e can be seen by a low-e r i n g o f c r i t i c a l heat f l u x as p r e s s u r e i n c r e a s e s . T h i s r e f l e c t s t h e r e d u c t i o n i n l a t e n t heat w i t h i n c r e a s -i n g p r e s s u r e . T h i s r e d u c t i o n i n c r i t i c a l heat f l u x i s c o n s i s t e n t w i t h t h e g e n e r a l t r e n d o f tube f l o w d a t a how-ever the e f f e c t of p r e s s u r e on c r i t i c a l heat f l u x i n tubes i s complex and has not been t h o r o u g h l y i n v e s t i -gated (5) . A c r i t i c a l heat f l u x of zer o does not c o r -respond t o z e r o Reynolds number. T h i s i s because t h e r e i s a minimum t h i c k n e s s a t which the f i l m b r e a k s up w i t h -out heat a d d i t i o n . T h i s i s i n agreement w i t h t h e r e s u l t s of o t h e r s (10, 1 9 ) . 'The minimum Reynolds number a t which f l o w b r e a k s up w i t h o u t heat a d d i t i o n i n c r e a s e s as temper-a t u r e i n c r e a s e s . T h i s i s t h e r e a s o n good r e s u l t s c o u l d not be o b t a i n e d a t t h e h i g h e r t e m p e r a t u r e s used (13°C and 18°C). The f i r s t r u n s were made u s i n g a B o l e x camera o p e r a t i n g a t 64 frames per second.and a m i c r o s c o p e i l -l u m i n a t i o n lamp as a l i g h t s o u r c e . When the h i g h speed camera was used a l a s e r was used as a l i g h t s o u r c e and t h i s changed t h e appearance o f t h e f i l m , on t h e n e g a t i v e . Smooth r e g i o n s on t h e f i l m were c h a r a c t e r i z e d by a mot- . t i e d e f f e c t as seen i n F i g u r e ( 2 7 ) . T h i s m o t t l i n g a f -f e c t e d MDM r e a d i n g s when t h e edge of t h e meniscus r e -gi o n was r e a c h e d . The MDM averages o p t i c a l d e n s i t y o ver the a r e a scanned and t h e m o t t l i n g l o w e r s t h i s average, d e n s i t y . When t h e edge o f t h e meniscus r e g i o n was reached i n t e n s i t y d i f f e r e n c e d i d not reduce t o z e r o as. would be ex p e c t e d but i n c r e a s e d as shown i n F i g u r e - ( 2 1 ) . M i c r o d e n s i t o m e t e r t r a c e s made on n e g a t i v e s t a k e n . w i t h . l a s e r l i g h t a r e v a l i d up t o the p o i n t where t h e f i l m becomes smooth. T h i s p o i n t was de t e r m i n e d by v i s u a l e x a m i n a t i o n . o f the n e g a t i v e s and by e x a m i n a t i o n of MDM t r a c e s done a t a r a t i o o f 50:1. F i g u r e (21) shows a t y p i c a l t r a c e and the edge of the d r y p a t c h and meniscus r e g i o n a re e a s i l y r e c o g n i z a b l e . E x p e r i m e n t s were s t a r t e d a t low te m p e r a t u r e (T = 2 UC) and c r i t i c a l heat f l u x was d e t e r m i n e d a t d i f - • f e r e n t Reynolds numbers a t t h i s t e m p e r a t u r e ( F i g u r e 2 3 ) . F i l m p r o f i l e s and c o n t a c t a n g l e s were found a t Reynolds, numbers r a n g i n g from 185 ( l a m i n a r f i l m ) - t o about iOOO ( t u r b u l e n t f i l m ) . T h i s p r o c e d u r e was r e p e a t e d a t T = 9°C, T .= 13°C and T = 18°C so t h a t any e f f e c t of f l u i d p r o p e r t i e s , p a r t i c u l a r l y s u r f a c e t e n s i o n c o u l d be o b s e r v e d . . . E q u a t i o n (2.13) shows t h a t c o n t a c t a n g l e de-pends on t h e s u r f a c e t e n s i o n of the l i q u i d ( a L/V"^ A N D the-magnitude of the a t t r a c t i o n of the s o l i d f o r t h e . l i -q u i d ( W 3 / L ) and s u r f a c e t e n s i o n d e c r e a s e s as t e m p e r a t u r e i n c r e a s e s . Assuming remains c o n s t a n t the c o n t a c t a n g l e must d e c r e a s e t o m a i n t a i n t h e e q u a l i t y . T h i s may be the case f o r a s t a t i c l i q u i d but e x a m i n a t i o n o f aver^-age c o n t a c t a n g l e v a l u e s a t d i f f e r e n t t e m p e r a t u r e s does not show a r e d u c t i o n as t e m p e r a t u r e i n c r e a s e s . Flow, c o n d i t i o n s seemed t o dominate any e f f e c t o f t e m p e r a t u r e on c o n t a c t a n g l e . A t s i m i l a r Reynolds numbers th e range of measured c o n t a c t a n g l e s was s i m i l a r no m a t t e r what the t e m p e r a t u r e . Measured f i l m t h i c k n e s s a t c o n s t a n t Reynolds number tended t o d e c r e a s e as t e m p e r a t u r e i n c r e a s e d which i s i n agreement w i t h t h e p r e d i c t i o n s o f H a r t l e y and Mur-g a t r o y d (11) t h a t c r i t i c a l t h i c k n e s s ( E q u a t i o n 2^3) s h o u l d reduce as t e m p e r a t u r e i n c r e a s e s . T h i s t r e n d i s e v i d e n t as temperature i s i n c r e a s e d from 9°C t o 18°C but at 2 C measured.film thickness i s thinner than ex-pected at a l l Reynolds numbers. Although f i l m thickness measured from negatives taken with the laser l i g h t source i s d i f f i c u l t to deter-mine for the reasons mentioned, i t was estimated from plotted p r o f i l e s and computer printouts of r e s u l t s . At any p a r t i c u l a r temperature f i l m thickness measured at a dry patch was approximately' the same at a l l Reynolds numbers. This agrees with the idea expressed by Simon and Hsu (.19) and others' (10)that f i l m break up occurs : when a minimum thickness i s reached and th i s minimum : thickness depends on f l u i d properties. There, was no evidence of Leidenfrost phenomen-on during the experiments even though dry patches were maintained for about one minute when pictures were tak-en. When heat flux was reduced the plate rewet immedi-ately and there was no evidence of sputtering at the edge of the dry patch as observed by Sun (18). 5.2 Low Reynolds Number Results There was no clear cut d i v i s i o n between flows at low and'high Reynolds numbers and the d i s t i n c t i o n here i s a r b i t r a r y . Low Reynolds number flows refer to those below Re •= 420.. There was a difference in the break up mechanism at low and high R'eynolds numbers. At Reynolds numbers about 200 the f i l m was v e r y t h i n (about 0.1 t o 0.3 mm a t T = 2°C) and d i f f i c u l t t o see. F i l m break up o c c u r r e d s u d d e n l y , d r y p a t c h e s spread r a p i d l y a c r o s s the p l a t e and t h e c l a s s i c i n v e r t -ed U-shape was obser v e d o n l y o c c a s i o n a l l y . F o r t h i s r eason i t was d i f f i c u l t t o get good r e s u l t s a t low f l o w s T h i s i s p a r t i c u l a r l y t r u e a t h i g h e r t e m p e r a t u r e s (T = 13°C and 18°C). The d i f f i c u l t y i s a t t r i b u t e d t o t h e e f f e c t o f reduced v i s c o s i t y a t t h e h i g h e r t e m p e r a t u r e s . A r e d u c -t i o n i n v i s c o s i t y causes a r e d u c t i o n i n f i l m t h i c k n e s s f o r t h e same Reynolds number. At h i g h e r t e m p e r a t u r e s (T = 18°C) f i l m t h i c k n e s s w i l l be even t h i n n e r than the 0.1 - 0.3 mm measured a t T = 2°C (Re = 185) and break up w i l l o c c u r .at v e r y low heat f l u x e s • b e c a u s e o n l y a s m a l l r e d u c t i o n i n f i l m t h i c k n e s s i s n e c e s s a r y t o r e a c h t h e minimum t h i c k n e s s . D r y i n g o f t e n o c c u r r e d p r e f e r e n t i a l l y from t h e s i d e o f the p l a t e and d r y pa t c h e s s p r e a d q u i c k l y a c r o s s the p l a t e . T h i s i s a t t r i b u t e d t o s u r f a c e t e n s i o n g r a d -i e n t s caused by unequal h e a t i n g of t h e f i l m . Unequal h e a t i n g r e s u l t s when t h e r e a r e v a r i a t i o n s i n f i l m t h i c k -ness due t o r i p p l e s i n the f i l m . T h i n r e g i o n s a re h e a t -ed f a s t e r than, t h i c k r e g i o n s c a u s i n g a; s u r f a c e t e n s i o n • d i f f e r e n c e and f l u i d i s drawn from t h i n n e r r e g i o n s • t o . the t h i c k e r r e g i o n s . T h i s t y p e o f f i l m breakup was ob-se r v e d a t low Reynolds numbers at a l l t e m p e r a t u r e s but the e f f e c t was most pronounced at t h e h i g h e r t e m p e r a t u r e s D r y i n g was v e r y s e n s i t i v e t o v o l t a g e change and a v e r y s m a l l i n c r e a s e i n v o l t a g e r e s u l t e d i n t h e f i l m van i s h i n g c o m p l e t e l y . I n i t i a l r uns were done a t 2°C and good, r e s u l t s . were o b t a i n e d down t o Re = 185. F i g u r e (28) shows' l i q u i d f i l m p r o f i l e s f o r a s t a t i o n a r y U-shaped d r y p a t c h a t Re = 185, T = 2°C and Q = 5500 W/m2. A l l p r o f i l e s have been moved t o a common o r i g i n t o compare c o n t a c t a n g l e s and p r o f i l e s . T h i s was done f o r a l l . r e s u l t s even though i n some cases the s t a g n a t i o n p o i n t was a d v a n c i n g o r r e -c e d i n g . T h i s d r y p a t c h was s t a t i o n a r y however c o n t a c t a n g l e v a r i e d and the v a r i a t i o n o f c o n t a c t a n g l e w i t h ' time i s shown i n F i g u r e ( 2 9 ) . E x a m i n a t i o n o f computer p l o t t e d p r o f i l e s of 11 c o n s e c u t i v e frames of t h i s f i l m p r o f i l e showed a p e r i o d i c v a r i a t i o n i n f i l m t h i c k n e s s . The p e r i o d i c v a r i a t i o n i n f i l m t h i c k n e s s seen i n F i g -ure (28) i s a t t r i b u t e d t o s u r f a c e waves. T h e s e . r e s u l t s were taken w i t h a B o l e x camera o p e r a t i n g a t 64 frames / per second and t h i s appeared too slow t o a n a l y s e the phenomenon. A h i g h speed (2500 frames per second) r o -t a t i n g p r i s m camera was used f o r a l l o t h e r n e g a t i v e s . F i g u r e (30) shows f i l m p r o f i l e s a t t h e s t a g -n a t i o n p o i n t a t T = 2°C, Re = 310 and Q = 12 000 W/m ,. and c o n t a c t a n g l e v a r i a t i o n w i t h time i s shown i n F i g -ure (3.1). At t h i s R eynolds number the f i l m i s t u r b u l e n t . T h i s d r y p a t c h o s c i l l a t e d and i t w i l l be noted from F i g -ure (31) t h a t a d v a n c i n g c o n t a c t angles, a r e g e n e r a l l y g r e a t er than r e c e d i n g c o n t a c t a n g l e s . At h i g h e r Reynolds number (Re = 420, T = 9°C) f o r a s t a t i o n a r y d r y p a t c h t h e v a r i a t i o n i n c o n t a c t ang-l e and p r o f i l e s can be seen from F i g u r e s (32) and ( 3 3 ) . Average v a l u e s of c o n t a c t . a n g l e do not appear t o be a f -f e c t e d by f l o w c o n d i t i o n s o v e r the t e m p e r a t u r e range 2°C t o 9°C. F i g u r e (34) shows a U-shaped d r y p a t c h a t Re.'= 185, T = 2°C, Q = 5500 W/m2. The p r o f i l e s shown i n F i g u r e (28) were measured from the n e g a t i v e from which t h e s e p r i n t s were made. These p i c t u r e s were taken w i t h an i n c a n d e s c e n t l i g h t s o u r c e and t h e d i f f e r e n c e i n ap-pearance between these.and photographs made, w i t h l a s e r l i g h t ( F i g u r e 27) can be seen. The g r a d e d • f i l t e r 'was i n -s t a l l e d w i t h t h e l i g h t . e n d up so t h a t t h e meniscus r e g i o n at t h e n e g a t i v e appeared dark ( i t r e c e i v e d more l i g h t ) and t h u s appears l i g h t e r on the p r i n t s . The d r y p a t c h s t a r t e d as a spot and grew outward and downstream. A t t = 0s ( F i g u r e 34a) when the f i r s t p r o f i l e was measured the d r y p a t c h was about 1.3 mm wide. The p a t c h c o n t i n -ues to. grow downstream ( F i g u r e 34b, t = 0.047s) and the bottom end opens a t about t = 0.094s ( F i g u r e 3 4 c ) . T h i s s t a t i o n a r y d r y p a t c h v a n i s h e d s u d d e n l y a t t = 0.297s but the camera speed was too slow t o r e c o r d t h i s . N u c l e a t i o n was not o b s e r v e d i n t h e f i l m a t low Reynolds number. 5.3 High Reynolds Number R e s u l t s At R e y n o l d s numbers g r e a t e r than 420 t h e f i l m was not smooth and l o n g i t u d i n a l r i d g e s were obse r v e d up t o about Re = 700. Dry p a t c h e s formed between t h e s e l o n g -i t u d i n a l r i d g e s . The f i l m became b l u r r y a t h i g h e r R e y n o l d s numbers and v i s u a l o b s e r v a t i o n was d i f f i c u l t b ut as c r i t -i c a l heat f l u x was approached .the f i l m smoothed and d r y p a t -ches c o u l d be o b s e r v e d . H e w i t t (16) a l s o noted a smoothing of t h e f i l m as c r i t i c a l heat f l u x was approached. Dry p a t -ches formed a t random l o c a t i o n s and rewet i m m e d i a t e l y b u t an i n c r e a s e i n heat f l u x a t about 10% ( c o r r e s p o n d i n g t o a v o l t -age i n c r e a s e o f about 1 v o l t ) caused t h e d r y p a t c h t o remain f o r a l o n g e r p e r i o d of. t i m e . ' C r i t i c a l heat f l u x was t a k e n as t h a t a t which d r y p a t c h e s remained f o r a f i n i t e p e r i o d o f time and grew i n s i z e . Dry p a t c h growth was t o o f a s t t o f o l l o w by eye however they c o u l d be see'n f o r m i n g . I t was d i f f i c u l t t o t e l l a t e x a c t l y what v o l t a g e a d r y p a t c h o c -c u r r e d and i t was p o s s i b l e t o i n c r e a s e v o l t a g e beyond t h e p o i n t a t which they formed. Readings were r e p e a t e d s e v e r -a l t i m e s i f t h e r e was doubt. • .•' Dry p a t c h f o r m a t i o n was. s t u d i e d by examining n e g a t i v e s taken w i t h a h i g h speed' camera o p e r a t i n g a t , 2500 frames per second. Dry p a t c h e s s t a r t e d as s p o t s and as t h e y i n c r e a s e d i n s i z e t h e r e appeared t o be a t h i n n i n g of t h e f i l m a t t h e bottom end o f the d r y p a t c h and l i q u i d i n t h i s r e g i o n was drawn outward c a u s i n g t h e d r y area t o grow downstream. An approximate U-shaped d r y pat c h formed when t h e f i l m b r o ke up i n t h i s manner. The breakup of t h i s p o r t i o n of the f i l m was s i m i l a r t o t h a t o b s e r v e d .at R e y n o l d s numbers i n t h e o r d e r of 200 a t h i g h e r t e m p e r a t u r e s (18°C). Dry p a t c h e s rewet when t u r -b u l e n t r o l l - w a v e s h i t them however t h e s e waves d i d not always cause r e w e t t i n g . R o l l - w a v e s caused the top of the p a t c h t o d i s t o r t and the d r y p a t c h t o reduce i n w i d t h but t h e y d i d not always r e s u l t i n r e w e t t i n g . The h i s t o r y of a d r y p a t c h f o r m i n g a t Re = 700, T = 9°C i s shown i n F i g u r e ( 2 7 ) . The v e r t i c a l l i n e i s the image of a c r o s s - h a i r i n t h e camera. The- d r y p a t c h s t a r t s as a spot a t t = 0s and expands t o a d i a m e t e r of about 0.8 mm a t t=0.012s ( F i g 2 7 a ) . T h i s p a t c h "form-ed i n a smooth r e g i o n of the f i l m i m m e d i a t e l y a f t e r a • wave pass e d . The m o t t l e d e f f e c t of t h e smooth f i l m can be seen i n t h i s f i g u r e . A nother d r y p a t c h can be seen f o r m i n g i n F i g (27b, t =. 0.024s) and t u r b u l e n t r e g i o n s can be seen a t t h e edge of t h e ph o t o g r a p h . F i g u r e ( 2 7 c , t = 0.048s) shows t h e p a t c h growing downstream as the bottom edge r e c e d e s . The bottom edge o f the d r y p a t c h t h i n n e d and l i q u i d was drawn from t h i s r e g i o n t o t h i c k e r r e g i o n s o f the f i l m . T h i s motion was s i m i l a r t o t h a t o bserved at low Reynolds numbers-and i s a t t r i b u t e d t o s u r f a c e t e n s i o n g r a d i e n t s caused by unequal h e a t i n g of the f i l m . The t h i n r e g i o n below t h e d r y p a t c h i s heated f a s t e r than t h e t h i c k e r r e g i o n s a t the edge and s u r f a c e 60 tension i s reduced. The patch continues to expand out-ward and downstream (Fig 27d, t = 0.080s) u n t i l a wave hits i t at t = 0.092s (Fig 27e) and d i s t o r t s the top edge (Fig 27f, t = 0.10s and Fig 27g, t = 0.104s). The top of the dry patch distorted to such an extent' that the p r o f i l e could not be measured. The width of the patch i s reduced but i t does not completely rewet and i t . wid-ens again when the wave passes (Fig 27h, t = 0.128s). The patch widens and the top edge advances and recedes s l i g h t l y during .the smooth portion of. the f i l m (Fig 27i, . t -r. 0.140s, Fig 27j , t = ' 0.148s) . ' The cycle i s repeated when another wave h i t s the dry patch and d i s t o r t s i t but does not cause rewet- . ting (Fig, 27k, t = 0.168s and Fig 271, -t = 0.184s). The f i l m smooths and the dry patch widens as the wave passes (Fig 27m, t = 0.212s). This patch remained un-t i l another wave h i t at t =•0.276s and rewet i t and an-other patch formed in the same location immediately af-ter the wave passed. At this flow condition turbulent waves were observed about every 0.08s. Turbulent waves of a similar nature were observed at a l l high Reynolds•number flow conditions. . ' ' ,: The va r i a t i o n of contact angle with time for this flow condition (Re = 700, T = 9°C) is. shown- in F i g - r ure 38). The•stagnation point recedes as'the dry patch ' expands and the contact angle i s reduced,, as would be • -expected from a receding l i q u i d . Contact angle remains c o n s t a n t when the s t a g n a t i o n p o i n t i s s t a t i o n a r y and then i n c r e a s e s as i t b e g i n s t o advance. The s t a g n a t i o n p o i n t i s d i s r u p t e d by a t u r b u l e n t wave d u r i n g t h e t i m e t = 0.080s to 0.120s and as the f i l m smooths the c y c l e r e p e a t s . . The i n c r e a s e i n c o n t a c t a n g l e w i t h an a d v a n c i n g f i l m can be seen i n F i g u r e •( 40) a t Re = 1080, T = 9°C. C o n t a c t a n g l e i n c r e a s e s s t e a d i l y from 40° ' t o 57° u n t i l the" p l a t e r e w e t s . Dry p a t c h e s always formed i n smooth s e c t i o n s o f the f i l m and F i g u r e s (35) (Re = 940, T = 2°C) (43) (Re = 885, T = 13°C) and (45) (Re = 750, T = 18°C) show t h a t the f i l m i s l e s s than 0.5 mm even though R e y n o l d s number was h i g h . O b s e r v a t i o n s o f t h e s e f i l m s showed t h a t they were t u r b u l e n t and d i f f i c u l t t o see because of b l u r r i n g , however when d r y p a t c h e s appeared the b l u r r i n g on the ob-s e r v a t i o n s c r e e n d i s a p p e a r e d and d r y p a t c h e s c o u l d be e a s i l y seen. F i l m v e l o c i t y was e s t i m a t e d t o be'about 0.1 t o 0.3 m/s o v e r t h i s range of Reynolds numbers. N u c l e a t i o n was observed i n t h e t h i c k e r f i l m . ' : a s s o c i a t e d w i t h h i g h Reynolds numbers. Bubbles were ob-. s e r v e d f a l l i n g w i t h the t u r b u l e n t waves forming, on the , p l a t e but n u c l e a t i o n d i d not cause dry p a t c h f o r m a t i o n . DISCUSSION 6.1 G e n e r a l . • Dynamic c o n t a c t a n g l e and l i q u i d f i l m p r o f i l e s have been measured at the s t a g n a t i o n p o i n t formed when a d r y p a t c h o c c u r s on a heated p l a t e . Measured f i l m t h i c k -ness upstream of a d r y p a t c h i s compared w i t h minimum f i l m t h i c k n e s s p r e d i c t e d by t h e a n a l y s e s o f H a r t l e y and M u rgatroyd (11) f o r an unheated p l a t e and Zuber and Staub (12) f o r a heated p l a t e and agreement at low Rey-n o l d s number i s ' g o o d . The assumptions made by t h e s e a u t h o r s l i m i t t h e a p p l i c a b i l i t y o f t h e i r a n a l y s e s t o l a m i n a r f i l m s , but s i n c e dry p a t c h e s always o c c u r r e d i n smooth r e g i o n s o f the f i l m i t was f e l t t h a t the t h e o r -e t i c a l a n a l y s e s might g i v e a good p r e d i c t i o n o f the m i n i -mum f i l m t h i c k n e s s even at h i g h Reynolds numbers and b o t h a n a l y s e s were a p p l i e d t o t u r b u l e n t f i l m . N e i t h e r a n a l y s i s gave a good p r e d i c t i o n of minimum f i l m t h i c k n e s s i n a t u r -b u l e n t f i l m . The s u g g e s t i o n s of McPherson (13) on dry p a t c h s t a b i l i t y a r e compared w i t h r e s u l t s o f the p r e s e n t e x p e r i -ments and appear t o be r e a s o n a b l e . A q u a s i - s t a b l e dry p a t c h i s e s t a b l i s h e d depending on a b a l a n c e between i n -e r t i a f o r c e which tends t o rewet the d r y p a t c h and s u r -f a c e t e n s i o n and t h e r m o c a p i l l a r y f o r c e s which cause i t t o s p r e a d . Dry p a t c h e s rewet when i n e r t i a f o r c e becomes l a r g e enough t o overcome s t a b i l i z i n g f o r c e s . The e x p e r i m e n t a l a p p a r a t u s was d e s i g n e d so t h a t the f o r m a t i o n of d r y p a t c h e s on a heated g l a s s p l a t e c o u l d be o b s e r v e d and the breakup r e c o r d e d by h i g h speed movies. The bottom 25 mm o f the p l a t e was o b s e r v e d s i n c e as heat, f l u x was i n c r e a s e d d r y p a t c h e s would form i n t h i s r e g i o n . The p o r t i o n of the p l a t e which c o u l d be obse r v e d by t h e camera was l i m i t e d by the s h u t t e r a p e r t u r e s i n c e no l e n s was used but t h i s , was not a major i n c o n v e n i e n c e s i n c e dry p a t c h e s formed randomly on t h e p l a t e and c o u l d be ob- .,_' served, i n . t h e camera v i e w f i n d e r . The camera c o u l d be r a i s -ed t o o b s e r v e a d i f f e r e n t p o r t i o n of t h e p l a t e i f neces-s a r y . There was no d i f f i c u l t y i n o p e r a t i n g t h e system at t h e t e m p e r a t u r e s chosen but a t 2°C c o n d e n s a t i o n o c c u r -r e d on t h e o b s e r v a t i o n ' p o r t s . N i t r o g e n was blown.on t h e o b s e r v a t i o n p o r t s t o p r e v e n t t h i s . The t r e n d of the c r i t i c a l heat f l u x v s Reynolds number d a t a i s as e x p e c t e d and i s s i m i l a r , t o t h a t f o r tube f l o w . C r i t i c a l heat f l u x i n c r e a s e s as Reynolds number i n -c r e a s e s and t h e r e i s a l e v e l l i n g o f f o f c r i t i c a l heat f l u x a t about Re = 800. T h i s was e v i d e n t i n i n d i v i d u a l t e s t s but the e f f e c t i s o b s c u r e d by s c a t t e r when a l l r e -s u l t s a r e . p l o t t e d t o g e t h e r . The s c a t t e r i n t h e r e s u l t s . i s due t o the. f a c t t h a t i t was d i f f i c u l t t o t e l l e x a c t -l y a t what v o l t a g e a d r y p a t c h formed a t h i g h Reynolds, number because .of the v e l o c i t y of the f i l m ( e s t i m a t e d t o be 0.1 t o 0.3 m/s). The o p t i c a l system enabled v e r y t h i n f i l m s t o be o b s e r v e d a l t h o u g h i t was d i f f i c u l t t o t e l l e x a c t l y when t h e s e f i l m s broke up.because when they b r o k e up dry p a t c h e s spread v e r y . r a p i d l y . ' • ' The l a s e r l i g h t s o u r c e p r o v i d e d an adequate i n t e n s i t y f o r a f r a m i n g r a t e of 2500 frames per second however i t . caused a m o t t l e d e f f e c t on smooth r e g i o n s of the f i l m . An e r r o r can o c c u r i n t h e f i l m t h i c k n e s s :meas urement because t h i s m o t t l i n g e f f e c t l o w e r s average i n t e n s i t y r e a d i n g s . T h i s means t h a t a v o l t a g e , d i f f e r e n c e i s i n d i c a t e d when t h e f i l m has no s l o p e and c a l c u l a t e d v a l -ues of f i l m t h i c k n e s s c o n t i n u a l l y i n c r e a s e s ( s ee E q u a t i o n 4.7). P r o f i l e s were p l o t t e d o n l y t o t h e p o i n t a t which i t was e s t i m a t e d the f i l m became smooth. T h i s was d e t e r -mined by e x a m i n a t i o n of t h e n e g a t i v e s and MDM t r a c e s a t a. r a t i o of .50:1 ( F i g u r e 2 1 ) . There can be a 10% e r r o r i n ' t h e e s t i m a t e d minimum f i l m t h i c k n e s s . T h i s V a l u e i s ' , based on e x a m i n a t i o n of the p l o t t e d p r o f i l e s and e x t r a -p o l a t i o n t o the p o i n t a t which. they become l e v e l . The e r r o r i n t h e p l o t t e d p r o f i l e s - and c o n t a c t a n g l e w i l l - depend on t h e c a l c u l a t e d v a l u e of t h e system c o n s t a n t . The l e n s p r o f i l e c a l c u l a t e d from o p t i c a l den-s i t y measurements i s c o r r e c t w i t h i n 5% of t h e c o r r e c t p r o f i l e a t a d i s t a n c e of about 6 mm from t h e edge and l e s s than t h i s c l o s e t o t h e edge (see F i g u r e 2 2 ) . C a l -c u l a t e d s u r f a c e p r o f i l e s and c o n t a c t a n g l e s s h o u l d a l s o be w i t h i n t h i s l i m i t . Compared w i t h s u r f a c e t e n s i o n t h e r e a r e v e r y few v a l u e s o f c o n t a c t a n g l e s quoted i n the l i t e r a t u r e . There were no v a l u e s o f s t a t i c c o n t a c t a n g l e s f o r l i q u i d CC^ quoted i n the l i t e r a t u r e . S h u t t l e w o r t h and B a i l e y (25) have s a i d t h a t c o n t a c t a n g l e can v a r y because of s u r f a c e roughness. There c o u l d be some v a r i a t i o n because of s u r -f a c e roughness of the' g l a s s p l a t e . The t r a n s p a r e n t h e a t -i n g f i l m c o u l d cause s u r f a c e v a r i a t i o n a l t h o u g h t h i s was not n o t i c e a b l e . The e f f e c t of s u r f a c e , roughness i n the p r e s e n t e x p e r i m e n t s i s p r o b a b l y a n e g l i g i b l e f a c t o r com-pared w i t h dynamic e f f e c t s due t o motion of the l i q u i d . F i g u r e (49) shows c o n t o u r s of the s t a g n a t i o n p o i n t a t Re = 7 0 0 , T = 9°C. L o n g i t u d i n a l r i d g e s and t r o u g h s can be seen w i t h a v a r i a t i o n i n f i l m t h i c k n e s s o f 0 . 3 mm. These r i d g e s and t r o u g h s c o u l d account f o r the v a r i a t i o n i n f i l m t h i c k n e s s between frames. Because of d i s t o r t i o n a t the s t a g n a t i o n p o i n t i t was p o s s i b l e t o measure a p r o f i l e which was s l i g h t l y s h i f t e d from one frame t o t h e n e x t . Care was taken t o ensure t h a t the same p a r t of the s t a g n a t i o n p o i n t was scanned each time to a v o i d t h i s problem. F i g u r e (49) shows a t y p i c a l shape of the l i q u i d edge and t h e c l a s s i c U-shaped dry p a t c h was observed o n l y o c c a s i o n a l l y . The shape of t h e d r y . p a t c h d i d t e n d t o a U-shape i f the p a t c h had time t o grow. F i g u r e (27) a l s o shows the shape of the s t a g n a t i o n p o i n t . C o n t a c t a n g l e can be a f f e c t e d by the c l e a n l i -ness o f t h e s u r f a c e . The heated s u r f a c e was exposed t o an atmosphere o f carbon d i o x i d e and t h e r e was l i t t l e pos-s i b i l i t y of s u r f a c e c o n t a m i n a t i o n . The heated s u r f a c e was wiped w i t h a c l e a n c l o t h when the t e s t s e c t i o n was d i s m a n t l e d and no t r a c e o f c o n t a m i n a t i o n was seen. V i s c o u s and s u r f a c e t e n s i o n e f f e c t s due t o the edges.of the channel were n e g l e c t e d . At Re = 185, T = 2°C o =0.17 ( a v e r a g e ) . The v a l u e o f the c o r r e c t i o n f a c t o r f o r v i s c o u s edge e f f e c t ( S e c t i o n 2.5) i s 0.013 and t h i s has a n e g l i g i b l e e f f e c t on Reynolds number. E x a m i n a t i o n of the f i l m s and n e g a t i v e s d i d not show any of t h e edge e f -f e c t s d i s c u s s e d i n S e c t i o n 2.5. I n f a c t a t low Reynolds numbers ( l e s s than about 400) d r y p a t c h e s tended t o spre a d from t h e s i d e o f the p l a t e . T h i s would not be ex p e c t e d i f f i l m t h i c k n e s s were t h i c k e r a t the edges due t o s u r -f a c e t e n s i o n . A t h i g h Reynolds numbers v i s c o u s and c a p i l -l a r y edge e f f e c t s have v e r y l i t t l e e f f e c t s i n c e t h e i r e f -f e c t s a r e c o n f i n e d t o a r e g i o n v e r y c l o s e to t h e w a l l . No edge e f f e c t s were obser v e d and a t h i g h Re d r y p a t -ches formed a t random on the p l a t e . 6.2 Low Reynolds Number At Reynolds numbers i n t h e o r d e r of 200 the • f i l m was about 0.1mm t h i c k and no r i p p l e s o r waves were observ e d a l t h o u g h e x a m i n a t i o n of n e g a t i v e s showed that, waves d i d o c c u r . . These c o u l d account f o r t h e v a r i a t i o n i n . f i l m t h i c k n e s s o b s e r v e d i n F i g u r e ( 2 8 ) . Measurements of f i l m p r o f i l e s a t Re = 185, T = 2°C showed a p e r i o d i c v a r i a t i o n i n f i l m t h i c k n e s s from 0.1 t o 0.2 mm w i t h a p e r i o d of 0.05s over t h e range of frames measured. The average f i l m t h i c k n e s s upstream o f the d r y p a t c h i s 0.17 mm. The dry p a t c h which formed a t Re = 185, T = 2°C s t a r t e d as a spot c l o s e t o the edge o f the p l a t e and spread r a p i d l y . Photographs o f t h i s d r y p a t c h a r e shown i n F i g u r e ( 3 4 ) . L a r g e t u r b u l e n t waves were not o b s e r v -ed even when the d r y p a t c h rewet. F i g u r e (29) shows t h e v a r i a t i o n of c o n t a c t a n g l e w i t h time.• The top o f the d r y p a t c h became narrow ( w i d t h reduced from about 1.3 mm t o 0.8 mm) and no measurements c o u l d be made because t h e w i d t h a t the top was too narrow t o s c a n . S i n c e s u r f a c e t e n s i o n f o r c e v a r i e s as 1-cosQ i t d e c r e a s e s as c o n t a c t a n g l e d e c r e a s e s , i s overcome.by i n e r t i a f o r c e and the d r y p a t c h r e w e t s . T h i s o c c u r r e d 0.125 seconds a f t e r the l a s t c o n t a c t a n g l e shown i n F i g u r e ( 2 9 ) . The edge of the. l i q -u i d moved down the p l a t e r e w e t t i n g the d r y p a t c h . H a r t -l e y and Mur g a t r o y d (11) suggest t h a t the d r y p a t c h r e -wets when i n e r t i a f o r c e overcomes s u r f a c e t e n s i o n f o r c e and t h e s e r e s u l t s seem t o c o n f i r m t h i s . . T h e i r a n a l y s i s 68 a p p l i e s t o an unheated p l a t e , but under t h e s e f l o w c o n d i -2 t i o n s heat f l u x was o n l y 5500 W/m and i t can be a p p l i e d as a f i r s t a p p r o x i m a t i o n . Assuming a l a m i n a r f i l m w i t h a p a r a b o l i c v e l o c i t y p r o f i l e a minimum f i l m t h i c k n e s s can be p r e d i c t e d from V 5 f -6 = 1.72 a. c .P. [pgj 2/ 5 (1-cosG) 1/5 (6.1) The c r i t i c a l f i l m t h i c k n e s s at 2°C and 6 = 48° p r e d i c t e d from t h i s e q u a t i o n i s shown i n T a b l e ( 6 . 1 ) . The shape of t h e p r o f i l e - and t h e f a c t t h a t the d r y p a t c h was s t a -t i o n a r y i n d i c a t e t h a t the v e l o c i t y p r o f i l e near the s t a g -n a t i o n p o i n t was not p a r a b o l i c and t h i s c o u l d account f o r the d i f f e r e n c e between measured and p r e d i c t e d minimum t h i c k n e s s . T h i s a n a l y s i s , does not c o n s i d e r h e a t i n g e f -f e c t s , but the s e would p r o b a b l y be s m a l l at t h i s low heat f l u x . Zuber and Staub's a n a l y s i s was a l s o used to p r e d i c t a minimum f i l m t h i c k n e s s under t h e s e f l o w con-d i t i o n s . T h e i r e x p r e s s i o n f o r minimum t h i c k n e s s i s 15 gAp p f v c a ( l - cos 9) do Q cos 9 9T k + p v Q .}* Ap c o s 2 9 (6.2) P r e d i c t e d minimum f i l m t h i c k n e s s i s shown i n T a b l e ( 6 . 1 ) . Simon and Hsu (19) found a Weber number c r i t e r i o n f o r w ater and w a t e r - g l y c e r o l f i l m s and used t h i s "minimum w e t t i n g t h i c k n e s s " Weber number (We = 0-0145) t o p r e d i c t minimum f i l m t h i c k n e s s . T h e i r e x p r e s s i o n i s c 0.666 f ,1/5 cr P .P. 2/5 (6.3) which i s s i m i l a r t o H a r t l e y and Murgatrdyd's but has a d i f f e r e n t c o n s t a n t and does not c o n t a i n c o n t a c t a n g l e . Minimum f i l m t h i c k n e s s p r e d i c t e d w i t h t h i s e x p r e s s i o n i s shown i n T a b l e ( 6 . 1 ) . T a b l e 6.1 Comparison of P r e d i c t e d and Measured Minimum F i l m T h i c k n e s s T = 2°C, Re = 185, 9 = 48° (average) H a r t l e y M u r g a t r o y d (11) Zuber Staub (12) Simon Hsu (19) Measured 0.076 mm 0.087 mm 0.037 mm 0.10 mm Bes t agreement w i t h measured r e s u l t s i s g i v e n by Zuber and Staub's a n a l y s i s which a c c o u n t s f o r thermo-c a p i l l a r y and vapor t h r u s t . Minimum t h i c k n e s s p r e d i c t e d w i t h H a r t l e y and Murgatroyd's a n a l y s i s would not be ex-pe c t e d t o agree as w e l l as Zuber and Staub's s i n c e i t does not account f o r any h e a t i n g e f f e c t s , but a t the low heat f l u x (5500 W/m ), h e a t i n g e f f e c t s a r e s m a l l and t h e r e i s r e a s o n a b l e agreement. Simon and Hsu's e x p r e s s i o n f o r minimum f i l m t h i c k n e s s was d e r i v e d from a minimum t h i c k ness Weber, number and does not i n c l u d e any c o n t a c t a n g l e ef f e c t s . F o r a s t a t i o n a r y d r y p a t c h where s u r f a c e t e n s i o n f o r c e b a l a n c e s i n e r t i a f o r c e - i t would be e x p e c t e d t h a t We-ber number would e q u a l 1 ( n e g l e c t i n g h e a t i n g and o t h e r e f -f e c t s ) , and Simon and Hsu's.Weber number would not g i v e a good p r e d i c t i o n of t h e minimum f i l m t h i c k n e s s . Zuber and Staub (12) suggest d i m e n s i o n l e s s groups to compare the r e l a t i v e magnitudes of t h e f o r c e s . The mag-n i t u d e s of t h e i r d i m e n s i o n l e s s groups have been e v a l u a t e d at 2°C and Re = 185 and r e s u l t s are p r e s e n t e d below w i t h a f i l m t h i c k n e s s of 0.10 mm and an average c o n t a c t a n g l e of 48°: V a l u e s of Zuber and Staub's D i m e n s i o n l e s s Groups 6 = 0.10 mm, 6. = 48° S u r f a c e t e n s i o n = TTI I n e r t i a _9_g_ Q cos9 T h e r m o c a p i l l a r y = T T 2 = 9T k = 0.146 I n e r t i a « , A , 2 = a ( l - c o s 9 ) 0.36 15 ( P f v j 65 71 Vapor T h r u s t = -JJ . p f Q 2 c o s z 9 Ap 2, {PV XJ Pf = 0.0094. I n e r t i a P * ( g A p ^ 2 15 l P f V J 6 ! F o r a s t a t i o n a r y d r y p a t c h such as t h i s one, i n e r -t i a f o r c e s h o u l d be b a l a n c e d by f o r c e s t e n d i n g t o spread t h e dry p a t c h and T T ^ + i\^ + T T^ s h o u l d e q u a l one. I n t h i s c a s e the sum i s 0.52 i n d i c a t i n g t h a t t h e d r y p a t c h s h o u l d rewet, a c c o r d i n g t o Zuber and Staub's t h e o r y . I t d i d rewet but not as soon as would be e x p e c t e d from t h e i r a n a l y s i s . F i l m t h i c k -ness appears t o t h e f i f t h power i n Zuber and Staub's e x p r e s -s i o n f o r i n e r t i a f o r c e so t h a t a s m a l l d i f f e r e n c e i n f i l m t h i c k n e s s can account f o r a l a r g e o v e r e s t i m a t i o n o f i n e r t i a f o r c e . F o r example i f f i l m t h i c k n e s s i s taken as 0.09 mm (0.10 l e s s 10%) t h e sum of Zuber and Staub's d i m e n s i o n l e s s groups i s 0.85. The r e l a t i v e magnitudes of t h e r m o c a p i l l a r y s u r f a c e t e n s i o n and vapor t h r u s t f o r c e s were found by Zuber and Staub by t a k i n g the r a t i o s of the above d i m e n s i o n l e s s groups. The v a l u e s o f t h e s e d i m e n s i o n l e s s groups a r e shown below f o r the same t e s t c o n d i t i o n s - ; • TT TT T h e r m o c a p i l l a r y =' __2 4 0.406 , S u r f a c e t e n s i o n T T ^ Vapor T h r u s t = /_3 = = 0.026 , S u r f a c e t e n s i o n TT 5 Vapor T h r u s t = ^5 = ^ 6 = 0.064 . T h e r m o c a p i l l a r y T T ^ I n e r t i a , s u r f a c e t e n s i o n and t h e r m o c a p i l l a r y f o r c e s are the most s i g n i f i c a n t and vapor t h r u s t has l i t t l e e f f e c t under t h e s e c o n d i t i o n s . Zuber and Staub found - T T 4 = 0.55, TT,- = 0.017 and T T ^ = 0.06 f o r a water f i l m 0.0102 mm t h i c k and 9 = 10° (assumed) but they do not say how t h e minimum t h i c k n e s s was found nor do they g i v e t h e source of t h e i r d a t a . McPherson's a n a l y s i s (13) of d r y p a t c h s t a b -i l i t y i n i t i a l l y , i n c l u d e d many terms ( F i g u r e 9 ) . but he c o n c l u d e s t h a t o n l y i n e r t i a , s u r f a c e t e n s i o n and shear at the l i q u i d - v a p o r i n t e r f a c e a r e s i g n i f i c a n t . There was no shear at t h e l i q u i d - v a p o r i n t e r f a c e i n t h e p r e -sent e x p e r i m e n t s and McPherson's e x p r e s s i o n f o r d r y p a t c h s t a b i l i t y r e d u c e s t o P fi (U 2 - U 2 )dfi•= a(0) - a ( 9 ) c o s 9 , (6.4) o " 1 0 0 1 E " . 2 where U 1 0 0 i s the v e l o c i t y upstream of the d r y p a t c h and IL _ i s t h e v e l o c i t y a t the edge of t h e d r y r e g i o n ( F i g u r e 9 ) . 1 o • T h e r m o c a p i l l a r i t y i s accounted f o r by c o n s i d e r i n g t h e s u r f a c e t e n s i o n of t h e b u l k l i q u i d Q ( 9 ) . S u r f a c e t e n s i o n at t h e t r i p l e i n t e r f a c e i s reduced due t o heat c o n d u c t i o n from the d r y r e g i o n . S i n c e the g l a s s p l a t e was d r y f o r o n l y a s h o r t p e r i o d of time i t - i s r e a s o n a b l e t o assume t h a t t h e r e was no v a r i a t i o n i n s u r f a c e t e n s i o n a t t h e t r i p l e i n t e r f a c e and a(0) = c r . (e )• V e l o c i t y a t the edge of t h e d r y p a t c h , U^E, i s z e r o s i n c e t h e d r y p a t c h was s t a t i o n a r y , and i f a p a r a b o l i c v e l o c i t y p r o f i l e i s assumed (McPherson assumed l i n e a r ) t h e i n e r t i a term i n E q u a t i o n (6.5) reduces t o the same e x p r e s -s i o n used"by H a r t l e y and M u r g a t r o y d . A t h i g h e r Reynolds numbers n e i t h e r t h e a n a l y s i s of H a r t l e y and M u r g a t r o y d o r Zuber and Staub' would be ex-pe c t e d t o g i v e a good p r e d i c t i o n of f i l m t h i c k n e s s s i n c e the assumption o f a p a r a b o l i c v e l o c i t y p r o f i l e does not h o l d at Re = 250 ( 2 9 ) . T a b l e 6.2 compares p r e d i c t e d v a l u e s of f i l m t h i c k n e s s e s a g a i n s t measured v a l u e s a t T = 2°C Re = 310 f o r 9 = 42°,for a s t a t i o n a r y d r y p a t c h . P r o f i l e s f o r s e l e c t e d frames a r e p l o t t e d i n F i g u r e ( 3 0 ) . T a b l e 6.2 Comparison of P r e d i c t e d and Measured Minimum F i l m T h i c k n e s s T = 2°C Re = 310. 9 = 42° H a r t l e y M u r g a t r o y d Zuber Staub Measured 0.073 mm 0.092 mm 0.-85 mm I t i s o b v i o u s t h a t n e i t h e r H a r t l e y and Murga-r t r o y d ' s o r Zuber and Staub's e x p r e s s i o n s p r e d i c t minimum f i l m t h i c k n e s s when t h e f i l m i s t u r b u l e n t . Simon and Hsu (19) suggested a Weber number c r i t e r i o n f o r f i l m break up and found a minimum w e t t i n g t h i c k n e s s We = 0.0145. A Weber number can be o b t a i n e d from H a r t l e y and Murgat r o y d ' s e x p r e s s i o n f o r minimum f i l m t h i c k -74-ness ( E q u a t i o n 6.1) by s u b s t i t u t i n g an average v e l o c i t y o b t a i n e d w i t h a p a r a b o l i c v e l o c i t y p r o f i l e and r e a r r a n g -i n g . The r e s u l t i n g e x p r e s s i o n i s We = 1.67 (1-cos 9). (6.5') I f i n e r t i a f o r c e i s b a l a n c e d by s u r f a c e t e n s i o n f o r c e , -Weber number s h o u l d e q u a l one. Weber number at. Re = 185, T = 2°C and 9 = 48° i s 0.55. The d i f f e r e n c e c o u l d be a c -counted f o r by the assumption of a p a r a b o l i c v e l o c i t y p r o -f i l e when, i n f a c t , t h e edge o f t h e d r y p a t c h was s t a t i o n -a r y . I f the d r y p a t c h i s s t a t i o n a r y body f o r c e due t o the s t a g n a n t l i q u i d a t t h e edge o f the d r y p a t c h i s b a l a n c -ed by s u r f a c e t e n s i o n f o r c e , n e g l e c t i n g h e a t i n g and o t h e r e f f e c t s . A d i m e n s i o n l e s s ' number which r e f l e c t s t h i s b a l -ance i s the Bond number ( t h e r a t i o of body f o r c e t o s u r -f a c e t e n s i o n f o r c e ) . V a l u e s o f the Bond number, c a l c u l a t -ed from measured f i l m t h i c k n e s s f o r s t a t i o n a r y d r y p a t c h e s a t low Reynolds'numbers a r e g i v e n i n T a b l e 6.3. T a b l e 6.3 E v a l u a t i o n of Bond Number a t Low Reyn o l d s Number T Re 6 Bo °C mm 2 185 0.17 (av.) 0.061 2 310 0.85* 1.51 . 9 420 0.75 1.57 * E s t i m a t e d f i l m t h i c k n e s s ' .75 An average f i l m t h i c k n e s s was used at Re = 185 s i n c e t h e r e was a v a r i a t i o n * of 6. from 0.10 t o 0.20 mm. T h i s i s t h e f i l m t h i c k n e s s 0.6 mm upstream of t h e d r y p a t c h ( F i g u r e 28).. The v a l u e of Bo found at Re = 185, T = 2°C i n d i c a t e s s u r -f a c e t e n s i o n f o r c e i s much g r e a t e r than g r a v i t y f o r c e and the d r y p a t c h s h o u l d move upstream, but i t was s t a t i o n a r y . The l a r g e d i f f e r e n c e can p o s s i b l y be e x p l a i n e d by the ex-i s t e n c e o f an a d d i t i o n a l i n e r t i a f o r c e due t o l i q u i d h i t -t i n g the top of t h e d r y p a t c h , d e c e l e r a t i n g and thus i n -c r e a s i n g t h i c k n e s s and f l o w i n g around th e d r y p a t c h . : Ob-s e r v a t i o n showed t h a t t h e r e was a t h i c k e n i n g o f the f i l m a l o n g the edges of the d r y p a t c h . V a l u e s found f o r Bo a t Re = 310, T = 2°C and Re = 420, T = 9°C f o r s t a t i o n a r y d r y p a t c h e s show t h a t g r a v i t y f o r c e i s g r e a t e r than s u r f a c e t e n s i o n f o r c e and the d r y p a t c h s h o u l d r e wet. T h e r m o c a p i l l a r y f o r c e s and vapor t h r u s t f o r c e s a l s o t e n d t o s t a b i l i z e the d r y p a t c h and t h e i n c l u s i o n of t h e s e two f o r c e s a l o n g w i t h s u r f a c e t e n s i o n f o r c e c o u l d account f o r the d i f f e r e n c e ' . A m o d i f i e d Bond number was c a l c u l a t e d from th e measured f i l m p r o f i l e s . Assuming s u r f a c e t e n s i o n b a l a n c e s the body f o r c e due t o the l i q u i d near the edge of a s t a g -nant d r y p a t c h th e m o d i f i e d Bond number i s given, by •. Bo = pg x A r e a under p r o f i l e . (6.5) a-T h i s e x p r e s s i o n n e g l e c t s any h e a t i n g e f f e c t s o r i n e r t i a e f -f e c t s due t o f l o w around the d r y p a t c h . The a r e a under t h e p r o f i l e a t t'= 0.094s, Re = 185, T = 2°C was measured back t o x = 0.5 mm, where the f i l m became smooth and t h i s r a t i o . ' was. found t o be, 0.159. .This i n d i c a t e s t h a t t h e d r y p a t c h . s h o u l d move upstream, when i n f a c t i t w a s . s t a t i o n a r y . The a r e a under the p r o f i l e f o r Re = 420, T =•• 9°C, t = 0.018s was a l s o measured and t h e r a t i o of body 'force t o s u r f a c e t e n s i o n was found t o be 1.41 which compares w i t h Bo = 1.57. These i n d i c a t e t h a t one c r i t e r i o n f o r a s t a t i o n -a r y d r y p a t c h i s a b a l a n c e of s u r f a c e t e n s i o n f o r c e a g a i n s t g r a v i t y f o r c e . T h i s a p p l i e s t o t u r b u l e n t and l a m i n a r f i l m s . A t h i g h e r t e m p e r a t u r e s ( 1 3 P C and 18°C). . U-shaped dry p a t c h e s were not .observed a t low Reynolds numbers. Dry patc h e s spread r a p i d l y a c r o s s t h e p l a t e and i t was d i f -f i c u l t t o .see. e x a c t l y when the d r y p a t c h s t a r t e d . F i l m • t h i c k n e s s d e c r e a s e s as t e m p e r a t u r e i n c r e a s e s f o r t h e same.: Reynolds number because of the e f f e c t o f v i s c o s i t y , ' a n d t h u s .at the h i g h e r t e m p e r a t u r e s break up o c c u r s w i t h o u t heat ad-d i t i o n a t a h i g h e r Reynolds number. . T h i s t r e n d can be. seen from F i g u r e s (23 t o 2 6 ) . At t h e h i g h e r t e m p e r a t u r e s dry p a t c h e s , s t a r t e d p r e f e r e n t i a l l y near the edge of the p l a t e and spread r a p i d l y a c r o s s t h e p l a t e . L i q u i d was drawn from the t h i n r e g i o n o f t h e f i l m t o t h e t h i c k e r r e -g i o n s of t h e f i l m due t o s u r f a c e t e n s i o n v a r i a t i o n s caus-ed by unequal h e a t i n g . No measurements c o u l d be made a t the h i g h e r t e m p e r a t u r e s because no stagnation., p o i n t s ; form-ed w i t h i n the f i e l d of v i e w . 6.3 High Reynolds Number At Reynolds numbers g r e a t e r than 420 l o n g i t u d -i n a l r i d g e s were e v i d e n t and d r y p a t c h e s o f t e n s t a r t e d be-tween t h e s e r i d g e s . F i g u r e (49) i n d i c a t e s t h e e x i s t e n c e of the l o n g i t u d i n a l r i d g e s and t h e r e i s a v a r i a t i o n i n f i l m t h i c k n e s s o f 0.3 mm a c r o s s t h e s t a g n a t i o n p o i n t . The e x i s t -ence of l o n g i t u d i n a l r i d g e s and t r o u g h s and t h e f a c t t h a t dry p a t c h e s formed between t h e s e r i d g e s i n d i c a t e s t h a t dry p a t c h e s are formed by s u r f a c e t e n s i o n g r a d i e n t s c a u s -ed by unequal h e a t i n g of the f i l m even., when the f i l m i s t u r -b u l e n t ... Flow at h i g h Reynolds numbers were c h a r a c t e r i z -ed by p e r i o d i c t u r b u l e n t r o l l - w a v e s . Between t h e s e waves the f i l m smoothed and d r y p a t c h e s , when they o c c u r r e d , formed d u r i n g t h i s smooth p e r i o d . The t u r b u l e n t waves caused r e w e t t i n g of t h e d r y p a t c h e s and when a wave pas-sed a d r y p a t c h would o f t e n form i m m e d i a t e l y a f t e r . R o l l -waves d i d not always r e s u l t i n t h e r e w e t t i n g of a d r y p a t c h as i s shown i n the sequence of photographs i n F i g u r e (27) a t Re = 700, T - 9°C. The wave caused d i s t o r t i o n of t h e s t a g n a t i o n p o i n t and n a r r o w i n g of t h e d r y p a t c h but i t d i d not cause r e w e t t i n g i n d i c a t i n g a l a r g e s u r f a c e t e n s i o n f o r -c e . At R e y n o l d s numbers i n the o r d e r of 1000 the image of the f i l m was v e r y b l u r r y and d i f f i c u l t t o o b s e r v e however as c r i t i c a l heat f l u x was approached the f i l m smoothed and d r y p a t c h e s c o u l d be seen form-i n g . I t was d i f f i c u l t t o t e l l e x a c t l y when a d r y p a t c h formed because they formed and v a n i s h e d v e r y q u i c k l y . Dry p a t c h e s formed as s p o t s and rewet when t h e f i l m f l o w e d over them but . a s l i g h t i n c r e a s e I n heat f l u x (about 10%) caused dry p a t c h e s t o grow. T h i s b e h a v i o r i n d i c a t e s t h a t f o r c e s due t o h e a t i n g are i m p o r t a n t a t h i g h Reynolds numbers (and c o r r e s p o n d i n g l y h i g h heat , f l u x e s ) . A d r y p a t c h can form because of s u r f a c e t e n s i o n g r a d i e n t s but s u r f a c e t e n s i o n f o r c e a t the s t a g -n a t i o n p o i n t i s not l a r g e enough t o w i t h s t a n d i n e r t i a f o r c e and t h e r m o c a p i l l a r y f o r c e i s i m p o r t a n t f o r dry p a t c h growth and s t a b i l i t y . The f o r m a t i o n of dry p a t c h e s i n t h i n smooth r e g i o n s of t h e f i l m s u g g e s t s t h a t t h e a n a l y s e s o f H a r t l e y and M u r g a t r o y d and Zuber and Staub might be used t o p r e d i c t minimum f i l m t h i c k n e s s a t h i g h Rey-nolds' numbers. A comparison of p r e d i c t e d .minimum' f i l m t h i c k n e s s e s f o r a s t a t i o n a r y d r y p a t c h , u s i n g a measured c o n t a c t angle, of 49.5°, at Re = . 1055,.. i s shown i n T a b l e 6.4. T a b l e 6.4 Comparison of P r e d i c t e d and Measured Minimum F i l m T h i c k n e s s . . T • = 18°C Re = 1055 Q := 65 6.00 .W/m H a r t l e y M u r g a t r o y d • . .Zuber Staub Measured 0.0613 mm 0.117 mm ' 0.50 mm H a r t l e y and M u r g a t r o y d ' s a n a l y s i s would h o t be e x p e c t e d t o g i v e good r e s u l t s because i t does not i n c l u d e any h e a t i n g e f f e c t s and the d i f f e r e n c e between t h e c r i t i c a l t h i c k n e s s p r e d i c t e d by H a r t l e y and M u r g a t r o y d and Zuber and Staub p r o b a b l y r e s u l t s from t h e r e l a t i v e l y l a r g e t h e r m o c a p i l l a r y f o r c e . N e i t h e r a n a l y s i s p r e d i c t s m i n i -mum f i l m t h i c k n e s s because t h e assumptions on w h i c h t h e y are based do not a p p l y f o r a t u r b u l e n t f i l m . The Bond number has been found f o r s t a t i o n a r y . . . dry p a t c h e s and the r e s u l t s a r e shown i n T a b l e 6.5. T a b l e 6.5 . E v a l u a t i o n of Bond Number at H i g h Reynolds Number T Re . 6 : B O ' °C mm 2 940 0.32 0.214 9 700 0.6 1.00 13 750 0.5 0.86 18 1055 0.56 1.48 Except a t 2°C the r a t i o i s c l o s e t o one, as would be ex-p e c t e d f o r a s t a t i o n a r y d r y p a t c h . The m o d i f i e d Bond number f o r a s t a t i o n a r y .pro-f i l e a t Re = 700, T = 9°C was found t o be 1.07. , Bond number f o r a r e c e d i n g l i q u i d edge a t Re = 700, T = 9°C • was found t o be 0.87 based on measured f i l m t h i c k n e s s . T h i s i n d i c a t e s t h a t s u r f a c e t e n s i o n f o r c e i s g r e a t e r t h a n body f o r c e and t h e l i q u i d edge s h o u l d r e c e d e . No h e a t i n g or i n e r t i a f o r c e due t o t h e motion of the l i q u i d upstream of t h e d r y p a t c h i s i n c l u d e d . The above r a t i o s of body f o r c e t o s u r f a c e t e n -s i o n a r e f a i r l y ' d o s e to one as they s h o u l d be f o r a s t a t i o n a r y d r y p a t c h i n d i c a t i n g t h a t f i l m t h i c k n e s s and l i q u i d f i l m p r o f i l e s can be measured a c c u r a t e l y w i t h • t h i s t e c h n i q u e . 6.4 R e w e t t i n g of Dry P a t c h e s T h e o r e t i c a l a n a l y s i s (11) i n d i c a t e s t h a t d r y pat c h e s w i l l rewet when i n e r t i a f o r c e overcomes s u r f a c e t e n s i o n and o t h e r f o r c e s t e n d i n g t o spread t h e d r y p a t c h . The p r e s e n t e x p e r i m e n t s show t h a t w h i l e the i n e r t i a f o r c e , based on measured t h i c k n e s s , may be v e r y l a r g e r e l a t i v e t o the o t h e r f o r c e s , t h e d r y p a t c h may not wet. M a r i y e t a l (35) i n t r o d u c e a t h e o r y which p r e d i c t s t h e ' e f f e c t s of s u r f a c e waves on t h e r e w e t t i n g of d r y p a t c h e s and s t r e s s the i m p o r t a n c e of s u r f a c e wave phemomena-on r e w e t t i n g . When a s u r f a c e wave h i t s a dry p a t c h t h e " s t a t i c and dy-namic f o r c e s a re s u f f i c i e n t t o overcome c a p i l l a r y f o r c e s and t h e p a t c h r e w e t s . The p r e s e n t e x p e r i m e n t s show t h a t s m a l l s u r f a c e waves of t h e t y p e r e f e r r e d t o i n (35) a r e not r e s p o n s i b l e f o r r e w e t t i n g but l a r g e , p e r i o d i c r o l l -waves cause r e w e t t i n g and even t h e s e may not rewet th e dry p a t c h . S u r f a c e waves may be r e s p o n s i b l e f o r t h e con-t a c t a n g l e v a r i a t i o n which was measured even f o r s t a t i o n -ary d r y p a t c h e s . T h i s dynamic b e h a v i o r a t t h e s t a g n a t i o n p o i n t has not been c o n s i d e r e d i n any a n a l y s i s . McPherson suggested t h a t . a - q u a s i - s t a b l e dry, -p a t c h was e s t a b l i s h e d based on a b a l a n c e o f f o r c e s a c t -i n g at. the s t a g n a t i o n p o i n t . Measurements o f t h e dy-namic c o n t a c t a n g l e i n t h e p r e s e n t e x p e r i m e n t s i n d i c a t e s t h a t s u r f a c e f o r c e , which i s a f u n c t i o n of (1 - cos 9 ) , v a r i e s t o b a l a n c e i n e r t i a f o r c e . As t h e s t a g n a t i o n p o i n t advances c o n t a c t a n g l e i n c r e a s e s and s u r f a c e f o r c e i n - . c r e a s e s u n t i l i n e r t i a f o r c e i s b a l a n c e d . The d r y p a t c h then remains s t a t i o n a r y o r r e c e d e s due t o s u r f a c e f o r c e b e i n g g r e a t e r - than i n e r t i a f o r c e . As t h e s t a g n a t i o n p o i n t r e c e d e s c o n t a c t a n g l e d e c r e a s e s t h u s r e d u c i n g t h e s u r f a c e tension. 1 f o r c e . At some p o i n t s u r f a c e t e n s i o n f o r c e i s ' a g a i n b a l a n c e d by i n e r t i a f o r c e , and t h e : c y c l e repeats.. F i g u r e (48) shows a sequence of. t h i s s o r t . At -1 = 0, 9 = 47°, t h e edge of the d r y p a t c h i s - s t a t i o n - , a r y and c o n t a c t a n g l e drops as t h e s t a g n a t i o n p o i n t r o -cedes. C o n t a c t a n g l e drops t o 39.5°, the s t a g n a t i o n ' p o i n t becomes s t a t i o n a r y and c o n t a c t a n g l e then i n c r e a s -es as he s t a g n a t i o n p o i n t advances u n t i l i t r e a c h e s 47° and t h e dry p a t c h a g a i n becomes s t a t i o n a r y . T h i s d r y p a t c h was r e w e t t e d by a r o l l - w a v e 0.005s a f t e r t h e l a s t frame a n a l y s e d . McPherson s u g g e s t s t h a t once a d r y p a t c h f o r ms-, i t can o n l y be r e w e t t e d by some p e r t u r b a t i o n o f t h e sys-. tern such as i n c r e a s e d f i l m f l o w or d r o p l e t d e p o s i t i o n r a t e . The e f f e c t o f c h a n g i n g f i l m f l o w r a t e was o b s e r v -ed by i n c r e a s i n g f l o w r a t e a t c o n s t a n t heat f l u x . A d r y p a t c h was formed a t 13°C, Re = 720 and Q = 38 000 W/m2 and f l o w r a t e was' i n c r e a s e d to Re = 785. . The p a t c h r e d u c -ed i n s i z e and t h e s t a g n a t i o n p o i n t o s c i l l a t e d but d i d not c o m p l e t e l y rewet. When f l o w was i n c r e a s e d t o Re = 820 the p a t c h c o m p l e t e l y rewet and d i d not r e f o r m . Reduc-i n g f l o w t o Re = 785 r e s u l t e d i n the p a t c h a l t e r n a t e l y r e f o r m i n g and r e w e t t i n g . An i n c r e a s e i n the f i l m f l o w r a t e w i l l c e r t a i n l y rewet a d r y p a t c h but i t r e q u i r e s more than a s l i g h t change. I f t h e s u r f a c e t e m p e r a t u r e . o f the dry p a t c h i n c r e a s e s t o t h e L e i d e n f r o s t t e m p e r a t u r e the p a t c h w i l l p r o b a b l y o n l y wet w i t h d i f f i c u l t y . - T h i s was not observed i n t h e p r e s e n t e x p e r i m e n t s s i n c e s u r -f a c e t e m p e r a t u r e d i d not r e a c h t h e L e i d e n f r o s t p o i n t d u r -i n g any t e s t . 7. SUMMARY AND CONCLUSIONS An e x p e r i m e n t a l i n v e s t i g a t i o n has been c a r r i e d out on t h e break up of t h i n l i q u i d films''and the s t a b i l i t y of d r y pa t c h e s formed on a heated p l a t e . A new e x p e r i -mental t e c h n i q u e has been used t o measure dynamic con-t a c t a n g l e and l i q u i d f i l m p r o f i l e s . These r e s u l t s a re the f i r s t measurements of dynamic c o n t a c t a n g l e and l i q -u i d f i l m p r o f i l e under f i l m break up c o n d i t i o n s . The measured v a l u e s have been used t o check p r e v i o u s t h e o r e t -i c a l a n a l y s e s of d r y p a t c h s t a b i l i t y , i : P r e v i o u s t h e o r e t i c a l a n a l y s e s i n d i c a t e d t h a t t h e s t a b i l i t y of d r y pa t c h e s formed i n t h i n l i q u i d . f i l m s i s dependent on dynamic c o n t a c t a n g l e . I t was not p r e -v i o u s l y p o s s i b l e t o check t h e s e ' a n a l y s e s a g a i n s t a c t u a l r e s u l t s because t h e r e were no p r e v i o u s measured v a l u e s o f dynamic c o n t a c t a n g l e s . Measured v a l u e s from t h e p r e s e n t e x p e r i m e n t s have been used t o check t h e t h e o r e t i c a l a n a l y -ses o f H a r t l e y and Murg a t r o y d (11) which c o n s i d e r e d f i l m -break up on an unheated s u r f a c e and Zuber and Staub (12) which c o n i s i d e r e d f o r c e s due t o h e a t i n g . Both of the s e a n a l y s e s b a l a n c e f o r c e s t e n d i n g t o rewet the d r y p a t c h a g a i n s t f o r c e s c a u s i n g i t t o spread and both depend on dynamic c o n t a c t a n g l e . They can be used t o p r e d i c t a minimum f i l m t h i c k n e s s a t which d r y patc h e s a r e formed. Minimum f i l m t h i c k n e s s p r e d i c t e d by bo t h a n a l y s e s agrees f a i r l y w e l l w i t h measured f i l m t h i c k n e s s at low heat f l u x and low Reynolds number a l t h o u g h r e s u l t s a t low Reynolds numbers are l i m i t e d . Zuber and Staub's a n a l y s i s g i v e s b e t t e r agreement w i t h measured r e s u l t s because i t i n c l u d -es h e a t i n g e f f e c t s . The r e l a t i v e magnitudes of i n e r t i a , s u r f a c e t e n s i o n , t h e r m o c a p i l l a r y and vapor t h r u s t p r e d i c t e d by Zuber and Staub agree f a i r l y w e l l w i t h measured r e s u l t s . When measured v a l u e s of f i l m t h i c k n e s s are used w i t h Zuber and Staub's a n a l y s i s t o e v a l u a t e the r e l a t i v e mag-n i t u d e s of the f o r c e s a c t i n g , i n e r t i a f o r c e , which tends t o rewet the dry p a t c h i s about 2 t i m e s t h e magnitude o f the f o r c e s t e n d i n g t o e n l a r g e the d r y p a t c h . T h i s i n d i c a t -es t h a t the dry p a t c h s h o u l d rewet when i n f a c t i t was s t a -t i o n a r y . The d i f f e r e n c e can be e x p l a i n e d by a s m a l l d i f f e r -ence i n measured f i l m t h i c k n e s s which appears t o t h e f i f t h power i n the i n e r t i a term. The e f f e c t of t h e r m o c a p i l l a r -i t y i s i m p o r t a n t even a t low heat f l u x e s and vapor t h r u s t i s n e g l i g i b l e a t a l l heat f l u x e s i n the p r e s e n t e x p e r i -ments. Both a n a l y s e s ( 1 1 , 12) were a p p l i e d t o d r y p a t c h f o r m a t i o n a t h i g h Reynolds numbers s i n c e d ry patches' a l -ways formed i n smooth r e g i o n s o f the f i l m , h o w e v e r n e i t h e r a n a l y s e s . p r e d i c t e d minimum f i l m t h i c k n e s s under t h e s e . c o n -d i t i o n s . One c r i t e r i o n which has been a p p l i e d t o s t a t i o n -a r y d r y p a t c h e s i n the p r e s e n t experiments- i s t h e b a l a n c e of body f o r c e by s u r f a c e t e n s i o n f o r c e . T h i s b a l a n c e , r e p r e s e n t e d by the Bond number, has not p r e v i o u s l y been a p p l i e d t o t h e a n a l y s i s o f d r y p a t c h s t a b i l i t y . The t h r e e - d i m e n s i o n a l n a t u r e o f t h e d r y p a t c h h a s n o t b e e n c o n s i d e r e d i n any a n a l y s i s a l t h o u g h M c P h e r -son s u g g e s t s t h a t d r y p a t c h e s w i l l grow by w i d e n i n g . H i s a s s u m p t i o n t h a t a l l l i q u i d e n t e r i n g t h e m e n i s c u s r e g i o n i s e v a p o r a t e d i s n o t a good a s s u m p t i o n . Even a t h i g h h e a t f l u x t h e c h a n g e i n f i l m t h i c k n e s s i s n o t a c c o u n t e d f o r by e v a p o r a t i o n ( e . g., F i g u r e 4 7 ) . S i n c e l i q u i d a p p r o a c h -i n g t h e d r y p a t c h i s n o t a l l e v a p o r a t e d i t . m u s t l e a d t o f l o w a r o u n d t h e d r y p a t c h and t h e t h r e e - d i m e n s i o n a l n a t -u r e o f t h e s t a g n a t i o n p o i n t must be c o n s i d e r e d b e f o r e a c o m p l e t e u n d e r s t a n d i n g o f d r y p a t c h s t a b i l i t y i s o b t a i n -e d . , M c P h e r s o n p o s t u l a t e s a m e c h a n i s m o f q u a s i - s t a b l e d r y p a t c h e s and m e a s u r e m e n t s o f c o n t a c t a n g l e a s a f u n c t i o n o f t i m e i n d i c a t e t h a t t h i s i s c o r r e c t , , A q u a s i - s t a b l e d r y p a t c h i s f o r m e d due t o t h e b a l a n c e o f f o r c e s a t the. t r i p l e i n t e r f a c e and c o n t a c t a n g l e v a r i e s t o b a l a n c e i n e r t i a f o r c e . The l i q u i d edge a d v a n c e s d o w n s t r e a m and c o n t a c t a n g l e i n -c r e a s e s u n t i l s u r f a c e t e n s i o n f o r c e b a l a n c e s i n e r t i a f o r c e . The d r y p a t c h t h e n r e m a i n s s t a t i o n a r y , i n e r t i a f o r c e i s r e -d u c e d and t h e d r y p a t c h r e c e d e s u p s t r e a m , and c o n t a c t • a n g l e d e c r e a s e s , t h u s r e d u c i n g s u r f a c e t e n s i o n f o r c e . The p a t c h w i l l o s c i l l a t e i n t h i s manner u n t i l i t r e w e t s . R e w e t t i n g o c c u r s when t u r b u l e n t r o l l - w a v e s h i t t h e d r y p a t c h , h o w e v e r i n some c a s e s s u r f a c e and t h e r m o -c a p i l l a r y forces can be large enough to prevent roll-waves from rewetting the dry patch. The mechanism of dry patch formation was d i f -ferent at low and high Reynolds numbers. At Reynolds numbers less than 400 dry patches formed and spread very rapidly by what appeared to be a surface tension force p u l l i n g l i q u i d from the thinner region, to a thicker re- . gion. This indicates that dry patches formed due to sur-face tension gradients due to unequal' heating of the f i l m . At Reynolds numbers greater than 400 cry pat-ches formed in smooth regions as spots and expanded. The bottom end of the dry patch thinned and broke up in the same manner as that observed at low Reynolds numbers indicating surface tension gradients are important even in turbulent f i l m s . The theor e t i c a l analysis of.Zuber and Staub can be used to predict minimum f i l m thickness at Reynolds numbers less than 250 however dynamic contact angle must be known before t h i s can be done. Further models are re-quired to predict f i l m break up and s t a b i l i t y in turbulent films and the three-dimensional nature of the flow at- the stagnation point should be considered for a more complete understanding of s t a b i l i t y . 87 D R Y O U T 'A * o o ° oo 0 ° 6 & 0 o0 a b o ^ o O o © 6 S I N G L E P H A S E S T E A M L I Q U I D D E F I C I E N T S P R A Y F L O W A N N U L A R F L O W S L U G F L O W B U B B L E F L O W S I N G L E P H A S E W A T E R Figure 1 Flow B o i l i n g Regimes., Upward Flow 8 8 F i g u r e 4 Flow B o i l i n g i n a Tube Showing the B e g i n n i n g o f the S l u g Flow Regime. C O 2 a t 1.7 MPa, Q = 5700W/m2, I n l e t Temp. - 30°C » « D X=0 F i g u r e 5 Some V a r i a b l e s I n v o l v e d i n Flow B o i l i n g and F i l m Breakup. F i g u r e 6 L a t e r a l M o t i o n Due t o S u r f a c e T e n s i o n V a r i a t i o n I • • U|oo 1 1 1 • 4 N. A • , v \ \ . \ \ \ \ \ \ \ \ «. .— : : 1--\V V V \ A V \ \ V V V : : : — • /(e) cost? force due to vapor thrust drag force over step in film stagnation force surface force <r(0) - <r(0)cos0 F i g u r e 7 F o r c e s A c t i n g a t a Dry P a t c h (Ref 13) 94 F i g u r e 8 L i q u i d Drop on a S o l i d S u r f a c e 95 S o l i d Sur face At A , At B, Apparent contact angle 0 = e + ^ Apparent contact angle 0 = e - <A \p= Surface Slope F i g u r e 9 V a r i a t i o n o f A p p a r e n t C o n t a c t A n g l e Due t o S u r f a c e Roughness 0-6 CO 'O x 0-4 X 3 5 ZD O >-cr Q 0-2 REGION OF UNCERTAINTY t s A / - — NOMINAL -^-=130 DATA A Freon-12 • C 0 2 P 1 5 5 psia 2 8 5 0 •334 in •238 0-5 1-0 MASS VELOCITY, Gx10" 1-5 I b m hr-ft2 2-0 F i g u r e 10 P r e d i c t i o n o f C r i t i c a l Heat F l u x i n Water a t 6.9 MPa U s i n g CC>2 a t 1.96 MPa 97 F i g u r e 11 Loop Flowsheet F i g u r e 12 T e s t S e c t i o n Figure 13 Test Section Holder Second Schlieren Lens Filter Film Plane Unexposed Region Incorrect Camera Position F i g u r e 14 S c h l i e r e n System w i t h a Graded F i l t e r , Show-i n g E f f e c t o f I n c o r r e c t Camera P o s i t i o n i n g ^ o o 1 0 1 F i g u r e 15 O p t i c a l Set-up at T e s t S e c t i o n 1 0 2 F i g u r e 16 M i c r o d e n s i t o m e t e r and A n a l y s i n g Equipment Reference L e v e l f I 0 AI=I f t-I Intensity corresponding to def lected region, I No reading taken in t h i s reg ion 620 mm= 1 mm F i g u r e 17 T y p i c a l M i c r o d e n s i t o m e t e r T r a c e 104 F i g u r e 18 R e f r a c t i o n o f L i g h t a t Curved L i q u i d S u r f a c e Undetected G l a s s Second F i l t e r F i l m P lane Plate Schlieren Lens F i g u r e 19 C a l i b r a t i o n Lens and Set-up. 106 Region Of Edge Curvature F i g u r e 20 M i c r o d e n s i t o m e t e r Scan P o s i t i o n Region across edge of dry patch(o*8mrr0 rReference Level,I, R e s 940 T = 2 ° C 62mm = l mm gure 21 Microdensitometer Trace' at 50:1 20 1-6 E 1-2 E m 9 c __ o j5 0-8 0-4 Lens Profile S Computed Ssc\ . — ' A c t u a l ss* s s o o 2 3 4 5 6 7 Distance From Edge, mm F i g u r e 22 Comparison o f C a l c u l a t e d and A c t u a l Lens P r o f i l e 8 7 1 1 1 I 1 I 1 1 1 1 6 T =2°C P = 3.62 M P a — Q L r x 5 • • • • • • • • — x 10 4 • • • • • • • 3 • • • • . : • • • • • • • • * • • — 2 • — 1 L _ . 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10 Re x 10 F i g u r e 23 B o i l i n g Number vs Reynolds Number, T = 2°C o X> i r T = 9°C P = 4 . 2 M P a J I I L Re x 10 - 2 10 11 12 F i g u r e 24 B o i l i n g Number vs Reynolds Number, T = ;9°C Q L r x x10 4 1 1 1 r T=13*C P= 4.8 MPa 0 Re x 10 - 2 10 F i g u r e 25 B o i l i n g ' Number vs Reyn o l d s Number, T = 13°C i r i r 7 L T = 18°C P= 5.5 M P a J_ ; L J L i _ L 10 11 Re x 10 -2 12 F i g u r e 26 B o i l i n g Number vs R e y n o l d s Number,. T = 18°C IV) 27(b) t = 0.024s M a g n i f i c a t i o n 14X D i s t a n c e a c r o s s d r y p a t c h , 1.2 mm F i g u r e 27 Formation of a Dry Patch Re = 700, 27 (c) t = 0.048s M a q n i f i c a t i o n 14X D i s t a n c e a c r o s s d r y p a t c h , 0.8 mm 27(d) t = 0.08s M a g n i f i c a t i o n 14X D i s t a n c e a c r o s s d r y p a t c h , 1.6 mm o F i g u r e 27 F o r m a t i o n of a Dry P a t c h Re = 700, T • 9 C „„, . M a g n i f i c a t i o n 14X 27(e) t = 0.92s D i s t a n c e a c r o s s dry p a t c h , 1.2 mm 2 7 ( f ) t = 0.10s M a g n i f i c a t i o n 14X D i s t a n c e a c r o s s d r y p a t c h , 2.0 mm F i g u r e 27 F o r m a t i o n of a Dry P a t c h Re = 700, T = 9°C 27(g) t = 0.104s M a g n i f i c a t i o n 14X D i s t a n c e a c r o s s d r y p a t c h , 1.6 mm 27(h) t = 0.128s M a g n i f i c a t i o n 14X D i s t a n c e a c r o s s d r y p a t c h , 1.5 mm F i g u r e 27 F o r m a t i o n of a Dry P a t c h Re = 700, T = 9 C 27(1) t = 0.140s M a 9 n i f i c a t i o n 14X D i s t a n c e a c r o s s d r y p a t c h , 1 . 6 mm 27(j) t • 0.148s M a g n i f i c a t i o n 14X Distance across dry patch, 2.1 mm F i g u r e 27 F o r m a t i o n of a Dry P a t c h Re = 700, T = 9°C 27(k) t = 0.168s M a g n i f i c a t i o n 14X D i s t a n c e a c r o s s d r y p a t c h , 1.9 mm 27(m) t = 0.212s M a g n i f i c a t i o n 1 4 x D i s t a n c e a c r o s s d r y p a t c h 1.2 mm F i q u r e 27 F o r m a t i o n o f a Dry P a t c h Re = 700, T = 9°C T T T 0-3 Profile at Edge of Dry Patch (stationary) R e = 1 8 5 q . 5500 W / m 2 T = 2°C P = 3.62 MPa (525 P s i a ) 0 2 E E JC o 0-1 Direction of Flow » 0 0 4 8 s 0.2 0-4 0.6 0.8 1.0 Distance From Edge , mm F i g u r e 28 F i l m P r o f i l e s T = 2°C Re = 185 ro o 60 50 40 30 5 20 Stationary Dry Patch Re = 185 T = 2 °C P = 3.62 MPa(525psia) Q = 5 500 W/m2 10 0 - L _L 0 6 8 10 Time, s xlO 2 12 14 16 18 20 F i g u r e 29 Contact Angle V a r i a t i o n with Time T :. 2°C Re = 185 : - • £ — — r — — , 1 — i 1 T 1—"—I 1 r 1.2 -1.1 1.0 _ Re = 310 R Reced ing T = 2°C A A d v a n c i n g 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 D I S T A N C E F R O M E D G E m m F i g u r e 30 F i l m P r o f i l e T = 2°C Re = 310 ro ro C O N T A C T A N G L E , D E G R E E S o Ul • o INS o IS} Ul CO o CO Ul o Ul Ul o 1 1 1 1 1 1 1 1 T I • o ro P" C fD i-3 O O II D rf ro cu o n > fD vQ P " II fD U> < 'p* C" O p-CU rr P-0 £ p-rt-00 IS} IS} P3 P-3 fD > -4 (/) H > H O z > o < Z 9 o z — o z o o m '</> CO O -0 H II II II (t» II - » CO IS> is} » O £ O " ° =- ° "0 3 "« IS} is> Ul TJ (A "CO J I I I L E E </> (fl 0) C J£ U IE 0*4 0'5 0-6 Distance From Edge, m m F i g u r e 32 F i l m P r o f i l e T = 9°C Re = 420 60 50 in a a 4 0 c < 8 c 30 20 S ta t i ona ry Dry Patch Re=420 T = 9 °C P = 4 . 3 M P a ( 6 2 5 P s i a ) Q = 15 800 W / m 2 10 6 Time , s *10 F i g u r e 33 C o n t a c t A n g l e V a r i a t i o n w i t h Time T = 9°C Re = 420 ro 126 34(a) t = 0.0s M a g n i f i c a t i o n 12X D i s t a n c e a c r o s s d r y p a t c h 1.5 mm (34(b) t = 0.047s M a g n i f i c a t i o n 12X F i g u r e 34 F o r m a t i o n o f a Dry P a t c h T * 2°C Re = 185 34(c) t = 0.094s M a g n i f i c a t i o n 12X Distance across dry patch 2.3 mm 34(d) t = 0.140s M a g n i f i c a t i o n 12X F i g u r e 34 Formation of a Dry Patch T = 2°C Re = 185 1.2 1.0 £ E 8 9) C u 5 0.8 0.6 Stat ionary Dry Patch Re= 9 4 0 T = 2 ° C P = 3 6 2 MPa ( 5 2 5 ps ia ) Q m 6 3 6 0 0 W / m 2 0.4 02 0 .0 0 0 0 5 s . 0 0 0 1 6 S •0 0 0 2 6 s O 0.1 0-2 0.3 OA 0-5 0.6 0.7 0-8 0.9 Distance From Edge , m m F i g u r e 35 F i l m P r o f i l e T" = 2°C Re = 940 ro co 60 50 4» <B >_ Ol a> Q O) c < (J c o u 40 30 20 Stationary Dry Patch Re-940 T = 2°C P = 3.62 MPa (525 psia) Q=63600 w/m2 10 0 0 6 Time , s x 103 F i g u r e 36 C o n t a c t A n g l e V a r i a t i o n w i t h Time T = 2°C Re = 940 Re=700 T = 9°C P = 4 2 MPa(610 ps ia ) Q = 25600 W / m 2 Distance From Edge , mm F i g u r e 37 F i l m P r o f i l e T = 9°C Re = 700 1 0 C O N T A C T A N G L E D E G R E E S c CO oo o II D rr IX) OJ on O rt .fD I—1 II fD -J < O OJ o 1-1 H -OJ rt H ' O D rt-h-3 fD H 3 m X co Re = 1080 T = 9 C P = 4 . 2 M P a ( 6 1 0 P s i a ) Q = 53 ,200 W / m 2 • .0 .021 s , A 0 .007 s , A 0.3 0 . 4 0 .5 0.6 0.7 D I S T A N C E F R O M EDGE . m m 0.8 0.9 F i g u r e 39 F i l m P r o f i l e T = 9 ° C Re = 1080 60 L 50 (/> a> £ O) <b a 40 a> c < 30 o a C o o 20 10 Re =1080 T= 9°C P= 4-2 M P a (610 psia) Q= 53200 W / m 2 0.5 1.0 1.5 2-0 2.5 3 0 T i m e , s x 1 0 2 3-5 4 0 4.5 F i g u r e 40 C o n t a c t A n g l e V a r i a t i o n w i t h Time T = 9°C Re = 1080 r-i CO CO I 1 1 1 1 ' I 1 1 I 1.2 . Re=750 T=13 °C 1-0 _ P=48 MPa (70O psia) Q=24 300W/m2 0-8 I Distance From Edge , mm F i g u r e 41 F i l m P r o f i l e T = 13°C Re = 750 Re =750 T = 13 °C P = 4.8 MPa(700psia) Q = 24 300 W/m 2 6 8 10 Time , s x io 3 12 14 16 18 F i g u r e 42 C o n t a c t A n g l e V a r i a t i o n w i t h Time T = 13°C Re = 750 1.2 L 1.0 L Re=885 T=13 °C P=4-8 MPa (700 psia) Q=31 800 w/m2 0-8 E E </> </> a> c JC u IE 0-6 0-4 0.2 0134 S, A Distance From Edge, mm F i g u r e 43 F i l m P r o f i l e T = 13°C Re = 885 137 LO 00 E •H En sz 4-> •H C O •H 4-> fO •H (fl CO > II <u ,H 0) c < u -P o U m fd r-t 4-) C II o U H (D S-j Z3 •H 60 L 50 40 (A 9) « at 9) a a Ul c < 30 u «5 •4-c o o 20 Re=750 T = 18 °C P= 5 5MPa(800psia) Qr 24 300 W/m 2 Stationary Dry P a t c h 10 0 J 0 Time , s xio 3 F i g u r e 46 C o n t a c t A n g l e V a r i a t i o n w i t h Time • T = 18°C Re = 750 Lo 1-2 L 1-0 0-8 Re=1055 T= 18°C P = 55 MPa (800 psia) Q = 65 600 W/m2 £ E in in 9) c _< o Z 0.6 L 0-4 L 0.2 L 0 .0 0067s, A # 0 0 1 2 S , S Distance From Edge , mm F i g u r e 47 F i l m P r o f i l e T = 18°C Re = 1055 o 141 0) £ •H H x: 4-> •H c o •H rO i n •H i n SH > o II 01 r H OJ c < • u -PO u co c o u CO OJ SH D VH s a a j 6 d Q ' d | 6 u v p e » u c o F i g u r e 50 Vapor P r e s s u r e of C 0 2 H i i f * O J 0 0 4 L 0 1 I I I , , , , , - 2 0 - 1 5 - 1 0 - 5 F i g u r e 51 0 5 10 15 20 25 30 35 Temperature , °c D e n s i t y of. S a t u r a t e d C 0 2 Vapor F i g u r e 52 D e n s i t y of L i q u i d CO2 300 L 250 200 150 100 L Temperature , °C F i g u r e 54 L a t e n t Heat of CQ2 F i g u r e 55 Thermal C o n d u c t i v i t y of CO Temperature , °C F i g u r e 56 S u r f a c e T e n s i o n of L i q u i d CO2 676 672 6-68 6-64 CM + CM c I Q. 6.60 X = 6328 A • A=546lA 6-56 Lorenz-Lcrentz Equation for C02 652 k p (n2+2) ( n 2 - l ) p , gm/c m 3 6 48 O 01 02 0.3 0-4 0-5 P2 06 07 08 0-9 10 F i g u r e 57 L o r e n z - L o r e n t z E q u a t i o n f o r C 0 2 en O 151 F i g u r e 58 V a l v e C a l i b r a t i o n I n s e r t 152 F i g u r e 59 L i q u i d J e t Used For C a l i b r a t i o n F i g u r e 64 System Geometry F i l t e r F i lm P l a n e Hi 158 REFERENCES 1. F i r m a n , E. C., Gardner, G. G., C l a p p , R. M. "A Review of the A p p l i c a t i o n of B o i l i n g Heat T r a n s f e r Develop-ments t o P l a n t P roblems", P r o c e e d i n g s , I n s t . Mech. Eng. 180, p i , 1965-66. 2. 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Eng. 49, p412, 1971. 29. D u k l e r , A. E., B e r g e l i n , 0. P. " C h a r a c t e r i s t i c s of Flow i n F a l l i n g L i q u i d F i l m s " , Chem. Eng. P r o g r e s s , 43, p 557, 1952. 30. T a i l b y , S. R., P o r t a l s k i , S. "The Hydrodynamics o f L i q u i d F i l m s F l o w i n g on V e r t i c a l S u r f a c e s " , T r a n s . I n s t . . Chem. Eng., 38, p324, 1960. 31. C a s t e l l a n a , F. S., B o n i l l a , C. F. " V e l o c i t y Measure-ments and The C r i t i c a l R e y n o l d s Number f o r Wave I n i t i -a t i o n i n F a l l i n g F i l m Flow", ASME, 70 - HT - 32, 1970. 32. Rotem, Z., Hauptmann, E. G. "Dryout i n U n i f o r m l y Heated Round Tubes U s i n g C0~ as a Working F l u i d " , P r o -g r e s s R e p o r t , O ct. - Dec. 1970, Dept. Mech. Eng., U n i v e r s i t y o f B r i t i s h C o lumbia, Dec. 1970. 33. Hauptmann,.E. G., Lee, V., McAdam, D. W. "Two-Phase M o d e l l i n g o f t h e C r i t i c a l Heat F l u x " , P r o c . T h i r d Canadian Congress of A p p l i e d Mechanics, May 1971. 34. Green, J , R. "F o r c e d C o n v e c t i o n Heat T r a n s f e r from a C y l i n d e r i n S u p e r c r i t i c a l Carbon D i o x i d e " , MASc T h e s i s , Dept. Mech. Eng., U n i v e r s i t y of B r i t i s h C o l -umbia, 1970. 35. M a r l y , A. H., E l - S h i r b i n i , A. A., Mu r g a t r o y d , W. "The E f f e c t of Waves on the M o t i o n of the T r i p l e -Phase' F r o n t of a Dry P a t c h Formed i n a T h i n M o t i -v a t e d L i q u i d F i l m " , I n t . J Heat and Mass T r a n s f e r , 17, p l l 4 1 , 1974. 36. H e w i t t , G. F., Ke a r s e y , H. A., Lacey, P. M. C , P u l -l i n g , D. J.- "Burnout and F i l m F l o w i n t h e Evapora-t i o n o f Water i n Tubes", P r o c . I n s t . Mech. Eng., 180 p206, 1965-66. 161 37. P h i l l i p s , P. "The R e l a t i o n Between the R e f r a c t i v -i t y and D e n s i t y o f Carbon D i o x i d e " , P r o c . R o y a l Soc. o f London,' 97, p225, ( 1 9 2 0 ) . 38. M i c h e l s , A., Harmer, J.,"The E f f e c t o f P r e s s u r e on Re-f r a c t i v e Index of Carbon D i o x i d e " , P h y s i c a , 4, p995, 1937. 39. H e w i t t , D..M., Pad, M. V.,. K u l o o r , N . R., H u g g i l l , J.A., "Thermodynamic F u n c t i o n s o f Gases", B_utterworths S c i e n t i -f i c P u b l i c a t i o n s , F. Din E d i t o r , London, 1956. 40. Quinn, E. L., "The S u r f a c e T e n s i o n of L i q u i d - C a r b o n D i o x -i d e " , J . o f A p p l i e d C h e m i s t r y , 49, p2704, 1927. 41. H e w i t t , G. F., H a l l - T a y l o r , N. S., " A n n u l a r Two-Phase Flow", Pergammon P r e s s , 1970. 42. Thompson, T. S., " R e w e t t i n g o f a Hot S u r f a c e " I n t e r -n a t i o n a l .Heat T r a n s f e r C o n f e r e n c e , Tokyo, 1974. APPENDIX A Properties of Carbon Dioxide 163 APPENDIX P r o p e r t i e s o f Carbon D i o x i d e i P r o p e r t i e s of l i q u i d carbon d i o x i d e a r e r e q u i r e d t o compare e x p e r i m e n t a l ' r e s u l t s w i t h a n a l y t i c a l models. The p r o p e r t i e s of CO^ are r e a d i l y a v a i l a b l e and have been p l o t t e d i n F i g u r e s (53 to 6 0 ) . A l l v a l u e s - h a v e been con-v e r t e d t o S. I . u n i t s . The r e f r a c t i v e i n d e x o f CC^ was c a l c u l a t e d from the L o r e n z - L o r e n t z r e l a t i o n s h i p between r e f r a c t i v e i n d e x and d e n s i t y . n 2 - 1 1 = c o n s t a n t - K? T ( A l ) n 2 + 2 P T h i s r e l a t i o n s h i p has been found t o be t r u e w i t h i n e x p e r i m e n t a l l i m i t s even w i t h t h e l a r g e change i n d e n s i t y e n c ountered between l i q u i d and va p o r . P h i l l i p s (37) s t a t e s t h a t t h e v a l u e o f K f o r water and water v a -por d i f f e r s by l e s s than 1% a t t h e same wa v e l e n g t h . The i n v e r s e of t h e L o r e n z - L o r e n t z r e l a t i o n s h i p ( /Kjj^) has been 2 p l o t t e d a g a i n s t P i n F i g u r e ( 5 7 ) . T h i s f i g u r e was ta k e n from (3.7) and d a t a o f M i c h e l s and Harmer (38) has been i n -c l u d e d . M i c h e l s and Harmer c a l c u l a t e d f o r d e n s i t i e s up t o 1.186 gm/cm^ and te m p e r a t u r e s t o 100°C and t h e i r d a t a shows t h a t t h e e f f e c t o f tem p e r a t u r e on a t p r e s -s u r e s up t o 100 atmospheres i s v e r y s m a l l . T h e i r d a t a f o r r e f r a c t i v e i n d e x a t 100°C and 25°C f o r a wavelength of 5676 A* has been i n c l u d e d i n F i g u r e (57) and the d i f f e r e n c e i s s m a l l . P h i l l i p s c a l c u l a t e d K from the measured v a l u e i_f JL-i of r e f r a c t i v e i n d e x a t 34°C and w i t h t h i s c a l c u l a t e d n a t 0°C and 1 atmosphere. H i s r e s u l t s agreed w i t h v a l u e s o f n measured by o t h e r s and i n d i c a t e s t h a t t h i s method can be used t o c a l c u l a t e r e f r a c t i v e i n d e x knowing a n <^ P* The v a l u e o f K ( a c t u a l l y 1/K ) a t t h e wavelength of the l a s e r l i g h t s o u r c e (6328 S)was found a t d i f f e r e n t d e n s i t i e s by i n t e r p o l a t i n g between wavelengths of 5876 R and 6678 8. T h i s c u r v e has been p l o t t e d i n F i g u r e ( 5 7 ) . P r o p e r t y v a l u e s a t t h e te m p e r a t u r e s used i n t h e p r e s e n t e x p e r i m e n t s a r e t a b u l a t e d i n T a b l e A l . The CC>2 used i n the p r e s e n t e x p e r i m e n t s was 99.9% pure. The main i m p u r i t i e s a r e 0^ and N^i w i t h a maximum combined l e v e l of 0.1%. The maximum a l l o w a b l e o i l c o n t e n t i s 10 ppm a l t h o u g h the s u p p l i e r s t a t e s t h a t t h e i r CC>2 i s o i l f r e e . Water c o n t e n t can be 50 ppm maximum. P r o p e r t y v a l u e s were o b t a i n e d from (37, 38, 39 and 4 0 ) . T a b l e A l P r o p e r t i e s o f CO^ . Temperature 2°C 9°C 13°C 18°C p ^  gm/cm3 0.91 0 . 8 6 5 0.84 0 .795 P v gm/cm3 • 0.104 ' 0.13 0 . 1 5 0 . 1 8 ]i j Pa. s 9.45(10~ 5) 8.45(10~ 5) 7 . 8 5 ( 1 0 ~ 5 ) 6.95(10~ 5) 2 v m /s 1.04(10~7) 9 . 7 K 1 0 - 8 ) 9 . 2 9 ( 1 0 ~ 8 ) 8.74(10" 8) cr ' N/m 4 . 2 5 ( 1 0 " 3 ) 3 . 0 5 ( 1 0 " 3 ) 2.4(10~ 3) 1 . 6 5 ( 1 0 - 3 ) A k J / k g 227 202 187 162.5 k l W/m°C 10 . 8 C 1 0 " 2 ) 9.95C10" 2) 9.45C10" 2) 8 . 7 ( 1 0 ~ 2 ) do N 8T m K - 0.167C10" 3) -0.163C10 - 3) - 0 . 1 5 8 C 1 0 " 3 ) -0.142C10" 3) • n l 1 . 2125 1.2019 1 . 1959 1 . 1 8 5 1 n V 1 . 030 1 . 0296 1 .0342 1.0411 cn APPENDIX B C a l i b r a t i o n of Flow C o n t r o l V a l v e APPENDIX B Cali b r a t i o n of Flow Control Valve Flow over the plate was controlled by a Nupro Metering valve with micrometer graduations on the handle. The valve was calibrated by measuring the height of a c o l -umn of CO2 r i s i n g from a tube at di f f e r e n t valve openings. Height was related to the v e l o c i t y of the jet emerging from the tube and from th i s , Reynolds number was calculated. The glass plate test section was replaced with a special insert Figure (62) which held the i n l e t tube so that i t pointed upwards. The jet of l i q u i d emerging from the tube was observed through one of the observation ports in the test section holder and height of r i s e was measured with a scale fixed behind the j e t . Figure (63) shows a column of l i q u i d r i s i n g from the tube. A very steady c o l -umn of l i q u i d could be obtained. Calib r a t i o n tests were done with the valve opening and clos i n g . Valve c a l i b r a t i o n curves at di f f e r e n t temperatures are shown in Figures (60 -63) . It was not possible to go down to exactly zero flow. At very low flows (below Re = 150) the height of the jet was too small to read accurately (less than 1 mm) although l i q u i d could be seen emerging from the tube. At these low flows, with the test section i n s t a l l e d > t h e plate did not completely wet but a r i v u l e t ran down the middle. No r e a d i n g s were taken under t h e s e c o n d i t i o n s so t h a t c a l i -b r a t i o n a t v e r y low f l o w s was not n e c e s s a r y . Reynolds number was c a l c u l a t e d d i r e c t l y from the h e i g h t o f r i s e from, Re = _r_ = P£ CD At /2cjh~ • ( B l ) ja taw tube d i s c h a r g e c o e f f i c i e n t , (= 0.98) a r e a of t u b e , h = h e i g h t of j e t r i s e , m 'D Tube d i s c h a r g e c o e f f i c i e n t was taken as 0.98. Reynolds number based on tube d i a m e t e r was l e s s than 14 000 i n d i c a t i n g a d i s c h a r g e c o e f f i c i e n t c l o s e t o 1. APPENDIX C Relation Between Angle of Refraction and Intensity Variation APPENDIX C R e l a t i o n Between A n g l e of R e f r a c t i o n and I n t e n s i t y V a r i a t i o n The r e l a t i o n s h i p between the a n g l e o f r e f r a c -t i o n a t t h e c u r v e d l i q u i d s u r f a c e and i n t e n s i t y v a r i a t i o n g i v e n i n S e c t i o n 4.3, as a = t a n - 1 B ( I - I ) o where B i s a c o n s t a n t depending on t h e l i g h t ' s o u r c e , f o -c a l l e n g t h s , graded f i l t e r c h a r a c t e r i s t i c s and o p t i c a l s e t up. The d i f f e r e n c e i n i n t e n s i t y I - I Q ^ s ^ d i f f e r e n c e between the o p t i c a l d e n s i t y between r e f r a c t -ed l i g h t and l i g h t p a s s i n g through the dry r e g i o n of t h e p l a t e , measured a t t h e f i l m p l a n e . T h i s d i f f e r e n c e i n o p t i c a l d e n s i t y i s measured w i t h a m i c r o d e n s i t o m e t e r and the s l o p e of the l i q u i d s u r f a c e i s found w i t h E q u a t i o n (4.6) o r (4.7) knowing the system c o n s t a n t B. The system c o n s t a n t i s found as d e s c r i b e d i n S e c t i o n (4.5) but i t can be shown t h a t i t i s a f u n c t i o n of the o p t i c a l s e t up and i s a c o n s t a n t f o r any p a r t i c -u l a r s e t up. R e f e r r i n g t o F i g u r e (64) and comparing s i m i -l a r t r i a n g l e s a + h. b + h. 2 + Y Y or. a + h. b + h. f 2 + Y S i m i l a r l y , or. fzA Y a. b 1 Y f 2 + Y E q u a t i n g CI and C2 a. b a + h, b + h. ab + ah„ = ab + bh. b * h 2 2 + Y h = h ( f2 + Y ) Y And, from F i g u r e 24 X t a n a S u b s t i t u t i n g i n C3 g i v e s 4 - «, ho f„ + Y tan ct = _2 , 2 . X Y The s h i f t at the graded f i l t e r , h 2 , can be found from i n t e n s i t y measurements a t t h e f o c a l p l a n e , and the f i l -t e r c h a r a c t e r i s t i c s . I n t e n s i t y at t h e f i l m p l a n e i s g i v e n by where: Q = i n t e n s i t y o f t h e l i g h t s o u r c e ( l u m e n s / u n i t area) m = m a g n i f i c a t i o n f 2 = f o c a l l e n g t h o f t h e 2nd s c h l i e r e n l e n s . When a f i l t e r i s i n s e r t e d a t the f o c a l l e n g t h o f the second s c h l i e r e n l e n s , i n t e n s i t y a t t h e f i l m p l a n e i s reduced t o I = (•• C6 where t i s t h e t r a n s m i s s i v i t y of t h e f i l t e r . S i n c e t h e f i l t e r used was a l i n e a r l y graded f i l t e r t r a n s m i s s i v i t y i s g i v e n by + t o C7 k f i l t e r c h a r a c t e r i s t i c (mm ) h 2 d i s t a n c e l o n g the f i l t e r (mm) t = t r a n s m i s s i v i t y c o r r e s p o n d i n g t o the u n d e f l e c t e d beam ( i . e . , a t x = 0 ) . assuming t h e f i l t e r i s i n s t a l l e d " l i g h t end" up. Then, f o r the u n d e f l e c t e d beam, a p p l y i n g Equa-t i o n C6 and E q u a t i o n C5 I = t C8 o i o where C l = ^ 2 2 Fo r the d e f l e c t e d beam C, (kh„ + t ). C9 1 2. o Then &I = I - I C l k h 2 + C l fco " C l fco C 1 k h 2 and h„_ &I CIO c a k S u b s t i t u t i n g f o r h^ i n E q u a t i o n C5 g i v e s a r e -l a t i o n f o r the angl e o f r e f r a c t i o n , a , i n terms of s y s -tem c h a r a c t e r i s t i c s and i n t e n s i t y measured a t t h e f i l m p l a n e . or tan a B Ai C l l f 2 + Y where B = ^ m Since voltages proportional to intensity were used B must be multiplied by a conversion factor so that tan a = B AE C12 Note that the constant B, Equation C12 would have a d i f f e r e n t value than that in C l l . Then, tan 1 B A'E and this can be used with Equation (4.7) to f i n d the slope on' the l i q u i d surface. APPENDIX D E f f e c t of Heat T r a n s f e r Through t h e P l a t e Heat i s t r a n s f e r r e d from t h e s u r f a c e o f t h e g l a s s p l a t e b oth i n t o the l i q u i d f i l m and i n t o the g l a s s p l a t e . The r e l a t i v e magnitude of heat t r a n s f e r r e d t o the f i l m and heat t r a n s f e r r e d t h rough t h e p l a t e i s g i v e n by the B i o t number ( B i = hm/k) where h i s the heat t r a n s f e r c o e f f i c i e n t , m i s the t h i c k n e s s of the g l a s s p l a t e (m = 3 mm) and k i s the t h e r m a l c o n d u c t i v i t y of t h e g l a s s (k = 0.03 W/m °C). The B i o t number f o r the s e c o n d i t i o n s i s g i v e n by B i = hm k 0.1 h. The heat t r a n s f e r c o e f f i c i e n t can be e s t i m a t e d from e q u a t i o n s g i v e n i n ( 3 9 ) . D e f i n i n g a heat t r a n s f e r c o e f f i c i e n t based on the temperature d i f f e r e n c e a c r o s s the f i l m , then h = k1 , DI 5 f o r a l i n e a r t emperature p r o f i l e . I f f i l m t h i c k n e s s i s c a l c u l a t e d . w i t h E q u a t i o n (2.15) w i t h Re = 185, T = 2°C the heat t r a n s f e r c o e f f i c i e n t i s 1300 W/m2 °C. The heat t r a n s f e r c o e f f i c i e n t found from E q u a t i o n DI u s i n g a meas-176 "'i ured f i l m thickness of 0.1 mm>-is 1100 W/m2 °C. Hewitt and Hall-Taylor (41) state that waves increase the heat transfer c o e f f i c i e n t by about 20% and th i s has not been considered. Biot number under these conditions i s 130, indicating that heat transferred into the f i l m i s much greater' than heat transferred into the plate. Heat flux can then be' found d i r e c t l y from voltage readings and no correction i s needed to account for heat transferred through the plate. The loca l heat transfer c o e f f i c i e n t can be estimated for turbu-lent flow using graphs of heat transfer c o e f f i c i e n t plotted against Reynolds number in (41). Local heat transfer coef-f i c i e n t at Re = 310, T = 2°C was estimated to be 1700 W/m2 °C. The Biot number i s then 170 indicating that heat transfer, through the plate i s not a s i g n i f i c a n t factor. C r i t i c a l heat flux was an average based on the area of the plate. It i s possible that l o c a l variations occurred because of variations in thickness of the heating f i l m . A thickness v a r i a t i o n would be indicated by dry patches always forming in one region of the plate. At low Reynolds numbers drying occurred p r e f e r e n t i a l l y from one side of the plate but thi s did not occur a l l the time. At high Reynolds numbers dry patches occurred randomly on the plate. While there may have been some l o c a l variations in heat flux because of v a r i -ations in heating f i l m thickness i t i s f e l t that t h i s does not have a s i g n i f i c a n t effect on the r e s u l t s . Thompson (42) s t a t e s t h a t r e w e t t i n g i s an a x i a l -c o n d u c t i o n - c o n t r o l l e d phenomenon and r e w e t t i n g r a t e i s i n v e r s e l y p r o p o r t i o n a l t o v o l u m e t r i c heat c a p a c i t y , temp-e r a t u r e o f the d r y s u r f a c e and t h e r m a l c o n d u c t i v i t y of the p l a t e . Thermal c o n d u c t i v i t y of t h e heated s u r f a c e i s i m p o r t a n t o n l y i f the t h i c k n e s s i s l e s s than some c r i t -i c a l t h i c k n e s s which i s .a f u n c t i o n of t h e r m a l c o n d u c t i v i t y , dry r e g i o n s u r f a c e t e m p e r a t u r e and ambient p r e s s u r e . No attempt was made t o measure r e w e t t i n g r a t e o r t h e e f f e c t of p l a t e t h i c k n e s s on r e w e t t i n g i n t h e p r e s e n t e x p e r i m e n t s . The e f f e c t o f p l a t e t h i c k n e s s c o u l d be determined by u s i n g d i f f e r e n t t h i c k n e s s of p l a t e and r e w e t t i n g r a t e ( t h e v e l o c -i t y o f t h e a d v a n c i n g l i q u i d edge) c o u l d be d e t e r m i n e d from the movie f i l m s of a d r y p a t c h r e w e t t i n g . Publ icat ions and Presentations 1. "Sulphur Hexafluoride - Its Properties and Use as a Gaseous Insulator in Van de Graaff Acce lerator s " , P.G. Ashhaugh, D. W. McAdam, M.F. James; I.E.E.E. Trans, on Nuclear Science, Vol . NS-12(3), pp. 266-269, 1965. 2. "Configuration Factors fo r Greenhouses", D.W. McAdam, A.K. Khatry, M. Iqbal; Trans. American Society of Agr i cu l tu ra l Engineers, Vol. 14(6), pp. 1068-1072, 1971. 3. "Two-Phase F lu id Modelling of the C r i t i c a l Heat Flux" E. G. Hauptmann, V. Lee, D.W. McAdam; Proc. 3rd Canadian Congress of Applied Mechanics, Calgary, A lberta, 1971. 4. "Two-Phase Modelling of the C r i t i c a l Heat F lux " , E.G. Hauptmann, V. Lee, D.W. McAdam; Proc. A.N.S. Conference on Reactor Heat Transfer, October 1973, Karlsruhe, West Germany. 5. Measurement of L iquid Fi lm P r o f i l e and Contact Angle in a Fa l l i n g F i lm, D.W. McAdam, E.G. Hauptmann, Western Canada Heat Transfer Conference, May 1974. 

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