UBC Theses and Dissertations

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UBC Theses and Dissertations

Diffusiophoresis under turbulent conditions Whitmore, Peter John 1976

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DIFFUSIOPHORESIS UNDER TURBULENT CONDITIONS by PETER JOHN WHITMORE B . S c , V i c t o r i a U n i v e r s i t y , W e l l i n g t o n , New Z e a l a n d , 1965 B.E., U n i v e r s i t y o f C a n t e r b u r y , C h r i s t c h u r c h , New Z e a l a n d , 1967 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e Department of CHEMICAL ENGINEERING We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 19 76 © P e t e r John Whitmore, 19 76 In p resent ing t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the 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 fo r reference and study. I f u r t h e r agree t h a t permiss ion for e x t e n s i v e copying of 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 granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l ga in s h a l l not be a l lowed without my w r i t t e n p e r m i s s i o n . Depa rtment The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 ABSTRACT T h i s t h e s i s d e s c r i b e s both t h e o r e t i c a l and experimental s t u d i e s o f d i f f u s i o p h o r e s i s , which i s the movement of a e r o s o l p a r t i c l e s when they are suspended i n a d i f f u s i n g gas mixture. The phenomenon was s t u d i e d under c o n d i t i o n s of t u r b u l e n t flow. P r e v i o u s workers have demonstrated the e f f i c a c y of d i f f u s i o p h o r e s i s i n c o n t i n u o u s l y removing p a r t i c l e s of the order of one micron (10 m) i n diameter from laminar gas streams. Such p a r t i c l e s are d i f f i c u l t t o remove by c o n v e n t i o n a l gas c l e a n i n g techniques. However, any i n d u s t r i a l a p p l i c a t i o n would probably r e q u i r e t h a t the gas be i n t u r b u l e n t flow, t o enable l i m i t a t i o n o f the equipment t o an economic s i z e . T h i s o b s e r v a t i o n p r o v i d e s the r a t i o n a l e f o r the c u r r e n t work, which can be d i v i d e d i n t o f o u r major p a r t s . The f i r s t p a r t i s the d e r i v a t i o n o f an e x p r e s s i o n f o r the d i f f u s i o p h o r e t i c v e l o c i t y o f a l a r g e p a r t i c l e ( i . e . , a p a r t i c l e whose r a d i u s i s l a r g e compared to the mean f r e e path of the gas) i n an undisturbed d i f f u s i n g gas mixture. The continuum mechanics' equations were s o l v e d i n a more r i g o r o u s manner than was h i t h e r t o a v a i l a b l e . P r e v i o u s d e r i v a t i o n s a l l i m p l i e d the e x i s t e n c e o f d i f f u s i o n s l i p a t the p a r t i c l e s u r f a c e , but t h i s was shown t o contravene the law of energy c o n s e r v a t i o n . With z e r o s l i p , t h e p a r t i c l e was f o u n d t o a d o p t t h e mean mass v e l o c i t y o f t h e f l u i d . T h i s r e s u l t , w h i c h was u s e d i n s u b s e q u e n t t h e o r y , d i f f e r s f r o m t h o s e o f e a r l i e r w o r k e r s . T h e s e c o n d p a r t i n v o l v e s t h e d e v e l o p m e n t o f a t h e o r y t o p r e d i c t t h e d i f f u s i o p h o r e t i c p a r t i c l e r e m o v a l c a u s e d b y d i f f u s i o n a l m a s s t r a n s f e r f r o m a m u l t i c o m p o n e n t g a s s t r e a m . Two s e p a r a t e d e r i v a t i o n s w e r e m a d e , t h e m o r e r i g o r o u s o f w h i c h i s b a s e d s o l e l y o n t h e n o n - s t e a d y - s t a t e f o r m s o f t h e c o n t i n u i t y e q u a t i o n s f o r t h e p a r t i c l e s a n d f o r t h e g a s m i x t u r e . I t i s t h e r e f o r e i n d e p e n d e n t o f t h e p a t t e r n s o f m a s s t r a n s f e r o r g a s f l o w . T h e o r e t i c a l p r e d i c t i o n s w e r e d e r i v e d f o r t h r e e p o s s i b l e v a l u e s o f t h e l o c a l p a r t i c l e v e l o c i t y . T h e s e w e r e t h e l o c a l mean m a s s v e l o c i t y o f t h e f l u i d , t h e l o c a l mean m o l a r v e l o c i t y , a n d a v e l o c i t y s u g g e s t e d b y S c h m i t t a n d W a l d m a n n ( 1 9 6 0 ) . T h e t h i r d p a r t c o n s i s t s o f e x p e r i m e n t a l s t u d i e s o f p a r t i c l e r e m o v a l b y d i f f u s i o p h o r e s i s f r o m t u r b u l e n t g a s s t r e a m s . A b i n a r y g a s m i x t u r e c o n t a i n i n g a e r o s o l p a r t i c l e s was p a s s e d u p t h r o u g h a w e t t e d w a l l c o l u m n ( 0 . 0 2 5 4 m I . D . a n d 0 . 7 7 m i n l e n g t h ) c o u n t e r c u r r e n t t o a f l o w o f w a t e r . One c o m p o n e n t was i n s o l u b l e , w h i l e t h e o t h e r was p a r t i a l l y a b s o r b e d . T h e r e s u l t i n g p a r t i c l e r e m o v a l was d e t e r m i n e d b y m e a s u r i n g t h e i n l e t a n d o u t l e t a e r o s o l n u m b e r c o n c e n t r a t i o n s i n t h e g a s . T h e s o l u b l e g a s e s t e s t e d w e r e a m m o n i a a n d t r i m e t h y l a m i n e , w h i l e t h e i n s o l u b l e g a s e s w e r e h e l i u m m e t h a n e , n i t r o g e n , a r g o n , a n d f r e o n 12 ( d i c h l o r o d i f l u o r o m e t h a n e ) . U n i f o r m l a t e x p a r t i c l e s o f 0 . 5 0 , 0 . 7 9 , 1 . 0 1 1 , 2 . 0 2 , a n d 5 . 7 m i c r o n s i n d i a m e t e r w e r e u s e d . T h e K n u d s e n n u m b e r s f o r t h e p a r t i c l e s r a n g e d f r o m 0.015 t o 0 . 3 0 . The e x p e r i m e n t a l r e s u l t s i n d i c a t e d t h a t t h e t h e o r y r e l a t i n g p a r t i c l e r emoval t o gas mass t r a n s f e r was s u b s t a n t i a l l y c o r r e c t . However, none o f t h e t h e o r e t i c a l p r e d i c t i o n s based on t h e t h r e e v e l o c i t y e x p r e s s i o n s agreed w i t h t h e e x p e r i m e n t a l r e s u l t s f o r e v e r y c a s e . I t was c o n c l u d e d t h a t t h i s was because the p a r t i c l e d i a m e t e r s were s u f f i c i e n t l y c l o s e t o t h e mean f r e e p a t h o f t h e gas t h a t t h e p a r t i c l e s f e l l i n t o t h e t r a n s i t i o n r e gime, i n w h i c h none of the v e l o c i t y e x p r e s s i o n s a p p l y p r e c i s e l y . The f o u r t h p a r t i s a p r e l i m i n a r y i n v e s t i g a t i o n i n t o the p r a c t i c a l a p p l i c a t i o n o f d i f f u s i o p h o r e s i s f o r removing p a r t i c u l a t e m a t t e r from i n d u s t r i a l gas s t r e a m s . The i m p o r t a n c e o f the type o f equipment and the gases employed was d e monstrated. I t was c o n c l u d e d t h a t d i f f u s i o p h o r e s i s used a l o n e would n o t be economic e x c e p t i n s p e c i a l c i r c u m s t a n c e s , b u t t h a t i t might be v a l u a b l e when used i n c o n j u n c t i o n w i t h o t h e r removal mechanisms. TABLE OF CONTENTS ;Page ABSTRACT PREFACE LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENTS C h a p t e r INTRODUCTION 1 1 1 .1 P r e a m b l e 1 1 .2 P a r t i c l e R e m o v a l f r o m I n d u s t r i a l G a s e s 2 1 . 3 T h e P r e s e n t S t u d y 4 1 . 3 . 1 O b j e c t i v e s 4 1 . 3 . 2 M e t h o d s a n d S c o p e 4 2 LITERATURE REVIEW 9 2 . 1 E a r l y Work 9 2 . 2 S m a l l P a r t i c l e s 10 2 . 3 L a r g e P a r t i c l e s 14 2 . 4 T h e o r i e s E n c o m p a s s i n g t h e T r a n s i t i o n R e g i m e 22 I i v x i x i i i x v i i i v C h a p t e r P a g e 2 . 5 C o n t i n u u m E q u a t i o n s 24 2 . 6 E x p e r i m e n t s u n d e r N o n - t u r b u l e n t C o n d i t i o n s 25 2 . 7 D i f f u s i o p h o r e s i s u n d e r T u r b u l e n t C o n d i t i o n s 28 2 . 8 R e v i e w A r t i c l e s 32 3 FUNDAMENTAL THEORY 33 3 . 1 O u t l i n e 33 3 . 2 T h e C o n t i n u u m M e c h a n i c s E q u a t i o n s 3 3 3 . 3 D e t e r m i n a t i o n o f t h e F r e e P a r t i c l e V e l o c i t y 41 3 . 4 T h e R a t e o f E n e r g y D i s s i p a t i o n 45 3 . 5 F u r t h e r R e f i n e m e n t s a n d A d d i t i o n s 48 3 . 5 . 1 N o n - S t e a d y S t a t e B e h a v i o u r 48 3 . 5 . 2 A S e c o n d O r d e r A p p r o x i m a t i o n f o r P a r t i c l e V e l o c i t y 50 3 . 5 . 3 P a r t i c l e V e l o c i t y i n a B i n a r y Gas M i x t u r e w i t h One S t a g n a n t C o m p o n e n t 53 3 . 6 C o n c l u s i o n s 54 4 DERIVED THEORY 55 4 . 1 T h e F i l m T h e o r y 55 4 . 2 T h e G e n e r a l C a s e 61 4 . 3 D i s c u s s i o n o f T h e o r y 71 5 EXPERIMENTAL APPARATUS AND PROCEDURE 73 5 . 1 G e n e r a l 7 3 v C h a p t e r P a g e 5 . 2 A p p a r a t u s 78 5 . 2 . 1 T h e A b s o r p t i o n S y s t e m 7 8 5 . 2 . 2 W e t t e d W a l l C o l u m n D e s i g n 79 5 . 2 . 3 Gas a n d L i q u i d S u p p l y S y s t e m s 84 5 . 2 . 4 A e r o s o l G e n e r a t i o n 86 5 . 2 . 5 A e r o s o l P a r t i c l e C o u n t e r 86 5 . 2 . 6 Gas A n a l y s e r 91 5 . 3 P r e l i m i n a r y P r o c e d u r e 92 5 . 3 . 1 R o t a m e t e r C a l i b r a t i o n 9 2 5 . 3 . 2 P a r t i c l e C o n t e n t o f G a s e s 9 3 5 . 3 . 3 C o l u m n T r i a l s 9 3 5 . 3 . 4 T e s t s f o r L i q u i d P h a s e M a s s T r a n s f e r R e s i s t a n c e 93 5 . 4 O p e r a t i o n P r o c e d u r e 94 5 . 4 . 1 C o u n t e r C a l i b r a t i o n f o r P a r t i c l e S i z e 94 5 . 4 . 2 C o u n t e r C a l i b r a t i o n f o r G a s C o m p o s i t i o n 9 5 5 . 4 . 3 P r e p a r a t i o n f o r a n E x p e r i m e n t a l Run 9 6 5 . 4 . 4 S a m p l i n g 9 8 5 . 4 . 5 P a r t i c l e R e m o v a l i n t h e A b s e n c e o f D i f f u s i o p h o r e s i s 100 5 . 4 . 6 I s o k i n e t i c S a m p l i n g 100 5 . 5 D e s i g n o f E x p e r i m e n t s 101 6 RESULTS AND D I S C U S S I O N 1 0 3 6 . 1 T h e D a t a 10 3 6 . 2 G e n e r a l T r e n d s 10 5 6 . 3 A c c u r a c y a n d E r r o r s 107 6 . 3 . 1 G e n e r a l 107 v i C h a p t e r P a g e 6 . 3 . 2 Random E r r o r s 108 6 . 3 . 3 S y s t e m a t i c E r r o r s 10 8 6 . 4 S t a t i s t i c a l A n a l y s i s 115 6 . 5 D e t a i l e d A n a l y s i s 122 6 . 5 . 1 H e l i u m - A m m o n i a 122 6 . 5 . 2 M e t h a n e - A m m o n i a 123 6 . 5 . 3 N i t r o g e n - A m m o n i a , P r e l i m i n a r y D a t a 123 6 . 5 . 4 N i t r o g e n - A m m o n i a , S h o r t C o l u m n D a t a 124 6 . 5 . 5 N i t r o g e n - A m m o n i a 12 4 6 . 5 . 6 A r g o n - A m m o n i a 125 6 . 5 . 7 F r e o n 1 2 - A m m o n i a 125 6 . 5 . 8 N i t r o g e n - T r i m e t h y l a m i n e 126 6 . 6 F u r t h e r D i s c u s s i o n 127 7 P R A C T I C A L A P P L I C A T I O N 149 7 . 1 G e n e r a l 149 7 . 2 I n v e s t i g a t i o n s b y O t h e r s 150 7 . 3 O p t i m a l V a p o u r U s e 150 7 . 4 O p e r a t i n g C o s t C a l c u l a t i o n 157 7 . 5 R e d u c t i o n o f H e a t R e q u i r e m e n t s 158 7 . 6 M u l t i p l e R e m o v a l M e c h a n i s m s 161 7 . 7 I n t e r a c t i o n s b e t w e e n M e c h a n i s m s 162 8 SUMMARY AND C O N C L U S I O N S 166 8 . 1 F u n d a m e n t a l T h e o r y 166 8 . 2 D e r i v e d T h e o r y 16 7 8 . 3 E x p e r i m e n t a l W o r k 16 8 8 . 4 P r a c t i c a l A p p l i c a t i o n 169 v i i Page NOMENCLATURE 171 REFERENCES 176 APPENDICES A ROTAMETER CALIBRATION DATA 180 B COLUMN MASS TRANSFER MODEL 186 B . l D e s c r i p t i o n 186 B. 2 C a l c u l a t i o n and R e s u l t s 188 C DATA ANALYSIS AND SAMPLE CALCULATIONS 191 C l Source of Sample Data 191 C. 2 Reduction of Raw Data 191 C.3 Counter C a l i b r a t i o n f o r Gas Composition 19 2 C.4 C a l c u l a t i o n Methods 194 C.4.1 General 194 C.4.2 The Input Data 194 C.4.3 C a l c u l a t i o n of Gas Mixture P r o p e r t i e s 206 C.4.4 C a l c u l a t i o n of the P a r t i c l e Removal E f f i c i e n c y 20 8 C.4.5 C a l c u l a t i o n o f the T h e o r e t i c a l Values f o r the P a r t i c l e Removal E f f i c i e n c y 208 C.4.6 C a l c u l a t i o n of Other Parameters 209 C.4.7 The Computed R e s u l t s 211 C.5 E r r o r A n a l y s i s 212 D TABULATED RESULTS 217 v i i i APPENDICES P a 9 e E STATISTICAL ANALYSIS 269 E . l G e n e r a l P o s i t i o n o f Data 269 E.2 T r a n s i t i o n Regime B e h a v i o u r and I n e r t i a l D e p o s i t i o n 269 ix LIST OF TABLES T a b l e P a g e I P u r c h a s e d E q u i p m e n t 76 I I G a s e s a n d P a r t i c l e s 77 I I I W e t t e d W a l l C o l u m n D e s i g n P a r a m e t e r s 81 I V E s t i m a t e o f S y s t e m a t i c E r r o r s 113 V C o m p a r i s o n o f D a t a w i t h T h e o r e t i c a l M o d e l s 116 V I E n h a n c e m e n t o f P a r t i c l e C a p t u r e 151 b y V a p o u r C o n d e n s a t i o n V I I V a p o u r R e q u i r e m e n t s t o A t t a i n 9 5% P a r t i c l e R e m o v a l 156 V I I I K e y t o C a l c u l a t i o n P r o g r a m N o m e n c l a t u r e 196 I X L i s t i n g o f C a l c u l a t i o n P r o g r a m 199 X P h y s i c a l P r o p e r t i e s o f G a s e s a t 1 a t m . a n d 20 ° C 205 X I D a t a f o r H e , N H 3 , 0.790 M i c r o n D i a m e t e r P a r t i c l e s 218 X I I D a t a f o r C H 4 , N H 3 , 0.790 M i c r o n D i a m e t e r P a r t i c l e s 220 X I I I D a t a f o r N 2 , N H 3 , 0.790 M i c r o n D i a m e t e r P a r t i c l e s - P r e l i m i n a r y Runs 222 x Table Page X I V Data for N 2, NH3, 0.790 Micron Diameter P a r t i c l e - Short Column 2 2 5 XV Data for N 2, NH3, 0.500 Micron Diameter P a r t i c l e s 227 X V I Data for N 2, NHo, 0.790 Micron Diameter P a r t i c l e s 2 2 9 X V I I Data for N 2, NH3, 1.011 Micron Diameter P a r t i c l e s 238 X V I I I Data for N 2, NH3, 2.020 Micron Diameter P a r t i c l e s - Series 1 241 X I X Data for N 2, NH3, 2.020 Micron Diameter P a r t i c l e s - Series 2 2 4 3 XX Data for Ar, NH3, 0.790 Micron Diameter P a r t i c l e s 246 X X I X X I I Data of CF 2C1 2 (Freon 12), NH3, 0.790 Micron Diameter P a r t i c l e s Data for CF 2C1 2 (Freon 12), NH3, 1.011 Micron Diameter P a r t i c l e s 249 253 X X I I I Data for CF 2C1 2 (Freon 12), NH3, 2.020 Micron Diameter P a r t i c l e s 255 X X I V Data for N 2, N(CH3) 3 (Trimethylamine), 0.500 Micron Diameter P a r t i c l e s 257 XXV Data for N 2, N(CH 3) 3 (Trimethylamine), 0.790 Micron Diameter P a r t i c l e s 259 X X V I Data for N 2, N(CH 3) 3 (Trimethylamine), 1.011 Micron Diameter P a r t i c l e s 2 6 1 X X V I I Data for N 2, N(CH3) 3 (Trimethylamine), 2.020 Micron Diameter P a r t i c l e s 264 X X V I I I Data for N 2, N(CH 3) 3 (Trimethylamine), 5.700 Micron Diameter P a r t i c l e s 2 6 8 x i LIST OF FIGURES F i g u r e Page 3.1 C o o r d i n a t e systems. 34 5.1 G e n e r a l view o f t h e equipment. 74 5.2 C l o s e u p view o f the w e t t e d w a l l columns. 75 5.3 Wetted w a l l column d e s i g n - t o p . 82 5.4 Wetted w a l l column d e s i g n - base. 83 5.5 Gas and l i q u i d s u p p l y systems. (Only one column shown.) 85 5.6 E l e c t r o n m i c r o g r a p h o f 0.50 m i c r o n d i a m e t e r l a t e x p a r t i c l e s . M a g n i f i c a t i o n 30,000 X. 87 5.7 E l e c t r o n m i c r o g r a p h o f 0.79 m i c r o n d i a m e t e r l a t e x p a r t i c l e s . M a g n i f i c a t i o n 10,000 X. 87 5.8 E l e c t r o n m i c r o g r a p h o f 1.011 m i c r o n d i a m e t e r l a t e x p a r t i c l e s . M a g n i f i c a t i o n 10,000 X. 88 5.9 E l e c t r o n m i c r o g r a p h o f 2.02 m i c r o n d i a m e t e r l a t e x p a r t i c l e s . 88 M a g n i f i c a t i o n 10,000 X. 5.10 E l e c t r o n m i c r o g r a p h o f 5.7 m i c r o n d i a m e t e r l a t e x p a r t i c l e s . M a g n i f i c a t i o n 3,000 X. 89 x i i R e s u l t s f o r h e l i u m , a m m o n i a , 0.79 m i c r o n d i a m e t e r p a r t i c l e s . I n l e t f l o w o f t r a n s f e r r e d g a s h e l d c o n s t a n t a t 6.0 x 10-4 m 3 / s e c . R e s u l t s f o r m e t h a n e , a m m o n i a , 0.79 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 5.98 x 1 0 ~ 4 m 3 / s e c . R e s u l t s f o r n i t r o g e n , a m m o n i a , 0.79 m i c r o n d i a m e t e r p a r t i c l e s - s h o r t c o l u m n . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 6.0 x 10"4 m 3 / s e c . R e s u l t s f o r n i t r o g e n , a m m o n i a , 0.50 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 6.0 x 10 _4 m 3 / s e c . R e s u l t s f o r n i t r o g e n , a m m o n i a , 0.79 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 6.0 x 10 m 3 / s e c . R e s u l t s f o r n i t r o g e n , a m m o n i a , 0.79 m i c r o n d i a m e t e r p a r t i c l e s . I n l e t f l o w r a t e o f t r a n s f e r r e d g a s h e l d c o n s t a n t a t 11.6 x I O - 4 m 3 / s e c . R e s u l t s f o r n i t r o g e n , a m m o n i a , 0.79 m i c r o n d i a m e t e r p a r t i c l e s . I n l e t g a s c o m p o s i t i o n h e l d c o n s t a n t a t 50 v% n i t r o g e n . R e s u l t s f o r n i t r o g e n , a m m o n i a , 1.011 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 6.0 x 10 m 3 / s e c . R e s u l t s f o r n i t r o g e n , a m m o n i a , 2.02 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 6.0 x 10 -4 m 3 / s e c . x i i i R e s u l t s f o r a r g o n , a m m o n i a , 0.79 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 5.6 x 1 0 - 4 mVsec. R e s u l t s f o r f r e o n 12 ( C F 2 C I 2 ) , a m m o n i a 0.79 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 0.98 x I O - 4 m 3 / s e c . R e s u l t s f o r f r e o n 12 ( C F 2 C I 2 ) / a m m o n i a 1.011 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 0.98 x I O - 4 m 3 / s e c . R e s u l t s f o r f r e o n 12 ( C F 2 C I 2 ) , a m m o n i a 2.0 2 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 0.98 x I O - 4 m 3 / s e c . R e s u l t s f o r n i t r o g e n , t r i m e t h y l a m i n e (N ( C H 3 ) 3 ),0.50 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 6.0 x I O - 4 m 3 / s e c . R e s u l t s f o r n i t r o g e n , t r i m e t h y l a m i n e (N (CH3) 3) , 0 . 79 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 6.0 x 1 0 - 4 m 3 / s e c . R e s u l t s f o r n i t r o g e n , t r i m e t h y l a m i n e (N (CH3) 3) , 1.011 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 6.0 x 1 0 - 4 m 3 / s e c . R e s u l t s f o r n i t r o g e n , t r i m e t h y l a m i n e (N (CH3) 3 ) , 2 . 02 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 6.0 x 1 0 - 4 m 3 / s e c . R e s u l t s f o r n i t r o g e n , t r i m e t h y l a m i n e (N (CH3) 3), 5.7 m i c r o n d i a m e t e r p a r t i -c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t 6.0 x 1 0 - 4 m 3 / s e c . xiv Gas t r e a t m e n t i n a s t a g e w i s e p r o c e s s . C a l i b r a t i o n c u r v e s f o r w a t e r and 32 w c a u s t i c soda s o l u t i o n i n the Brooks l i q u i d r o t a m e t e r . L i q u i d c o n d i t i o n s -2 0°C and a p p r o x i m a t e l y 1 atmosphere. C a l i b r a t i o n c u r v e s f o r n i t r o g e n i n th e B rooks i n e r t gas r o t a t m e t e r . Gas c o n d i t i o n s - 4.40 atmospheres and 20°C. C a l i b r a t i o n c u r v e f o r car b o n d i o x i d e i n t he s i z e 3 G i l m o n t t r a n s f e r r e d gas r o t a m e t e r . Gas c o n d i t i o n s -1 atmosphere and 20°C. C a l i b r a t i o n c u r v e f o r carbon d i o x i d e i n t he s i z e 4 G i l m o n t t r a n s f e r r e d gas r o t a m e t e r . Gas c o n d i t i o n s -1 atmosphere and 20°C. C a l i b r a t i o n c u r v e f o r ammonia i n the Brooks t r a n s f e r r e d gas r o t a m e t e r . Gas c o n d i t i o n s - 1 atmosphere and 20°C. E f f e c t o f l i q u i d r a t e on o u t l e t gas c o m p o s i t i o n . C a l i b r a t i o n c o r r e c t i o n r a t i o f o r n i t r o g e n , ammonia, 0.79 m i c r o n d i a m e t e r p a r t i c l e s . The t r i a n g l e s denote mean v a l u e s f o r a g i v e n mole f r a c t i o n . xv ACKNOWLEDGEMENTS I w i s h t o t h a n k my s u p e r v i s o r , D r . A x e l M e i s e n , who d e v o t e d many h o u r s t o o u r d i s c u s s i o n s , a n d made h e l p f u l a n d c o n s t r u c t i v e s u g g e s t i o n s t h r o u g h o u t t h e c o u r s e o f t h i s w o r k . T h a n k s a r e a l s o d u e t o o t h e r p e o p l e i n t h e D e p a r t m e n t o f C h e m i c a l E n g i n e e r i n g who h a v e g i v e n me a d v i c e a n d a s s i s t a n c e ; i n p a r t i c u l a r , t h e p r e s e n t a n d f o r m e r s t a f f o f t h e w o r k s h o p a n d s t o r e s , who h e l p e d me t o c o n s t r u c t t h e e x p e r i m e n t a l e q u i p m e n t a n d m a i n t a i n i t i n a n o p e r a t i o n a l s t a t e . T h e m a n u s c r i p t was t y p e d b y C h r i s t i n e F o n g , w h o s e w o r k i s much a p p r e c i a t e d . I w o u l d l i k e t o t h a n k t h e N a t i o n a l R e s e a r c h C o u n c i l , t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , a n d t h e G o v e r n m e n t o f B r i t i s h C o l u m b i a f o r f i n a n c i a l a s s i s t a n c e . F i n a l l y , a t t h i s p o i n t I w o u l d l i k e t o a c k n o w l e d g e t h e p a s t h e l p f r o m my p a r e n t s a n d t e a c h e r s , a n d t o t h a n k my w i f e J i l l f o r h e r s u p p o r t a n d f o r t h e c o n f i d e n c e s h e h a s s h o w n i n me t h r o u g h o u t t h i s s t u d y . x v i PREFACE I have t r i e d i n t h i s work to make a contribution to the general understanding of diffusiophoresis, rather than concentrating only on some s p e c i f i c problem. I hope that, by orienting t h i s study i n a p r a c t i c a l d i r e c t i o n , I have also produced some information of value i n the control of particulate emissions i n gas streams. Peter Whitmore Vancouver July, 1976 xvii 1. Chapter 1 INTRODUCTION 1.1 Preamble •f When an a e r o s o l p a r t i c l e i s suspended i n an i s o t h e r m a l o d i f f u s i n g gas m i x t u r e , i t e x p e r i e n c e s a f o r c e which causes i t t o move. T h i s phenomenon i s termed d i f f u s i o p h o r e s i s . The f o r c e a r i s e s because t h e gas m o l e c u l e s bombard t h e p a r t i c l e w i t h d i f f e r -e n t masses and v e l o c i t i e s . The analogous movement o f a p a r t i c l e suspended i n a gas th r o u g h w h i c h h e a t i s b e i n g conducted i s c a l l e d t hermophores!s, and the two phenomena o f t e n o c c u r t o g e t h e r . D i f f u s i o p h o r e s i s p l a y s a r o l e i n v a r i o u s n a t u r a l p r o -c e s s e s such as a e r o s o l c a p t u r e d u r i n g the f o r m a t i o n and growth o f r a i n d r o p l e t s due t o d i f f u s i o n o f water vapour. A n o t h e r example i s t h e movement o f d u s t p a r t i c l e s i n the l u n g d u r i n g the t r a n s f e r o f oxygen, c a r b o n d i o x i d e , and wa t e r vapour. The n a t u r e o f t h e d i f f u s i o p h o r e t i c e f f e c t depends on An a e r o s o l i s a s o l i d o r l i q u i d d i s p e r s e phase l o c a t e d i n a c o n t i n u o u s gas phase medium. The term a e r o s o l p a r t i c l e i s n o r m a l l y r e s e r v e d f o r p a r t i c l e s l e s s than 1 mm i n d i a m e t e r . 2. the s i z e o f the p a r t i c l e r e l a t i v e t o t h e mean f r e e p a t h o f t h e s u r r o u n d i n g gas m o l e c u l e s . (Mean f r e e p a t h s o f common gases a re of t h e o r d e r o f 0.05 ym^ under ambient c o n d i t i o n s ) . Throughout t h i s work p a r t i c l e s w i l l be d e s c r i b e d as " l a r g e " o r " s m a l l " a c c o r d i n g t o t h i s c r i t e r i o n . D i f f e r e n t laws have been found t o govern t h e m o t i o n o f p a r t i c l e s o f t h e s e two t y p e s , and t h o s e t h a t f a l l i n t o t h e i n t e r m e d i a t e t r a n s i t i o n regime. 1.2 P a r t i c l e Removal from I n d u s t r i a l Gases I n many m a t e r i a l s - h a n d l i n g and:-processing o p e r a t i o n s t h e e f f l u e n t gases c o n t a i n suspended p a r t i c l e s . The d i s c h a r g e o f t h e s e p a r t i c l e s t o t h e atmosphere sometimes r e p r e s e n t s an economic l o s s t o t h e p r o c e s s . F u r t h e r m o r e , i t can have unde-s i r a b l e e n v i r o n m e n t a l e f f e c t s , and hence may be r e g u l a t e d by law. I t i s t h e r e f o r e common p r a c t i c e t o attempt t o reduce the p a r t i c u l a t e l o a d i n g o f e f f l u e n t gases b e f o r e d i s c h a r g e . I n common gases and gas m i x t u r e s , a t p r e s s u r e s o f the o r d e r o f 1 atmosphere and.at t y p i c a l p r o c e s s t e m p e r a t u r e s , p a r t i c l e s g r e a t e r t h a n 500 ym i n di a m e t e r can u s u a l l y be removed e f f e c t i v e l y by g r a v i t a t i o n a l s e t t l i n g . F o r s m a l l e r p a r t i c l e s methods based on i n e r t i a l s e p a r a t i o n a r e o f t e n used. S t a n d a r d c y c l o n e s can c o l l e c t p a r t i c l e s down to. about 10 um, h i g h e f f i c i e n c y c y c l o n e s t o 5 um, and v a r i o u s t y p e s o f wet s c r u b b e r s as low as 0.5 ym. 1 ym = 10 m However, s i n c e i n e r t i a l e f f e c t s depend b a s i c a l l y on the square o: the p a r t i c l e d i a m e t e r , gas v e l o c i t i e s and hence power c o s t s must r i s e r a p i d l y as p a r t i c l e s i z e d e c r e a s e s , i n o r d e r t o m a i n t a i n a g i v e n removal e f f i c i e n c y . T h i s p l a c e s an economic l i m i t on t h e use o f t h e s e d e v i c e s . P a r t i c l e s s m a l l e r t h a n 0.1 ym e x h i b i t s i g n i f i c a n t Brownian m o t i o n , and can t h e r e f o r e be removed by d i f f u s i o n a l d e p o s i t i o n i n s c r u b b e r s or f i l t e r s . These may a l s o be used t o remove l a r g e p a r t i c l e s by i n e r t i a l i m p a c t i o n and i n t e r c e p t i o n , b u t are o n l y e f f e c t i v e f o r p a r t i c l e s o f t h e o r d e r o f 1 ym a t the expense o f h i g h gas p r e s s u r e drop and power con-sumption. P a r t i c l e s w i t h d i a m e t e r s i n t h e range o f 0.1 t o 5 ym e x p e r i e n c e o n l y weak d i f f u s i o n a l and i n e r t i a l e f f e c t s , and are t h e r e f o r e o f t e n removed by e l e c t r o s t a t i c p r e c i p i t a t i o n . However the h i g h c o s t makes t h i s an e x p e n s i v e o p t i o n . A l s o , p a r t i c l e s w i t h low e l e c t r i c a l c o n d u c t i v i t i e s and gases t h a t a r e n o t r i c h i n e l e c t r o n e g a t i v e m o l e c u l e s cause o p e r a t i n g d i f f i c u l t i e s . There i s c o n s e q u e n t l y a need t o examine u n c o n v e n t i o n a l methods f o r s e p a r a t i n g m i c r o n - s i z e d p a r t i c l e s from gases. D i f f u s i o p h o r e s i s i s p o t e n t i a l l y a t t r a c t i v e f o r t h i s purpose because th e i n d u c e d p a r t i c l e v e l o c i t y i s l a r g e l y i ndepen dent of p a r t i c l e s i z e . S i n c e the mean f r e e pa t h s o f most common gases are o f the o r d e r o f 0.05 ym under ambient c o n d i t i o n s , p a r t i c l e s i n t h e 0.1 t o 5 ym range s h o u l d e x h i b i t t r a n s i t i o n o r l a r g e p a r t i c l e b e h a v i o u r . P u b l i s h e d e x p e r i m e n t a l s t u d i e s have demonstrated t h e e f f i c a c y o f d i f f u s i o p h o r e s i s i n removing p a r t i c l e s from l a m i n a r gas s t r e a m s , b u t p r a c t i c a l a p p l i c a t i o n 4. under t h e s e c o n d i t i o n s i s u n l i k e l y because o f the low mass t r a n s f e r rates of the vapour and>Jconsequent l a r g e c o l l e c t i n g s u r f a c e s r e q u i r e d . However, under t u r b u l e n t c o n d i t i o n s , h i g h mass t r a n s f e r r a t e s can be a c h i e v e d , and h i g h p a r t i c l e removal r a t e s s h o u l d be a t t a i n a b l e . 1.3 The P r e s e n t Study 1.3.1 O b j e c t i v e s The f o l l o w i n g o b j e c t i v e s were s e t f o r t h i s work: ( i ) The e x p e r i m e n t a l s t u d y o f d i f f u s i o p h o r e s i s under c o n d i t i o n s o f t u r b u l e n t gas f l o w , ( i i ) The development o f a t h e o r y t o e x p l a i n t h e r e s u l t s o b t a i n e d , ( i i i ) T e s t i n g o f t h e e x i s t i n g fundamental t h e o r y o f d i f f u s i o p h o r e s i s o v e r a w i d e r range o f v a r i a b l e s t h a n p r e v i o u s l y used, and d e v e l o p -ment o f a new fundamental t h e o r y i f r e q u i r e d , ( i v ) The s t u d y o f d i f f u s i o p h o r e s i s i n gas m i x t u r e s n o t p r e v i o u s l y used,and.in gas m i x t u r e s whose components have w i d e l y d i f f e r e n t m o l e c u l a r w e i g h t s . 1.3.2 Methods and Scope D i f f u s i o p h o r e s i s i s a s s o c i a t e d w i t h d i f f u s i o n i n gas m i x t u r e s due t o c o n c e n t r a t i o n g r a d i e n t s . Such g r a d i e n t s can be e s t a b l i s h e d by b r i n g i n g b i n a r y gas m i x t u r e s i n t o c o n t a c t w i t h 5. l i q u i d s o r s o l i d s f o r which one gas component has a h i g h a f f i n i t y . I n c h o o s i n g an e x p e r i m e n t a l system i t was d e s i r a b l e t h a t p a r t i c l e s borne t o the phase boundary n o t be r e - e n t r a i n e d , a n d t h a t the o p e r a -t i o n be e s s e n t i a l l y i s o t h e r m a l . I t was a l s o p r e f e r a b l e t h a t the a b s o r b e n t o r a d s o r b e n t be easy t o h a n d l e , o f low c o s t o r e l s e s i m p l e t o r e g e n e r a t e , and t h a t i t o f f e r low r e s i s t a n c e t o mass t r a n s f e r . F or t h e s e reasons s o l i d a d s o r b e n t s were r u l e d o u t , and a l l e x p e r i m e n t s were made u s i n g w a t e r as t h e a b s o r p t i o n medium. T h i s system was s i m p l e and a l l o w e d the e x p e r i m e n t a l o b j e c t i v e s t o be met. A w e t t e d w a l l column was chosen t o p e r f o r m the a b s o r p -t i o n o p e r a t i o n f o r the f o l l o w i n g main r e a s o n s : ( i ) S i m p l e c o n s t r u c t i o n , ( i i ) Mass t r a n s f e r a r e a and l i q u i d and gas v e l o c i t i e s a r e w e l l d e f i n e d compared t o most o t h e r t y p e s o f mass t r a n s f e r equipment, ( i i i ) I f t h e column i s c o n s t r u c t e d o f g l a s s , the b e h a v i o u r i n t h e i n t e r i o r can be o b s e r v e d , ( i v ) P a r t i c l e c a p t u r e due t o i n e r t i a l mechanisms s h o u l d be lower than i n equipment such as packed towers where sudden changes i n gas f l o w d i r e c t i o n o c c u r . The l a s t r e a s o n i s i m p o r t a n t i n a t t e m p t i n g t o s t u d y d i f f u s i o -p h o r e s i s i n i s o l a t i o n from o t h e r removal mechanisms. I n the e x p e r i m e n t , p a r t i c l e s were added t o an i n e r t (non-absorbable) gas s t r e a m u s i n g an a e r o s o l g e n e r a t o r . T h i s s t r e a m was t h e n mixed w i t h a s t r e a m o f t h e gas t o be t r a n s f e r r e d , 6. t o g i v e the r e q u i r e d f e e d c o m p o s i t i o n . As t h e r e s u l t i n g m i x t u r e f l o w e d up t h r o u g h the w e t t e d w a l l column, p a r t o f the gas was absorbed .and a f r a c t i o n o f t h e p a r t i c l e s were c o l l e c t e d i n t h e downflowing w a t e r . The i n l e t and o u t l e t gas streams were a n a l y s e d f o r gas c o m p o s i t i o n by O r s a t a n a l y s i s , and f o r p a r t i c l e concen-t r a t i o n u s i n g a c o m m e r c i a l l y a v a i l a b l e o p t i c a l c o u n t e r . The f r a c t i o n a l p a r t i c l e removal o b t a i n e d from t h e s e measurements c o u l d t h e n be r e l a t e d t o t h e change i n gas c o m p o s i t i o n i n t h e equipment. The f o l l o w i n g gas m i x t u r e s were used. I n e r t s p e c i e s T r a n s f e r r e d s p e c i e s h e l i u m ammonia methane ammonia n i t r o g e n ammonia argon ammonia f r e o n 12 ammonia ( d i c h l o r o d i f l u o r o m e t h a n e ) n i t r o g e n t r i m e t h y l a m i n e P a r t i c l e s o f d i a m e t e r 0.5, 0.79, 1.011, 2.02, and 5.7 ym were used. Once the fundamental t h e o r y g i v i n g t h e v e l o c i t y o f a p a r t i c l e i n an u n d i s t u r b e d d i f f u s i n g gas m i x t u r e i s known, a " d e r i v e d " t h e o r y r e l a t i n g p a r t i c l e removal t o mass t r a n s f e r r a t e i n the w e t t e d w a l l column can be d e v e l o p e d . Under l a m i n a r gas f l o w c o n d i t i o n s t h i s problem i s conceptually r e l a t i v e l y s i m p l e , s i n c e t h e continuum mechanics e q u a t i o n s c o m p l e t e l y d e f i n e the 7. system and a l l o w t h e p a r t i c l e v e l o c i t y t o be c a l c u l a t e d a t any p o i n t . However, i n p r a c t i c e i t i s e x c e e d i n g l y d i f f i c u l t s i n c e n o n - l i n e a r p a r t i a l d i f f e r e n t i a l e q u a t i o n s must be s o l v e d . F o r t u r b u l e n t f l o w s a n o t h e r approach must be used, s i n c e l o c a l c o n d i t i o n s i n the t u r b u l e n t c o r e are unknown. I n the o r i g i n a l d e r i v a t i o n made d u r i n g t h i s s t u d y , p a r t i c l e t r a n s f e r was t r e a t e d i n an analogous manner t o mass t r a n s f e r from a t u r -b u l e n t f l u i d t h r o u g h a l a m i n a r f i l m . T h i s approach was v e r y s a t i s f a c t o r y s i n c e i t a l l o w e d s e v e r a l v a r i a b l e s t o be e l i m i n a t e d and v e r y s i m p l e r e s u l t s t o be o b t a i n e d . The o r i g i n a l t h e o r y was not c o m p l e t e l y r i g o r o u s i n t h a t i t assumed the mass t r a n s f e r boundary l a y e r t o be l a m i n a r , when i n f a c t i t i s p a r t l y t u r b u l e n t . S u b s e q u e n t l y , however, a more p o w e r f u l t h e o r y , w h i c h d i d not r e q u i r e t h i s a s s u m p t i o n , was d e r i v e d by co m b i n i n g the gas and p a r t i c l e c o n t i n u i t y e q u a t i o n s . The new t h e o r y c o n f i r m e d t h e r e s u l t s o f the o r i g i n a l one, and showed them t o be t r u e r e g a r d l e s s o f c o n d i t i o n s i n t h e boundary l a y e r o r even i n t h e c o r e . Thus the improved t h e o r y h o l d s even f o r l a m i n a r f l o w . A l l p u b l i s h e d fundamental t h e o r i e s f o r t h e d i f f u s i o -p h o r e t i c v e l o c i t y o f a l a r g e p a r t i c l e i n an u n d i s t u r b e d d i f f u s i n g gas m i x t u r e e i t h e r i n v o k e the co n c e p t o f d i f f u s i o n s l i p a t the p a r t i c l e s u r f a c e d i r e c t l y , o r i m p l y i t s e x i s t e n c e by t h e i r r e s u l t s . D i f f u s i o n s l i p r e f e r s t o the non-zero v e l o c i t y o f a gas i n c o n t a c t w i t h a s o l i d s u r f a c e , w h i c h i s c l a i m e d t o a r i s e i n d i f f u s i n g systems. I t was d i f f i c u l t t o u n d e r s t a n d i n t u i t i v e l y how t h i s 8. s l i p c o u l d be p r e s e n t around a p a r t i c l e , and e v e n t u a l l y i t was found t h a t i t s e x i s t e n c e v i o l a t e d energy c o n s e r v a t i o n i n t h e system. T h i s r e v e l a t i o n l e d t o t h e development o f a new t h e o r y o f d i f f u s i o p h o r e s i s f o r l a r g e p a r t i c l e s . D i f f u s i o p h o r e s i s c o u l d be employed i n a p r a c t i c a l gas c l e a n i n g system e i t h e r e n t i r e l y on i t s own, o r e l s e t o enhance and/or supplement p a r t i c l e removal by o t h e r mechanisms. A p r e l i m i n a r y economic e v a l u a t i o n o f the former p o s s i b i l i t y r e q u i r e s not o n l y i n f o r m a t i o n on p a r t i c l e c o l l e c t i o n r a t e s , b u t a l s o knowledge o f t h e optimum method o f u s i n g t h e t r a n s f e r r e d vapour. T h i s i n v o l v e s q u e s t i o n s such as what vapour c o n c e n t r a -t i o n s t o use, whether t o adopt a s t a g e w l s e o p e r a t i o n , and whether t o attempt h e a t r e c o v e r y f o r f u r t h e r vapour g e n e r a t i o n . The o t h e r p o s s i b i l i t y , o f e m p l o y i n g d i f f u s i o p h o r e s i s t o g e t h e r w i t h o t h e r removal mechanisms, cannot be a s s e s s e d a t t h i s t i m e w i t h o u t more s p e c i f i c d e t a i l s , and a b e t t e r u n d e r s t a n d i n g o f how d i f f u s i o p h o r e s i s o p e r a t e s i n c o n j u n c t i o n w i t h t h e s e mechanisms. 9. C h a p t e r 2 LITERATURE REVIEW 2 . 1 E a r l y Work T h e f i r s t k n o w n r e p o r t o f t h e e x i s t e n c e o f d i f f u s i o -p h o r e s i s i s c o n t a i n e d i n t h e v o l u m i n o u s p a p e r b y A i t k e n (188 3) . He o b s e r v e d t h e f o r m a t i o n o f d u s t - f r e e s p a c e s n e x t t o m o i s t s u r f a c e s , a n d c o r r e c t l y a t t r i b u t e d t h e m t o t h e e v a p o r a t i o n o f w a t e r . H o w e v e r , h e made n o a t t e m p t t o f i n d a q u a n t i t a t i v e r e l a t i o n s h i p b e t w e e n t h e m a g n i t u d e o f t h e d u s t - f r e e s p a c e a n d e v a p o r a t i o n r a t e o r p a r t i c l e s i z e . D e r j a g u i n a n d D u k h i n ( 1 9 5 6 a , 1 9 5 6 b , 1957) p r e d i c t e d t h e e x i s t e n c e o f t h e e f f e c t t h e o r e t i c a l l y . T h e y w e r e a p p a r e n t l y u n a w a r e o f A i t k e n ' s e a r l i e r w o r k . T h e i r i n t e r e s t i n t h e f o r c e s b e t w e e n two e v a p o r a t i n g d r o p l e t s s e e m s t o h a v e l e d t h e m t o t h e r e a l i s a t i o n t h a t d i f f u s i n g g a s m i x t u r e s c a n c a u s e p a r t i c l e m o t i o n . I n i t i a l l y t h e y p o s t u l a t e d t h a t t h e p a r t i c l e a d o p t s t h e S t e f a n v e l o c i t y , t h a t i s t h e g a s mean mass v e l o c i t y w h i c h S t e f a n (1881) h a d s h o w n t o a r i s e i n d i f f u s i n g m i x t u r e s . L a t e r t h e y r e c o g n i z e d t h a t t h e p a r t i c l e b e h a v i o u r i s i n f l u e n c e d b y t h e K n u d s e n n u m b e r , K n , w h i c h i s t h e r a t i o o f g a s mean f r e e p a t h t o 10. p a r t i c l e r a d i u s . The v a l u e o f t h i s number can be used t o d e l i n e a t e t h e continuum (Kn << 1 ) , t r a n s i t i o n (Kn - 1 ) , and f r e e m o l e c u l e t (Kn >> 1) regimes ; and t h e p a r t i c l e s f a l l i n g i n t o t h e s e may be d e s c r i b e d as l a r g e , i n t e r m e d i a t e , o r s m a l l i n comparison t o the mean f r e e p a t h o f the gas. The f i r s t modern e x p e r i m e n t a l p r o o f o f the e x i s t e n c e o f d i f f u s i o p h o r e s i s was p r o v i d e d by F r e i s e (1957) and Facy (19 58a,: b) . These a u t h o r s a l s o appear t o have been unaware of A i t k e n ' s work. F r e i s e demonstrated t h e movement o f s m a l l p a r t i c l e s i n d i f f u s i n g l i q u i d s , and e s t i m a t e d t h a t they moved a t a p p r o x i m a t e l y t h e S t e f a n v e l o c i t y . Facy made some q u a l i t a t i v e s t u d i e s on the movement o f s m a l l p a r t i c l e s i n a i r near growing and e v a p o r a t i n g d r o p l e t s and a l s o a t t e m p t e d t o d e v e l o p t h e o r e t i c a l e x p r e s s i o n s f o r p a r t i c l e v e l o c i t y . He r e c o g n i z e d t h e importance o f Knudsen number, and by f o l l o w i n g the t e c h n i q u e E i n s t e i n (1924) had used t o d e r i v e an approximate t h e o r y f o r t h e r m o p h o r e s i s , he was a b l e t o deduce the g e n e r a l forms o f the v e l o c i t y e x p r e s s i o n s f o r s m a l l and l a r g e p a r t i c l e s . 2.2 S m a l l P a r t i c l e s The f i r s t comprehensive t h e o r y o f d i f f u s i o p h o r e s i s was In the continuum regime the gas properties can be regarded as continuous, whereas i n the free molecule regime the molecular behaviour becomes important. d e v e l o p e d by D e r j a g u i n and Bakanov (1957) f o r a s m a l l s p h e r i c a l p a r t i c l e . They used a m o l e c u l a r mechanics a p p r o a c h , and r e c o g n i z e d t h a t the v e l o c i t y d i s t r i b u t i o n o f m o l e c u l e s s t r i k i n g the p a r t i c l e c l o s e l y resembles t h a t i n the b u l k o f t h e gas. The d i s t r i b u t i o n o f the i n c i d e n t m o l e c u l e s can t h e r e f o r e be o b t a i n e d from t h e Chapman-Enskog f o r m u l a e , as g i v e n by Chapman and C o w l i n g (1964). By assuming s p e c u l a r ( i . e . e l a s t i c ) m o l e c u l e - p a r t i c l e c o l l i s i o n s , D e r j a g u i n and Bakanov were a l s o a b l e t o f i n d the v e l o c i t y d i s t r i b u t i o n of the r e b o u n d i n g m o l e c u l e s . The d i f f u s i o -p h o r e t i c v e l o c i t y was th e n c a l c u l a t e d by s e t t i n g t h e n e t momentum t r a n s f e r t o t h e p a r t i c l e e q u a l t o z e r o . Waldmann (1959) i n d e p e n d e n t l y c o n c e i v e d a s i m i l a r t h e o r y , b u t assumed (more r e a l i s t i c a l l y ) t h a t the m o l e c u l e -p a r t i c l e c o l l i s i o n s were p a r t l y s p e c u l a r and p a r t l y d i f f u s e . H i s e x p r e s s i o n f o r t h e d i f f u s i o p h o r e t i c v e l o c i t y o f a s m a l l p a r t i c l e l o c a t e d i n a b i n a r y gas m i x t u r e u n d e r g o i n g e q u i m o l a r *t" c o u n t e r - d i f f u s i o n i s (1 + £ e 2 ) /m2 - (1 + /n^ ( i + " J e ^ Y ^ + ( i + f e 2 ) y 2 / m ^ D ( V Y o ) I t i s u s u a l i n the l i t e r a t u r e t o e x p r e s s v e l o c i t i e s i n terms o f the c o n c e n t r a t i o n g r a d i e n t o f component 1. The s u b s c r i p t s "1" and "2" i n t h e remainder o f t h e e x p r e s s i o n would t h e n appear i n the r e v e r s e o r d e r t o t h a t g i v e n h e r e . However, t h e c o n v e n t i o n used i n t h i s work i s more c o n v e n i e n t when d e a l i n g w i t h multicomponent m i x t u r e s . Here m^, and are t h e m o l e c u l e mass, accomodation c o e f f i -c i e n t ( f r a c t i o n o f m o l e c u l e s r e f l e c t e d d i f f u s e l y from the s u r f a c e ) , and mole f r a c t i o n o f s p e c i e s i r e s p e c t i v e l y , D i s the gas d i f f u s i v i t y , and (Vy 2^ m i-s t n e c o n c e n t r a t i o n g r a d i e n t i n t h e u n d i s t u r b e d gas. The v e l o c i t y y_p i s measured here w i t h r e s p e c t t o the gas mean molar v e l o c i t y . L a t e r , S c h m i t t (1961) showed how the t h e o r y c o u l d be m o d i f i e d f o r t h e case where component 2 o f the gas d i f f u s e s t h r o u g h component 1 w h i c h i s s t a g n a n t . He found t h e p a r t i c l e v e l o c i t y measured w i t h r e s p e c t t o t h e s t a g n a n t component t o be (1 + v fP2 ) D (IY 2) (1 + 8*1^1' m 1 + (1 + 8 B2) Y 2 , 'm. Subsequent improvements i n the d i f f u s i o p h o r e t i c t h e o r y f o r s m a l l p a r t i c l e s have been m i n o r . Bakanov and D e r j a g u i n (19 60) p u b l i s h e d a n o t h e r t h e o r e t i c a l paper s i m i l a r t o t h e i r e a r l i e r one, but a l l o w e d f o r a temp e r a t u r e g r a d i e n t i n the gas. They improved t h e a c c u r a c y o f t h e a n a l y s i s by c a r r y i n g an e x t r a term i n the v e l o c i t y d i s t r i b u t i o n f u n c t i o n f o r the m o l e c u l e s . When r e w r i t t e n i n term o f common gas p r o p e r t i e s , and i f temperature e f f e c t s a r e i g n o r e d , t h e i r e x p r e s s i o n f o r e q u i m o l a r c o u n t e r - d i f f u s i o n becomes v ^2 "/ m l Y 1d ]_ + y 2d_. y,/m, + Y0vm, 2 O ^ Y - I Y 0'1'2 Yn/m-L + Y 2 / m 2 D(Vy 2) where d Q , d^ ^ and d _ 1 are parameters dependent on the gas p r o p e r t i e s T h e f i r s t t e r m a g r e e s w i t h W a l d m a n n ' s e x p r e s s i o n when t h e a c c o m m o -d a t i o n c o e f f i c i e n t s a r e u n i t y . T h e s e c o n d t e r m a r i s e s f r o m t h e u s e o f a b e t t e r a p p r o x i m a t i o n t o t h e d i s t r i b u t i o n f u n c t i o n , a n d i s o f t h e same o r d e r a s -a T/5 ( a n d e q u a l t o -a T/5 when m^ ^ a n d Y]_ << Y 2 o r Y 2 < < Y ^ ) • H o w e v e r , t h e t h e r m a l d i f f u s i o n t f a c t o r , a T , i s n o r m a l l y s m a l l , s o t h a t t h i s t e r m c a n u s u a l l y b e n e g l e c t e d . D e r j a g u i n a n d Y a l a m o v (1972) l a t e r p r e s e n t e d t h e t h e o r y i n g r e a t e r d e t a i l . T h e e s s e n t i a l f e a t u r e s o f t h e i r e x p r e s s i o n c a n b e e a s i l y s e e n i n t h e c a s e w h e r e t h e a c c o m m o d a t i o n c o e f f i c i e n t s a r e u n i t y ( w h i c h i s c l o s e t o r e a l i t y ) . v Y l / E l + Y 2 / E 2 Y l d l + Y 2 d - 1 1 + £ d 0 Y l Y 2 + Y 2 / m 2 D ( V j 2 ) I n c o m p a r i s o n w i t h B a k a n o v a n d D e r j a g u i n ' s (1960) r e s u l t , t h e T h e r m a l d i f f u s i o n t o s e p a r a t e when s u b j e c t e d t o t h e r m a l d i f f u s i o n f a c t o r i s a s e p a r a t i o n . i s t h e t e n d e n c y o f a g a s m i x t u r e a t e m p e r a t u r e g r a d i e n t ; a n d t h e c o n s t a n t r e l a t e d t o t h e r a t e o f 14. second term i s now m u l t i p l i e d by 1/(1 + ^ ) , i . e . 1/1.393, i n p l a c e o f t h e p r e v i o u s f a c t o r o f 1/2. Mason and Chapman (1962) r e d e r i v e d t h e t h e o r y by r e g a r d i n g t h e suspended p a r t i c l e as a l a r g e m o l e c u l e . They assumed a c o m b i n a t i o n o f s p e c u l a r r e f l e c t i o n , and d i f f u s e r e f l e c t i o n b u t a t unchanged speed. The f i n a l r e s u l t i s i d e n t i c a l t o Waldmann's e x c e p t t h a t t h e ^ f a c t o r m u l t i p l y i n g the accomo-d a t i o n c o e f f i c i e n t s i s r e p l a c e d by 4/9. 2.3 L a r g e P a r t i c l e The d e r i v a t i o n o f a s a t i s f a c t o r y t h e o r y f o r l a r g e p a r t i c l e s has proven much more d i f f i c u l t . For t h i s m o l e c u l a r regime one might t h i n k t h a t the continuum mechanics e q u a t i o n s would d e s c r i b e the system a d e q u a t e l y , and y i e l d a s o l u t i o n f o r t h e p a r t i c l e v e l o c i t y . However, i t has g e n e r a l l y been b e l i e v e d t h a t t h e s e e q u a t i o n s do not h o l d c l o s e t o the p a r t i c l e because o f t h e complex i n t e r a c t i o n s o f m o l e c u l e s w i t h t h e p a r t i c l e s u r f a c e and w i t h each o t h e r . I n t h i s case th e methods o f mole-c u l a r mechanics must be used h e r e . Nor i s the s o l u t i o n o f the continuum mechanics e q u a t i o n s t h e m s e l v e s s t r a i g h t f o r w a r d , s i n c e f l u i d p r o p e r t i e s are n o t c o n s t a n t i n d i f f u s i n g systems, and time-dependent terms are p r e s e n t . The work of Kramers and K i s t e m a k e r (1943) has had an i m p o r t a n t i n f l u e n c e on the subsequent development o f t h e o r y f o r l a r g e p a r t i c l e s . These a u t h o r s had p r e d i c t e d t h e o r e t i c a l l y t h a t 1 5 . when a b i n a r y g a s m i x t u r e d i f f u s e s p a r a l l e l t o a f l a t p l a n e o f i n f i n i t e e x t e n t , t h e v e l o c i t y o f t h e g a s i s n o t g e n e r a l l y z e r o a t t h e s u r f a c e ( o r m o r e s t r i c t l y o f t h e o r d e r o f o n e m e a n f r e e p a t h away f r o m t h e s u r f a c e ) . T h i s v e l o c i t y d i s c o n t i n u i t y t h e y t e r m e d d i f f u s i o n s l i p . K r a m e r s a n d K i s t e m a k e r ' s d e r i v a t i o n o f t h e s l i p v e l o c i t y i s b a s e d o n a momentum b a l a n c e i n t h e d i r e c t i o n o f d i f f u s i o n , f o r m o l e c u l e s a r r i v i n g a t a n d l e a v i n g t h e s u r f a c e . The n e t momentum t r a n s f e r t o t h e s u r f a c e i s t h e n s e t t o z e r o t o y i e l d . v s l i p m 2 " m i T i m , + y 0 m ' S -, 1 1 1 . T Y „ l l l „ / — , / — 1 1 '2 2 Y 1 ^ m 1 + y2*m2 dy. D dx w h e r e d Y 2 / d x i s t h e m o l e f r a c t i o n g r a d i e n t a l o n g t h e s u r f a c e . Two i m p o r t a n t s i m p l i f i c a t i o n s w e r e made i n t h e i r t r e a t m e n t . M a x w e l l i a m m e t h o d s w e r e a s s u m e d a d e q u a t e t o y i e l d a n a p p r o x i m a t e momentum b a l a n c e , a n d i n t e r a c t i o n s b e t w e e n i n c o m i n g a n d r e b o u n d i n g m o l e c u l e s n e a r t h e s u r f a c e w e r e i g n o r e d . L a t e r d e r i v a t i o n s o f s l i p v e l o c i t y a r e s i m i l a r , b u t a t t e m p t t o i m p r o v e o n t h e s e s i m p l i -f i c a t i o n s . A n i m p o r t a n t i m p l i c i t c o n d i t i o n , w h i c h i s n o t r e l a x e d i n l a t e r t r e a t m e n t s , i s t h a t t h e s h e a r s t r e s s o n t h e s u r f a c e i s z e r o . K r a m e r s a n d K i s t e m a k e r a l s o a t t e m p t e d t o d e t e c t s l i p e x p e r i m e n t a l l y . I n a w e l l - d e s i g n e d e x p e r i m e n t , a i r a n d h y d r o g e n w e r e a l l o w e d t o d i f f u s e i n o p p o s i t e d i r e c t i o n s t h r o u g h a c a p i l l a r y t u b e , a n d t h e r e s u l t i n g p r e s s u r e d r o p a c r o s s t h e t u b e was m e a s u r e d . 1 6 . U s i n g e l e m e n t a r y m e t h o d s o f f l u i d d y n a m i c s t h e y p r e d i c t e d t h a t t h e e x i s t e n c e o f s l i p w o u l d a p p r o x i m a t e l y h a l v e t h e p r e s s u r e d r o p a l o n g t h e t u b e c o m p a r e d t o t h a t w i t h o u t s l i p . T h e i r m e a s u r e m e n t s i n d i c a t e d t h a t t h e r e d u c t i o n i n p r e s s u r e d r o p was o f t h i s o r d e r , a n d t h e y t h e r e f o r e c o n c l u d e d t h a t s l i p e x i s t e d . T h e f i r s t c o m p l e t e d e r i v a t i o n o f a n e x p r e s s i o n f o r t h e d i f f u s i o p h o r e t i c v e l o c i t y o f a l a r g e p a r t i c l e was p r e s e n t e d b y S c h m i t t a n d W a l d m a n n ( 1 9 6 0 ) . T h e y s o l v e d t h e c o n t i n u u m m e c h a n i c s e q u a t i o n s s u b j e c t t o a b o u n d a r y c o n d i t i o n a t t h e p a r t i c l e s u r f a c e t h a t a l l o w s f o r t h e n o n - c o n t i n u u m b e h a v i o u r i n t h i s r e g i o n . T h e f o l l o w i n g s i m p l i f i e d f o r m s o f t h e c o n t i n u u m m e c h a n i c s e q u a t i o n s w e r e u s e d i n o r d e r t o f i n d t h e v e l o c i t y o f a s p h e r i c a l p a r t i c l e i n a b i n a r y g a s m i x t u r e u n d e r g o i n g e q u i m o l a r c o u n t e r - d i f f u s i o n : N a v i e r - S t o k e s (NS) T o t a l c o n t i n u i t y (TC) P a r t i a l c o n t i n u i t y (PC) T h e s e e q u a t i o n s h a v e a l s o b e e n u s e d i n m o s t l a t e r t h e o r i e s , a n d a d i s c u s s i o n o f t h e m i s d e f e r r e d t i l l l a t e r i n t h i s c h a p t e r . T h e b o u n d a r y c o n d i t i o n a t t h e p a r t i c l e s u r f a c e was o b t a i n e d b y r e p l a c i n g t h e g r a d i e n t i n K r a m e r s a n d K i s t e m a k e r ' s s l i p e x p r e s s i o n d Y 2 / ^ x ' b y t h e e q u i v a l e n t f o r m f o r a s p h e r e , ( 1 / r 6.^2/^) s - T h e v a l i d i t y o f t h i s s t e p i s i n d o u b t , b e c a u s e , w h i l e t h e s h e a r s t r e s s m i g h t v a n i s h f o r e q u i m o l a r c o u n t e r d i f f u s i o n o v e r a f l a t s u r f a c e , i t d o e s n o t v a n i s h f o r a c u r v e d s u r f a c e . T h e same t r a n s i t i o n was a l s o made b y l a t e r w o r k e r s . y V_ v = Vp V . v = 0 V 2 Y 2 = 0 F r o m t h e s o l u t i o n o f t h e p a r t i a l c o n t i n u i t y e q u a t i o n , S c h m i t t a n d W a l d m a n n w e r e a b l e t o e v a l u a t e t h e c o n c e n t r a t i o n g r a d i e n t a l o n g t h e p a r t i c l e s u r f a c e ^ d y ^ / d e ) , a n d t h u s f i n d t h e s l i p c o n d i t i o n a n d d e t e r m i n e t h e p a r t i c l e v e l o c i t y . v -P / m 2 - ^ 1 Y l / m 7 + Y 2 / S U J D ( v y 2 ) T h i s e x p r e s s i o n i n d i c a t e s t h a t t h e p a r t i c l e v e l o c i t y i s i n t h e same d i r e c t i o n , b u t i s a l w a y s s m a l l e r t h a n t h e mean m a s s v e l o c i t y o f t h e g a s m i x t u r e , n u - m. w = ' — D ( V Y o ) Y l m l + Y 2 m 2 2 " T h e mean m o l a r v e l o c i t y i s o f c o u r s e b y d e f i n i t i o n z e r o . T h e f a c t t h a t t h e p a r t i c l e v e l o c i t y d o e s n o t d e p e n d o n p a r t i c l e s i z e h a d b e e n d e d u c e d e a r l i e r b y F a c y (195 8 a ) . B r o c k (196 3) r e f i n e d t h e t h e o r y o f s l i p a t a f l a t s u r f a c e . He u s e d t h e C h a p m a n - E n s k o g e q u a t i o n s ( s e e C h a p m a n a n d C o w l i n g (1964)) t o a l l o w f o r t h e n o n - M a x w e l l i a n n a t u r e o f t h e g a s . T h e e f f e c t o f i n t e r a c t i o n s b e t w e e n i n c i d e n t a n d r e b o u n d i n g m o l e -c u l e s n e a r t h e s u r f a c e was a s s u m e d t o b e n e g l i g i b l e . H e n c e t h e s e e q u a t i o n s c o u l d b e u s e d t o c a l c u l a t e t h e i n c o m i n g m o l e c u l a r momentum. T o d e s c r i b e t h e b e h a v i o u r o f m o l e c u l e s l e a v i n g t h e s u r f a c e he i n t r o d u c e d M a x w e l l ' s e m p i r i c a l a c c o m m o d a t i o n c o e f f i c i e n t s . 1 8 . A f r a c t i o n o f o f t h e m o l e c u l e s o f s p e c i e s i r e a c h i n g t h e s u r -f a c e a r e a s s u m e d t o r e b o u n d d i f f u s e l y , a n d t h e r e m a i n d e r t o u n d e r g o s p e c u l a r c o l l i s i o n s . B r o c k ' s s l i p e x p r e s s i o n i s o f l i m i t e d u t i l i t y s i n c e i t c o n t a i n s a c c o m m o d a t i o n c o e f f i c i e n t s w h i c h c a n o n l y b e d e t e r m i n e d e x p e r i m e n t a l l y . H o w e v e r , a c c o r d i n g t o D e r j a g u i n a n d Y a l a m o v (19 72) t h e s e c o e f f i c i e n t s c a n b e a p p r o x i m a t e d a s u n i t y , i n w h i c h c a s e t h e e x p r e s s i o n b e c o m e s f o r b i n a r y g a s m i x t u r e s v s l i p m. mi ^ 2 - / m ^ Y l m l + Y 2 m 2 Vml + Y 2 / m 2 1 1 Y l d l + Y 2 d - 1 2 d 0 Y l Y 2 y1v/m^ + V2^™2 dy. D d x B r o c k d i s c u s s e s t h e f o r c e o n a p a r t i c l e i n a d i f f u s i n g s y s t e m f o r v a r i o u s c a s e s . H o w e v e r , i t i s m o r e i l l u s t r a t i v e t o g i v e a S c h m i t t a n d W a l d m a n n - t y p e s o l u t i o n f o r p a r t i c l e v e l o c i t y , u s i n g B r o c k ' s s l i p e x p r e s s i o n a s t h e b o u n d a r y c o n d i t i o n : v /1TI2 - /m-^ "P Y 1 ^ T + Y 2 / m 2 Y l d l + Y 2 d - 1 2 d v v ; = ; = I D ( I Y 2 ) 19 B r o c k ' s a n a l y s i s i s v a l i d f o r the d i l u t e case ( Y 2 < < Y ^ ) / a n d f o r s m a l l c o n c e n t r a t i o n g r a d i e n t s . When m^ ^ m 2 t h e f i r s t term c o r r e s p o n d s t o t h a t o f S c h m i t t and Waldmann's e x p r e s s i o n , and t h e second term can be s i m p l i f i e d u s i n g the t h e r m a l d i f f u s i o n r a t i o t o g i v e - ± a T D ( V Y 2 ) A , • Thus t h e c o n t r i b u t i o n o f the second term i s mi n o r , b u t i t does i n d i c a t e t h a t f o r m-^  = m 2, t h e p a r t i c l e may t r a v e l i n e i t h e r d i r e c t i o n , depending on t h e s i g n o f a T . I t i s no c o i n c i d e n c e t h a t B r o c k ' s e x p r e s s i o n f o r l a r g e p a r t i c l e s i s i d e n t i c a l t o t h a t d e r i v e d by Bakanov and D e r j a g u i n (1960) f o r s m a l l p a r t i c l e s (when t h e accommodation c o e f f i c i e n t s a r e u n i t y ) . T h i s i s a consequence o f t h e a s s u m p t i o n , made i n b o t h c a s e s , t h a t m o l e c u l e m o l e c u l e i n t e r a c t i o n near t h e s u r f a c e i s n e g l i g i b l e . D e r j a g u i n and Yalamov (19 7 2) a t t e m p t e d t o improve B r o c k ' s a n a l y s i s by a l l o w i n g f o r m o l e c u l a r i n t e r a c t i o n s near the p a r t i c l e s u r f a c e . Even though the work was r e s t r i c t e d t o d i l u t e systems ( Y 2 K < Y ^ ) w i t h s m a l l c o n c e n t r a t i o n g r a d i e n t s , t h e c a l c u l a t i o n s become v e r y i n v o l v e d , and the r e s u l t s a r e e x p r e s s e d i n terms o f c o l l i s i o n i n t e g r a l s w h i c h must be c a l c u l a t e d numeri-c a l l y . The p r e d i c t e d s l i p v e l o c i t y i s 2 0 . w h e r e 6 i s a f u n c t i o n o f s e v e r a l c o l l i s i o n i n t e g r a l s . C o m p a r i s o n w i t h K r a m e r s a n d K i s t e m a k e r ' s s l i p e x p r e s s i o n f o r t h e c a s e w h e r e Y 2 << Yj_ a n d m^ ^ shows t h a t D e r j a g u i n a n d Y a l a m o v ' s d e r i v a t i o n r e s u l t s i n a n e x t r a t e r m (6-1) F o r t h e a i r - w a t e r v a p o u r s y s t e m 6 i s . g i v e n a s 1 . 2 5 3 s o t h a t v s l i p = 0 . 3 6 5 D dx K r a m e r s a n d K i s t e m a k e r ' s p r o p o r t i o n a l i t y c o n s t a n t e v a l u a t e d f o r t h e same s y s t e m i s 0 . 1 6 7 . I n t u i t i o n s t r o n g l y s u g g e s t s t h a t a n y i n t e r a c t i o n b e t w e e n i n c o m i n g a n d r e b o u n d i n g m o l e c u l e s s h o u l d r e d u c e t h e s l i p v e l o c i t y , n o t i n c r e a s e i t . T h i s p r e d i c t i o n m u s t t h e r e f o r e b e v i e w e d w i t h some s c e p t i c i s m . A n e n t i r e l y d i f f e r e n t a p p r o a c h t o d i f f u s i o p h o r e s i s was t a k e n b y D e r j a g u i n e t a l . (1966) who u s e d a " p h e n o m e n o l o g i c a l " t e c h n i q u e . T h i s m e t h o d r e l i e s o n a c o m b i n a t i o n o f i r r e v e r s i b l e t h e r m o d y n a m i c s a n d c o n t i n u u m m e c h a n i c s t o d e t e r m i n e p a r t i c l e v e l o c i t y . T h e y c o n s i d e r two r e s e r v o i r s c o n t a i n i n g d i f f e r e n t g a s e s a n d s e p a r a t e d b y a p o r o u s " p a r t i t i o n " made u p o f r a n d o m l y a r r a n g e d s p h e r e s r i g i d l y f i x e d i n s p a c e , a t a s p a c i n g much l a r g e r t h a n t h e i r r a d i u s . T h e b e h a v i o u r o f t h i s s y s t e m i s u s e d t o d e d u c e t h e v e l o c i t y o f a f r e e a e r o s o l p a r t i c l e i n t h e g a s m i x t u r e . S l i p was a s s u m e d t o b e i n s i g n i f i c a n t . I n ' t h e i r d e r i v a t i o n t h e a u t h o r s make a c o r r e c t i o n f o r l o c a l d i f f u s i o n s t r e a m s c a u s e d b y p r e s s u r e g r a d i e n t s a r o u n d t h e p a r t i c l e . H o w e v e r , s i n c e p r e s s u r e d i f f u s i o n c a n b e s h o w n t o b e i n s i g n i f i c a n t c o m p a r e d t o o r d i n a r y d i f f u s i o n i n t h i s p r o b l e m ( s e e f o r e x a m p l e B i r d e t a l . ( 1 9 6 2 ) ) , a n d s i n c e t h e i r d i f f u s i o n e q u a t i o n i s n o t d i r e c t l y c o u p l e d t o t h e i r momentum e q u a t i o n , i t i s u n c l e a r why t h i s c o r r e c t i o n i s n e c e s s a r y . T h e f i n a l e x p r e s s i o n o b t a i n e d f o r t h e p a r t i c l e v e l o c i t y i s e q u i v a l e n t t o t h e g a s mean m o l a r v e l o c i t y i n t h e i r s y s t e m , a l t h o u g h t h e a u t h o r s d o n o t s t a t e t h i s e x p l i c i t l y . U s i n g t h e i r a s s u m p t i o n o f n e g l i g i b l e s l i p , t h e p a r t i c l e v e l o c i t y c a n b e f o u n d d i r e c t l y f r o m t h e c o n t i n u u m e q u a -t i o n s g i v e n i n t h e i r p a p e r , w i t h o u t r e c o u r s e t o t h e r m o d y n a m i c m e t h o d s . T h i s y i e l d s a d i f f e r e n t r e s u l t . . D e r j a g u i n a n d Y a l a m o v (1972) l a t e r p r e s e n t e d t h e a p p r o a c h i n m o r e d e t a i l , a l l o w i n g f o r t h e e x i s t e n c e o f s l i p a t t h e p a r t i c l e s u r f a c e . T h e y c o n c l u d e d t h a t n o r m a l d i f f u s i o n s l i p a n d b a r o - o r - p r e s s u r e - d i f f u s i o n s l i p e x a c t l y c a n c e l l e d o u t . T h u s t h e p r o b l e m b e c a m e e q u i v a l e n t t o t h e i r p r e v i o u s o n e a n d y i e l d e d t h e same r e s u l t . D e r j a g u i n a n d Y a l a m o v (1972) c o m p a r e d t h e i r p r e d i c t e d p a r t i c l e v e l o c i t i e s d e r i v e d f r o m t h e " p h e n o m e n o l o g i c a l " m e t h o d w i t h t h e r e s u l t s o b t a i n e d b y s o l v i n g t h e c o n t i n u u m m e c h a n i c s e q u a t i o n u s i n g t h e i r s l i p b o u n d a r y c o n d i t i o n . T h e two m e t h o d s s h o w e d r e a s o n a b l e a g r e e m e n t f o r t h e a i r - w a t e r v a p o u r s y s t e m a n d t h e y c o n c l u d e d t h a t t h e d i f f e r e n c e was d u e t o n u m e r i c a l e r r o r s 22. a r i s i n g i n the second method. I f t h i s were the case, then one c o u l d deduce t h a t the s l i p v e l o c i t y p a s t a f l a t s u r f a c e would always be such t h a t the mean molar v e l o c i t y i s zero w i t h r e s p e c t to the s u r f a c e . Despite the agreement, there are s u f f i c i e n t areas of concern to c a s t doubt on the accuracy of both t h e i r t h e o r i e s . 2.4 Theories Encompassing the T r a n s i t i o n Regime A n a l y s i s of p a r t i c l e behaviour i n the t r a n s i t i o n regime (Kn ^ 1) presents major d i f f i c u l t i e s , and was f i r s t attempted by Brock (1968). He adopted a f i r s t - o r d e r p e r t u r b a t i o n technique to c a l c u l a t e the v e l o c i t y d i s t r i b u t i o n f u n c t i o n f o r the gas molecules near the p a r t i c l e . T h i s gave the p a r t i c l e v e l o c i t y v mn 1 - m 2 / J 2m, m l + m 2 12 0.311/Kn D ( V y 2 ) 1 - 0.360/Kn where r ^ 2 = ( r ^ + x^)/2 and r ^ and r 2 are the e f f e c t i v e m olecular r a d i i o f s p e c i e s 1 and 2. Since the d e r i v a t i o n r e q u i r e s t h a t \, Y 2 > > > a n <3 hence ^^m\ + ^2*^^. ~ m 2 2 ' ^ n e e < 3 u a t l o n reduces t o the simple v e l o c i t y e x p r e s s i o n f o r s m a l l p a r t i c l e s when the Knudsen number i s l a r g e . For s m a l l Knudsen numbers i t g i v e s 23. v -P The l a c k o f agreement between t h i s and o t h e r l a r g e p a r t i c l e t h e o r i e s i s i n d i c a t i v e o f t h e approximate n a t u r e of the d e r i v a -t i o n . B rock found moderate agreement between h i s t h e o r y and s e l e c t e d e x p e r i m e n t a l r e s u l t s o f S c h m i t t and Waldmann (1960). A n n i s e t a l . (1973) used a n o v e l t e c h n i q u e which t h e y c l a i m a l l o w s t h e d e r i v a t i o n o f a t h e o r y t h a t h o l d s f o r a l l p a r t i -c l e s i z e s . The groundwork f o r t h e i r method i s l a i d i n an e a r l i e r paper (1972) d e a l i n g w i t h t h e d r a g on a p a r t i c l e i n a n o n - d i f f u s i n g gas. I n t h e i r method t h e p a r t i c l e i s t r e a t e d as a l a r g e m o l e c u l e , and t h e m o l e c u l a r d i f f u s i o n e q u a t i o n (see H i r s c h f e l d e r e t a l . (1964)) i s used t o o b t a i n the p a r t i c l e v e l o c i t y . T h e i r g e n e r a l v e l o c i t y e x p r e s s i o n i s a f u n c t i o n o f two v a r i a b l e s , b o t h c l o s e l y r e l a t e d t o t h e Knudsen number. F o r s m a l l p a r t i c l e s and e q u i m o l a r c o u n t e r - d i f f u s i o n i t y i e l d s v = --P ie ie where a., b., and c. depend on t h e i n t e r a c t i o n o f m o l e c u l e s w i t h i x 1 c the p a r t i c l e s u r f a c e . T h i s i s o f the same form as Waldmann's (1959) e x p r e s s i o n . F o r l a r g e p a r t i c l e s t h e r e s u l t becomes * * * (c 2/a2b 2)vm. * * * ( c 1 / a 1 b 1 ) • m 1 /m. + ( c 0 / a 0 b 0 ) y -(c^/a^b^) y^ 1 "'2_ ' v"~2X "2J~'2' '2'iLl2 /m. D(Vy 2) ( l / a * ) / ^ - (l/a^/m-L D ( V Y 2 ) O O ( l / a 1 ) y 1 / m 1 + ( l / a 2 ) y2^2 w h i c h agrees w i t h S c h m i t t and Waldmann's (1960) e x p r e s s i o n when th e i n t e r a c t i o n s o f b o t h m o l e c u l a r s p e c i e s w i t h the sphere a re * * s i m i l a r , i . e . , a ^ = a 2 . I n a l a t e r paper A n n i s and Mason (1975) expanded t h e t h e o r y t o i n c l u d e a l s o thermophores!s, and showed t h a t when b o t h t e m p e r a t u r e and c o n c e n t r a t i o n g r a d i e n t s a re p r e s e n t , d i f f u s i o p h o r e s i s i s augmented by a t h e r m a l d i f f u s i o n c o n t r i b u t i o n as w e l l as a s m a l l a d d i t i o n a l c o u p l i n g term. A l t h o u g h t h i s method i s e x c e l l e n t f o r s m a l l p a r t i c l e s , i t s a p p l i c a t i o n i n t h e t r a n s i t i o n and continuum regimes i s u n s a t i s f a c t o r y . The d i f f u s i o n e q u a t i o n , on w h i c h the t h e o r y r e s t s , i s c o r r e c t . o n l y when the p a r t i c l e r a d i u s i s much s m a l l e r t h a n the gas mean f r e e p a t h . Large p a r t i c l e s do n o t a l t e r the s u r r o u n d i n g gas c o n c e n t r a t i o n , a s t h i s e q u a t i o n i m p l i e s , b u t r a t h e r form a s e p a r a t e phase i n t h e system. 2.5 The Continuum E q u a t i o n s We r e t u r n now t o an e x a m i n a t i o n o f t h e continuum mechanics e q u a t i o n s . The s i m p l e forms g i v e n e a r l i e r were used by a l l a u t h o r s e x c e p t Brock (1963). A l t h o u g h i n t u i t i o n might s u g g e s t the use o f t h e s e forms, no one has r i g o r o u s l y e s t a b l i s h e d t h e i r v a l i d i t y i n t h i s problem. S c h m i t t and Waldmann (19 60) used the e q u a t i o n s e s s e n t i a l l y w i t h o u t comment. D e r j a g u i n e t a l . v -P (1966) a s s u m e d t h a t t h e s i m p l e e q u a t i o n s w e r e v a l i d f o r l o w v e l o c i t i e s a n d a s m a l l r e l a t i v e d e n s i t y o f o n e c o m p o n e n t . T h i s was i n d i c a t e d i n two e a r l i e r p a p e r s b y D e r j a g u i n a n d D u k h i n ( 1 9 5 6 ) . A p a r t i a l j u s t i f i c a t i o n f o r t h e v a l i d i t y o f t h e e q u a t i o n s u n d e r t h e same c o n d i t i o n s was l a t e r g i v e n b y D e r j a g u i n a n d Y a l a m o v ( 1 9 7 2 ) . B r o c k u s e d a m o r e a c c u r a t e f o r m o f t h e p a r t i a l c o n t i n u i t y e q u a t i o n a n d s h o w e d how t h i s c o u l d b e s i m p l i f i e d i n c e r t a i n c a s e s . S y s t e -m a t i c s i m p l i f i c a t i o n o f t h e t h r e e b a s i c e q u a t i o n s i s t h e r e f o r e s t i l l l a c k i n g . 2 . 6 E x p e r i m e n t s u n d e r N o n - t u r b u l e n t C o n d i t i o n s T h e p r i m a r y o b j e c t i v e o f m o s t s t u d i e s h a s b e e n t o m e a s u r e p a r t i c l e v e l o c i t y f o r c o m p a r i s o n w i t h t h e v a r i o u s t h e o r i e s . . Some w o r k e r s h a v e a l s o b e e n i n t e r e s t e d i n d e m o n s t r a t i n g t h e a b i l i t y o f d i f f u s i o p h o r e s i s t o r e m o v e p a r t i c l e s o n a c o n t i n u o u s b a s i s f r o m a g a s s t r e a m . T h e e a r l i e s t q u a n t i t a t i v e v e l o c i t y m e a s u r e m e n t s a r e t h o s e o f S c h m i t t a n d W a l d m a n n (1960) . T h e s e w e r e made i n a m o d i f i e d M i l l i k a n o i l d r o p a p p a r a t u s ( s e e M i l l i k a n ( 1 9 1 1 ) ) c o n s i s t i n g o f a v e r t i c a l g l a s s t u b e c o n n e c t e d a t e a c h e n d t o a f l a s k c o n t a i n i n g a p u r e g a s . T h u s a b i n a r y d i f f u s i o n f i e l d c o u l d b e e s t a b l i s h e d i n t h e t u b e . Two c h a r g e d p l a t e s w e r e u s e d t o h o l d s i l i c o n o i l d r o p l e t s i n a f i x e d p o s i t i o n when r e q u i r e d , a n d t h e d r o p l e t v e l o c i t i e s w e r e d i r e c t l y m e a s u r e d b y m i c r o s c o p e . S c h m i t t a n d W a l d m a n n ' s w o r k h a s b e e n s e v e r e l y c r i t i c i s e d b y D e r j a g u i n a n d Y a l a m o v (19 7 2) b e c a u s e o f t h e h i g h e x p e r i m e n t a l e r r o r a n d t h e p o s s i b i l i t y o f e x t r a n e o u s c o n v e c t i v e g a s f l o w s i n the a p p a r a t u s . I n a d d i t i o n , a l t h o u g h S c h m i t t and Waldmann o b v i o u s l y b e l i e v e d t h a t d i f f u s i o n s l i p e x i s t e d , they gave no i n d i c a t i o n t h a t they made an a l l o w a n c e f o r t h i s e f f e c t a t the t u b e w a l l s . F u r t h e r m o r e , they do not m ention t h e i m p o r t a n c e o f a e r o s o l p o s i t i o n w i t h r e s p e c t t o the tube w a l l , and i t i s t h e r e -f o r e p o s s i b l e t h a t they d i d not p r o p e r l y a l l o w f o r the p a r a b o l i c gas v e l o c i t y p r o f i l e . I n any case t h e i r d a t a do not agree w i t h any proposed t h e o r y . T h e i r work must t h e r e f o r e be d i s c o u n t e d . The same c r i t i c i s m s a p p l y t o the l a t e r work o f S c h m i t t (1961) f o r s t e a m - a i r m i x t u r e s . S c h m i t t ' s paper a l s o mentions a s i m p l e p a r t i c l e c o l l e c t o r made o f two h o r i z o n t a l p a r a l l e l p l a t e s between which a i r c o n t a i n i n g c i g a r e t t e smoke was p a s s e d . Steam was i n j e c t e d t h r ough the upper porous a s b e s t o s p l a t e and condensed on the l o wer copper p l a t e . No o p e r a t i o n a l d e t a i l s a r e given' e x c e p t t h a t t h e c o l l e c t o r was a b l e t o c o m p l e t e l y remove the smoke from the a i r . G o l d s m i t h , D e l a f i e l d and Cox (1963a, 1963b) a l s o worked w i t h a p a r a l l e l p l a t e c o l l e c t o r , but i n t h e i r d e s i g n one p l a t e was l i n e d w i t h a b s o r b e n t paper and s a t u r a t e d w i t h w a t e r , w h i l e t h e o t h e r was l i n e d w i t h paper s a t u r a t e d w i t h s u l f u r i c a c i d . Very s m a l l r a d i o a c t i v e p a r t i c l e s were passed i n an a i r s t r e a m between t h e p l a t e s , and t h e d e p o s i t e d p a r t i c l e s were d e t e c t e d by t h e i r r a d i a t i o n . From t h e measurements G o l d s m i t h e t a l . were a b l e t o deduce t h e p a r t i c l e v e l o c i t y , w h i c h agreed w e l l w i t h Waldmann's (1959) t h e o r e t i c a l e x p r e s s i o n f o r s m a l l p a r t i c l e s when the accommodation c o e f f i c i e n c i e s i n t h i s e x p r e s s i o n were u n i t y . S t o r o z h i l o v a (1964) d e v i s e d a d i f f e r e n t t e c h n i q u e f o r m e a s u r i n g p a r t i c l e v e l o c i t y . , w h e r e b y a f i n e s t r e a m o f a e r o s o l p a r t i c l e s was i n j e c t e d i n t o a f u l l y d e v e l o p e d l a m i n a r f l o w b e t w e e n two p a r a l l e l p l a t e s . A c o n c e n t r a t i o n g r a d i e n t was m a i n t a i n e d b e t w e e n t h e p l a t e s , a n d t h e d i f f u s i o p h o r e t i c v e l o c i t y c o u l d b e d e d u c e d f r o m t h e t r a j e c t o r y o f t h e p a r t i c l e s a s o b s e r v e d b y m i c r o s c o p e . A l l e x p e r i m e n t s w e r e made u s i n g t h e a i r - w a t e r v a p o u r s y s t e m . A l t h o u g h t h i s t y p e o f e x p e r i m e n t may e l i m i n a t e some s o u r c e s o f e r r o r , t h e d a t a s h o w e d c o n s i d e r a b l e s c a t t e r , p a r t i c u l a r l y f o r K n u d s e n n u m b e r s o f l e s s t h a n 1. F u r t h e r m o r e , t h e e x p e r i m e n t s e x t e n d e d o n l y down t o K n u d s e n n u m b e r s o f a b o u t 0 . 3 , w h i c h may s t i l l f a l l i n t h e t r a n s i t i o n r e g i m e . H e n c e D e r j a g u i n a n d Y a l a m o v ' s (19 72) c o n t e n t i o n , t h a t t h e s e d a t a p r o v e t h e i r t h e o r y f o r l a r g e p a r t i c l e s u n a m b i g u o u s l y , c a n n o t b e a c c e p t e d . H o w e v e r , f o r K n u d s e n n u m b e r s g r e a t e r t h a n 0 . 7 5 t h e d a t a show g o o d a g r e e m e n t w i t h s m a l l p a r t i c l e t h e o r y . S t i n c h c o m b e a n d G o l d s m i t h (1966) p e r f o r m e d e x p e r i m e n t s i n w h i c h i o d i n e was r e m o v e d f r o m a m i x t u r e o f s t e a m a n d a i r b y c o n d e n s i n g t h e s t e a m i n a v e r t i c a l , w a t e r - c o o l e d t u b e . T h e g a s f l o w was l a m i n a r . P a r t o f t h e i o d i n e was p r e s e n t i n g a s e o u s f o r m a n d p a r t a s p a r t i c u l a t e s . T h e y e s t i m a t e d t h a t t h e p a r t i c u -l a t e r e m o v a l was 95 t o 9 9 % , a n d a t t r i b u t e d t h i s t o t h e e f f e c t s o f d i f f u s i o - a n d t h e r m o p h o r e s i s , a n d t o i n e r t i a l a n d g r a v i t a t i o n a l d e p o s i t i o n . H o w e v e r , t h e l a t t e r two m e c h a n i s m s p r o b a b l y h a d a m i n i m a l i n f l u e n c e u n d e r t h e i r e x p e r i m e n t a l c o n d i t i o n s . No t h e o r e t i c a l a n a l y s i s i s g i v e n . 2 8 . M e i s e n e t a l . (1971) a l s o w o r k e d w i t h t h e a i r - w a t e r v a p o u r s y s t e m i n a h o r i z o n t a l p a r a l l e l p l a t e c o l l e c t o r . T h e p l a t e s w e r e made o f b l o t t i n g p a p e r h e l d i n p l a c e b y s t a i n l e s s s t e e l w i r e s , t h e t o p o n e b e i n g i m p r e g n a t e d w i t h s t e a m w h i l e t h e b o t t o m o n e l a y o n t h e s u r f a c e o f a b a t h o f c o o l i n g w a t e r . T h u s a w a t e r v a p o u r g r a d i e n t was e s t a b l i s h e d b e t w e e n t h e p l a t e s , a n d c i g a r e t t e smoke c o u l d b e r e m o v e d c o n t i n u o u s l y f r o m a n a i r s t r e a m . T h e e x p e r i m e n t a l r e s u l t s c o r r e l a t e d s a t i s f a c t o r i l y w i t h S c h m i t t a n d W a l d m a n n ' s ~ t h e o r y , a s w e l l a s t h e h y p o t h e s i s t h a t t h e p a r t i -c l e s m o v e d a t t h e g a s mean mass v e l o c i t y . T h i s h i g h l i g h t s t h e d i f f i c u l t y o f o b t a i n i n g d e f i n i t i v e r e s u l t s w h e n m-^  a n d m 2 a r e o f s i m i l a r m a g n i t u d e . F u l l d e t a i l s o f t h e w o r k a r e g i v e n b y M e i s e n (1970) . 2 . 7 D i f f u s i o p h o r e s i s u n d e r T u r b u l e n t C o n d i t i o n s I n t h e f i r s t p u b l i s h e d p a p e r c o n c e r n i n g t u r b u l e n t c o n d i t i o n s ( W h i t m o r e a n d M e i s e n ( 1 9 7 3 ) ) t h e t h e o r y o f p a r t i c l e t r a n s f e r was t r e a t e d a n a l o g o u s l y t o t h a t o f m a s s t r a n s f e r i n t u r b u l e n t f l o w . T h i s t h e o r y was d e v e l o p e d f o r g a s a b s o r p t i o n i n a w e t t e d w a l l c o l u m n , b u t i t s w i d e r a p p l i c a t i o n was r e a l i z e d . T h e g a s c o r e was a s s u m e d t o b e w e l l m i x e d w i t h r e s p e c t t o b o t h p a r t i c l e s a n d g a s c o m p o n e n t s , a n d t h e c o n c e n t r a t i o n g r a d i e n t s w e r e a s s u m e d t o b e c o n f i n e d t o a t h i n m a s s t r a n s f e r b o u n d a r y l a y e r . I n t h i s way a s i m p l e t h e o r y c o u l d b e c o n s t r u c t e d r e l a t i n g , p a r t i c l e t r a n s f e r r a t e t o i n l e t a n d o u t l e t g a s c o m p o -s i t i o n s a n d m o l e c u l a r w e i g h t s . T h i s t h e o r y i s p r e s e n t e d i n d e t a i l i n Chapter 4. P r e l i m i n a r y e x p e r i m e n t a l r e s u l t s were a l s o p r e s e n t e d f o r t h e ammonia-nitrogen system f o r l a r g e p a r t i c l e s , w h i c h i n d i c a t e d t h a t the t h e o r y was s a t i s f a c t o r y , and t h a t the p a r t i c l e s moved a t a p p r o x i m a t e l y the gas mean mass v e l o c i t y . These r e s u l t s a r e g i v e n i n Chapter 6. I n a l a t e r paper (Whitmore and M e i s e n , t o be p u b l i s h e d i n the Canadian J o u r n a l o f C h e m i c a l E n g i n e e r i n g ) t h e t h e o r y i s extended t o i n c l u d e d i f f u s i o p h o r e s i s i n multicomponent gases and l i q u i d s , and t h e r m o p h o r e s i s i n gases and l i q u i d s . B oth s m a l l and l a r g e p a r t i c l e s are c o n s i d e r e d . R e l e v a n t m a t e r i a l from t h i s p a p e r - i s g i v e n i n Chapter 4. -The o n l y o t h e r paper c o n c e r n i n g d i f f u s i o p h o r e s i s under t u r b u l e n t c o n d i t i o n s i s t h a t o f A z a r n i o u c h e t a l . (19 7 5 ) , w h i c h i s based on t h e d o c t o r a l work o f A z a r n i o u c h (1974). The t h e o r y p r e s e n t e d i n t h i s paper i s open t o s e v e r a l c r i t i c i s m s , and i s d i s c u s s e d i n d e t a i l i n Chapter 4. A z a r n i o u c h passed a m i x t u r e o f steam and a i r c o n t a i n i n g a s u l f u r i c a c i d m i s t downwards th r o u g h a v e r t i c a l t u b u l a r con-d e n s e r . The m i s t removal was d e t e r m i n e d by t i t r a t i n g f o r s u l f u r i c a c i d i n t h e condensate. The e x p e r i m e n t a l c o n d i t i o n s were such t h a t b o t h i n e r t i a l d e p o s i t i o n and d i f f u s i o p h o r e s i s were i m p o r t a n t removal mechanisms. (The c o n t r i b u t i o n o f t h e r m o p h o r e s i s was p r o b a b l y a l s o s i g n i f i c a n t , b u t i t was n e g l e c t e d . ) A l t h o u g h A z a r n i o u c h attempted t o e s t i m a t e t h e i n e r t i a l c o n t r i b u t i o n u s i n g a m a t h e m a t i c a l model, no e x p e r i m e n t a l d a t a a r e p r e s e n t e d f o r i n e r t i a l d e p o s i t i o n a l o n e . S i n c e d e p o s i t i o n models are g e n e r a l l y 30 . i m p r e c i s e , i t i s n o t p o s s i b l e t o d e t e r m i n e t h e s e p a r a t e i n e r t i a l a n d d i f f u s i o p h o r e t i c c o n t r i b u t i o n s w i t h a n y a c c u r a c y . T h i s d i f f i c u l t y i s c o m p o u n d e d b y t h e s c a t t e r i n t h e d a t a . A n o t h e r p r o b l e m i s t h a t A z a r n i o u c h a p p e a r s t o h a v e m i s i n t e r p r e t e d h i s own m o d e l b y f a i l i n g t o r e c o g n i z e t h e p o s s i b i l i t y o f i n t e r a c t i o n s b e t w e e n i n e r t i a l a n d d i f f u s i o p h o r e t i c m e c h a n i s m s , w h i c h f u r t h e r c o m p l i c a t e s t h e i n t e r p r e t a t i o n o f t h e d a t a . T h i s i s d i s c u s s e d i n C h a p t e r 7 . A n o t h e r s e r i o u s d i f f i c u l t y w i t h t h e w o r k o f A z a r n i o u c h e t a l . c o n c e r n s t h e p a r t i c l e s i z e . A l t h o u g h t h e s i z e o f m i s t d r o p l e t s i m m e d i a t e l y a f t e r g e n e r a t i o n was m e a s u r e d , t h e s i z e a f t e r a d d i t i o n o f s t e a m , a n d t h e o u t l e t s i z e f r o m t h e c o n d e n s e r , w e r e n o t d e t e r m i n e d e x p e r i m e n t a l l y . I n s t e a d A z a r n i o u c h e t a l . (1973) made a t h e o r e t i c a l s t u d y o f t h e g r o w t h r a t e o f . s u l f u r i c a c i d d r o p l e t s a t 1 0 0 ° C f o r r e l a t i v e h u m i d i t i e s up t o 0 . 3 . T h e y c o n c l u d e d t h a t i n t h e i r e x p e r i m e n t s t h e d r o p s w o u l d g r o w v e r y -2 r a p i d l y ( i n a b o u t 10 s e c o n d s ) t o a s t a b l e c o n d i t i o n o f a b o u t d o u b l e t h e i r i n i t i a l d i a m e t e r . T h e p a r t i c l e s i z e a t t h e i n l e t t o t h e c o n d e n s e r i s t h e r e f o r e e s t a b l i s h e d , t h o u g h i m p r e c i s e l y . H o w e v e r , a n i m p o r t a n t f a c t o r w h i c h h a s n o t b e e n c o n s i d e r e d i n t h e i r e x p e r i m e n t a l s t u d y i s t h e p o s s i b i l i t y o f f u r t h e r d r o p l e t g r o w t h w i t h i n t h e c o n d e n s e r . I n r e g i o n s o f h i g h r e l a t i v e h u m i d i t y w h i c h w i l l b e p r e s e n t i n t h e c o n d e n s e r , r a p i d p a r t i c l e g r o w t h c a n b e e x p e c t e d a c c o r d i n g t o t h e i r e a r l i e r t h e o r e t i c a l s t u d y . I t m u s t b e c o n c l u d e d t h a t t h e a c t u a l p a r t i c l e s i z e v a r i e s w i t h p o s i t i o n i n t h e c o n d e n s e r a n d w i t h e x p e r i m e n t a l c o n d i t i o n s , a n d i s u n k n o w n . I t i s t h u s i m p o s s i b l e t o d e t e r m i n e t h e i n f l u e n c e o f i n e r t i a l mechanisms, o r t o r e l a t e t h e p a r t i c l e s i z e t o the mean f r e e p a t h o f the gas. A r e l a t e d paper o f i n t e r e s t i s t h a t o f B y e r s and C a l v e r t (1969) i n which t h e y p u b l i s h a model f o r t h e r m o p h o r e t i c p a r t i c l e d e p o s i t i o n from a gas i n a tub e w i t h c o n s t a n t w a l l t e m p e r a t u r e . U n f o r t u n a t e l y , t h e i r t h e o r y does n o t a l l o w f o r t h e e f f e c t o f t e m p e r a t u r e v a r i a t i o n s on gas d e n s i t y , s i n c e t h e d e n s i t y was assumed t o be c o n s t a n t . Our t h e o r y (Whitmore and M e i s e n , t o be p u b l i s h e d i n the Canadian J o u r n a l o f Chemical. E n g i n e e r i n g ) i n d i c a t e s t h a t c o n t r a c t i o n o f t h e gas upon c o o l i n g i n c r e a s e s t h e p a r t i c l e c o n c e n t r a t i o n based on u n i t volume o f gas more than i t i s reduced by p a r t i c l e d e p o s i t i o n . I t i s t h e r e f o r e n o t s u r -p r i s i n g t h a t t h e i r model does n o t g i v e v e r y good agreement w i t h t h e i r e x p e r i m e n t a l d a t a . F u r t h e r d i s c u s s i o n of t h i s work appears i n C h a p t e r 4. A l t h o u g h A z a r n i o u c h ' s (19 75) model i s t h e d i r e c t mass t r a n s f e r analogue o f B y e r s and C a l v e r t ' s (19 69) model, he makes no r e f e r e n c e t o t h e i r work. I n a l a t e r paper N i s h i o e t a l . (19 74) d e r i v e a n o t h e r model f o r t h e r m o p h o r e t i c d e p o s i t i o n i n a tube w i t h c o n s t a n t w a l l t e m p e r a t u r e . The d e r i v a t i o n i s s l i g h t l y more d i r e c t t h a n t h a t o f B y e r s and C a l v e r t , b u t t h e problem o f assuming c o n s t a n t f l u i d d e n s i t y r e m a i n s . However, t h e a u t h o r s do g e t moderate agreement between t h e i r model and t h e i r d a t a . No analogue o f t h i s model f o r t he case o f d i f f u s i o p h o r e s i s e x i s t s . I f c o n s t r u c t e d , however, i t s h o u l d be an improvement on t h a t o f A z a r n i o u c h e t a l . The work i s f u r t h e r d i s c u s s e d i n Ch a p t e r 4. 32. 2.8 Review A r t i c l e s G e n e r a l r e v i e w s o f v a r i o u s a s p e c t s o f d i f f u s i o p h o r e s i s have been made by Waldmann (1961), Waldmann and S c h m i t t (1966), G o l d s m i t h and May (1966), M e i s e n (19 7 0 ) , D e r j a g u i n and Yalamov (1972), and A z a r n i o u c h (19 7 4 ) . Chapter 3 FUNDAMENTAL THEORY 3.1 O u t l i n e The fundamental t h e o r y o f d i f f u s i o p h o r e s i s f o r a l a r g e p a r t i c l e i n a b i n a r y gas m i x t u r e u n d e r g o i n g e q u i m o l a r c o u n t e r -d i f f u s i o n i s p r e s e n t e d i n s e v e r a l s e c t i o n s . F i r s t l y , t h e continuum e q u a t i o n s a r e s i m p l i f i e d , s u b j e c t t o c e r t a i n c o n d i t i o n s . S e c o n d l y , u s i n g t h e s e e q u a t i o n s , t h e f r e e p a r t i c l e v e l o c i t y i s de t e r m i n e d f o r an a r b i t r a r y s l i p c o n d i t i o n a t i t s s u r f a c e . T h i r d l y , the r a t e o f energy d i s s i p a t i o n i n the gas i s c a l c u l a t e d i n o r d e r t o deduce t h e s l i p c o n d i t i o n ; and f i n a l l y , t he t h e o r y i s f u r t h e r r e f i n e d and ex t e n d e d . 3.2 The Continuum Mechanics E q u a t i o n s The s i m p l i f i e d continuum mechanics e q u a t i o n s a r e now de v e l o p e d f o r the case o f a s p h e r i c a l p a r t i c l e suspended i n a b i n a r y gas m i x t u r e . The m i x t u r e i s c o n s i d e r e d t o undergo e q u i m o l a r c o u n t e r - d i f f u s i o n f a r away from the p a r t i c l e as i n d i c a t e d i n * BODY CENTRED COORDINATES NUMBER CENTRED COORDINATES • -F i g u r e 3.1 C o o r d i n a t e systems. F i g u r e 3.1. These e q u a t i o n s w i l l be used t o f i n d the f r e e p a r t i -c l e v e l o c i t y . L a t e r a s i m p l e e x t e n s i o n w i l l be g i v e n t o t h e case o f more p r a c t i c a l i n t e r e s t where one gas d i f f u s e s t h r o u g h a n o t h e r w h i c h i s s t a g n a n t . Two t y p e s o f c o o r d i n a t e systems a r e needed i n t h e d e r i v a t i o n ; c o o r d i n a t e s w i t h r e s p e c t t o which the mean molar v e l o c i t y o f t h e gas f a r from the p a r t i c l e i s z e r o , and c o o r d i n a t e s t h a t have t h e i r o r i g i n a t t h e c e n t r e o f t h e p a r t i c l e . F o r b r e v i t y t h e s e w i l l be termed "number-centred" and "bo d y - c e n t r e d " c o o r d i -n a t e s , r e s p e c t i v e l y . The b e h a v i o u r o f the f l u i d i n the system i s governed by t h r e e e q u a t i o n s , the N a v i e r - S t o k e s e q u a t i o n (NS), the t o t a l c o n t i n u i t y e q u a t i o n (TC), and the p a r t i a l c o n t i n u i t y e q u a t i o n (PC). These ensure c o n s e r v a t i o n o f momentum, t o t a l mass, and mass o f one component r e s p e c t i v e l y . -Vp - V . T_ + pg = 0 (NS) (3.1) | | + V.pv = 0 (TC) (3.2) 9 p l / p l \ T F + I - P ] X = Z - P D l\jr)  ( P C ) ( 3 - 3 ) S i n c e the Reynolds number o f p a r t i c l e s u n d e r g o i n g d i f f u s i o p h o r e s i s i s s m a l l (<<1) , the i n e r t i a l terms i n t h e N a v i e r - S t o k e s e q u a t i o n have been i g n o r e d . The p a r t i a l c o n t i n u i t y e q u a t i o n w i l l be s o l v e d f o r 36 . c o n s t a n t d i f f u s i v i t y , D , a n d t h e N a v i e r - S t o k e s e q u a t i o n f o r c o n s t a n t v i s c o s i t y , y • S i n c e t h e d i f f u s i v i t y i s e s s e n t i a l l y c o n s t a n t a n d t h e v i s c o s i t y shows l i t t l e v a r i a t i o n i n many b i n a r y -m i x t u r e s , t h e s e a r e s a t i s f a c t o r y a p p r o x i m a t i o n s . I n a n y c a s e i t i s n o t e x p e c t e d t h a t t h e p r e d i c t e d p a r t i c l e v e l o c i t y w o u l d b e v e r y s e n s i t i v e t o v a r i a t i o n s i n y o r D o v e r t h e f l o w f i e l d . T h e f o l l o w i n g i d e n t i t i e s w i l l b e u s e d . ( T h e s e i d e n t i t i e s a n d t h e b a s i c c o n t i n u u m e q u a t i o n s c a n b e f o u n d f o r e x a m p l e i n B I R D e t a l . (1960) .) c.^ = y ^ c , c 2 = Y 2 c / c = c i + c 2 = c o n s t a n t ( 3 . 4 ) p l = M l c l ' p 2 = M 2 C 2 ' p = p l + p 2 ( 3 . 5 ) F a r f r o m t h e p a r t i c l e t h e d i f f u s i o n i s d e s c r i b e d b y t h e e q u a t i o n s , N , = - D c = - N , ( 3 . 6 ) s o t h a t i t f o l l o w s t h a t ( 8 Y O / 9 X ) i s a c o n s t a n t . T h e mean m a s s v e l o c i t y o f t h e g a s i n t h i s r e g i o n , w i t h r e s p e c t t o n u m b e r - c e n t r e d c o o r d i n a t e s , i s t h e r e f o r e w h e r e M i s t h e mean m o l e c u l a r w e i g h t , Y-|M., + . 37. The s i m p l i f i c a t i o n o f the N a v i e r - S t o k e s e q u a t i o n f o r axisymmetrical.' systems w i t h c o n s t a n t f l u i d d e n s i t y i s w e l l known. A s i m i l a r s i m p l i f i c a t i o n i s now made i n the g e n e r a l c a s e . (The subsequent development i s s i m i l a r t o t h a t g i v e n by Happel and Brenner ( 1 9 6 5 ) ) . T a k i n g t h e c u r l o f E q u a t i o n (3.1) e l i m i n a t e s the g r a d i e n t s o f s c a l a r s and the pg t e r m , g i v i n g V x (V .T_) = 0 (3.8) For Newtonian f l u i d s t h e s t r e s s t e n s o r can be w r i t t e n as x = - y ( V v + ( V v ) + ) + (| - K ) ( V . V ) 6_ (3.9) where (V^ v) + i s t h e t r a n s p o s e o f V_ v , u i s t h e she a r v i s c o s i t y , K i s t h e b u l k v i s c o s i t y , and S_ i s the u n i t t e n s o r . The form o f the s t r e s s t e n s o r i s t h a t used by B i r d e t a l . (1960), w h i c h does not i n c l u d e t h e a b s o l u t e p r e s s u r e . A f t e r some m a n i p u l a t i o n one can show t h a t V . T _ - - y ( V _ 2 V + V ( V . V ) ) + V ( - | - K) ( V . V ) (3.10) For u c o n s t a n t t h e N a v i e r - S t o k e s e q u a t i o n t h e n reduces t o V _x ( 1 x_'(_V 2 1 v) ) = 0 (3.11) which i s i d e n t i c a l t o t h e form o b t a i n e d f o r c o n s t a n t d e n s i t y systems. I n t h a t case,however,the e q u a t i o n can be r e w r i t t e n i n 38. t e r m s o f a s i n g l e s c a l a r v a r i a b l e , t h e s t r e a m f u n c t i o n , s o t h a t t h e f l o w f i e l d i s c o m p l e t e l y d e t e r m i n e d . H e r e t h i s i s n o t p o s s i b l e . T h e p a r t i a l c o n t i n u i t y e q u a t i o n c a n b e s i m p l i f i e d f o r c o n s t a n t D b y e l i m i n a t i n g p-^. U s i n g t h e t o t a l c o n t i n u i t y t o e l i m i n a t e t e r m s a n d e x p a n d i n g g i v e s V . v = ( 3 . 1 2 ) T o f a c i l i t a t e s i m p l i f i c a t i o n o f t h e t h r e e b a s i c e q u a -t i o n s t h e y a r e now r e c a s t i n d i m e n s i o n l e s s f o r m . A n g u l a r b r a c k e t s d e n o t e d i m e n s i o n l e s s v a r i a b l e s . H e n c e v w < v > = ^ - < ° > = t - = < * > - * ^ (3-i3» w h e r e p Q a n d w Q a r e t h e v a l u e s o f t h e s e v a r i a b l e s f o r l a r g e r a n d 0 = TT/2 i n b o d y - c e n t r e d c o o r d i n a t e s . F r o m t h e e x p r e s s i o n f o r w g i v e n p r e v i o u s l y , t h e f o l l o w i n g r e l a t i o n s h i p i s f o u n d , w h e r e n i s t h e d i m e n s i o n l e s s d e n s i t y g r a d i e n t f a r f r o m t h e p a r t i c l e . n ( 3 . 1 4 ) T h i s e q u a t i o n i s o n l y s t r i c t l y c o r r e c t when t h e p a r t i c l e m o v e s a t t h e mean m o l a r v e l o c i t y . T h e e r r o r i n v o l v e d w i l l b e d i s c u s s e d 39. l a t e r . I n d i m e n s i o n l e s s terms t h e f l u i d e q u a t i o n s become (3.15) (3.16) (PC) (3.17) I f the p a r t i c l e moves a t o t h e r than the mean molar v e l o c i t y , the v a l u e o f 3p/3t w i t h r e s p e c t t o b o d y - c e n t r e d c o o r d i n a t e s i s n o t z e r o . As an a p p r o x i m a t i o n i t may be assumed t h a t a q u a s i - s t e a d y s t a t e e x i s t s , such t h a t , w i t h r e s p e c t t o t h e p a r t i c l e , 3p/3t i s c o n s t a n t everywhere t h r o u g h o u t the f i e l d . I t f o l l o w s t h a t <3 p \ /( <}_p_\ ( 3X \ \ 3 t / M 3x / I 3t / / n V p where v^ i s t h e p a r t i c l e v e l o c i t y w i t h r e s p e c t t o a number-c e n t r e d c o o r d i n a t e system. Hence t h e t o t a l c o n t i n u i t y e q u a t i o n becomes v p + V . p v ^ = 0 (3.19) The b e h a v i o u r o f the system depends on t h e parameter n . I f n i - s s m a l l (as i s n o r m a l l y the case i n p r a c t i c a l s i t u a -t i o n s ) , f u r t h e r s i m p l i f i c a t i o n i s p o s s i b l e . From the t o t a l c o n t i n u i t y e q u a t i o n , 40. - v . y p - n v £ 1 (3.20) so t h a t ^ V - y ^ i s o f o r d e r n. Hence i n g e n e r a l ^ V - y ^ << ^ | y_ | ^ , and the N a v i e r Stokes e q u a t i o n can be s o l v e d w i t h r e s p e c t t o b o d y - c e n t r e d c o o r d i n a t e s t o a good a p p r o x i m a t i o n by s e t t i n g V.v e q u a l .to z e r o . I f the p a r t i c l e moved e s s e n t i a l l y a t the mean mass v e l o c i t y , t h e n ^^_-Y^ would n o t be s m a l l everywhere compared t° ^ 1 — 1 ^ ^ * However, i n t h i s case v e l o c i t i e s i n t h e f l o w f i e l d a r e o f o r d e r n, so t h a t t h e e r r o r i n t h e p r e d i c t e d p a r t i c l e v e l o c i t y i s s t i l l s m a l l . F o r y_.v = 0 the N a v i e r - S t o k e s e q u a t i o n can be r e w r i t t e n i n terms o f the stream func t i o n ij> (see f o r example Happel and Brenner ( 1 9 6 5 ) ) , E 2(E 2tM = E % = 0 (3.21) 2 where E i s the d i f f e r e n t i a l o p e r a t o r . E 2 = _iL + s i n — — ( 1 (3 22) r 2 39 ( s i n 6 89 J (J.**) The v e l o c i t y components can be found from the stream f u n c t i o n . v s i n 9 30 v, = + r s i n 3jj_ 3r (3.23) 41. A s i m i l a r s i m p l i f i c a t i o n c a n b e made f o r t h e p a r t i a l c o n t i n u i t y e q u a t i o n , when n i s s m a l l , t o y i e l d = 0 ( 3 . 2 4 ) T h i s e q u a t i o n c a n b e s o l v e d w i t h r e s p e c t t o b o d y - c e n t r e d c o o r d i -n a t e s w i t h t h e b o u n d a r y c o n d i t i o n s <CP^ » = + n r c o s ^ , | | | ^ = 0 ( 3 . 2 5 ) t o y i e l d t h e r e s u l t < ^ > = <^ 1 + n ( r + - ^ _ ) c o s 0^> ( 3 . 2 6 ) H e n c e , l e a v i n g a s i d e n o n - s t e a d y - s t a t e a s p e c t s , t h e use o f t h e s i m p l e f o r m s o f t h e c o n t i n u u m m e c h a n i c s e q u a t i o n s h a s b e e n j u s t i f i e d o n c o n d i t i o n t h a t n i s s m a l l . . I n p a r t i c u l a r i t i s not r e q u i r e d t h a t t h e c o n c e n t r a t i o n o f o n e c o m p o n e n t r e l a t i v e t o t h e o t h e r b e s m a l l , a s some w o r k e r s b e l i e v e d . 3 . 3 D e t e r m i n a t i o n o f t h e F r e e P a r t i c l e V e l o c i t y T h e g e n e r a l s o l u t i o n o f t h e s t r e a m f u n c t i o n f o r f l o w a r o u n d a s o l i d s p h e r e i s ( s e e H a p p e l a n d B r e n n e r ( 1 9 6 5 ) ) = + B ' r + C ' r 2 + D ' r 4 \ s i n 2 0 ( 3 . 2 7 ) where A ' , B * , c' and D ' are constants whose values are to be determined. I t follows that cos 9 ( 3 . 2 8 ) s i n 9 ( 3 . 2 9 ) The boundary conditions for large r are given by <^vr^>= - ^ v ^ c o s 0, <v Q^> = +<v o o^ s i n 6 , where v ^ i s the f l u i d v e l o c i t y with respect to the sphere for large r, and i s assumed constant. (This condition i s discussed later'.-), I t follows that C* = v / 2 and D ' = 0 , so that CO / \ / 2 A " ^ 2B' x •<v = • + — v' Provided that any s l i p phenomenon i s confined to a region close to the p a r t i c l e surface, i t i s v a l i d to introduce cos 6 ( 3 . 3 1 ) i t as a boundary c o n d i t i o n . T h i s i s the case f o r a l a r g e p a r t i c l e . A l l proposed e x p r e s s i o n s f o r s l i p a t a f l a t s u r f a c e have taken the form dYp v s i i P = a D "diT ( 3 - 3 3 ) where a i s a s l i p c o e f f i c i e n t u s u a l l y dependent on , M 2, and Y 2« When n i s s m a l l , a w i l l be a constant t o a good approximation, Expressed i n terms of dimensionless v a r i a b l e s and s p h e r i c a l c o o r d i n a t e s , the s l i p v e l o c i t y i s < * . i i p > - -V<! fe)>s • where the s l i p c o e f f i c i e n t has been r e d e f i n e d f o r convenience as i M 0 1 = M 2 - M x a • ( 3 ' 3 5 ) S u b s t i t u t i n g f o r the d e n s i t y g r a d i e n t g i v e s the s u r f a c e boundary c o n d i t i o n f o r v Q , w h i l e t h a t f o r v i s i m p l i e d by the impermeable o r p a r t i c l e s u r f a c e <v\> = 0, <(vQy = < ^ s l i p ^ > = + | a ' s i n 6, at<r>= 1 (3.36) 44. T h e c o e f f i c i e n t s A ' a n d B 1 c a n now b e d e t e r m i n e d ' v m - 3 a \ y .v / 3 ( a - v _ f ^ ( 3 . 3 7 ) s o t h a t t h e f l o w f i e l d i s s o l v e d i n t e r m s o f v a n d d.1. co I t c a n b e shown ( s e e H a p p e l a n d B r e n n e r ( 1 9 6 5 ) ) t h a t t h e f o r c e o n t h e s p h e r e i s g i v e n b y F = + 8 T r y w Q R < B ^ > ( 3 . 3 8 ) T o f i n d t h e f r e e p a r t i c l e v e l o c i t y , t h e c o e f f i c i e n t B" i s s e t t o z e r o , s o t h a t <(v^y = a ' ( 3 . 3 9 ) o r i n d i m e n s i o n a l t e r m s v = aD I ( 3 . 4 0 ) °° V 3x / H e n c e t h e p a r t i c l e v e l o c i t y w i t h r e s p e c t t o n u m b e r - c e n t r e d c o o r d i -n a t e s i s M - M V p = W - Voo = t- 2 M 1 " " I 0 1-^ ) <3-41> 45. T h e v e l o c i t y c a n now b e f o u n d f o r a n y s l i p c o e f f i c i e n t . F o r e x a m p l e , K r a m e r s a n d K i s t e m a k e r (1943) g i v e a (3.42) s o t h a t v /M2 -Y l 1 + Y l 2 D (3.43) 3.4 T h e R a t e o f E n e r g y D i s s i p a t i o n T h e e n e r g y d i s s i p a t i o n r a t e , E, i n t h e f l o w f i e l d i s now c a l c u l a t e d f o r r e a s o n s t h a t w i l l b e c o m e c l e a r s h o r t l y . A c c o r d i n g t o B i r d e t a l . (1962) t h i s i s g i v e n b y E 2TT =o CO e = 0' r=R. 2 ( x : V v) r d r s i n 0 d0d<}> (3.44) R e w r i t i n g t h e i n t e g r a l i n d i m e n s i o n l e s s f o r m , a n d i n s e r t i n g t h e c o m p o n e n t s o f _r:V_ v g i v e s J . ( 3 . 4 5 ) S u b s t i t u t i n g f o r v and v Q u s i n g E q u a t i o n s ( 3 . 3 1 ) and ( 3 . 3 2 ) r o y i e l d s E = 2 T r y R w o 2 < ^ 2 4 A ' 2 + 1 6 A ' B ' + 8 B ' 2 ^ ( 3 . 4 6 ) Hence by u s i n g the v a l u e o f A 1 from E q u a t i o n ( 3 . 3 7 ) , s u b j e c t t o the c o n d i t i o n t h a t B ' = 0 , one f i n d s E = 12TTyRw o 2a.' 2 . ( 3 . 4 7 ) I t i s i m m e d i a t e l y c l e a r t h a t the r a t e o f energy d i s s i p a t i o n i s o n l y z e r o when a 1 i s z e r o . I n t h i s case t h e r e i s no s l i p and the p a r t i c l e moves a t t h e mean mass v e l o c i t y , so t h a t w i t h r e s p e c t t o number-centred c o o r d i n a t e s , 47. M2 - M i _ (!2A P M \3x ) m One can a l s o show t h a t the r a t e o f energy d i s s i p a t i o n as g i v e n by E q u a t i o n (3.47) i s n o t g e n e r a l l y s m a l l , by comparing i t w i t h the d i s s i p a t i o n r a t e f o r a sphere w i t h o u t s l i p a t the s u r f a c e , and moving w i t h r e s p e c t t o t h e f l u i d a t the same v e l o c i t y , v ,which e q u a l s a 1 w„. ^ o E . . = Fv = 6iryRv 2 (3.49) no s l i p oo r oo I t f o l l o w s t h a t E ,. /E ,. = 2. s l i p no s l i p N o r m a l l y one would e x p e c t t h a t the f r e e p a r t i c l e v e l o c i t y would a d j u s t t i l l t he energy d i s s i p a t i o n r a t e were z e r o . This does n o t happen h e r e , w h i c h r a i s e s t h e q u e s t i o n o f t h e s o u r c e o f the energy. The energy d i s s i p a t i o n r a t e i n t h e u n d i s t u r b e d d i f f u s i o n f i e l d i s e s s e n t i a l l y z e r o , so t h a t energy cannot e a s i l y be s u p p l i e d by the d i f f u s i o n p r o c e s s . (More p r e c i s e l y , the energy d i s s i p a t i o n r a t e per u n i t volume i n the u n d i s t u r b e d gas i s e q u a l t o in (|n) .) C l o s e r e x a m i n a t i o n r e v e a l s t h a t the energy o r i g i n a t e s a t the p a r t i c l e s u r f a c e . The s l i p c o n d i t i o n c r e a t e s a s i t u a t i o n where the gas i s b e i n g dragged around th e s u r f a c e o f the sphere a g a i n s t the f o r c e o f t h e r e s u l t i n g s hear s t r e s s e s . Thus a s m a l l m o l e c u l a r e f f e c t i s t h e s o u r c e o f l a r g e q u a n t i t i e s o f energy'. 48. I t must be c o n c l u d e d t h a t t h e s h e a r s t r e s s e s w i l l h e a v i l y s u p p r e s s any tendency f o r s l i p t o o c c u r , and t h a t the p a r t i c l e w i l l move e s s e n t i a l l y a t the mean mass v e l o c i t y o f t h e gas. T h i s r e s u l t i s t r u e r e g a r d l e s s o f p a r t i c l e shape, s i n c e the u n c o u p l i n g o f t h e continuum e q u a t i o n s i s s t i l l v a l i d , a n d the f o r c e on t h e p a r t i c l e i s t h e r e f o r e always z e r o when i t moves a t t h e gas mean mass v e l o c i t y . The e x i s t e n c e o f s l i p a t a f l a t s u r f a c e , however, i s not c h a l l e n g e d h e r e . (The a u t h o r i n t e n d s t o show a t a l a t e r d a t e t h a t the s l i p v e l o c i t y a t a f l a t s u r f a c e i s much s m a l l e r t h a n . c u r r e n t t h e o r i e s p r e d i c t . However, t h i s f a l l s beyond the scope o f the c u r r e n t study.) 3.5 F u r t h e r Refinements and A d d i t i o n s 3.5.1 Non-Steady S t a t e B e h a v i o u r The problem has so f a r been t r e a t e d as a s t e a d y s t a t e one, t a k i n g t h e mean mass v e l o c i t y o f t h e gas t o be c o n s t a n t f a r from t h e p a r t i c l e . A c t u a l l y , w i t h r e s p e c t t o number-centred c o o r d i n a t e s , t h i s v e l o c i t y i n c r e a s e s i n the x d i r e c t i o n a t a r a t e g i v e n by 3w 3x (3.50) Thus f o r example, t h e v e l o c i t i e s s h o u l d s t r i c t l y n o t have been made d i m e n s i o n l e s s w i t h r e s p e c t t o a v a l u e o f w a t f i x e d body-49 . c e n t r e d c o o r d i n a t e s . The t r u e p a r t i c l e v e l o c i t y i n these circum-stances i s g i v e n by a d i f f e r e n t i a l e q uation of the second order with r e s p e c t t o time, and i s not of p r a c t i c a l i n t e r e s t . I n stead we d e r i v e the c o n d i t i o n under which the time-dependent e f f e c t s can be i g n o r e d . One might expect t h a t the p a r t i c l e v e l o c i t y would always be s l i g h t l y l e s s than the surrounding gas v e l o c i t y , which i s i n c r e a s i n g i n the x d i r e c t i o n . T h i s d i f f e r e n c e w i l l cause the p a r t i c l e t o a c c e l e r a t e . Thus, i f the p a r t i c l e v e l o c i t y i s fw where w i s the gas v e l o c i t y w i t h r e s p e c t to number-centred c o o r d i n a t e s , and f i s a con s t a n t c l o s e to u n i t y , then a c c o r d i n g t o Stokes' law _ F 6iryR(w-fw) , . . where M and a denote the p a r t i c l e mass and a c c e l e r a t i o n , P P r e s p e c t i v e l y . The f l u i d a c c e l e r a t i o n i n terms o f the same co o r d i n a t e s i s For q u a s i - s t e a d y s t a t e these a c c e l e r a t i o n s w i l l be approximately e q u a l , from which i t f o l l o w s t h a t 50. P 2 f Ci 1 - 2/9 -E- ^ (3.53) where p i s t h e p a r t i c u l a t e d e n s i t y and Sc i s the Schmidt number, P u/pD. S i n c e Sc—1 f o r g a s e s , time-dependent e f f e c t s w i l l be s m a l l f o r 2 p o 2/9 n << 1 (3.54) T h i s c r i t e r i o n i s n o r m a l l y met f o r a e r o s o l p a r t i c l e s e x c e p t when the gas mass t r a n s f e r r a t e s a re e x t r e m e l y h i g h . 3.5.2 A Second Order A p p r o x i m a t i o n f o r P a r t i c l e V e l o c i t y A second o r d e r a p p r o x i m a t i o n f o r t h e f r e e sphere v e l o c i t y i s now d e r i v e d , t a k i n g i n t o a c c o u n t t h a t the v a l u e o f y_.v i s not e x a c t l y z e r o . A c c o r d i n g t o t h e t o t a l c o n t i n u i t y e q u a t i o n I f t he p a r t i c l e v e l o c i t y i s c l o s e t o the gas mean mass v e l o c i t y , t h e n ^|v|^= n and ^ v p ^ ~ Thus the f i r s t term on the r i g h t hand s i d e o f E q u a t i o n (3.55) i s much s m a l l e r t h a n the second, and (3.55) 51. can be i g n o r e d . Hence one o b t a i n s (3.56) This must be s o l v e d i n c o n j u n c t i o n w i t h </v (v_. x_ (y_ x_ v) ) ^ = V x   v  v ) ) > = 0 . (3.57) The v e l o c i t y components t h a t s a t i s f y these equations are of the form (-2~V + ~ + v o o ) cos 9 + n(r + ^ ) cos2 6>(3.58) \ r r r {v^y = + + ~ + V c o ) s i n 6 + n r c o s 9 s i n ^ / (3.59) where v^ i s the gas v e l o c i t y p a s t the sphere f o r l a r g e r , and A 1 , B ' and G 1 are c o n s t a n t s . Since v r i s zero a t the s u r f a c e , 2 A ' + 2B* + v = 0 , G ' = -1 . (3.60) A l s o the f i r s t term i n the e x p r e s s i o n f o r v Q must be zero a t the s u r f a c e i f the energy d i s s i p a t i o n r a t e i s to be ( e s s e n t i a l l y ) z e r o . - A ' + B * + v • = 0 (3.61) T h e v e l o c i t y c o m p o n e n t s a r e t h e r e f o r e 2r" + 1 ) v m c o s 9 + n ( r — ^ ) c o s 9 r ( 3 . 6 2 ) + 1 ) v s i n 9 + n r c o s 0 s i n 9 . ( 3 . 6 3 ) N o t e t h a t a l t h o u g h i t was c o n c l u d e d e a r l i e r t h a t t h e r e c o u l d b e e s s e n t i a l l y n o s u r f a c e s l i p , t h e c o n t i n u u m m e c h a n i c s e q u a t i o n s demand t h a t ( v Q ) d o e s n o t v a n i s h i f V . v i s n o t z e r o . T h i s o s — — e f f e c t h o w e v e r i s s m a l l . I t i s f o u n d t h a t t h e s e c o n d o r d e r t e r m s i n t h e v e l o c i t y e x p r e s s i o n s make n o c o n t r i b u t i o n t o t h e d r a g f o r c e o n t h e p a r t i c l e . I t f o l l o w s t h a t t h e f l o w f i e l d a r o u n d t h e f r e e p a r t i c l e i s g i v e n b y , ( 3 . 6 4 ) ( 3 . 6 5 ) a n d t h a t t h e p a r t i c l e a g a i n t r a v e l s a t t h e g a s mean m a s s v e l o c i t y a s t h e f i r s t o r d e r a p p r o x i m a t i o n i n d i c a t e d . 53. 3.5.3 P a r t i c l e V e l o c i t y i n a B i n a r y Gas M i x t u r e w i t h One  Sta g n a n t Component L a s t l y , t h e p a r t i c l e v e l o c i t y i n a system where component 2 o f the gas d i f f u s e s t h r o u g h component.1, w h i c h i s s t a g n a n t , i s d e r i v e d . The d i f f u s i o n e q u a t i o n s f a r from t h e p a r t i c l e a r e (3.66) and the mean molar v e l o c i t y w i t h r e s p e c t t o t h e s t a g n a n t gas i s (3.67) W i t h r e s p e c t t o a c o o r d i n a t e system moving a t t h i s c o n s t a n t v e l o c i t y , t he gas components e x h i b i t e q u i m o l a r c o u n t e r - d i f f u s i o n . Hence t o f i n d t he p a r t i c l e v e l o c i t y i n t h i s system one need o n l y add t h e mean mass v e l o c i t y w i t h r e s p e c t t o these c o o r d i n a t e s , t o the v e l o c i t y o f t h e c o o r d i n a t e system. VP - - — — D W / „ " ^ W ; -B-^vsr/. ( 3- 6 8 ) T h i s i s s i m p l y t h e mean mass v e l o c i t y o f the gas i n t h e system. 54. 3.6 C o n c l u s i o n s P r o v i d e d t h a t the f r a c t i o n a l change i n f l u i d d e n s i t y o v e r t h e l e n g t h o f the p a r t i c l e i s s m a l l , i t i s v a l i d t o uncouple the continuum mechanics e q u a t i o n s . The v e l o c i t y f i e l d around the p a r t i c l e i s the n g i v e n by t h e N a v i e r Stokes e q u a t i o n w i t h V_.v = 0, and the f r e e p a r t i c l e v e l o c i t y can be found f o r any s l i p c o n d i t i o n . The e x i s t e n c e o f s l i p , however, i s a s s o c i a t e d w i t h a s i g n i f i c a n t r a t e o f energy d i s s i p a t i o n , w hich appears t o exceed t h e r a t e a t wh i c h energy c o u l d be s u p p l i e d i n t h e system. I t i s t h e r e f o r e b e l i e v e d t h a t t h e presence o f shear s t r e s s e s a t the p a r t i c l e s u r f a c e must s t r o n g l y s u p p r e s s any tendency f o r s l i p t o o c c u r . I n t h e s e c i r c u m s t a n c e s , t h e p a r t i c l e w i l l move a t e s s e n t i a l l y the gas mean mass v e l o c i t y , r e g a r d l e s s o f i t s shape. T h i s w i l l be t r u e i n b o t h e q u i m o l a r c o u n t e r - d i f f u s i n g systems, and systems w i t h one component s t a g n a n t . A second o r d e r a p p r o x i -m a t i o n y i e l d s t he same r e s u l t . D e v i a t i o n s from the t h e o r y caused by a c c e l e r a t i v e e f f e c t s , p r e s s u r e d i f f u s i o n , and v a r i a t i o n s i n y and D w i l l n o r m a l l y be s m a l l f o r a e r o s o l p a r t i c l e s . T h i s t h e o r y i s n o t i n agreement w i t h o t h e r s p r o p o s e d r e c e n t l y . U n f o r t u n a t e l y , e x p e r i m e n t a l e v i d e n c e p u b l i s h e d t o date i s i n a d e q u a t e t o c l a r i f y t he s i t u a t i o n . 55. C h a p t e r 4 DERIVED THEORY 4 . 1 T h e F i l m T h e o r y T h e t h e o r y f o r t h e r a t e o f p a r t i c l e d e p o s i t i o n b y d i f f u s i o p h o r e s i s c a n b e d e r i v e d o n c e t h e f u n d a m e n t a l p a r t i c l e v e l o c i t y i s k n o w n . I n m a k i n g t h e d e r i v a t i o n , t h r e e d i f f e r e n t v e l o c i t y e x p r e s s i o n s w i l l b e u s e d . T h e f i r s t i s t h e g a s mean m o l a r v e l o c i t y p r e d i c t e d b y D e r j a g u i n e t a l . (1966) a n d D e r j a g u i n a n d Y a l a m o v ( 1 9 7 2 ) , w h i l e t h e s e c o n d i s t h e g a s mean m a s s v e l o c i t y p r e d i c t e d i n t h i s w o r k . T h e s e e x p r e s s i o n s p r o b a b l y e s t a b l i s h t h e u p p e r a n d l o w e r l i m i t s f o r t h e p a r t i c l e v e l o c i t y i n a l l r e g i m e s ( m o l e c u l a r , t r a n s i t i o n , a n d c o n t i n u u m ) , s i n c e , i f o n e i g n o r e s s m a l l s e c o n d - o r d e r e f f e c t s , i t i s d i f f i c u l t t o c o n c e i v e how a p a r t i c l e c o u l d t a k e o n a v e l o c i t y o u t s i d e t h i s r a n g e . T h e t h i r d e x p r e s s i o n i s t h a t o b t a i n e d b y S c h m i t t a n d W a l d m a n n (1960) f o r l a r g e p a r t i c l e s . T h i s i s a l s o t h e r e s u l t g i v e n b y B r o c k ' s (196 3) w o r k , w h e n s e c o n d - o r d e r t e r m s a r e i g n o r e d a n d t h e a c c o m m o d a t i o n c o e f f i c i e n t s a r e t a k e n a s u n i t y . M o r e i m p o r t a n t l y , i t i s t h e g e n e r a l l y a c c e p t e d e x p r e s s i o n f o r s m a l l p a r t i c l e s u n d e r t h e s e same c o n d i t i o n s , a n d h e n c e may b e u s e f u l i n d e t e r m i n i n g w h e t h e r e x p e r i m e n t a l r e s u l t s i n d i c a t e t r a n s i t i o n regime b e h a v i o u r . S i n c e the d e r i v a t i o n o f t h e t h e o r y does not r e q u i r e any knowledge o f equipment geometry, i t i s p r e s e n t e d here f o r the g e n e r a l case and not s p e c i f i c a l l y f o r a w e t t e d w a l l column. C o n s i d e r a u n i t o f t r a n s f e r equipment o f a r b i t r a r y geometry. The t u r b u l e n t f l u i d c o n t a i n i n g suspended p a r t i c l e s t r a v e l s from i n l e t t o o u t l e t by some p a t h (not n e c e s s a r i l y l i n e a r ) , w h i c h i s measured by t h e z c o o r d i n a t e . The x c o o r d i n a t e i s t a k e n t o be p e r p e n d i c u l a r t o t h e i n t e r f a c e o r s u r f a c e a c r o s s w h i c h t r a n s f e r o c c u r s . The i n t e r f a c i a l o r t r a n s f e r a r e a per u n i t d i s t a n c e i n t h e d i r e c t i o n o f f l u i d f l o w , a, may be a f u n c t i o n o f z. The f o l l o w i n g c o n d i t i o n s are assumed t o h o l d : ( i ) Steady s t a t e c o n d i t i o n s p r e v a i l ( a t l e a s t i n a t i m e - a v e r a g e d sense) and t h e gas t e m p e r a t u r e and p r e s s u r e are c o n s t a n t , ( i i ) A t any v a l u e o f the z c o o r d i n a t e , t h e b u l k o f the gas i s w e l l mixed w i t h r e s p e c t t o p a r t i c l e and gas c o n c e n t r a t i o n s , ( i i i ) Mass t r a n s f e r r e s i s t a n c e i n t h e gas phase i s c o n f i n e d t o a t h i n f i l m a d j a c e n t t o the t r a n s f e r s u r f a c e , ( i v ) Mass t r a n s f e r i n the z d i r e c t i o n i n t h e b u l k o f the gas o c c u r s by c o n v e c t i o n o n l y , w h i l e i n the f i l m i t i s n e g l i g i b l e , (v) The h o l d u p o f p a r t i c l e s i n t h e f i l m i s s m a l l . ( v i ) D i f f u s i o p h o r e s i s i s t h e o n l y mechanism w h i c h t r a n s p o r t s p a r t i c l e s a c r o s s the f i l m , ( v i i ) P a r t i c l e s w h i c h r e a c h th e t r a n s f e r s u r f a c e a r e r e t a i n e d . ( v i i i ) The volume f r a c t i o n o f p a r t i c l e s i n t h e gas i s s m a l l . These c o n d i t i o n s , e x c e p t f o r t h o s e s p e c i f i c a l l y c o n c e r n i n g p a r t i c l e s , a r e e i t h e r the same a s , o r analogous t o , t h o s e i n v o k e d i n d e v e l o p i n g t h e s i m p l e t h e o r y o f mass t r a n s f e r from t u r b u l e n t f l o w (see f o r example T r e y b a l ( 1 9 6 8 ) ) . A l t h o u g h t h e , d e r i v a t i o n f o r multicomponent systems i s q u i t e s t r a i g h t f o r w a r d , f o r s i m p l i c i t y a b i n a r y m i x t u r e w i l l be c o n s i d e r e d i n w h i c h component 1 i s i n e r t and component 2 i s t r a n s f e r r e d . A p a r t i c l e b a l a n c e over th e d i f f e r e n t i a l l e n g t h dz g i v e s d(Gn/c) = -m^a dz , where the l e f t hand s i d e r e p r e s e n t s t h e r a t e o f change i n t h e number o f p a r t i c l e s i n t h e c o r e , and the r i g h t hand s i d e r e p r e -s e n t s the r a t e o f t r a n s p o r t o f p a r t i c l e s i n t o t h e f i l m , and hence t h e i r r a t e o f c a p t u r e . Here G i s t h e molar gas f l o w r a t e , c i s t h e m o l ar gas c o n c e n t r a t i o n , n i s t h e p a r t i c l e number c o n c e n t r a t i o n , and v ^ i s t h e p a r t i c l e v e l o c i t y i n the x d i r e c t i o n . S i m i l a r l y , a mass b a l a n c e f o r the gas y i e l d s dG = -N 0a dz 58. where N 2 i s the f l u x o f component 2 i n t o the f i l m . S i n c e compo-nent l i s i n e r t , i t i s c o n v e n i e n t t o i n t r o d u c e the p a r t i c l e c o n c e n t r a t i o n based on u n i t volume o f t h i s s p e c i e s n l = n / y l and t h e m o l a r f l o w r a t e o f component 1 which i s c o n s t a n t G 1 = Gy1 , where i s t h e mole f r a c t i o n o f component 1. The p a r t i c l e and mass b a l a n c e s t h e n become G-^dn^ = ~ Y i n i c v p a d z and G 1 d ( l / Y 1 ) = -N 2a dz , s i n c e c i s c o n s t a n t . Combining t h e s e e q u a t i o n s y i e l d s I f subscripts " i n " and "out" denote the terminal conditions, then the p a r t i c l e removal e f f i c i e n c y i s obtained by integration. n. - n, . 1, i n 1,out n = 1 1, i n exp out i n Y l C V p d ( l / Y l ) This expression can be evaluated once v^ and N 2 are s p e c i f i e d . The concentration n^, and the e f f i c i e n c y based on i t , are inde-pendent of gas composition. Hence the e f f i c i e n c y i s influenced only by p a r t i c l e removal, and not by composition changes occurring during mass transfer. This e f f i c i e n c y i s i d e n t i c a l to the usual one based on the t o t a l number of p a r t i c l e s entering and leaving the equipment. An expression for the p a r t i c l e v e l o c i t y i s required for the case when component 2 diffuses through component 1 which i s stagnant i n the thin f i l m . This expression can be deduced from that applicable to equimolar counter-diffusion, i n the manner indicated i n Chapter 3. Since the fluxes i n the mass transfer f i l m are given by N x • = 0 and N _ DC ^2 2 y dx where D i s the gas d i f f u s i v i t y , the p a r t i c l e v e l o c i t y expressions can be recast in terms of the flux of component 2 . There are three cases: ( i ) The p a r t i c l e s move with the gas mean molar v e l o c i t y . - JD. ^ 2 = ^ 2 V P dx c and hence ep ~ 1 " [ Y l ] i n / [ Y l ] o u t ' ( i i ) The p a r t i c l e s move with the gas mean mass v e l o c i t y . v = - !V D _ * 2 = ^ ^ 2 . P M Y-J_ dx M c where M 2 i s the molecular weight of component 2 and M i s the mean molecular weight defined as Y-L + Y 2 M 2 * H e n c e i [ M / Y l ] o u t Also the molecule masses m. can be replaced by the molecular weights . 1 C i i i ) The p a r t i c l e s move with the v e l o c i t y suggested by Schmitt and Waldmann. v P Y l 1 + Y _D_ ^ 2 2vw-2 Y l Y l 1 + Y 2 / M 2 and hence = 1 - out [ ( Y - L ^ + Y 2 / M 2 ) / Y 1 ] [ ( Y L ^ + Y 2 v ^ 2 ) / Y 1 ] . N T h i s d e r i v a t i o n i s not q u i t e r i g o r o u s i f t h e mass t r a n s f e r boundary l a y e r i s p a r t i a l l y t u r b u l e n t , s i n c e the e x p r e s s i o n f o r t h e mass t r a n s f e r f l u x s h o u l d be w r i t t e n i n terms o f t h e e f f e c t i v e d i f f u s i v i t y r a t h e r t h a n t h e m o l e c u l a r d i f f u s i v i t y . I t i s , however, p l a u s i b l e under t h e s e c o n d i t i o n s t o make the same change i n t h e p a r t i c l e v e l o c i t y e x p r e s s i o n s , so t h a t t h e f i n a l r e s u l t s remain u n a l t e r e d . T h i s work was p u b l i s h e d by Whitmore and M e i s e n (1973). 4.2. The G e n e r a l Case A f t e r t h e f i l m t h e o r y was d e v e l o p e d , i t was found t h a t much more g e n e r a l r e s u l t s c o u l d be o b t a i n e d by a n a l y s i n g t h e n o n - s t e a d y - s t a t e forms, o f t h e p a r t i c l e and f l u i d c o n t i n u i t y e q u a t i o n s . F o r t h i s p u r p o s e , the f l u i d c o n t i n u i t y 62. e q u a t i o n i s d e r i v e d i n terms o f t h e v e l o c i t y adopted by a p a r t i c l e i n a d i f f u s i n g system. The f o l l o w i n g c o n d i t i o n s a re r e q u i r e d . ( i ) The p a r t i c l e s move r e l a t i v e t o the s u r r o u n d i n g f l u i d o n l y by d i f f u s i o p h o r e s i s . ( i i ) The volume f r a c t i o n o f p a r t i c l e s i n t h e f l u i d i s s m a l l . ( i i i ) P a r t i c l e s w h i c h r e a c h t h e t r a n s f e r s u r f a c e a r e r e t a i n e d . The c o n t i n u i t y e q u a t i o n f o r p a r t i c l e s i s where v must now be i n t e r p r e t e d as t h e p a r t i c l e v e l o c i t y due t o bot h d i f f u s i o p h o r e s i s and b u l k f l u i d f l o w . A g a i n , t h e r e are t h r e e cases t o c o n s i d e r i n d e v e l o p i n g the f l u i d c o n t i n u i t y e q u a t i o n s . The b a s i c forms o f t h e s e e q u a t i o n s can be found, f o r example, i n B i r d e t a l . (1960). ( i ) The p a r t i c l e s move at the f l u i d mean mass v e l o c i t y . S i n c e the p a r t i c l e v e l o c i t y e q u a l s the mean mass v e l o c i t y o f the f l u i d , v, the normal form o f t h e c o n t i n u i t y e q u a t i o n f o r the f l u i d i s r e q u i r e d . 63. ff + V - pv . 0 ( i i ) The p a r t i c l e s move at the f l u i d mean molar v e l o c i t y . W r i t t e n i n terms o f the mean molar v e l o c i t y of the f l u i d , ' v*, the continuity equation becomes |H + V . cv* = 0 3 t ( i i i ) The p a r t i c l e s move at Schmitt and Waldmann's v e l o c i t y . B e f o r e d e v e l o p i n g the a p p r o p r i a t e f l u i d c o n t i n u i t y e q u a t i o n , an e x p r e s s i o n i s needed f o r the p a r t i c l e v e l o c i t y i n a multicomponent gas. S c h m i t t and Waldmann showed t h a t t h i s v e l o c i t y i s e q u i v a l e n t t o t h a t adopted by a f r e e f l a t s u r f a c e i n c o n t a c t w i t h a gas m i x t u r e whose mean molar v e l o c i t y i s z e r o , and w h i c h i s d i f f u s i n g p a r a l l e l t o t h e s u r f a c e . Kramers and K i s t e m a k e r (1943) d e r i v e d t h i s v e l o c i t y f o r a b i n a r y gas, and by use o f t h e i r t e c h n i q u e i t i s s t r a i g h t f o r w a r d t o deduce the r e s u l t f o r k components 64. k dy • I / M 7 D. . ^ , 1 i dx i = l U = - r w k T Y • > / M 7 1 = 1 1 1 where and dY^/dx are t h e d i f f u s i v i t y and mole f r a c t i o n g r a d i e n t a l o n g t h e s u r f a c e f o r component i . The e q u i v a l e n t e x p r e s s i o n f o r the case where the mean molar v e l o c i t y o f t h e m i x t u r e , N/c, i s not z e r o , can be found by a d d i t i o n . T h i s i s t h e n a l s o the g e n e r a l e x p r e s s i o n f o r p a r t i c l e v e l o c i t y . N , N i = l V P = . o:+ Uw = c " k dy. y / M . D. - 5 - ^ L n l l dx y Y • ^ M T . s • i i 1 = 1 The e x p r e s s i o n may be s i m p l i f i e d by i n t r o d u c i n g the m o lar f l u x e s o f the i n d i v i d u a l s p e c i e s dy • N. = Y - N - D.c - r - i -l l l dx so t h a t I n o r d e r t o d e r i v e a f l u i d c o n t i n u i t y e q u a t i o n i n terms o f t h i s t y p e o f v e l o c i t y , a new u n i t w h i c h may be termed t h e " r o o t mass c o n c e n t r a t i o n " i s d e f i n e d : c . = / M. c • 1 1 1 Other r e l a t e d v a r i a b l e s can t h e n be d e f i n e d t o form a c o m p a t i b l e system. N. r = N. y/W7 — l — l l k r V r c = . L ^  c. i = l l k I N. i = l - 1 r v r c The v e l o c i t y v-, i s now i d e n t i c a l t o v as - -P r e q u i r e d . The f l u i d c o n t i n u i t y e q u a t i o n i n terms o f t h e s e q u a n t i t i e s can be d e r i v e d from the k s i n g l e component c o n t i n u i t y e q u a t i o n s M u l t i p l y i n g each o f t h e s e by ^M^ and summing y i e l d s j £ (JV/ M 7 ) + V . (I^/MT) = 0. I n s e r t i n g t h e i d e n t i t i e s above g i v e s _L „ R R "3T + V . c- v = 0 I n each o f the t h r e e cases t h e c o n t i n u i t y e q u a t i o n s f o r p a r t i c l e s and f l u i d can be w r i t t e n i n t h e f o l l o w i n g form, | | + V . „v' = 0 9c' 9t + V . c'v' = 0 where v' i s one o f the t h r e e v e l o c i t i e s , and c' i s t h e a p p r o p r i a t e r e l a t e d c o n c e n t r a t i o n . M u l t i p l y i n g the f i r s t e q u a t i o n by 1/c" and the second by n / ( c ' ) 2 and s u b t r a c t i n g y i e l d s 9 ( n / c ) , i „ , / t , 3 1 + v . V ( n / c ) = 0 f o r c 0. T h i s c a n b e w r i t t e n a s D ( n / c ' ) _ D t w h e r e D 3 _L • D t = 9 t + 2 T h e q u a n t i t y D / D t i s t h e t i m e d e r i v a t i v e f o r a n e l e m e n t f o l l o w i n g t h e f l u i d a s i t m o v e s w i t h v e l o c i t y v ' . When v 1 = v , t h i s i s e q u a l t o t h e w e l l - k n o w n s u b s t a n t i a l d e r i v a t i v e . I t f o l l o w s t h a t e i t h e r n / c ' = 0 ( t r i v i a l s o l u t i o n ) o r n / c ' i s c o n s t a n t . T h e p a r t i c l e r e m o v a l e f f i c i e n c y f o r a n a r b i t r a r y p i e c e o f e q u i p m e n t c a n now b e d e t e r m i n e d b a s e d o n t h e r a t e a t w h i c h p a r t i c l e s e n t e r a n d l e a v e . T h e q u a n t i t y n / c ' . m u s t b e c o n s t a n t throughout the i n l e t gas. T h i s i s t r u e i f the i n l e t gas i s w e l l mixed. Hence n v ' d A A . ' i n n v d A o u t A . i n n v d A 68. where A i n and A Q u t are the i n l e t and o u t l e t c r o s s - s e c t i o n a l areas, and v ' i s the component of v ' perpendicular to dA. S i m i l a r l y , the f r a c t i o n of gas removed measured i n appropriate units i s c ' v ' d A -A. > i n A c ' v ' d A b u t A. m c 1 v ' d A Since n/c i s constant, i t follows that e = e . Hence P g e p = 1 " c ' o u t v out A o u t / c ' i n v ' i n A i n where the subscripted values of c ' and v ' are appropriate averages for the terminal c o n d i t i o n s . However, since component 1 i s i n e r t , i t follows that t i I I c v A = c v A l , m i n i n l,out out out Hence e = 1 - [c'/c'] V t c ' / c ' ] . p ' l J o u t ' L ' l J i n This r e s u l t can now be in terpre ted for the three cases. 69. (i) v = v . -p -In t h i s case c" = p, and i t f o l l o w s t h a t the f r a c t i o n of p a r t i c l e s removed equals the f r a c t i o n of the t o t a l mass of f l u i d removed. In the case of gases the r e s u l t can be w r i t t e n as e = 1 - [M/Y, ] j./fM/Y-, ] • p L ' ' l J o u t / L ' ' l J i n ( i i ) v = v* . -P -Here c' = c, and the g e n e r a l r e s u l t i s t h a t the f r a c t i o n a l p a r t i c l e removal equals the f r a c t i o n of t o t a l motes of f l u i d removed. Since c i s con s t a n t f o r gases, a very simple r e s u l t f o l l o w s £ p = 1 - [ Y ^ / t Y - L ^ t • , . . . , r (^^^) v = v -P -i r In t h i s case, c = c , and p a r t i c l e removal e f f i c i e n c y equals the f r a c t i o n a l removal of root mass units o f f l u i d . The r e s u l t f o r gases i s 70. k k eP = 1 ~ [ <i=i y^hi W / f ( J i Y i ^ ) A i ] i n • The above e x p r e s s i o n s a re v a l i d p r o v i d e d t h a t the n e t t r a n s f e r e x p r e s s e d i n a p p r o p r i a t e u n i t s i s always d i r e c t e d o ut o f t h e f l u i d a t t h e t r a n s f e r s u r f a c e . I n i t s more g e n e r a l form, t h e S c h m i t t and Waldmann t y p e v e l o c i t y e x p r e s s i o n i n c l u d e s k c o e f f i c i e n t s , a^, whose v a l u e depends on t h e i n t e r a c t i o n o f the m o l e c u l e s w i t h t h e p a r t i c l e s u r f a c e , and on t h e Knudsen number. v Y a . / M T N . i = l I i = l Y . a . /M. 11 l l P r o c e e d i n g as b e f o r e , b u t d e f i n i n g c ^ s l i g h t l y d i f f e r e n t l y as c . r = aVM.c. , l i i i one can show t h a t f o r gases = 1 " [ ( k I i = l Y • a. ' l I M 1 ) / Y 1 Iout/[ ( J ^ i ^ ^ l hn 4 . 3 D i s c u s s i o n o f T h e o r y T h e d e r i v a t i o n s b a s e d o n t h e n o n - s t e a d y s t a t e f o r m s o f t h e f l u i d a n d p a r t i c l e e q u a t i o n s a r e q u i t e g e n e r a l f o r a n y f l u i d u n d e r c o n d i t i o n s n o r m a l l y e n c o u n t e r e d i n e q u i p m e n t o p e r a t i o n , s i n c e t h e y f o l l o w f r o m s i m p l e c o n s e r v a t i o n l a w s . I n p a r t i c u l a r , t h e y h o l d w h e t h e r t h e f l u i d i s l a m i n a r o r t u r b u l e n t . T h e i r a p p l i c a t i o n i n t h e l a m i n a r c a s e c o u l d l e a d t o new a n d i m p r o v e d m e t h o d s o f m e a s u r i n g d i f f u s i o p h o r e t i c p a r t i c l e v e l o c i t y . T h e o n l y p u b l i s h e d p a p e r o n d i f f u s i o p h o r e s i s u n d e r t u r b u l e n t c o n d i t i o n s b y o t h e r a u t h o r s i s t h a t o f A z a r n i o u c h e t a l . ( 1 9 7 5 ) . T h e i r t h e o r y , w h i c h r e s e m b l e s t h a t o f W h i t m o r e a n d M e i s e n ( 1 9 7 3 ) i n i t s g e n e r a l a p p r o a c h , c a n b e c r i t i c i s e d i n s e v e r a l r e s p e c t s . T h e i r d i f f e r e n t i a l m a s s a n d p a r t i c l e b a l a n c e s a r e c o r r e c t o n l y f o r d i l u t e s y s t e m s (Y 2 ^ 0 . 1 ) . E v e n t h o u g h i t i s k n o w n t h a t h i g h e r c o n c e n t r a t i o n s c a n r e s u l t i n s i g n i f i c a n t e r r o r , t h e a u t h o r s a p p l i e d t h e i r d e r i v e d e x p r e s s i o n s t o s i t u a t i o n s w h e r e Y 2 e x c e e d e d 0 . 6 . A z a r n i o u c h e t a l . a s s u m e d t h a t m a s s t r a n s f e r t o o k p l a c e a c r o s s a l a m i n a r f i l m . T h e c o n c e n t r a t i o n g r a d i e n t i n t h e f i l m was t a k e n t o b e l i n e a r , e v e n t h o u g h t h i s i s t r u e o n l y f o r d i l u t e s y s t e m s . T h e m a g n i t u d e o f t h e g r a d i e n t was t h e n d e t e r m i n e d f r o m t h e f i l m t h i c k n e s s u s i n g t h e m e t h o d e m p l o y e d e a r l i e r b y B y e r s a n d C a l v e r t ( 1 9 6 9 ) i n t h e i r t h e o r y o f t h e r m o p h o e r e t i c d e p o s i t i o n f r o m t u r b u l e n t f l o w . I n t h i s m e t h o d , t h e t h i c k n e s s o f t h e mass t r a n s f e r f i l m i s f o u n d b y e q u a t i n g i t t o t h e momentum t r a n s f e r b o u n d a r y l a y e r t h i c k n e s s , a n d e x p r e s s i n g t h e l a t t e r i n t e r m s o f h y d r o d y n a m i c v a r i a b l e s . I t w o u l d h a v e b e e n m o r e d i r e c t t o d e d u c e t h e t h i c k n e s s o f t h e mass t r a n s f e r boundary l a y e r from t h e mass t r a n s f e r c o e f f i c i e n t . N i s h i o e t a l . (1974) adopted t h i s approach f o r h e a t t r a n s f e r , and were a b l e t o improve on B y e r s 1 and C a l v e r t ' t h e o r y . Once the g r a d i e n t was d e t e r m i n e d , the d i f f u s i o p h o r e t i c v e l o c i t y i n the boundary l a y e r c o u l d be c a l c u l a t e d , and t h e d i f f e r e n t i a l p a r t i c l e b a l a n c e e q u a t i o n i n t e g r a t e d o ver the l e n g t h o f t h e a p p a r a t u s t o g i v e t h e removal e f f i c i e n c y . The t h e o r y r e q u i r e s t h a t t h e c o n c e n t r a t i o n o f t h e d i f f u s i n g s p e c i e s a t the t r a n s f e r s u r f a c e be known, and t h e i n t e g r a t i o n i s n o t s t r a i g h t -f o r w a r d u n l e s s t h i s c o n c e n t r a t i o n has a c o n s t a n t v a l u e . The f i n a l r e s u l t o f A z a r n i o u c h e t a l . i s more complex t h a n t h a t o f Whitmore and Meisen (19 7 3 ) , even when w r i t t e n i n n o n - p r e d i c t i v e form ( i . e . , i n a form dependent on t h e gas i n l e t and o u t l e t c o n d i t i o n s ) , w h i l e b e i n g more l i m i t e d i n i t s a p p l i c a t i o n , and l e s s r i g o r o u s i n i t s d e r i v a t i o n . C h a p t e r 5 EXPERIMENTAL APPARATUS AND PROCEDURE 5 . 1 G e n e r a l T h e a p p a r a t u s c a n b e d i v i d e d i n t o f o u r b a s i c p a r t s , o f w h i c h t h e wetted wall column i s t h e c e n t r a l o n e a n d t h e o t h e r s a r e p e r i p h e r a l . I n t h e e x p e r i m e n t a l w o r k a n aerosol generator was u s e d t o p r o d u c e a s t r e a m o f i n s o l u b l e ( i n e r t ) p a r t i c l e - b e a r i n g g a s . T h i s s t r e a m was t h e n m i x e d w i t h a s t r e a m o f s o l u b l e ( t r a n s f e r r e d ) g a s t o g i v e t h e d e s i r e d g a s c o m p o s i t i o n . T h e r e s u l t i n g m i x t u r e was p a s s e d u p t h r o u g h t h e w e t t e d w a l l c o l u m n c o u n t e r - c u r r e n t t o t h e w a t e r f l o w . P a r t o f t h e g a s was t h u s a b s o r b e d , a n d a f r a c t i o n o f t h e p a r t i c l e s r e m o v e d f r o m t h e g a s a n d t r a p p e d i n t h e w a t e r . T h e d e g r e e o f p a r t i c l e r e m o v a l was g a u g e d b y m e a s u r i n g t h e p a r t i c l e c o n c e n t r a t i o n s i n t h e i n l e t a n d o u t l e t g a s s t r e a m s o f t h e c o l u m n u s i n g a n aerosol particle counter T h e c h a n g e i n g a s c o m p o s i t i o n i n t h e c o l u m n was d e t e r m i n e d u s i n g a n Orsat apparatus . T h e p a r t i c l e r e m o v a l e f f i c i e n c y c o u l d t h e n b e r e l a t e d t o t h i s c h a n g e i n g a s c o m p o s i t i o n . A g e n e r a l v i e w o f t h e e q u i p m e n t a p p e a r s i n F i g u r e 5 . 1 , a n d a c l o s e u p o f t h e c o l u m n s i n F i g u r e 5 . 2 . D e t a i l s o f p u r c h a s e d e q u i p m e n t i s g i v e n i n T a b l e I 74. Figure 5.1 General view of the equipment. Figure 5.2 Closeup view of the wetted wall columns. T a b l e I P u r c h a s e d E q u i p m e n t D e s c r i p t i o n M a n u f a c t u r e r M o d e l A e r o s o l p a r t i c l e g e n e r a t o r Roy c o 256 A e r o s o l p a r t i c l e s e n s o r R o y c o 241 A e r o s o l p a r t i c l e m o n i t o r Roy c o 225 D i g i t a l d i s p l a y R o y c o 264 C o n s t a n t t e m p e r a t u r e b a t h L a u d a NB-5 15/12 Wet g a s m e t e r P r e c i s i o n S c i e n t i f i c C o . 3110 L i q u i d pump E a s t e r n D l l L i q u i d r o t a m e t e r B r o o k s 1110 t u b e R-8M-25-2 f l o a t 8 -RS-14 I n e r t g a s r o t a m e t e r B r o o k s 1110 t u b e R-7M-25-1 f l o a t s - g l a s s a n d s t a i n l e s s s t e e l s p h e r e s T r a n s f e r r e d g a s r o t a m e t e r G i l m o n t s i z e 3 T r a n s f e r r e d g a s r o t a m e t e r G i l m o n t s i z e 4 T r a n s f e r r e d g a s r o t a m e t e r B r o o k s 1110 t u b e R-8M-25-2 f l o a t 8-RV-14 Table I I Gases and P a r t i c l e s Gas S u p p l i e r Grade P u r i t y ammonia Canadian I n d u s t r i e s L t d . anhydrous 99.995% min. argon Canadian L i q u i d A i r s t a n d a r d 99.995% min. f r e o n 12 Matheson s t a n d a r d 99% min. h e l i u m Canadian L i q u i d A i r s t a n d a r d 99.995% min. methane Matheson t e c h n i c a l 98% min. n i t r o g e n Canadian L i q u i d A i r g grade 99.5% min. t r i m e t h y l a m i n e Matheson s t a n d a r d 99% min. P a r t i c l e Diameter (ym) S u p p l i e r M a t e r i a l S t a n d a r d D e v i a t i o n (ym) 0.5 Dow p o l y s t y r e n e l a t e x 0.0027 0.79 Dow p o l y s t y r e n e l a t e x 0.0044 1.011 Dow p o l y s t y r e n e l a t e x 0.0054 2.02 Dow p o l y v i n y l t o l u e n e l a t e x 0.0135 5.7 Dow s t y r e n e d i v i n y l -benzene l a t e x 1.5 78. and o f the gases and p a r t i c l e s used i n T a b l e I I . 5.2 A p p a r a t u s 5.2.1 The A b s o r p t i o n System . The i n i t i a l c h o i c e o f l i q u i d a b s o r b e n t s r a t h e r t h a n s o l i d a b - o r a d s o r b e n t s has been d i s c u s s e d i n C h a p t e r 1. Water vapour was the most o b v i o u s c h o i c e f o r the t r a n s f e r r e d gas because o f i t s low c o s t , p o t e n t i a l i n d u s t r i a l a p p l i c a b i l i t y , and i t s use by o t h e r workers i n s t u d i e s o f d i f f u s i o p h o r e s i s under l a m i n a r gas c o n d i t i o n s . I t c o u l d be absorbed i n a r e g e n e r a b l e l i q u i d such as l i t h i u m c h l o r i d e s o l u t i o n . There were however two problems w i t h t h i s system. F i r s t l y , mass t r a n s f e r c a l c u l a t i o n s i n d i c a t e d t h a t the l i q u i d phase r e s i s t a n c e would not be n e g l i g i b l e , and thus the e q u i l i b r i u m c o n d i t i o n s a t the l i q u i d s u r f a c e would not be known. (However, the t h e o r y d e v e l o p e d l a t e r , and d e s c r i b e d i n Chapter 4, showed t h a t a knowledge o f gas c o m p o s i t i o n a t t h e s u r f a c e was not n e c e s s a r y i n d e t e r m i n i n g p a r t i c l e removal r a t e s ! ) Use o f s t r o n g e r a b s o r b e n t s such as c o n c e n t r a t e d s u l f u r i c a c i d would reduce t h e l i q u i d phase r e s i s t a n c e , b u t they would be d i f f i c u l t t o h a n d l e , and t h e i r h i g h h e a t s o f a b s o r p t i o n would make i t more d i f f i c u l t t o approximate i s o t h e r m a l a b s o r p t i o n i n t h e column. S e c o n d l y , s i g n i f i c a n t p a r t i c l e removal would r e q u i r e h i g h vapour concen-t r a t i o n s i n t h e i n l e t gas, w h i c h i n t u r n i m p l i e d t e m p e r a t u r e s o f the o r d e r o f 80°C. T h i s would i n t r o d u c e t h e d i f f i c u l t e x p e r i m e n t a l 79. problem o f a v o i d i n g m i s t f o r m a t i o n i n t h e a p p a r a t u s and gas l i n e s . (The p a r t i c l e c o u n t e r p u r c h a s e d l a t e r o p e r a t e s o n l y up t o 50°C.) The use o f w a t e r vapour systems was t h e r e f o r e r u l e d o u t . S e v e r a l o t h e r gases w h i c h are e a s i l y absorbed were c o n s i d e r e d . Of t h e s e , ammonia and carbon d i o x i d e appeared t h e most s u i t a b l e because o f t h e i r low t o x i c i t y and c o r r o s i v e n e s s , low c o s t , and common a v a i l a b i l i t y . The column was t h e r e f o r e d e s i g n e d f o r t r a n s f e r o f c a r b o n d i o x i d e i n t o sodium h y d r o x i d e s o l u t i o n s . S i n c e the d e s i g n methods f o r gas a b s o r p t i o n w i t h c h e m i c a l r e a c t i o n are v e r y u n r e l i a b l e , i t was r e c o g n i z e d t h a t t h e r e was a r e a s o n a b l e p o s s i b i l i t y o f i n a d e q u a t e equipment p e r -formance. However, c a l c u l a t i o n s i n d i c a t e d t h a t h i g h a b s o r p t i o n r a t e s would be a c h i e v a b l e w i t h ammonia, and s a t i s f a c t o r y e q u i p -ment performance s h o u l d r e s u l t . 5.2.2 Wetted W a l l Column D e s i g n . The d e s i g n c a l c u l a t i o n s f o r mass t r a n s f e r w i t h c h e m i c a l r e a c t i o n f o l l o w e d t h e methods o f Dankwerts (1970). V a l u e s f o r the gas s i d e mass t r a n s f e r c o e f f i c i e n t s were e s t i m a t e d from the c o r r e -l a t i o n o f Sherwood and G i l l i l a n d (1934), w h i l e l i q u i d s i d e c o e f f i -c i e n t s were t a k e n from Sherwood and P i g f o r d (1952). Data on f l o o d i n g were t a k e n from W a l l i s (1969). Other i n f o r m a t i o n came from T r e y b a l (1968) and P e r r y (1963). P h y s i c a l p r o p e r t i e s f o r the l i q u i d and gas were t a k e n from P e r r y (196 3 ) , I n t e r n a t i o n a l C r i t i c a l T a b l e s (1926), Handbook of P h y s i c s and C h e m i s t r y (1970), and Dankwerts (1970). 80. T h e f l o w r a t e o f t h e l i q u i d was c h o s e n s o a s t o g i v e t u r b u l e n c e , b u t e v e n s o c a l c u l a t i o n s s h o w e d t h a t a h i g h c o n c e n -t r a t i o n o f NaOH (32 w%) was n e c e s s a r y t o k e e p t h e l i q u i d s i d e m a s s t r a n s f e r r e s i s t a n c e s m a l l . T h e g a s r a t e was s e t s o t h a t t h e i n e r t g a s , i f p r e s e n t o n i t s o w n , w o u l d e x h i b i t t u r b u l e n t f l o w w i t h r e s p e c t t o t h e d r y c o l u m n w a l l . T h e c a l c u l a t e d c o l u m n h e i g h t was i n c r e a s e d b y a p p r o x i m a t e l y 50% i n t h e f i n a l d e s i g n . F u r t h e r i n c r e a s e was l i m i t e d b y t h e c o n s t r u c t i o n m a t e r i a l s c h o s e n . D e t a i l s o f t h e d e s i g n a r e g i v e n i n T a b l e I I I . E s s e n t i a l f e a t u r e s o f t h e c o l u m n d e s i g n a r e s h o w n i n F i g u r e s 5.3 a n d 5.4. T h e c o l u m n was a 1" ID p r e c i s i o n b o r e g l a s s t u b e s u p p o r t e d b y 0 r i n g s . I t was e n c l o s e d b y a 3" n o m . D g l a s s p i p e s e c t i o n t o p r o v i d e p r o t e c t i o n , m e c h a n i c a l r i g i d i t y , a n d w a t e r j a c k e t i n g i f r e q u i r e d . T h e l i q u i d d i s t r i b u t o r a n d c o l l e c t o r w e r e d e s i g n e d t o m i n i m i z e t h e e x p o s e d l i q u i d s u r f a c e a r e a w h i l e a l l o w i n g e v e n , d r o p l e t - f r e e f l o w . T h e g a s i n l e t a n d o u t l e t t u b e s w e r e c o n s t r u c t e d o f 1" t u b i n g w h i c h m a t c h e d t h e c o l u m n d i a m e t e r , a n d w e r e e q u i p p e d w i t h s a m p l i n g p o i n t s . T h e i n l e t t u b e was a l s o d e s i g n e d t o a c t a s a m i x i n g c h a m b e r f o r t h e p a r t i c l e - b e a r i n g s t r e a m a n d t h e r e m a i n d e r o f t h e g a s . A s e c o n d c o l u m n o f i d e n t i c a l d e s i g n , e x c e p t f o r i t s s h o r t e r l e n g t h , was a l s o c o n s t r u c t e d s o a s t o a l l o w c o r r e c t i o n f o r e n d e f f e c t s i f d e s i r e d . T a b l e I I I Wetted W a l l Column Design Parameters l i q u i d phase gas phase u n i t s I n l e t c o m p o s i t i o n 32 w l NaOH 68 w% H 20 50 v% C 0 2 50 v% a i r O u t l e t c o m p o s i t i o n s u b s t a n t i a l l y unchanged 20 v% C 0 2 80 v% a i r • I n l e t f l o w 2.37 x 1 0 4 99.4 g mole/m 2/sec Mass t r a n s f e r c o e f f i c i e n t 24.1 0.648 g mole/m 2/sec Enhancement f a c t o r due t o c h e m i c a l r e a c t i o n 360 — R e s i s t a n c e o f phase ( c o n t r i b u t i o n i n e s t i m a t i n g 1/K^ .) 0.16 3 1.54 m sec/g mole-O v e r a l l mass t r a n s f e r c o e f f i c i e n t , Column d i a m e t e r 0 .588 g mole/m / sec 0 .0254 m C a l c u l a t e d h e i g h t 0 .49 m D e s i g n h e i g h t 0 .77 m 8 2 . Screw to flange B o l t s through upper and. lower flanges hold i n t e r -mediate glass i n compression -1" OD gas o u t l e t tuba .1" ID p r e c i s i o n bore glass tube Standard glass pipe 'QVF PS 2/4 L i q u i d i n l e t 3/8" pipe 'thread .Standard QVF coupling holds glass pipe i n compression against flange above. -Standard glass pipe QVF PS 3/6 or 3/24. M a t e r i a l : 316 s t a i n l e s s s t e e l unless s p e c i f i e d . Figure 5.3 Wetted wall column - top. Standard glass pipe QVF PS 3/ 0 r i n g s e a l NA/V1 Standard QVF coupling holds glass pipe i n compression against flange. Headspace pressure release 1/8" thread. 1" p r e c i s i o n bore glass tube. Length of f l a r e > 50 mm Max diameter of f l a r e < 60 mm Standard glass pipe QVF PS 3/6 1" OD gas i n l e t tube 0 r i n g to allow height adjustment c o l l a r to allow fo r pipe 3/8" pipe thread fcJ M a t e r i a l : 316 s t a i n l e s s s t e e l unless s p e c i f i e d . Figure 5.4 Wetted wall column-base. 84. 5.2.3 Gas and L i q u i d Supply Systems. The d e s i g n o f the l i q u i d and gas s u p p l y systems i s shown i n F i g u r e 5.5. The i n e r t gas was s u p p l i e d from a c y l i n d e r and metered by a r o t a m e t e r under p r e s s u r e ( n o r m a l l y 50 p s i g ) . The f l o w was t h e n d i v i d e d , w i t h p a r t g o i n g t o the a e r o s o l g e n e r a t o r . T h i s u n i t r e q u i r e d an i n l e t p r e s s u r e of about 30 p s i g o r g r e a t e r . The remainder was t h r o t t l e d down i n p r e s s u r e and mixed w i t h the t r a n s f e r r e d gas b e f o r e b e i n g passed t o t h e column. The t r a n s -f e r r e d gas, w h i c h was a l s o s u p p l i e d from a c y l i n d e r , was t h r o t t l e d t h r o u g h a c o n t r o l v a l v e b e f o r e b e i n g metered by a r o t a m e t e r and mixed w i t h t h e c l e a n i n e r t s t r e a m ready f o r passage t o t h e column. Both i n e r t and t r a n s f e r r e d gas streams were e q u i l i b r a t e d t o the l i q u i d s u p p l y t e m p e r a t u r e by b e i n g passed t h r o u g h temperature c o n t r o l c o i l s immersed i n the l i q u i d s t o r a g e t a n k . The gas m i x t u r e l e a v i n g t h e column was e x h a u s t e d t o the atmosphere. The l i q u i d was s u p p l i e d from a tank o f a p p r o x i m a t e l y 180 l i t r e s c a p a c i t y . Water from a c i r c u l a t i n g t e m p e r a t u r e b a t h passed t h r o u g h c o i l s immersed i n t h e l i q u i d i n o r d e r t o m a i n t a i n t h e d e s i r e d t e m p e r a t u r e . The l i q u i d was pumped from the tank t h r o u g h a c o n t r o l v a l v e and m e t e r i n g r o t a m e t e r t o the t o p o f t h e column. L i q u i d l e a v i n g the column passed t h r o u g h a c o n s t a n t head t a n k , w h i c h c o n t r o l l e d t h e l e v e l o f the l i q u i d , p o o l a t the base o f the column, and was t h e n d i s c h a r g e d t o t h e d r a i n . Pressure/ gauge Cont r o l valve Aerosol generator Sample port 1 Pressure r e l i e f valve Bypass valve Gas rotameters Pressure regulators-' •M-H Control valve gas temperature c o n t r o l ^ --c o i l s I n e r t gas supply Tr a n s f e r r e d gas supply water temperature c o n t r o l c o i l Wetted w a l l column Exhaust gas to atmosphere A Sample port Constant head tank Exhaust l i q u i d to d r a i n Bypass •N water supply \ L i q u i d c o n t r o l valve Pump L i q u i d p i p i n g : schedule 40 3/8 and 3/4 inch 316 s t a i n l e s s s t e e l pipe (except f l e x i b l e l i n k s to column). Gas p i p i n g : 3/8 inch copper tubing (except f l e x i b l e l i n k s to column and aerosol generator, and 3/8 inch 316 s t a i n l e s s s t e e l tubing for temperature c o n t r o l c o i l s ) F i g u r e 5.5 Gas and l i q u i d s u p p l y systems. (Only one column shown.) CO U l 8 6 . 5 . 2 . 4 A e r o s o l G e n e r a t i o n . I n t h e a e r o s o l g e n e r a t o r a d i l u t e s u s p e n s i o n o f u n i f o r m l y s i z e d l a t e x o r p o l y m e r s p h e r e s i n d i s t i l l e d w a t e r was a t o m i z e d i n a j e t o f g a s . T h e r e s u l t i n g d r o p l e t s w e r e t h e n e v a p o r a t e d b y a d d i t i o n o f f u r t h e r d r y g a s , l e a v i n g o n l y t h e s p h e r e s . T h i s t y p e o f g e n e r a t i o n was a d v a n t a g e o u s s i n c e i t p r o d u c e d a m o n o d i s p e r s e a e r o s o l . T h e e f f e c t o f p a r t i c l e d i a m e t e r c o u l d b e e a s i l y i n v e s t i g a t e d b y t h e u s e o f s e v e r a l d i f f e r e n t s i z e s o f s p h e r e . E l e c t r o n m i c r o g r a p h s o f t h e p a r t i c l e s u s e d a r e shown i n F i g u r e s 5 . 6 t o 5 . 1 0 . 5 . 2 . 5 A e r o s o l P a r t i c l e C o u n t e r . A e r o s o l c o n c e n t r a t i o n s a t t h e c o l u m n i n l e t a n d o u t l e t w e r e d e t e r m i n e d b y w i t h d r a w i n g a n d a n a l y s i n g s a m p l e s t r e a m s w i t h t h e p a r t i c l e c o u n t e r . T h i s i n s t r u m e n t u s e d a p h o t o m u l t i p l i e r t u b e t o d e t e c t i n d i v i d u a l p a r t i c l e s b y f o r w a r d l i g h t s c a t t e r i n g . T h e m a g n i t u d e o f t h e r e s u l t i n g e l e c t r i c a l i m p u l s e s i n c r e a s e d w i t h p a r t i c l e s i z e . P a r t i c l e s g r e a t e r t h a n 1 . 2 ym D w e r e c o u n t e d o n o n e c h a n n e l , a n d t h o s e s m a l l e r o n a n o t h e r . T h e i n s t r u m e n t d e t e c t e d p a r t i c l e s a s s m a l l a s a p p r o x i m a t e l y 0 . 3 ym D . P a r t i c l e 3 c o n c e n t r a t i o n s w e r e k e p t b e l o w ^ 3 , 0 0 0 , 0 0 0 / m . A t t h i s l e v e l c o - i n c i d e n c e e r r o r s d u e t o t w o p a r t i c l e s p a s s i n g t h r o u g h t h e s e n s i t i v e v o l u m e s i m u l t a n e o u s l y b e c o m e s i g n i f i c a n t . T h e maximum s a m p l e t e m p e r a t u r e t h a t c a n b e t o l e r a t e d b y t h e p a r t i c l e c o u n t e r i s 5 0 ° C . 87. F i g u r e 5.6 E l e c t r o n m i c r o g r a p h o f 0.50 m i c r o n d i a m e t e r l a t e x p a r t i c l e s . M a g n i f i c a t i o n 30,000 X. F i g u r e 5.7 E l e c t r o n m i c r o g r a p h o f 0.79 m i c r o n d i a m e t e r l a t e x p a r t i c l e s . M a g n i f i c a t i o n 10,000 X. F i g u r e 5.8 E l e c t r o n m i c r o g r a p h of 1.011 m i c r o n d i a m e t e r l a t e x p a r t i c l e s . M a g n i f i c a t i o n 10,000 X. F i g u r e 5.10 E l e c t r o n m i c r o g r a p h o f 5.7 m i c r o n d i a m e t e r l a t e x p a r t i c l e s . M a g n i f i c a t i o n 3,000 X. 9 0 . Three m o d i f i c a t i o n s were made t o the c o u n t e r as pu r c h a s e d . F i r s t , t he l i g h t p i p e i n t h e s e n s o r , which was made o f "Lexan" (a p o l y c a r b o n a t e ) , was a t t a c k e d by ammonia d u r i n g e a r l y e x p e r i m e n t a l work t i l l t h e c o u n t e r f i n a l l y became i n o p e r a b l e . A r e p l a c e m e n t g l a s s f i b r e o p t i c s l i g h t p i p e has been c o m p l e t e l y s a t i s f a c t o r y . Second, t h e c o u n t e r was d e s i g n e d t o draw 0.1 c u b i c - 3 3 f e e t o f a i r p e r minute (2.8 x 10 m /min) a t a u n i f o r m r a t e so t h a t the p a r t i c l e c o n c e n t r a t i o n c o u l d be d e t e r m i n e d by c o u n t i n g f o r a s e t t i m e . However, t h e f l o w r a t e changed s u b s t a n t i a l l y when gases o f d i f f e r e n t c o m p o s i t i o n were used. T h i s was t o be e x p e c t e d , s i n c e t h e gas r e c y c l e r a t e w i t h i n t h e c o u n t e r and the gas ex h a u s t r a t e from t h e c o u n t e r were c o n t r o l l e d by s m a l l o r i f i c e s , making t h e f l o w r a t e s dependent on t h e gas m o l e c u l a r w e i g h t . F o r t h i s r e a s o n , m o d i f i c a t i o n s were made t o t h e c o u n t e r so t h a t the gas c o u l d be c o l l e c t e d from t h e ex h a u s t o r i f i c e . I t was then passed t h r o u g h a s c r u b b e r system and t h e r e m a i n i n g i n e r t gas f l o w measured w i t h a wet gas meter. By t h i s means t h e count p e r u n i t volume o f i n e r t gas c o u l d be e s t a b l i s h e d . I n i t i a l l y t h e s c r u b b e r c o n s i s t e d o f t h r e e g l a s s f l a s k s i n s e r i e s , each o f a p p r o x i m a t e l y 2000 ml c a p a c i t y and p a r t i a l l y f i l l e d w i t h c o n c e n t r a t e d s u l f u r i c a c i d . A l t h o u g h t h i s system was v e r y e f f e c t i v e , e a r l y e x p e r i m e n t s showed t h a t the a c i d s u r f a c e t e n d e d t o cake up. A l s o , c r y s t a l l i n e d e p o s i t s formed i n e n t r a n c e and e x i t t u b e s , i n h i b i t i n g gas f l o w s and g i v i n g e r r o n e o u s r e a d i n g s . A p r e l i m i n a r y s c r u b b e r was t h e r e f o r e added, i n w hich the gas f l o w was c o n t a c t e d w i t h f l o w i n g water i n a g l a s s f l a s k , removing most o f the s o l u b l e gas. The water f l o w was k e p t low enough t h a t the q u a n t i t i e s o f d i s s o l v e d a i r r e l e a s e d from t h e w a t e r , and o f i n e r t gas d i s s o l v i n g i n t o i t , were n e g l i g i b l e . F i n a l l y , t he "Gast" vacuum pump model 1531, used t o draw the sample t h r o u g h t h e c o u n t e r , was d e s i g n e d t o purge a s m a l l amount o f gas o u t o f t h e pump chamber t h r o u g h the b e a r i n g . T h i s p r e v e n t e d d i r t and o i l e n t e r i n g t h e pump chamber and i n t e r f e r i n g w i t h the movement o f t h e carbon vanes. By r e a r r a n g i n g the b e a r i n g s e a l s and d r i l l i n g a s m a l l h o l e i n t o t h e c a v i t y near t h e b e a r i n g , i t was p o s s i b l e t o r e c a p t u r e t h i s purge s t r e a m and combine i t w i t h t h e main f l o w t o t h e gas s c r u b b e r t r a i n . I n e a r l y work t h e e x i s t e n c e o f t h i s purge was not. r e c o g n i z e d , b u t i t s e f f e c t was c o r r e c t e d f o r by the c o u n t e r c a l i b r a t i o n (see S e c t i o n 5.4.1). 5.2.6 Gas A n a l y s e r . The i n l e t and o u t l e t gas streams from the column were a n a l y s e d u s i n g a m o d i f i e d O r s a t a p p a r a t u s c o n s t r u c t e d f o r t h e p r e s e n t s t u d y . The gas chamber o f t h e O r s a t was formed from a 50 ml b u r e t t e , w h i c h e n a b l e d t h e s o l u b l e gas t o be a n a l y s e d i n c o n c e n t r a t i o n s from z e r o t o over 95 v%. (Gases i n c o n c e n t r a t i o n s e x c e e d i n g 50 v% cannot be a n a l y s e d i n normal O r s a t equipment.) Mercury was used f o r the b a l a n c i n g l i q u i d s i n c e even l i q u i d s such as p a r a f f i n and c o n c e n t r a t e d NaOH s o l u t i o n were found t o absorb s i g n i f i c a n t amounts o f ammonia. 5.3 P r e l i m i n a r y P r o c e d u r e 5.3.1 Rotameter C a l i b r a t i o n . The p r i m a r y c a l i b r a t i o n s f o r the gas r o t a m e t e r s were made by p a s s i n g t h e gas from t h e r o t a m e t e r s t h r o u g h a wet gas meter. F o r h i g h e r f l o w s , two gas meters i n p a r a l l e l were used. An a c c u r a c y o f ±1/2% a t 60% o f d e s i g n c a p a c i t y i s c l a i m e d f o r the m e t e r s . I t i s t h e r e f o r e e x p e c t e d t h a t c a l i b r a t i o n s a r e w i t h i n ±1% f o r low f l o w r a t e s and ±2% f o r h i g h e r f l o w r a t e s where two meters were needed. Comparison o f t h e 3 meters used w i t h each o t h e r showed good agreement up t o t h e i r d e s i g n c a p a c i t y . The i n e r t gas meter was c a l i b r a t e d w i t h n i t r o g e n f o r bot h g l a s s and s t a i n l e s s s t e e l s p h e r i c a l f l o a t s t o c o v e r a wide range o f f l o w r a t e s . The "G i l m o n t " r o t a m e t e r s used f o r t h e t r a n s f e r r e d gas were c a l i b r a t e d w i t h c a r b o n d i o x i d e . L a t e r , a t h i r d t r a n s f e r r e d gas r o t a m e t e r was added t o a l l o w h i g h e r f l o w r a t e s t o be measured. T h i s was c a l i b r a t e d u s i n g ammonia,by m i x i n g t h e o u t p u t w i t h a known n i t r o g e n f l o w , and a n a l y s i n g the r e s u l t i n g m i x t u r e . Secondary c a l i b r a t i o n f o r o t h e r gases was made by s c a l i n g t h e p r i m a r y c a l i b r a t i o n a c c o r d i n g t o the gas p r o p e r t i e s , u s i n g s t a n d a r d r o t a m e t e r s i z i n g f o r m u l a e . The l i q u i d r o t a m e t e r was c a l i b r a t e d f o r w a t e r and 32 w% NaOH s o l u t i o n , u s i n g a g r a d u a t e d f l a s k and s t o p w a t c h . I t was not e x p e c t e d t h a t the p a r t i c l e d e p o s i t i o n would be a s t r o n g f u n c t i o n o f gas o r l i q u i d f l o w r a t e s , so t h a t h i g h a c c u r a c y i n d e t e r m i n i n g t h e a b s o l u t e f l o w r a t e s was n o t e s s e n t i a l . L i q u i d and gas c a l i b r a t i o n c u r v e s a r e g i v e n i n Appendix A. 5 . 3 . 2 P a r t i c l e C o n t e n t o f G a s e s . T h e c o m p r e s s e d c y l i n d e r g a s e s w e r e f o u n d t o b e e x t r e m e l y f r e e o f p a r t i c u l a t e m a t t e r . I n a l l c a s e s , when t h e s e g a s e s w e r e s a m p l e d d i r e c t l y b y t h e c o u n t e r , t h e p a r t i c l e c o n c e n -t r a t i o n was e s s e n t i a l l y z e r o . F i l t r a t i o n was t h e r e f o r e n o t r e q u i r e d . 5 . 3 . 3 C o l u m n T r i a l s . I n i t i a l t r i a l s w i t h N 2 - C 0 2 m i x t u r e s a n d 32 w% NaOH s o l u t i o n g a v e C 0 2 a b s o r p t i o n w e l l b e l o w t h a t i n d i c a t e d b y t h e d e s i g n c a l c u l a t i o n s . E v e n w i t h h i g h C 0 2 i n l e t c o n c e n t r a t i o n s a n d h i g h l i q u i d f l o w r a t e s t h e a b s o r p t i o n was i n a d e q u a t e f o r s a t i s f a c t o r y p a r t i c l e r e m o v a l . T h i s i s p r o b a b l y b e c a u s e t h e p r e d i c t e d e n h a n c e m e n t o f m a s s t r a n s f e r d u e t o c h e m i c a l r e a c t i o n f a r e x c e e d s t h a t w h i c h e x i s t s i n r e a l i t y . T h e C 0 2 was t h e r e f o r e r e p l a c e d w i t h N H ^ , a n d t h e NaOH s o l u t i o n w i t h w a t e r . A b s o r p t i o n w i t h t h e new s y s t e m was q u i t e s a t i s f a c t o r y . 5 . 3 . 4 T e s t s f o r L i q u i d P h a s e M a s s T r a n s f e r R e s i s t a n c e . T h e t r a d i t i o n a l t e s t f o r l i q u i d p h a s e r e s i s t a n c e i s t o v a r y t h e l i q u i d flow r a t e w h i l e keeping a constant i n l e t gas flow r a t e a n d c o m p o s i t i o n . I f t h e o u t l e t g a s c o m p o s i t i o n r e m a i n s e s s e n t i a l l y u n c h a n g e d , t h e n t h e l i q u i d r e s i s t a n c e i s n e g l i g i b l e . T h e p r o b l e m w i t h t h i s t e s t i s t h a t t h e g a s s i d e m a s s t r a n s f e r c o e f f i c i e n t i s 94. dependent on t h e gas Reynolds number, measured w i t h r e s p e c t t o the l i q u i d s u r f a c e r a t h e r t h a n t o t h e s u r f a c e o f t h e d r y column. Hence a change i n l i q u i d f l o w r a t e s h o u l d produce.a s m a l l change i n o u t -l e t gas c o m p o s i t i o n , even i f the l i q u i d r e s i s t a n c e i s n e g l i g i b l e . To t e s t f o r n e g l i g i b l e l i q u i d r e s i s t a n c e , a m a t h e m a t i c a l model was c o n s t r u c t e d i n w h i c h t h e i n f l u e n c e o f t h e l i q u i d r a t e on gas s i d e mass t r a n s f e r was a l l o w e d f o r . D e t a i l s o f t h i s model are g i v e n i n Appendix B. Agreement between th e model and e x p e r i m e n t a l r e s u l t s was s a t i s f a c t o r y , though t h e r e was some i n d i c a t i o n t h a t the l i q u i d phase o f f e r e d a s m a l l mass t r a n s f e r r e s i s t a n c e . L a t e r t h e o r e t i c a l work showed t h a t t h e s u r f a c e gas c o n c e n t r a t i o n s need n o t be known i n e s t i m a t i n g p a r t i c l e d e p o s i t i o n r a t e s . N e g l i g i b l e l i q u i d s i d e mass t r a n s f e r r e s i s t a n c e was t h e r e -f o r e n o t n e c e s s a r y . 5.4 O p e r a t i n g P r o c e d u r e 5.4.1 C o u n t e r C a l i b r a t i o n f o r P a r t i c l e S i z e . The p r i m a r y c a l i b r a t i o n i s made by an i n t e r n a l a d justment w h i c h s e t s t h e h e i g h t o f the v o l t a g e peak which i s produced when a p a r t i c l e o f known s i z e i s c o u n t e d . T h i s e n s u r e s t h a t the c o u n t e r d i s t i n g u i s h e s c o r r e c t l y between p a r t i c l e s s m a l l e r and l a r g e r t h a n 1.2 ym D. S i n c e i n t h i s work the s i z e s o f t h e p a r t i c l e s c ounted were always known, a c c u r a t e p r i m a r y c a l i b r a t i o n was n o t n e c e s s a r y . N e v e r t h e l e s s , the v o l t a g e peak h e i g h t s were o c c a s i o n a l l y checked and a d j u s t e d when r e q u i r e d . The i n s t r u m e n t i s d e s i g n e d so t h a t a secondary c a l i -b r a t i o n can be made by f e e d i n g an i n t e r n a l r e f e r e n c e s i g n a l t o th e p h o t o m u l t i p l i e r t u b e , and a d j u s t i n g t h e o u t p u t by means o f an e x t e r n a l c o n t r o l t i l l i t matches t h e i n t e r n a l p r i m a r y s t a n d a r d . T h i s p r o c e d u r e was f o l l o w e d each time the c o u n t e r was s w i t c h e d on, and a t f r e q u e n t i n t e r v a l s d u r i n g o p e r a t i o n . 5.4.2 Counter C a l i b r a t i o n f o r Gas C o m p o s i t i o n . I f an i n e r t , a e r o s o l - b e a r i n g s t r e a m i s mixed w i t h v a r y i n g q u a n t i t i e s o f the t r a n s f e r r e d gas and t h e m i x t u r e sampled, t h e c o u n t r a t e r e g i s t e r e d p e r u n i t volume of i n e r t gas i s found t o v a r y a c c o r d i n g t o t h e c o m p o s i t i o n o f t h e sampled gas. The main r e a s o n f o r t h i s i s b e l i e v e d t o be t h a t , f o r gases o t h e r t h a n a i r , a l l the p a r t i c l e s do not pass t h r o u g h t h e c o u n t e r s e n s i t i v e volume. (The m a n u f a c t u r e r c l a i m s t h a t when a i r i s sam-pled, a l l p a r t i c l e s do pass t h r o u g h t h i s volume, and hence e v e r y p a r t i c l e i s counted.) Thus t h e f r a c t i o n o f gas i n which p a r t i c l e s a r e c o unted w i l l depend s l i g h t l y on t h e gas c o m p o s i t i o n . M i n o r l e a k s , such as t h o s e t h r o u g h t h e pump s e a l s and i n t h e a b s o r b e r t r a i n , m a y a l s o be c o n t r i b u t i n g f a c t o r s . The c o u n t e r was t h e r e f o r e c a l i b r a t e d t o e l i m i n a t e t h i s e r r o r . A f i x e d i n e r t p a r t i c l e - b e a r i n g s t r e a m was mixed w i t h v a r i o u s q u a n t i t i e s o f t r a n s f e r r e d gas and sampled w i t h t h e c o u n t e r . The s a m p l i n g scheme was s i m i l a r t o t h a t used d u r i n g t h e a c t u a l e x p e r i m e n t (see S e c t i o n 5.4.4), b u t i n t h i s case the r e a d i n g s were t a k e n w i t h t h e t r a n s f e r r e d gas b o t h p r e s e n t and a b s e n t . I n 96. t h i s way a c a l i b r a t i o n c u r v e r e l a t i n g t he r e c o r d e d count t o t h e t r u e count f o r i n e r t gas o n l y was e s t a b l i s h e d f o r v a r i o u s gas c o m p o s i t i o n s . T h i s c a l i b r a t i o n c u r v e was s u b s e q u e n t l y used t o c o r r e c t the e x p e r i m e n t a l p a r t i c l e counts f o r gases o f d i f f e r e n t c o m p o s i t i o n s . I n l a t e r runs an improvement i n e x p e r i m e n t a l t e c h n i q u e was i n t r o d u c e d t o f u r t h e r reduce c a l i b r a t i o n e r r o r s . I n a l l cases t h e c a l i b r a t i o n c o r r e c t i o n i n c r e a s e d w i t h i n c r e a s i n g t r a n s f e r r e d gas c o n c e n t r a t i o n . The l a r g e r c o r r e c t i o n was t h e r e -f o r e a t t h e base o f t h e column. U s u a l l y t h i s c o r r e c t i o n was l e s s t h a n 10% o f the r e a d i n g , b u t i n extreme cases i t c o u l d be up t o 40%. I t was t h e r e f o r e d e c i d e d t o ta k e the bottom r e a d i n g w i t h t h e t r a n s f e r r e d gas t u r n e d o f f . T h i s e l i m i n a t e d the need f o r a bottom c a l i b r a t i o n c o r r e c t i o n e n t i r e l y . A l s o , s i n c e t h e p a r t i c l e l o s s e s i n the column were n e g l i g i b l e i n t h e absence o f d i f f u s i o -p h o r e s i s , t h e "bottom" sample c o u l d be withdrawn from t h e t o p i f d e s i r e d . The c a l i b r a t i o n c o r r e c t i o n f o r the top r e a d i n g was n o r m a l l y l e s s t h a n 5%. 5.4.3, P r e p a r a t i o n f o r an E x p e r i m e n t a l Run. Some time b e f o r e the r u n t h e l i q u i d s t o r a g e t a n k was charged w i t h c o l d t a p w a t e r . The wat e r was t h e n h e a t e d t o about 25°C and a g i t a t e d by means o f a c i r c u l a t i n g pump b e f o r e b e i n g c o o l e d t o t h e o p e r a t i n g t e m p e r a t u r e o f 20°C. T h i s p r o c e d u r e e l i m i n a t e d t h e f o r m a t i o n o f l i q u i d d r o p l e t s i n t h e column,asso-97. c i a t e d w i t h t h e r e l e a s e o f s m a l l a i r b u b b l e s . To p r e p a r e the a t o m i s a t i o n s o l u t i o n f o r the a e r o s o l g e n e r a t o r , a s m a l l q u a n t i t y ( u s u a l l y 1 t o 10 drops) o f the con-c e n t r a t e d s u s p e n s i o n (10 v%) o f p a r t i c l e s o f t h e r e q u i r e d s i z e , as s u p p l i e d by Dow,were added t o 20 ml o f d i s t i l l e d w a t e r . The a e r o s o l c o n c e n t r a t i o n i n the gas i s s e t p r i m a r i l y by c h o o s i n g t h e c o r r e c t d i l u t i o n o f t h e c o n c e n t r a t e d s u s p e n s i o n , and s e c o n d a r i l y by a d j u s t i n g the gas p r e s s u r e t o the a t o m i s i n g chamber. The lower l i m i t on c o n c e n t r a t i o n was s e t so t h a t the a e r o s o l count would be s u b s t a n t i a l l y h i g h e r t h a n the background coun t r e g i s t e r e d when no a e r o s o l was added t o t h e gas. T h i s background count c o u l d a r i s e from d r o p l e t e n t r a i n m e n t o r m i s t f o r m a t i o n i n t h e column, e n t r a i n e d d i r t from the gas p i p i n g o r t u b i n g , d i r t i n t h e compressed gases ( s m a l l ) , o r e l e c t r o n i c n o i s e ( n o r m a l l y n e g l i g i b l e ) . The 3 background coun t was u s u a l l y l e s s t h a n 3,000 p a r t i c l e s / m , b u t 3 c o u l d exceed 10,000 p a r t i c l e s / m f o r h i g h gas f l o w r a t e s i n some c a s e s . E x p e r i m e n t a l a e r o s o l c o n c e n t r a t i o n s used were t y p i c a l l y 3 ^ 1,000,000 p a r t i c l e s / m . P a r t i c l e - p a r t i c l e i n t e r a c t i o n i n the gas was n e g l i g i b l e under t h e s e c o n d i t i o n s s i n c e the average -2 4 i n t e r - p a r t i c l e d i s t a n c e was ^ 1 0 m o r ^ 10 p a r t i c l e d i a m e t e r s . -12 The volume f r a c t i o n o f p a r t i c l e s i n the gas phase was ^ 10 A t the s t a r t o f a r u n , t h e c o u n t e r e l e c t r o n i c s were warmed up, and a secondary c a l i b r a t i o n was made f o r p a r t i c l e s i z e . The c o u n t e r was then t e s t e d by b e i n g f e d w i t h pure gas, and by b e i n g a l l o w e d t o r e c y c l e i t s own i n t e r n a l gas w i t h o u t . a n y sample b e i n g drawn. These t e s t s d e t e c t e d d i r t l o d g e d i n t h e s e n s i n g 98. h e a d , l e a k i n g i n t e r n a l f i l t e r s , h i g h e l e c t r o n i c n o i s e l e v e l s , a n d l e a k s i n t h e c o u n t e r o r s c r u b b e r t r a i n . T h e s e t e s t s w e r e r e p e a t e d p e r i o d i c a l l y d u r i n g t h e r u n . T h e g a s f l o w s w e r e s e t t o t h e r e q u i r e d r a t e s . N o r m a l l y , a l l o f t h e i n e r t g a s was p a s s e d t h r o u g h t h e a e r o s o l g e n e r a t o r , a n d n o n e t h r o u g h t h e b y p a s s t o b e m i x e d w i t h t h e t r a n s f e r r e d g a s . T h i s e l i m i n a t e d a p o s s i b l e m i n o r e r r o r i n t h e t r a n s f e r r e d g a s r o t a m e t e r r e a d i n g w h i c h c o u l d b e c a u s e d b y s l i g h t a d d e d b a c k -p r e s s u r e f r o m t h e b y p a s s i n e r t s t r e a m . A t v e r y h i g h i n e r t f l o w r a t e s , h o w e v e r , t h e u s e o f t h e b y p a s s was n e c e s s a r y . T h e l i q u i d f l o w was s e t a t 35 m l / s e c f o r a l l r u n s . 5 . 4 . 4 S a m p l i n g . T h e a e r o s o l c o u n t e r was c o n n e c t e d t o a n i n l e t ( o r o u t l e t ) s a m p l i n g p o i n t , s o t h a t i t d r e w o f f a c o n t i n u o u s s t r e a m o f g a s . C o u n t s w e r e t h e n r e c o r d e d f o r a g i v e n i n e r t g a s v o l u m e , m e a s u r e d b y t h e w e t g a s m e t e r . T h e g a s v o l u m e c h o s e n v a r i e d f r o m 0 . 0 1 t o 0 . 1 f t 3 ( 0 . 0 0 0 2 8 t o 0 . 0 0 2 8 m 3 ) d e p e n d i n g o n t h e i n e r t g a s c o n c e n t r a t i o n i n t h e g a s m i x t u r e a n d t h e g a s e s b e i n g u s e d . E a c h t i m e t h e c o m p o s i t i o n o f t h e g a s s a m p l e d was c h a n g e d , t h e c o u n t e r was l e f t a p p r o x i m a t e l y o n e m i n u t e f o r s t e a d y s t a t e c o n d i t i o n s t o b e e s t a b l i s h e d . H o w e v e r t h e c o u n t s t i l l s h o w e d r a n d o m f l u c t u a t i o n s , t y p i c a l l y i n t h e r a n g e o f ± 5 % . T h e s e f l u c t u a t i o n s w e r e t o o l a r g e t o b e c a u s e d b y t h e s m a l l v a r i a t i o n s i n p a r t i c l e c o n c e n t r a t i o n o f t h e s o l u t i o n i n t h e a t o m i s e r . I t i s b e l i e v e d t h a t t h e y w e r e d u e t o v e r y s m a l l c h a n g e s i n t h e a t o m i z e r g a s f e e d , c a u s e d b y s m a l l p r e s s u r e f l u c t u a t i o n s p r o d u c e d b y t h e a e r o s o l g e n e r a t o r g a s r e g u l a t o r . T h e c o u n t a l s o o c c a -s i o n a l l y e x h i b i t e d a s l o w d r i f t w i t h t i m e . A f t e r t h e c o u n t h a d s t a b i l i z e d , a n d p r o v i d e d a n y d r i f t was m i n o r , f o u r c o n s e c u t i v e c o u n t s w e r e r e c o r d e d f o r c a l c u l a t i o n p u r p o s e s ( i n some c a s e s two c o u n t s o f l o n g e r d u r a t i o n w e r e u s e d ) . A n y c o u n t s c l e a r l y f a l l i n g o u t s i d e t h e t y p i c a l r a n g e , a n d t h a t c o u l d n o t b e r e p r o d u c e d , w e r e d i s c a r d e d . T h e s a m p l e t u b e was t h e n c o n n e c t e d t o t h e o t h e r e n d o f t h e c o l u m n a n d t h e p r o c e s s r e p e a t e d t o g i v e f o u r m o r e r e a d i n g s . F i n a l l y , t h e s a m p l e t u b e was r e c o n n e c t e d t o t h e o r i g i n a l e n d o f t h e c o l u m n t o o b t a i n t h e f o u r f i n a l r e a d i n g s . T h e a e r o s o l g e n e r a t o r was t h e n s h u t o f f a n d t h e i n e r t g a s f l o w r e s t o r e d t o i t s p r e v i o u s l e v e l . T h e b a c k g r o u n d c o u n t r a t e f o r t h e a e r o s o l f r e e g a s m i x t u r e a t t h e t o p a n d b o t t o m o f t h e c o l u m n was t h e n m e a s u r e d . T h e f o u r i n i t i a l a n d f o u r f i n a l c o u n t s w e r e a v e r a g e d t o g e t h e r , a n d t h e f o u r c e n t r a l r e a d i n g s w e r e a l s o a v e r a g e d . F r o m t h e s e a v e r a g e s , t h e a p p r o p r i a t e a v e r a g e b a c k g r o u n d c o u n t s w e r e s u b t r a c t e d t o g i v e t h e c o r r e c t e d t o p a n d b o t t o m c o u n t s . T h e s e w e r e t h e n u s e d t o c a l c u l a t e t h e p a r t i c l e r e m o v a l e f f i c i e n c y . By b r a c k e t i n g a n d a v e r a g i n g t h e r e a d i n g s i n t h i s way t h e e f f e c t o f a n y d r i f t was m i n i m i z e d , a n d t h e i n f l u e n c e o f t h e r a n d o m f l u c t u a t i o n s was r e d u c e d . Gas a n a l y s e s w e r e a l s o made a t t h e t o p a n d b o t t o m o f t h e c o l u m n . Two c o n s e c u t i v e r e a d i n g s a g r e e i n g w i t h i n ±0.4% w e r e c o n s i d e r e d s a t i s f a c t o r y . 1 0 0 . 5.4.5 P a r t i c l e Removal i n t h e Absence o f D i f f u s i o p h o r e s i s . I t was p o s s i b l e t h a t some p a r t i c l e removal was o c c u r r i n g i n t h e column due t o mechanisms o t h e r t h a n d i f f u s i o p h o r e s i s . T h i s would p r o b a b l y be p r i m a r i l y t h e r e s u l t o f i n e r t i a l d e p o s i t i o n , s i n c e Brownian d i f f u s i o n and g r a v i t a t i o n a l s e t t l i n g were e x p e c t e d t o be minor f o r p a r t i c l e s i n t h e s i z e range used. D e p o s i t i o n t e s t s were made by p a s s i n g a h i g h f l o w o f p a r t i c l e - b e a r i n g i n e r t gas t h r o u g h the column ( i n e r t i a l d e p o s i t i o n i s f a v o u r e d by h i g h v e l o c i t i e s ) , and s a m p l i n g i n t h e normal manner t o d e t e c t any change i n p a r t i c l e c o n c e n t r a t i o n . I n no case was any s i g n i f i c a n t p a r t i c l e d e p o s i t i o n d e t e c t e d . 5.4.6 I s o k i n e t i c Sampling. I t i s w e l l known t h a t i n s a m p l i n g p a r t i c l e - b e a r i n g s t r e a m s , e r r o r may be i n t r o d u c e d i f the gas i s not sampled i s o k i n e t i c a l l y . I n t h e p r e s e n t e x p e r i m e n t , i s o k i n e t i c s a m p l i n g was n o t p r a c t i c a b l e because o f t h e wide range o f gas v e l o c i t i e s used i n t h e column, and because t h e s a m p l i n g r a t e was d e t e r m i n e d by t h e c o u n t e r s u c t i o n r a t e , w h i c h i n t u r n depended on the gas c o m p o s i t i o n . I n any c a s e , c a l c u l a t i o n s i n d i c a t e d t h a t the e r r o r would be n e g l i g i b l e f o r p a r t i c l e s up t o ^ 2um D . E x p e r i m e n t s i n w h i c h a known f l o w o f i n e r t p a r t i c l e b e a r i n g - g a s was mixed w i t h a range o f known f l o w s of c l e a n i n e r t gas so as t o a c h i e v e d i f f e r e n t v e l o c i t i e s t h r o u g h the column c o n f i r m e d t h i s . However, f o r t h e l a r g e r p a r t i c l e s i z e s t h e r e was some t h e o r e t i c a l p o s s i b i l i t y o f s i g n i f i c a n t s a m p l i n g e r r o r . A s p e c i a l s a m p l i n g head f o r t h e 101. t o p o f the column was t h e r e f o r e d e s i g n e d , w h i c h i s shown.mounted on one o f t h e columns i n F i g u r e 5.2. I n t h i s head, t h e c r o s s s e c t i o n a l a r e a was g r a d u a l l y i n c r e a s e d t i l l t h e mean gas v e l o c i t y had been reduced by 36 t i m e s . The sample was the n drawn from t h i s low v e l o c i t y r e g i o n t h r o u g h a t a p e r e d o f f t a k e . I n t h i s way b o t h t h e v e l o c i t y o f the main gas stream and t h e v e l o c i t y o f the gas e n t e r i n g t h e sample tube were k e p t low enough t o make e r r o r s due t o l a c k o f i s o k i n e t i c s a m p l i n g i n s i g n i f i c a n t . I t was n o t p o s s i b l e t o e a s i l y f i t a s i m i l a r s a m p l i n g head a t the base o f the column. The runs made w i t h the s p e c i a l s a m p l i n g head t h e r e f o r e used the t e c h n i q u e where the "bottom" sample i s t a k e n from the t o p o f the column, b u t w i t h t h e t r a n s f e r r e d gas t u r n e d o f f . 5.5 De s i g n o f Ex p e r i m e n t s F o r a g i v e n gas m i x t u r e , t h e c o n d i t i o n s i n t h e column, and hence the p a r t i c l e removal e f f i c i e n c y , depended on the i n l e t gas f l o w r a t e and c o m p o s i t i o n . (The l i q u i d f l o w r a t e was always h e l d c o n s t a n t a t 35 ml/sec.) These parameters can be c o m p l e t e l y s p e c i f i e d i n terms o f two independent o p e r a t i n g v a r i a b l e s , w h i c h c o u l d be, f o r example, the f l o w r a t e s o f t h e two component g a s e s , o r a l t e r n a t i v e l y , t he i n l e t f l o w r a t e o f one gas and t h e i n l e t c o m p o s i t i o n o f t h e m i x t u r e . Every major s e r i e s o f e x p e r i m e n t s was made by a l t e r i n g one o p e r a t i n g v a r i a b l e w h i l e h o l d i n g t h e o t h e r c o n s t a n t . T h i s p r o c e d u r e had t h e advantages o f p r o d u c i n g d a t a whose t r e n d s c o u l d e a s i l y be d i s c e r n e d by a p p r o p r i a t e p l o t t i n g . 102. The f o l l o w i n g t y p e s o f e x p e r i m e n t s were performed. Ci) The f l o w r a t e o f the i n e r t gas was h e l d c o n s t a n t , and the f l o w r a t e o f the t r a n s f e r r e d gas t o the column was v a r i e d , ( i i ) The f l o w r a t e o f the t r a n s f e r r e d gas t o the column was h e l d c o n s t a n t , and t h e f l o w r a t e o f the i n e r t gas was v a r i e d , ( i i i ) The i n l e t c o m p o s i t i o n was h e l d c o n s t a n t , and t h e t o t a l i n l e t f l o w r a t e was v a r i e d . Most e x p e r i m e n t s were o f t h e f i r s t t y p e . However, e x p e r i m e n t s o f a l l t h r e e t y p e s were made f o r t h e nitrogen-ammonia system w i t h 0.79 ym p a r t i c l e s , i n o r d e r t o r u l e o u t f o r t h e whole s e r i e s o f e x p e r i m e n t s the e x i s t e n c e o f any u n r e c o g n i s e d f a c t o r s i n f l u e n c i n g p a r t i c l e r e m o v a l . 1 0 3 . C h a p t e r 6 RESULTS AND DISCUSSION 6 . 1 T h e D a t a T h e r e a r e 17 s e t s o f e x p e r i m e n t a l d a t a f o r v a r i o u s g a s m i x t u r e s a n d p a r t i c l e s i z e s . T h e s e a r e g i v e n b e l o w , l i s t e d f i r s t l y i n o r d e r o f i n c r e a s i n g m o l e c u l a r w e i g h t o f t h e i n e r t s p e c i e s , a n d s e c o n d l y i n o r d e r o f i n c r e a s i n g m o l e c u l a r w e i g h t o f t h e t r a n s f e r r e d s p e c i e s . S y s t e m H e l i u m - a m m o n i a M e t h a n e - a m m o n i a N i t r o g e n - a m m o n i a P r e l i m i n a r y d a t a , N i t r o g e n - a m m o n i a S h o r t c o l u m n d a t a , N i t r o g e n - a m m o n i a N i t r o g e n - a m m o n i a N i t r o g e n - a m m o n i a N i t r o g e n - a m m o n i a P a r t i c l e  s i z e  (ym) 0 . 7 9 0 .79 0 . 7 9 0 . 7 9 0 0 , 1, 2. 50 79 011 02 S y s t e m A r g o n - a m m o n i a F r e o n 1 2 - a m m o n i a F r e o n 1 2 - a m m o n i a F r e o n 1 2 - a m m o n i a N i t r o g e n -N i t r o g e n -N i t r o g e n -N i t r o g e n -N i t r o g e n -• t r i m e t h y l a m i n e - t r i m e t h y l a m i n e - t r i m e t h y l a m i n e - t r i m e t h y l a m i n e • t r ime t h y 1 a m i ne P a r t i c l e s i z e • (ym) 0 .79 0 .79 1 . 0 1 1 2 . 0 2 0 . 5 0 0 . 7 9 1 . 0 1 1 2 . 0 2 5 . 7 1 0 4 . A l l d a t a w e r e t a k e n u s i n g t h e n o r m a l c o l u m n 0 . 7 7 m i n l e n g t h , w i t h t h e e x c e p t i o n o f t h e " s h o r t c o l u m n d a t a " f o r t h e n i t r o g e n - a m m o n i a s y s t e m w i t h 0 . 7 9 um p a r t i c l e s . T h e s e d a t a w e r e o b t a i n e d w i t h t h e 0 . 3 2 m c o l u m n . A l l e x p e r i m e n t a l r e s u l t s a r e p r e s e n t e d i n t a b u l a r f o r m i n A p p e n d i x D . A n e x p l a n a t i o n o f t h e t a b l e s a n d o f t h e c a l c u l a t i o n m e t h o d s u s e d i n t h e i r p r e p a r a t i o n i s g i v e n i n A p p e n d i x C . T h e r e i s o n e t a b l e f o r e a c h s e t o f d a t a , e x c e p t i n t h e c a s e o f t h e n i t r o g e n - a m m o n i a m i x t u r e w i t h 2 . 0 2 ym p a r t i c l e s , f o r w h i c h t h e r e a r e two t a b l e s . T h e s e c o n t a i n d a t a f o r two s e r i e s o f r u n s made a t d i f f e r e n t t i m e s . T h e c a l i b r a t i o n c o r r e c t i o n s f o r e a c h o f t h e s e w e r e f o u n d t o b e d i f f e r e n t . H o w e v e r , t h e c o r r e c t e d e f f i c i e n c i e s s h o w e d e x c e l l e n t a g r e e m e n t , a n d b o t h s e t s o f d a t a w e r e t h e r e f o r e i n c l u d e d . T h e r e s u l t s f o r e a c h g a s m i x t u r e a n d p a r t i c l e s i z e a r e p l o t t e d i n F i g u r e s 6 . 1 t o 6 . 1 8 . T h e p r e l i m i n a r y d a t a f o r t h e n i t r o g e n - a m m o n i a m i x t u r e w i t h 0 . 7 9 ym p a r t i c l e s , w h i c h h a s b e e n p r e s e n t e d e l s e w h e r e ( s e e W h i t m o r e a n d M e i s e n ( 1 9 7 3 ) ) , i s n o t s h o w n . T h e r e m a i n i n g r e s u l t s f o r t h i s m i x t u r e w i t h 0 . 7 9 ym p a r t i c l e s a r e g i v e n i n t h r e e p l o t s ( F i g u r e s 6 . 5 t o 6 . 7 ) c o r r e s -p o n d i n g t o t h e t h r e e t y p e s o f e x p e r i m e n t s made ( s e e S e c t i o n 5 . 5 ) . G e n e r a l l y a l l d a t a a r e s h o w n f o r e a c h g a s m i x t u r e , b u t i n some c a s e s r u n s w e r e made u n d e r . ^ a t y p i c a l e x p e r i m e n t a l c o n d i t i o n s , a n d h e n c e c o u l d n o t b e p l o t t e d . H o w e v e r , t h e s e r u n s w e r e i n c l u d e d i n t h e s t a t i s t i c a l a n a l y s i s g i v e n i n s e c t i o n 6 . 4 . T h r e e t h e o r e t i c a l v a l u e s f o r t h e p a r t i c l e r e m o v a l e f f i c i e n c y a r e a l s o s h o w n o n e a c h f i g u r e . T h e s e w e r e c a l c u l a t e d 105. u s i n g t h e t h e o r y d e v e l o p e d i n Chapter 4, and c o r r e s p o n d t o t h e assumptions t h a t t h e p a r t i c l e s , t r a v e l r e s p e c t i v e l y w i t h e i t h e r t h e l o c a l gas mean mass v e l o c i t y , t h e mean molar v e l o c i t y , o r the v e l o c i t y p r e d i c t e d by S c h m i t t and Waldmann. 6.2 G e n e r a l Trends F i g u r e s 6.1 t o 6.18 show t h a t t h e e x p e r i m e n t a l d a t a t e n d t o l i e w i t h i n t h e en v e l o p e formed by t h e e f f i c i e n c y p r e -d i c t i o n s o f the mean mass and mean molar v e l o c i t y models. F u r t h e r m o r e , t h e t r e n d e x h i b i t e d by t h e s e t o f d a t a f o r each s p e c i f i c gas system, p a r t i c l e s i z e , and t y p e o f e x p e r i m e n t , i s v e r y s i m i l a r t o the t r e n d s o f t h e t h r e e t h e o r e t i c a l p r e d i c t i o n s . S i n c e t h e e x p e r i m e n t s c o v e r such a wide range o f mass t r a n s f e r c o n d i t i o n s and gas p h y s i c a l p r o p e r t i e s , such agreement p r o v i d e s s t r o n g e v i d e n c e t h a t t h e g e n e r a l t h e o r y o f p a r t i c l e d e p o s i t i o n p r e s e n t e d i n Chapter 4 i s c o r r e c t , a t l e a s t as a f i r s t o r d e r a p p r o x i m a t i o n . T h i s i s n o t s u r p r i s i n g c o n s i d e r i n g t h e br o a d g e n e r a l i t y o f t h a t t h e o r y . A t t h e same t i m e , the p o s i t i o n o f the d a t a r e l a t i v e t o the t h r e e models v a r i e s w i t h b o t h gas system and p a r t i c l e s i z e , and t h e d a t a as a whole do n o t c o r r e l a t e w e l l around t h e p r e d i c t i o n s o f any s p e c i f i c model. As d i s c u s s e d i n S e c t i o n 6.3, i n a l m o s t e v e r y case the p o s s i b l e s y s t e m a t i c e r r o r s a l o n e a r e l a r g e enough t o a c c o u n t f o r t h e l a c k o f c o r r e l a t i o n w i t h t h e mean mass v e l o c i t y model. T h i s does n o t mean, however, t h a t the p o s i t i o n o f the 106 . d a t a r e l a t i v e t o t h e v a r i o u s m o d e l s i s w i t h o u t s i g n i f i c a n c e . T h e e r r o r e s t i m a t e s a r e t h e maximum e x p e c t e d e r r o r s , a n d n o t t h e p r o b a b l e e r r o r s , w h i c h a r e much s m a l l e r . I n a n y c a s e , i t i s u n l i k e l y t h a t t h e v a r i a t i o n i n d a t a p o s i t i o n i s c a u s e d p r i m a r i l y b y s y s t e m a t i c e r r o r s , a s t h e s e w o u l d t e n d t o n u l l i f y t h e o b s e r v e d s i m i l a r i t y b e t w e e n t h e t r e n d s s h o w n b y e a c h s e t o f d a t a a n d t h e c o r r e s p o n d i n g m o d e l p r e d i c t i o n s . T h e o n l y o b v i o u s r e m a i n i n g e x p l a n a t i o n f o r t h e e x p e r i -m e n t a l r e s u l t s o b t a i n e d i s t h a t t h e p a r t i c l e s w e r e e x h i b i t i n g t r a n -s i t i o n regime b e h a v i o u r . A c c o r d i n g t o t h e t h e o r y d e v e l o p e d i n C h a p t e r 3, l a r g e p a r t i c l e s w i l l move w i t h t h e mean m a s s v e l o c i t y o f t h e f l u i d . S m a l l p a r t i c l e s w i l l t r a v e l a t e s s e n t i a l l y t h e S c h m i t t a n d W a l d m a n n v e l o c i t y , i f t h e i r i n t e r a c t i o n s w i t h b o t h m o l e c u l a r s p e c i e s a r e s i m i l a r , a s d i s c u s s e d i n C h a p t e r 2. W i t h d i s s i m i l a r i n t e r a c t i o n s , t h e p a r t i c l e s w i l l move a t a s l i g h t l y d i f f e r e n t v e l o c i t y , w h i c h i n t u i t i v e l y c a n b e e x p e c t e d t o l i e b e t w e e n t h e mean m a s s a n d mean m o l a r v e l o c i t i e s . H e n c e t h e r e m o v a l e f f i c i e n c i e s i n t h e t r a n s i t i o n r e g i m e s h o u l d f a l l b e t w e e n t h e l i m i t s p r e s c r i b e d b y t h e p r e d i c t i o n s o f t h e mean m a s s a n d mean m o l a r v e l o c i t y m o d e l s . F u r t h e r m o r e , f o r a g i v e n g a s s y s t e m a n d p a r t i c l e s i z e , t h e s e e f f i c i e n c i e s s h o u l d show t h e same t r e n d a s t h e m o d e l p r e d i c t i o n s , when e x p e r i m e n t a l c o n d i t i o n s a r e f . . . . s y s t e m a t i c a l l y v a r i e d . S i n c e t h e o u t l i n e d b e h a v i o u r i s , i d e n t i -c a l t o t h a t e x h i b i t e d b y t h e e x p e r i m e n t a l r e s u l t s o b t a i n e d i n A f u l l e r d i s c u s s i o n o f t h e t h e o r y o f p a r t i c l e r e m o v a l i n t h e t r a n s i t i o n r e g i m e w i l l b e f o u n d i n A p p e n d i x E . 107. t h e p r e s e n t s t u d y , i t i s c o n c l u d e d t h a t t h e p a r t i c l e s g e n e r a l l y f e l l w i t h i n t h e t r a n s i t i o n r e g i m e . T h e t r a n s i t i o n r e g i m e b e h a v i o u r p r e c l u d e s d e f i n i t e c o n f i r m a t i o n t h a t l a r g e p a r t i c l e s move a t t h e mean m a s s v e l o c i t y . T h e r e i s , h o w e v e r , a n i n d i c a t i o n t h a t t h e y d o , s i n c e f o r s m a l l K n u d s e n n u m b e r s t h e d a t a t e n d t o c o r r e l a t e u a r o u n d t h e c o r r e s -p o n d i n g m o d e l p r e d i c t i o n s . I n c o n t r a s t , o n l y a s m a l l f r a c t i o n o f t h e d a t a a g r e e w i t h t h e p r e d i c t i o n s o f t h e mean m o l a r v e l o c i t y m o d e l . T h i s s u g g e s t s t h a t t h e t h e o r i e s o f D e r j a g u i n e t a l . (1966) a n d D e r j a g u i n a n d Y a l a m o v (19 7 2 ) , w h i c h p r e d i c t e d t h i s v e l o c i t y f o r l a r g e p a r t i c l e s , may b e i n c o r r e c t . 6 . 3 A c c u r a c y a n d E r r o r s 6 . 3 . 1 G e n e r a l T h e e r r o r s c a n b e d i v i d e d i n t o two g r o u p s . Random e r r o r s p r o d u c e s c a t t e r i n t h e d a t a , b u t a n i n c r e a s i n g l y a c c u r a t e mean v a l u e c a n b e o b t a i n e d a s m o r e r e a d i n g s a r e t a k e n . S y s t e m a t i c e r r o r s l e a d t o a n o f f s e t b e t w e e n t h e mean e x p e r i m e n t a l v a l u e a n d t h e t r u e v a l u e . T h e s e t w o t y p e s o f e r r o r s a r e d i s c u s s e d i n t h e f o l l o w i n g two s u b s e c t i o n s . S a m p l e e r r o r c a l c u l a t i o n s a p p e a r i n A p p e n d i x C . A n i m p o r t a n t t e s t o f t h e e x p e r i m e n t a l p r o c e d u r e i s t h e r e p r o d u c i b i l i t y o f t h e d a t a . G o o d r e p r o d u c i b i l i t y was o b t a i n e d w i t h i n t h e n o r m a l e x p e r i m e n t a l s c a t t e r f o r c o n s e c u t i v e r e a d i n g s t a k e n u n d e r t h e same e x p e r i m e n t a l c o n d i t i o n s . ( R e a d i n g s o f t h i s t y p e b e a r t h e same r u n n u m b e r i n A p p e n d i x D . ) I n a d d i t i o n , r e p l i c a t e r u n s , s o m e t i m e s made w e e k s o r m o n t h s l a t e r , s h o w e d g o o d a g r e e m e n t w i t h t h e o r i g i n a l d a t a . 6 . 3 . 2 Random E r r o r s T h e r e a r e two m a i n s o u r c e s o f r a n d o m e r r o r s . T h e m o s t i m p o r t a n t i s t h e r a n d o m c h a n g e i n t h e a e r o s o l c o n c e n t r a t i o n p r o d u c e d b y t h e a e r o s o l g e n e r a t o r . T h e s e c o n d i s t h e e r r o r i n d e t e r m i n i n g t h e t i m e f o r a g i v e n v o l u m e o f g a s t o p a s s t h r o u g h t h e g a s m e t e r . T h i s i s e s t i m a t e d t o i n t r o d u c e a n e r r o r o f a p p r o x i m a t e l y ±1% i n t h e p a r t i c l e c o u n t . B o t h t h e s e e r r o r s w e r e r e d u c e d b y t h e b r a c k e t i n g a n d a v e r a g i n g m e t h o d s u s e d i n t h e d a t a a n a l y s i s ( s e e A p p e n d i x C ) , a n d t h e i r i n f l u e n c e o n t h e e s t i m a t e d e f f i c i e n c i e s i s b e s t o b t a i n e d f r o m s t a t i s t i c a l a n a l y s i s o f t h e f i n a l d a t a ( s e e S e c t i o n 6 . 4 ) . 6 . 3 . 3 S y s t e m a t i c E r r o r s S e v e r a l s o u r c e s w h i c h m i g h t g i v e r i s e t o s i g n i f i c a n t e r r o r s w e r e r e c o g n i z e d , a n d t h e s e a r e d i s c u s s e d i n a p p r o x i m a t e o r d e r o f d e c r e a s i n g i m p o r t a n c e . T h e m a i n e r r o r a r i s e s i n t h e a e r o s o l c o u n t e r c a l i b r a -t i o n f o r g a s c o m p o s i t i o n . T h e c a l i b r a t i o n e f f e c t i s u s u a l l y s m a l l , p r o d u c i n g a c h a n g e i n t h e t r u e c o u n t o f l e s s t h a n 10%. H o w e v e r , t h e e x p e r i m e n t a l s c a t t e r i n d e t e r m i n i n g the c a l i b r a t i o n c u r v e i s a p p r e c i a b l e i n r e l a t i o n t o t h i s c o r r e c t i o n , b e i n g o f t h e o r d e r o f ±5%. A l s o , t h e c a l i b r a t i o n c o r r e c t i o n b e c o m e s l e s s d e f i n i t e a s t h e m o l e f r a c t i o n o f t h e t r a n s f e r r e d g a s i n c r e a s e s , 109 . iDecause o f .incre a s e d random e r r o r s . E r r o r s i n gas a n a l y s e s do n o t i n f l u e n c e t h e experimen-t a l r emoval e f f i c i e n c y , faut they do a f f e c t the t h e o r e t i c a l model p r e d i c t i o n s . S i n c e t h e gas a n a l y s e s f o r each e x p e r i m e n t a l c o n d i t i o n were n o r m a l l y done o n l y t w i c e t o o b t a i n r e a d i n g s w i t h i n ±0.4%, t h e r e i s no e s t i m a t e of the s c a t t e r and the e r r o r i s t r e a t e d as s y s t e m a t i c . A n o t h e r s o u r c e o f e r r o r i n t h e gas a n a l y s i s i s t h e presence o f more tha n two components i n t h e gas m i x t u r e . S i n c e t h e a e r o s o l was g e n e r a t e d from a w a t e r s u s p e n s i o n , the gas m i x t u r e c o n t a i n e d some wa t e r vapour. However, c a l c u l a t i o n s showed t h a t t h i s q u a n t i t y was n e g l i g i b l e . A second p o s s i b l e s o u r c e o f wa t e r vapour was e v a p o r a t i o n o f t h e l i q u i d f i l m i n the column. T h i s was a l s o a s s e s s e d t o be n e g l i g i b l e , s i n c e no.water vapour c o u l d be d e t e c t e d i n t h e gas l e a v i n g the column. I n any c a s e , t h e s a t u r a t i o n c o n c e n t r a t i o n o f w a t e r vapour a t 20°C (the approximate t e m p e r a t u r e o f the e x i t i n g gas) i s q u i t e s m a l l . A l t h o u g h r e l e a s e o f h e a t o f a b s o r p t i o n a t the wa t e r s u r f a c e would enhance e v a p o r a t i o n , t h e t r a n s f e r o f t h i s vapour i n t o t h e b u l k o f t h e gas i s i n t u r n i n h i b i t e d by the s t r o n g f l u x o f t r a n s f e r r e d gas towards the l i q u i d s u r f a c e . ( E r r o r s i n t h e r o t a m e t e r r e a d i n g s do not d i r e c t l y i n t r o d u c e any e r r o r s i n e s t i m a t i n g the t h e o r e t i c a l e f f i c i e n c i e s , s i n c e t h e s e a r e based on t h e gas a n a l y s e s and component m o l e c u l a r w e i g h t s alone.) Other gas components can a l s o r e s u l t from i m p u r i t i e s i n t h e c y l i n d e r gases (see T a b l e I I ) . T h i s was e s t i m a t e d t o i n t r o d u c e an a b s o l u t e e r r o r i n the f r a c t i o n a l e f f i c i e n c i e s 110. p r e d i c t e d by the models o f o r d e r (x + y)/8, where x and y are the f r a c t i o n a l i m p u r i t y l e v e l s i n the i n e r t and t r a n s f e r r e d gas components (see Appendix C ) . S i n c e most gases were r e l a t i v e l y p u re, t h i s s o u r c e o f e r r o r was s m a l l . A n o t h e r s o u r c e o f e r r o r a r i s e s from p a r t i c l e l o s s e s due t o i n e r t i a l d e p o s i t i o n i n t h e column. The e x i s t e n c e o f t h e s e l o s s e s was however never d e t e c t e d , and t h e o r e t i c a l c a l c u l a t i o n i n d i c a t e d t h a t t hey would be n e g l i g i b l e . Lack o f i s o k i n e t i c s a m p l i n g c o u l d i n t r o d u c e e r r o r , b u t t h i s c o u l d n o t be d e t e c t e d i n e x p e r i m e n t a l t e s t s . Moreover, a s p e c i a l s a m p l i n g p o r t (see Chapter 5) was used f o r t h e l a r g e r p a r t i c l e s , so t h a t any e r r o r was m i n i m i z e d . A l t h o u g h t h e column was d e s i g n e d t o o p e r a t e a t c l o s e t o i s o t h e r m a l c o n d i t i o n s , the h e a t l i b e r a t e d d u r i n g the gas a b s o r p t i o n i n e v i t a b l y produced a t e m p e r a t u r e r i s e i n t h e l i q u i d as i t passed t h r o u g h t h e column. T h i s was t y p i c a l l y a few degrees C e l s i u s , b u t c o u l d be as h i g h as" 10°C under extreme c o n d i t i o n s . However, th e o v e r a l l change i n gas t e m p e r a t u r e was s u b s t a n t i a l l y l e s s t h a n t h i s , s i n c e , a l t h o u g h the gas may be h e a t e d by t h e l i q u i d a t the base b f the column, i t l o s e s h e a t back t o t h e l i q u i d a t t h e t o p o f t h e column. The o v e r a l l change i n gas t e m p e r a t u r e was t h e r e f o r e s m a l l . F o r example, under t h e h i g h e s t mass t r a n s f e r r a t e s used w i t h t h e nitrogen-ammonia system, t h e l i q u i d tempera-t u r e i n c r e a s e d 10°C, w h i l e the gas temperature i n c r e a s e d o n l y 3°C i n p a s s i n g t h r o u g h t h e column. On t h i s b a s i s , the i n h i b i t i o n o f p a r t i c l e d e p o s i t i o n caused by t h e r m o p h o r e s i s was e s t i m a t e d t o be n e g l i g i b l e (see 111. Whitmore and M e i s e n , t o be p u b l i s h e d , Canadian J o u r n a l o f C h e m i c a l E n g i n e e r i n g ) . The above argument presupposes t h a t the thermo-p h o r e t i c f o r c e i s a t no p o i n t s t r o n g enough t o c o m p l e t e l y s u p p r e s s p a r t i c l e d e p o s i t i o n , a s u p p o s i t i o n which was c o n f i r m e d by c a l -c u l a t i o n . The l a s t s o u r c e of e r r o r was p a r t i c l e g e n e r a t i o n i n t h e column. P a r t i c l e s c o u l d be formed by e n t r a i n m e n t of l i q u i d d r o p l e t s o r d i r t from i n t e r i o r s u r f a c e s . However, t e s t s showed t h a t t h e s e s o u r c e s were n o t s i g n i f i c a n t . I n any c a s e they would be i n c l u d e d i n t h e background c o u n t , and hence e l i m i n a t e d (see S e c t i o n 5.4). The o t h e r s o u r c e o f p a r t i c l e s was from m i s t f o r m a t i o n i n t h e column. A l t h o u g h t h e o u t l e t w a t e r vapour c o n c e n t r a t i o n was n o r m a l l y s m a l l , i t i s s t i l l c o n c e i v a b l e t h a t t h e gas c o u l d become l o c a l l y s u p e r s a t u r a t e d . T h i s would o c c u r because the gas i n c o n t a c t w i t h the l i q u i d a t t h e base o f the column p i c k s up some water vapour. I t t h e n tends t o move i n t o t h e c o o l e r r e g i o n s f u r t h e r up t h e column. More i m p o r t a n t l y , the gas volume s h r i n k s as the t r a n s f e r r e d gas i s a b s orbed, w h i c h i n t u r n c o n c e n t r a t e s the w a t e r vapour. These c o n s i d e r a t i o n s a r e p r o b a b l y n o t i m p o r t a n t e x c e p t under the extreme mass t r a n s f e r c o n d i t i o n s e n c o u n t e r e d i n some of t h e f r e o n 12-ammonia e x p e r i m e n t s . F o r example, i n one i n s t a n c e t h e ammonia t r a n s f e r - was so l a r g e t h a t t h e v o l u m e t r i c gas f l o w d e c r e a s e d by a f a c t o r o f 6 between the column i n l e t and o u t l e t . The d i f f i c u l t y i n a s s e s s i n g t h i s e r r o r i s t h a t the d r o p l e t f o r m a t i o n u s u a l l y o n l y o c c u r r e d i n t h e p r e s ence of the 112. p a r t i c l e s , w h i c h p r e s u m a b l y a c t e d a s t h e i n i t i a l c o n d e n s a t i o n n u c l e i f o r t h e s u p e r s a t u r a t e d g a s . T h u s i t was n o t p o s s i b l e t o c o u n t t h e n u m b e r o f m i s t p a r t i c l e s , o r t e s t f o r t h e i r p r e s e n c e w i t h t h e f l o w o f a e r o s o l p a r t i c l e s s h u t o f f . H o w e v e r , i t was f o u n d t h a t s p u r i o u s r e s u l t s w e r e o b t a i n e d w h e n e v e r u n u s u a l l y l a r g e n u m b e r s o f p a r t i c l e s w e r e r e c o r d e d o n t h e c o u n t e r c h a n n e l o n w h i c h t h e l a t e x p a r t i c l e s w e r e not r e g i s t e r i n g . N o r m a l l y t h e c o u n t o n t h a t c h a n n e l w o u l d b e s m a l l . F o r t u n a t e l y , t h e p h e n o m e n o n o f m i s t f o r m a t i o n a s j u d g e d b y t h i s t e s t c o u l d o f t e n b e a v o i d e d b y u s i n g a s t a r t u p p r o c e d u r e w h i c h m i n i m i z e d h i g h t r a n s i e n t g a s t e m p e r a t u r e s . A l s o , m i s t f o r m a t i o n was t y p i c a l l y n o t e s t a b l i s h e d f o r some t i m e , i f a t a l l . H o w e v e r , s i n c e n o d i r e c t t e s t c o u l d b e m a d e , t h e p r e s e n c e o f s m a l l b u t s i g n i f i c a n t n u m b e r s o f m i s t d r o p l e t s i n t h e same s i z e r a n g e a s t h e l a t e x p a r t i c l e s c a n n o t b e a l t o g e t h e r r u l e d o u t . T h e e r r o r i s e x p e c t e d t o b e s m a l l , a n d t o b e p r e s e n t o n l y w h e n t h e f r a c t i o n a l v o l u m e c h a n g e f o r t h e g a s p a s s i n g t h r o u g h t h e c o l u m n i s l a r g e . T a b l e I V l i s t s f o r e a c h g a s s y s t e m a n d p a r t i c l e s i z e , e s t i m a t e s o f t h e p o s s i b l e s y s t e m a t i c e r r o r s i n t h e p r e d i c t i o n s o f t h e m e a n mass v e l o c i t y m o d e l a n d i n t h e m e a s u r e d e x p e r i m e n t a l e f f i c i e n c y , a s w e l l a s t h e sum o f t h e s e e r r o r s . T h e m o d e l e r r o r i s a c o m b i n a t i o n o f i n a c c u r a c i e s r e s u l t i n g f r o m t h e g a s a n a l y s i s a n d t h e p r e s e n c e o f m o r e t h a n two g a s c o m p o n e n t s i n t h e g a s m i x t u r e . T h e e x p e r i m e n t a l e r r o r q u o t e d a r i s e s f r o m u n c e r t a i n t i e s i n t h e c o u n t e r c a l i b r a t i o n , s i n c e t h e o t h e r e x p e r i m e n t a l e r r o r s w e r e a l l e s t i m a t e d t o b e n e g l i g i b l e . T a b l e IV E s t i m a t e s o f S y s t e m a t i c E r r o r s Gas m i x t u r e P a r t i c l e s i z e (ym) P o s s i b l e a b s o l u t e e r r o r i n t h e o r e t i c a l model p r e -d i c t i o n P o s s i b l e a b s o l u t e e r r o r i n ^ e x p e r i m e n t a l e f f i c i e n c y T o t a l p o s s i b l e a b s o l u t e e r r o r He-NH 3 0 .79 ±.01 ±.04 ±.05 CH 4-NH 3 0 .79 .01 .02 .03 N2-NH"3 0.79 .01 .06 .07 P r e l i m i n a r y d a t a N 2-NH 3 0.79 .01 .05 .06 S h o r t column d a t a N 2-NH 3 0.50 .01 .05 .06 N 2-NH 3 0 .79 .01 .02 .03 N 2-NH 3 1.011 .01 .04 .05 N 2-NH 3 2.02 .01 .05 .06 A r-NH 3 0 . 79 .01 .05 .06 c o n t i n u e d T a b l e I V / c o n t ' d .... Gas m i x t u r e P a r t i c l e s i z e (ym) P o s s i b l e a b s o l u t e e r r o r i n t h e o r e t i c a l model p r e -d i c t i o n P o s s i b l e a b s o l u t e e r r o r i n e x p e r i m e n t a l e f f i c i e n c y T o t a l p o s s i b l e a b s o l u t e e r r o r F r e o n 12-NH, 0.79 .02 .08 .10 F r e o n 12-NH, 1.011 .02 .08 .10 Freon 12-NH 3 2.02 .02 .08 .10 N 2-N(CH 3) 3 N 2 - N ( C H 3 ) 3 N 2-N(CH 3) 3 N 2-N(CH 3) 3 N 2 - N ( C H 3 ) 3 0 .50 0 .79 1.011 2 .02 5.7 .01 .01 .01 .01 .01 .03 .04 .05 .06 .08 .04 .05 .06 .07 .09 6.4 S t a t i s t i c a l A n a l y s e s The d a t a f o r each gas m i x t u r e and p a r t i c l e s i z e were s t a t i s t i c a l l y a n a l y s e d . I n a d d i t i o n , the e x t e n s i v e d a t a f o r t h e nitrogen-ammonia system w i t h 0.79 um p a r t i c l e s were a l s o d i v i d e d i n t o s u b s e t s c o n t a i n i n g the r e s u l t s o f t h e t h r e e t y p e s o f e x p e r i -ments performed (see S e c t i o n 5.5). These s u b s e t s were a n a l y s e d s e p a r a t e l y . The aim o f the s t a t i s t i c a l a n a l y s i s was t o c o n f i r m t h e g e n e r a l c o n c l u s i o n s a l r e a d y r e a c h e d i n S e c t i o n 6.2. I t was a l s o d e s i r e d t o t e s t f o r p o s s i b l e i n f l u e n c e s o f t r a n s i t i o n regime b e h a v i o u r and i n e r t i a l d e p o s i t i o n l o s s e s , w h i c h were n o t o b v i o u s from a v i s u a l i n s p e c t i o n o f F i g u r e s 6.1 t o 6.18. D e t a i l s o f the s t a t i s t i c a l methods used are g i v e n i n Appendix E. I n the f i r s t p a r t o f the a n a l y s i s a mean o f f s e t was c a l c u l a t e d from t h e d i f f e r e n c e between each e x p e r i m e n t a l e f f i -c i e n c y and t h e c o r r e s p o n d i n g model p r e d i c t i o n . The c a l c u l a t i o n was performed f o r each i n d i v i d u a l s e t and s u b s e t o f d a t a , u s i n g each o f t h e t h r e e t h e o r e t i c a l models. T h i s e s t a b l i s h e s t h e r e l a t i v e p o s i t i o n o f the d a t a w i t h r e s p e c t t o t h e models, the model t h a t g i v e s t h e b e s t agreement, and t h e s i g n i f i c a n c e o f the o f f s e t from t h e mean mass v e l o c i t y model i n terms of the s c a t t e r i n t h e d a t a . The r e s u l t s o f t h i s a n a l y s i s are g i v e n i n T a b l e V. The o f f s e t from the mean mass v e l o c i t y model, g i v e n i n column 4, i s p o s i t i v e when t h e e x p e r i m e n t a l e f f i c i e n c i e s a r e , on a v e r a g e , g r e a t e r than t h e model p r e d i c t i o n s . The s i g n i f i c a n c e o f t h i s o f f s e t , d e t e r m i n e d a t the 90 and 95% c o n f i d e n c e l e v e l s u s i n g t h e s t a t i s t i c a l t - t e s t , i s shown i n column 5. O f f s e t s o f lower s i g n i f i c a n c e a r e c l a s s i f i e d as n o t s i g n i f i c a n t (N.S.). A s i g n i -T a b l e V Comparison o f Data w i t h T h e o r e t i c a l Models Gas M i x t u r e P a r t i -c l e s i z e (ym) Number o f d a t a p o i n t s Average a b s o l u t e o f f s e t o f d a t a from mean mass v e l o c i t y model G e n e r a l p o s i t i o n o f d a t a r e l a t i v e t o models Va l u e o f o f f s e t S i g n i -f i c a n c e Beyond me an mass Mean mass t o S c h m i t t and Waldmann S c h m i t t and Waldmann t o mean molar Beyond mean molar C l o s e r t o mean mass C l o s e r t o . Schmitt and Wald-mann C l o s e r t o S c h m i t t and Wald-mann C l o s e r t o mean molar He-NH 3 0.79 14 -0.1298 95 X CH 4-NH 3 0.79 13 -0.0141 95 X N 2-NH 3 , P r e l i - '" minary d a t a . 0.79 29 -0.0177 95 X N 2-NH 3 S h o r t column . d a t a . 0.79 14 -0.0168 95 X c o n t i n u e d T a b l e V / c o n t ' d . . . . N 2 - N H 3 0 . 5 0 25 0 . 0 6 6 4 95 X N 2 - N H 3 0 . 7 9 123 0 . 0 1 7 1 95 X N 2 - N H 3 0 .79 36 0 . 0 1 8 4 95 X c o n s t a n t i n e r t g a s r a t e . N 2 - N H 3 0 . 79 59 0 . 0 2 3 9 95 X c o n s t a n t i n l e t t r a n s -f e r r e d g a s r a t e . N 2 - N H 3 0 . 7 9 47 0 . 0 1 2 7 95 X c o n s t a n t i n l e t g a s c o m p o s i -t i o n N 2 - N H 3 1 . 0 1 1 57 - 0 . 0 0 6 9 95 X N 2 - N H 3 2 . 0 2 49 0 . 0 4 0 9 95 X A r - N H 3 0 . 79 26 0 . 0 1 2 9 90 X F r e o n 1 2 -NH3 F r e o n 1 2 -NH3 F r e o n 1 2 -NH. 3 0 . 7 9 1 . 0 1 1 2 . 0 2 52 15 15 - 0 . 1 2 9 9 0 . 1 8 2 1 0 . 2 5 9 0 95 95 95 X X X -118. f i c a n t o f f s e t means t h a t , c o n s i d e r i n g o n l y the random e r r o r as e v i d e n c e d by t h e s c a t t e r i n t h e d a t a , t h e e x p e r i m e n t a l r e s u l t s a r e p r o b a b l y d i f f e r e n t from the t h e o r e t i c a l model p r e d i c t i o n s . The f i n a l s i x columns i n d i c a t e the p o s i t i o n o f the d a t a w i t h r e s p e c t t o the p r e d i c t i o n s o f the t h r e e models, and show which model g i v e s the b e s t agreement. Thus, i n t h e case o f the f i r s t e n t r y , w h i c h i s f o r helium-ammonia w i t h 0.79 um p a r t i c l e s , t h e d a t a l i e between the p r e d i c t i o n s o f t h e S c h m i t t and Waldmann model and t h e mean molar v e l o c i t y model, and are c l o s e r t o t h e former. C l a s s i f i c a t i o n i n t h i s manner i s p o s s i b l e because the p r e d i c t i o n s o f t h e S c h m i t t and Waldmann model always f a l l between thos e o f t h e o t h e r two. Based on t h e mean o f f s e t o f the d a t a from th e p r e -d i c t i o n s o f e a ch model, o n l y t h e r e s u l t s f o r methane-ammonia w i t h 0.79 ym p a r t i c l e s l i e o u t s i d e t h e t h e o r e t i c a l e n v e l o p e and beyond th e e f f i c i e n c i e s p r e d i c t e d by t h e mean molar v e l o c i t y model. However t h i s o f f s e t i s not s i g n i f i c a n t even i n terms of t h e s c a t t e r i n t h e d a t a . I n f a c t the t h r e e model p r e d i c t i o n s a r e so c l o s e t o g e t h e r f o r t h i s gas m i x t u r e t h a t t h e d a t a show al m o s t as good agreement w i t h t h e mean mass v e l o c i t y model as w i t h t h e o t h e r s . A t t h e o t h e r extreme, o n l y the p r e l i m i n a r y d a t a f o r nitrogen-ammonia w i t h 0.79 ym p a r t i c l e s , and the d a t a f o r nitrogen-ammonia w i t h 1.011 ym p a r t i c l e s , l i e beyond the mean mass v e l o c i t y model. A l t h o u g h i n each case the o f f s e t i s s i g n i -f i c a n t i n terms of the s c a t t e r i n t h e d a t a , i t i s s m a l l i n c omparison w i t h t h e p o s s i b l e a b s o l u t e e r r o r s . The e x p e r i m e n t s a r e t h e r e f o r e i n agreement w i t h t h e t e n t a t i v e c o n c l u s i o n r e a c h e d 119 . i n C h a p t e r 4, namely t h a t t h e f l u i d mean mass and mean molar v e l o c i t i e s a r e t h e l i m i t i n g v e l o c i t i e s t h a t can be a t t a i n e d by a p a r t i c l e i n any regime. F o r t h e 17 c o m b i n a t i o n s o f gas m i x t u r e s and p a r t i c l e s i z e s s t u d i e d , 6 g i v e b e s t agreement w i t h the mean mass v e l o c i t y t h e o r y , 8 w i t h t h a t o f S c h m i t t and Waldmann, and o n l y 3 w i t h t h e mean molar v e l o c i t y t h e o r y . Of the l a t t e r , t h e methane-ammonia case i s c e r t a i n l y n o t s i g n i f i c a n t , as s t a t e d b e f o r e . There i s no o b v i o u s r e a s o n t o d i s c o u n t t h e s i g n i f i c a n c e o f the o t h e r two c a s e s . However, the w e i g h t o f e v i d e n c e c a s t s s e r i o u s doubt on the v a l i d i t y o f the mean molar v e l o c i t y t h e o r y f o r l a r g e p a r t i c l e s . T h i s i s not s u r p r i s i n g i f one a c c e p t s t h e c r i t i c i s m s o f t h i s t h e o r y made i n Chapter 2. The second p a r t o f the a n a l y s i s i n v o l v e d t e s t i n g whether t r a n s i t i o n b e h a v i o u r o r i n e r t i a l d e p o s i t i o n were h a v i n g a s i g n i f i c a n t i n f l u e n c e on the e x p e r i m e n t a l r e s u l t s . A l l the d a t a s e t s and s u b s e t s used p r e v i o u s l y were t e s t e d . I n a d d i t i o n , where more th a n one p a r t i c l e s i z e had been e x p e r i m e n t a l l y examined w i t h a g i v e n gas m i x t u r e , a l l t h e d a t a f o r the m i x t u r e were grouped t o g e t h e r . (The d a t a f o r 5.7 um p a r t i c l e s were n o t i n c l u d e d i n the n i t r o g e n - t r i m e t h y l a m i n e group because o f t h e i r l a r g e s c a t t e r . ) T h i s had s e v e r a l p o t e n t i a l b e n e f i t s . The ranges o f v a l u e s f o r the parameters used i n t e s t i n g f o r t h e two e f f e c t s were g r e a t l y i n c r e a s e d , and more d a t a p o i n t s were a v a i l a b l e t h a n f o r i n d i v i d u a l p a r t i c l e s i z e s . Thus t h e chances o f o b t a i n i n g s i g n i f i c a n t r e s u l t s were improved. A l s o , s y s t e m a t i c e r r o r s were e x p e c t e d t o have d i s s i m i l a r e f f e c t s on t h e r e s u l t s f o r p a r t i c l e s of d i f f e r e n t s i z e s . 120. I t was t h e r e f o r e h o p e d t h a t b y g r o u p i n g t h e s e r e s u l t s , s y s t e m a t i c e r r o r s , w h i c h c o u l d mask t r e n d s w i t h i n i n d i v i d u a l d a t a s e t s , w o u l d b e h a v e a s r a n d o m e r r o r s . T h e e x i s t e n c e o f t r a n s i t i o n r e g i m e b e h a v i o u r c a n b e i n v e s t i g a t e d u s i n g t h e K n u d s e n n u m b e r . T h e p a r a m e t e r c h o s e n i n t e s t i n g f o r i n e r t i a l d e p o s i t i o n was t h e R e y n o l d s n u m b e r m u l t i p l i e d b y t h e p a r t i c l e d i a m e t e r s q u a r e d . T h i s p a r a m e t e r i s c l o s e l y r e l a t e d t o t h e S t o k e s s t o p p i n g d i s t a n c e . F o r f i r s t - o r d e r t e s t i n g o v e r t h e l i m i t e d R e y n o l d s n u m b e r a n d p a r t i c l e d i a m e t e r r a n g e s c o v e r e d i n t h i s w o r k , i t s h o u l d b e a d e q u a t e t o a s s u m e t h a t i n e r t i a l d e p o s i t i o n e x h i b i t s a l i n e a r d e p e n d e n c e o n t h e s t o p p i n g d i s t a n c e p a r a m e t e r . A s s h o w n i n T a b l e V , t h e v a l u e o f t h e a v e r a g e o f f s e t f r o m t h e mean m a s s v e l o c i t y m o d e l v a r i e d w i t h g a s m i x t u r e a n d p a r t i c l e s i z e u s e d . T h i s i n d i c a t e s t h a t t h e p a r t i c l e s a r e p r o b a b l y i n t h e t r a n s i t i o n r e g i m e , b u t i s n o t c o n c l u s i v e . F o r e x a m p l e , i t d o e s n o t c o n f i r m t h a t t h e t r e n d shown b y t h e d a t a i s g e n e r a l l y s i m i l a r t o t h a t o f t h e m o d e l p r e d i c t i o n s . I n f a c t , no s i m p l e a n d u n a m b i g u o u s t e s t f o r t r a n s i t i o n r e g i m e b e h a v i o u r c o u l d b e d e v i s e d . A t r a n s i t i o n r e g i m e m o d e l f o r p a r t i c l e r e m o v a l e f f i -c i e n c y was t h e r e f o r e c o n s t r u c t e d , a n d t h e d a t a w e r e t e s t e d t o s e e w h e t h e r t h e y c o u l d b e a d e q u a t e l y d e s c r i b e d b y i t . T h e d e t a i l e d d e v e l o p m e n t o f t h e m o d e l i s g i v e n i n A p p e n d i x E . I t was d e r i v e d b y a s s u m i n g t h a t p a r t i c l e v e l o c i t i e s i n t h e t r a n s i t i o n r e g i m e c o u l d b e r e p r e s e n t e d a s t h e sum o f a p p r o p r i a t e s m a l l a n d l a r g e p a r t i c l e v e l o c i t y c o m p o n e n t s . One c o m p o n e n t was o b t a i n e d b y 121. m u l t i p l y i n g t h e s m a l l p a r t i c l e v e l o c i t y ( i . e . , S c h m i t t a n d . W a l d m a n n ' s r e s u l t ) b y a l i n e a r f u n c t i o n o f K n u d s e n n u m b e r , a n d t h e o t h e r was o b t a i n e d b y m u l t i p l y i n g t h e l a r g e p a r t i c l e v e l o c i t y ( i . e . , t h e m e a n m a s s v e l o c i t y o f t h e f l u i d ) b y o n e m i n u s t h i s f u n c t i o n . T h e a s s u m p t i o n o f l i n e a r i t y s h o u l d b e a d e q u a t e o v e r t h e K n u d s e n n u m b e r r a n g e i n v o l v e d . T h e m o d e l y i e l d e d t h e f o l l o w i n g e q u a t i o n f o r t h e r e m o v a l e f f i c i e n c y d u e t o d i f f u s i o p h o r e s i s a n d i n e r t i a l d e p o s i t i o n i n t h e t r a n s i t i o n r e g i m e : e p = V e S W " W + B r ( e S W " e M A ) K n + C r S + E M A H e r e S i s t h e s t o p p i n g d i s t a n c e p a r a m e t e r , a n d a n d a r e t h e p r e d i c t i o n s o f t h e mean m a s s a n d S c h m i t t a n d W a l d m a n n v e l o c i t y m o d e l s , r e s p e c t i v e l y . T h e m a g n i t u d e o f t h e c o e f f i c i e n t s A r a n d B r d e p e n d o n t h e q u a n t i t a t i v e r e l a t i o n s h i p b e t w e e n p a r t i c l e b e h a v i o u r a n d K n u d s e n n u m b e r i n t h e t r a n s i t i o n r e g i m e , w h i l e C r d e p e n d s o n t h e r a t e o f i n e r t i a l d e p o s i t i o n . T h e e x i s t e n c e o f t h e two e f f e c t s may b e c o n f i r m e d i f t h e e x p e r i m e n t a l v a l u e s f o r r e m o v a l e f f i c i e n c y i n a d a t a s e t c a n b e s a t i s f a c t o r i l y c o r r e l a t e d u s i n g t h e e q u a t i o n . T h e t e s t s w e r e made u s i n g a s t e p w i s e m u l t i p l e r e g r e s s i o n t e c h n i q u e , a s d e s c r i b e d i n A p p e n d i x E . T h e r e s u l t s o f t h e t e s t s f o r t r a n s i t i o n b e h a v i o u r w e r e i n c o n c l u s i v e , e v e n f o r t h e g r o u p e d d a t a . T h i s was a t t r i b u t e d t o t h e i n f l u e n c e s o f r a n d o m s c a t t e r i n t h e d a t a a n d o f s y s t e m a t i c e r r o r s . I t d o e s n o t i m p l y , h o w e v e r , t h a t t h e e f f e c t d i d n o t e x i s t , b u t o n l y t h a t t h e d a t a w e r e n o t a c c u r a t e e n o u g h t o e s t a -b l i s h w i t h c o n f i d e n c e i t s p r e s e n c e . F o r t h e same r e a s o n s , t h e i n f l u e n c e o f i n e r t i a l d e p o s i t i o n was a l s o u n c l e a r , b u t i t c a n b e c o n c l u d e d t h a t i t h a d a v e r y s m a l l i n f l u e n c e , b e i n g r e s p o n s i b l e f o r a l o s s o f much l e s s t h a n 1% f o r 1 ym p a r t i c l e s u n d e r t y p i c a l c o n d i t i o n s . 6.5 D e t a i l e d A n a l y s i s 6.5.1 H e l i u m - A m m o n i a T h e r e s u l t s f o r 0.79 ym p a r t i c l e s ( F i g u r e 6.1) show m o d e r a t e a g r e e m e n t w i t h S c h m i t t a n d W a l d m a n n f s t h e o r y . T h e mean K n u d s e n n u m b e r f o r t h e d a t a was 0.24, w h i c h i s c o n s i d e r a b l y h i g h e r t h a n f o r a n y o t h e r s y s t e m , a n d r e f l e c t s t h e l a r g e mean f r e e p a t h o f h e l i u m m o l e c u l e s . I t i s t h e r e f o r e v e r y p r o b a b l e t h a t t h e p a r t i c l e b e h a v i o u r f e l l w e l l i n t o t h e t r a n s i t i o n r e g i m e . T h e w i d e r a n g e o f m o l e c u l a r w e i g h t s a l l o w e d g o o d r e s o l u t i o n b e t w e e n t h e m o d e l s , b u t a t t h e same t i m e t e n d e d t o g i v e a l a r g e r c o u n t e r c a l i b r a t i o n e r r o r . F o r m o s t g a s m i x t u r e s t h e f l o w r a t e o f t h e i n e r t g a s was s e t t o g i v e t u r b u l e n c e w i t h r e s p e c t t o t h e d r y c o l u m n , a n d t h e f l o w r a t e o f t h e t r a n s f e r r e d g a s was v a r i e d . H o w e v e r , f o r h e l i u m t h i s was e c o n o m i c a l l y p r o h i b i t i v e , s o i n s t e a d t h e a m m o n i a f l o w r a t e was h e l d c o n s t a n t a n d t h e h e l i u m f l o w r a t e v a r i e d . T h e r e s u l t was t h a t t h e o u t l e t R e y n o l d s n u m b e r f e l l b e l o w 2000 i n m o s t r u n s , a n d i n t h e w o r s t c a s e w e n t a s l o w a s 320. W h i l e t h i s was u n d e s i r a b l e i n a s t u d y s p e c i f i c a l l y a i m e d a t t u r b u l e n t c o n d i t i o n s , t h e r e s u l t s i n d i c a t e t h a t t h e t r a n s i t i o n f l o w i s n o t i n f l u e n c i n g t h e t r e n d o f d a t a . T h i s was p r e d i c t e d b y t h e g e n e r a l t h e o r y d e r i v e d i n C h a p t e r 4 , w h i c h s h o w e d t h a t p a r t i c l e r e m o v a l i s i n d e p e n d e n t o f f l o w c o n d i t i o n s . 6 . 5 . 2 M e t h a n e - A m m o n i a T h e s i g n i f i c a n t f e a t u r e o f t h i s m i x t u r e i s t h e v e r y s m a l l r a t i o o f m o l e c u l a r w e i g h t s , 1 6 . 0 4 / 1 7 . 0 3 . T h i s means r e s o l u t i o n b e t w e e n t h e m o d e l s i s p o o r . A t t h e same t i m e no c a l i b r a t i o n c o r r e c t i o n was r e q u i r e d , a n d t h e c a l i b r a t i o n e r r o r was e s t i m a t e d t o b e s m a l l . T h e e x c e l l e n t a g r e e m e n t b e t w e e n t h e d a t a a n d t h e m o d e l s ( s e e F i g u r e 6 . 2 ) i n d i c a t e s t h a t t h e e x p e r i -m e n t a l t e c h n i q u e was s a t i s f a c t o r y , a n d t h a t t h e g e n e r a l t h e o r y g i v e n i n C h a p t e r 4 i s s u b s t a n t i a l l y c o r r e c t i n t h e s p e c i a l c a s e o f s i m i l a r m o l e c u l a r w e i g h t s . 6 . 5 . 3 N i t r o g e n - A m m o n i a , P r e l i m i n a r y D a t a T h e s e r e s u l t s f o r 0 . 7 9 ym p a r t i c l e s w e r e o b t a i n e d v e r y e a r l y d u r i n g t h e e x p e r i m e n t a l w o r k , a f t e r w h i c h t i m e s e v e r a l i m p r o v e m e n t s w e r e made i n t h e e q u i p m e n t a n d t e c h n i q u e . A l t h o u g h t h e r e i s a s m a l l o f f s e t b e t w e e n t h e s e a n d l a t e r d a t a , i t i s n o t s i g n i f i c a n t i n t e r m s o f t h e p o s s i b l e e x p e r i m e n t a l e r r o r s . 6 . 5 . 4 N i t r o g e n - A m m o n i a , S h o r t C o l u m n D a t a S i n c e t h e e x p e r i m e n t a l a p p a r a t u s was c o n s t r u c t e d b e f o r e t h e t h e o r y was d e r i v e d , a s h o r t c o l u m n was i n c l u d e d s o t h a t e n d e f f e c t s c o u l d b e s u b t r a c t e d o u t i f n e c e s s a r y . T h e t h e o r y i n d i -c a t e d , h o w e v e r , t h a t e n d e f f e c t s w e r e n o t r e l e v a n t , a n d a n e x p l o r a t o r y s e t o f d a t a t a k e n u s i n g 0 . 7 9 ym p a r t i c l e s i n t h e s h o r t c o l u m n c o n f i r m e d t h i s a f t e r c o m p a r i s o n w i t h t h e r e g u l a r c o l u m n d a t a ( s e e F i g u r e 6 . 3 ) . 6 . 5 . 5 N i t r o g e n - T A i r t m o n i a T h e r e was a t e n d e n c y f o r t h e d a t a t o move down t o w a r d s t h e mean m a s s v e l o c i t y m o d e l p r e d i c t i o n a s t h e p a r t i c l e s i z e i n c r e a s e d f r o m 0 . 5 t o 1 . 0 1 1 ym, a s s h o w n i n f i g u r e s 6 . 4 t o 6 . 9 . ( T h e 2 . 0 2 ym p a r t i c l e s show a r e v e r s e i n t h i s t r e n d , w h i c h i s , h o w e v e r > s m a l l i n r e l a t i o n t o p o s s i b l e e r r o r s . ) T h i s p r o v i d e s g o o d e v i d e n c e t h a t t h e p a r t i c l e s f e l l i n t o t h e t r a n s i t i o n r e g i m e , e v e n t h o u g h s t a t i s t i c a l t e s t s w e r e i n c o n c l u s i v e . T h e m o s t c o m p r e h e n s i v e s e r i e s o f r u n s i n t h e w h o l e s t u d y was made w i t h t h i s g a s m i x t u r e , u s i n g 0 . 7 9 ym p a r t i c l e s . T h e t h r e e d i f f e r e n t s e t s o f d a t a t a k e n w i t h c o n s t a n t f l o w r a t e t o t h e c o l u m n o f t h e i n e r t g a s , o f t h e t r a n s f e r r e d g a s , a n d w i t h c o n s t a n t i n l e t g a s c o m p o s i t i o n ( F i g u r e s 6 . 5 t o 6 . 7 ) e n a b l e d a w i d e r a n g e o f e x p e r i m e n t a l c o n d i t i o n s t o b e i n v e s t i g a t e d . T h e y a l s o m i n i m i z e d t h e p o s s i b i l i t y o f i m p o r t a n t v a r i a b l e s o r e f f e c t s b e i n g o v e r l o o k e d b e c a u s e o f t h e i r s t r o n g c o r r e l a t i o n w i t h o t h e r p a r a m e t e r s . I n d i v i d u a l a n a l y s i s f o r t h e t h r e e s e t s o f d a t a s h o w e d 1 2 5 . t h a t t h e y w e r e s t a t i s t i c a l l y i n d i s t i n g u i s h a b l e f r o m e a c h o t h e r i n b o t h t h e i r p o s i t i o n a n d t r e n d w i t h r e s p e c t t o t h e mean m a s s v e l o c i t y m o d e l . 6 . 5 . 6 A r g o n - A m m o n i a T h e b e h a v i o u r o f t h i s g a s m i x t u r e w i t h 0 . 7 9 ym p a r t i c l e s was e x p c t e d t o b e v e r y s i m i l a r t o t h a t o f n i t r o g e n - a m m o n i a , s i n c e t h e p h y s i c a l p r o p e r t i e s o f t h e two a r e s o s i m i l a r . T h i s was c o n f i r m e d b y e x p e r i m e n t ( s e e F i g u r e 6 . 1 0 ) . 6 . 5 . 7 F r e o n 1 2 - A m m o n i a T h e d a t a f o r t h i s g a s m i x t u r e a r e d i f f i c u l t t o e x p l a i n ( F i g u r e s 6 . 1 1 t o 6 . 1 3 ) . A l t h o u g h t h e p o s s i b l e e x p e r i m e n t a l e r r o r i s q u i t e l a r g e , i t i s s t i l l s u r p r i s i n g t h a t t h e d a t a t e n d t o a g r e e w i t h S c h m i t t a n d W a l d m a n n ' s t h e o r y f o r a l l p a r t i c l e s i z e s , s i n c e t h e K n u d s e n n u m b e r s a r e c o m p a r a t i v e l y s m a l l . F o r e x a m p l e , t h e mean K n u d s e n n u m b e r f o r t h e 1 . 0 1 1 ym p a r t i c l e d a t a i s 0 . 0 4 . T h i s d o e s n o t , h o w e v e r , d i s p r o v e t h e c o n t e n t i o n t h a t t h e mean m a s s v e l o c i t y m o d e l i s a p p r o p r i a t e f o r l a r g e p a r t i c l e s , s i n c e t h e r e i s s i g n i f i c a n t p o s s i b l e e r r o r , a n d s i n c e t r a n s i t i o n b e h a v i o u r may s t i l l p e r s i s t . T h e f r e o n 12 m o l e c u l e i s r e l a t i v e l y l a r g e a n d c o m p l e x c o m p a r e d t o t h a t o f a m m o n i a . I t i s t h e r e f o r e p o s s i b l e t h a t i t s i n t e r a c t i o n w i t h t h e p a r t i c l e s u r f a c e i s s o m e w h a t d i f f e r e n t . T h i s c o u l d l e a d t o m o r e p e r s i s t e n t t r a n s i t i o n r e g i m e b e h a v i o u r 126. t h a n t h a t s h o w n b y n u r t u r e s o f s i m i l a r m o l e c u l e s . I n p a r t i c u l a r , the onset o f t r a n s i t i o n m i g h t b e m o r e r a p i d w i t h i n c r e a s i n g K n u d s e n n u m b e r . T h e e x p e r i m e n t a l p r o b l e m s e n c o u n t e r e d w i t h t h e f r e o n 12-a m m o n i a s y s t e m w e r e m o r e s e v e r e t h a n i n a n y o t h e r c a s e . B e c a u s e o f t h e h i g h m o l e c u l a r w e i g h t o f f r e o n 12, v e r y l a r g e q u a n t i t i e s o f a m m o n i a h a d t o b e t r a n s f e r r e d t o o b t a i n s a t i s f a c t o r y p a r t i c l e r e m o v a l . T h i s c r e a t e d t h e p o t e n t i a l p r o b l e m o f m i s t f o r m a t i o n o u t l i n e d i n S e c t i o n 6.3. A l s o t h e g a s a n a l y s e s a t t h e t o p o f t h e c o l u m n g a v e v e r y h i g h f r e o n 12 c o n c e n t r a t i o n s , w h i c h w e r e d i f f i -c u l t t o a n a l y s e a c c u r a t e l y . F u r t h e r m o r e , t h e p a r t i c l e c o u n t e r was f o u n d t o b e c o m e m o r e u n r e l i a b l e a s t h e r a t i o o f m o l e c u l a r w e i g h t s o f t h e c o m p o n e n t g a s e s i n c r e a s e d . T h e r a t i o o f 120.9 3/ 17.0 3 f o r t h i s s y s t e m was t h e l a r g e s t e n c o u n t e r e d . T h e r e i s t h e r e f o r e a p o s s i b i l i t y t h a t t h e e r r o r s s h o w n i n T a b l e I V may b e a n u n d e r - e s t i m a t e i n t h e c a s e o f t h i s m i x t u r e . 6.5.8 N i t r o g e n - T r i m e t h y l a m i n e T h i s g a s m i x t u r e was c h o s e n t o t e s t t h e t h e o r y f o r a t r a n s f e r r e d g a s o t h e r t h a n a m m o n i a . T h e h i g h m o l e c u l a r w e i g h t f o r t r i m e t h y l a m i n e o f 59.11 was a l s o u s e f u l i n i m p r o v i n g t h e r e s o l u t i o n b e t w e e n t h e m o d e l s . T h e d a t a show n o o b v i o u s t r e n d w i t h p a r t i c l e s i z e ( s e e F i g u r e s 6.14 t o 6.18). T h e r u n s f o r 5.7 ym p a r t i c l e s w e r e s t r e t c h i n g t h e c a p a b i l i t i e s o f t h e e x p e r i -m e n t a l s y s t e m , a n d t h e s c a t t e r w i t h t h e m i s s e v e r e . A c c o r d i n g t o t h e s t a t i s t i c a l a n a l y s i s g i v e n i n T a b l e V , t h e o f f s e t o f 5.7 ym d a t a f r o m t h e mean m a s s v e l o c i t y m o d e l i s v e r y s m a l l , a n d s t a t i s -1 2 7 . t i c a l l y n o t s i g n i f i c a n t . H o w e v e r , a l t h o u g h t h e K n u d s e n n u m b e r i s s m a l l , c o n s i d e r i n g t h e s c a t t e r a n d t h e l i m i t e d n u m b e r o f d a t a p o i n t s , t h i s c a n n o t b e i n t e r p r e t e d a s a v a l i d a t i o n o f t h e mean m a s s v e l o c i t y t h e o r y . 6 . 6 F u r t h e r D i s c u s s i o n I t i s r e a s o n a b l e t o c o n c l u d e t h a t t h e g e n e r a l p a r t i c l e d e p o s i t i o n m o d e l p r e s e n t e d i n C h a p t e r 4 i s i n d e e d s a t i s f a c t o r y , a n d f u r t h e r m o r e , t h a t i n e r t i a l d e p o s i t i o n was a s m a l l o r i n s i g n i -f i c a n t e f f e c t i n t h e p r e s e n t e x p e r i m e n t a l s t u d y . I t s e e m s v e r y p r o b a b l e t h a t t h e t e n d e n c y o f d a t a t o b e o f f s e t f r o m t h e mean m a s s v e l o c i t y m o d e l i s d u e a t l e a s t i n p a r t t o t r a n s i t i o n b e h a v i o u r . H o w e v e r , d e f i n i t i v e p r o o f o f t h i s h y p o t h e s i s u s i n g s t a t i s t i c a l m e t h o d s was n o t p o s s i b l e . T h i s was p r e s u m e d t o b e p r i m a r i l y d u e t o t h e c o n f o u n d i n g i n f l u e n c e o f s m a l l s y s t e m a t i c e x p e r i m e n t a l e r r o r s i n t h e d a t a . T h e e x p e r i m e n t s o f o t h e r w o r k e r s may e l u c i d a t e t h e s i t u a t i o n b y i n d i c a t i n g t h e e x t e n t o f t h e t r a n s i t i o n r e g i m e , a n d t h u s s h o w i n g w h e t h e r t r a n s i t i o n b e h a v i o u r s h o u l d b e e x p e c t e d . S t o r o z h i l o v a (1964) was a b l e t o e x a m i n e p a r t i c l e b e h a v i o u r o v e r a c o n t i n u o u s r a n g e o f K n u d s e n n u m b e r s b y a l t e r i n g t h e g a s p r e s s u r e i n t h e e x p e r i m e n t a l u n i t . T h e d a t a a p p e a r t o show a r a p i d t r a n s i t i o n f r o m s m a l l p a r t i c l e b e h a v i o u r t o l a r g e p a r t i c l e b e h a v i o u r o v e r a K n u d s e n n u m b e r r a n g e o f a p p r o x i m a t e l y 1 t o 0 . 5 . T h e r e a r e t h r e e d i f f i c u l t i e s i n a c c e p t i n g t h i s c o n c l u s i o n . I n t u i t i v e l y i t s e e m s u n l i k e l y t h a t c o n t i n u u m c o n d i t i o n s c o u l d b e 128. e s t a b l i s h e d f o r a Knudsen number of 0.5. A l s o t h e l o w e s t Knudsen number f o r w h i c h d a t a are p r e s e n t e d i s a p p r o x i m a t e l y 0.3,so t h e t r u e e s t a b l i s h m e n t o f l a r g e p a r t i c l e b e h a v i o u r i s s t i l l i n doubt. L a s t l y , the d a t a i n the Knudsen number range o f 0.3 t o 0.5 a r e shown t o c o r r e l a t e w i t h t h e f l u i d mean molar v e l o c i t y . However, t h e t h e o r y p r e d i c t i n g t h i s v e l o c i t y was s u b s t a n t i a l l y c r i t i c i s e d i n Chapter 2 , a n d i t i s n ot i n agreement w i t h the p r e s e n t e x p e r i -m e n t a l r e s u l t s . F o r t h e s e r e a s o n s S t o r o z h i l o v a ' s d a t a cannot be r e g a r d e d as d e t e r m i n i n g the e x t e n t o f t h e t r a n s i t i o n regime. The e a r l i e r e x p e r i m e n t a l work o f S c h m i t t and Waldmann (1960) was c r i t i c a l l y r e v i e w e d i n Chapter 2. However, w h i l e t h e i r measurements o f a b s o l u t e p a r t i c l e v e l o c i t i e s may not be r e l i a b l e , the d a t a , which c o v e r a c o n t i n u o u s Knudsen number range, c o u l d i n d i c a t e t h e e x t e n t o f t h e t r a n s i t i o n regime. The a u t h o r s have f i t t e d c u r v e s t o t h i s d a t a w h i c h i m p l y t h a t l a r g e p a r t i c l e b e h a v i o u r i s e s t a b l i s h e d a t a Knudsen number of a p p r o x i m a t e l y 0.2. However, i n many ca s e s t h e d a t a d i v e r g e from t h e s e c u r v e s as t h e Knudsen number f a l l s t o 0.1, w h i c h was t h e l i m i t o f t h e i r e x p e r i -ments. The l i m i t i n g Knudsen number f o r the t r a n s i t i o n regime i s t h e r e f o r e a g a i n u n c l e a r , b u t i s p r o b a b l y lower t h a n 0.2, a f i g u r e t h a t seems more r e a l i s t i c t h a n t h a t s u g g e s t e d by S t o r o z h i l o -v a 1 s d a t a . Data on t h e r m o p h o r e s i s are a v a i l a b l e t h a t c o v e r a much w i d e r Knudsen number range. F o r example Waldmann and S c h m i t t (1966) quote e x p e r i m e n t s w i t h Knudsen numbers r a n g i n g from 0.05 t o 5. S i n c e d i f f u s i o - and t h e r m o p h o r e s i s are r e l a t e d phenomena, the t r a n s i t i o n r e g i o n might be e x p e c t e d t o c o v e r a s i m i l a r range 129 . f o r b o t h c a s e s . T h e d a t a show t h a t t r a n s i t i o n s t a r t s a t a K n u d s e n n u m b e r o f a b o u t 5 , e x t e n d s b e l o w 0 . 1 , a n d may n o t b e c o m p l e t e e v e n a t 0 . 0 5 . T h i s w o u l d i m p l y t h a t a l m o s t a l l t h e d a t a i n t h i s w o r k s h o u l d show some t r a n s i t i o n b e h a v i o u r . I n t h e c a s e o f t h e r m o p h o r e s i s t h e t r a n s i t i o n b e t w e e n r e g i m e s c a n b e d e s c r i b e d b y a s m o o t h c u r v e . S u c h s i m p l e b e h a v i o u r may n o t b e e x h i b i t e d i n d i f f u s i o p h o r e t i c s y s t e m s . A l t h o u g h t h e p r o c e d u r e u s e d t o c a l c u l a t e t h e mean f r e e p a t h i n t h i s w o r k was a d e q u a t e f o r t h e p u r p o s e , i t i s s o m e w h a t s i m p l i s t i c . I n f a c t e a c h m o l e c u l a r s p e c i e s h a s i t s own mean f r e e p a t h w h i c h i s a f u n c t i o n o f t h e m o l e f r a c t i o n s , m o l e c u l a r w e i g h t s , a n d c o l l i s i o n d i a m e t e r s o f b o t h m o l e c u l a r s p e c i e s ( s e e f o r e x a m p l e C h a p m a n a n d C o w l i n g ( 1 9 6 4 ) ) . I t t h e r e f o r e i s p l a u s i b l e t h a t t h e o n s e t o f t r a n s i t i o n f o r t h e d i f f e r e n t g a s s p e c i e s c a n o c c u r a t d i f f e r e n t c o n d i t i o n s . I f t h i s i s s o , t h e p a r t i c l e b e h a v i o u r i n t h e t r a n s i -t i o n r e g i m e may b e q u i t e c o m p l e x , a n d n o t r e p r e s e n t a b l e b y s u c h a s i m p l e c u r v e a s i n t h e c a s e o f t h e r m o p h o r e s i s . A f u r t h e r f a c t o r w h i c h may c o m p l i c a t e t r a n s i t i o n b e h a v i o u r i s t h e d i f f e r e n t i n t e r a c t i o n c h a r a c t e r i s t i c s o f t h e m o l e c u l a r s p e c i e s w i t h t h e p a r t i c l e s u r f a c e , d i s c u s s e d i n S e c t i o n 6 . 5 . T h e i n v e s t i g a t i o n o f t h e s e p o s s i b i l i t i e s f e l l o u t s i d e t h e s c o p e o f p r e s e n t e x p e r i m e n t s . H o w e v e r , t h e y may h a v e b e e n a d d i t i o n a l f a c t o r s i n c o n f u s i n g t h e s e a r c h f o r d e f i n i t e p r o o f o f t r a n s i t i o n b e h a v i o u r . I t i s a l s o p o s s i b l e t h a t t h e y h a v e m i s l e a d other w o r k e r s a s t o t h e e x t e n t o f t h e t r a n s i t i o n r e g i m e . I t i s c o n c l u d e d t h a t i n m o s t o f t h e r u n s i t i s h i g h l y 130. probable that the particles exhibited some transition behaviour, and that this factor i s in part responsible for the variation in data position for different systems and particle sizes. In addition, there i s some indication that large particles do travel at, or close to the local mean mass velocity of the f l u i d , as predicted in Chapter 3. The data certainly do not support the contention that these particles travel at the mean molar velocity. 1 .0 0.8 - 0 . 6 cr > s: LU ce LU _j 0 . 4 -cr. cr 0.2 0 . 0 L 0.0 THEORETICAL MODEL: MEAN MASS MEAN MOLAR SCHMITT I WALDM. 0.2 0.4 0.6 0.8 1.0 MOLE FRACTION OF INERT AT INLET F i g u r e 6.1 R e s u l t s f o r h e l i u m , ammonia, 0.79 m i c r o n d i a m e t e r p a r t i c l e s . I n l e t f l o w r a t e o f t r a n s f e r r e d gas h e l d c o n s t a n t , a t 6.0 x 10 m 3/sec. 132, 0.6, 0 . 5 o . 4 _ o UJ I—I CJ I—I b_ Lx_ UJ g O . 3 O 31 LU LY LU _J CJ LY CT. CL. : o . 2 0 . 1 o . o l 0 . 0 THEORETICAL MODEL: MEAN MASS MEAN MOLAR SCHMITT & WALDM. -0 .2 0 . 4 0.6 0 .8 MOLE FRACTION OF INERT AT INLET F i g u r e 6.2 R e s u l t s f o r methane, ammonia, 0.79 m i c r o n d i a m e t e r p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d c o n s t a n t a t 5.9 8 x I O - 4 m3/sec. 0.6, 0.5 LU »—i CJ Lt_ U_ LU ? 0 . 3 | o n LU or LU o CE Q_ -0 .2 0 . 1 0.0L_ 0.0 THEORETICAL MODEL: MERN MRSS -MERN M0LRR -SCHMITT I WRLDM. -0.2 0 . 4 0.6 0.8 l.C MOLE FRRCTI0N OP INERT RT INLET F i g u r e 6.3 R e s u l t s f o r n i t r o g e n , ammonia, 0.79 mi c r o n d i a m e t e r p a r t i c l e s - s h o r t column. Flow r a t e o f i n e r t gas h e l d c o n s t a n t a t 6.0 x 1 0 ~ 4 m 3/sec. 0.6, 0.5 0 . 4 -LxJ •—4 C J i — t L u U_ LU 50.31 o 2Z LU OL LU _ J OZ CX ft.2 0.1 0.0 1 THEQRETICRL MODEL'. MERN MR55 MERN MOLRR SCHMITT Ic VRLDM. -0.0 0.2 0.4 0.6 0.8 MOLE FRRCTI0N OF INERT RT INLET F i g u r e 6.4 R e s u l t s f o r n i t r o g e n , ammonia, 0.50 m i c r o n d i a m e t e r p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d c o n s t a n t a t 6.0 x I O - 4 m 3/sec. 135. MOLE FRACTION OF INERT AT INLET F i g u r e 6.5 R e s u l t s f o r n i t r o g e n , ammonia, 0.79 m i c r o n d i a m e t e r p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d c o n s t a n t .-a t 6.0 x 1 0 - 4 m 3/sec. 136. THEORETICAL MODEL: MEAN MASS MOLE FRACTION OF INERT AT INLET F i g u r e 6.6 R e s u l t s f o r n i t r o g e n , ammonia, 0.79 m i c r o n d i a m e t e r p a r t i c l e s . I n l e t f l o w r a t e o f t r a n s f e r r e d gas h e l d c o n s t a n t a t 11.6 x I O - 4 m3/sec. 0.6, 0.5 cr a. 0.1 0.0 THEORETICAL MODEL MEAN MASS MEAN MOLAR SCHMITT & WALDM. • 0.0 0.3 0.6 0.9 1.2 INERT FLOW RATE. M 3/SEC X 1 0 3 F i g u r e 6.7 R e s u l t s f o r n i t r o g e n , ammonia, 0.79 m i c r o n d i a m e t e r p a r t i c l e s . I n l e t gas c o m p o s i t i o n h e l d c o n s t a n t a t 50 v% n i t r o g e n . 0.6. 0.5 0.4L o U J •—i c_) i—i u_ u_ LU g O . 3 O 51 U J CH U J _ J : o . 2 L cr <X Q_ 0.1 0.0 THEORETICRL MODEL: MERN MR55 — MERN MOLRR — SCHMITT & WRLDM. 0.0 0.2 0.4 0.6 0.8 MOLE FRACTION OF INERT RT INLET F i g u r e 6.8 R e s u l t s f o r n i t r o g e n , ammonia, 1.011 m i c r o n d i a m e t e r p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d c o n s t a n t a t 6.0 x 10~4 m 3/sec. 139. MOLE FRACTION OF INERT AT INLET F i g u r e 6.9 R e s u l t s f o r n i t r o g e n , ammonia, 2.0 2 m i c r o n d i a m e t e r p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d c o n s t a n t a t 6.0 x 1 0 ~ 4 m3/sec. 0 . 6 0 . 5 ! >— o LU • — i CJ 0 . 4 -LU ^ 0 . 3 O LU QU LU _J CJ CE : o . 2 O . l L 0 . 0 \ T H E O R E T I C A L M O D E L : MEAN MASS MEAN MOLAR S C H M I T T I WALDM. 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 MOLE F R A C T I O N OF I N E R T AT I N L E T F i g u r e 6.10 R e s u l t s f o r a r g o n , ammonia, 0.79 m i c r o n d i a m e t e r p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d c o n s t a n t a t 5.6 x 1 0 ~ 4 m 3/sec. 8 0 T H E O R E T I C A L MODEL: MEAN MASS MEAN MOLAR S C H M I T T I WALDM. 4l 0 0 . 2 0 . 4 0 . 6 0 . 8 1 MOLE F R A C T I O N OF I N E R T AT I N L E T F i g u r e 6.11 R e s u l t s f o r f r e o n 12 ( C F 2 C I 2 ) , ammonia 0.79 m i c r o n d i a m e t e r p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d c o n s t a n t ; . a t . 0.98 x 1 0 ~ 4 m 3/sec. 142. 1 . 0 0 . 8 LJ LU »—i CJ 0 . 6 LU CE O LU cr UjO.4 _J CJ cr. cr a. 0 . 2 0 . 0 L 0 . 0 T H E O R E T I C R L MODEL: MERN MASS MEAN MOLAR S C H M I T T I WALDM. 0 . 2 0 . 4 0 . 6 0 . 8 1 MOLE F R A C T I O N OF INERT AT I N L E T F i g u r e 6.12 R e s u l t s f o r f r e o n 12 ( C F 2 C l 2 ) / ammonia, 1.011 m i c r o n d i a m e t e r p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d c o n s t a n t a t 0.98 x I O - 4 m 3/sec. 143, 1 .0 0.8 21 LU go. 6! LU CE cr LU0.41 _j CE 0.2 THEORETICAL MODEL: 0.01 0.0 \ \ \* \ MEAN MASS MEAN MOLAR SCHMITT & WALDM. 0.2 , 0 . 4 0.G 0.8 1.0 MOLE FRACTION OF INERT AT INLET F i g u r e 6.13 R e s u l t s f o r f r e o n 12 (CF 2 C I 2 ) , ammonia, 2.02 micron diameter p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d constant a t 0.98 x 10~ 4 m 3/sec. 144. MOLE F R R C T I O N OF I N E R T AT I N L E T F i g u r e 6.14 R e s u l t s f o r n i t r o g e n , t r i m e t h y l a m i n e (N(CH 3) 3 ) , 0 .50 m i c r o n d i a m e t e r p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d c o n s t a n t a t 6.0 x 1 0 - 4 m / s e c . MOLE F R A C T I O N OF INERT AT I N L E T F i g u r e 6.15 R e s u l t s f o r n i t r o g e n , t r i m e t h y l a m i n e (N(CH3)3), 0.79 m i c r o n d i a m e t e r p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d c o n s t a n t a t 6.0 x 10 ~ 4 m 3/sec. 146 . F i g u r e 6 . 1 6 R e s u l t s f o r n i t r o g e n , t r i m e t h y l a m i n e ( N ( C H 3 ) 3 ) , 1 . 0 1 1 m i c r o n d i a m e t e r p a r t i c l e s . F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t r a t 6 . 0 x 1 0 - 4 m 3 / s e c . 14 7. MOLE F R A C T I O N OF I N E R T AT I N L E T F i g u r e 6.17 R e s u l t s f o r n i t r o g e n , t r i m e t h y l a m i n e (N(CH 3)3),2.02 m i c r o n d i a m e t e r p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d c o n s t a n t a t 6.0 x 1 0 - 4 m 3/sec. 14 8. MOLE F R A C T I O N OF I N E R T FIT I N L E T F i g u r e 6.18 R e s u l t s f o r n i t r o g e n , t r i m e t h y l a m i n e (N(CH3)3), 5.7 m i c r o n d i a m e t e r p a r t i c l e s . Flow r a t e o f i n e r t gas h e l d c o n s t a n t a t 6.0 x I O " 4 m / s e c . 149 . Chapter 7 PRACTICAL APPLICATION 7.1 G e n e r a l I t has been e s t a b l i s h e d i n t h i s s t u d y t h a t d i f f u s i o -p h o r e s i s can be an e f f e c t i v e method f o r removing m i c r o n - s i z e d p a r t i c l e s from t u r b u l e n t gas streams. However, i t s p o t e n t i a l f o r p r a c t i c a l a p p l i c a t i o n depends on i t s c o s t r e l a t i v e t o o t h e r gas c l e a n i n g methods. Only t h e p r i m a r y c o s t s o f h e a t f o r vapour g e n e r a t i o n and c o o l i n g w a t e r f o r vapour c o n d e n s a t i o n a re c o n s i -d e red i n the p r e l i m i n a r y assessment w h i c h f o l l o w s . These can be e s t i m a t e d from the l a t e n t h e a t o f v a p o r i z a t i o n and r a t e o f vapour usage. The p o s s i b i l i t y o f u s i n g d i f f u s i o p h o r e s i s t o enhance and/or supplement p a r t i c l e removal by a n o t h e r mechanism i s a l s o d i s c u s s e d . However, no economic assessment i s p o s s i b l e i n t h i s case w i t h o u t s p e c i f i c knowledge o f t h e a c t u a l a p p l i c a t i o n , and a b e t t e r u n d e r s t a n d i n g o f t h e importance o f i n t e r a c t i v e e f f e c t s between mechanisms. 150 . 7.2 I n v e s t i g a t i o n s by Others A l t h o u g h t h e r e i s no c l e a r d i v i d i n g l i n e , some r e s e a r c h has been o r i e n t e d more towards d e v e l o p i n g p r a c t i c a l methods f o r p a r t i c l e r e m o v a l , t h a n towards v e r i f y i n g fundamental t h e o r y or d e m o n s t r a t i n g the gas c l e a n i n g a b i l i t y o f d i f f u s i o p h o r e s i s under s i m p l e c o n d i t i o n s . O f t e n i n t h e s e p r a c t i c a l s t u d i e s , d i f f u s i o -p h o r e s i s i s o n l y one o f a number o f removal mechanisms o p e r a t i n g . The b r i e f summary o f p r e v i o u s s t u d i e s g i v e n i n T a b l e VI i s n o t i n t e n d e d t o be comprehensive, b u t r a t h e r t o i n d i c a t e the t ype o f work t h a t has been done by o t h e r s . I t i s a p p a r e n t from t h e s e s t u d i e s t h a t t h e i n f l u e n c e o f d i f f u s i o p h o r e s i s was n o t w e l l u n d e r s t o o d i n many i n s t a n c e s . Some wo r k e r s never mentioned i t , o r gave i t o n l y c u r s o r y a t t e n t i o n . O t h e r s r e a c h e d c o n f l i c t i n g c o n c l u s i o n s about i t s i m p o r t a n c e , even when e x p e r i m e n t i n g w i t h s i m i l a r equipment. T h i s u n c e r t a i n t y i s n o t s u r p r i s i n g c o n s i d e r i n g the v a r i e t y of mechanisms by w h i c h vapour c o n d e n s a t i o n from a d u s t y gas may i n f l u e n c e p a r t i c l e r e m o v a l . 7.3 O p t i m a l Vapour Use P a r t i c l e s w i l l be removed from a m i x t u r e o f a vapour and an i n e r t gas, when the vapour i s t r a n s f e r r e d o u t o f the gas phase. The p a r t i c l e removal e f f i c i e n c y o b t a i n e d can be i n c r e a s e d by i n c r e a s i n g t h e i n i t i a l vapour c o n c e n t r a t i o n i n the m i x t u r e . However, t h e improvement becomes l e s s w i t h each e x t r a u n i t o f TABLE VI Enhancement o f P a r t i c l e Capture by Vapour C o n d e n s a t i o n I n v e s t i g a t o r s D e s c r i p t i o n o f Study Vapour Used Major e f f e c t s A s s e s s e d importance o f d i f f u -s i o p h o r e s i s Fahnoe e t a l . (1951) Removal of s o l u b l e and i n s o l u b l e p a r t i c l e s w i t h a c y c l o n e and a wet s c r u b b e r . Steam and e t h y l e n e g l y c o l P a r t i c l e growth Not mentioned Schauer (1951) Removal o f d i o c t y l p t h a -l a t e smoke i n a wet s c r u b b e r . Steam P a r t i c l e growth Not mentioned L a p p l e and Kamak (1955) Dust removal i n a wet s c r u b b e r . Steam P a r t i c l e growth P r o b a b l y s i g n i f i c a n t Semrau e t a l . (1958) Treatment o f r e c o v e r y f u r n a c e fume u s i n g v a r i o u s t y p e s o f s c r u b b e r s . Steam P a r t i c l e growth, d i f f u s i o p h o r e s i s , and f o g forma-t i o n . S i g n i f i c a n t when s c r u b -b i n g w i t h c o l d w a t e r . Fuchs and K i r s c h (1965) A d s o r p t i o n and evapora-t i o n o f e t h e r from a packed bed o f s i l i c a g e l p a r t i c l e s . E t h e r D i f f u s i o p h o r e s i s Major e f f e c t '<• -c o n t i n u e d TABLE V l / c o n t i n u e d I n v e s t i g a t o r s D e s c r i p t i o n o f Study Vapour Used Major e f f e c t s A s s e s s e d importance o f d i f f u -s i o p h o r e s i s L i t v i n o v (1967) P a r t i c l e removal w i t h a v e n t u r i tube and s i e v e t r a y s c r u b b e r . Steam C o a g u l a t i o n Only impor-t a n t f o r s m a l l p a r -t i c l e s (<0 .1 um) Rozen and K o s t i n (1967) P a r t i c l e removal i n a column w i t h a l t e r n a t e e v a p o r a t i o n and con-d e n s a t i o n p l a t e s . Steam P a r t i c l e growth N e g l i g i b l e Sparks and P i l a t (1970) T h e o r e t i c a l study o f the i n f l u e n c e o f d i f f u -s i o p h o r e s i s on p a r t i c l e c o l l e c t i o n i n s c r u b b e r s . Steam Has a s i g -n i f i c a n t i n f l u e n c e on p a r t i c l e c a p t u r e by water drop-l e t s . T r u i t t and D a v i s (1971) P a r t i c l e removal i n a t u b u l a r condenser s c r u b b e r . Steam V a r i o u s e f f e c t s S i g n i f i c a n t c o n t i n u e d TABLE V I / c o n t i n u e d I n v e s t i g a t o r s D e s c r i p t i o n o f Study Vapour Used Major e f f e c t s A s s e s s e d i m p o r t a nce o f d i f f u -s i o p h o r e s i s L a n c a s t e r and S t a u s s (1971) P a r t i c l e removal i n s c r u b b e r s . Steam P a r t i c l e growth Not impor-t a n t C a l v e r t e t a l . (1973) Comprehensive e x p e r i -mental and t h e o r e t i c a l s t u d i e s on p a r t i c l e removal by s c r u b b i n g . Steam Can be s i g -n i f i c a n t , depending on c o n d i -t i o n s . P r a k a s h and Murray (1975) P a r t i c l e growth by i n j e c t i o n and con-d e n s a t i o n o f steam. Steam P a r t i c l e growth N e g l i g i b l e 154. vapour added, because the i n e r t gas i s d i l u t e d , and the p a r t i c l e c o n c e n t r a t i o n r e d u c e d . I t i s t h e r e f o r e p r e f e r a b l e t o add and remove s m a l l e r q u a n t i t i e s o f vapour i n s e v e r a l s e p a r a t e s t a g e s . The l i m i t i n g c a s e , which g i v e s t h e o p t i m a l r e s u l t , i s t o con-t i n u o u s l y add and remove vapour a l l a l o n g the i n e r t gas f l o w p a t h . T h i s c o u l d be a c h i e v e d , f o r example, when the i n e r t gas f l o w s between two p a r a l l e l p l a t e s . Steam i s d i f f u s e d i n t o the gas t h r o u g h one o f these p l a t e s and condensed o ut a t the o t h e r . a d d i t i o n under t u r b u l e n t c o n d i t i o n s i s s i m i l a r t o the case where a l l t he vapour i s added i n i t i a l l y (see Chapter 4 ) . U s i n g the same n o t a t i o n , a p a r t i c l e b a l a n c e over an e l e m e n t a l l e n g t h o f the c o l l e c t o r y i e l d s where a r e f e r s o n l y t o the c o l l e c t o r a r e a p e r u n i t l e n g t h . F o r developed c o n d i t i o n s , when the c r o s s f l o w o f vapour between i t s s o u r c e and s i n k i s f u l l y e s t a b l i s h e d , G i s c o n s t a n t and e q u a l t o G , /Y-, . Hence The d e r i v a t i o n o f the t h e o r y f o r c o n t i n u o u s vapour nv a dz P dn n a dz I n t h e remainder o f t h i s s e c t i o n i t i s assumed t h a t t h e p a r t i c l e s move w i t h t h e l o c a l mean mass v e l o c i t y o f the gas. S i m i l a r analyses can r e a d i l y be made f o r other cases. S u b s t i t u t i n g f o r v the e x p r e s s i o n f o r mean mass v e l o c i t y (Equation 3.68) and i n t e g r a t i n g g i v e s n o u t Y 1 M 2 N 2 7 . i n 1 where Z i s the c o l l e c t o r l e n g t h . I f 0,^ denotes the t o t a l molar c r o s s flow of the d i f f u s i n g component, then n i n ~ n o u t n , Y 1 M 2 G 2 , e = = 1 - exp { - - — - } . r i n 1 When the vapour c o n c e n t r a t i o n i s s m a l l , ( i . e . Y-j_ - 1 ) / the expo-nent i s equal to the mass o f vapour used per mass of i n e r t gas t r e a t e d . The importance of the method of vapour a d d i t i o n can be i l l u s t r a t e d by c a l c u l a t i n g the vapour requirements to achieve 95% p a r t i c l e removal. T h i s can be done f o r continuous vapour a d d i t i o n u s i n g the theory j u s t d e r i v e d , and f o r a stagewise process using the theory developed i n Chapter 4. For s i m p l i c i t y the vapour c o n c e n t r a t i o n i s assumed to be s m a l l i n the case of continuous vapour a d d i t i o n . In the stagewise process the vapour i s taken t o be d i v i d e d evenly between stages, and to be completely absorbed i n each stage. The r e s u l t s are summarized i n Table V I I . In c o n t r a s t to t h i s , one can show t h a t f o r laminar flow between p a r a l l e l p l a t e s whose l e n g t h i s much g r e a t e r than TABLE V I I Vapour Requirements t o A t t a i n 9 5% P a r t i c l e Removal T o t a l number mass o f vapour per stage t o t a l mass o f vapour used o f s t a g e s mass o f i n e r t gas t r e a t e d mass o f i n e r t gas t r e a t e d 1 19 19 2 3.5 6 .9 3 1.7 5 .1 4 1.1 4 .5 * i n f i n i t y - 3 .0 * T h i s i s e q u i v a l e n t t o c o n t i n u o u s vapour a d d i t i o n w i t h low vapour c o n c e n t r a t i o n . 157 the i n t e r - p l a t e s p a c i n g , the p a r t i c l e removal e f f i c i e n c y becomes 100% when t h e c r o s s f l o w of vapour between t h e p l a t e s i s g i v e n by G 2 = M G 1 / y 1 M 2 Thus, when the vapour c o n c e n t r a t i o n i s s m a l l ( i . e . y-^  = 1 ) / a l l p a r t i c l e s a r e removed u s i n g u n i t mass o f vapour per u n i t mass o f i n e r t g a s . Under t u r b u l e n t c o n d i t i o n s , t h e random n a t u r e o f the f l u i d m o t i o n p r e c l u d e s t h e p o s s i b i l i t y o f complete p a r t i c l e r e m o v a l . 7.4 O p e r a t i n g C o s t C a l c u l a t i o n F o r comparison w i t h o t h e r p a r t i c l e r emoval methods, t h e o p e r a t i n g c o s t s a r e now c a l c u l a t e d f o r t r e a t i n g p a r t i c l e -b e a r i n g a i r w i t h u n i t mass of steam per mass o f a i r . W i t h c o n t i n u o u s vapour a d d i t i o n a t low vapour c o n c e n t r a t i o n s t h i s w i l l remove 6 3% o f t h e p a r t i c l e s i f they adopt t h e mean mass v e l o c i t y o f t h e gas. The c o s t s f o r steam and c o o l i n g w a t e r are t a k e n as $2/1000 l b ($4 4/MKg) , and 2C/1000 US g a l (0.53«r/m 3), r e s p e c t i v e l y . Twenty pounds of c o o l i n g water are assumed t o be n e c e s s a r y f o r c o n d e n s i n g 1 pound of steam. The c o s t o f t r e a t i n g 1000 s c f o f a i r u s i n g 1 l b o f steam per pound o f a i r can t h e n be c a l c u l a t e d . 1 5 8 . s t e a m , 7 5 . 3 l b : 1 5 c e n t s c o o l i n g w a t e r , 1 5 0 6 l b : 0 . 3 6 c e n t s t o t a l c o s t : 1 5 . 4 c e n t s 3 ( T h i s i s e q u i v a l e n t t o 0 .54<r/ m a i r . ) T h e s e c o s t s a r e m o r e t h a n a n o r d e r o f m a g n i t u d e h i g h e r t h a n t h o s e f o r c o m m e r c i a l p a r t i c l e c o l l e c t o r s o p e r a t i n g w i t h s i m i l a r e f f i c i e n c i e s ( P e r r y ( 1 9 7 3 ) ) . 7 . 5 R e d u c t i o n o f H e a t R e q u i r e m e n t s T h e o p e r a t i n g c o s t s f o r p a r t i c l e r e m o v a l b y d i f f u s i o -p h o r e s i s a r e p r i m a r i l y a f u n c t i o n o f t h e c o s t o f v a p o u r g e n e r a t i o n . T h i s c a n b e r e d u c e d b y u s i n g a p r o c e s s t h a t a l l o w s some h e a t r e c o v e r y , o r b y u s i n g a v a p o u r w i t h a l o w e r l a t e n t h e a t t h a n w a t e r . H e a t r e c o v e r y c a n b e a c h i e v e d i n a m u l t i s t a g e s y s t e m , s u c h a s t h a t s h o w n i n F i g u r e 7 . 1 , w h e r e w a t e r v a p o u r i s u s e d w i t h l i t h i u m c h l o r i d e s o l u t i o n a s a b s o r b e n t . E a c h s t a g e c o n s i s t s o f a n e v a p o r a t i o n a n d a n a b s o r p t i o n s e c t i o n . I n t h e e v a p o r a t i v e s e c t i o n o f t h e f i r s t s t a g e , v a p o u r i s p r o d u c e d b y b r i n g i n g t h e i n l e t g a s i n t o c o n t a c t w i t h a l i q u i d w h i c h h a s b e e n h e a t e d b y a n e x t e r n a l s o u r c e . T h e g a s - v a p o u r m i x t u r e t h e n p a s s e s t o t h e a b s o r p t i o n s e c t i o n , w h e r e p a r t o f t h e v a p o u r i s r e m o v e d b y b e i n g b r o u g h t i n t o c o n t a c t w i t h t h e c o o l e d l i q u i d l e a v i n g t h e e v a p o r a -t o r . T h e g a s t h e n f l o w s i n t o t h e s e c o n d s t a g e , w h i c h o p e r a t e s i n a s i m i l a r m a n n e r , b u t a t a l o w e r t e m p e r a t u r e . T h e h e a t e x t r a c t e d f r o m t h e l i q u i d l e a v i n g t h e f i r s t s t a g e e v a p o r a t o r i s u s e d t o h e a t t h e l i q u i d f e d t o t h e s e c o n d s t a g e e v a p o r a t o r , t h u s r e m o v i n g 159 outlet g a s external — ^ cooling ^ £ water cycle (stage 3) low concentration LiCI cycle (stage 2) i n t e r s t a g e heat exchanger high concentration LiCI cycle (stage 1) stage 2 dilute stream \ - s t a g e 2 c o n c e n t r a t e d s t r e a m - o v e r f l o w from stage 2 absorber < ^ external < heat supply evaporator • inlet j g a s Figure 7.1 Gas treatment in a stagewise process. 160. the need f o r e x t e r n a l h e a t i n the second and subsequent s t a g e s . F i n a l l y , e x t e r n a l c o o l i n g i s used t o remove h e a t from the l i q u i d l e a v i n g the e v a p o r a t o r i n the l a s t s t a g e . The use o f water i s r e s t r i c t e d n o t o n l y by i t s h i g h l a t e n t h e a t o f v a p o r i z a t i o n , b u t a l s o because most p r a c t i c a l a b s o r p t i o n systems cannot reduce the w a t e r vapour c o n c e n t r a t i o n i n t h e gas t o low l e v e l s a t t e m p e r a t u r e s h i g h e r than about 100°C. T h i s f a c t reduces the number o f s t a g e s t h a t can be used w i t h h e a t r e c o v e r y . Many o r g a n i c l i q u i d s have much lower l a t e n t h e a t s t h a n w a t e r , some b e i n g l e s s t h a n 100 B t u / l b (233 J o u l e / g ) compared t o about 10 00 B t u / l b (2 330 J o u l e / g ) f o r w a t e r . However, pure l i q u i d s a r e o n l y u s e f u l o v e r t h e t e m p e r a t u r e range a t which they e x e r t s i g n i f i c a n t vapour p r e s s u r e s and y e t can be e a s i l y a bsorbed and r e g e n e r a t e d . T h i s s u g g e s t s t h e use o f a m i x t u r e o f l i q u i d s o f d i f f e r e n t b o i l i n g p o i n t s , b o t h t o p r o v i d e the vapour and t o a c t as the a b s o r p t i o n l i q u i d . The method of o p e r a t i o n c o u l d be the same as t h a t d e s c r i b e d e a r l i e r f o r a m u l t i s t a g e system. The h i g h b o i l i n g p o i n t components are c o n c e n t r a t e d i n the f i r s t s t a g e , and t h e b o i l i n g p o i n t s s u c c e s s i v e l y d e c r e a s e i n l a t e r s t a g e s . I n essence t h i s p r o c e s s i s s i m i l a r t o p a s s i n g a d u s t y gas up t h r o u g h a column i n which a multicomponent d i s t i l l a t i o n t a k e s p l a c e . However, the a b s o r p t i o n o f the l e s s v o l a t i l e components and the e v a p o r a t i o n o f t h e more v o l a t i l e components must be c a r r i e d o u t s e p a r a t e l y i n each s t a g e , o t h e r w i s e the d i f f u s i o p h o r e t i c v e l o c i t i e s w i l l be s m a l l , and may even be d i r e c t e d so as t o impede p a r t i c l e c o l l e c t i o n . 161. 7.6 M u l t i p l e Removal Mechanisms D i f f u s i o p h o r e s i s may form a u s e f u l a d j u n c t t o a n o t h e r p a r t i c l e removal mechanism d u r i n g gas c l e a n i n g , and c o u l d be used t o i n c r e a s e t h e e f f i c i e n c y o f some t y p e s o f e x i s t i n g equipment. Fo r example, when a humid gas i s t r e a t e d i n a wet s c r u b b e r the normal i n e r t i a l mechanisms a r e accompanied by d i f f u s i o p h o r e t i c e f f e c t s , and the p a r t i c l e removal e f f i c i e n c y i n c r e a s e s . The magnitude o f t h i s i n c r e a s e i n t h e case where'there a re no i n t e r -a c t i o n s between removal mechanisms ( i . e . , t he mechanisms are l o c a l l y a d d i t i v e ) can now be d e t e r m i n e d . To examine t h i s case i t i s u s e f u l t o i n t r o d u c e t h e p a r t i c l e p e n e t r a t i o n , which i s d e f i n e d as P = 1 - e P A d i f f e r e n t i a l p a r t i c l e b a l a n c e o v e r a l e n g t h o f the f l o w p a t h dz f o r the gas f l o w i n g t h r o u g h the equipment g i v e s dn = n v p , i a i d z + n v p , n a i i d z + where each term on the r i g h t r e p r e s e n t s t h e p a r t i c l e removal by one mechanism, v T , v .... b e i n g t h e p a r t i c l e v e l o c i t i e s P / J- P / -L -L and a I # a-r-r-/ .... b e i n g the e f f e c t i v e t r a n s f e r a r e a s f o r each mechanism. I n t e g r a t i o n o f t h i s e x p r e s s i o n y i e l d s 162. o u t = P = p P P n. I I I I I I i n where each p e n e t r a t i o n must be e x p r e s s e d on the same b a s i s , e.g., p a r t i c l e s p e r mole o f i n e r t f l u i d . Thus the t o t a l p e n e t r a t i o n e q u a l s t h e p e n e t r a t i o n o b t a i n e d i f the f l u i d p asses t h r o u g h a s e r i e s o f s t a g e s , i n each o f which o n l y one removal mechanism,' o p e r a t e s . The p r e d i c t e d t o t a l p e n e t r a t i o n i s g e n e r a l l y v a l i d f o r one p a r t i c l e s i z e and d e n s i t y , e x c e p t i n the case o f thermo-and d i f f u s i o p h o r e t i c removal,where t h e s e f a c t o r s have no i n f l u e n c e o u t s i d e t h e t r a n s i t i o n regime. Thus, when t h e c o n d i t i o n s r e q u i r e d f o r the p a r t i c l e removal t h e o r y h o l d (see C h a p t e r 4 ) , i t i s s t r a i g h t f o r w a r d t o d e t e r m i n e t h e amount o f removal due t o d i f f u -s i o p h o r e s i s i n t h e p r e s e n c e o f o t h e r mechanisms. 7.7 I n t e r a c t i o n s between Mechanisms The t h e o r y i n the p r e v i o u s s e c t i o n i s c o n t i n g e n t on t h e c o n d i t i o n t h a t i n t e r a c t i o n s between removal mechanisms do n o t o c c u r . T h i s i s n o t always t h e c a s e . For example, the work o f A n n i s and Mason (19 75) i n d i c a t e s t h a t , when a s m a l l p a r t i c l e s i m u l t a n e o u s l y undergoes thermo- and d i f f u s i o p h o r e s i s , t h e p a r t i c l e v e l o c i t y i s n o t s i m p l y the sum o f the v e l o c i t i e s caused by the i n d i v i d u a l mechanisms, b u t i n v o l v e s a l s o a s m a l l i n t e r a c t i v e term. Second-order i n t e r a c t i v e e f f e c t s such as t h i s have l i t t l e i n f l u e n c e on p a r t i c l e c o l l e c t i o n e f f i c i e n c y , 163. a n d a r e t h e r e f o r e m a i n l y o f a c a d e m i c i n t e r e s t . I t i s s u g g e s t e d i n t h i s s t u d y , h o w e v e r , t h a t u n d e r c e r t a i n c o n d i t i o n s a s i g n i f i c a n t i n t e r a c t i o n may e x i s t b e t w e e n i n e r t i a l d e p o s i t i o n a n d o t h e r r e m o v a l m e c h a n i s m s , s u c h a s d i f f u -s i o p h o r e s i s . T h i s s i t u a t i o n c a n a r i s e when t h e m a j o r r e s i s t a n c e t o i n e r t i a l r e m o v a l i s i n p a r t i c l e t r a n s p o r t a c r o s s t h e momentum t r a n s f e r b o u n d a r y l a y e r , r a t h e r than i n t r a n s p o r t f r o m t h e t u r b u l e n t c o r e i n t o t h e b o u n d a r y l a y e r . I n t h e s e c i r c u m s t a n c e s , a n y m e c h a n i s m s u c h a s d i f f u s i o p h o r e s i s , w h i c h c a n a s s i s t i n c a r r y i n g p a r t i c l e s a c r o s s t h e b o u n d a r y l a y e r , s h o u l d s u b s t a n t i a l l y e n h a n c e t h e r a t e o f i n e r t i a l d e p o s i t i o n a n d e x t e n d t h e i n f l u e n c e o f t h e i n e r t i a l m e c h a n i s m t o s m a l l e r p a r t i c l e s i z e s . T h e p o s s i b i l i t y o f s u c h a n i n t e r a c t i o n a p p e a r s n o t t o h a v e b e e n r e c o g n i z e d b y o t h e r s . E a r l y d e p o s i t i o n m o d e l s s u c h a s t h o s e o f F r i e d l a n d e r a n d J o h n s t o n e (1957), D a v i e s (1966), a n d B e a l (1970), w e r e t o o c r u d e f o r t h e p o s s i b i l i t y o f i n t e r a c t i o n t o b e d e t e c t e d . T h e y w o u l d i n f a c t p r e d i c t r e d u c e d r e m o v a l , a s b o t h m e c h a n i s m s c o m p e t e f o r p a r t i c l e s f r o m t h e t u r b u l e n t c o r e , t h e r e b y l o w e r i n g t h e p a r t i c l e c o n c e n t r a t i o n a t t h e e d g e o f t h e b o u n d a r y l a y e r . T h e p a p e r o f H u t c h i n s o n e t a l . (1971) p r o v i d e s a m o r e d e t a i l e d m o d e l . I t p r e d i c t s t h a t u n d e r c e r t a i n c o n d i t i o n s t h e c o n c e n t r a -t i o n o f p a r t i c l e s c a n r e a c h a p e a k n e a r t h e t r a n s f e r s u r f a c e . T h i s o c c u r s when t h e f r a c t i o n o f p a r t i c l e s w h i c h a p p r o a c h t h e s u r f a c e i s l a r g e , b u t t h e f r a c t i o n a b l e t o p e n e t r a t e t h e b o u n d a r y l a y e r a n d r e a c h t h e s u r f a c e i s s m a l l . T h i s b e h a v i o u r h a s b e e n o b s e r v e d e x p e r i m e n t a l l y . U n d e r t h e s e c o n d i t i o n s e v e n a s m a l l 164. d i f f u s i o p h o r e t i c e f f e c t could provide a means of conveying p a r t i -cles across the boundary layer and thus completing the removal process. The experimental conditions i n t h i s study were chosen so that i n e r t i a l deposition would be n e g l i g i b l e , and consequently no i n t e r a c t i v e effects were observed. By contrast, i n the work of Azarniouch et a l . (1975) both i n e r t i a l and d i f f u s i o p h o r e t i c removal were s i g n i f i c a n t . They used the method of Hutchinson et a l . , to predict that the resistance to i n e r t i a l deposition lay v i r t u a l l y e n t i r e l y i n p a r t i c l e transport across the boundary layer. Thus, strong i n t e r a c t i o n should be expected, since even a small d i f f u s i o p h o r e t i c v e l o c i t y w i l l move a p a r t i c l e across the boundary layer, once i t i s deposited there by i n e r t i a l mechanisms. Azarniouch et a l . did not reach these conclusions, and make no mention of possible interactions. Furthermore, t h e i r experimental re s u l t s do not confirm th i s prediction since a l l e f f i c i e n c i e s were considerably less than unity, and some were as low as 0.4. In view of the c r i t i c i s m s of t h e i r experimental work made e a r l i e r , i t i s not possible to draw any d e f i n i t e conclusions regarding interactions from these r e s u l t s . However, i t appears as i f the i n t e r a c t i v e effects are smaller than the Hutchinson model indicates. This probably r e f l e c t s the fact that the model, although more refined than previous ones, s t i l l does not f u l l y describe the behaviour i n the boundary layer. The p o s s i b i l i t y allowed by the model, that v i r t u a l l y a l l p a r t i c l e s can be removed from the core and concentrated i n the boundary layer, i s not r e a l i s t i c . Even i n the boundary layer eddies must 165. s t i l l play some role, and in particular must provide a mechanism for returning particles to the gas core. I t i s expected that a more accurate model would predict a lower enhancement of removal by interactive effects. If indeed there are strong interactive effects between i n e r t i a l and diffusiophoretic removal mechanisms, this could have important implications in the design of certain particle removal equipment. However, because of lack of adequate theory and experimental data, no definite conclusions can be reached at present about the existence of such effects. 1 6 6 . C h a p t e r 8 SUMMARY AND CONCLUSIONS 8 . 1 F u n d a m e n t a l T h e o r y E x p r e s s i o n s f o r t h e v e l o c i t y o f a s m a l l p a r t i c l e i n a n u n d i s t u r b e d d i f f u s i n g g a s m i x t u r e h a v e b e e n d e r i v e d b y s e v e r a l w o r k e r s . T h e y a r e a l l s u b s t a n t i a l l y t h e s a m e , a n d g i v e s a t i s -f a c t o r y a g r e e m e n t w i t h e x p e r i m e n t a l m e a s u r e m e n t s . H o w e v e r , f o r l a r g e p a r t i c l e s , two d i f f e r e n t e x p r e s s i o n s h a v e p r e v i o u s l y b e e n p r o p o s e d ( i g n o r i n g s e c o n d - o r d e r t e r m s ) . T h e s e a r e d e r i v e d f r o m t h e o r i e s w h i c h i n v o k e o r i m p l y t h e e x i s t e n c e o f d i f f u s i o n s l i p a t t h e p a r t i c l e s u r f a c e . I n t h e c u r r e n t s t u d y t h e c o n t i n u u m m e c h a n i c s e q u a t i o n s w e r e s o l v e d i n a m o r e r i g o r o u s m a n n e r t h a n was h i t h e r t o a v a i l a b l e . T h e g a s was t a k e n t o b e a t r e s t a t t h e s u r f a c e o f t h e p a r t i c l e , s i n c e s i g n i f i c a n t s l i p was s h o w n t o v i o l a t e t h e c o n d i t i o n o f e n e r g y c o n s e r v a t i o n . H e n c e , t h e p a r t i c l e was shown t o a d o p t t h e mean m a s s v e l o c i t y o f t h e g a s . I n a d e q u a t e e x p e r i m e n t a l w o r k e x i s t e d t o s u b s t a n t i a t e t h i s r e s u l t . 167. 8 . 2 D e r i v e d T h e o r y A t h e o r y was d e v e l o p e d t o p r e d i c t t h e d i f f u s i o p h o r e t i c p a r t i c l e r e m o v a l c a u s e d b y d i f f u s i o n a l m a s s t r a n s f e r f r o m a m u l t i c o m p o n e n t g a s s t r e a m . Two s e p a r a t e d e r i v a t i o n s w e r e m a d e . T h e f i r s t a s s u m e s t h a t m a s s t r a n s f e r t a k e s p l a c e f r o m a t u r b u l e n t a n d w e l l - m i x e d g a s c o r e a c r o s s a l a m i n a r f i l m a d j a c e n t t o t h e t r a n s f e r s u r f a c e . T h e s e c o n d i s m o r e r i g o r o u s , s i n c e i t i s b a s e d s o l e l y o n t h e n o n - s t e a d y - s t a t e f o r m s o f t h e c o n t i n u i t y e q u a t i o n s f o r t h e p a r t i c l e a n d f o r t h e g a s m i x t u r e . I t i s t h e r e f o r e i n d e p e n d e n t o f t h e p a t t e r n s o f m a s s t r a n s f e r o r g a s f l o w . T h e two d e r i v a t i o n s g a v e i d e n t i c a l r e s u l t s . T h e t h e o r e t i c a l p r e d i c t i o n s f o r p a r t i c l e r e m o v a l d e p e n d o n t h e v a l u e o f t h e l o c a l p a r t i c l e v e l o c i t y . I t was f o u n d t h a t i f t h e p a r t i c l e s a d o p t t h e l o c a l mean mass v e l o c i t y o f t h e f l u i d ( a s p r e d i c t e d f o r l a r g e p a r t i c l e s i n t h e p r e s e n t s t u d y ) , t h e n t h e f r a c t i o n a l r e m o v a l o f p a r t i c l e s i s i d e n t i c a l t o t h e m a s s f r a c t i o n o f t h e g a s t r a n s f e r r e d . S i m i l a r l y , i f t h e y a d o p t t h e l o c a l mean m o l a r v e l o c i t y o f t h e f l u i d , t h e n t h e r e m o v a l e f f i c i e n c y e q u a l s t h e m o l a r f r a c t i o n o f g a s t r a n s f e r r e d . A s i m p l e r e s u l t was a l s o o b t a i n e d w h e n t h e p a r t i c l e s w e r e a s s u m e d t o t r a v e l a t t h e v e l o c i t y p r e d i c t e d b y S c h m i t t a n d W a l d m a n n (1960) . A z a r n i o u c h e t a l . (1975) d e r i v e d a s i m i l a r t h e o r y f o r p a r t i c l e r e m o v a l b y d i f f u s i o p h o r e s i s , a n d a n a l o g o u s t h e o r i e s h a v e b e e n p r e s e n t e d f o r t h e r m o p h o r e s i s b y s e v e r a l a u t h o r s . B o t h t h e o r i e s p r e s e n t e d i n t h e c u r r e n t s t u d y a r e m o r e r i g o r o u s t h a n 168. any o f t h e s e , and y i e l d s i m p l e r r e s u l t s . However, no s u i t a b l e e x p e r i m e n t a l work was p r e v i o u s l y a v a i l a b l e a g a i n s t w h i c h t o t e s t them. 8.3 E x p e r i m e n t a l Work E x p e r i m e n t a l s t u d i e s were made o f p a r t i c l e removal by d i f f u s i o p h o r e s i s from t u r b u l e n t gas s t r e a m s . A b i n a r y gas m i x t u r e c o n t a i n i n g a e r o s o l p a r t i c l e s was pass e d up t h r o u g h a w e t t e d w a l l column (0.0254 m I.D. and 0.77 m i n l e n g t h ) , c o u n t e r c u r r e n t t o a f l o w o f w a t e r . One component was i n s o l u b l e , w h i l e the o t h e r was p a r t i a l l y a b s o r b e d . The r e s u l t i n g p a r t i c l e removal was d e t e r -mined by measuring the i n l e t and o u t l e t a e r o s o l number concen-t r a t i o n s i n the gas. The s o l u b l e gases t e s t e d were ammonia and t r i m e t h y l a m i n e , w h i l e the i n s o l u b l e gases were h e l i u m , methane, n i t r o g e n , a r g o n , and f r e o n 12 ( d i c h l o r o d i f l u o r o m e t h a n e ) . U n i f o r m l a t e x p a r t i c l e s o f 0.50, 0.79, 1.011, 2.02, and 5.7 m i c r o n s i n d i a m e t e r were used. The measured p a r t i c l e removal e f f i c i e n c i e s were compared w i t h t h r e e t h e o r e t i c a l p r e d i c t i o n s based on t h e t h r e e v e l o c i t y e x p r e s s i o n s mentioned p r e v i o u s l y . I t was found t h a t they always tended t o l i e between t h e p r e d i c t i o n s o f t h e mean mass and mean molar v e l o c i t y models. A l s o , t h e d a t a f o r each e x p e r i m e n t showed a s i m i l a r t r e n d t o t h e t h r e e p r e d i c t i o n s , w h i l e g e n e r a l l y n o t a g r e e i n g w i t h any o f them. I t was t h e r e f o r e c o n c l u d e d t h a t t h e t h e o r y o f p a r t i c l e removal was s u b s t a n t i a l l y c o r r e c t , b u t t h a t t h e p a r t i c l e s probably f e l l i n t o the t r a n s i t i o n regime, 1 6 9 . i n which none of the v e l o c i t y e x p r e s s i o n s a p p l i e d . Consequently, the fundamental theory f o r the v e l o c i t y of l a r g e p a r t i c l e s c o u l d not be d e f i n i t i v e l y t e s t e d . I t was, however, concluded t h a t the mean molar v e l o c i t y was not a p p r o p r i a t e , s i n c e almost none of the data f e l l c l o s e to the c o r r e s p o n d i n g t h e o r e t i c a l p r e d i c t i o n s . Attempts to c o n f i r m the e x i s t e n c e of t r a n s i t i o n regime behaviour by s t a t i s t i c a l l y comparing the data w i t h a t r a n s i t i o n model were u n s u c c e s s f u l . Previous s t u d i e s which p u r p o r t to show the e x t e n t o f the t r a n s i t i o n regime i n d i c a t e t h a t l a r g e p a r t i c l e behaviour should have been expected i n most o f the c u r r e n t experiments. Those s t u d i e s are, however, open to c r i t i c i s m . The e x t e n t of the t r a n s i t i o n regime, and the manner i n which p a r t i c l e v e l o c i t y v a r i e s w i t h Knudsen number w i t h i n t h i s r e g i o n , are d i f f i c u l t t o p r e d i c t because o f the complex i n t e r a c t i o n s of m o l e c u l a r s p e c i e s with the p a r t i c l e s u r f a c e and with each o t h e r . 8.4 P r a c t i c a l A p p l i c a t i o n I t has been e s t a b l i s h e d i n t h i s study t h a t d i f f u s i o -p h o r e s i s can be an e f f e c t i v e method o f removing m i c r o n - s i z e d p a r t i c l e s from t u r b u l e n t gas streams. However, i t s p o t e n t i a l f o r p r a c t i c a l a p p l i c a t i o n depends on i t s c o s t r e l a t i v e t o o t h e r gas c l e a n i n g methods. The t r a n s f e r r e d gas can c o n v e n i e n t l y be produced e i t h e r by e v a p o r a t i o n of a l i q u i d or by d e s o r p t i o n of the gas from s o l u t i o n . The primary c o s t s are f o r heat r e q u i r e d to c a r r y out t h i s o p e r a t i o n , and f o r c o o l i n g to recondense the gas or remove the heat e v o l v e d d u r i n g r e - a b s o r p t i o n . The way i n 170. w h i c h the t r a n s f e r r e d gas i s used was found t o have a l a r g e e f f e c t on the p a r t i c l e removal e f f i c i e n c y o b t a i n e d , and hence on the c o s t . The use o f steam as t h e t r a n s f e r r e d gas was shown t o be uneconomic e x c e p t p o s s i b l y i n s p e c i a l c i r c u m s t a n c e s , s i n c e t h e c o s t was an o r d e r o f magnitude h i g h e r than f o r o t h e r removal methods. R e d u c t i o n s i n c o s t may be p o s s i b l e t h r o u g h the use o f h e a t r e c o v e r y , o r through t h e employment o f gases w h i c h r e q u i r e l e s s h e a t i n t h e i r g e n e r a t i o n . D i f f u s i o p h o r e s i s c o u l d i n some i n s t a n c e s p r e s e n t a u s e f u l supplement t o p a r t i c l e removal by o t h e r mechanisms. There i s a l s o some e v i d e n c e t h a t i t may i n t e r a c t w i t h the i n e r t i a l d e p o s i t i o n mechanism under c e r t a i n c o n d i t i o n s t o g i v e s u b s t a n -t i a l l y enhanced p a r t i c l e r e m o v a l . However, no s a t i s f a c t o r y e x p e r i m e n t a l work has been p u b l i s h e d a g a i n s t which t o t e s t t h i s c o n j e c t u r e . 171. NOMENCLATURE Symbol E x p l a n a t i o n and t y p i c a l u n i t s a i n t e r f a c i a l a r e a , m. * a., a. c o e f f i c i e n t s dependent on i n t e r a c t i o n o f gas m o l e c u l e s w i t h s u r f a c e . a^ p a r t i c l e a c c e l e r a t i o n , m/sec. 2 A c r o s s s e c t i o n a r e a , m . A ' c o n s t a n t i n s o l u t i o n f o r stream f u n c t i o n . A R c o n s t a n t i n e x p r e s s i o n f o r p a r t i c l e removal e f f i c i e n c y . * b^ c o e f f i c i e n t dependent on i n t e r a c t i o n of gas m o l e c u l e s w i t h s u r f a c e . 1 B ' c o n s t a n t i n s o l u t i o n f o r stream f u n c t i o n . B r c o n s t a n t i n e x p r e s s i o n f o r p a r t i c l e removal e f f i c i e n c y . 3 c molar c o n c e n t r a t i o n , Kg mole/m . c p a r t i a l m o l ar c o n c e n t r a t i o n f o r s p e c i e s i , Kg mole/m 3. c' g e n e r a l c o n c e n t r a t i o n . c! p a r t i a l g e n e r a l c o n c e n t r a t i o n f o r s p e c i e s i . c r o o t mass c o n c e n t r a t i o n , (Kg) (Kg mole) 2/m . p a r t i a l r o o t mass c o n c e n t r a t i o n f o r s p e c i e s i , l (Kg) 3* (Kg mole )Vni 3 1 7 2 . S y m b o l E x p l a n a t i o n a n d t y p i c a l u n i t s c' c o n s t a n t i n s o l u t i o n f o r s t r e a m f u n c t i o n . C r c o n s t a n t i n e x p r e s s i o n f o r p a r t i c l e r e m o v a l e f f i c i e n c y . d Q , d ^ , d _ ^ p a r a m e t e r s d e p e n d e n t o n g a s c o m p o s i t i o n . 2 D d i f f u s i v i t y o f b i n a r y m i x t u r e , m / s e c . d i f f u s i v i t y o f c o m p o n e n t i i n a m u l t i c o m p o n e n t m i x t u r e , m ^ / s e c . D 1 c o n s t a n t i n s o l u t i o n f o r s t r e a m f u n c t i o n . 2 2 E v e c t o r o p e r a t o r , / m E e n e r g y d i s s i p a t i o n r a t e , J o u l e / s e c . f c o n s t a n t . 2 F f o r c e o n p a r t i c l e , K g m / s e c . 2 g m a g n i t u d e o f g r a v i t a t i o n a l a c c e l e r a t i o n , m / s e c . 2 g g r a v i t a t i o n a l a c c e l e r a t i o n v e c t o r , m / s e c . G m o l a r f l o w r a t e o f g a s , K g m o l e / s e c . G ^ m o l a r f l o w r a t e o f c o m p o n e n t 1, K g m o l e / s e c . Q>2 m o l a r c r o s s f l o w r a t e o f c o m p o n e n t 2, K g m o l e / s e c , G ' c o n s t a n t i n s o l u t i o n f o r v . i g a s c o m p o n e n t . k n u m b e r o f g a s c o m p o n e n t s . K n K n u d s e n n u m b e r . irw m o l e c u l e w e i g h t f o r s p e c i e s i , K g . M mean m o l e c u l a r w e i g h t , g / g m o l e . M^ m o l e c u l a r w e i g h t f o r s p e c i e s i , g / g m o l e . Mp p a r t i c l e m a s s , K g . 3 n p a r t i c l e n u m b e r c o n c e n t r a t i o n , #/m . n-, p a r t i c l e n u m b e r c o n c e n t r a t i o n b a s e d o n s p e c i e s 1, #/m3. 173. Symbol E x p l a n a t i o n and t y p i c a l u n i t s 2 molar f l u x o f s p e c i e s i , Kg mole/m s e c . ' . j, • j, 2 ~ r o o t mass f l u x o f species i , (Kg) 2(Kg mole) 2/m sec. p p r e s s u r e , Kg/m s e c ^ . P p e n e t r a t i o n . r r a d i a l c o o r d i n a t e , m. r ^ m o l e c u l a r r a d i u s f o r s p e c i e s i , m. r 1 2 (r1 + r 2 ) / 2 , m. R p a r t i c l e r a d i u s , m. Re Reynolds number. 2 S S t o p p i n g d i s t a n c e parameter, m . Sc Schmidt number, t t i m e , s e c . v e l o c i t y o f f r e e f l a t s u r f a c e , m/sec. v mean mass v e l o c i t y o f f l u i d , m/sec. v* mean molar v e l o c i t y o f f l u i d , m/sec. v mean r o o t mass v e l o c i t y o f f l u i d , m/sec. v' g e n e r a l v e l o c i t y , m/sec. Vp p a r t i c l e v e l o c i t y i n x d i r e c t i o n , m/sec. Vp p a r t i c l e v e l o c i t y v e c t o r , m/sec. v r , v Q f l u i d v e l o c i t y components i n b o d y - c e n t r e d c o o r d i n a t e s , m/sec. v^ f l u i d v e l o c i t y w i t h r e s p e c t t o p a r t i c l e f o r l a r g e r , m/sec. v ,. s l i p v e l o c i t y , m/sec. s l i p v 1 w mean mass v e l o c i t y o f gas w i t h r e s p e c t t o number-centred c o o r d i n a t e s , m/sec. 174 . S y m b o l E x p l a n a t i o n a n d t y p i c a l u n i t s w Q v a l u e o f w f o r l a r g e r a n d 6 = TT/2, m / s e c . x c o o r d i n a t e i n d i r e c t i o n o f d i f f u s i o n o f u n d i s t u r b e d g a s , m. z c o o r d i n a t e i n d i r e c t i o n o f f l u i d f l o w , m. Z c o l l e c t o r l e n g t h , m. a s l i p c o e f f i c i e n t . a 1 s l i p c o e f f i c i e n t r e d e f i n e d . a T t h e r m a l d i f f u s i o n f a c t o r . 3^ accommodation c o e f f i c i e n t f o r s p e c i e s i . m o l e f r a c t i o n o f s p e c i e s i . 6 f u n c t i o n o f c o l l i s i o n i n t e g r a l s e f r a c t i o n o f g a s r e m o v e d . g £p p a r t i c l e r e m o v a l e f f i c i e n c y . £.„, p r e d i c t i o n o f mean mass v e l o c i t y m o d e l . MA r J p r e d i c t i o n o f S c h m i t t a n d W a l d m a n n m o d e l . e m t > p r e d i c t i o n o f t r a n s i t i o n r e g i m e m o d e l . n d i m e n s i o n l e s s d e n s i t y g r a d i e n t f o r l a r g e r . 0 p o l a r c o o r d i n a t e . K b u l k v i s c o s i t y , K g / m s e c . Vi s h e a r v i s c o s i t y , K g / m s e c . 3 p d e n s i t y o f f l u i d , K g / m . p d e n s i t y o f f l u i d f o r l a r g e r a n d 0 = i r/2, ° Kg/m3. 3 p^ p a r t i a l d e n s i t y o f c o m p o n e n t i , K g / m . 1 7 5 . Symbol E x p l a n a t i o n and t y p i c a l u n i t s 2 T s t r e s s t e n s o r , Kg/m sec . <j> p o l a r c o o r d i n a t e . ip stream f u n c t i o n . V d e l o p e r a t o r , /m. x v e c t o r c r o s s p r o d u c t o p e r a t o r . v e c t o r d o t p r o d u c t o p e r a t o r . D/Dt d i f f e r e n t i a l o p e r a t o r as d e f i n e d i n t e x t . q u a n t i t i e s e n c l o s e d a r e d i m e n s i o n l e s s . + ( s u p e r s c r i p t ) t r a n s p o s e o f t e n s o r . S u b s c r i p t s i v a l u e f o r component i . p v a l u e f o r the p a r t i c l e , s v a l u e a t t h e p a r t i c l e s u r f a c e . 0 0 v a l u e f o r l a r g e r . o v a l u e f o r l a r g e r and 6 = ir/2. i n (mean) i n l e t v a l u e , o u t (mean) o u t l e t v a l u e . I , I I , ... v a l u e s f o r v a r i o u s removal mechanisms. 176 . REFERENCES A i t k e n , J . , T r a n s . R o y . S o c . E d i n b . , _32, 239 ( 1 8 8 3 ) . A n n i s , B . K . , M a l i n a u s k a s , A . P . a n d M a s o n , E . A . , J . A e r o s o l S c i . , 3 , 55 (1972) A n n i s , B . K . , M a l i n a u s k a s , A . P . a n d M a s o n , E . A . , J . A e r o s o l S c i . , 4, 271 (1973) . A n n i s , B . K . a n d M a s o n , E . A . , J . A e r o s o l S c i . , 6_, 105 ( 1 9 7 5 ) . A z a r n i o u c h , M . K . , D o c t o r a l T h e s i s , D e p t . o f C h e m . E n g . , M c G i l l U n i v e r s i t y , M o n t r e a l (1974) . A z a r n i o u c h , M . K . , B o b k o w i c z , A . J . , C o o k e , N . E . a n d F a r k a s , E . J . , C a n . J . C h e m . E n g . , 5 1 , 590 (1973) A z a r n i o u c h , M . K . , B o b k o w i c z , A . J . , C o o k e , N . E . a n d F a r k a s , E . J . , C a n . J . C h e m . E n g . , 5_3, 278 ( 1 9 7 5 ) . B a k a n o v , S . P . a n d D e r j a g u i n , B . V . , D i s c . F a r a d a y S o c , 30_, 130 ( 1 9 6 0 ) . B e a l , S . K . , N u c l . S c i . E n g . , £ 0 , - 1 ( 1 9 7 0 ) . B i r d , R. B . , S t e w a r t , W. E . a n d L i g h t f o o t , E . N . , " T r a n s p o r t P h e n o m e n a " , W i l e y , N . Y . , ( 1 9 6 2 ) . B r o c k , J . R . , J . C o l l o i d S c i . , 1_8, 489 ( 1 9 6 3 ) . B r o c k , J . R. , J . C o l l o i d I n t e r f a c e S c i . , 27_, 95 ( 1 9 6 8 ) . B y e r s , R . L . a n d C a l v e r t , S . , I n d . E n g . C h e m . F u n d a m , 8_, 646 ( 1 9 6 9 ) . C a l v e r t , S . , G o l d s h m i d , J . , L e i t h , D . a n d M e h t a , D . , " F e a s i b i l i t y o f F l u x F o r c e / C o n d e n s a t i o n S c r u b b i n g f o r F i n e P a r t i c l e C o l l e c t i o n " A . P . T . I n c . , R i v e r s i d e , C a l i f . , N . T . I . S . # P B - 2 2 7 - 3 0 7 , ( 1 9 7 3 ) . C h a p m a n , S . a n d C o w l i n g , T . G . , " T h e M a t h e m a t i c a l T h e o r y o f N o n -U n i f o r m G a s e s " , C a m b r i d g e U n i v e r s i t y P r e s s , L o n d o n ( 1 9 6 4 ) . 177. Dankwerts, P. V., " G a s - L i q u i d R e a c t i o n s " , M c G r a w - H i l l , N.Y. (1970). D a v i e s , C. N. " A e r o s o l S c i e n c e " , Academic P r e s s , N.Y. (1966). D e r j a g u i n , B. V. and Bakanov, S. P., D o k l . Akad. Nauk SSSR, 117, 959 (1957). D e r j a g u i n , B. V. and Dukhin, S. S., D o k l . Akad. Nauk SSSR (Phys. Chem.) 106, 851; 111, 613 (1956). D e r j a g u i n , B. V. and Dukhin, S. S., D o k l . Akad. Nauk SSSR, 112, 407 (1957). D e r j a g u i n , B. V. and Yalamov, Yu. I . , i n " T o p i c s i n C u r r e n t A e r o s o l R e s e a r c h " , ( E d i t e d by H i d y , G. M. and B r o c k , J . R . ) , V o l . 3, Pergamon P r e s s , O x f o r d (19 72). D e r j a g u i n , B. V., Yalamov, Yu. I . and S t o r o z h i l o v a , A. I . , J . C o l l o i d I n t e r f a c e S c i . , 22_, 117 (1966). E i n s t e i n , A., Z. Phys., 27, 1 (1924). Facy, L., Comptes rend u s , 246, 102; 246, 3161 (1958). Fahnoe, F., L i n d r o o s , A. E. and A b e l s o n , R. J . , I n d . Eng. Chem., 43, 1336 (1951). F r e i s e , V., J . Chem. P h y s i q u e , 5_4, 879 (1957). F r i e d l a n d e r , S. K. and J o h n s t o n e , H. F., I n d . Eng. Chem., 49, 1151 (1957). Fuchs, N. and K i r s c h , A., Chem. Eng. S c i . , 2_0, 181 (1965). G o l d s m i t h , P., D e l a f i e l d , H. J . and Cox, L. C , Geof. P u r a . A p p l i c . , 50, 278 (1963). G o l d s m i t h , P. , D e l a f i e l d , H. J . and Cox, L. C.,Q.J.R. Met Soc. 89, 43 (1963). G o l d s m i t h , P. and May, F. G., i n " A e r o s o l S c i e n c e " ( E d i t e d by D a v i e s , C. N.), Academic P r e s s , London (1966). "Handbook o f P h y s i c s and C h e m i s t r y " ( E d i t e d by Weast, R. C ) , Ch e m i c a l Rubber Co., C l e v e l a n d , Ohio (1970). H a p p e l , J . and B r e n n e r , H., "Low Reynolds Number Hydrodynamics", P r e n t i c e - H a l l , New J e r s e y (1965). H i r s c h f e l d e r , J . 0., C u r t i s s , C. F. and B i r d , R. B., " M o l e c u l a r Theory o f Gases and L i q u i d s " , W i l e y , N.Y. (1964). 1 7 8 . H u t c h i n s o n , P . , H e w i t t , G . F . a n d D u k l e r , A . E . , C h e m . E n g . S c i . , 2 6 , 419 (1971) I n t e r n a t i o n a l B u s i n e s s M a c h i n e s C o r p . , " S y s t e m / 3 6 0 C o n t i n u o u s S y s t e m M o d e l l i n g P r o g r a m U s e r s ' M a n u a l " , I . B . M . , N . Y . ( 1 9 6 9 ) . " I n t e r n a t i o n a l C r i t i c a l T a b l e s " , M c G r a w - H i l l , N . Y . ( 1 9 2 6 ) . K r a m e r s , H . A . a n d K i s t e m a k e r , J . , P h y s i c a , 10_, 699 ( 1 9 4 3 ) . L a n c a s t e r , B . W. a n d S t r a u s s , W . , I n d . E n g . C h e m . F u n d a m . , 1 0 , 362 ( 1 9 7 1 ) . L a p p l e , C . E . a n d K a m a c k , H . J . , C h e m . E n g . P r o g . , 5 1 , 110 ( 1 9 5 5 ) . L e , C . D . , "UBC S F R P S m a l l F r e e - F o r m a t R e g r e s s i o n P a c k a g e " , U n i v e r s i t y o f B r i t i s h C o l u m b i a C o m p u t i n g C e n t r e , B . C . ( 1 9 7 5 ) . L i t v i n o v , A . T . , Z h . P r i k l a d . K h i m . , 40_, 353 ( 1 9 6 7 ) . M a s o n , E . A . a n d C h a p m a n , S . , J . C h e m . P h y s . , 36_, 627 ( 1 9 6 2 ) . " M a t h e s o n Gas D a t a B o o k " , 4 t h E d n , T h e M a t h e s o n C o . , New J e r s e y (1966) . M e i s e n , A . , D o c t o r a l T h e s i s , D e p t . o f C h e m . E n g . , M c G i l l U n i v e r s i t y , M o n t r e a l (19 7 0 ) . M e i s e n , A . , B o b k o w i c z , A . J . , C o o k e , N . E . a n d F a r k a s , E . J . , C a n . J . C h e m . E n g . , 49_, 449 ( 1 9 7 1 ) . M i l l i k a n , R . A . , P h y s . R e v . , 3 2 , 382 ( 1 9 1 1 ) . N i s h i o , G . , K i t a n i , S . a n d T a k a h a s h i , K . , I n d . E n g . C h e m . , P r o c e s s D e s . D e v e l o p . , 1 3 , 408 ( 1 9 7 4 ) . P e r r y , J . H . ( E d i t o r ) " C h e m i c a l E n g i n e e r s ' H a n d b o o k " , 4 t h e d n . (1963) . P e r r y , J . H . a n d C h i l t o n , C . H . , ( E d i t o r s ) , " C h e m i c a l E n g i n e e r s ' H a n d b o o k " , 5 t h e d n . ( 1 9 7 3 ) . P r a k a s h , C . B . a n d M u r r a y , F . E . , A I C h E S y m p o s i u m S e r i e s , 7 1 , 81 ( 1 9 7 5 ) . R o z e n , A . M . a n d K o s t i n , V . M . , I n t e r n a t . C h e m . E n g . , 1_, 464 (1967) . S h a u e r , P . J . , I n d . E n g . C h e m . , 4_3, 1532 ( 1 9 5 1 ) . S c h m i t t , K . H . , S t a u b , 2 1 , 173 ( 1 9 6 1 ) . 179 . S c h m i t t , K . H . a n d W a l d m a n n , L . , Z . N a t u r f . , 1 5 a , 843 ( 1 9 6 0 ) . S e m r a u , K . T . , M a r y n o w s k i , C . W . , L u n d e , K . E . a n d L a p p l e , C . E . , I n d . E n g . C h e m . 5 0 , 1615 ( 1 9 5 8 ) . S h e r w o o d , T . K . a n d G i l l i l a n d , E . R . , I n d . E n g . C h e m . , 26_, 516 (1934) . S h e r w o o d , T . K . a n d P i g f o r d , R. L . , " A b s o r p t i o n a n d E x t r a c t i o n " , 2 n d e d n . , M c G r a w - H i l l , N . Y . ( 1 9 5 2 ) . S p a r k s , L . E . a n d P i l a t , M . J . , A t m o s . E n v i r o n . , £ , 651 ( 1 9 7 0 ) . S t e f a n , J . , W i e n . B e r . , 8_3, 943 (1881) S t i n c h c o m b e , R. A . a n d G o l d s m i t h , P . , J . N u c l e a r E n e r g y , 20_, 261 (1966) . S t o r o z h i l o v a , A . I . , D o k l . A k a d . Nauk S S S R , 1 5 5 , 426 ( 1 9 6 4 ) . T r e y b a l , R. E . , " M a s s T r a n s f e r O p e r a t i o n s " , 2 n d e d n . , M c G r a w - H i l l , N . Y . ( 1 9 6 8 ) . T r u i t t , J . a n d D a v i s , R. J . , A m e r . I n d . H y g . A s s . J . , 3_2, 583 (1971) . W a l d m a n n , L . , Z . N a t u r f . , 1 4 a , 589 ( 1 9 5 9 ) . W a l d m a n n , L . , i n " R a r i f i e d G a s D y n a m i c s " , ( E d i t e d b y T a l b o t , L . ) , A c a d e m i c P r e s s , N . Y . (1961) . W a l d m a n n , L . a n d S c h m i t t , K . H . , i n " A e r o s o l S c i e n c e " , ( E d i t e d b y D a v i e s , C . N . ) , A c a d e m i c P r e s s , L o n d o n ( 1 9 6 6 ) . W a l l i s , G . ' B . , "One D i m e n s i o n a l Two P h a s e F l o w " , M c G r a w - H i l l , N . Y . ( 1 9 6 9 ) . W h i t m o r e , P . J . a n d M e i s e n , A . , J . A e r o s o l S c i . , i_r 435 (1973) . W h i t m o r e , P . J . a n d M e i s e n , A . , J . A e r o s o l S c i . , t o b e p u b l i s h e d . W h i t m o r e , P . J . a n d M e i s e n , A . , C a n . J . C h e m . E n g . , t o b e p u b l i s h e d . 180. Appendix A ROTAMETER CALIBRATION DATA The p r i m a r y c a l i b r a t i o n c u r v e s f o r the l i q u i d and gas r o t a m e t e r s a re shown i n f i g u r e s A . l t o A.5. Secondary c a l i b r a -t i o n s o f the r o t a m e t e r s f o r o t h e r gases were made by s c a l i n g t he p r i m a r y c a l i b r a t i o n s , u s i n g the f o r m u l a suggested by the manu-f a c t u r e r ( B r o o k s ) . T h i s f o r m u l a i s e s s e n t i a l l y t he same as t h a t g i v e n by P e r r y (19 6 3 ) . Here Q, p, T, and P are the v o l u m e t r i c f l o w r a t e a t s t a n d a r d c o n d i t i o n s , d e n s i t y , temperature and p r e s s u r e o f gases A and B. F i g u r e A . l C a l i b r a t i o n c u r v e s f o r w a t e r and 32 w% c a u s t i c soda s o l u t i o n i n t h e Brooks l i q u i d r o t a m e t e r . L i q u i d c o n d i t i o n s -20°C and a p p r o x i m a t e l y 1 atmosphere. 0.01 I 1 I I I 0 50 100 150 200 250 ROTRMETER READING F i g u r e A.2 C a l i b r a t i o n c u r v e s f o r n i t r o g e n i n t h e Brooks i n e r t gas r o t a m e t e r . Gas c o n d i t i o n - 4.40 atmospheres and 20°C. 18 3. O.OL I I I | I 0 2 0 4 0 6 0 8 0 100 ROTAMETER R E A D I N G F i g u r e A.3 C a l i b r a t i o n c u r v e f o r c a r b o n d i o x i d e i n the s i z e 3 Gi l m o n t t r a n s f e r r e d gas r o t a m e t e r . Gas c o n d i t i o n s - 1 atmosphere and 20°C. 0 F i g u r e A. 4 C a l i b r a t i o n c urve f o r c a r b o n d i o x i d e i n t h e s i z e 4 G i l m o n t t r a n s f e r r e d gas r o t a m e t e r . Gas c o n d i t i o n s -1 atmosphere and 20°C. F i g u r e A.5 C a l i b r a t i o n c u r v e f o r ammonia i n t h e Brooks t r a n s f e r r e d gas r o t a m e t e r . Gas c o n d i t i o n s - 1 atmosphere and 20°C. 186. Appendix B COLUMN MASS TRANSFER MODEL B.1 D e s c r i p t i o n The purpose o f the model was t o a s c e r t a i n whether the l i q u i d phase mass t r a n s f e r r e s i s t a n c e i n t h e column was n e g l i g i b l e compared t o t h a t o f t h e gas phase. S i n c e t h i s c o n d i t i o n was l a t e r shown t o be un n e c e s s a r y f o r the e x p e r i m e n t s , t h e m o d e l l i n g was abandoned a f t e r some p r e l i m i n a r y work. The model was c o n s t r u c t e d as f o l l o w s . The gas phase mass t r a n s f e r c o e f f i c i e n t was assumed t o be g i v e n by the c o r r e -l a t i o n o f Sherwood and G i l l i l a n d (1934), v i a the Sherwood number, Sh. _, _ 0.83 „ 0.44 Sh = K Re Sc However, t h e c o n s t a n t K was t e m p o r a r i l y l e f t u n d e f i n e d , and the Reynolds number was measured w i t h r e s p e c t t o t h e l i q u i d s u r f a c e r a t h e r than to the surface of the dry column. The model also required a knowledge o f t h e l i q u i d s u r f a c e v e l o c i t y and f i l m t h i c k n e s s p r o f i l e s f o r t h e column. I n f o r m a t i o n on the l i q u i d f i l m b e h a v i o u r was t a k e n 1 8 7 . f r o m B i r d , S t e w a r t , a n d L i g h t f o o t ( 1 9 6 0 ) , a n d W a l l i s ( 1 9 6 9 ) . T h e b e h a v i o u r o f l a m i n a r f i l m s u n d e r f u l l y d e v e l o p e d c o n d i t i o n s i s w e l l u n d e r s t o o d , b u t i n t h e p r e s e n t s t u d y t h e f i l m a c c e l e r a t e d a f t e r e n t e r i n g t h e c o l u m n , a n d t h e b o t t o m s e c t i o n a p p e a r e d t u r b u l e n t . T h e f i l m R e y n o l d s n u m b e r i s g i v e n b y j L P L D c Re„ = w h e r e J L i s t h e v o l u m e t r i c f l u x b a s e d o n t h e t o t a l c o l u m n c r o s s s e c t i o n , D i s t h e c o l u m n d i a m e t e r , a n d p T a n d y T a r e t h e l i q u i d C L i XJ d e n s i t y a n d v i s c o s i t y , r e s p e c t i v e l y . T h e o n s e t o f t u r b u l e n c e i s i n t h e R e y n o l d s n u m b e r r a n g e o f 1 0 0 0 t o 2 0 0 0 , w h i l e t h e R e y n o l d s n u m b e r u n d e r e x p e r i m e n t a l c o n d i t i o n s was 1 7 6 0 i n a l l c a s e s , c o r r e s p o n d i n g t o a w a t e r f l o w o f 3 5 m l / s e c . U n d e r l a m i n a r c o n d i t i o n s t h e s u r f a c e v e l o c i t y i s 1 . 5 t i m e s t h e mean f i l m v e l o c i t y , a n d t h e e q u a t i o n s g i v e n b y W a l l i s ( 1 9 6 9 ) i m p l y t h a t t h i s i s a l s o a g o o d a p p r o x i m a t i o n a t l o w l e v e l s o f t u r b u l e n c e . I t was t h e r e f o r e a s s u m e d t h a t t h i s c o n d i t i o n h e l d a t a l l t i m e s . T h e f i l m a c c e l e r a t i o n was t r e a t e d a s f o l l o w s . F o r c o n s t a n t f l o w o n e c a n c a l c u l a t e t h e a c c e l e r a t i v e f i e l d s t r e n g t h b , u n d e r w h i c h a f i l m o f g i v e n t h i c k n e s s w o u l d b e s t a b l e . I t was t h e n a s s u m e d t h a t t h e d i f f e r e n c e b e t w e e n t h i s f i e l d s t r e n g t h a n d t h e a c t u a l f i e l d s t r e n g t h , g , was a v a i l a b l e t o f r e e l y a c c e l e -r a t e t h e l i q u i d f i l m s u r f a c e . T h i s a p p r o x i m a t i o n g i v e s t h e c o r r e c t t e r m i n a l v e l o c i t y . A t t h e c o l u m n i n l e t t h e l i q u i d v e l o c i t y m u s t b e g r e a t e r t h a n z e r o o r t h e f i l m t h i c k n e s s w o u l d b e i n f i n i t e . 188. The surface v e l o c i t y of the i n l e t l i q u i d was estimated.by measuring the h e i g h t o f the l i q u i d p o o l above the t o p o f t h e column, and assuming t h e s k i n v e l o c i t y was t h a t a t t a i n e d by f r e e f a l l t h r o u g h t h i s d i s t a n c e . T y p i c a l v a l u e s f o r t h i s v e l o c i t y were o f the o r d e r o f 0.3 m/s, which appeared r e a l i s t i c . The model o p e r a t e d as f o l l o w s . A v a l u e was assumed f o r t he c o n c e n t r a t i o n o f ammonia i n the o u t l e t gas. C a l c u l a t i o n s t h e n s t a r t e d a t t h e t o p of t h e column and proceeded downwards. The l o c a l mass t r a n s f e r r a t e was found a t each p o i n t from the l o c a l d i a m e t e r , Reynolds number, and Schmidt number. The t o t a l mass t r a n s f e r down t o t h a t p o i n t was o b t a i n e d by i n t e g r a t i o n . Thus t h e c o r r e s p o n d i n g c o n c e n t r a t i o n o f ammonia i n the i n l e t gas was d e t e r m i n e d . I f t h i s was not i n agreement w i t h the s p e c i f i e d i n l e t c o n d i t i o n s , t h e n a new o u t l e t ammonia c o n c e n t r a t i o n was assumed and t h e c a l c u l a t i o n s were r e p e a t e d . Hence, e v e n t u a l l y an o u t l e t c o n c e n t r a t i o n was p r e d i c t e d w h i c h c o r r e s p o n d e d t o t h e r e q u i r e d i n l e t c o n d i t i o n s . B.2 C a l c u l a t i o n and R e s u l t s The model c a l c u l a t i o n s were made u s i n g the computer s i m u l a t i o n language CSMP ( I n t e r n a t i o n a l B u s i n e s s Machines ( 1 9 6 9 ) ) . T e s t s o f t h e model were made u s i n g a t y p i c a l s e t o f e x p e r i m e n t a l c o n d i t i o n s f o r t h e ammonia-nitrogen system. The -4 3 n i t r o g e n f l o w r a t e was t a k e n as 6 x 10 m / s e c , and t h e i n l e t mole f r a c t i o n o f ammonia was s e t a t 0.450. The c o n s t a n t i n the f o r m u l a f o r the gas phase mass t r a n s f e r c o e f f i c i e n t was the n 189. a d j u s t e d t i l l t h e model p r e d i c t e d t h e same mole f r a c t i o n o f ammonia i n the o u t l e t gas as was measured e x p e r i m e n t a l l y . T h i s — ft adjustment was made f o r t h e u s u a l water f l o w r a t e o f 0.35 x 10 3 m / s e c . Ex p e r i m e n t s were a l s o made u s i n g t h e same i n l e t gas r a t e and c o m p o s i t i o n , b u t w i t h a lower and a h i g h e r w a t e r f l o w r a t e . S i m i l a r r e s u l t s were o b t a i n e d when t h e s e e x p e r i m e n t s were s i m u l a t e d by t h e model, as i s shown i n F i g u r e B . l . The s m a l l d i f f e r e n c e between e x p e r i m e n t a l measurements and model p r e d i c t i o n s may i n d i c a t e a s l i g h t r e s i s t a n c e i n the l i q u i d phase. E f f e c t s o f s u r f a c e r i p p l i n g and l i q u i d - i n d u c e d gas t u r b u l e n c e were beyond the scope o f t h i s s t u d y . F i g u r e B . l E f f e c t o f l i q u i d r a t e on o u t l e t gas c o m p o s i t i o n . 191. Appendix C DATA ANALYSIS AND SAMPLE CALCULATIONS C.1 Source of Sample Data The data used t o i l l u s t r a t e the methods of a n a l y s i s are taken from run 35011, and are f o r 0.79 um p a r t i c l e s with a nitrogen-ammonia gas mixture. Run 35011 l i e s i n the mid-range of a s e r i e s of runs forming an experiment i n which the flow r a t e o f the i n e r t gas was h e l d c o n s t a n t . The data f o r t h i s run are t h e r e f o r e t y p i c a l , s i n c e they are f o r the most commonly used p a r t i c l e s i z e , gas mixture, and type of experiment. The run a l s o forms p a r t of a s e r i e s of runs i n which the i n l e t gas composition was h e l d c o n s t a n t a t approximately 5 0 v% n i t r o g e n , while the flow r a t e was v a r i e d . The r e s u l t s f o r t h i s run can be found i n Appendix D, Table XVI. C.2 Reduction of Raw Data Three r e s u l t s f o r f r a c t i o n a l p a r t i c l e removal e f f i -c i e n c y were c a l c u l a t e d from the c o n s e c u t i v e readings taken d u r i n g run 35011. These appear i n c h r o n o l o g i c a l order i n Table XVI. 192. The c a l c u l a t i o n o f t h e second r e s u l t i s g i v e n h e r e . Measurements o f the p a r t i c l e count per u n i t volume o f i n e r t gas were made a l t e r n a t e l y a t the top and base o f t h e column, as d e s c r i b e d i n Chapter 5, t o y i e l d t h e f o l l o w i n g d a t a : Column t o p Column base Column t o p 5858 9058 6466 6345 8537 6243 6362 8604 5672 5808 9086 6120 These d a t a d i d n o t c o n t a i n any o b v i o u s l y s p u r i o u s r e a d i n g s o r e x h i b i t any marked d r i f t , and were t h e r e f o r e a c c e p t e d and averaged. Column t o p Column base ( b r a c k e t e d average) Mean 6109.25 8821.25 V a r i a n c e 87113.13 84736.00 Standard d e v i a t i o n 295 .15 291.09 Number o f r e a d i n g s 8 4 The s t a n d a r d d e v i a t i o n s o f l e s s t h a n 5% o f the means were q u i t e s a t i s f a c t o r y , and were comparable w i t h t h o s e o b t a i n e d i n t h e o t h e r two s e t s o f r e s u l t s d e r i v e d from t h e r u n . The r e s u l t s were t h e r e f o r e a c c e p t e d . The background c o u n t s t a k e n a t the t o p and base o f the column w i t h t h e p a r t i c l e g e n e r a t o r t u r n e d o f f were n e g l i g i b l e ( < 5) , and c o r r e c t i o n o f t h e means c a l c u l a t e d p r e v i o u s l y was t h e r e f o r e n o t n e c e s s a r y . The raw p a r t i c l e removal e f f i c i e n c y was t h e n c a l c u l a t e d . 19 3. EPEXP = 1 - 6109.25/8821.25 = 0.3074 The v a r i a b l e names g i v e n a re those used i n t h e computer program and the d a t a t a b l e s i n Appendix D (see T a b l e V I I I ) . C.3 Counter C a l i b r a t i o n f o r Gas C o m p o s i t i o n The e f f i c i e n c y , E P E X P , must be c o r r e c t e d f o r t h e i n f l u e n c e o f gas c o m p o s i t i o n on p a r t i c l e c o u n t , as d e s c r i b e d i n Chapter 5. Runs were t h e r e f o r e performed i n w h i c h p a r t i c l e s were added t o a n i t r o g e n s t r e a m t o form an a e r o s o l o f c o n s t a n t c o n c e n t r a t i o n . T h i s was t h e n d i l u t e d w i t h v a r i o u s p r o p o r t i o n s o f ammonia. The r e a d i n g s w i t h the ammonia p r e s e n t , and t h o s e w i t h i t a b s e n t , were averaged i n a manner analogous t o t h a t used i n c a l c u l a t i n g the p a r t i c l e removal e f f i c i e n c y . Thus, t h e f o l l o w i n g r e s u l t s were o b t a i n e d f o r t h e r a t i o o f counts w i t h ammonia p r e s e n t t o counts w i t h ammonia a b s e n t , w h i c h i s termed t h e c a l i b r a t i o n c o r r e c t i o n r a t i o , F. Mole f r a c t i o n o f n i t r o g e n 0.5040 0.6300 0.7600 when ammonia i s p r e s e n t C a l i b r a t i o n c o r r e c t i o n 0.9289 0.9732 0.9913 r a t i o 0.9580 0.9607 0.9791 0.9621 0.9969 0.9634 0.9387 0.9720 0.9757 0.9357 0.9512 0.9402 0.9432 Mean v a l u e 0.9438 0.9708 0.9774 1 9 4 . T h e s e r e s u l t s a r e s h o w n p l o t t e d i n F i g u r e C . l . A l s o , b y d e f i n i t i o n , t h e c o r r e c t i o n r a t i o m u s t b e u n i t y when t h e m o l e f r a c t i o n o f n i t r o g e n , Y I N T , i s o n e , s o t h a t t h e c a l i b r a t i o n c u r v e m u s t p a s s t h r o u g h t h i s p o i n t . S i n c e t o a g o o d a p p r o x i m a t i o n t h e mean v a l u e s o f t h e c o r r e c t i o n r a t i o s l i e a l o n g a s t r a i g h t l i n e , t h e c a l i b r a t i o n c o r r e c t i o n c a n b e e x p r e s s e d a s a l i n e a r e q u a t i o n : F = 0 . 8 9 9 2 + 0 . 1 0 0 8 Y I N T C . 4 C a l c u l a t i o n M e t h o d s C . 4 . 1 G e n e r a l o C a l c u l a t i o n o f t h e c o r r e c t e d p a r t i c l e r e m o v a l e f f i -c i e n c y , o f t h e e f f i c i e n c i e s g i v e n b y t h e t h r e e m o d e l s f o r t h e same e x p e r i m e n t a l c o n d i t i o n s , a n d o f v a r i o u s o t h e r r e l e v a n t p a r a m e t e r s was d o n e b y means o f t h e c o m p u t e r p r o g r a m g i v e n i n T a b l e I X . T h e n o m e n c l a t u r e u s e d i n t h e p r o g r a m i s e x p l a i n e d i n t h e k e y g i v e n i n T a b l e V I I I . S i n c e some o f t h e v a r i a b l e s u s e d i n t h e s a m p l e c a l c u l a t i o n a r e n o t r e f e r r e d t o e x c e p t i n t h i s a p p e n d i x , i t i s c o n v e n i e n t t o u s e t h e p r o g r a m n o m e n c l a t u r e . C . 4 . 2 T h e I n p u t D a t a T h e f o l l o w i n g e x p e r i m e n t a l d a t a a r e r e q u i r e d t o i d e n t i f y e a c h e x p e r i m e n t a l r e s u l t a n d s p e c i f y t h e e x p e r i m e n t a l c o n d i t i o n s . ] .00 0 . 9 8 L cr 0 , 9 6 LU CXL CH O O 0 . 9 4 L cr CtL CQ cr o 0 . 9 2 0 . 9 0 1 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 MOLE F R A C T I O N OF N I T R O G E N 1 0 F i g u r e C l C a l i b r a t i o n c o r r e c t i o n r a t i o f o r n i t r o g e n , ammonia, 0.79 m i c r o n d i a m e t e r p a r t i c l e s . The t r i a n g l e s denote mean v a l u e s f o r a g i v e n mole f r a c t i o n . 196. T a b l e V I I I K e y t o C a l c u l a t i o n P r o g r a m N o m e n c l a t u r e P r o g r a m S y m b o l i n I - . - I . I _ -, . J . . E x p l a n a t i o n n o m e n c l a t u r e t e x t ^ A - C o n s t a n t i n e q u a t i o n f o r c a l i -b r a t i o n c o r r e c t i o n r a t i o . B - C o n s t a n t i n e q u a t i o n f o r c a l i -b r a t i o n c o r r e c t i o n r a t i o . C - C o n s t a n t i n e q u a t i o n f o r c a l i -b r a t i o n c o r r e c t i o n r a t i o . 3 D c M o l a r d e n s i t y , K g m o l e / m . DC - C o l u m n d i a m e t e r , , m . 2 D I F F D D i f f u s i v i t y , m / s e c . 3 DM P M a s s d e n s i t y K g / m . DP - P a r t i c l e d i a m e t e r , m . DPMU - P a r t i c l e d i a m e t e r , m . D R I V E - L o g mean m a s s t r a n s f e r d r i v i n g f r c e . F r a c t i o n a l m o l a r r e m o v a l o f t o t a l g a s . F r a c t i o n a l m o l a r r e m o v a l o f t r a n s f e r r e d g a s . C o r r e c t e d p a r t i c l e r e m o v a l e f f i c i e n c y . E x p e r i m e n t a l v a l u e f o r p a r t i c l e r e m o v a l e f f i c i e n c y . E f f i c i e n c y p r e d i c t i o n f o r mean m a s s v e l o c i t y m o d e l . E f f i c i e n c y p r e d i c t i o n f o r mean m o l a r v e l o c i t y m o d e l -EMO EMT EPCORR e P E P E X P EPMA E m a c o n t i n u e d 197. T a b l e V H I / c o n t ' d Program Symbol i n „ n , . -i , , , E x p l a n a t i o n n o menclature t e x t ^ EPSW e g w E f f i c i e n c y p r e d i c t i o n f o r S c h m i t t and Waldmann model. F - C a l i b r a t i o n c o r r e c t i o n r a t i o . FILM - Mass t r a n s f e r f i l m t h i c k n e s s , m. FILMR - R a t i o o f f i l m t h i c k n e s s t o column r a d i u s . FLUX N Mass t r a n s f e r f l u x , Kg mole/ m2 sec . FR - E x p e r i m e n t a l p e n e t r a t i o n . FRCORR P C o r r e c t e d p e n e t r a t i o n . GAS - C h e m i c a l f o r m u l a f o r gas . G G Gas molar f l o w r a t e Kg mo l e / s e c . KN Kn Knudsen number. MTC ' - Mass t r a n s f e r c o e f f i c i e n t m/sec . N - I d e n t i f i c a t i o n number f o r gas . NLINE - L i n e c o u n t e r f o r p a g i n g . P - . Mean f r e e p a t h , m. PR P P r e s s u r e , atm. 3 Q - V o l u m e t r i c f l o w r a t e , m / s e c . 3 RATE - T o t a l mass t r a n s f e r r a t e , m / s e c . RE Re Reynolds number. RMA - R a t i o o f i n e r t gas t o t r a n s f e r r e d gas m o l e c u l a r w e i g h t s . RSW - , Square r o o t o f r a t i o o f i n e r t gas t o t r a n s f e r r e d gas m o l e c u l a r weights. c o n t i n u e d 198. T a b l e V H I / c o n t ' d Program Symbol i n E x p l a n a t i o n nomenclature t e x t RUN - Run i d e n t i f i c a t i o n number. SQ - Square r o o t o f m o l e c u l a r w e i g h t , (g/g m o l e ) ^ . T - Temperature, °K. TYPE - Type o f e x p e r i m e n t . U - Mean a x i a l v e l o c i t y , m/sec. UR - R a t i o of r a d i a l v e l o c i t y i n f i l m t o mean a x i a l v e l o c i t y . URAD - R a d i a l v e l o c i t y i n f i l m , m/sec. V y V i s c o s i t y , K g / m s e c . VERBAL - V e r b a l message c o n c e r n i n g d a t a i n t a b l e . V3 - Cube r o o t o f m o l e c u l a r volume, (m/g mole) 1/3. W M M o l e c u l a r w e i g h t , g/g mole. Y Y Mole f r a c t i o n . ZC - Column l e n g t h , m. P o s t s c r i p t s -INT V a l u e f o r i n e r t g a s . -TRN V a l u e f o r t r a n s f e r r e d gas . -MIX V a l u e f o r gas m i x t u r e • - I V a l u e a t gas i n l e t . -0 V a l u e a t gas o u t l e t . -LM V a l u e where the mass t r a n s f e r d r i v i n g f o r c e e q u a l s t h e l o g mean d r i v i n g f o r c e o v e r the column. 199 . TABLE IX L i s t i n g o f C a l c u l a t i o n Program 1 C 2 C PROGRAM CORRECTS EXPERIMENTAL PARTICLE 3E30VAL 3 C EFFICIENCY, AND GENERATES CORRESPONDING I'd E03ETICAL 4 c VALUES, PLUS OTHER SIGNIFICANT PARAMETERS. 5 c 6 INTEGER RUN 7 REAL KN,MTC 8 3EAL*8 GAS(10),VEREAL(8),GASINT,GAST3N 9 DIMENSION W (10) ,DM (10) ,V (10) ,? (10) ,V3 (10) 10 c 11 c SET CONSTANTS 12 c 13 N = 10 14 DC=0.0254 15 1=293.0 16 PR=1.0 17 c 18 c READ GAS PROPERTIES. 19 c 20 READ(2,201) (GAS (I) ,1=1,N) 21 201 FORMAT(10 A8) 22 READ(2, 202) (W (I) ,1=1,N) 23 202 FORMAT(10?15.0) 24 READ(2,2C2) (DM (I) , 1- 1, N) 25 READ (2,202) (V(I) ,1=1,N) 26 READ(2,202) (P(I) ,1=1,N) 27 3EAD(2,202) (V3 (I) , 1= 1 , N) 28 c 29 c READ GENERAL EXPERIMENTAL CONDITIONS. 30 c 31 READ(1,105) (VERBAL (I) ,1=1 ,8) 32 105 PORMAT(8A8) 33 HEAD(1,103)DP,ZC 34 103 FORMAT(2F15.0) 35 3EAD(1,104)NINT,NTSN 36 104 F0RMAT(2I2) 37 READ (1,106) AI,BI,CI,AO,BO,CO 38 106 FORMAT (6F1 5. 0) 39 c •, 40 c SET GAS PROPERTIES AND OTHER VARIABLES. 41 c 42 DPMU=DP*1.02+06 43 GASINX=GAS (NINT) 44 GASTHN=GAS (NTRN) 45 HINT=W (NINT) 46 WTPN=W (NTRN) 47 SQWINT= HINT**.5 48 SQWTRN=WTRN**.5 49 DKINT=DH (NINT), 50 DKTPN = DM (NTRN) 51 VINT=V(NINT) 52 VTRN=V(NTRN) 53 ?INT=P (NINT) 54 PTRN=P (NTRN) 55 V3INT=V3 (NINT) 56 V3TRN=V3(NTRN) 57 DMIX= DMINT/HINT 58 3MA = HINT/WT3N 200. 59 RSW =(WINT/WTRN)**.5 6 0 AREA=3.14159*DC*ZC 6 1 C 6 2 C CALCULATE DIFFUSIVITY BY GILLILAND'S METHOD. 6 3 C 61 DIFF=0.4 3E-10*T**1.5/PR/(V3INT+V3TRN) * * 2 65 1*(1./VINT+1./WTRN)**0.5 6 6 C 67 C WRITS TITLE AND GAS PROPERTIES. 6 8 C 6 9 • WRITE{6,601) 70 601 FORMAT(•1•///' ',6X,26X,'TABLE'/) 7 1 WRITE (6,615)GASINT,GASTRN,DPMU 72 615 FORKATC ',6X,'DATA FOR ',A8,', • , 7 3 1A8,', ',F5.3,' MICRON DIAMETER PARTICLES..') 74 WRITE(6,621) 75 621 FORMAT(' ' , 6X ,•******************************• t 77 WRITE (6,620) (VSR3AL (I) ,1=1,8) 78 620 FORMAT (• ',6X,8A8) 79 WRITE(6,608) T,PR 80 603 FORMAT (' ' , 6 X, ' INLET TEMP. (DEG. K) »,1PG11..4, 81 1', PRESSURE (ATM.) ',1PG11.4/) 82 WRITS(6,622)AI,BI,CI,AO,SO,CO 8 3 622 FORMAT(' ',6X,•CALIBRATION CORRECTION: COUNT/TROE COUNT'/ 84 1' •,6X,'INLET: ', 8 5 2F7.4,' • • ,F7. 4, ••YINTI • ',F7.4,'*YTRNI/YINTI«/ 8 6 3' ',6X,'OUTLET: 87 4F7.4," + • ,F7.4, '*YINTO • • , F7. 4, « *YTRNO/Y INTO • /) 33 WRITE(6,602)GASINT,GASTRN 89 602 FORMAT(' ' , 6 X , ' G A S •,15X,2(7X ,A8)) 90 WRITS(6,609) 91 609 FORMAT(• ',6X,30X,' (INERT) 92 1' (TRANSFERRED)•/) 93 WRITE(6,614) WINT,WTRN 94 614 FORMAT (' 1 , 6X,•KOLEC. WEIGHT 95 1'(G/GMOLE) •,2 (4X , 1PG11.4)) 96 WRITE(6,603)DMINT,DMTRN 97 603 F 0 R M A T (' ' ,6X,1 DENSITY 9 8 1'(KG/M**3) •,2 (4X,1PG11.4)) 99 KRI?E(6,604)VINT,VTRN 100 604 FORMAT(' •,6X,•VISCOSITY ', 101 V(KG/M/SEC) •,2 (4X, 1PG11.4)) 102 WRITE(6,605)PINT,PTRN 103 605 FOSMATC ',6X,':iEAN FREE PATH ', 104 1 * (M) •,2(4X,1PG11.4)) 105 WRITE(6,606)V3INT,V3TRN 106 606 FORMAT (' • ,6X,'VCLUME** (1/3) ', 107 1 • (K/GMOLE** (1/3) ) ' , 3X, 1 PG 1 1. 4 , 4X, 1 PG 11 . 4/) 108 WRITE (6,607) DIFF 109 607 FORMAT(' ',6X,'DIFFUSIVITY 110 1' (K**2/SEC) •,1IX,1PG11.4/) 111 C 112 C SET LINE COUNTER 113 C 114 NLINE=32 1 1 5 4 CONTINUE 1 1 6 C 201. 117 C WRITE HEADINGS. 118 C 119 WRITE (6,612) 120 612 FORMAT(* »,6X,«RUN 'YINTI ',• EPEXP t f 121 1' EPMO • ,' Q.INT FILMR SEI MTC 122 WRITE (6,613) 123 613 FORMATC '^Xj'TYPE ','YINTO ',« EPC02R i 9 124 1' EPSW •,• PLM ',• KN REO ') 125 WRITE (6,616) 126 616 FORMATC ' ,6 X, 6 X , ' YINTLM EMT •, 127 1' EPMA ULM ',* UR HELM V ) 128 c 129 c CALCULATION LOOP. 130 c 131 1 CONTINUE 132 READ(1,101)RUN,QINT,YINTO,YINTI,EPEXP,TYPE 133 101 FORMAT(15,F6.0,2F5.4,F10.0,A4) 134 IF (RUN .SQ. 0)GO TO 2 135 c 136 c CONVERT QINT TO S.I. UNITS. 137 c 138 QINT=QINT*1.0E-06 139 c 140 c CORRECT EXPERIMENTAL PARTICAL REMOVAL EFFICIENCY. 141 c 142 FR=1.-EPEXP 143 FI=AI + BI*YINTH-CI* (1.-YINTI) /YINTI 144 F0=A0+30*YINT0+C0* (1.-YINTO)/YINTO 145 FRCORR=FR*FI/FO 146 EPCORR=1.-FRCORR 147 c 148 c CALCULATE THEORETICAL REMOVAL EFFICIENCIES. 149 c 150 EMO=1.-YINTI/YINTO 151 EPMO=SMO 152 EPMA=1. - (1.-EMO) * (1 .+ YIKTO*(RMA-1 . ) ) / (1..+ Y INTI * (RM A- 1. )) 153 EPSW=1. - (1 . -EMO) * (1. +YIHTO* (RSW-1.))/(1.+YINTI*{RSW-1. )) 154 c 155 c CALCULATE MASS TRANSFER RATE,.DRIVING FORCE, 156 c MASS TRANSFER COEFFICIENT, FLUX, 157 c LOG MEAN DRIVING FORCE CONDITION, 158 c FILM THICKNESS, RATIO FILM THICKNESS TO 159 c COLUMN 'DIAMETER, AND MASS TRANSFER EFFICIENCY.. 160 c 161 RAT2=QINT*(1./YINTI-1./YINTO) 162 DRIVE = -(ALOG(YINTI)-ALOG (YINTO))/ 163 1ALOG{ALOG (YINTI) /ALOG (YINTO)) 164 MTC=EATE/DRIVE/AREA 165 FLUX=RATE*DHIX/AREA 166 YINTLM=EXP(-DRIVE) 167 FILMLM=-DIFF*DMIX/FLUX*ALOG(YINTLM) 168 FILKR=FILMLM*2./DC 169 EMT=(1./YINTI-1./YINTO)/(1./YINTI-1.) 170 c 171 c CALCULATE INLET PEYNOLDS NUMBER. 172 c 173 YINT=YINTI 174 Y TRN=1.-YlNT 202 • 175 GINT=QINT* DMINT/WINT 176 GMIX=GINT/YINT 177 WMIX=WINT*YINT+WTRN*YTRN 178 VMIX = (YTRN*SQWTRN*VTRN + YINT*SQWINT*VINT) / 179 1(YTP.N*SQWTRN + YINT*SQWINT) 180 U=GKIX/DMIX*1. 2732/DC/DC 181 REI=DC*DMIX*U/VMIX*WMIX 182 C 183 C CALCULATE OUTLET REYNOLDS NUMBER. 184 C 185 YINT=YINTO ' 186 YTRN=1.-YINT 187 GINT=QINT*DMINT/WINT 188 GMIX=GINT/YINT 189 WMIX=WINT*YINT+WTRN*YTRN 190 VKIX=(YT3N*SQW?RN*VT3N+YINT*SQWIKT*VINT,/ 191 1 (YT?.N*SQWT?.N+YINT*SQWINT) 192 U = G!'.IX/DKIX*1. 2732/DC/DC 193 RSO=DC*DMIX*U/VMIX*WMIX 194 C 195 C CALCULATE REYNOLDS NUMBER AT LOG MEAN CONDITION. 196 C 197 YINT=YINTLM 198 YTRN=1.-YlNT 199 GINT=QINT*DMINT/HINT 200 GMIX=GIHX/YINT 201 WMIX="»'INT*YINT + WTRN*YTRN 202 VMIX= (YTF.N*SQWT3N*VTRN + YINT*SQWINT*VINT) / 203 1(YTRN*SCMTRN+YINT*SQWINT) 204 U=GMIX/DMIX*1.2732/DC/DC 205 R2LK=DC*DMIX*U/VMIX*tfMIX 206 ULM=U 207 C 208 C CALCULATE RATIO OF RADIAL VELOCITY AT EDGE OF FILM 209 C TO MEAN AXIAL VELOCITY AT LOG MEAN CONDITION.. 210 C 211 UF.AD=WTRN*FLUX/WMIX/DMIX 212 UR=URAD/U 213 C 214 C CALCULATE RATIO OF GAS MEAN FREE PATH AT 213 C LOG MEAN CONDITION TO PARTICLE RADIUS. 216 C 217 PLK=VMIX/DMIX/WMIX/ 218 1 ( YINT*VI NT/DMINT/P.TNT +YTRN*VT3 N/DMTRN/PTRN) 219 KN=PLM*2./DP 220 C 221 C WRITE RESULTS. 222 C 223 WRITS(6,610)RUN,YINTI,EPEXP,E?MO,3INI,FILMH,REI,MTC 224 610 FORMAT{' •,6X,15,1X,F6.4,1X,F7.4,1X,FS.4,1X, 225 11PG10.4,1X,0P?6.4,1X,F5.0,1X,1PG10.4) 226 WRITE (6,61 1) TYPE, Y INTO , EPCORR , EPS'W , PLH ,KN, SEO 227 611 FORM AT ( 1 • , 6 X, f.U , 2X , F6 . 4 , 1 X , F7 . 4 , 1 X, c 6 . 4 , 1 X, 228 11PG10.4,1X,0PF6". 4,1 X ,F 6.0,1 X) 229 WRITE(6,617) YINTLM , E.1T , EPM A, ULK, U ?., R2LN 230 617 FOR MAT ( ' • , 6 X,6X , F6. 4 , 1 X , F7. 4 , 1X , F6..4 , 1X, 231 11PG 10.4,1X,0PF6.4,1X,F6.0,IX) 232 C 203 . 233 . C CHECK FOR BOTTOM OF PAGE. 234 C 235 NLINE=NLINE*3 236 IF (N LIN E .GT. 56)GO TO 3 237 GO TO 1 238 C 239 C PAGE ADVANCE. 240 C 241 3 CONTINUE 242 WRITS (6,619)GASINT,GASTRN,DPMD 243 619 FORMAT ('1 •///* ',6X,A8,', '^8,', *,F5.3, 244 1 ' MICRON D. PARTICLES (CONTINUED).,'/) 245 NLINE=9 246 GO TO 4 247 2 CONTINUE 248 WRITE (6,618) 249 618 FORMAT (' 1«) 250 STOP 251 END 2 0 4 . Run n u m b e r (RUN) 35011 T y p e o f e x p e r i m e n t (TYPE) I C - 4 3 I n e r t g a s v o l u m e t r i c f l o w r a t e (QINT) 6 x 10 m / s e c I n e r t g a s m o l e f r a c t i o n a t i n l e t ( Y I N T i ) 0 . 5 0 4 0 I n e r t g a s m o l e f r a c t i o n a t o u t l e t (YINTO) 0 . 7 8 6 0 R e c o r d e d e x p e r i m e n t a l e f f i c i e n c y ( E P E X P ) 0 . 3 0 7 4 T h e v a l u e o f t h e v a r i a b l e T Y P E i n d i c a t e s t h e s o r t o f e x p e r i m e n t i n w h i c h t h e d a t a w e r e t a k e n . V a l u e s u s e d a r e : I F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t . T I n l e t f l o w r a t e o f t r a n s f e r r e d g a s h e l d c o n s t a n t . C I n l e t g a s c o m p o s i t i o n h e l d c o n s t a n t . 1 2 , 1 3 F l o w r a t e o f i n e r t g a s h e l d c o n s t a n t a t a d i f f e r e n t v a l u e t h a n t h a t u s e d i n t h e o t h e r e x p e r i m e n t ( s ) . C o m b i n a t i o n s T h e d a t a b e l o n g t o m o r e t h a n o n e t y p e o f l e t t e r s o f e x p e r i m e n t . O t h e r g e n e r a l d a t a i s r e q u i r e d f o r t h e w h o l e s e r i e s o f e x p e r i m e n t s . ( i ) D i m e n s i o n a l d a t a . P a r t i c l e d i a m e t e r (DC) 0 . 7 9 ym C o l u m n l e n g t h (ZC) 0 . 7 7 ym ( i i ) P h y s i c a l p r o p e r t i e s o f t h e g a s e s u s e d . T h e s e p r o p e r t i e s , w h i c h a r e s h o w n i n T a b l e X t o g e t h e r w i t h t h e i r s o u r c e s , m u s t b e k n o w n i n o r d e r t o c a l c u l a t e t h e t h e o r e t i c a l p a r t i c l e r e m o v a l e f f i c i e n c i e s , a n d t h e p h y s i c a l p r o p e r t i e s o f t h e g a s m i x t u r e . ( i i i ) T h e c o u n t e r c a l i b r a t i o n c o r r e c t i o n . I t was f o u n d t h a t t h e c a l i b r a t i o n c o r r e c t i o n r a t i o T a b l e X P h y s i c a l P r o p e r t i e s o f G a s e s a t 1 a t m . a n d 2 0 ° C . Gas M o l e c u l a r W e i g h t D e n s i t y ( c a l c u -l a t e d f r o m t h e i d e a l g a s law) D e n s i t y ( a c t u a l ) V i s c o s i t y M e a n f r e e p a t h ( e s t i m a t e d f r o m t h e v i s c o s i t y ) C o l l i -s i o n d i a m e -t e r K g / m 3 K g / m 3 K g / m s e c - 5 * 10 , . - 8 m * 10 m * 1 0 ~ 1 0 a m m o n i a 1 7 . 0 3 0 . 7 0 7 9 0 . 7 1 8 2 ( a ) 0 . 9 8 2 ( c ) 4 . 5 7 2 . 6 2 4 ( a ) a r g o n 3 9 . 9 1 1 . 6 3 4 1 1 . 6 6 1 1 ( a ) 2 . 2 1 7 ( c ) 6 . 7 8 3 . 4 1 8 ( a ) f r e o n 12 ( d i f l u o r o -d i c h l o r o m e t h a n e ) 1 2 0 . 9 3 5 . 0 2 7 0 5 . 1 3 6 1 ( b ) 1 . 2 5 (b) 2 . 1 8 5 . 1 1 0 ( a ) h e l i u m 4 . 0 0 0 . 1 6 6 3 0 . 1 6 4 8 ( a ) 1. 9 4 ( c ) 1 8 . 8 6 2 . 7 0 (a) m e t h a n e 16 . 0 3 0 . 6 6 6 4 0 . 6 6 7 8 ( a ) 1 . 0 8 7 ( c ) 5 . 2 5 3 . 8 8 2 ( a ) n i t r o g e n 28 . 0 2 1 . 1 6 4 8 1 . 1 6 5 3 ( a ) 1 . 7 4 8 ( c ) 6 . 3 9 3 . 6 8 1 ( a ) t r i m e t h y l a m i n e 5 9 . 1 1 2 . 4 5 7 2 2 . 5 1 (b) 0 . 7 5 3 ( d ) 1 . 8 8 5 . 3 5 2 ( e ) S o u r c e : (a) P e r r y (1963) (b) M a t h e s o n d a t a b o o k (1966) (c) H a n d b o o k o f P h y s i c s a n d C h e m i s t r y (1970) (d) E s t i m a t e d b y B r o m l e y - W i l k e m e t h o d , s e e P e r r y (196 3) (e) E s t i m a t e d f r o m m o l a l v o l u m e d a t a , s e e P e r r y (196 3) 206. c o u l d a l w a y s b e e x p r e s s e d a s a l i n e a r f u n c t i o n o f g a s c o m p o s i t i o n , i n o n e o f two f o r m s . T h i s f u n c t i o n i s s h o w n i n e a c h t a b l e i n A p p e n d i x D , a n d v a r i e s w i t h b o t h g a s s y s t e m a n d p a r t i c l e s i z e . W h e r e t h e i n l e t c o u n t s w e r e made w i t h t h e t r a n s f e r r e d g a s a b s e n t , o n l y a n o u t l e t c o r r e c t i o n i s s h o w n . U s i n g t h e c a l i b r a t i o n c o r r e c -t i o n f u n c t i o n , t h e c o r r e c t e d p a r t i c l e r e m o v a l e f f i c i e n c y (EPCORR) c a n b e c a l c u l a t e d f r o m t h e e x p e r i m e n t a l v a l u e ( E P E X P ) . C . 4 . 3 C a l c u l a t i o n o f G a s M i x t u r e P r o p e r t i e s P h y s i c a l p r o p e r t i e s o f t h e g a s m i x t u r e m u s t b e d e t e r -m i n e d a s i n t e r m e d i a t e s t e p i n t h e c a l c u l a t i o n o f o t h e r p a r a m e t e r s s u c h a s K n u d s e n a n d R e y n o l d s n u m b e r s . T h e f o l l o w i n g c a l c u l a t i o n i d e n t i t i e s w e r e u s e d . ( i ) M o l e c u l a r w e i g h t . WMIX = WINT * Y I N T + WTRN * YTRN ( i i ) D e n s i t y . DMMIX = DMIX*WMIX ( i i i ) V i s c o s i t y . „-,-,-_, YTRN * V T R N * /WTRN + Y I N T * V I N T * /WINT VMIX = -----2 YTRN * /WTRN + Y I N T * /WINT T h e f o r m u l a i s t a k e n f r o m P e r r y ( 1 9 6 3 ) , a n d i s n o r m a l l y a c c u r a t e t o w i t h i n 2%. 207, ( i v ) D i f f u s i v i t y . D.FF - 4.3 * 10 1 0 „ £ f J-L? + ^ R N PR[ (VINT) 1 / / 3 + ( V T R N ) 1 / / 3 j T h i s r e l a t i o n was s u g g e s t e d by G i l l i l a n d , and i s g i v e n by P e r r y (1963) . (v) Mean f r e e p a t h . = VMIX DMMIX YINT * VINT YTRN * VTRN DMINT * PINT DMTRN * PTRN The f o r m u l a f o r t h e gas mean f r e e p a t h , L . , was d e r i v e d f r o m an c mix a p p r o x i m a t i o n r e l a t i n g i t t o t h e m i x t u r e v i s c o s i t y , P m ; j _ x f t h e d e n s i t y , p . , and t h e mean m o l e c u l a r v e l o c i t y i n t h e m i x t u r e mix c • mix y . = 0.499 p . c . L . mix mix mix mix H e r e , t h e mean m o l e c u l a r v e l o c i t y i s o b t a i n e d f r o m t h e r e l a t i o n C m i x = Y l C l + Y 2 C 2 ' where c ^ and c2 a r e t h e component m o l e c u l a r v e l o c i t i e s . The r e l a t i o n s h i p i s a n a l o g o u s t o t h a t f o r a p u r e gas (see f o r example, Chapman and C o w l i n g (1964)). y = 0.499 p c L 208. C.4.4 C a l c u l a t i o n o f the P a r t i c l e Removal E f f i c i e n c y The c o r r e c t e d e f f i c i e n c y i s o b t a i n e d from t h e raw e f f i c i e n c y , u s i n g t h e f o r m u l a EPCORR = 1 - (1 - EPEXP) FI/FO where F I and FO a r e the i n l e t and o u t l e t c o r r e c t i o n r a t i o s . Run 35011 was made u s i n g t h e t e c h n i q u e where t h e bottom r e a d i n g i s t a k e n w i t h t h e t r a n s f e r r e d gas s h u t o f f . T h i s can be deduced from T a b l e XVI, s i n c e no c a l i b r a t i o n c o r r e c t i o n i s i n d i c a t e d a t th e gas i n l e t . The t r u e t o p c o u n t i s s l i g h t l y g r e a t e r t h a n t h e r e c o r d e d c o u n t , so t h a t the t r u e removal e f f i c i e n c y i s s l i g h t l y l o w er t h a n t h e u n c o r r e c t e d v a l u e . EPCORR = 1 - (1 - 0.3074) 1/0.9784 = 0.2921 C.4-5 C a l c u l a t i o n o f t h e T h e o r e t i c a l V a l u e s f o r P a r t i c l e Removal  E f f i c i e n c y Three t h e o r e t i c a l v a l u e s f o r t h e removal e f f i c i e n c y were c a l c u l a t e d , based on t h e measured i n l e t and o u t l e t i n e r t gas c o n c e n t r a t i o n s (YINTI and YINTO), and t h e gas component m o l e c u l a r w e i g h t s . These were d e r i v e d from the t h r e e models g i v e n i n Chapter 4, i n w h i c h t h e p a r t i c l e was assumed t o move w i t h t h e l o c a l mean mass v e l o c i t y o f the f l u i d (EPMA), the l o c a l mean molar v e l o c i t y (EPMO), o r t h e v e l o c i t y s u g g e s t e d by S c h m i t t and Walmann (EPSW). 209 . C.4.6 C a l c u l a t i o n o f O t h e r P a r a m e t e r s M o s t o f t h e s e p a r a m e t e r s w e r e c a l c u l a t e d b e c a u s e t h e i r v a l u e s i n d i c a t e w h e t h e r a d i v e r g e n c e m i g h t b e e x p e c t e d b e t w e e n t h e d a t a a n d t h e mean m a s s v e l o c i t y m o d e l p r e d i c t i o n s . W i t h t h e e x c e p t i o n o f t h e i n l e t a n d o u t l e t R e y n o l d s n u m b e r s ( R E I a n d R E O ) , t h e p a r a m e t e r s w e r e c a l c u l a t e d f o r a mean g a s c o m p o s i t i o n , w h i c h was r e p r e s e n t a t i v e o f t h e mean c o n d i t i o n s i n t h e c o l u m n . S i n c e t h e t o t a l m a s s t r a n s f e r was n o t a l i n e a r f u n c t i o n o f d i s t a n c e f r o m t h e b a s e o f t h e c o l u m n , a s i m p l e a v e r a g e o f i n l e t a n d o u t l e t c o n c e n t r a t i o n s d i d n o t y i e l d a s a t i s f a c t o r y m e a n . I n s t e a d , t h e mean was t a k e n t o o c c u r a t t h e p o s i t i o n w h e r e t h e l o c a l m a s s t r a n s f e r d r i v i n g f o r c e ( a s s u m i n g n e g l i g i b l e l i q u i d p h a s e r e s i s -t a n c e ) e q u a l e d t h e l o g mean d r i v i n g f o r c e o v e r t h e c o l u m n . T h e c o n c e n t r a t i o n a t t h i s p o i n t f o r t h e i n e r t g a s , Y I N T L M , i s g i v e n b y t h e f o l l o w i n g e q u a t i o n s . D R I V E = - l " l n ( Y I N T I ) ~ l n ( Y I N T O ) ] l n [ l n ( Y I N T I ) / l n ( Y I N T O ) ] Y I N T L M = E X P ( - D R I V E ) F o u r m a j o r p a r a m e t e r s w e r e c a l c u l a t e d a t t h i s mean c o n c e n t r a t i o n . ( i ) T h e R e y n o l d s n u m b e r ( R E L M ) . A n y p a r t i c l e l o s s e s , o t h e r t h a n b y d i f f u s i o p h o r e s i s , w e r e p r o b a b l y a t t r i b u t a b l e t o i n e r t i a l d e p o s i t i o n . F o r a g i v e n p a r t i c l e s i z e , t h e s e l o s s e s s h o u l d i n c r e a s e a s t h e R e y n o l d s 210. number i n c r e a s e s . ( i i ) The Knudsen number (KN). The o n s e t o f t r a n s i t i o n b e h a v i o u r i s dependent on the v a l u e o f t h e Knudsen number. As t h i s number i n c r e a s e s , i n c r e a s i n g d e v i a t i o n s from l a r g e . p a r t i c l e b e h a v i o u r can be e x p e c t e d . ( i i i ) The r a t i o o f f i l m t h i c k n e s s t o column r a d i u s (FILMR). When t h i s r a t i o becomes s i g n i f i c a n t , t h e f i l m t h e o r y o f p a r t i c l e d e p o s i t i o n no l o n g e r h o l d s . However, i n t h e more g e n e r a l t h e o r y t h e f i l m t h i c k n e s s has no i n f l u e n c e , and t h e v a l u e o f t h e r a t i o was t h e r e f o r e n o t e x p e c t e d t o be i m p o r t a n t . S t a t i s -t i c a l t e s t s on t h e parameter w i l l n o t y i e l d u s e f u l i n f o r m a t i o n because o f i t s v e r y c l o s e c o r r e l a t i o n w i t h Reynolds number. The r a t i o was c a l c u l a t e d u s i n g e l e m e n t a r y mass t r a n s f e r f i l m t h e o r y (see T r e y b a l (196 8 ) ) . ( i v ) The r a t i o o f gas r a d i a l v e l o c i t y i n the f i l m t o mean a x i a l v e l o c i t y (UR). As i n the p r e v i o u s c a s e , t h i s r a t i o r e l a t e s t o p o s s i b l e breakdown o f t h e f i l m model, b u t i n t h i s i n s t a n c e i t i s due t o i m p e r f e c t m i x i n g i n t h e gas c o r e a t v e r y h i g h mass t r a n s f e r r a t e s . A g a i n , t h e more g e n e r a l t h e o r y i n d i c a t e s t h a t t h e parameter i s n o t i m p o r t a n t , and t h e c l o s e c o r r e l a t i o n w i t h Reynolds number makes s t a t i s t i c a l t e s t i n g i m p o s s i b l e . The r a t i o was c a l c u l a t e d u s i n g t h e r a d i a l gas mean mass v e l o c i t y a t t h e edge o f t h e f i l m a d j a c e n t t o t h e t u r b u l e n t c o r e , which can be d e t e r m i n e d from e l e m e n t a r y f i l m t h e o r y (see T r e y b a l ( 1 9 6 8 ) ) . Other parameters c a l c u l a t e d o n l y f o r t h e i r g e n e r a l i n t e r e s t were t h e mass t r a n s f e r c o e f f i c i e n t (MTC), and t h e mass 2 1 1 . t r a n s f e r e f f i c i e n c y e x p r e s s e d i n t e r m s o f t h e f r a c t i o n a l m o l a r r e m o v a l o f t h e t r a n s f e r r e d g a s ( E M T ) . C . 4 . 7 T h e C o m p u t e d R e s u l t s T h e o u t p u t o f t h e p r o g r a m i s t h e t a b u l a t e d d a t a i n A p p e n d i x D . F o r e a c h e x p e r i m e n t a l r e a d i n g t h e f o l l o w i n g i n f o r m a -t i o n i s g i v e n . Run n u m b e r (RUN) 35011 T y p e o f e x p e r i m e n t (TYPE) I C - 4 3 I n e r t g a s v o l u m e t r i c f l o w r a t e (QINT) 6 x 10 m / s e I n e r t g a s m o l e f r a c t i o n a t i n l e t ( Y I N T I ) 0 . 5 0 4 0 I n e r t g a s m o l e f r a c t i o n a t o u t l e t (YINTO) 0 . 7 8 6 0 R e c o r d e d e x p e r i m e n t a l e f f i c i e n c y ( E P E X P ) 0 . 3 0 7 4 C o r r e c t e d e x p e r i m e n t a l e f f i c i e n c y ( E P C O R R ) 0 . 2 9 2 1 M e a n mass v e l o c i t y m o d e l p r e d i c t i o n (EPMA) 0 . 2 7 0 7 M e a n m o l a r v e l o c i t y m o d e l p r e d i c t i o n (EPMO) 0 . 3 5 8 8 S c h m i t t a n d W a l d m a n n v e l o c i t y m o d e l p r e d i c t i o n (EPSW) 0 . 3 1 4 0 I n e r t g a s m o l e f r a c t i o n a t t h e mean c o n c e n t r a t i o n (YINTLM) 0 . 6 5 3 8 R a t i o o f f i l m t h i c k n e s s t o c o l u m n r a d i u s a t t h e mean c o n c e n t r a t i o n ( F I L M R ) 0 . 1 1 1 7 G a s mean f r e e p a t h a t t h e mean c o n - o c e n t r a t i o n (PLM) 5 . 8 8 7 7 x 10 K n u d s e n n u m b e r a t t h e mean c o n c e n -t r a t i o n (KN) 0 . 1 4 9 1 2 1 2 Mean a x i a l v e l o c i t y a t t h e mean c o n - 1 . 8 1 1 m/s c e n t r a t i o n (ULM) R a t i o o f r a d i a l v e l o c i t y i n t h e f i l m t o mean a x i a l v e l o c i t y a t t h e mean c o n c e n t r a t i o n (UR) 0 . 0 0 2 7 R e y n o l d s n u m b e r a t t h e mean c o n c e n -t r a t i o n (RELM) 30 39 R e y n o l d s - n u m b e r a t i n l e t ( R E I ) 3 9 5 7 R e y n o l d s n u m b e r a t o u t l e t (REO) 2 5 3 1 M a s s t r a n s f e r c o e f f i c i e n t (MTC) 1 . 6 3 5 8 x 10 m/s M a s s t r a n s f e r e f f i c i e n c y (EMT) 0 . 7 3 2 2 I n a d d i t i o n , t h e p h y s i c a l p r o p e r t i e s o f t h e g a s c o m p o n e n t s a r e g i v e n , a s a r e t h e c a l i b r a t i o n c o r r e c t i o n s u s e d f o r t h e i n l e t a n d o u t l e t g a s . -2 C . 5 E r r o r A n a l y s i s T h e m a g n i t u d e o f p o s s i b l e e r r o r s , a n d t h e i r i n f l u e n c e o n t h e e x p e r i m e n t a l r e m o v a l e f f i c i e n c i e s a n d t h e o r e t i c a l m o d e l p r e d i c t i o n s , a r e c o n s i d e r e d i n t h i s s e c t i o n . ( i ) Random s c a t t e r i n t h e a e r o s o l c o u n t s . T h e s c a t t e r a r o s e f r o m r a n d o m f l u c t u a t i o n s i n a e r o s o l c o n c e n t r a t i o n , a n d f r o m e x p e r i m e n t a l e r r o r s i n d e t e r m i n i n g t h e t i m e f o r a g i v e n v o l u m e o f g a s t o p a s s t h r o u g h t h e g a s m e t e r . T h e l a t t e r c o u l d h a v e b e e n c a u s e d b y e r r o r s i n t h e g a s m e t e r o r b y t i m i n g e r r o r s . S i n c e t h e g a s m e t e r was c l a i m e d t o h a v e a n a b s o l u t e a c c u r a c y o f ±%%, a n d o n l y r e l a t i v e a c c u r a c y b e t w e e n r e a d i n g s was n e c e s s a r y , t h e p o s s i b l e e r r o r f r o m t h i s s o u r c e was e x p e c t e d t o b e s m a l l . T h e t i m i n g e r r o r was e s t i m a t e d a s ± 1 % . N e i t h e r o f 2 1 3 . t h e s e e r r o r s w i l l b e s y s t e m a t i c . Random e r r o r s a r e b e s t t r e a t e d b y s t a t i s t i c a l m e t h o d s ( s e e S e c t i o n C . 6 ) . ( i i ) T h e C a l i b r a t i o n C o r r e c t i o n . T h e p o s s i b l e e r r o r i n t h e c a l i b r a t i o n c o r r e c t i o n r a t i o i s i n d i c a t e d b y t h e s c a t t e r i n t h e d a t a u s e d t o e s t a b l i s h t h e c o r r e c t i o n c u r v e . T h i s e r r o r i n c r e a s e d a s t h e m o l e f r a c t i o n o f t r a n s f e r r e d g a s i n c r e a s e d . H o w e v e r , f o r m a t h e m a t i c a l r e a s o n s , a g i v e n f r a c t i o n a l e r r o r i n t h e c o r r e c t i o n r a t i o l e a d s t o a n a b s o l u t e e r r o r i n t h e m e a s u r e d p a r t i c l e r e m o v a l e f f i c i e n c y w h i c h i s l a r g e s t a t l o w e f f i c i e n c i e s . H e n c e t h e m a g n i t u d e o f t h e e r r o r d e p e n d s i n a c o m p l e x way o n g a s c o m p o s i t i o n . T h e v a l u e s q u o t e d i n T a b l e I V a r e t y p i c a l v a l u e s f o r i n t e r m e d i a t e e x p e r i m e n t a l c o n d i t i o n s . T h e p o s s i b l e e r r o r i n r u n 35011 c a n b e c a l c u l a t e d a s f o l l o w s . S i n c e t h e b o t t o m r e a d i n g was t a k e n w i t h t h e a m m o n i a a b s e n t , t h e c o r r e c t i o n o n l y a p p l i e s t o t h e t o p r e a d i n g . T h e m o l e f r a c t i o n o f n i t r o g e n a t t h e o u t l e t was 0 . 7 8 6 0 . F i g u r e C l i n d i c a t e s t h a t t h e p o s s i b l e p e r c e n t a g e e r r o r i n t h e c o r r e c t i o n r a t i o f o r t h i s m o l e f r a c t i o n i s ^ ± 1 . 5 % . T h e a b s o l u t e e r r o r i n t h e e f f i c i e n c y c a n t h e n b e c a l c u l a t e d EPCORR = 1 - 0 . 6 9 2 6 x 1 / ( 0 . 9 7 4 8 ± 1 . 5 % ) = 1 - (0 . 7 0 7 9 ± 1 . 5 % ) = 0 . 2 9 2 ± 0 . 0 1 1 ( i i i ) E r r o r s i n t h e t h e o r e t i c a l m o d e l p r e d i c t i o n s . T h e s e e r r o r s may h a v e b e e n c a u s e d e i t h e r b y e r r o r s i n 2 1 4 . t h e g a s a n a l y s e s u s e d t o s p e c i f y e x p e r i m e n t a l c o n d i t i o n s , o r b y e r r o r s w h i c h w e r e d u e t o e x t r a n e o u s s p e c i e s b e i n g p r e s e n t i n t h e g a s . T h e s e s p e c i e s w o u l d a r i s e m a i n l y a s i m p u r i t i e s i n t h e g a s e s a s s u p p l i e d . T h e e f f e c t o f p o s s i b l e g a s a n a l y s i s e r r o r s f o r r u n 35011 i s now c a l c u l a t e d . [ ( 0 . 7 8 6 0 ± 0 . 0 0 4 ) 2 8 . 0 2 + ( 0 . 2 1 4 0 ± 0 . 0 0 4 ) 1 7 . 0 3 ] / ( 0 . 7 8 6 0 ± 0 . 0 0 4 ) EPMA = 1 -[ ( 0 . 5 0 4 0 ± 0 . 0 0 4 ) 2 8 . 0 2 + ( 0 . 4 9 6 0 ± 0 . 0 0 4 ) 1 7 . 0 3 ] / ( 0 . 5 0 4 ± 0 . 0 0 4 ) ( 2 5 . 6 6 ± 0 . 0 5 ) / ( 0 . 7 8 6 0 ± 0 . 0 0 4 ) = 1 ( 2 2 . 5 6 ± 0 . 0 5 ) / ( 0 . 5 0 4 0 ± 0 . 0 0 4 ) ( 2 5 . 6 6 ± 0 . 1 9 % ) / ( 0 . 7 8 6 0 ± 0 . 5 1 % ) = 1 ( 2 2 . 5 6 ± 0 . 2 2 % ) / ( 0 . 5 0 40 ± 0 . 7 9 % ) ( 3 2 . 6 4 ± 0 . 3 2 % ) 1 ( 4 4 . 7 6 ± 0.57%) = 1 - ( 0 . 7 2 9 ± 0 . 8 9 % ) = 0 . 2 7 1 ± 0 . 0 0 6 S i n c e t h e e r r o r s i n t h e t e r m s i n t h e n u m e r a t o r a r e i n t e r r e l a t e d , t h e s i g n s m u s t b e t a k e n i n t o a c c o u n t w h e n t h e y a r e c o m b i n e d . T h e same a p p l i e s t o t h e d e n o m i n a t o r e r r o r s . T h e a n a l y s i s i n d i c a t e s t h a t , i n g e n e r a l , t h e a b s o l u t e e r r o r i n t h e e f f i c i e n c y w i l l b e o f t h e o r d e r o f t w i c e t h e a b s o l u t e e r r o r i n t h e g a s a n a l y s i s . T h e 2 1 5 . g a s a n a l y s i s e r r o r was e s t i m a t e d a s ± 0 . 0 0 4 e x c e p t f o r t h e f r e o n 12 r e s u l t s w h e r e i t was t a k e n a s ± 0 . 0 0 8 b e c a u s e o f t h e d i f f i c u l t i e s i n a n a l y s i n g v e r y h i g h i n e r t f r a c t i o n s , a n d t h e v e r y s l i g h t s o l u b i l i t y o f f r e o n 12 i n t h e a b s o r b i n g s o l u t i o n . T h e e r r o r i n t h e mean m a s s v e l o c i t y m o d e l d u e t o t h e p r e s e n c e o f e x t r a n e o u s g a s s p e c i e s was e s t i m a t e d a s f o l l o w s . S u p p o s e t h e f r a c t i o n a l ' i m p u r i t y l e v e l s i n t h e i n e r t a n d t r a n s f e r r e d g a s e s a s s u p p l i e d a r e x a n d y , r e s p e c t i v e l y . A s s u m e t h a t t h e s e i m p u r i t i e s c a n h a v e a m o l e c u l a r w e i g h t o f f r o m ^ t o ±h t i m e s t h e m o l e c u l a r w e i g h t o f t h e p u r e c o m p o n e n t . A s s u m e f o r t h e i n e r t g a s t y p i c a l i n l e t a n d o u t l e t m o l e f r a c t i o n s o f 0 . 5 a n d 0 . 7 5 . T h e e r r o r c a n b e c o n s i d e r e d a s a r i s i n g f r o m t h e m o l e c u l a r w e i g h t o n l y . The i n l e t m o l e c u l a r w e i g h t i s 0 . 5 (WINT ± x ^ y ^ ) + 0 . 5 ( W T R N ± y !!Lii™) I f t h e m o l e c u l a r w e i g h t s o f t h e i n e r t a n d t r a n s f e r r e d s p e c i e s a r e o f t h e same o r d e r , t h e n t h e f r a c t i o n a l e r r o r i n t h e " i n l e t m o l e -c u l a r w e i g h t i s g i v e n b y ± ( x + y ) / 4 . S i m i l a r l y , t h e f r a c t i o n a l e r r o r i n t h e o u t l e t m o l e c u l a r w e i g h t i s ± ( 3 x / 8 + y / 8 ) . S i n c e t h e s i g n s o f t h e s e e r r o r s a r e r e l a t e d f o r e a c h g a s , t h e f r a c t i o n a l e r r o r i n t h e p e n e t r a t i o n i s g i v e n b y t h e d i f f e r e n c e , ± ( x + y ) / 8 . T h i s w i l l t r a n s l a t e i n t o a n a b s o l u t e e r r o r i n t h e p a r t i c l e r e m o v a l e f f i c i e n c y o f u p t o ± ( x + y ) / 8 . E r r o r s o f t h e same o r d e r w i l l a r i s e i n t h e o t h e r two m o d e l p r e d i c t i o n s , ( i v ) O t h e r e r r o r s . I t was n o t p o s s i b l e t o q u a n t i f y t h e e r r o r s a r i s i n g f r o m 216. other sources such as i n e r t i a l d e p o s i t i o n , i s o k i n e t i c e f f e c t s , thermophoretic i n f l u e n c e s , and p a r t i c l e generation i n the column. However, i t was b e l i e v e d t h a t these could not introduce an abso-l u t e e r r o r of more than approximately ±0.015 i n the f r a c t i o n a l p a r t i c l e removal e f f i c i e n c y during normal op e r a t i o n , and the probable e r r o r was expected to be n e g l i g i b l e . Appendix D TABULATED RESULTS A l l e x p e r i m e n t a l r e s u l t s , the c o n d i t i o n s under w h i c h they were o b t a i n e d , and v a r i o u s a s s o c i a t e d parameters such as p r e d i c t e d p a r t i c l e r e m o v a l e f f i c i e n c i e s , a r e l i s t e d i n t h e f o l l o w i n g t a b l e s . A complete e x p l a n a t i o n o f n o t a t i o n used and the r e l e v a n c e o f the v a r i a b l e s appears i n Appendix C. 218. TABLE XI DATA FOR HE , IMH3 , 0.790 MICRON DIAMETER PARTICLES. TRANSFERRED GAS FLDW RATE CONSTANT EXCEPT IM RUM 36493» INLET TEMP. (DEG. K) 293.0 , PRESSURE (ATM.) 1.000 CALIBRATION CORRECTION INLET: loOOOO + 0.0 *YINTI + OUTLET: 1.1800 + -0. 1800#YI NTQ + COUNT/TRUE COUNT 0.0 #¥TRNI/YI\ITI 0.0 *YTRNO/ YINT3 GAS HE (INERT) NH3 (TRANSFERRED) MOLECo WEIGHT DENSITY VISCOS ITY ^EAM FREE PATH V0LUME**(l/3) (G/GMOLE) ( KG/M**3) (KG/M/SEC) ( M l (M/GMQLE**(1/3)) 4.00Q 0.1648 1.941QE-Q5 1.8860E-Q7 2o 2880E-02 17.03 0»7i82 9.8200E-06 4.5700E-08 2.2240E-02 DIFFUSI VITY < M**2/SEC) 5.8859E-05 RUN YINTI EPEXP EPMO OINT FILMR RE I MTC TYPE YINTO EPCORR EPSW PLM KN REQ YINTLM EMT EPMA ULM UR *ELM 36486 0. 3030 0. 6689 0, 6 02 9 2.6100E -04 0.3411 2026. 1.3589E -0 2 0.7630 0.6824 0.7144 6.7740E -08 Oo 1715 320. 0o5369 0.8650 0.7848 0.9594 0.0150 759. 36492 0. 4440 0.5072 0.4464 4. 7900E -04 0.2684 2005. 1.7270E -02 0.8020 0.5242 0.5 788 7.7890E -08 Oo 1972 502. 0.6352 0.8028 0.6760 1.488 0.0132 959. 36491 0.5300 0.4140 0.35 91 6.7600E -04 0.2292 20L9, .2. 0.218 E-0 2 0.8270 0.4317 0.4941 8.5554E -08 0.2166 639. 0.6916 0. 7641 0.6041 1.929 0.0082 1093. 36491 0.5300 0.4402 0.3591 6.7600E -04 0.2292 2019. 2.0218E -02 0»8270 0.4571 0.4941 8.5.554E -08 0.2166 639. 0.6916 0.7641 0.6041 1.929 0.0082 1093. 36490 0.6340 0.3638 0.2398 1.0390E -03 0. 2158 2090. 2.1473E -02 0.8340 0.3823 0.3562 9.4024E -08 0.2380 954. 0.7424 0.6552 0.465 7 2. 762 0.0054 1380. 36490 0.6340 0.3521 0.2398 1.0390E -03 0.2158 2090. 2. 1473E -02 0. 8340 0. 3709 0.3562 9.4024E -08 0.2380 954. 0.7424 0.6552 0.4657 2.762 0.0054 1380. 36489 0.6970 0.2147 0.1857 1.3800E -0.3 0.1889 21 85. 2o 4533E -02 0. 8560 0.2345 0.2899 1.G230E -07 0.2590 1155. 0.7835 0.6130 0.3980 3.476 0.0043 1558o 36489 0.6970 0.2260 0.1857 1.3800E -03 0.1889 2185. 2.4533E -02 0.8560 0.2456 0. 2899 1.0230E -07 0.2590 1155. 0.7835 0. 6130 0.3980 3.476 0.0043 1558. 36488 0.7440 0.1975 0.1429 1.7440E -03 0.1779 2302. 2.6044E -02 0.8680 0. 2161 0.2317 lo0875E -07 0.2753 1386„ 0.8112 0.55 80 0.3316 4.243 Oo 0034 1760. 219. HE , NH3 , 0*790 MICRON D. PARTICLES {CONTINUED}. RUN YINT I EPEXP EPMO Q INT F ILMR RE I MIC TYPE Yl NTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 36488 Oo 7440 0«2046 0.1429 lo7440E- 03 0.1779 2302. 2.6G44E -02 Oo 8680 Oo 2231 0„ 2317 lo0875E- 07 0o2753 1386. Oo81L2 Oo5580 0o3316 4o243 Oo 0034 1760, 36487 Oo 8060 0. 0604 0 o0944 2»4930E- 03 0.1571 2570. 2.9501E -02 0 o8900 Oo0786 Ool614 l o l 9 6 8 E - 07 0 o 3030 1800. 0 o8513 Oo 4.865 0»2462 5.780 0o0024 2129. 36487 0. 8060 0o0869 0o09 44 2. 4930E-03 Oo1571 2 5 70. 2.9501E -02 0o8900 0ol046 0ol614 lo1968E- 07 Oo 3030 1800, Oo 8513 0»4865 0»2462 5«780 0„0024 2129. 36493 0o4340 0.3172 0„ 3364 2 0 OOOOE-03 0,1115 8717» 4.1581E -0 2 0 o6540 0o3572 0»4333 6 08464E-08 Oo173 3 3 730. Oo 5451 Oo 5943 0 C5Q36 7o241 0.0060 5637. 36493 0o4340 0o3975 Oo 3364 2o0000E- 03 0.1115 8717. 4ol581E -02 0o6540 0o4328 0 o4333 6 08464E-08 Oo1733 3730. 0o5451 Oo 5943 Oo 5 03 6 7.241 Oo 006 0 5637. 220 . TABLE X I I DATA FOR CH4 , NH3 , 0.790 MICRON DIAMETER PARTICLES. * * * * * * * * * * * * * * * * * * * * * * * * * * 4 t * f j c * * * * i § t 4 t * * * * INERT GAS FL3W RATE CONSTANT IN ALL RUNS. INLET TEMP. (DEG. K) 293.Q , PRESSURE iATM. ) 1.000 CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: loOOOO + 0.0 *YINTI + 0.0. *YTRNI/YI^TI 3UTLET: 1.0000 + 0.0 *YINTO + 0.0 *YTRNO/Y INTO GAS cm .INERT) MH3 (TRANSFERRED) MOLECo .WEIGHT DENSITY VISCOS ITY MEAN FREE PATH VOLUME**.1/3) (G/GMOLE) {KG/M**3) (KG/M/SEC) (M) <M/GMOLE**(1/3)) 16.03 0.6678 1.0870E-05 5.2500E-08 3.2900E-02 17.03 0.7182 9.8200E-06 4.5 700E-08 2.2240E-02 DIFFUSI VI TY (M**2/SEC) 2.4684E-05 RUN YINT I EPEXP EPMO QINT FILMR MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RE LM 3192 5 0. 4960 0.3186 0.3575 5.9800E- 04 0.1230 4029. 1.5806E-•02 0.7720 0.3186 0.3629 5.0169E- 08 0. 1270 2475, 0.6416 0.7094 0.3682 1.839 0.0040 3042. 3192 5 0.4960 0.3503 0.3575 5.9800E- 04 0.1230 4029. 1.580SE- 02 0.7720 0.3503 0.3629 5. 0169E- 08 0.1270 2475. 0.6416 0.7094 0.3682 1.83 9 0.0040 3042. 31925 0.4960 0.3752 0.3575 5.9800E- 04 0. 123 0 4029. 1.5806E-02 0.7720 0.3752 0.3629 5.0169E- 08 0.1270 2475. 0.6416 0. 7094 0.3682 1.839 0.004 0 3042. 31926 0.6200 0.2524 0.2671 5.9800E- 04 0. 1372 3159. 1.4171E-•02 0.8460 0.2524 0.2722 5.0.322E-08 0.1287 2232. 0.7438 0.703 0 0. 27 72 1. 587 0.0028 2581. 31926 0.6200 0.2397 0.2671 5.9800E- 04 0.1372 3159, i . 4 i 7i e- 02 0.8460 0.2397 0.2722 5.0822E- 08 0.1287 2232. 0.7438 0. 7030 0.2772 1. 587 0.0028 2581. 31927 0.4060 0.4081 0.4233 5.9800E- 04 0.1118 4994, 1.7389E- 02 0. 7040 0.4081 0.4285 4.9640E- 08 0.1257 2744. 0.5579 0.7126 0.4336 2. 115 0. 0050 3 546. 31927 0.4060 0.3995 0.4233 5 o9800E- 04 0.1118 4994. 1.7389E- 02 0.7040 0.3995 0. 428 5 4.9640E- 08 0.1257 2 744. 0.5579 0.7126 0.4336 2.115 0. 0050 3546. 31927 0.7170 0.1948 0.1935 5.9800E- 04 0.1531 2689. 1.2695E- 02 0.8890 0. 1948 0.1977 5. 12 70E-08 0.1298 2109. 0.8131 0.6837 0.2020 1.451 0.0019 2334. 3192 7 0. 7170 0. 1902 0.1935 5.9800E- 04 0.1531 2689. 1.2695E- 02 0.8890 0.1902 0.1977 5. 1270E-08 0.1298 2109. 0.8131 0.6837 0.2020 1.451 0.0019 2334. 221. CH4 , NH3 , 0,790 MICRON D.. PARTICLES (CONTINUED). RUN YI NT I EPEXP EPMO QINT F ILMR RE I MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 31928 0.3460 0.4837 0.4594 5.980QE- 04 0.1068 5917. 1.8201E -02 Oo6400 0.4837 0.4642 4.9226E- 08 0.1246 3050. 0 o4917 0.7024 0*4689 2.400 0.0055 4067, 31928 Oc 3460 0.4744 0.4594 5.9800E- 04 0.1068 5917. 1.3201E -3 2 0o6400 0.4744 0.4642 4. 9226E- 08 Oo 1246 3050. 0o4917 0.7024 0.4689 2.400 0.0055 4067. 31928 0.2520 0.5447 0.5299 5. 9800E-04 0.0904 8249. 2.1504E -02 0 o5360 0.5447 0.5339 4.8574E- 08 0.1230 3704, 0.3861 0. 7084 0.5378 3.056 0.0069 5268. 31928 0.2520 0. 52 93 0 o5299 5.9800E- 04 Oo 0904 8 249» 2.1504E -02 0.5360 0.5293 Q„5339 4.8574E- 08 0.1230 3 704. 0. 3861 0. 7084 0.5378 3.056 0.0069 5268. 222. TABLE XIII DATA FOR N2 , NH3 t 0.7.90 MICRON DIAMETER PARTICLES-******************************************** ***************** PRELIMINARY RUNS. ***************** DATA FOR VARIOUS TYPES OF RUNS, INLET TEMP. {DEGo K) 293.0 , PRESSURE (ATM.) 1.000 CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: 1.0000 + 0.0 *YINTI + -0.0420*YTRNI/YINTI OUTLET: 1.0000 + 0.0 *YINT0 + -0,042Q#YTRNO/YINTO GAS N2 (INERT) NH3 (TRANSFERRED) MOLEC. WEIGHT {G/GMQLE) DENSITY <KG/M**3) VISCOSITY (KG/M/SEC) MEAN FREE PATH (M) V0LUME**U/3) (M/GMQLE**(l/3) ) 28.02 1.165 1.7480E-05 6.3900E-08 3.1190E-02 17.03 0.7182 9.8200E-06 4.570GE-08 2.2240E-02 DIFF USIVITY (M**2/SEC) 2.3212E-05 RUN YINTI EPEXP EPMO QI NT FILMR REI MTC TYPE YINTO EPCORR EPSM PLM KN REO YINTLM EMT EPMA ULM UR RELM 26451 0.4720 0.3002 0.3361 1.1000E- 03 0.0744 7759. 2.4553E -02 T 0.7110 0.3215 0. 2966 5.7979E- 08 0.1468 5124. 0.5950 0. 63 66 0.2577 3.649 0.0025 6128. 26452 0.5090 0.1863 0.3008 1.2400E- 03 0.0726 8096. 2. 5159E -02 TC 0. 7280 0. 206 8 0.2630 5.8402E-•08 0.1479 5642. 0.6225 0.6127 0.2264 3. 931 0.0022 6600. 26454 0.4420 0.3176 0.3695 9.7000E- 04 0.0768 7319, 2.3811E -02 T 0.7010 0.3420 0.3284 5.7662E-•08 0.1460 4583. 0.5745 0.6621 0.2 875 3.332 0.0029 5598. 26455 0.4050 0.2514 0.4018 8.3000E- 04 0.0834 6853. 2.1918E--02 T 0.6 770 0.2832 0.3605 5.7160E- 08 0.1447 4060. Oo 5426 0.6752 0.3185 3.019 0.0033 5077. 26456 0.3550 0.2611 0.4462 6.7000E- 04 0.0932 6340. 1.9605E -02 T 0.6410 0.3010 0. 4055 5.6429E- 08 0.1429 3462. 0.4971 0.6917 0.3630 2.660 0. 0039 4482. 26457 0.4930 0.1886 0,3720 6.0000E-04 0.1076 4047. 1.6982E -02 IC 0.7850 0. 2146 0.3265 5. 8789E-08 0.1488 2534. 0.6480 0.733 7 0.2822 1.827 0.0028 3067. 26459 0.5050 0.2638 0.4121 2.9500E- 04 0.1649 1942. 1.1086E -02 C 0.8590 0.2892 0.3606 5.960IE- 0. 1509 1141. 0.7023 0.8325 0.3108 0.8290 0.0033 1391. 26460 0.5140 0.2836 0.4263 2.0000E- 0-4 0.2088 1293. 8.7539E -03 C 0.8960 0.308 7 0.3722 6.G079E- 08 0.1521 742o 0. 7346 0.877 2 0.3201 0.5373 04 0.0034 902. 26461 0.4980 0.3405 0.4628 l.OOOOE- 0.3384 668. 5.4010E -03 C 0.9270 0. 3663 0.4057 6.Q389E- 08 0. 1529 359. 0.7558 0. 9219 0.3502 0.26 LI 0.0039 438. 2 2 3 . N2 , NH3 t 0 o 7 9 0 M I C R O N Do P A R T I C L E S ( C O N T I N U E D ) . RUN Y I N T I E P E X P EPMO QINT F I L M R R E I MTC T Y P E Y I N T O E P C O R R EPSW P L M K N R E O Y I N T L M EMT E P M A U L M UR R E L M 2 6 4 6 2 0 o 4 5 1 0 0 . 3 0 9 1 0 . 5 3 1 2 5 . 0 0 0 0 E - 0 5 0 . 4 7 7 9 3 7 0 . 3 . 8 2 4 8 E - 03 C 0 o 9 6 2 0 0 . 3 4 3 3 0 . 4 7 1 1 6 . 0 7 1 8 E - 0 8 0 . 1 5 3 7 1 7 3 . 0 . 7 7 8 3 0 . 9 6 7 6 0 . 4 1 1 4 0 . 1 2 6 8 0 . 0 0 5 0 2 1 3 . 2 6 4 6 3 0 o 2 9 5 0 0 . 3 4 3 6 0 . 5 0 7 5 6 . 0 0 0 0 E - 0 4 0 . 0 8 8 8 6 8 7 9 . 2 . 0 5 8 7 E - 02 I 0 » 5 9 9 0 0 . 3 9 2 4 0 . 4 6 8 4 5 . 5 5 2 1 E - 0 8 0 . 1 4 0 6 3 3 2 0 . 0 . 4 4 2 2 0 . 7 1 9 9 0 . 4 2 6 3 2 . 6 7 8 0 . 0 0 4 9 4 5 2 6 . 2 6 4 6 4 0 o 3 4 8 0 0 . 3 4 1 1 0 . 4 6 9 5 6 . 0 0 0 0 E - 0 4 0 . 0 9 5 8 5 7 9 6 . 1 . 9 0 7 3 E - 02 I T 0 . 6 5 6 0 0 . 3 7 9 3 0 . 4 2 7 5 5 . 6 4 9 6 E - •08 0 . 1 4 3 0 3 0 2 9 . 0 . 5 0 1 2 0 . 7 2 0 1 0 . 3 8 3 4 2 . 3 6 2 0 . 0 0 4 2 3 9 8 0 . 2 6 4 6 5 0 . 4 0 6 0 0 . 2 6 4 2 0 . 4 3 6 1 6 . 0 0 0 0 E - •04 0 . 0 9 8 9 4 9 4 2 . 1 . 8 4 8 1 E - •02 I 0 . 7 2 0 0 0 . 2 9 7 9 0 . 3 9 1 2 5 . 7 5 4 3 E - •08 0 . 1 4 5 7 2 7 6 0 . 0 . 5 6 6 9 0 . 7 3 4 2 0 . 3 4 5 6 2 . 0 8 9 0 . 0 0 3 7 3 5 1 0 . 2 6 4 6 7 0 . 6 2 0 0 0 . 1 4 9 5 0 . 2 7 4 0 6 . 0 0 0 0 E - •04 0 . 1 2 2 4 3 2 0 6 . 1 . 4 9 3 6 E - •02 I 0 . 8 5 4 0 0 . 1 6 54 0 . 2 3 3 1 6 . 0 2 9 1 E - •08 0 . 1 5 2 6 2 3 3 4 . 0 . 7 4 9 1 0 . 7 2 1 1 0 . 1 9 5 7 1 . 5 8 1 0 . 0 0 1 8 2 6 5 4 . 2 6 4 6 8 0 . 76 00 0 . 0 0 0 3 0 . 1 6 8 5 6 . 0 0 0 0 E - • 0 4 0 . 1 3 9 6 2 6 1 6 . 1 . 3 0 9 1 E - •02 I 0 . 9 1 4 0 0 . 0 0 9 6 0 . 1 3 8 7 6 . 1 7 1 8 E - -08 0 . 1 5 6 2 2 1 8 5 . 0 . 8 4 7 6 0 . 7 0 2 0 0 . 1 1 3 0 1 . 3 9 7 . 0 . 0 0 1 0 2 3 5 1 . 2 6 4 6 9 0 . 4 6 5 0 0 . 2 3 9 6 0 . 4 2 4 5 4 . 0 0 0 0 E - -04 0 . 1 3 2 9 2 8 6 5 . 1 . 3 7 5 3 E - -02 C 0 . 8 0 8 0 0 . 2 6 9 0 0 . 3 7 5 2 5 . 8 8 0 6 E - -08 0 . 1 4 8 9 1 6 4 2 . 0 . 6 4 9 1 0 . 7 9 3 5 0 . 3 2 6 5 1 . 2 1 6 0 . 0 0 3 4 2 0 4 1 . 2 6 4 7 0 0 . 4 9 9 0 0 . 1 7 9 8 0 . 3 4 2 6 8 . 0 0 0 0 E - -04 0 . 0 9 2 8 5 3 3 0 . 1 . 9 7 0 5 E - -02 C 0 . 7 5 9 0 0 . 2 0 3 8 0 . 3 0 0 2 5 . 8 5 9 8 E - -08 0 . 1 4 8 3 3 4 9 3 . 0 . 6 3 5 3 0 . 6 8 3 7 0 . 2 5 9 1 2 . 4 8 5 0 . 0 0 2 6 4 1 7 1 . 2 6 4 7 1 0 . 5 0 9 0 0 . 2 0 1 3 0 . 3 1 3 1 1 . 0 0 0 0 E - -03 0 . 0 8 4 4 6 5 2 9 . 2 . 1 6 5 1 E - -02 C 0 . 7 4 1 0 0 . 2 2 2 2 0 . 2 7 3 7 5 . 8 5 1 3 E - -08 0 . 1 4 8 1 4 4 7 1 . 0 , 6 2 9 8 0 . 6 3 7 7 0 . 2 3 57 3 . 1 3 4 0 . 0 0 2 3 5 2 6 0 . 2 6 4 7 2 0 . 5 0 9 0 0 . 1 3 8 2 0 . 3 0 0 8 1 . 2 4 0 0 E - - 0 3 0 . 0 7 2 6 8 0 9 6 . 2 . 5 1 5 9 E - -02 T C 0 . 7 2 8 0 0 . 1 5 9 9 0 . 2 6 3 0 5 . 8 4 0 2 E - -08 0 . 1 4 7 9 5 6 4 2 . 0 . 6 2 2 5 0 . 6 1 2 7 0 . 2 2 6 4 3 . 9 3 1 0 . 0 0 2 2 6 6 0 0 . 2 6 4 7 3 0 . 5 3 6 0 0 . 1 1 7 9 0 . 2 6 7 8 1 . 3 6 0 0 E - -03 0 . 0 7 4 4 8 4 2 3 . 2 . 4 5 7 4 E - -02 T 0 . 7 3 2 0 0 . 1 3 6 7 0 . 2 3 2 5 5 . 8 6 3 3 E - - 0 8 0 . 1 4 8 4 6 1 5 5 . 0 . 6 3 7 7 0 . 5 7 7 1 0 . 1 9 8 9 4 . 2 0 9 0 . 0 0 1 9 7 0 6 5 . 2 6 4 7 4 0 . 2 5 0 0 0 . 4 3 4 0 0 . 5 9 8 1 4 . 3 0 0 0 E - - 0 4 0 . 0 9 2 9 5 8 5 4 . 1 . 9 6 8 1 E - - 0 2 T 0 . 6 2 2 0 0 . 4 9 2 4 0 . 5 5 8 6 5 . 5 2 6 6 E - - 0 8 0 . 1 3 9 9 2 2 9 0 . 0 . 4 2 7 1 0 . 7 9 7 4 0 . 5 1 5 0 1 . 9 8 7 0 . 0 0 6 6 3 3 6 1 . 2 6 4 7 5 0 . 1 1 8 0 0 . 6 9 6 5 0 . 8 0 5 9 1 . 8 0 0 0 E - - 0 4 0 . 1 0 2 8 5 3 2 6 . 1 . 7 7 8 6 E - - 0 2 T 0 . 6 0 8 0 0 . 7 8 6 0 0 . 7 7 9 9 5 . 3 4 5 3 E - - 0 8 0 . 1 3 5 3 9 8 1 . 0 . 3 2 4 7 0 . 9 1 3 7 0 . 7 4 8 9 1 . 0 9 4 0 . 0 1 5 1 1 8 6 8 . 2 6 4 8 0 0 . 5 0 9 0 0 . 2 0 0 9 0 . 3 0 0 8 1 . 2 4 0 0 E - - 0 3 0 . 0 7 2 6 8 0 9 6 . 2 . 5 1 5 9 E - - 0 2 T C 0 . 7 2 8 0 0 . 2 2 1 1 0 . 2 6 3 0 5 . 8 4 0 2 E - - 0 8 0 . 1 4 7 9 5 6 4 2 . 0 . 6 2 2 5 0 . 6 1 2 7 0 . 2 2 6 4 3 . 9 3 1 0 . 0 0 2 2 6 6 0 0 . 2 6 4 8 1 0 . 5 3 6 0 0 . 2 2 9 6 0 . 2 6 7 8 1 . 3 6 0 0 E - - 0 3 0 . 0 7 4 4 8 4 2 3 . 2 . 4 5 7 4 E - - 0 2 T 0 . 7 3 2 0 0 . 2 4 6 0 0 . 2 3 2 5 5 . 8 6 3 3 E -- 0 8 0 . 1 4 8 4 6 1 5 5 . 0 . 6 3 7 7 0 . 5 7 7 1 0 . 1 9 8 9 4 . 2 0 9 0 . 0 0 1 9 7 0 6 5 . 2 6 4 8 2 0 . 5 5 8 0 0 . 1 8 6 1 0 . 2 6 3 9 1 . 4 9 0 0 E - 0 3 0 . 0 6 5 6 8 8 5 8 . 2 . 7 8 7 2 E -- 0 2 T 0 . 7 5 8 0 0 . 2 0 2 5 0 . 2 2 7 9 5 . 9 0 1 I E - 0 8 0 . 1 4 9 4 6 5 1 4 . 0 . 6 6 2 7 0 . 5 9 7 0 0 . 1 9 4 0 4 . 4 3 7 0 . 0 0 1 8 7 4 4 6 . 2 2 4 . N 2 , N H 3 , 0 . 7 9 0 M I C R O N D . P A R T I C L E S ( C O N T I N U E D ) . R U N Y I N T I EPEXP E P M O Q I N T F I L M R RE I M T C T Y P E Y I N T O E P C O R R E P S W P L M K N RED Y I N T L M E M T E P M A U L M U R R E L M 2 6 4 8 3 0 . 4 7 2 0 0 . 2 6 9 2 0 . 3 3 6 1 1 . 1 0 0 0 E - 0 3 0 . 0 7 4 4 7 7 5 9 . 2 . 4 5 5 3 E - 0 2 T 0 . 7 1 1 0 0 . 2 9 1 4 0 . 2 9 6 6 5 . 7 9 7 9 E - 0 8 0 . 1 4 6 8 5 1 2 4 . -0 . 5 9 5 0 0 . 6 3 6 6 0 . 2 5 7 7 3 . 6 4 9 0 . 0 0 2 5 6 1 2 8 . 2 6 4 8 4 0 . 3 5 5 0 0 . 3 3 9 8 0 . 4 4 6 2 6 . 7 0 0 0 E - • 0 4 0 . 0 9 3 2 6 3 4 0 . 1 . 9 6 0 5 E - 0 2 T 0 . 6 4 1 0 0 . 3 7 5 5 0 . 4 0 5 5 5 < » 6 4 2 9 E - 0 8 0 . 1 4 2 9 3 4 6 2 . 0 . 4 9 7 1 0 . 6 9 1 7 0 . 3 6 3 0 2 . 6 6 0 0 . 0 0 3 9 4 4 8 2 . 2 6 4 8 5 0 . 4 4 2 0 0 . 2 5 2 6 0 . 3 6 9 5 9 . 7 0 0 0 E - 0 4 0 . 0 7 6 8 7 3 1 9 . 2 . 3 . 8 1 1 E - - 0 2 T 0 . 7 0 1 0 0 . 2 7 9 3 0 . 3 2 8 4 5 . 7 6 6 2 E - 0 8 0 . 1 4 6 0 4 5 8 3 . 0 . 5 7 4 5 0 . 6 6 2 1 0 . 2 8 7 5 3 . 3 3 2 0 . 0 0 2 9 5 5 9 8 . 2 6 4 8 6 0 . 4 0 5 0 0 . 2 9 8 8 0 . 4 0 1 8 8 . 3 0 0 0 E - 0 4 0 . 0 8 3 4 6 8 5 3 . 2 . 1 9 1 8 E - 0 2 T 0 . 6 7 7 0 Oo 3 2 8 6 0 . 3 6 0 5 5 . 7 1 6 0 E - 0 8 0 . 1 4 4 7 4 0 6 0 . 0 . 5 4 2 6 0 . 6 7 5 2 0 . 3 1 8 5 3 . 0 1 9 0 . 0 0 3 3 5 0 7 7 . 225. TABLE XIV DATA FOR N2 , NH3 , 0o790 MICRON DIAMETER P ARTICLES-* * * * ^^^^^^^^3^^^^^^^e^^^2^^^^#^^4 '3(e'3^3Ceaje4ejtc39c4e4c4t4c4c4t{t * * * j c * * * je * * * * * * * * * SHORT COLUMN* . ************* INERT GAS FLOW RATE CONSTANT IN ALL RUNS. INLET TEMPo (DEG. K) 293«0 , PRESSURE (AT Mo} 1.000 CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: loOOOO + 0.0 *YINTI + 0.0 *YT RNI/YINT I OUTLET: 1.0900 + -0.0900*YINTQ + 0.0 *YTRNO/YINTO GAS N2 (INERT) NH3 (TRANSFERRED) MOLEC. WEIGHT DENSITY VISCOSITY (G/GMOLE) (KG/M**3) (KG/M/SEC) MEAN FREE PATH (M) V0LUME**(l/3) (M/GMOLE**(1/3)) 28.02 1.165 1.7480E-05 6.3900E-08 3.1190E-02 17.03 0.7182 9.8200E-06 4.5700E-08 2.2240E-02 DIFFUSIVITY (M**2/SEC3 2.3212E-05 RUN Y I NT I EPEXP EPMO Q INT F I L M R REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR R ELM 37068 0. 2610 0.2507 0.3203 6.0000E-•04 0.0722 7811. 2.5311E -02 0.3840 0.2901 0.2983 5.3367E- 08 0. 1351 5234. 0.3200 0.4334 0.2741 3.700 0.0065 6321. 3 7068 0.2610 0.2461 0. 3203 6.0000E-•04 0.0722 7811. 2.5311E -02 0.3840 0.2857 0.2983 5.3367E- 08 0.1351 5234. 0.3200 0.4334 0.2741 3.700 0.0065 6321. 37068 0.2610 0. 2507 0.3203 6. OOOOE-04 0.0722 7811. 2.5311E -02 0.3840 0.2901 0.2983 5.3367E- 08 Oo1351 5234. 0. 3 200 0.4334 0.2741 3.700 0.0065 6321. 37069 0.3480 0.2710 0.3 095 6.0000E- 04 0.0750 5796. 2.43 85E -02 0.5040 0.3022 0.2818 5.5220E- 08 0.1398 3957. 0. 4244 0.4747 0.2528 2.790 0.0059 4721. 37069 0.3480 0.2256 0.3095 6.OOOOE-04 0.0750 5796. 2.4385E -02 0.5040 0.2587 0.2818 5.5220E- 08 0.1398 3957. 0.4244 0. 4747 0.25 28 2.790 0. 005 9 4721. 37069 0.3480 0.2298 0.3095 6.OOOOE-04 0.0750 5796. 2.4385E -02 0. 5040 0.2627 0.2818 5.5220E- 08 0.139 8 3957. 0.4244 0.4747 0.2528 2. 790 0.0059 4721. 3 7070 0.4100 0.1861 0.2807 6.0000E- 04 0o0811 4892. 2.25 24E -02 0. 5700 0. 2164 0.2515 5.6307E- 08 0.1425 3491. 0.4896 0.4758 0.2220 2.419 0. 0051 4076. 37070 0.4100 0.1951 0.2807 6.0000E- 04 0.0811 4892. 2.2524E -02 0.5700 0. 22 61 0.2515 5. 6307E- 08 0.1425 3 491. 0.4896 0.4758 0.2220 2.419 0.0051 4076 D 37071 0.4980 0. 1564 0.2409 6.0000E- 04 0.0881 4006. 2.0743E -02 0.6560 0. 1817 0.2111 5.7719E- 08 0.145 1 3029. 0.5782 0.4798 0.18 23 2.048 0.0040 3441. N2 , NH3 , 0.790 MICRON D. 226. PARTICLES (CONTINUED). RUN YINT I EPEXP EPMO QINT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 37071 0. 4980 0.1880 0.2409 6.0000E- 04 0.0881 4006. 2.0743E -02 0.6560 0.2124 0.2111 5.7719E- 08 0.1461 3029. 0.5782 0*4798 0.1823 2.04 8 ' 0.0040 3441. 37071 0.4980 0. 1903 0.2409 6.OOOOE-04 0.0881 4006. 2.0743E -02 0.6560 0.2146 0.2111 5.7719E- 08 0.1461 3 029. 0.5782 0.4798 0.1823 2.048 0.0040 3441. 37072 0.6210 0.1464 0. 1786 6.0000E- 04 0.0999 3 201. 1.8292E -02 0.7560 0. 1647 0.1519 5.9436E- 08 0.1505 2630. 0.6912 0. 4 712 0.1275 1.713 0.0027 2875. 3 7072 0.6210 0. 1322 0. 1786 6.DODOE-04 0.0999 3 201. 1.8292E -02 0.7560 0.1508 0.1519 S' 9436E- 08 0.1505 2630. 0. 6912 0.4712 0.1275 1.713 0.0027 2875. 37072 0.6210 0.1145 0.1786 6.0000E- 04 0.0999 3201. 1. 8292E -02 0. 7560 0.1335 0.1519 5.9436E- 08 0.1505 2630. 0. 6912 0.4712 0.1275 1. 713 0.0027 2875. 227. TABLE XV DATA FOR N2 , NH3 , Oo500 MICRON DIAMETER PARTICLESo ****** *$********$*$*^$$*?$ *********** ***********^« ****** ******* INERT GAS FLOW RATE CONSTANT IN ALL RUNS. INLET TEMP. (DEG. K) 293.0 , PRESSURE (ATM.) 1. 000 CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: 1.0000 + 0.0 *YINTI «• 0.0 *YTRNI/YINTI OUTLET: 0.8769 + 0 o1231*YINT0 + 0.0 *YTRNO/YINTD GAS N2 (INERT) NH3 (TRANSFERRED} MOLEC. WEIGHT DENSITY VISCOSITY MEAN FREE PATH V0LUME**U/3) (G/GMOLE) (KG/M**3) (KG/M/SEC) (M) <M/GM0LE**(l/3) ) 2 8.02 1.165 1.7480E-05 6.3900E-08 3.1190E-Q2 17. 03 0.7182 9.8200E-06 4.5700E-08 2.2240E-02 DIFFUSIVITY (M**2/SEC) 2.3212E-05 RUN YINTI EPEXP EPMO QI NT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM " KN REO YINTLM EMT EPMA ULM UR R ELM 35706 0.2740 0.5203 0.4869 6.OOOOE-04 0.0970 7427. 1.8840E -02 0.5340 0.4911 0.4519 5.4767E-08 0.2191 3730. 0.3981 0. 6706 0.4137 2. 974 0.0046 5 043. 35706 0.2740 0.5279 0.4869 6.0000E- 04 0.0970 7427. ".I. 8840E -02 0. 5340 0.4992 0.4519 5.4767E-08 0.2191 3730. 0.3981 0.6706 0.4137 2.974 0.0046 5043. 35706 Oo 2740 0.5282 0 o4869 6.0000E- 04 0.0970 7427. I.8840E -02 0. 534 0 0.4995 0.4519 5.4767E-08 0.2191 3730. 0.3981 0.6706 0.4137 2.974 0.0046 5043. 3 5707 0.3050 0.5151 0.4831 6.0000E-•04 0.0961 6645. 1.9013E -02 0.5900 0.4893 0. 4447 5.5541E- 08 0.2222 3371. 0.4433 0.6950 0.4036 2.671 0.0045 4513. 35707 0.3050 0.5075 0.4831 6.0000E-04 0.0961 6645. 1.9013E -02 0.5900 0.4813 0.4447 5„5541E- 08 0.2222 3371. 0.4433 0.6950 0.4036 2.671 0.0045 4513, 35707 0. 3050 0.4829 0.4831 6.0000E-•04 0.0961 6645 . L.9013E -0 2 0.5900 0.4554 0. 4447 5.5541E- 08 0. 2222 3371. 0.4433 0.6950 0.4036 2.671 0.0045 4513. 35708 0.3 510 0.4914 0.460 8 6. OOOOE-04 0.0988 5744. 1.8505E -02 0.6510 0.4686 0.4192 5.6480E- 08 0.2259 3053, 0. 500 2 0. 7101 0.3757 2.367 0.0041 3988. 35708 0.3510 0. 4870 0. 4608 6.0000E- 04 0.0988 5744. 1.8505E -02 0 o6510 0.4640 0.4192 5.6480E- 08 0.2259 3053. 0.5 002 0. 7101 0.3757 2.367 0.0041 3983. 35708 0.3510 0.4628 0.4608 6.OOOOE-04 0. 0988 5744. 1.85 05E -02 0.6510 0.4387 0«4192 5.6480E- 08 0.2259 3053. 0.5002 0.7101 0.3757 2.367 0.0041 3988. * Z 9 I Z 5000*0 l e s ' ! 0 9 5 0 " 0 2 0 0 1 *0 0 7 Z 6 * 0 " 2 8 0 Z £ I S Z ° 0 80 - 3 7 l 8 Z ° 9 Z 0 1 0 * 0 8 Z 8 0 ° 0 0 6 5 6 * 0 z o - • 3 6 9 £ Z * T * 6 1 Z Z e m * o 70 - 3 0 0 0 0 ° 9 9 1 8 0 "0 7 Z 6 0 *0 0 5 1 8 * 0 soi.se • Z 9 I Z 5000*0 T 8 Z * I 0 9 5 0 * 0 Z.001°0 0 7 Z 6 ° 0 °180Z E1.SZ°0 80 - 3 7 I 8 Z °9 Z 0 2 0 * 0 6 9 8 0 * 0 0 6 5 6 * 0 20-• 3 6 9 £ Z * T a6LZZ 8 £ v l ° 0 70 - 3 0 0 0 0 * 9 9180 *0 5 1 6 0 *0 0518 °0 501 S£ °Z9TZ 5 0 0 0 * 0 T 8 Z ° T 0 9 S 0 ° 0 1 0 0 2 ° 0 0 7 Z 6 ° 0 °Z80Z ETSZ°0 80 - 3 7 T 8 Z °9 Z 0 2 0 °0 6 £ I T *0 0 6 5 6 * 0 Z O -•369£Z°T * 6 1 Z Z 82.71*0 - 3 0 0 0 0 ' 9 9180 *0 7 8 1 1 * 0 05 2 8 * 0 S 0 1 5 E «TS£Z 0 1 0 0 * 0 1 6 £ * T o e n °0 0 Z 0 1 * 0 9 2 7 8 * 0 * S 8 1 Z 69^ Z°0 80 - 3 8 T I T *9 1 8 £ I °0 0511 °0 0 7 1 6 * 0 z o - • 3 T 6 0 € , T ° 9 I 9 Z 96£I*0 7 0 - 3 0 0 0 0 * 9 589T*0' 1 £ 8 1 ° 0 0 0 9 2 * 0 702 5 £ °TS£Z 0100 °0 Z.6£°I 0 £ I I*0 0 Z 0 1 ° 0 9 2 7 8 * 0 * S 8 1 Z 69+rZ*Q 80 - 3 8 T 2 T * 9 2 8 £ T * 0 5511*0 0716 °0 z o - • 3 I 6 0 E *T' ° 9 I 9 Z 9 6 £ T ° 0 7 0 - 3 0 0 0 0 ° 9 58.91 °0 Z 7 8 T ° 0 0 0 9 2 * 0 702 5 £ ° 1 S £ Z OTOO °0 1 6 £ * T 0 E T 1 *Q OZOZ. *0 9278 *0 * S 8 T Z 69vZ°0 80 - 3 8 1 2 1 * 9 18 £1*0 8 9 7 l ° 0 0 7 1 6 * 0 z o - •3I60e ET ° 9 I 9 Z 96£T°0 70 - 3 0 0 0 0 °9 5891°0 8551 °0 0 0 9 1 * 0 7 c z s e *TS£Z 0 T 0 0 80 1 6 £ * T 0£1T "0 OZOZ *0 9278 *0 " 5 8 T Z 6 9 7 Z * o 80-- 3 8 T Z T * 9 2 8 E T * 0 Z 8 7 l ° 0 0716 °0 z o - •3T.6Q£ e T ° 9 I 9 Z 9 6 £ T ° 0 70 - 3 0 0 0 0 °9 5 8 9 1 * 0 Z 1 S I ° 0 0 0 9 2 * 0 7025 £ * S E 9 Z 8 T 0 0 ° 0 6 9 5 * 1 1181*0 9£1Z.°0 2751 *0 °8Z£Z 5T.7Z°0 80 - 3 £ 2 £ 0 ° 9 I 7 Z Z ° 0 9 6 7 Z ° 0 0 9 5 8 ° 0 z o - " S S T E £SZT°0 70 - 3 0 0 0 0 ° 9 0 7 9 Z ° 0 6 Z 9 Z »0 00£9 *0 TT2S£ *S£9Z 8 T 0 0 * 0 6 9 9 ° ! 1 Z 8 T * 0 9 £12 *0 2751 "0 •8Z£Z ST7Z °0 80 - 3 E 2£0 * 9 T 7 Z Z ° 0 Z 7 9 Z ° 0 0 9 5 8 * 0 z o - 3 6 E S 7 ° T *SST£ ZSZT°0 70-- 3 0 0 0 0 °9 0 7 9 Z "0 ZLLZ°0 00£9 °0 T T 1 S E 8 5 E 9 Z 8 1 0 0 * 0 6 9 5 * 1 1 1 8 1 * 0 9 £ I 1 ° 0 1 7 5 2 ° 0 *8Z£Z STvZ °0 80 - 3 E 1£0 ° 9 T 7 Z Z ° 0 £ Z 5 Z ° 0 0 9 5 8 * 0 z o - 3 6 £ S 7 * T * S 5 I £ 1 5 Z T * 0 70-- 3 0 0 0 0 °9 079Z°0 9 5 9 Z * 0 00£9 "0 i u s e e 6 £ 0 £ A Z 0 0 ° 0 118*1 Z.02Z°0 ££Z2°0 8 £ 5 9 * 0 * T E S Z 5 5 £ Z °0 80 - 3 2 2 8 8 ° S 0 7 l £ o 0 7 2 T £ ° 0 0 9 8 1 * 0 z o - 3 85 £ 9 * 1 *Z.S6£ Z.TT1°0 70' - 3 0 0 0 0 ° 9 8 8 S E * 0 v S £ E * 0 0 ? 0 5 "0 0 1 2 S e °6£0E 2ZOO*0 T T 8 ° I 2 G 1 Z ° 0 £ £ Z 1 ° 0 8£59 *0 *T.£SZ 5SEZ°0 80-- 3 2 2 8 8 " S 0 7 T E ° 0 T8Z£"0 0 9 8 2 * 0 z o - 385£9*T * 2 5 6 £ Z T T f O 70-- 3 0 0 0 0 * 9 885e*0 8 S 7 £ * 0 0705 °0 0 1 2 S £ e 6 £ 0 £ Z.Z00 °0 T I 8 ° T I 0 1 Z ° 0 £ £ Z 1 * 0 8 £ 5 9 ° 0 * i e s z 5 S £ Z * 0 80-- 3 1 2 8 8 *S OvT£*0 7 S 7 £ * 0 0 9 8 1 * 0 z o - 385£9*T * 2 S 6 £ 2 1 1 1 * 0 70-- 3 0 0 0 0 ° 9 8 8 5 £ ° 0 9 Z 9 £ ° 0 0 7 0 5 * 0 0 T 2 S E ° 9 8 v £ 7£00 °0 5 2 0 * Z 8 £ Z £ ° 0 1511*0 8 0 1 5 * 0 " 9 1 1 Z 7 0 £ Z ° 0 80-- 3 £ 0 9 2 * S Z Z 1 £ ° 0 2 8 0 7 * 0 0912 °0 z o - 3 6 £ £ 2 ° T ° S 6 l 7 7 5 0 1 * 0 70 - 3 0 0 0 0 ° 9 Z 9 l 7 ° 0 7 6 Z 7 ° 0 0 8 l 7 ° 0 6 0 2 S e c 9 8 7 £ 7 £ 0 0 * 0 510 °Z 8 1 Z £ * 0 1 5 1 2 *0 8 0 1 5 * 0 * 9 2 2 Z v O £ Z a O 80-- 3 € 0 9 2 ° S Z Z 1 £ * 0 17 0 7 * 0 0 9 1 2 * 0 z o - 3 6 £ £ Z ° I °S6Z.7 v S 0 I°0 70-- 3 0 0 0 0 °9 Z 9 T 7 ° 0 6 7 Z 7 ° 0 0 8 1 7 * 0 6 0 2 5 e * 9 8 7 £ 7 £ 0 0 * 0 5 2 0 *Z 82Z£*0 15 12 *0 8 0 2 5 * 0 * 9 2 1 Z 7 0 £ Z * 0 80-- 3 £ 0 9 2 * 5 Z Z 1 £ ° 0 T 1 Z 7 ° 0 0 9 I 2 ° 0 z o - 36£££*I °562.7 v S O I °0 c o - - 3 0 0 0 0 °9 Z 9 l 7 * 0 1 2 7 7 * 0 0 8 1 7 * 0 6 0 1 s e W13« yn win VWd3 1W3 W H N I A 0 3 * NX Wld HSd3 U800d3 O i N I A 3 d A l 01W 13*1 IN 10 OWd'3 d X 3 d 3 U N I A *(Q3nNIiNO0J S 3 1 0 I I * i V d *C NOyGIW 0 0 5 * 0 4 £HN * ZN * 8 Z Z 229 . TABLE XVI DATA FOR N2 , NH3 , 0.790 M ICRON DIAMETER PARTICLESo ****************************************** DATA FOR VARIOUS TYPES OF RUNS, INLET TEMP© i DEGo IC I 293.0 , PRESSURE { A TMo J loOOO CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: OUTLET: GAS loOOOO + OoO *YINTI + 0.8992 + 0 o1008*YINTQ + OoO OoO *YTRNI/YlNTI •YTRM0/YINT3 MOLECo WEIGHT DENSITY VISCOSITY MEAN FREE PATH VOLUME**(1/3) DIFFUSIVITY (G/GMOLE) (KG/M**3) (KG/M/SEC) ( M) (M/GMOLE**(l/3) ) (M**2/SEC) N2 (INERT ) 280 02 U 1 6 5 1.7480E-05 6 o3900E-08 3.1190E-02 NH3 (TRANSFERRED) 17o03 0o7182 9.8200E-06 4. 5700E-08 2.2240E-02 2o 3212E-05 RUN YINTI EPEXP EPMO QINT FILMR REI TYPE YINTO EPCORR EPSW PLM KN RED YINTLM EMT EPMA ULM UR RELM 35007 0 . 2 7 4 0 0.4572 0.4869 6.OOOOE-04 0.0970 7427. I 0.5340 0.4304 0.4519 5.4767E- 08 Q.1387 3730. 0.3981 0.6706 0. 4137 2.974 0.0046 5043. 35010 0.3050 0.4417 0.4831 6.0000E- 04 0.0961 6645. I - 0.5900 0.4176 0.4447 5.5541E- 08 0.1406 3371. 0.4433 0.6950 0.4036 2.671 0.0045 4513. 3 5 010 0 . 3 0 5 0 0 o4736 0.4831 6 0 O O O O E - 04 0.0961 6645. I 0. 5900 0.45 09 0.4447 5.5541E- 08 0.1406 3371. 0.4433 0.6950 0.4036 2.671 0. 0045 4513. 35010 0.3050 0.4752 0.4831 6.0000E-•04 0.0961 6645. I 0.5900 0.4526 0. 4447 5.5541E- 08 0.1406 3371. 0.4433 0.6950 0.4036 2.671 0.0045 4513. 35 012 0.3510 0. 4486 0.4608 6.000GE- 04 0.0988 5744. IT 0.6510 0.42 85 0.4192 5.6480E- 08 0.143 0 3053. 0.5002 0.7101 0.3757 2.36 7 0.0041 3988. 3 5012 0. 3510 0.4480 0.4608 6.0000E- 04 0.0988 5744. IT 0.6510 0.4279 0.4192 5. 648QE-08 0.143 0 3 053. 0.5002 0.7101 0.3757 2.36 7 0.0041 3988. 35013 0.4180 0.346 8 0.4162 6. OOOOE-04 0.1054 4 795. I 0.7160 0.3275 0 . 3 7 2 2 5.7603E- 08 0.1458 2776. 0.5708 0. 7151 0.3278 2.075 0.0034 3486. 35013 0.4180 0.3617 0.4162 6.OOOOE-04 0.1054 4795. I 0.7160 0.3429 0.3722 5.7603E- 08 0.1458 2 776. 0. 5708 0.7151 0.3273 2.075 0.0034 3486. 3 5013 0.4180 0.3734 0.4162 6. OOOOE-04 0. 1054 4795. I 0.7160 0.3549 0.3722 5.7603E- 08 0.1458 2776. 0.5708 0. 7151 0.3278 2. 075 0.0034 3486. MTC 1.8840E-02 1. 9013E-02 1.9013E-02 1.9013E-02 I.8505E-02 1.8505£-02 1.7339E-0 2 1.7339E-02 1.7339E-02 230. N2 , NH3 , 0.790 MICRON Do PARTICLES {CONTINUED). RUN YINTI EPEXP EPMO QI NT FILMR REI MTC TYPE Y INTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR R ELM 35011 0.5040 0.3162 0.3588 6.0Q00E-•04 0. 1117 3957. 1.6358E -02 IC Oo 7860 0.3011 0.3140 5.8877E-•08 0.1491 2531. 0.6538 0. 7233 0.2707 1. 811 0.0027 3039. 35011 0.5040 0.3074 0.3588 6.0000E- 04 0.1117 3957, 1.6358E -02 IC 0.786 0 0.29 21 0.3140 5.8877E-•08 0.1491 2531. 0.6538 0. 7233 0.2707 1.811 0.0027 3039. 35011 0.5040 0.2980 0.3588 6o0000E-•04 0.1117 3957. 1.6358E -02 IG 0.7860 0.2825 0.3140 5.8877E-•08 0.1491 2531. 0.6538 0.7233 0.2707 1.811 Oo 0027 3 039. 35009 0.6300 0.2074 0.2640 6.0000E-•04 0.1257 3155. 1.4539E -02 I 0.8560 0. 1957 0,2241 6.0373E-•08 0. 1528 2328. 0.7547 0.7136 0.1877 1.569 0.0018 2635. 35009 0.6300 0.2225 0,2640 6.G000E-•04 0.1257 3155. 1.4539E -02 I 0.8560 0.2110 0. 2241 6. 0373E- 08 0.1528 2328, 0.7547 0.7136 0.1877 1.569 0.0018 2635. 3 5 009 0, 6300 0.2342 0,2640 6.000QE-•04 0.1257 3155. 1.4539E -02 I 0.8560 0.2229 0.2241 6. 0373E- 08 0. 1528 2328. 0.7547 0.7136 0.1877 1.569 0.0018 2635. 35023 0. 76 00 0. 13 81 0.168 5 6.0000E-•04 0.1396 2616. 1.3091E -02 I 0.9140 0.1306 0.1387 6.1718E- 08 0.1562 2185, 0. 8476 0.7020 0.1130 1.397 0.0010 2351, 35023 0.7600 0.1225 0. 1685 6. 000OE- 04 0. 1396 2616. 1.3091E -02 I 0.9140 0.1148 0.1387 6.1718E- 08 0.1562 2185. 0. 8476 0.7020 0.1130 1.397 0.0010 2351. 35023 0.7600 0.1256 0.1685 6.0000E- 04 0. 1396 2616. 1.3091E -02 I 0.9140 0.1180 0.1387 6.1718E-•08 0.1562 2185. 0.8476 0.7020 0. 1130 1.397 0.0010 2 3 51. 35023 0.7600 0.1247 0.1685 6.OOOOE-04 0.1396 2616. 1.3091E -02 I 0.9140 0.1170 0.1387 6.1718E- 08 0.1562 2185, 0.8476 0. 7020 0. 1130 1.397 0.0010 2351. 35023 0.7600 0.1311 0.1685 6.0000E- 04 0.1396 2616, 1. 3091E -02 I 0. 9140 0.1235 0.1387 6.1718E- 08 0.1562 2185, 0.8476 0.7020 0.1130 1.397 0. 0010 2351, 35023 0.7600 0.1301 0.1685 6.OOQOE-04 0.1396 2616, 1.3091E -02 I 0. 9140 0.1225 0, 1387 6. 171 8E-08 0.1562 2185. 0.8476 0.7020 0.1130 1.397 0.0010 2351, 35024 0. 8750 0.0096 0.0876 6.0Q00E-04 0.1478 2279, 1.2369E -02 I 0.9590 0, 0055 0. 0702 6.2814E- 08 0. 1590 2087. 0.9240 0.7007 0,0560 1.281 0.0005 2162. 35024 0. 8750 0. 066 8 0.0876 6.0000E- 04 0.1478 2279, 1.23 69E -02 I 0.9590 0.0629 0.0702 6.2814E- 08 0. 1590 2087. 0.9240 0.7007 0.0560 1.281 0.0005 2162. 35024 0.8750 0, 0465 0.0876 6.OOOQE-04 0.1478 2 2 79. 1.2369E -02 I 0.9590 0.0425 0.0702 6. 2814E-08 0.1590 2087, 0,9240 0.7007 0.0560 1.281 0.0005 2162. 35025 0.2740 0.4839 0. 4869 6.OOOOE-04 0.0970 7427. 1.8840E -02 I 0.5340 0.4585 0.4519 5 04767E- 08 0.1387 3730. 0.3981 0. 6706 0.4137 2.974 0.0046 5043. 231. N2 , NH3 , 0.790 MICRON D. PARTICLES (CONTINUED). RUN YINTI EPEXP EPMO 01 NT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR ^ ELM 3 5025 0.2740 0.4957 0.4869 6, OOOOE-04 0.0970 7427. 1.8840E -02 I 0.5340 0.4708 0.4519 5.4767E- 08 0.1387 3730. 0. 3981 0.6706 0.4137 2,974 0.0046 5043, 35025 0.2740 0.4693 0.4869 6.0000E- 04 0. 0970 7427. 1.8840E -02 I 0.5340 0.4431 0.4519 5.4767E- 08 0.138 7 3 730. 0.3981 0.6706 0.4137 2.974 0.0046 5043, 35025 0.2740 0.4886 0.4869 6.OOOOE-04 0.0970 7427, 1.8840E -02 I 0.5340 0.4634 0.4519 5.4767E- 08 0.1387 3730. 0.3981 0.6706 0.4137 2.974 0.0046 5043, 35025 0.2740 0.4736 0.4869 6.Q000E- 04 0.0970 7427. 1.8840E -02 I 0. 5340 0.4477 0,4519 5.4767E- 08 0.1387 3 730, 0.3981 0. 6706 0.4137 2.974 0.0046 5043. 35025 0.2740 0.4408 0.4869 6.000QE- 04 0.0970 7427. I. 8840E -02 I 0. 5340 0.4132 0.4519 5.4767E- 08 0.1387 3730. 0.3981 0.6706 0.4137 2.974 * 0. 0046 5043. 35026 0.3050 0.4428 0.4831 6.Q000E-04 0.0961 6645. 1.90 13 E -02 I 0.5900 0.4188 0. 4447 5.5541E- 08 0.1406 3371. 0.4433 0.6950 0.4036 2.671 0.0045 4513. 3 5 026 0.3050 0.4318 0.4831 6.0000E- 04 0.0961 6645. 1.9013E -02 I 0.5900 0. 4073 G. 4447 5.5541E- 08 0.1406 3371. 0.4433 0.6950 0.4036 2.671 0.0045 4513. 35026 0.3050 0.4152 0.4831 6.0000E- 04 0.0961 6645. 1.9013E -02 I 0.5900 0.3900 0.4447 5.5541E- 08 0. 1406 3371. 0.4433 0.6950 0.4036 2.671 0.0045 4513. 35027 0.3510 0.3823 0.4608 6.OOOOE-04 0.0988 5744. -1.8505E -0 2 IT 0.6510 0.3598 0.4192 5.6480E- 08 0.1430 3 053, 0.5002 0.7101 0.3757 2.367 0.0041 3988. 35027 0.3510 0. 4261 0. 4608 6.OOOOE-04 0.0988 5744. 1.8505E -02 IT 0.6510 0.4052 0.4192 5.6480E- 08 0.1430 3053. 0. 5002 0. 7101 0.3757 2.367 0.0041 3988. 35027 0.3510 0.4307 0.4608 6.OOOOE-04 0. 0988 5744. 1.8505E -02 IT 0.6510 0.4099 0.4192 5.6480E- 08 0.1430 3053. 0.5 002 0.7101 0,37 57 2. 36 7 0.0041 3988. 35037 0.1180 0.7825 0.8059 1.8000E- 04 0. 1028 5326, 1.7786E -02 T 0.6080 0.7736 0.7799 5.3453E-•08 0.1353 981. 0.3247 0. 9137 0. 7489 1.094 0.0151 1868. 35037 0.1180 0.7839 0.8059 1.8000E- 04 0.1028 5326. 1.7786E -02 T 0.6080 0.7750 0.7799 5.3453E- 08 0.1353 981. 0.3247 0.913 7 0. 7489 1.094 0.0151 1 868. 35031 0.3550 0.2762 0.4462 6.7Q00E- 04 0.0932 6340. 1.9605E -02 T 0. 6410 0.2490 0.4055 5.6429E-•08 0.1429 3462. 0.4971 0.6917 0.3630 2. 660 0. 0039 4482. 35037 0.1180 0.7921 0.8059 1.8000E- 04 0. 1028 5326. 1.7786E -02 T 0.6080 0. 783 5 0. 7799 5.3453E- 08 0. 1353 981. 0.3247 0.9137 0.7489 1.094 0.0151 1868, 3 5 037 0.1180 0. 7815 0.8059 1.8000E-•04 0.1028 5326. 1.7786E -02 T 0.6080 0. 7725 0.7799 5.3453E- 08 0.1353 981. 0.3247 0.9137 Oo 7489 1.094 0.0151 1868. N2 , NH3 , 0.790 MICRON D. PARTICLES (CONTINUED). RUN YINTI EPEXP EPMO Q INT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 3 5 033 0.4420 0.2931 0.3695 9.7000E-•04 0.0768 7319. 2.3811E -02 T 0.7010 0. 2711 0. 3284 5.7662E-•08 0.1460 4583. 0.5745 0.6621 0.2875 3.332 0.0029 5598. 35033 0.4420 0.2915 0.3 695 9.7000E-•04 0.0768 7319. 2.3811E -02 T 0.7010 0.2695 0.3284 5. 7662E- 08 0. 1460 4583. 0.5745 0.6621 0.2875 3.332 0.0029 5598, 35033 0.4420 0.3175 0.3695 9. 7000E-•04 0.0768 7319. 2.38UE -02 T 0.7010 0.2963 0.3284 5. 7662E- 08 0.1460 4583. 0.5745 0.6621 0.2875 3.332 0.0029 5598. 35034 0.4720 0.3106 0. 3361 1. 1000E-•03 0.0744 7759. 2.4553E -02 T 0.7110 0o2899 0.2966 5.7979E- 08 0.1468 5124. 0. 5950 0. 6366 0.2577 3.649 0.0025 6128. 35034 0.4720 0.3033 0.3361 1.1000E-•03 0.0744 7759. 2.4553E -02 T 0.7110 0.2824 0.2966 5.7979E-•08 0.1468 5124. 0.5950 0.6366 0.2577 3.649 0.0025 5128. 35034 0.4720 0.3090 0.3361 1.1000E- 03 0. 0744 7759. 2.4553E -02 T 0.7110 0.2883 0.2966 5.7979E-•08 0.146 8 5124. 0.5950 0. 63 66 0.2577 3.649 0.002 5 6128. 35035 0.5090 0.2875 0.3008 1.2400E- 03 0<,0726 8096. 2. 5159E -02 TC 0. 7280 0.26 74 0.2630 5.8402E-•08 0.1479 5642. 0.6225 0.6127 0.2264 3.931 0.0022 6600. 35035 0.5090 0.2727 0.3008 1.2400E-•03 0.0726 8096. 2.5159E -02 TC 0.7280 0.2522 0.2 63 0 5.8402E-•0 8 0.1479 5642. 0.6225 0.6127 0.2264 3. 931 0. 002 2 6600, 35035 0.5090 0.2675 0.3008 1.2400E- 03 0.0726 8096. 2.5159E -02 TC 0.7280 0. 2468 0. 2630 5. 8402E-08 0.1479 5642. 0.6225 0.6127 0.2264 3.931 0.0022 6600. 35035 0. 5 090 0.2655 0.3 008 1.2400E-•03 0,0726 8096. 2.5159E -02 TC 0.7280 0.2448 0.2630 5.8402E- 08 0.1479 5642. 0.6225 0.6127 0.2264 3.931 0.0022 6600. 35036 0.2500 0.5441 0. 5981 4.3000E- 04 0.0929 5854, 1.9681E -02 T 0.6220 0.5260 0.5586 5. 5266E-08 0.1399 2290. 0.4271 0.7974 0.5150 1.987 0.0066 3361. 35036 0.2500 0. 5594 0. 5981 4. 3000E-04 0.0929 5854. 1.9681E -02 T 0.6220 0.5419 0.5586 5.5266E- 08 0.1399 2290. 0. 4271 0. 7974 0.5150 1.987 0.0066 3361. 35036 0.2500 0. 5718 0.5981 4.3Q00E- 04 0.0929 5 854. 1.9681E -02 T 0.6220 0.5548 0.5586 5.5266E- 08 0.1399 2290. 0.4271 0.7974 0.5150 1.987 0.0066 3361. 35038 0.3550 0.4564 0.4462 6.7000E- 04 0. 0932 6340. 1.9605E -02 T 0.6410 0.4360 0.4055 5.6429E- 08 0.1429 3462. 0.4971 0. 6917 0. 3630 2. 660 0.0039 4482. 3503 8 0.3550 0.4463 0.4462 6.7000E- 04 0.0932 6340 B 1. 9605E -02 T 0. 6410 0. 4255 0.4055 5.6429E- 08 0.1429 3462. 0.49 71 0.6917 0.3630 2. 660 0.0039 4482. 35038 0.3550 0.4310 0.4462 6.7Q00E- 04 0.0932 6340. lo 96G5E -02 T 0. 641 0 0. 4096 0.4055 5.6429E- 08 0.1429 3 462. 0.4971 0.6917 0. 3630 2.660 0.0039 4482. 233. N2 , NH3 , 0o790 MICRON Do PARTICLES (CONTINUED). RUN YINTI EPEXP EPMO QINT FILMR REI MTC TYPE Y l NTO EPCORR EPSW PLM KN RED YINTLM E MT EPMA ULM UR RELM 35 03 8 0 o3550 0.4231 0.4462 6. 7000E-•04 0.0932 6340. - lo 9605E--02 T Oo 6410 0.4014 0.4055 5.6429E--08 0.1429 3462. 0»4971 0.6917 0.3630 2. 660 0.0039 4482. 3 5 03 8 G.355Q 0.4077 0.4462 6.7000E--04 0.0932 6340. 1.9605E-•02 T Oo 6410 0, 3 855 0. 4055 5.6429E--08 0.1429 3462. 0 o4971 0.6917 0.3630 2.660 0.0039 4482, 35039 0.4050 0.3820 0.4018 8.3000E-•04 0.0834 6853. 2,1918E--02 T 0.6770 0. 3612 0.3605 5.7160E--08 0.1447 40 60. 0o5426 0.6752 0.3185 3.019 0.0033 5077. 35 03 9 Oo 4050 0.3713 0.4 018 8.3000E--04 0.0834 6853. 2.1918E--0 2 T 0.6770 0.3501 0.3605 5. 7160E-•08 0. 1447 4060. 0o5426 0.6752 0.3185 3.019 0.0033 5077. 35039 0.4050 0.3597 0.4018 8.3000E--04 0.0834 6 853. 2.1918E--0 2 T 0.6770 0.3381 0.3605 5.7160E-•08 0.1447 4060. 0«5426 0.6752 0.3185 3,019 0,0033 5077. 35039 Go 4050 0.3802 0. 4018 8.3000E-•04 0.0834 6853. 2.1918E-•0 2 T 0o6770 0.3593 0.3605 5. 7160E-•08 0.1447 4060. Oo 5426 0.6752 0.3185 3.019 0.0033 5077. 35040 0.4720 0.3088 0.3361 1.1000E-•03 0.0744 7759. 2.4553E-•02 T 0.7110 0.2881 0.2966 5.7979E-•08 0.1468 5124. 0«5950 0. 63 66 0. 2577 3. 649 0. 0025 5128. 35040 0 o4720 0.2999 0.3361 1. 1000E-03 0. 0744 7759. 2.4553E- 02 T 0.7110 0.2789 0.2966 5.7979E-•08 0.1468 5124. 0.5950 0. 6366 0.2 577 3. 64 9 0.0025 5128. 35040 0.4720 0.3042 0.3361 1.1000E- 03 0.0744 7759„ 2. 4553E-02 T 0. 7110 0.2833 0.2 966 5.7979E-•08 0.1468 5124. 0.5950 0.6366 0.2577 3.649 0.0025 6128. 35040 0.4720 0.2878 0.3361 1.1000E-•03 0.0744 7759. 2.4553E- 02 T 0.7110 0.2664 0.2 966 5.7979E-•08 0.1468 5124. 0.5950 0.6366 0.2577 3.649 0. 002 5 6128, 35041 Oo 5090 0.2850 0.3008 1.2400E-•03 0.0726 8096. 2.5159E- 02 TC 0.7280 0. 2659 0. 2630 5. 8402E-08 0.1479 5642. 0.6225 0.6127 0.2264 3.931 0.0022 6600, 3 5041 0. 5 090 0.2859 0.3 008 1.2400E-•03 0.0726 8096. 2.5159E- 02 TC 0.7280 0.2658 0.2630 5.8402E- 08 0.1479 5642. 0.6225 0.6127 0.2264 3.931 0.0022 6600. 3 5041 0.5090 0.2902 0.3 008 1.2400E-03 0.0726 8096. 2.5159E-0 2 TC 0.7280 0.2702 0.2630 5.8402E- 08 0. 1479 5642. 0.6225 0.6127 0.2264 3.931 0.0022 6600. 35042 0.1180 0.8146 0. 8059 1.8000E- 04 0.1023 5326. 1.7786E- 02 T 0.6080 0.8070 0.7799 5.3453E- 08 0.1353 981. 0. 3247 0. 913 7 0. 7489 1.094 0.0151 1868. 35042 0.1180 0. 7917 0.8059 1.8000E- 04 0.1028 5326. 1.7786E- 02 T 0.6080 0o7831 0.7799 5.3453E- 08 0.1353 981. 0.3247 0. 9137 0. 7489 1.094 0.0151 1868. 35042 0.1180 0.7790 0. 8059 1.8000E- 04 0. 1028 53 26. 1.7786E- 02 T 0.6080 0.7699 0.7799 5.3453E- 08 0.1353 981. 0.3247 0. 9137 0. 7489 1. 094 0.0151 1868. 234. N2 , NH3 t 0o790 MICRON Do PARTICLES CONTINUED). RUN YINT I EPEXP EPMO QI NT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN RED YINTLM EMT EPMA ULM UR RELM 35042 0.1180 0.8042 0.8059 1.8000E- 04 0. 1028 5326. 1.7786E -02 T Oo 6080 0.7961 0.7799 5.3453E-•08 0.135 3 981. 0.3247 0.9137 0. 7489 1.094 0.0151 1868. 3 5043 0.2 500 0.5417 0.5981 4.3000E- 04 0.0929 5854. 1.9681E -02 T 0.622 0 0. 5235 0.5586 5.5266E-•08 0.1399 2290. 0.4271 0. 7974 0.5150 1.987 0.006 6 3361. 35043 0.2 500 0.5487 0.5981 4.3000E- 04 0.0929 5854. .1. 9681E -02 T 0. 6220 0. 53 08 0.5586 5.5266E-•08 0.1399 2290. 0.4271 0.7974 0.5150 1.987 0. 0066 3361. 35043 0.2500 0.54 45 0.5981 4.3000E- 04 0.0929 5854. 1.9681E -02 T 0.6220 0. 5265 0. 5586 5. 52 66E-•08 0. 1399 2290. 0.4271 0.7974 0.5150 1.987 0.0066 3361. 35044 0. 5090 0. 2928 0.3131 l.OOOOE- 03 0.0844 65 29. 2.1651E -02 C 0.7410 0.2 73 8 0.2737 5.8513E- 08 0. 148 1 4471. 0.6298 0.6377 0.2357 3. 134 0.0023 5260. 3 5044 0. 5090 0. 2806 0.3131 l.OOOOE- 03 0.0844 5529. 2.1651E -02 C 0.7410 0.2613 0.2737 5» 8513E- 08 0.1481 4471. 0.6298 0.6377 0.2357 3.134 0.0023 5260. 35 044 0.5090 0.2784 0.3131 1. OOOOE-03 0.0844 6529. 2.1651E -02 r 0.7410 0.2591 0.2737 5,8513E- 08 0.1481 4471. 0.6298 0.63 77 0,2357 3.134 0.0023 5260. 35044 0.5090 0.3195 0.3131 l.OOOOE- 03 0.0844 6529. 2.1651E -02 C 0.7410 0.3013 0.2737 5.8513E- 08 0.1481 4471. 0. 6298 0.6377 0.2357 3.134 0.0023 5260. 35045 0.4990 0.2755 0.3426 8.0000E- 04 0. 0928 5330. 1.9705E -02 C 0.7590 0.2575 0.3002 5.8598E- 08 0.1483 3493. 0.6353 0.6837 0.2 591 2.485 0,0026 4171. 35045 0.4990 0.2647 0.3426 8.0000E- 04 0.092 8 53 30, .1.9705E -02 C 0.7590 0.2464 0.3 002 5.8598E-•08 0,1483 3493. 0.6353 0.6 837 0. 2591 2.485 0.0026 4171. 35045 0.4990 0.2758 0.3426 8.000QE- 04 0.0928 5330. 1.9705E -02 C 0. 7590 0.2578 0.3 002 5.8598E-•08 0.1483 3493. 0.6353 0.6837 0.2591 2.485 0.0026 4171. 35046 0.4990 0.2651 0.3426 8.0000E- 04 0.0928 5330. 1.9705E -02 C 0.7590 0.2468 0. 3002 5. 8598E-08 0.1483 3493. 0o6353 0.6837 0.2 591 2.485 0.0026 4171, 35046 0.4990 0.2781 0.3426 8.0000E- 04 0.0928 5330. 1.9705E' -02 u 0.7590 0.2601 0. 3002 5. 8598E-08 0.1483 3493. 0.6353 0.6837 0.2591 2.485 0.0026 4171, 35046 0. 4990 0.2842 0.3426 8.0000E- 04 0.0928 5330, 1.9705E -02 C 0.7590 0.2664 0.3002 5. 8598E- 08 0. 1483 3493. 0.6353 0.6837 0.2591 2.485 0.0026 4171, 3 504 7 0.465 0 0.3555 0.4245 4.0000E-04 0.1329 2865. 1.3753E -02 C 0.8080 0.3428 0.3752 5.8 806E-08 Oo 1489 1642. 0.6491 0.7935 0.3265 1.216 0.0034 2041. 35047 0.4650 0. 3503 0.4245 4. OOOOE-04 0.1329 2365. 1.3753E -02 C 0.8080 0.3375 0.3752 5.8806E- 08 0.1489 1642. 0. 6491 0. 7935 0.3265 1.216 0.0034 2041. 235. M2 , NH 3 « Oo 790 MICRON D. PARTICLES (CONTINUED). RUN YINTI EPEXP EPMO QINT FIL MR REI MTC TYPE YINTO EPCORR EPsy PLM KN RED YINTLM EM? EPMA ULM r UR RELM 35047 0*4650 0* 3470 0. 4245 4. OOOOE-04 0.1329 2865* 1.3753E -02 C 0*8.080 0.3341 0*3 752 5.8806E- 08 0.1489 1642, 0*6491 0*793 5 0.3265 1.216 0.0034 2041. 3 5047 0*4650 0.3506 0*4245 4.0000E- 04 0.1329 2865. 1.3753E -02 C 0*8080 0*3378 0*3 752 5.S8Q6E- 08 0*1489 1642, 0* 6491 0.7935 0.3265 1.216 0.0034 2041, 35048 0*5050 0*3285 0.4121 2.9500E- 04 0. 1649 1942. 1.1086E -02 C 0* 8590 0*3188 0.3606 5.9601E-08 0*1509 1141. 0* 7023 0. 8325 0*3108 0. 8290 0*003 3 1391. 35048 0*5050 0.3084 0.4121 2.9500E- 04 0.1649 1942, 1. 1086E -02 C 0o8590 0. 2984 0.36 06 5.9.601E-08 0.1509 1141. 0.7023 0. 8325 0.3108 0*8290 0. 0033 1391. 35048 0*5050 0*3205 0.4121 2.9500E- 04 0.1649 .1942. 1.1086E -02 r 0. 8590 0.3107 0.3606 5.96Q1E-•08 0.1509 1141. 0*7023 0*8325 0.3108 0.8290 0. 0033 1391. 35049 0*5140 0.2958 0.4263 2.00Q0E- 04 0.2088 1293. 8.7539E -03 C 0.8960 0,2883 0.3722 6,Q079E- 08 0.1521 742. 0*7346 0*8772 0*3201 0.5373 * 0*0034 902. 35049 0. 5140 0.3182 0.4263 2.0000E- 04 0.2088 1293. 8.7539E -03 C 0.8960 0*3110 0.3722 6.0079E- 08 0*1521 742. 0*7,346 0.8772 0.3201 0*5373 0*0034 902. 3 5049 0. 5140 0.3346 0.4263 2.0000E- 04 0,2088 1293. 8.7539E -03 C 0.8960 0.32 75 0.3722 6.00 79E- 08 0. 1521 742. 0* 7346 0*8772 0*3201 0*53 73 0.0034 902. 3 5049 0.5140 0.32 96 0.4263 2.0000E-04 0.2088 1293. 8.7539E -03 C 0.8960 0*3225 0*3722 6.0079E- 08 0.1521 742. 0.7346 0.8772 0.3201 0.5373 0.0034 902. 35702 0*4510 0. 42 51 0.5312 5. OOOOE-05 0,4779 370o ,3.8248E -03 C 0*9620 0*4229 0.4711 6.0718E- 08 0*1537 173. 0. 7783 0. 9676 0.4114 0.1268 0,0050 213, 35702 0*4510 0*4262 0.5312 5.0000E- 05 0.4779 370. 3.8248E -03 C 0*9620 0*4240 0*4711 6.0718E-•08 0*1537 173, 0. 7783 0. 9676 0.4114 0,1268 0.0050 213. 35702 0.4510 0*4194 0.5312 5. OOOOE-05 0* 4779 370. 3.8248E -03 C 0.9620 0.4172 0.4711 6.0718E- 08 0,1537 173, 0.7783 0. 96 76 0.4114 0. 1268 0.0050 213* 35702 0.4510 0*4192 0.5312 5.GQO0E-05 0,4779 370, 3.8248E -03 C 0.9620 0.4170 0.4711 6.0718E- 08 0.1537 173. 0.7783 0. 9676 0*4114 0*1268 0,0050 213, 3 5 720 0*4980 0*3630 0*4628 I.OQOOE-04 0.3384 668. 5.4010E -03 C 0* 9270 0.3583 0.405 7 6.0389E- 08 0.1529 359. 0*7558 0.9219 0.350 2 0. 2611 0. 003 9 438. 35720 0*4980 0*3559 0*4628 l.OOOOE-•04 0.3384 668, 5.4010E -03 C 0.9270 0. 3511 0. 4057 6.0389E-•08 0.152 9 3 59* 0*7558 0.9219 0.3502 0*2611 0.0039 438, 3 5720 0. 4980 0.3698 0,4628 l.OOOOE-•04 0.3384 663. 5.4010E -03 u 0.9270 0.3651 0. 405 7 6.G389E-•08 0.1529 359. 0*7558 0.9219 0*350 2 0*2611 0*0039 438. 236. N2 , NH3 , 0.790 MICRON D. PARTICLES (CONTINUED). RUN YINT I EPEXP EPMO Q INT FILMR REI MTC TYPE Yl NTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 35720 0.4980 0.3699 0,4628 l.OOOOE-•04 0.3384 668. 5.4010E -03 C 0.9270 0.3652 0. 405 7 6.0389E- 08 0. 1529 359. 0.7558 0.9219 0.3502 0.2611 0.003 9 438. 35721 0.5090 0.2154 0.3131 l.OOOOE-•03 0.0844 6529. 2.1651E -02 C 0.7410 0.1944 0.2737 5. 8513E-•08 0. 1481 4471. 0.6298 0.6377 0.2357 3. 134 0.0023 5260. 35721 0.5090 0.2369 0.3131 l.OOOOE-•03 0.0844 6529. 2.1651E -02 C 0.7410 0.2164 0.2737 5.8513E- 08 0.1481 4471, 0.6298 0.63 77 0.2357 3.134 0.0023 5260. 35721 0.5090 0.2531 0,3131 l.OOOOE-•03 0,0844 S529, 2.1651E -02 C 0.7410 0.2331 0.2737 5.8513E- 08 0.1481 4471. 0.62 98 0.6377 0,2357 3,134 0.0023 5260. 3 5721 0.5090 0.2817 0.3131 l.OOOOE-•03 0.0844 6529. 2.1651E -02 C 0.7410 0.2624 0.2737 5.8513E-•0 8 0.1481 4471. 0.6298 0.6377 0.2357 3. 134 0.0023 5260. 35722 0.5090 0.2623 0.3008 1.2400E- 03 0. 0726 8096. 2.5159E -02 TC 0.7280 0.2415 0.2630 5.8402E-•08 0.1479 5642. 0.6225 0. 6127 0. 2264 3. 931 0.0022 6600, 35722 0.5090 0.2763 0.3008 1.2400E- 03 0.0726 3096. 2.5159E -02 TC 0. 7280 0.2559 0.263 0 5.8402E-•08 0.1479 5642. 0.6225 0.6127 0.2264 3.931 0.0022 6600. 3 572 2 0.5090 0o2824 0.3008 1.2400E- 03 0.0726 S096. 2.5159E -02 TC 0. 7280 0.2622 0.2630 5.8402E-•08 0.1479 5642. 0.6225 0.6127 0.2264 3. 931 0. 002 2 6600, 35722 0. 5090 0.2909 0.3008 1.2400E- 03 0.0726 8096. 2.5159E -02 TC 0.7280 0.2709 0. 2630 5. 8402E- 08 0.1479 5642. 0.6225 0.6127 0.2264 3.931 0.0022 6600. 3 5 723 0. 3550 0.3962 0.4462 6.7000E- 04 0.0932 6340. .1.9605 E--02 T 0.6410 0.3735 0.4055 5.6429E- 08 0.1429 3462. 0.4971 0.6917 0.3630 2,660 0.0039 4482. 35723 0.35 50 0.4068 0.4462 6.7000E-0 4 0.0932 6340. 1.9605E -0 2 T 0.6410 0.3845 0.4055 5.6429E- 08 0. 1429 3462, 0.4971 0.6917 0.3630 2.660 0.0039 4482, 35723 0.3550 0.4008 0. 4462 6.7000E- 04 0.0932 6340. 1.9605E -02 T 0.6410 0.3783 0.4055 5.6429E- 08 0.1429 3462. 0. 4971 0.6917 0.363 0 2.660 0.0039 4482. 35723 0.3550 0.3913 0.4462 6.7000E- 04 0. 0932 6340, 1.9605E -02 T 0.6410 0.3684 0.4055 5.6429E- 08 0.1429 3462. 0. 4971 0. 6917 0, 3630 2.660 0.0039 4482, 35723 0.3550 0.3748 0.4462 6.7000E- 04 0.0932 6340. 1. 9605E' -02 T 0.6410 0.3513 0.4055 5.6429E- 08 0.1429 3462. 0.49 71 0.6917 0.3630 2. 660 0.0039 4482. 35723 0.3550 0.3712 0.4462 6.7000E- 04 0.0932 6340, 1, 96056--02 T 0. 6410 0.3476 0.4055 5.6429E- 08 0.1429 3462. 0.4971 0.6917 0. 3630 2.660 0.0039 4482, 35724 0.4050 0.3740 0.4018 8.3000E- 04 0.0834 6853. 2. 1918E--02 T 0. 6770 0,352 9 0.3605 5.7160E-08 0.1447 4060, 0.5426 0.6752 0.3185 3.019 0. 0033 5077. 237. N2 , NH3 » 0 .790 MICRON D. PARTICLES (CONTIMUED). RUN YINTI EPEXP EPMO QI NT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN RED YINTLM EMT EPMA ULM UR RELM 35724 0o4050 0.3749 0.4018 8.3000E-04 0.0834 6853. 2. 1918E -02 T 0o6770 0.3539 0.3605 5.7160E-08 0.1447 4060. 0.5426 0.6752 0.3185 3.019 0. 003 3 5077. 35724 Oo4050 0.3545 0.4018 8.3000E-04 0.0834 6853. 2.1918E -02 T 0.6770 0. 3328 0. 3 605 5. 7160E-•08 0.1447 4060. 0o5426 0.6752 0.3185 3.019 0.0033 5077. 238. TABLE XVII DATA FOR N2 , NH3 , 1.011 MICRON DIAMETER PARTICLESo **************************************** INERT GAS FLOW RATE CONSTANT IN ALL RUNS. INLET TEMPo i DEGo K) 293o0 , PRESSURE (ATM,) loOOO CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: 1.0000 + 0.0 *YINTI + OoO *YTRNI/YINTI OUTLET : 1.0000 + 0.0 *YINTO + 0.035Q*YTRNQ/YIUT3 GAS MOLEC. WEIGHT DENSITY VISCOSITY MEAN FREE PATH VOLUME**(1/3) DIFFUSIVITY (G/GMOLE) (KG/M**3) ( KG/M/SEC) (M) (M/GM0LE**(l/3) ) (M**2/SEC) N2 { INERT) 28o 02 1.165 1.7480E-05 6.3900E-08 3.1190E-02 NH3 {TRANSFERRED) 17o 03 0.7182 9.8200E-06 4. 5700E-08 2.2240E-02 2.3212E-05 RUN YINTI EPEXP EPMO QINT FILMR REI TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 37089 0.2740 0.3770 0.4869 6.OOOOE-04 0.0970 7427. 0.5340 0.3955 0.4519 5.4767E-•08 0.1083 3730. 0.3981 0. 6706 0. 4137 2.974 0.0046 5043o 37089 0.2740 0.3733 0.4869 6.0000E- 04 0.0970 7427. 0.5340 0.3919 0.4519 5.4767E-•08 0.1083 3 730. 0. 3981 0.6706 0.4137 2.974 0 o0046 5043. 37089 0.2740 0.3646 0.4869 6.0000E- 04 0.0970 7427. 0. 5340 0. 3834 0.4519 5.4767E-•08 0.1083 3 730. 0.3981 0.6706 0.4137 2. 974 0. 0046 5043. 3 7089 0.2740 0.4185 0.4869 6.0000E-•04 0.0970 7427. 0.5340 0.4357 0.4519 5. 4767E-•08 0.1083 3730. 0.3981 0.6706 0.4137 2.974 0.0046 5 043, 37089 Oo 2740 0.4080 0.4869 6.0000E-•04 0.0970 7427. 0.5340 0. 42 55 0.4519 5.4767E- 08 0. 1083 3730o 0.3981 0.6706 0.4137 2.974 0.0046 5043. 37090 0.3510 G. 3424 0.4608 6.OOOOE-04 0.0988 5744. 0.6510 0.3545 0.4192 5.6480E- 08 0.1117 3053. 0.5002 0.7101 0.3757 2.367 0.0041 3938. 37090 0. 3510 0.3469 0. 4608 6.OOOOE-04 0.0988 5744. 0.6510 0.3589 0.4192 5.6480E- 08 0.1117 3053. 0.5002 0.7101 0.3757 2.367 0.0041 3988. 37090 0. 3510 0.3515 0. 4608 6. OOOOE-04 0.0988 5744. 0.6510 0.3634 0.4192 5.6480E- 08 0.1117 3053. 0. 5002 0. 71 01 0.3757 2.367 0.0041 3988. 37090 0.3510 0.3608 0.460 8 6.0000E- 04 0. 0988 5744. 0.6510 0.3726 0.4192 5.6480E- 08 0.1117 3 053. 0.5002 0.7101 0.3757 2.367 0.0041 3988. MTC 1.8840E-02 .lo8840E-02 lo8840E-02 1.8840E-02 1.8840E-02 1.8505E-02 1.8505E-02 1.8505E-02 lo 8505E-02 239. N2 , NH3 , l o O l l MICRON Do PARTICLES {CONTINUED} RUN YINT1 EPEXP EPMO QI NT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR R ELM 37091 0.4180 0.3089 0.4162 6.OOOOE-•04 0. 1054 4795. 1.7339E -02 0o7160 0.3184 0.3722 5.7603E-•08 0.1140 2776. 0.5708 0.7151 0. 3278 2.075 0.0034 3486. 37091 0.4180 0.3027 0.4162 6. OOOOE-•04 0.1054 4795. 1.7339E -02 0.7160 0.3122 0.3722 5.7603E--08 0.1140 2776. 0o5708 0. 7151 0. 32 78 2.075 0.0034 3486. 37091 0.4180 0.3107 0.4162 6.0000E- 04 0.1054 4795. 1.7339E -02 Oo 7160 0.3201 0.3722 5.7603E--08 0.1140 2776. 0o5708 0.7151 0.3278 2.075 0. 0034 3486. 37092 0.5040 0.2588 0.3588 6.0000E--04 0.1117 3957. 1.6358E -02 0.7860 0.265 8 0.3140 5.8877E--08 0.1165 2531. 0.6538 0.7233 0.2707 1.811 0. 0027 3039. 37092 0.5040 0.2772 0.3588 6.QQ00E-•04 0.1117 3957. 1.6358E -02 0.7860 0.2840 0.3140 5.8877E-•08 0. 1165 2531. 0.6538 0.7233 0.2707 lo811 0.0027 3039. 37092 0. 5040 0.2789 0.3588 6.0000E-•04 0.1117 3957. 1.6358E -02 0.7860 0.2857 0.3140 5.8877E- 08 0. 1165 2531. 0.6538 0.7233 0.2707 1.811 0.0027 3039. 3 7093 0. 63 00 0. 1924 0. 2640 6.0000E-•04 0.1257 3155. 1.4539E -02 0.8560 0.1971 0.2241 6. 03 73E- 08 0.1194 2328. 0.7547 0.7136 0.1877 1.569 0.0018 2635. 37 093 0.6300 0.198 5 0. 2640 6.OOOOE-•04 0.1257 3155. 1.45 39E -02 0.8560 0.2032 0.2241 6.0373E- 08 0.1194 2328. 0. 7547 0.7136 0.1877 1.569 0.0018 2635. 37093 0. 6300 0. 1952 0. 2640 6.OOOOE-04 0.1257 3155. 1.4539E -02 0.8560 0.1999 0.2241 6.0373E- 08 0.1194 2328. 0. 7547 0. 7136 0.1877 1.569 0.0018 2 635. 37094 0.7600 0.0847 0. 16 85 6.OOOOE-04 0. 1396 2616. 1.3091E -02 Oo 9140 0.0877 0.1387 6.1718E- 08 0.1221 2185. 0. 8476 0.7020 0. 1130 1.397 0.0010 2351. 37094 0.7600 0.0787 0.1685 6.0000E- 04 0.1396 2616. 1.3091E -02 0.9140 0, 0817 0.1387 6.1718E-•08 0.1221 2185. 0. 84 76 0. 7020 0.1130 1.397 0. 0010 2351. 37094 0.7600 0.0836 0.1685 6.QQ00E- 04 0.1396 2616. 1.3091E -02 0. 9140 0. 0866 0.1387 6.I718E- 08 0.1221 2185. 0.8476 0.7020 0.1130 1.397 0. 0010 2351. 37095 0.8750 0 o0352 0.0876 6.0000E- 04 0.1478 2279. 1.2369E--02 0.9590 0. 0366 0. 0702 6.2814E- 08 0.1243 2087. 0.9240 0.7007 0.0560 1.281 0.0005 2162. 3 7095 0.8750 0. 0417 0.0876 6.0000E- 04 0.1478 2 279. 1.2369E--02 0.9590 0.0431 0.0702 6.2314E- 08 0.1243 2087. 0.9240 0.7007 0 o0560 1.281 0.0005 2162. 37095 0. 8750 0. 0069 0.0876 6.0000E-04 0.1478 2279. 1.2369E--0 2 0.9590 0.0084 0.0702 6. 2814E-08 0. 1243 2087. 0.9240 0.7007 0.0560 1.281 0.0005 2162. 37095 0. 8750 0.0504 0.0876 6. OOOOE-04 0.1478 2279. 1.2369E--02 0.9590 0.0518 0. 0702 6.2814E- 08 0.1243 2087. 0.9240 0.7007 0. 0560 1.281 0.0005 2162. N2 , NH3 , 1.011 MICRON Do PARTICLES (CONTINUED). RUN YINTI EPEXP EPMO 01 NT FIL^IR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 37095 0.8750 0.1212 0.0876 6. OOOOE-•04 0.1478 2279. 1.2369E -02 0.9590 0.1225 0.0702 6.2814E-•08 0.1243 2087. 0.9240 0. 7007 0. 0560 1.281 0.0005 2162. 37095 Oo 8750 0.0926 0. 0 876 6.0000E-•04 0.1478 2279, 1.2369E -0 2 0.9590 0.0940 0.0702 6.2814E-•08 0.1243 2087. 0, 9240 0.7007 0. 0560 1.281 0.0005 2162. 3709 5 0.8750 0.0701 0.0876 6.0000E-•04 0.1478 2279. 1.2369E -02 0.9590 0.0715 0.0702 6.2814E-•08 0.1243 2087. 0.9240 0. 7007 0. 0560 1.281 0.0005 2162. 37100 0.2740 0.3827 0.4869 6.0000E-•04 Oo 0970 7427. 1.8840E -02 0.5340 0.4010 0.4519 5.4767E-•08 0.1083 3 7 30. 0.3981 0. 6706 0.4137 2.974 0.0046 5043. 37100 0.2740 0.3708 0.4869 6.0000E- 04 0.0970 7427. , 1. 8840E -02 0. 5340 0.3894 0.4519 5.4767E- 08 0.1083 3730. 0.3981 0.6706 0.4137 2.974 0o0046 5043, 37100 0.2740 0.3746 0.4,869 6.0000E- 04 0.0970 7427. 1. 8840E -02 0. 5340 0.3931 0.4519 5.4767E- 08 0.1083 3730. 0.3981 0.6706 0.4137 2.974 0.0046 5 043. 37100 0.2740 0.3685 0.4869 6.0000E-•04 0.0970 7427. 1.8840E -02 0.5340 0.3872 0. 4519 5.4767E-•08 0.1083 3 730. 0.3981 0.6706 0.4137 2.974 0.0046 5043, 38651 0. 3510 0.3685 0.4608 6.0000E- 04 0.0988 5744. 1.8505E -02 0. 6510 0. 3801 0.4192 5.6480E- 08 0.1117 3053. 0.5002 0.7101 0.3757 2o367 0.0041 3988, 38651 0. 3510 0.3519 0.4608 6cOOOOE-•04 0.0988 5744. .1.8505 E--02 0.6510 0.3638 0.4192 5. 6480E-08 0. 1117 3053. 0.5002 0.7101 0.3757 2.367 0.0041 3988. 38651 0.3510 0.3398 0. 4608 6o OQOOE-04 0.0988 5744. 1.8505E -02 0.6510 0.3520 0.4192 5.6480E- 08 0.1117 3053, 0.5002 0.7101 0.3 757 2.367 0.0041 3988. 38651 0.3510 0.3509 0.4608 6.OOOOE-04 0. 0988 5744. 1.8505E' -02 0.6510 0.3629 0.4192 5.6480E- 08 0.1117 3 053. 0.5002 0. 71 01 0.3757 2.367 0.0041 3988. 3 865 2 0.4180 0.2971 0.4162 6. OOOOE-04 0. 1054 4795 0 1.7339E--02 0.7160 0.3067 0.3722 5.7603E- 08 0.1140 2776. 0.5708 0. 7151 0.3278 2. 075 0.0034 3 4 36. 38652 0.4180 0.3098 0.4162 6.OOOOE-04 0.1054 4795. ,lo 7339E--02 0.7160 0.3193 0.3722 5.7603E- 08 0.1140 2776. 0.5708 0. 7151 0.32 78 2. 075 0.0034 3486. 38652 0.4180 0.3155 0.4162 6.0000E- 04 0.1054 4795. 1.7339E--02 0, 7160 0.3249 0.3722 5.7603E-08 0.1140 2776. 0.5708 0.7151 0.3278 2. 075 0. 0034 3486. 241. TABLE X V I I I DATA FOR N2 , NH3 , 2.020 MICRON DIAMETER PARTICLES-^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ • ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ • ^ ^ ^ ^ ***************** SERIES l o INERT GAS FLOW RATE CONSTANT IN ALL RUNSo INLET TEMPo (DEGo K) 293.0 , PRESSURE { AT Mo J 1.000 CALIBRATION CORRECT ION; INLET: 1.0000 + 0.0 OUTLET: 1.0000 + 0.0 COUNT/TRUE COUNT *YINTI + 0.0 *YTRNI/YINTI *YINT0 + 0.0 *YTRN0/YINT0 GAS N2 (INERT) NH3 (TRANSFERRED) MOLEC. WEIGHT DENSITY VISCOSITY (G/GMOLE) IKG/M**3) (KG/M/SEC) MEAN FREE PATH (M) V0LUME**( l/3) (M/GM0LE**(1/3)) 28.02 1.165 1.7480E-05 6.3900E-08 3.1190E-02 17.03 0.7182 9.8200E-06 4.5700E-08 2.2240E-02 DIFFUSIVITY (M**2/SECi 2.3212E-05 RUN YI NT I EPEXP EPMO QINT FILMR REI MTC TYPE Yl NTO EPCORR EPSW PLM KN RED YINTLM EMT EPMA ULM UR RELM 34414 0. 6300 0. 1982 0.2640 6.0000E- 04 0.1257 3155. 1.4539E -02 0.8560 0.1982 0.2241 6.0373E- 08 0. 059 8 2328. 0.7547 0.7136 0.1877 1.569 0.0018 2635. 34414 0.6300 0.2247 0. 2640 6. OOOOE-04 0.1257 3155. 1.4539E -02 0.8560 0.2247 0.2241 6. 0373E-08 0.0598 2328. 0.7547 0.7136 0,1877 1.569 0,0018 2635. 34414 0.6300 0. 1690 0.2640 6.OOOOE-04 0.1257 3155. 1.4539E -02 0.8560 0ol690 0.2241 6.0373E- 08 0.0598 2328. 0. 7547 0.7136 0.1877 1 .569 0.0018 2635. 34414 0.6300 0»2294 0.2640 6.Q000E- 04 0. 1257 3155. 1.4539E -02 0.8560 0.2294 0.2241 6.Q373E- 08 0.0598 2328. 0.7547 0.713 6 0.1877 1. 569 0.0018 2635. 34414 0.6300 0.1,98 5 0.2640 6.0000E- 04 0.1257 3155, 1.4539E -02 0.8560 0.1985 0.2241 6.0373E- 08 0.0598 2328. 0.7547 0.7136 0. 1877 1. 569 0. 0018 2635. 34416 0.5040 0.3451 0.3588 6.OOOOE-04 0.1117 3957. 1.63 58E -02 0. 786 0 0.3451 0.3140 5.8877E- 08 0.0583 2531. 0.6538 0.7233 0.2707 1.811 0.0027 3 039. 34416 0.5040 0.3081 0 o3588 6.0000E- 04 0.1117 3957. 1.6358E -02 0.7860 0.3081 0. 3140 5.8877E- 08 0.0583 2531. 0.6538 0.7233 0.2707 1. 811 0. 0027 3039. 34416 0.5040 0.2985 0.3588 6.0000E- 04 0.1117 3957. 1.6358E--02 0.7860 0. 298 5 0.3140 5. 8877E-08 0.0583 2531. 0.6538 0.7233 0.2707 1.811 0.0027 3039. 34416 0. 5040 0.3142 0,3588 6.0000E-04 0.1117 3957. 1.6358E -02 0,7860 0.3142 0.3140 5.8877E- 08 0. 0583 2531. 0.6538 0.7233 0.2707 1.811 0,0027 3 039. 242. N2 , NH3 , 2.020 MICRON D. PARTICLES (CONTINUED)0 RUN YINTI EPEXP EPMO QINT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 34417 Oo 4180 0.3748 0.4162 6.0QQ0E- •04 0.105 4 4795. 1.7339E -02 0 „ 7 1 6 0 0.3748 0. 3722 5.7603E-•08 Oo 0570 2776. 0.5708 0.7151 0.3278 2.075 0.0034 3486. 34417 0.4180 0.3973 0.4162 6.0000E-•04 0.1054 4795. 1.7339E -02 0.7160 0.3973 0.3722 5. 7603E-•08 0. 0570 2 776. 0.5708 0.7151 0.3278 2.07 5 0.0034 3486. 34417 0.4180 0.3857 0.4162 6. OOOOE-•04 0.1054 4795, 1.7339E -02 0.7160 0.3857 0.3722 5.7603E- 08 0.0570 2776. 0.5708 0.7151 0.3278 2.075 0.0034 3486. 34418 0.2740 0. 5043 0. 4869 6. OOOOE- 04 0.0970 7427, 1.8840E -02 0.5340 0.5043 0.4519 5.476 7E- 08 0.0542 3 730, Oo 3981 0.6706 0.4137 2.974 0.0046 5043, 3441 8 0.2740 0.5051 0.4869 6. OOOOE- 04 0. 0970 7427. 1.8840E -02 0.5340 0.5051 0.4519 5.4767E- 08 0.0542 3730, 0.3981 0. 6706 0.4137 2. 974 0.0046 5043. 34420 0.3050 0.4776 0.4831 6.0000E- 04 0.0961 6645. 1.9013E -02 0.5900 0.4776 0.4447 5.5541E-•08 0.0550 3371. 0.4433 0.6950 0. 4036 2.671 0,0045 4513. 34420 0.3050 0.4821 0.4831 6.OOOOE- 04 0.0961 6645, 1.9013E -02 0. 5900 0.4821 0. 4447 5.5541E- 08 0.0550 3371. 0.4433 0.6950 0.4036 2.671 0.0045 4513. 34420 0.3050 0.4823 0.4831 6.0000E- 04 0.0961 6645. :1.9013E -02 0.5900 0.4823 0.4447 5.5541E- 08 0.0550 3371. 0.4433 0.6950 0.4036 2.671 0.0045 4513. 34421 0.3510 0.3936 0.4608 6.00G0E- 04 0.0988 5744. 1.8505E -02 0. 6510 0. 3936 0.4192 5o 64 80E- 08 0.0559 3053. 0.5002 0.7101 0.3757 2.367 0.0041 3988. 34421 Oc 3510 0.3855 0.4608 6.0000E- 04 0.0988 5 744. i ,8505E--02 0.6510 0.3855 0.4192 5.6480E- 03 0. 055 9 3053, 0.5002 0.7101 0.3757 2.36 7 0.0041 3988. 34421 0. 3510 0.3917 0.4608 6.QOOOE- 04 0.0988 5744. 1.8505E--02 0.6510 0.3917 0.4192 5. 6480E- 08 0. 0559 3 053. 0.5002 0.7.101 0.3757 2,367 0.0041 3983, 34421 0.3510 0.4178 0.4608 6. OOOOE- 04 0.0988 5744. 1,8505E--02 0.6510 0.4178 0.4192 5.6480E- 08 0.0559 3053. 0.5002 0.7101 0.3757 2.367 0.0041 3988. 34421 0.3510 0.4325 0. 4608 6.OOOOE- 04 0.0988 5744, lo8505E--02 0o6510 0*43 25 0.4192 5.6480E- 08 0.0559 3053. Oo 5002 0. 71 01 0.3757 2.367 0.0041 3988, 243. TABLE XIX DATA FOR N2 , NH3 , 2o020 MICRON DIAMETER PARTICLES-******** ******************* * * * * * * ^ * * * * * * * * # * * * * * * # * * * SERIES 2o * * * i « * * * * * INERT GAS FLOW RATE CONSTANT IN ALL RUNS. INLET TEMP* (DEGo .KJ 293 o0 , PRESSURE (ATMoJ, loOOO CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: loOOOO + 0.0 *YINTI + 0.0 * YTRNI/YINTI OUTLET: 0.8550 + 0.1450*YINTQ • 0.0 *YTRN0/YINT3 GAS MOLEC. WEIGHT DENSITY VISCOSITY MEAN FREE PATH V0LUME**(l/3) DIFFUSIVITY ( G/GMQLE ) tKG/M**3) (KG/M/SEC) IM) <M/GM0LE**(l/3)) (M**2/S£C) N2 { INERT ) 28.02 1.165 1.7480E-05 6.3900E-08 3.1190E-02 NH3 I TRANSFERRED) 17. 03 0.7182 9.8200E-06 4. 5700E-08 2.2240E-02 2.3212E-05 RUN YINTI EPEXP EPMO QI NT F ILMR REI TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 34436 0.2740 0.5283 0.4869 6. OOOOE-04 0.0970 7427, 0.5340 0.4941 0.4519 5.4767E-•08 0.0542 3 730. 0.3981 0.6706 0.4137 2.974 0.0046 5043. 34436 0.2740 0.5100 0.4869 6.0000E- 04 0.0970 7427. 0. 5340 0.4745 0.4519 5.4767E- 08 0.0542 3 730, 0.3981 0.6706 0.4137 2.974 0.0046 5043, 34436 0.2740 0.5134 0.4869 6.0000E- 04 0.0970 7427. 0. 5340 0.4781 0.4519 5.4767E- 08 0.0542 3 730, 0.3981 0.6706 0.4137 2.974 0. 0046 5043, 34442 0.3050 0.4958 0,4831 6.0000E- 04 0.0961 6645, 0.5900 0. 4639 0, 4447 5.5541E-•08 0.0550 3371, 0.4433 0.6950 0.4036 2.671 0.0045 4513, 34442 0. 3050 0,4739 0,4831 6.0000E-•04 0.0961 6645, 0.5900 0. 4406 0.4447 5.5541E- 08 Oo 0550 3371, 0.4433 0.6950 0.4036 2.671 0.0045 4513. 34442 Oc 3 05 0 0*4712 0.4831 6,OOOOE-04 0.0961 6645o 0.5900 0.4378 0.4447 5, 5541E- 08 0. 0550 3371. 0.4433 0.6950 0.4036 2.671 0.0045 4513. 3443 8 0.3510 0. 42 85 0.4608 6.OOOOE-04 0.0988 5744. 0.6510 0.3980 0.4192 5.6480E- 08 0.055 9 3053. 0.5002 0.7101 0,3757 2.367 0.0041 3988. 3443 8 0. 3510 0. 4534 0. 4608 6. OO.OOE-04 0.0988 5744, 0.6510 0.4243 0.4192 5.6480E- 08 0.0559 3053. 0. 5002 0. 71 01 0.3757 2.367 0.0041 3988. 3443 8 0.3510 0.4535 0.4608 6.0000E- 04 0. 0988 5 744. 0.6510 0.4,244 0.4192 5.6480E- 08 0.0559 3053. 0.5002 0. 7101 0.3757 2.367 0.0041 3988. MTC 1.8840E-02 lo 8840E-02 ,1. 8840E-02 1.9013E-02 l,9013E-02 1.9013E-02 1.8505E-02 1.8505E-02 1.8505E-02 244. N2 , NH3 , 2o020 MICRON Do PARTICLES (CONTINUED) RUN YINTI EPEXP EPMO QI NT FILMR REI MTC TYPE Y INTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR R ELM 3443 8 0o3510 0.4502 0.4608 6.0000E-•04 0.0988 5 744. 1.8505E -02 0o6510 0.4209 0.4192 5.6480E- 08 0.0559 3053. 0o5002 0.7101 0. 3757 2.36 7 0.0041 3983. 34439 0o4180 0.3928 0.4162 6.0000E- 04 0.1054 4795, 1.7339E -02 0o7160 0.3667 0.3722 5.7603E-•08 0.0570 2776, 0o5708 0. 7151 0. 3278 2.075 0.0034 3 4 86. 34439 0.4180 0.3978 0.4162 6.0000E- 04 Oo1054 4795. 1.7339E -02 0o7160 0.3719 0.3722 5.7603E-•08 0.0570 2776. 0o5708 0.7151 0.3278 2. 075 0. 0034 34 86. 3443 9 0o4180 0.4090 0.4162 6 0 O O O O E - 04 0.1054 4795. 1.7339E -02 0c7160 0.383 6 0.3722 5.7603E-•08 0.0570 2776. 0o5708 0.7151 0.3278 2o 075 0.0034 3486, 34440 Oo 5040 0.2779 0.3588 6.0000E- 04 0.1117 3957. 1.6358E -02 Oo 7860 0. 2548 0.3140 5.8877E- 08 0.0583 2531. 0o6538 0.7233 0.2707 1.8.11 0.0027 3039. 34440 Oo 5040 0.3288 0.3588 6.0000E- 04 0.1117 3957, 1.6358E -02 0 » 7 8 6 0 0.3073 0.3140 5. 8877E- 08 0. 0583 2531. 0o6538 0.7233 0.2707 1.811 0.0027 3039, 34440 Oo 5040 0.3536 0. 3 58 8 6.OOOOE- 04 0,1117 3957. 1.6358E -02 0o7860 0.3329 0.3140 5. 8877E- 08 0.0583 2531, 0o6538 0.7233 0.2707 1.811 " 0,0027 3039. 34441 0.6300 0.2304 0.2640 6.0000E- 04 0.1257 3155, 1.4539E -02 0.8560 0.2140 0.2241 6.0373E- 08 0.059 8 2328. 0o 7547 0.7136 0.1877 1.569 0,0018 2635. 34441 0o6300 0.2346 0.2640 6.0000E- 04 0, 1257 3155. 1.4539E -02 0o8560 0.2183 0.2241 6.Q373E- 08 0.0598 2328. 0.7547 0. 7136 0. 18 77 1. 569 0,0018 2 635. 34441 0.6300 0.2434 0.2640 6.0000E- 04 0.1257 3155. 1.4539E -02 0.8560 0.2273 0.2241 6.03 73E-08 0.0598 2328. 0.7547 0. 7136 0. 1877 1. 569 0.0018 2635, 34443 0.7600 0.1393 0.168 5 6.0000E- 04 Oo1396 2616. 1. 3091E -02 0. 9140 0.1284 0.1387 6.1718E- 08 0 .0611 2185. 0.8476 0.7020 0.1130 1.3.97 0. 0 0 1 0 2351. 34443 0.7600 0.1443 0.1685 6.0000E- 04 0.1396 2616. 1.3091E--02 0.9140 0.1335 0. 1387 6. 1718E- 08 0.0611 2185. 0.8476 0.7020 0.1130 1.3 97 0 . 0 0 1 0 2351, 34443 0.7600 0.1488 0.1685 6.0000E- 04 0 .139 6 2616. 1.3091E--02 0.9140 0. 1381 0. 1387 6.1718E- 08 0.0611 2185. 0.8476 0.7020 0.1130 1.397 0 . 0 0 1 0 2351. 34443 0.76 00 0.1796 0.1685 6.0000E- 04 0.1396 2616. 1.3091E--02 0.9.140 0.1692 Oo 1387 6. 1718E- 08 0.0611 2185. 0.8476 0.7020 Oo 1130 1.397 0.0010 2351, 34444 0.8750 0. 0651 0.08 76 6.0000E- 04 0.1478 2279. 1.2369E--02 0.9590 0.0595 0.0702 6o2814E- 08 0.0622 2087. 0. 9240 0.7007 0.0560 1.281 0.0005 2162. 34444 0.8750 0.0520 0.0876 6. OOOOE- 04 0.1478 2279, 1.2369E -02 0.9590 0.0463 0.0702 6.2814E- 08 0.0622 2087. 0. 9240 0.7007 0.0560 1.281 0.0005 2162. 245. N 2 , M H 3 , 2 o 0 2 0 M I C R O N Oo P A R T I C L E S ( C O N T I N U E D ) . R U N Y I N T I E P E X P E P M O O I N T F I L M R R E I M T C T Y P E Y I N T O E P C O R R E P S W P L M K N R E D Y I N T L M E M T E P M A U L M UR R E L M 3 4 4 4 4 0 , 8 7 5 0 0 , 0 8 4 2 0 , 0 8 7 6 6 , O O O O E - 0 4 0 . 1 4 7 8 2 2 7 9 , 1 . 2 3 6 9 E - 0 2 0 , 9 5 9 0 0 . 0 7 8 7 0 , 0 7 0 2 6 o 2 8 1 4 E - 0 8 0 . 0 6 2 2 2 0 8 7 . Oo 9 2 4 0 0 , 7 0 0 7 0 , 0 5 6 0 1 . 2 8 1 0 , 0 0 0 5 2 1 6 2 . 3 4 4 4 4 0 o 8 7 5 0 0 , 1 1 5 2 0 , 0 8 7 6 6 . 0 0 0 0 E - 0 4 0 . 1 4 7 8 2 2 7 9 . 1 . 2 3 6 9 E - 0 2 0 o 9 5 9 0 G o 1 0 9 9 O o O 7 0 2 6 . 2 8 1 4 E - 0 8 0 . 0 6 2 2 2 0 8 7 o 0 , 9 2 4 0 0 , 7 0 0 7 0 , 0 5 6 0 1 . 2 8 1 0 . 0 0 0 5 2 1 6 2 . TABLE XX DATA FOR AR , NH3 , 0.790 MICRON DIAMETER PARTICLES. **************************************** INERT GAS FLOW RATE CONSTANT IN ALL RUNS. INLET TEMP. (DEG. K) 293.0 , PRESSURE (ATM.) 1.000 CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: 1.0000 + 0.0 #YINTI + 0.0 #YTRNI/YIMTI OUTLET: 1.0000 + 0.0 *YINTQ + 0.0 *YTRN0/YINT3 GAS MOLEC. WEIGHT DENSITY VISCOSITY MEAN FREE PATH V0LUME**(l/3) (G/GMOLE) (KG/M**3) (KG/M/SEC) (M) (M/GMOLE**( 1/3) ) AR (INERT) 39.91 '1.661 2.2170E-Q5 6.7900E-08 2. 8970E-02 NH3 (TRANSFERRED) 17.03 0.7182 9.8200E-06 4.5700E-08 2.2240E-02 DIFFUSI VITY ( M**2/SEC) 2.3802E-05 RUN YINTI EPEXP EPMO QINT FILMR REI • MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 31905 0. 5080 0.1671 0.3658 5.6000E-•04 0.1165 3 791. 1.6082E- 02 0.8010 0.1671 0.2881 6.1662E- 08 0.1561 2522. 0.6649 0.7435 0.2174 l o 6 6 2 0.0021 2964. 31905 0.5080 0. 1610 0.3658 5.6000E-•04 0.1165 3 791. 1.6082E-•02 0.8010 0.1610 0.2881 6.1662E- 08 0.1561 2522. 0.6649 0.7435 0.2174 1.662 0.0021 2964. 3190 5 0,5080 0.2124 0. 3658 5. 6000E- 04 0. 1165 3 791. 1.6082E-•02 0.8010 0.2124 0.2881 6.1662E- 08 0.1561 2522. 0. 6649 0. 7435 0.2174 1.662 0.0021 2964. 31906 0.4360 0.2579 0.4248 5. 6000E- 04 0. 1064 4382. 1.7619E-•02 0,7580 0.2579 0.3450 6oQ634E- 08 0.153 5 2644. 0.6041 0. 753 2 0. 2679 1. 829 0.0027 3231. 31906 0.4360 0.3078 0.4248 5. 6000E- 04 0»1064 4382. 1.7619E- 02 0,7580 0.3078 0.3450 6.0634E- 08 0.1535 2644. 0.6041 0. 7532 0. 2679 1. 829 0.0027 3 231. 31906 0.4360 0.3235 0.4248 5.6000E- 04 0.1064 4382. 1.7619E- 02 0. 7580 0.323 5 0.3450 6.0634E- 08 0.1535 2644. 0.6041 0.753 2 0. 2679 1. 829 0. 0027 3231. 31907 0. 3600 0.3426 0.4857 5.6000E- 04 0.0963 5279. 1.9460E- 02 0.7000 0.3426 0. 4078 5. 9407E-08 0.1504 2833. 0.5316 0.7589 0.3274 2. 079 0.0035 3 633. 31907 0.3600 0.3729 0.4857 5.6000E- 04 0.0963 5279, 1.9460E- 02 0,7000 0.3729 0. 4078 5. 9407E-08 0.1504 2833. 0.5316 0.7589 0.3274 2.079 0.0035 3633. 31908 0.6240 0.1928 0.2794 5.6000E- 04 0.1268 3133. 1.4786E- 02 0.8660 0.1928 0.2099 6.32 79E-08 0. 1602 2363. 0.7588 0.7432 0.1520 1.456 0.0014 2642. 2 4 7 . AR » NH3 , Oo790 MICRON Do PARTICLES (CONTINUED). RUN YINT I EPEXP EPMO QINT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 31908 0.6240 0.1845 0.2794 5.6000E--04 0.1268 3138. 1.4786E -02 0.8660 0.1845 0.2099 6.3279E-•08 0,1602 2363. 0.7588 0.7432 0.1520 1,456 0.0014 2642. 31909 0.7960 0. 0669 0. 1404 5.6000E--04 0,1621 2536. 1.1559E -02 0.9260 0.0669 0.0987 6.5304E-•08 0. 1653 2237. 0.8702 0«6882 0.0678 1.270 0,0006 2354. 31909 0. 7960 0.0564 0.1404 5. 6000E--04 0.1621 2536. 1.1559E -02 0.9260 0.0564 0.0987 6.5304E- 08 0.1653 2237. 0. 8702 0.6882 0.0678 1.270 0,0006 2354. 31909 0.7960 0. 0474 0.1404 5.6000E-•04 0. 1621 2536. 1.1559E -02 0.9260 0.0474 0 o0987 6.5304E- 08 0.1653 2237. 0. 87 02 0. 6882 0.0678 1,270 0.0006 23 54. 31912 0.3600 0.3761 0.4857 5.6000E-•04 0, 0963 52 79. 1.9460E -02 0.7000 0.3761 0,4078 5.9407E-•08 0.1504 2833. 0. 5316 0.75 89 0.3274 2. 079 0.0035 3633. 31913 0.3600 0.3088 0.4857 5,6000E- 04 0.0963 5 279. 1.9460E -02 0.7000 0.3088 0.4078 5.9407E-•08 0.1504 2833. 0.5316 0. 7589 0. 32 74 2o 079 0.0035 3633. 31913 0.3 600 0.3253 0.4857 5.6000E- 04 0.0963 5279. 1,9460E -02 0. 7000 0.32 53 0.4078 5.9407E-•08 0. 1504 2 833. 0.5316 0.7589 0.3274 2.079 0. 003 5 3633. 31914 0.4360 0.3395 0.4248 5.6000E- 04 0.1064 4382. 1.7619E -02 0.7580 0. 3395 0.3 450 6. 0634E-•08 0.1535 2644. 0.6041 0.7532 0.2679 1.829 0.0027 3 231. 31914 0. 4360 0.32 01 0.4248 5.6000E-•04 0.1064 4382. 1.7619E -02 0.7580 0. 32 01 0.3450 6.0634E- 08 0. 1535 2644. 0.6041 0.7532 0 o2679 1.829 0.0027 3231. 31915 0.5080 0. 2510 0.3658 5.6000E- 04 0.1165 3791. 1.6082E--02 0.8010 0.2510 0.2881 6.1662E- 08 0. 1561 2522. 0.6649 0.7435 0.2174 1.662 0.0021 2964. 31916 0. 6240 0.1481 0. 2794 5. 6000E-04 0.1268 3138. 1.4786E--02 0.8660 0,1481 0.2099 6.3279E- 08 0.1602 2363. 0.7588 0. 7432 0.1520 1.456 0,0014 2642. 31916 0.6240 0.1506 0. 2794 5.6000E- 04 0. 1268 3138. 1.4786E -02 0.8660 0.1506 0.2099 6.3279E- 08 0.1602 2363. 0. 7588 0.7432 0.1520 1.456 0.0014 2 642. 31918 0.4360 0.2479 0.4248 5. 6000E-04 0. 1064 4382. 1.7619E--02 0.7580 0.2479 0.3450 6.0634E- 08 0.1535 2644. 0.6041 0. 7532 0. 2679 1, 829 0.0027 3231. 31918 0.4360 0.2595 0.4248 5.6000E- 04 0.1064 43 82» 1. 7619E--02 0.7580 0.2595 0.345 0 6,0634E- 08 0.1535 2644. 0.6041 0.7532 0, 2679 1,829 0.0027 3 231, 31919 0.3600 0.3753 0.4857 5o6000E- 04 0.0963 5279. lo 9460E--02 0. 7000 0.3753 0.4078 5,9407E-08 0,1504 2833. 0.5316 0.7589 0.3274 2. 079 0.0035 3633. 31919 0. 3600 0.3940 0.4857 5.6000E-04 0.0963 5279. 1.9460E--02 0.7000 0.3940 0.4078 5.9407E- 08 0.1504 2833. 0.5316 0.7589 0,3274 2.079 0.0035 3633. 248. AR , NH3 t 0.790 MICRON D. PARTICLES (CQNTIMUED). RUN YINTI EPEXP EPMO QINT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 31920 0.6240 0.1462 0.2794 5.6000E-04 0.1268 3138. 1.4786E-02 0.8660 0. 1462 0.2099 6.3279E-08 0.1602 2363. 0.7588 0.7432 0.1520 1.456 0.0014 2642. 249 . TABLE XXI DATA FOR CF2CL2 , NHS , 0.790 MICRON DIAMETER PARTlCLESo THREE CONSTANT INERT GAS FLOW RATES USED, INLET TEMP. (DEGc K) 293.0 , PRESSURE (ATM 0) 1.000 CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: 1.0000+ 0 o0 *YINTI' •+ 0.0303*YTRNI/YINTI OUTLET: 1.0000 + 0 o0 *YINT0 + 0o0308*YTRN0/YIMTQ GAS MOLEC. WEIGHT DENSITY VISCOSITY ( G/GMOLE i (KG/M**3) (KG/M/SEC) MEAN FREE PATH (M) VOLUME** (1/3) (M/GMOLE**(l/3) ) CF2CL2 ( INERT) 120 o 9 5,136 1.2500E-05 2,1800E-Q8 4.3310E-02 NH3 (TRANSFERRED) 1 7o 03 0,7182 9.8200E-06 4, 5700E-08 2.2240E-02 DIFFUSIVITY (M**2/SEC) 1.2991E-Q5 RUN Y1NTI EPEXP EPMO QI NT FILMR REI TYPE YINTO EPCORR EPSW PLM KN REO YlNTLM EMT EPMA ULM UR R ELM 32807 0,1400 0,6455 0,8313 9.8000E- 05 0.0816 4426. 11 0,8300 0,5811 0.6742 1.9825E- 08 0.0502 2109. 0,4699 0, 9667 0. 4484 0. 4116 0. 0060 2498. 32307 0,1400 0.7035 0,8313 9.8000E- 05 0.0816 4426. 11 0, 8300 0,6497 0.6742 1.9825E-•08 0.0502 2109. 0,4699 0, 9667 0,448 4 0.4116 0. 006 0 2498. 32807 0ol400 0,6828 0.8313 9.8000E-•05 0.0816 4426. 11 0,8300 0,62 52 0,6742 1,9825E- 08 0.0502 2109. 0,4699 0,9667 0,4484 0.4116 0. 0060 2498, 32807 0, 1400 0,6499 0.8313 9.8000E-•05 0.0816 4426. 11 0,8300 0,5863 0, 6 742 1.9825E- 08 0.0502 2109. 0,4699 0,9667 0.4484 0.4116 0.0060 2498. 32813 0, 2600 0 o5545 0,7216 9.8000E- 05 0.0991 3179. I 1 0,9340 0,5165 0.5036 1.8923E- 08 0.0479 2050. 0,6513 0.9752 0.2790 0.2970 0.0030 2251, 32813 Oo 26 00 0,52 52 0.7216 9.8000E-05 0.0991 3179. 11 0,9340 0,4847 0.5036 1.8923E- 08 0. 0479 2050. 0,6513 0,9752 0.2790 0,2970 0.0030 2251. 32816 0, 4300 0,3725 0. 5567 9, 8000E-05 0.1213 2 579. 11 0,9700 0,3475 0.3244 1.9239E- 08 0.0487 2 032, 0, 7828 0,9767 0.1536 0.2471 0.0014 2141. 32816 0,4300 0,3604 0.5567 9.8000E-05 0. 1213 2579, 11 0,970 0 0,3349 0.3244 1.9239E- 08 0.0487 2032. 0, 782 8 0, 9767 0.1536 0,2471 0.0014 2141. 32816 0,4300 0,3596 0.5567 9,8000E- 05 0. 1213 2 5 79. 11 0,9700 0,3341 0.3244 1,9239E- 08 0.0487 2032. 0,7828 0, 9767 0. 1536 0, 2471 0.0014 2141. MTC 1.2539E-02 1. 2539E-02 1.2539E-02 1.2539E-02 1.0323E-02 1.0323E-02 8.4315E-03 8.4315E-03 8.4315E-03 2 5 0 . C F 2 C L 2 , N H 3 , 0 o 7 9 0 M I C R O N Do P A R T I C L E S C O N T I N U E D ) . RUN Y I N T I E P E X P EPMO QI NT F I L M R R E I • MTC T Y P E Y I N T O E P C O R R EPSW P L M KN R E O Y I N T L M EMT EPMA U L M UR R E L M 3 2 8 1 6 0 . 4 3 0 0 0 . 3 6 4 0 0 . 5 5 6 7 9 . 8 0 0 0 E - 0 5 0 . 1 2 1 3 2 5 7 9 . 8 . 4 3 1 5 E - 0 3 11 Oo 9 7 0 0 0 . 3 3 8 7 0 . 3 2 4 4 1 . 9 2 3 9 E - •08 0 . 0 4 8 7 2 0 3 2 . 0 , 7 8 2 8 0 . 9 7 6 7 0 . 1 5 3 6 0 . 2 4 7 1 Oo 0 0 1 4 2 1 4 1 . 3 2 8 1 7 0 , 6 5 1 0 0 . 0 9 7 7 0 . 3 4 1 1 9 . 8 0 0 0 E - 05 0 . 1 4 3 0 2 2 5 2 . 7 0 1 5 3 7 E - 0 3 I 1 0 . 9 8 8 0 0 . 0 8 3 2 0 . 1 6 3 7 2 . 0 1 2 4 E - •08 0 . 0 5 0 9 2 0 2 4 . 0 , 8 8 9 7 0 . 9 7 7 3 0 . 0 6 8 6 0 . 2 1 7 4 0 . 0 0 0 6 20 7 3 . 3 2 8 1 7 0 , 6 5 1 0 0 . 1 0 2 2 Oo 3.411 9 . 8 0 0 0 E - 0 5 0 . 1 4 3 0 2 2 5 2 . 7 . 1 5 3 7 E - 0 3 I 1 0 , 9 8 8 0 0 . 0 8 7 7 0 . 1 6 3 7 2 . 0 1 2 4 E - •08 0 . 0 5 0 9 2 0 2 4 . 0 , 8 8 9 7 0 . 9 7 7 3 0 , 0 6 8 6 0 . 2 1 7 4 0 . 0 0 0 6 2 0 7 3 o 3 2 8 1 7 0 , 6 5 1 0 0 . 1 1 8 1 0 , 3 4 1 1 9 . 8 0 0 0 E - 0 5 0 . 1 4 3 0 2 2 5 2 . 7 . 1 5 3 7 E - 0 3 I 1 0 , 9 8 8 0 0 . 1 0 3 9 0 . 1 6 3 7 2 . 0 1 2 4 E - •08 0 . 0 5 0 9 2 0 2 4 . 0 , 8 8 9 7 0 . 9 7 7 3 0 , 0 6 8 6 0 . 2 1 7 4 0 . 0 0 0 6 2 0 7 3 , 3 2 8 1 7 0 , 6 5 1 0 0 . 1 2 71 0 . 3 4 1 1 9 . 8 0 0 0 E - •05 0 . 1 4 3 0 2 2 5 2 . 7 . 1 5 3 7 E - 0 3 I 1 0 . 9 8 8 0 0 . 1 1 3 0 0 . 1 6 3 7 2 . 0 1 2 4 E - 0 8 0 . 0 5 0 9 20 2 4 , 0 . 8 8 9 7 0 o 9 7 7 3 0 . 0 6 8 6 0 . 2 1 7 4 0 . 0 0 0 6 2 0 7 3 , 3 2 8 1 7 0 , 6 5 1 0 0 . 1 4 5 4 0 . 3 4 1 1 9 . 8 0 0 0 E - •05 0 . 1 4 3 0 2 2 5 2 . 7 . 1 5 3 7 E -0.3 I I 0 . 9 8 8 0 0 . 1 3 1 6 0 . 1 6 3 7 2 . 0 1 2 4 E - 0 8 0 . 0 5 0 9 2 0 2 4 . 0 . 8 8 9 7 0 o 9 7 7 3 0 . 0 6 8 6 0 . 2 1 7 4 0 . 0 0 0 6 2 0 7 3 . 3 2 8 1 8 0 . 1 8 4 0 0 . 5 76 7 0 . 7 9 3 3 9 . 8 0 0 0 E -•05 0 . 0 8 7 6 3 7 8 6 , 1 . 1 6 7 3 E - 0 2 11 0 . 8 9 0 0 0 . 5 2 0 8 0 . 6 0 7 2 U 9 1 9 5 E - 0 8 0 . 0 4 8 6 2 0 7 3 . 0 . 5 5 4 9 0 . 9 7 2 1 0 . 3 7 3 7 0 . 3 4 8 6 0 . 0 0 4 5 2 3 6 4 . 3 2 8 1 8 0 , 1 8 4 0 0 . 5 9 2 1 0 , 7 9 3 3 9o 8 0 0 0 E - 05 0 . 0 8 7 6 3 7 8 6 . 1 . 1 6 7 3 E - 0 2 11 0 . 8 9 0 0 0 . 5 3 8 2 0 . 6 0 7 2 1 . 9 1 9 5 E - 0 8 0 . 0 4 8 6 2 0 7 3 . 0 . 5 5 4 9 0 . 9 7 2 1 0 , 3 7 3 7 0 . 3 4 8 6 0 . 0 0 4 5 2 3 6 4 . 3 2 8 1 8 0 , 1 8 4 0 0 . 5 8 4 3 0 . 7 9 3 3 9 . 8 0 0 0 E - 0 5 0 . 0 8 7 6 3 7 8 6 . 1 . 1 6 7 3 E - 0 2 11 0 . 8 9 0 0 0 . 5 2 9 4 0 . 6 0 7 2 1 . 9 1 9 5 E - 0 8 0 . 0 4 8 6 2 0 7 3 . 0 . 5 5 4 9 0 . 9 7 2 1 0 . 3 7 3 7 0 . 3 4 8 6 0 . 0 0 4 5 2 3 6 4 , 3 2 8 2 2 0 . 2 8 5 0 0 . 3 6 7 8 0 . 6 3 1 8 2 . 4 8 0 0 E - 0 4 0 . 0 7 1 9 7 7 1 4 , l o 4 2 3 2 E - 0 2 13 0 . 7 7 4 0 0 , 3 2 5 1 0 . 4 2 85 1 . 9 3 1 8 E - 08 0 . 0 4 8 9 5 4 3 3 . Oo 5 3 3 3 0 . 8 8 3 6 0 . 2 3 0 7 0 . 9 1 7 7 0 . 0 0 2 3 5 0 5 8 , 3 2 8 2 2 0 . 2 8 5 0 0 . 3 4 8 3 0 . 6 3 1 8 2 . 4 8 0 0 E - 0 4 0 . 0 7 1 9 7 7 1 4 , 1 . 4 2 3 2 E - 0 2 1 3 Oo 7 7 4 0 0 . 3 0 4 2 0 . 4 2 85 1 . 9 3 1 8 E - 0 8 0 . 0 4 8 9 5 4 3 3 , 0 . 5 3 3 3 0 . 8 8 3 6 0 . 2 3 0 7 0 o 9 1 7 7 0 . 0 0 2 3 6 0 5 8 , 3 2 8 2 2 , . 0 o 2 8 5 0 0 . 3 5 2 0 0 o 6 3 1 8 2 . 4 8 0 0 E - 0 4 Oo 0 7 1 9 7 7 1 4 . 1 . 4 2 32E - 0 2 13 0 . 7 7 4 0 0 . 3 0 8 2 0 . 4 2 8 5 1 . 9 3 1 8 E - 0 8 0 . 0 4 8 9 5 4 3 3 . 0 . 5 3 3 3 0 . 8 8 3 6 0 . 2 3 0 7 0 . 9 1 7 7 0 . 0 0 2 3 6 0 5 8 . 3 2 8 2 2 0 . 2 8 5 0 0 , 3 6 2 5 0 . 6 3 1 8 2 . 4 8 0 0 E - 0 4 0 . 0 7 1 9 7 7 1 4 . 1 . 4 2 3 2 E - 0 2 13 0 . 7 7 4 0 0 . 3 1 9 4 0 , 42 85 1 . 9 3 1 8 E - 08 0 . 048 9 5 4 3 3 . 0 . 5 3 3 3 0 . 8 8 3 6 0 . 2 3 0 7 0 . 9 1 7 7 0 . 0 0 2 3 6 0 5 8 . 3 2 8 2 2 0 . 2 8 5 0 0 . 3 4 2 9 0 . 6 3 1 8 2 . 4 8 0 0 E - 0 4 0 . 0 7 1 9 7 7 1 4 , I . 4 2 3 2 E - 0 2 13 0 . 7 7 4 0 0 . 2 9 8 5 0 . 4 2 8 5 1 . 9 3 1 8 E - 08 0 . 0 4 8 9 5 4 3 3 . Oo 5.333 0 . 8 8 3 6 0 . 2 3 0 7 0 . 9 1 7 7 0 . 0 0 2 3 6 0 5 8 . 3 2 8 2 6 0 . 5 9 7 0 0 . 0 5 1 6 0 , 3 7 4 9 1 . 9 2 0 Q E - 0 4 0 . 1 0 1 4 4 5 2 7 , 1 . 0 0 9 2 E - 0 2 12 0 . 9 5 5 0 0 . 0 3 3 3 0 , 1 8 8 0 1 . 9 5 0 2 E - 08 0 . 0 4 9 4 3 9 9 6 o 0 . 8 2 3 3 0 , 9 3 0 2 0 . 0 8 0 8 0 . 4 6 0 2 0 . 0 0 0 7 4 1 4 0 . 3 2 8 2 6 0 . 5 9 7 0 0 . 0 6 1 4 0 . 3 7 4 9 1 . 9 2 0 0 E - 0 4 0 . 1 0 1 4 4 5 2 7 . 1 . 0 0 9 2 E - 0 2 12 0 . 9 5 5 0 0 . 0 4 3 3 0 . 1 8 8 0 1 . 9 5 0 2 E - 0 8 0 . 0 4 9 4 3 9 9 6 . 0 . 8 2 3 3 0 . 93 02 0 . 0 8 0 8 0 . 4 6 0 2 0 . 0 0 0 7 4 1 4 0 . 2 5 1 . CF2CL2 , NH3 , 0.790 MICRON D. PARTICLES (CONTINUED). RUN YINTI EPEXP EPMO QINT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 32826 Oo 5970 0.0649 0. 3749 1.9200E-•04 0.1014 4527. 1.0092E--02 12 0.9550 0,0469 0.1880 1.9502E- 08 0.0494 3996. 0.8233 0.9302 0. 0808 0.4602 0.0007 4140. 32826 0«5970 0.0544 0,3749 1. 9200E-•04 Oo 1014 4527, 1.0092E--0 2 12 0.9550 0.0362 0.1880 U9502E- 08 Oo 0494 3996. Oo 8233 0. 93 02 0.0808 0.4602 0.0007 4140. 32831 0.5970 0. 1103 0.3749 1.9200E- 04 Oo 1014 4527. 1.0092E-•02 12 0 o9550 0.0931 0.1880 1.9502E-•08 0,0494 3996. 0o8233 0. 93 02 0.0808 0.4602 0.0007 4140. 32831 0o5970 0.1342 0.3 749 1.9200E- 04 0.1014 4527. 1.0092E-•02 12 0o9550 0.1175 0.1880 1.95Q2E-•08 0,049 4 3996. 0.8233 0. 9302 0. 0808 0. 4602 0,0007 4140. 32831 0o5970 0.1076 0.3749 1.9200E- 04 OolOI4 4527. 1.0092E-•02 I 2 0. 955 0 0. 0904 0.1880 1,9502E-•08 0.0494 3 996, 0.8233 0.9302 0.0808 0.4602 0. 0007 4140. 32831 0.5970 0.1173 0.3749 1.9200E-•04 0.1014 4527. 1,0092E- 02 12 0,9550 0. 1003 0. 1880 1.9502E-•08 0.0494 3996. 0 o8233 0,9302 0.0808 0.4602 0.0007 4140. 32831 0.5970 0.1386 0.3749 1.9200E- 04 0.1014 45 27, 1,0092E- 02 12 0,9550 0. 1220 0. 1880 1.9502E- 08 Oo 0494 3996, 0.8233 0.9302 O 0 O 8 O 8 0.4602 0.0007 4140, 32833 0,4120 0. 1290 0,5432 1.9200E-•04 0.0904 5133, 1.1313E- 02 12 0,9020 0.0938 0,3222 1.8940E- 08 0. 0480 4049. 0.6947 0.9239 0,1546 0.5454 0.0014 4331. 32833 0,4120 0. 1293 0,5432 1.9200E-04 0.0904 5133, 1.1313E- 02 12 0o9020 0.0941 0.3222 1. 8940E-08 Oo 0480 4049, 0,6947 0.92 39 0.1546 0,5454 0.0014 4331. 32833 0,4120 0.1492 0.5432 1.9200E- 04 0.0904 5133. 1.1313E-02 12 0,9020 0.1148 0.3222 1.8940E- 08 0.0480 4049. 0, 6947 0.9239 0.1546 0.5454 0.0014 4331. 32833 0,4120 0. 1774 0.5432 1.9200E- 04 0.0904 5133, 1.1313E-•02 12 0.9020 0.1441 0*3222 1.8940E- 08 Oo 0480 4049, 0, 6947 0. 92 39 0.1546 0.5454 0,0014 4331, 32835 0.2450 0,1708 0.6564 2. 4800E-04 Oo 0709 8276, 1.4425E- 02 13 0,7130 0.1033 0.4662 1.9799E-08 0.0501 5554, 0,4725 0. 8694 0.2631 1. 036 0.0027 6310, 32835 0,2450 0.1802 0.6564 2.4800E- 04 0.0709 8276, 1.4425E- 02 13 0.7130 0.1134 0.4662 1.9799E- 08 0.0501 5554. 0.4725 0. 86 94 0. 2631 1.036 0. 002 7 6310o 32835 0,2450 0ol827 0.6564 2.4800E- 04 0.0709 8 276. 1.4425E- 02 I 3 0. 7130 0. 1161 0.4662 1.9799E-08 0.0501 5554, 0.4725 0.8694 0.2631 lo 036 0. 002 7 6310, 32835 0. 2450 0.2222 0.6564 2.4800E- 04 0.0709 8276. 1.4425E- 02 13 0.7130 0.1589 0. 4662 1. 9799E-08 0.0501 5554. 0.4725 0.86 94 0.2631 1.036 0.0027 6310, 32835 0.2450 0.2407 0,6564 2.4800E- 04 0.0709 8276, 1,4425E- 02 13 0.7130 0. 1789 0. 4662 1. 9799E-08 0.0501 5554, 0.4725 0.8694 0.2631 lo036 ' 0.0027 6 310, 252. CF2CL2 , NH3 , 0.790 MICRON D. PARTICLES .CONTINUED). RUN YINTI EPEXP EPMO Q INT FILMR REI MTC TYPE Yl NTO EPCORR EPSW PLM KN REG YINTLM EMT EPMA ULM UR RELM 32837 0.1940 0.4037 0.6959 2,4800E-•04 0.0650 9313. 1.5743E -02 13 0.6380 0. 3390 0. 5260 2. 0698E-•08 0.0524 5732. 0.3986 0.8634 0.3187 1.228 0.0034 6713. 32837 0. 1940 0.3689 0.6959 2.4800E-•04 0.0650 9313. 1.5743E -02 13 0.6380 0.3004 0.5260 2.0698E-•08 0. 0524 5732. 0.3986 0.8634 0.3187 1.228 0.0034 6713. 32 837 0.1940 0.3817 0.6959 2.4800E-•04 0.0650 9313. 1.5743E -02 13 0.6380 0.3146 0.5260 2.0698E- 08 0. 0524 5 732. 0.3986 0.8634 0.3187 1.228 0.0034 6713. 32841 0.2450 0.2649 0.6564 2.4800E- 04 0.0709 3276, 1.4425E -0 2 13 0.7130 0.2050 0.4662 1.9799E- 08 0.0501 5554, 0.4725 0. 8694 0.2631 1.036 0.0027 6310, 32841 0.2450 0.2520 0,6564 2.4800E- 04 0.0709 8276, 1.4425E -02 13 0.7130 0.1911 0.4662 1.9799E- 08 0,0501 5554. 0. 4725 0. 8694 0,2631 1.036 0.002 7 5310, 32841 0.2450 0.2771 0.6564 2. 4800E- 04 0. 0709 8276. 1.4425E -02 13 0.7130 0.2182 0,4662 1.9799E- 08 0.0501 5554, 0.4725 0. 8694 0, 2631 1. 036 0.0027 6310, 32841 0.2450 0.3059 0,6564 2.4800E- 04 0.0709 8276. 1.4425E -02 13 0.7130 0.2494 0.4662 1.9799E- 08 0.0501 5554. 0.4725 0. 8694 0, 2631 1.036 0. 0027 6310, 32846 0.2850 0.1935 0.6318 2.4800E- 04 0.0719 7714. 1.4232E -02 13 0. 7740 0,1390 0.4285 1.9318E- 08 0.0489 5433, 0.5333 0.8836 0,2307 0. 9177 0.0023 6058, 32846 0.2850 0.2001 0.6318 2.4800E- 04 0.0719 7714, 1.4232E--02 13 0.7740 0. 1460 0,42 85 1. 9318E-08 0.0489 5433, 0.5333 0. 8836 0.2307 0, 9177 0.0023 6058, 32846 0.2850 0.1915 0.6318 2.4800E- 04 0.0719 7714. 1.4232E' -02 13 0.7740 0. 1368 0.4285 1.9318E- 08 0.0439 5433. 0.5333 0.8836 0.2307 0.9177 0.0023 6053. 32 846 0. 2850 0. 1628 0.6318 2.4800E-04 0.0719 7714. 1.4232E--02 13 0.7740 0.1062 0.4285 1.9318E- 08 0. 0489 5433. 0.5333 0.8836 0.2307 0,9177 0.0023 6058. 2 5 3 . TABLE XXII DATA FOR CF2CL2 , NH3 , l o O l l MICRON DIAMETER PARTICLES. INERT GAS FLOW FLOW RATE CONSTANT IN ALL RUNS. INLET TEMP. (DEG. K) 293.0 , PRESSURE (ATM.) 1.000 CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: 1.0000 + 0.0 *YINTI + 0.0 *YTRNI/YINTI OUTLET: 1.0000 + 0.0 *YINTO • O.Q *YTRN0/YIMT3 GAS CF2CL2 (INERT) NH3 (TRANSFERRED) MOLEC. WEIGHT DENSITY VISCOSITY MEAN FREE PATH VOLUME**(1/3) (G/GMOLE) (KG/M**3) (KG/M/SEC) (M) (M/GM0LE**(l/3) I 120.9 5.136 1.2500E-05 2.1800E-08 4.3310E-02 17.03 0. 7182 9.8200E-06 4.5700E-08 2.2240E-02 DIFFUSIVITY (M**2/SEC) 1.2991E-05 RUN YINTI EPEXP EPMO QI NT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 36475 0.1400 0.6686 0.8313 9. 8000E- 05 0.0316 4426. 1.2539E -02 0.8300 0.6686 0.6742 1.9825E- 08 0.0392 2109. 0.4699 0. 966 7 0.4484 0. 4116 0.0060 2498. 36475 0.1400 0.6604 0.8313 9.8000E- 05 0. 0816 4426. 1.2539E -02 0. 8300 0.66 04 0.6742 1.9825E-•08 0.039 2 2109, 0.4699 0.966 7 0.4484 0.4116 0. 0060 2498. 36475 0. 1400 0.6575 0.8313 9.8000E- 05 0.0816 4426, 1.2539E -02 0. 8300 0.65 75 0.6 742 1.9 825E-•08 0.0392 2109. 0.4699 0.9667 0.4484 0.4116 0.0060 2498. 36476 0. 1840 0.6132 0.7933 9.8Q0OE- •05 0.0876 3786. 1.1673E -02 0.8900 0.6132 0.6072 1.9195E- 08 0. 0380 2 073. 0.5549 0.9721 0.3737 0.3486 0.0045 2364. 3 6476 0. 1840 0.6049 0.7933 9.8000E- 05 0.0876 3 786. 1.1673E -02 0.8900 0.6049 0.6072 1.9195E- 08 0. 0380 20 73. 0.5549 0.9721 0.3737 0.3486 0.0045 2364. 36476 0. 1840 0.5937 0.7933 9o 80GQE- 05 0.0876 3786. 1.1673E -0 2 0.8900 0.5937 0.6072 1.919 5E- 08 0. 0380 2073. 0.5549 0.9721 0.3737 0.3486 0.0045 2364. 3 6477 0.2600 0.4930 0. 7216 9. 8000E- 05 0.0991 3179. 1.03 23E -02 0.9340 0.4930 0.5036 1.8923E- 08 0.0374 2050. 0.6513 0.9752 0.2790 0.2970 0.0030 2251. 36477 0.2600 0.4781 0. 7216 9. 8000E- 05 0.0991 3179. 1.0323E -02 0.9340 0.4781 0.5036 1.8923E- 08 0.0374 2050. 0.6513 0.9752 0.2 790 0.2970 0.0030 2251. 36477 0.2600 0.4663 0.7216 9. 8000E- 05 0.0991 3179. 1.0323E -02 0.9340 0.4663 0.5036 1.8923E-•08 0.0374 2050. 0.6513 0.9752 0.2790 0.2970 0.003 0 2251. 254. CF2CL2 , NH3 , 1.011 MICRON D. PARTICLES (CONTINUED), RUN YINTI EPEXP EPMO 01 NT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YlNTLM EMT EPMA ULM UR RELM 36474 0.4300 0,3098 0.5567 9.8000E- 05 0.1213 2579, 8.4315E- 03 0,9700 0.3098 0,3244 1.9239E- 08 0.0381 2032. 0,7828 0,9767 0. 1536 0.2471 0.0014 2141. 36474 0,4300 0.3077 0.556 7 9.8000E- 05 0. 1213 2579. 8.4315E- 03 0,9700 0,3077 0.3244 1.9239E- 08 0.0381 2032. 0. 7828 0.9767 0. 1536 0.2471 0.0014 2141. 36474 0o4300 0,3173 0.5567 9.8000E- 05 0.1213 2579. .8. 4315E-03 Oo 9700 0,3173 0.3244 1.9239E-•08 0.0381 2032. 0.7828 0.9767 0.1536 0.2471 0.0014 2141. 36473 0.6510 0.1584 0.3411 9.8000E- 05 0.1430 2252. .; 7. 15 37E-03 Oo 9880 0. 1584 0.1637 2.0124E-•08 0.039 8 2024. 0,8897 0.9773 0.0686 0.2174 0. 0006 2 0 73, 36473 0.6.510 0.1766 0.3411 9.8000E- 05 0.143 0 2252. 7.1537E- 03 0,9880 0, 1766 0. 1637 2. 0124E-•08 0. 0398 2024. 0.8897 0.9773 0.0686 0.2174 0.0006 2073. 36473 0, 6510 0.1966 0,3411 9.8000E- 05 0,1430 2252. 7.1537E- 03 0,9880 0. 1966 0. 1637 2.0124E- 08 0. 0398 2024. 0.8897 0.9773 0.0686 0.2174 0,0006 2073. 255. TABLE X X I I I DATA FOR CF2CL2 * NH3 , 2.020 MICRON DIAMETER PARTICLES. ***************** ******************************************** INERT GAS FLOW RATE CONSTANT IN ALL RUNS. INLET TEMP. (DEG. K) 293.0 , PRESSURE (ATM.) 1.000 CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: OUTLET : GAS 1.0000 1*1.400 + 0*0 *YINTI + + -0*1400*YINTO + 0* 0 0*0 *YTRNI/YINTI *YTRN0/YINT3 MOLECo WEIGHT DENSITY VISCOSITY (G/GMOLE) (KG/M##3) (KG/M/SEC) MEAN FREE PATH (M) V0LUME**(l/3) <M/GM0LE**ll/3)) CF2CL2 ( INERT ) 120. 9 5.136 1.2500E-05 2.1800E-03 4.3310E-02 NH3 I TRANSFERRED) 17.03 0.7182 9.8200E-06 4. 5700E-08 2.2240E-02 DIFFUSIVITY (M**2/S£C) 1.2991E-05 RUN YINTI EPEXP EPMO OINT FILMR REI TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 36478 0.1400 0.7295 0* 8313 9.8000E- 05 0*0816 4426. 0. 8300 0.7358 0.6742 1.9825E-08 0.0196 2109, 0.4699 0. 9667 0*4484 0.4116 0. 006 0 2498. 3 6478 0.1400 0*7297 0*8313 9.8000E- 05 0*0816 4426. 0. 83 00 0. 7360 0,6742 1.9825E-08 0.0196 2109. 0*4699 0*9667 0.4484 0* 4116 0. 0060 2498. 36478 0*1400 0.73 50 0*8313 9.8000E- 05 0*0816 4426. 0.8300 0.7412 0,6742 1.9825E- 08 0.0196 2109. 0*4699 0.9667 0*4484 0*4116 0. 006 0 2498. 36479 0.1840 0.6698 0.7933 9.8000E- 05 0,0876 3786. 0.8900 0.6 748 0, 6072 1. 9195E-08 0,0190 2073, 0.5549 0*9721 0.3 737 0.3486 0*0045 2364. 36479 0. 1840 0* 6578 0.7933 9.8000E- 05 0.0876 3786. 0.8900 0. 6630 0.6072 1.9195E- 08 0. 019 0 2073, 0*5549 0*9721 0*3737 0*3486 0*0045 2364. 36479 0. 1840 0. 6595 0.7933 9.8000E- 05 0.0876 3 786. 0*8900 0*6647 0*6072 1. 9195E- 08 0. 0190 2073. 0*5549 0*9721 0*3737 0.3486 0.0045 2364. 36480 0.2600 0.5670 0. 7216 9. 8000E- 05 0.0991 3179. 0.9340 0*5710 0.5036 1.8923E- 08 0.0187 2050, 0.6513 0.9752 0.2790 0.2970 0.0030 2251. 36480 0,2600 0. 5744 0. 7216 9. 8000E- 05 0.0991 3179, 0*9340 0.5783 0.5036 1.8923E- 08 0.0187 2 050. 0. 6513 0.9752 0.2 790 0.2970 0.0030 2251. 36480 0* 2600 0*5660 0.7216 9. 8000E- 05 0. 0991 3179, 0*9340 0*5700 0*5036 1.8923E- 08 0.0187 2050, 0.6513 0.9752 0.2790 0.2 970 0.0030 2251. MTC 1.2539E-02 1.2539E-02 1.2539E-02 1.1673E-02 1.1673E-02 1.1673E-02 1.0323E -02 1.0323E-02 1.0323E-02 256. CF2CL2 . NH3 , 2.020 MICRON Do PARTICLES *C0NTINUED. o RUN YINTI EPEXP EPMO QI NT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 36481 0o4300 0o3567 0.5567 9.8Q0QE- 05 0. 1213 2579. 8.4315E -03 0o9700 0o3594 0.3244 1.9239E- 08 0.0190 2032. Oo 7828 Oo 9767 Oo 1536 0.2471 0.0014 2141. 36481 0o4300 0 o3681 0,5567 9.8000E- 05 0.1213 2 5 79. 8, 4315E -03 0o9700 0.370 7 0.3244 1.9239E- 08 0,0190 2032. 0o7828 Oo 9767 0. 1536 0.2471 0. 0014 2141. 36481 0o4300 0.3791 0.5567 9.8000E- 05 0.1213 2 5 79. 8o4315E -03 0o9700 0.3817 0.3244 1.9239E- 08 0.0190 2032. 0o7828 0.9767 0.1536 0, 2471 0. 0014 2141. 36482 0o6510 0 o2715 0.3411 9.8000E- 05 0.1430 2252. 7.1537E -03 Oo 9880 0o2 72 7 0. 16 37 2.0124E- 08 0.0199 2024. 0o8897 0,9773 0.0686 0.2174 0. 0006 2073. 36482 0»6510 Oo2690 0.3411 9.8000E- 05 0.1430 2252. 7.1537E -03 0 o9880 0.2702 0. 1637 2.0124E- 08 0,0199 2024. 0o8897 0,9773 0.0686 0.2174 0.0006 2073. 36482 0o6510 0»2637 0.3411 9.8000E- 05 0,1430 2252. 7.1537E -03 0„9880 0o2649 0,1637 2.0124E- 08 0.0199 2024. Oo 8897 0*9773 0.0686 0.2174 0,0006 2073. 25 7. TABLE XXIV DATA FOR N2 » N(CH3)3 , 0*500 MICRON DIAMETER PARTICLESo ALL RUNS FOR CONSTANT INERT RATE. INLET TEMP. I DEC K ) 293.0 , PRESSURE (ATM.) 1. 000 CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: i.0000 + 0.0 *YINTI • 0.0 OUTLET: 0.5600 + 0*44Q0*YINT0 + 0.0 *YTRNI/YINTI *YTRNO/YINTO GAS N2 (INERT) N(CH3)3 (TRANSFERRED) MOLEC. WEIGHT DENSITY VISCOSITY (G/GMOLE) (KG/M**3) (KG/M/SEC) MEAN FREE PATH (M) VOLUME** (1/3) <M/GN0.LE**<l/3) ) 28. 02 1.165 1.7480E-05 6.3900E-08 3.1190E-02 59.11 2.510 7.5300E-06 U8800E-08 4.5360E-02 DIFFUSIVITY (M**2/SEC) 8.44116-06 RUN YINTI TYPE YINTO YINTLM EPEXP EPMO QINT FILMR REI EPCORR EPSW PLM KN REO EMT EPMA ULM UR R ELM MTC 36762 0.6890 0.2812 0*1739 6. 000OE- 04 0* 071 7 5053. 9.2 749E -03 0. 8340 0.2246 0.2214 4.5287E- 08 0.1811 3263. 0.7667 0. 5590 0*2727 1* 544 0.0027 3 988. 36762 0.6890 0*2686 0*1739 6*0000E- 04 0.0717 5053. 9. 2749E -03 0. 8340 0.2110 0.2214 4.5287E- 08 0.1811 3263. 0.7667 0.5590 0*2727 1*544 0.0027 3988. 36762 0.6890 0*2553 0*1739 6.0000E- 04 0*0717 5053. 9.2749E -03 0. 8340 0.1966 0.2214 4. 5287E-08 0. 1811 3263, 0.7667 0.5590 0* 2727 1. 544 0.0027 3988, 3 6763 0.7780 0.1928 0*1229 6.0000E- 04 0*0765 3855. 8.6912E -03 0.8870 0. 1506 0. 1622 4.9955E- 08 0.1998 2792. 0.8374 0.5535 0.2080 1*414 0*0019 3231. 3 6763 0.7780 0.2004 0.122 9 6.0000E- 04 0.076 5 3855. 8.6912E -03 0.8870 0. 1586 0. 1622 4.9955E- 08 0.1998 2792. 0.8374 0*5535 0*2080 1*414 0*0019 32 31, 36763 0. 7780 0.2192 0*1229 6.0000E- 04 0.0765 3 855. 8.59I2E -0 3 0.8870 0.1783 0. 1622 4*9955E- 08 0. 1998 2792. 0.8374 0*5535 0*2080 1*414 0.0019 3231. 36 764 0.8300 0.1685 0.0929 6* OOOOE-04 0.0300 3302. 8*3040£ -03 0.9150 0*1362 0* 1253 5* 2869E-08 0.2115 2572. 0.8767 0.5465 0*1649 1.351 0.0015 2878. 36 764 0.8300 0* 1545 0. 0929 6. OOOOE-04 0.0800 3302. 8.3040E -03 0.9150 0*1216 0*1253 5.2869E- 08 0*2115 2 572. 0. 8767 0* 5465 0.1649 1*351 0.0015 2878. 36 764 0.8300 0.1502 0.0929 6* OOOOE-04 0. 0300 3302. 8.3 040E -03 0.9150 0*1172 0.1253 5.2869E-•08 0.2115 2572. 0.8767 0*5465 0. 1649 1. 351 0.0015 2 878. 258. N2 , N(CH3)3 , 0*500 MICRON Do PARTICLES (CONTINUED)* RUN YINTI EPEXP EPMO QINT FILMR REI MTC TYPE YINTO EPCQRR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 36765 0,8840 0,0964 0*0596 6.000GE- 04 0,0900 2 817, 7.3871E- 03 0*9400 0,0719 0,0822 5*5945E-•08 0,2238 2390, 0.9148 0,5136 0, 1113 1,294 0*0010 2574, 36765 0,8840 0,1221 0*0596 6*0000E- 04 Oo 0900 2817, 7.3871E- 03 0,9400 0,0983 0,0822 5.5945E- 08 0,2238 2390* 0,9148 0, 5136 0, 1113 1*294 0,0010 2574, 36765 0,8840 Ool217 0o0596 6*0000E- 04 0*0900 2 817o 7.3871E- 03 0, 9400 0,0979 0,0822 5,5945E-•08 0,2238 2390, 0,9148 0.5136 0,1113 1*294 0,0010 2574, 36766 Oo 9490 OoQ405 0*0247 6 , o o o o e - 04 0*1009 2328, 6. 5892E-03 Oo 9730 Oo 0290 0, 0350 6,0173E-•08 0,2407 2170, 0,9622 0,4836 Oo 0492 1*231 0, 0004 2240, 36766 Oo9490 0*0579 0,0 247 6.GQ00E-•04 0,1009 2328, 6.5892E- 03 0,9730 0, 0466 0, 0350 6.0173E-•08 0,2407 2170, 0,9622 0,4836 0 o0492 10 231 0*0004 2240, 36 766 0, 9490 0,0634 0,0247 6 0 O O O O E - 04 0, 100 9 2328, 6.5892E-•03 0,9730 0,0521 0*0350 6*0173E- 08 0,2407 2170, 0,9622 0*4836 0*0492 1*231 0*0004 2240. 259. TABLE XXV DATA FOR N2 t N(CH3)3 , 0.790 MICRON DIAMETER PARTICLES. ***************************************** INERT GAS FLOW RATE CONSTANT IN ALL RUNS. INLET TEMP. (DEG. K) 293.0 , PRESSURE (ATM.) 1.000 CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: 1.0000 + 0.0 *YINTI + 0.0 *YTRNI/YI NT I OUTLET: 0.6000 + 0.4000*YINT0 + 0.0 *YTRNO/YINTD GAS MOLEC. WEIGHT DENSITY VISCOSITY MEAN FREE PATH V0LUME**<l/3) DIFFUSIVITY (G/GMOLE) <KG/M**3) (KG/M/SEC) (M) (M/GM0LE**(l/3) ) (M**2/SEC) N2 (INERT) 28. 02 1.165 1.7480E-05 6.3900E-08 3.1190E-02 N(CH3)3 (TRANSFERRED) 59.11 2.510 7.5300E-06 1.8800E-08 4.5360E-02 8.4411E-06 RUN YINTI EPEXP EPMO QINT FILMR REI TYPE YINTO EPCORR EPSW PLM KN REO YlNTLM EMT EPMA ULM UR RELM 36786 0.6890 0.2442 0.1739 6. OOOOE-04 0. 0717 5 053. 0. 8340 0.1904 0.2214 4.5287E- 08 0.1147 3263. 0.7667 0. 5590 0. 2727 1. 544 0.0027 3988. 36786 0.6890 0.2799 0.1739 6.0000E- 04 0.0717 5053. 0. 8340 0.2287 0.2214 4.5287E- 08 0.1147 3263. 0.7667 0.5590 0.2727 1.544 0.0027 3 988. 36786 0.6890 0.2486 0.1739 6.0000E- 04 0.0717 5053. 0. 8340 0.1952 0.2214 4.5287E- 08 0.1147 3263. 0.7667 0.5590 0.2727 1. 544 0. 0027 3983. 36 786 0.6890 0.2349 0.1739 6.0000E- 04 0.0717 5053. 0. 8340 0. 1805 0. 2214 4. 5287E-08 0.1147 3263. 0.7667 0.5590 0. 2727 1.544 0.002 7 3 988* 36786 0.6890 0.2339 0.173 9 6.0000E-•04 0.0717 5053. 0.8340 0. 1794 0. 2214 4. 5287E- 08 0.1147 3263. 0.7667 0.5590 0.2727 1.544 0.0027 3988. 36788 0. 7780 0.2019 0. 1229 6.0000E- 04 0.0765 3855. 0.8870 0.1641 0.1622 4. 9955E- 08 0.1265 2 792. 0.8374 0.5535 0. 2080 1.414 0.0019 3231. 36788 0.7780 0.2094 0.1229 6.OOOOE-•0 4 0. 0765 3 855. 0.8870 0.1720 0.1622 4.9955E- 08 0. 1265 2792. 0.8374 0.5535 0.2080 1.414 0.0019 3231. 3 6788 0.7780 0. 1870 0. 1229 6. OOOOE-•04 0.0765 3 8 55. 0.8870 0.1485 0.1622 4.9955E- 08 0.1265 2792. 0. 8374 0.5535 0.2080 1.414 0.0019 3231. 36789 0.8300 0. 2110 0.0929 6.0000E-•04 0.0800 3302. 0.9150 0.1832 0.1253 5.2869E- 08 0.1338 2572. 0. 8767 0. 5465 0.1649 1.351 0.0015 2878. MTC 9.2749E-03 9. 2749E-03 ,9. 2749E-03 9.2749E-03 9.2749E-03 8.6912E-03 8.6912E-03 8.6912E-03 8.3040E-03 260. N2 , N(CH3)3 • 0.790 MICRON Do PARTICLES (CONTINUED). RUN YINTI EPEXP EPMO QI NT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 3 6 789 0.8300 0,1658 0.0929 6.0000E- 04 0. 0800 3 3 02. 8.3 040E -03 0 o9150 0,1364 0„1253 5.2869E- 08 0.1338 2572. Oo 8767 0, 5465 0.1649 1.351 0.0015 2878. 36789 0,8300 0,1176 0.0929 6.0000E- 04 0. 0800 3302. 8.3 040E -03 0o9150 0,0865 0.1253 5.2869E- 08 0.1338 2572. 0,8767 0, 5465 0, 1649 1.351 0.0015 2873. 36792 0„8840 0,0636 0.0596 6.0000E- 04 0.0900 2317, 7. 3871E -03 0,940 0 0, 0406 0.0822 5.5945E- 08 0.1416 2390. 0,9148 0,5136 0.1113 1.294 0.0010 2574. 36792 0,8840 0,13 38 0.0596 6o0000E- 04 0,0900 2817. 7.3871E -03 0, 9400 0, 1125 0.0822 5.5945E- 08 0.1416 2390. 0,9148 0,5136 0.1113 1.294 0. 0010 2 574. 36 792 0,8840 0,1543 0,0596 6.QGQ0E-04 0.0900 2817. 7.3871E -03 0,9400 0, 133 5 0.0822 5.5945E- 08 0.1416 2390. 0,9148 0,5136 0.1113 1.294 0.0010 2574. 36792 Oo 88 40 0,1186 0, 05 96 6.0000E-•04 0.090 0 2817. 7.38 71E -03 0,9400 0, 0969 0.0822 5o5945E- 08 0.1416 23 90. 0,9148 0 o5136 0.1113 1,294 0,0010 2 574. 36793 0, 9490 0,0529 0. 0247 6.0000E- 04 0.1009 2328. 6.5892E -03 0,9730 0,0426 0.03 50 6.0173E- 08 0. 1523 2170. 0,9622 0,4836 0.0492 1.231 0.0004 2240. 36 793 0,9490 0,0415 0. 0247 6.OOOOE-04 0.1009 2328. 6.5892E -03 0,9730 0,0310 0.03 50 6.0173E- 08 0.1523 2170. 0,9622 0,4836 0, 0492 1.231 0.0004 2240. 36793 0,9490 0, 0390 0, 0247 6.OOOOE-04 0.1009 2328, 6.5892E -03 0,9730 0,0285 0.0350 6.0173E- 08 0.1523 2170. Oo 9622 0.4836 0. 0492 1.23.1 0.0004 2 2 40. 261. T A B L E X X V I D A T A F O R N2 , N ( C H 3 ) 3 , l o O l l M I C R O N D I A M E T E R P A R T I C L E S o ****** ************************************** ***************** I N E R T G A S FLOW R A T E C O N S T A N T I N A L L R U N S , I N L E T T E M P o {DEGo K ) 2 9 3 . 0 , P R E S S U R E ( A T M . ) 1 . 0 0 0 C A L I B R A T I O N C O R R E C T I O N : C O U N T / T R U E COUNT I N L E T : 1 . 0 0 0 0 + OoO * Y I N T I + O o O * Y T R N I / Y l N T I O U T L E T : l o O O O O + OoO * Y I N T 0 • - 0 * 0 * Y T R N 0 / Y I M T 3 G A S N2 ( I N E R T ) N ( C H 3 ) 3 ( T R A N S F E R R E D ) M O L E C o W E I G H T ( G / G M O L E ) D E N S I T Y ( K G / M * * 3 ) V I S C O S I T Y ( K G / M / S E C ) MEAN F R E E P A T H (M) V 0 L U M E * * ( l / 3 ) ( M / G M 0 L E * * ( l / 3 ) ) 2 8 0 0 2 1 . 1 6 5 1 . 7 4 8 0 E - Q 5 6 o 3 9 0 0 E - 0 8 3 . I 1 9 0 E - 0 2 5 9 . 1 1 2 . 5 1 0 7 . 5 3 0 0 E - 0 6 1. 8 8 0 0 E - 0 8 4 . 5 3 6 0 E - 0 2 D I F P U S I V I T Y ( M * * 2 / S E C ) 8 o 4 4 1 1 E - 0 6 RUN Y I N T I E P E X P EPMO 01 NT F I L M R R E I MTC T Y P E Y I N T O E P C O R R EPSW P L M KN R E O Y I N T L M EMT E P M A U L M UR R E L M 3 6 4 9 9 0 » 6 8 9 0 0 . 1 8 4 8 0 . 1 7 3 9 6 „ O O O O E - 0 4 0 . 0 7 1 7 5 0 5 3 » 9 . 2 7 4 9 E - 0 3 0 . 8 3 4 0 0 . 1 8 4 8 0 . 2 2 1 4 4 . 5 2 8 7 E - 08 0 . 0 8 9 6 3 2 6 3 . 0 . 7 6 6 7 0 . 5 5 9 0 0 . 2 7 2 7 1. 5 4 4 0 . 0 0 2 7 3 9 8 3 . 3 6 4 9 9 0 . 6 8 9 0 0 . 1 7 2 3 0 . 1 7 3 9 6 . 0 0 0 0 E - 0 4 0 . 0 . 7 1 7 5 0 5 3 » . 9 . 2 7 4 9 E - 0 3 0 . 8 3 4 0 0 . 1 7 2 3 0 . 2 2 1 4 4 . 5 2 8 7 E - 08 0 . 0 8 9 6 3 2 6 3 . 0 . 7 6 6 7 0 . 5 5 9 0 0 . 2 7 2 7 1 . 5 4 4 0 . 0 0 2 7 3 9 8 8 0 3 6 4 9 9 0 . 6 8 9 0 0 . 1 7 7 1 0 . 1 7 3 9 6 . 0 0 Q 0 E - 0 4 0 . 0 7 1 7 5 0 5 3 o 9 . 2 7 4 9 E - 0 3 0 . 8 3 4 0 0 . 1 7 7 1 0 . 2 2 1 4 4 . 5 2 8 7 E - 08 0 . 0 8 9 6 3 2 6 3 . 0 . 7 6 6 7 Oo 5 5 9 0 0 . 2 7 2 7 1 . 5 4 4 0 . 0 0 2 7 3 9 8 8 . 9 . 2 7 4 9 E 3 6 4 9 9 0 o 6 8 9 0 0 . 1 7 7 5 0 . 1 7 3 9 6 . 0 Q 0 0 E - 0 4 0 . 0 7 1 7 5 0 5 3 . - 0 3 0 . 8 3 4 0 0 . 1 7 7 5 0 . 2 2 1 4 4 . 5 2 8 7 E - 08 0 . 0 8 9 6 3 2 6 3 . 0 . 7 6 6 7 0 . 5 5 9 0 0 . 2 7 2 7 1 . 5 4 4 0 . 0 0 2 7 3 9 8 8 . 3 6 5 0 0 0 . 7 7 8 0 0 . 1 0 6 4 0 . 1 2 2 9 6 . 0 0 0 0 E - •04 0 . 0 7 6 5 3 8 5 5 . 8 . 6 9 1 2 E - 0 3 0 . 8 8 7 0 0 . 1 0 6 4 0 . 1 6 2 2 4 . 9 9 5 5 E - 0 8 0 . 0 9 8 8 2 7 9 2 . Oo 8 3 7 4 0.5.5 35 0 . 2 0 8 0 1 . 4 1 4 0 . 0 0 1 9 3 2 3 1 . 3 6 5 0 0 0 . 7 7 8 0 0 . 1 4 6 1 O o l 2 2 9 6 . 0 0 0 0 E - 0 4 0 . 0 7 6 5 3 8 5 5 . 8 . 6 9 1 2 E - 0 3 0 . 8 8 7 0 0 . 1 4 6 1 0 . 1 6 2 2 4 . 9 9 5 5 E - 0 8 0 . 0 9 8 8 2 7 9 2 . 0 . 8 3 7 4 0 . 5 5 3 5 0 . 2 0 8 0 1 . 4 1 4 0 . 0 0 1 9 3 2 3 1 . 3 6 5 0 0 0 . 7 7 8 0 0 . 1 4 6 3 0 . 1 2 2 9 6 . 0 0 0 0 E - 0 4 0 . 0 7 6 5 3 8 5 5 . 8 . 6 9 1 2 E - 0 3 0 . 8 8 7 0 0 . 1 4 6 3 0 . 1 6 2 2 4 . 9 9 5 5 E - 0 8 0 . 0 9 8 8 2 7 9 2 . 0 . 8 3 7 4 0 . 5 5 3 5 0 . 2 0 8 0 1 . 4 1 4 0 . 0 0 1 9 3 2 3 1 . 3 6 751 0 . 8 3 0 0 0 . 1 0 8 9 0 . 0 9 2 9 6 . 0 0 0 0 E - 04 0 . 0 8 0 0 3 3 0 2 . 8 . 3 0 4 0 E - 0 3 0 . 9 1 5 0 0 . 1 0 8 9 0 o l 2 5 3 5 . 2 8 6 9 E - 0 8 0 . 1 0 4 6 2 5 7 2 . 0 . 8 7 6 7 0 . 5 4 6 5 0 . 1 6 4 9 1 . 3 5 1 0 . 0 0 1 5 2 8 7 8 . 3 6 7 5 1 0 . 8 3 0 0 0 . 1 0 6 5 0 . 0 9 2 9 6 . O O O O E - 0 4 0 . 0 8 0 0 3 3 0 2 . 8 . 3 0 4 0 E - 0 3 0 . 9 1 5 0 0 . 1 0 6 5 0 . 1 2 5 3 5 . 2 8 6 9 E - 0 8 0 . 1 0 4 6 2 5 7 2 . 0 . 8 7 6 7 0 . 5 4 6 5 0 . 1 6 4 9 1 . 3 5 1 0 . 0 0 1 5 2 8 7 8 . 262. N2 , N(CH3)3 , l o O l l MICRON Do PARTICLES (CONTINUED). RUN YINTI EPEXP EPMO QI NT FILMR REI MTC TYPE Y INTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 36752 Oo 8840 Oo 0766 0.0596 6.0000E- 04 0. 0900 2817. 7.3871E -03 0o9400 0.0766 0.08 22 5.5945E-08 0.1107 2390. 0.9148 0.5136 Oo 1113 1.2 94 0.0010 2574. 36752 0.8840 0.1041 0.0596 6.0000E- 04 0.0900 2817. 7.3871E -03 Oo 9400 0.1041 0.0822 5.5945E- 08 0 .110 7 2390. 0,9148 0. 5136 0.1113 1.294 0.0010 2574. 36752 Oo 8840 0.0927 0.0596 6.0000E- 04 0.0900 2817. . 7 . 3871E' -03 Oo 9400 Oo 0927 0.0822 5.5945E- 08 0.1107 2390. 0o9148 0.5136 0.1113 1.294 0.0010 2 574. 36753 0 o9490 0.0146 0.0247 6.0Q0QE-04 0.1009 2328. 6.5892E -03 0.9730 0.0146 0. 0350 6.0173E- 08 0.1190 2170. 0o9622 0.4836 0.0492 1.231 0.0004 2240. 36753 Oo 9490 0. 0160 0.0247 6.0000E- 04 0.1009 2328. 6.5892E -03 0o9730 0.0160 0. 0350 6.0173E- 08 0.1190 2170. 0.9622 0.4836 0.0492 1.231 0.0004 2240. 36753 0. 9490 0.0038 0. 0247 6.0Q00E-04 0.1009 2328. S.5892E - 0 3 0.9730 0.0038 0.0350 6.0173E- 08 0. 1190 2170. 0.9622 0.4836 0.0492 1.231 0.0004 2240. 36753 0. 9490 0.0192 0. 0247 6.0000E- 04 0.1009 2328. 6.5892E -0 3 0.9730 0.0192 0.0350 6.0173E- 08 0.1190 2170. 0.9622 0.4836 0.0492 1.231 0.0004 2240. 3 7062 0.6890 0.1752 Oo 1739 6.OOOOE-04 0.0717 5053. 9.2749E -03 0.8340 0.1752 0.2214 4.5287E- 08 0.0896 3263. 0. 7667 0.5590 0.2727 1.544 0.0027 3988. 37062 0.6890 0.1463 0.1739 6 0 O O O O E - 04 Oo 0717 5053. 9.2749E -03 0.8340 0.1453 0.2214 4.5287E- 08 0.0896 3263. 0.7667 0.55 90 0.27 27 1.544 0.002 7 3988. 37062 0.6.890 0.1347 0.1739 6.0G00E- 04 0. 0717 5053. 9.2749E -03 0.8340 0.1347 0.2214 4.5287E- 08 0.0896 3263. 0.7667 0. 5590 0.2727 1. 544 0.0027 3988. 37063 0.7780 0.1424 0.1229 6.0000E- 04 0.0765 3 855. .8. 6912E -03 0„ 8870 0.1424 0.1622 4.9955E-•08 0.0988 2792. 0.8374 0.5535 0.2080 1.414 0.0019 3231. 37063 0 o7780 0.1229 0.1229 6.0000E- 04 0.0765 3855. 8.6912E -03 0. 8870 0.1229 0.1622 4.9955E- 08 0.0988 2 792. 0.8374 0.5535 0.2080 io 4 1 4 0.0019 3231. 37063 0.7.780 0ol409 0.1229 6.0000E- 04 0.076 5 3855. 8.6912E -03 0.8870 0. 1409 0.1622 4.9955E- 08 0.0988 2792. 0.8374 0.5535 0.2080 lo4 1 4 0.0019 3231. 37064 0. 8300 0.1052 0.0929 6.0000E- 04 0.0800 3302. 8.3040E -03 0.9150 0. 1052 0.1253 5.2869E- 08 0.1046 2572. 0.8767 0.5465 0.1649 1.351 0.0015 2873. 37064 0. 8300 0.0884 0.0929 6.0000E-04 0.0800 3302. 8.3040E -03 0.9150 0.0884 0.1253 5. 2869E- 08 0.1046 2572. 0.8767 0.5465 0.1649 1.351 0.0015 2878. 37064 0. 8300 0.0982 0.0929 6. 0000E- 04 0.0800 3302. 8.3040E -03 0.9150 0.098 2 0.1253 5o2869E- 08 0.1046 2572, 0.8767 0. 5465 0.1649 1.351 0.0015 2878. 2 6 3 . N2 , N(CH313 t 1 . 0 1 1 M I C R O N Do P A R T I C L E S ICONTINUED). R U N Y I N T I E P E X P EPMO QINT F I L M R R E I MTC T Y P E Y I N T O E P C O R R EPSW P L M K N R E O Y I N T L M EMT EPMA ULM UR R E L M 3 7 0 6 5 0 o 8 8 4 0 Oo 0 7 9 2 0 . 0 5 9 6 6 . O O O O E - 0 4 0 . 0 9 0 0 2 8 1 7 . 7 . 3 8 7 1 E - 0 3 0 o 9 4 0 0 0 o 0 7 9 2 0 . 0 8 2 2 5 o 5 9 4 5 E - 0 8 0 . 1 1 0 7 2 3 9 0 , 0 „ 9 1 4 8 0 . 5 1 3 6 0 . 1 1 1 3 1 . 2 94 O o O O l O 2 5 7 4 . 3 7 0 6 5 Oo 8 8 4 0 0 . 0 8 3 2 0 . 0 5 9 6 6 . 0 0 0 0 E - 04 0 . 0 9 0 0 2 8 1 7 , 7 . 3 8 7 1 E - 0 3 0 o 9 4 0 0 0 . 0 8 3 2 O o 0 8 2 2 5 . 5 9 4 5 E - 0 8 Oo 1 1 0 7 2 3 9 0 . 0 , 9 1 4 8 0 . 5 1 3 6 0 . 1 1 1 3 1 . 2 9 4 0 . 0 0 1 0 2 5 7 4 . 3 7 0 6 5 0 o 8 8 4 0 0 . 0 7 9 7 0 o 0 5 9 6 6 . 0 0 0 0 E - 0 4 0 . 0 9 0 0 2 8 1 7 . 7 . 3 8 7 1 E - 0 3 0 o 9 4 0 0 0 . 0 7 9 7 0 . 0 8 2 2 5 . 5 9 4 5 E - 0 8 0 . 1 1 0 7 2 3 9 0 . 0 o 9 1 4 8 0 . 5 1 3 6 0 . 1 1 1 3 1 . 2 9 4 0 . 0 0 1 0 2 5 7 4 . 3 7 0 6 6 0 o 9 4 9 0 0 . 0 3 3 0 0 . 0 2 4 7 6 . 0 0 0 0 E - 0 4 0 . 1 0 0 9 2 3 2 8 . 6 . 5 8 9 2 E - 0 3 0 » 9 7 3 0 0 . 0 3 3 0 0 . 0 3 5 0 6 . 0 1 7 3 E - 0 8 0 . 1 1 9 0 2 1 7 0 . 0 » 9 6 2 2 0 . 4 8 3 6 0 . 0 4 9 2 1 . 2 3 1 Oo 0 0 0 4 2 2 4 0 . 3 7 0 6 6 0 . 9 4 9 0 0 o 0 1 2 4 0 . 0 2 4 7 6 . 0 0 0 0 E - 0 4 0 . 1 0 0 9 2 3 2 3 . 6 . 5 8 9 2 E - 0 3 Oo 9 7 3 0 0 . 0 1 2 4 0 . 03 5 0 6 . 0 1 7 3 E - 08 0 . 1 1 9 0 2 1 7 0 . 0 o 9 6 2 2 0 . 4 8 3 6 0 . 0 4 9 2 1 . 2 3 1 Oo 0 0 0 4 2 2 4 0 . 3 7 0 6 6 Oo 9 4 9 0 - 0 . 0 1 6 8 0 . 0 2 4 7 6 . 0 G 0 0 E - 0 4 0 . 1 0 0 9 2 3 2 8 . 6 . 5 8 9 2 E - 0 3 0 » 9 7 3 0 - 0 . 0 1 6 8 0 . 0 3 5 0 6 . 0 1 7 3 E - 0 8 0 . 1 1 9 0 2 1 7 0 . 0 » 9 6 2 2 0 . 4 8 3 6 0 . 0 4 9 2 1 . 2 3 1 0 . 0 0 0 4 2 2 4 0 . 264. TABLE X X V I I I DATA FOR N2 , N(CH3)3 , 2.020 MICRON DIAMETER PARTICLES. *************************************** ***************** INERT GAS FLOW RATE CONSTANT IN ALL RUNS. INLET TEMP. (DEG. K) 293.0 , PRESSURE (ATM.) 1.000 CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: 1.0000 + 0.0 *YINTI + 0.0 *YTRNI/YINTI OUTLET: 0.3500 + O„650O*YINT0 + 0.0 *YTRNO/YINTO GAS N2 (INERT) N(CH3 )3 (TRANSFERRED) MOLECo WEIGHT DENSITY VISCOSITY (G/GMOLE) ( KG/M**3) (KG/M/SEC) MEAN FREE PATH (M) VOLUME * * U/3) (M/GMOLE**(1/3)) 28.02 1.165 U7.480E-05 6.3900E-08 3.1190E-G2 59.11 2.510 7. 5300E-06 1.8800E-08 4.5360E-02 DIFFUSIVITY (M**2/SEC) 8.441LE-06 RUN YINTI EPEXP EPMO Q INT F ILMR REI MTC TYPE Yl NTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 3 676 8 0. 6890 0.2582 0.1739 6.0000E- 04 0.0717 5053. 9.2749E -03 0.8340 0.1685 0.2214 4. 5287E-08 0.0448 3263. 0.7667 0.5590 0.2727 1. 544 0.0027 3988. 3 676 8 0.6890 0.2770 0.1739 6.0000E-04 0.0717 5 053. 9.2749E -0 3 0.8340 0.1896 0.2214 4. 5287E- 08 0. 044 8 3 263. 0.7667 0.5590 0.2727 1.544 0.0027 3 988. 36768 0.6890 0.3094 0. 1739 6. OOOOE-04 0.0717 5053. 9.2749E -03 0.8340 0.2259 0.2214 4.5287E- 08 0.0448 3263, 0. 7667 0. 5590 0.2727 1.544 0.0027 3988. 36 76 8 0. 6890 0. 3002 0.1739 6.OOOOE-04 0.0717 5053. 9.2749E -03 0.8340 0.2156 0.2214 4.5287E- 08 0.0448 3263. 0. 7667 0. 5590 0.2727 1.544 0.0027 3988. 36 769 0.7780 0.2061 0.1229 6. OOOOE-04 0. 0765 3355. 8.6912E -03 0.8870 0.1432 0.1622 4.9955E- 08 0.0495 2792. 0. 8374 0.5535 0. 2080 1.414 0.0019 3231. 36769 0.7780 0.2761 0.1229 6.0000E- 04 0.0765 3855. 8.6912E -03 0.8870 0.2187 0. 1622 4.9955E- 08 0.0495 2792. 0.8374 0. 5535 0.2080 1.414 0.0019 3231. 36769 0.7780 0.2220 0.1229 6.0G00E- 04 0.0765 3 855. 8. 6912E -03 0. 8870 0. 1603 0.1622 4.9955E- 08 0.049 5 2792. 0.8374 0.5535 Oc 2080 1.414 0. 0019 3231. 36769 0. 7780 0.2141 0.1229 6.000QE-04 0.0765 3855. 8.6912E -03 0.8870 0. 1518 0. 1622 4.995 5E-08 0.0495 2792. 0.8374 0.5535 0.2080 1.414 0.0019 3231. 36769 0.7780 0. 21 09 0.1229 6.0000E- 04 0.0765 3855. 8.6912E -03 0.8870 0. 1483 0.1622 4.9955E- 08 0. 04 95 2792. 0.8374 0.5.535 0.2080 1.414 0.0019 3231. 265. N2 , N(CH3)3 f 2.020 MICRON D. PARTICLES (CONTINUED) RUN YINTI EPEXP EPMO OINT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 36 771 0. 8840 0 . 1 1 8 9 0 . 0 5 9 6 6 . 0 0 0 0 E - •04 0.0900 2817. 7.3871E -03 0.9400 0. 0831 0.0822 5.5945E-•08 0. 0554 2390o 0 . 9 1 4 8 0.5136 0 . 1 1 1 3 1.294 0.0010 2 5 74. 3 6771 0„ 8840 0. 1877 0.0596 6.0000E-•04 0.0900 2817. 7.3871E -03 Go 9400 0.1547 0.0822 5. 594 5E-•08 0. 0554 2390 o 0.9148 0.5136 0 . 1 1 1 3 1.294 OoOOlO 2574. 36771 0o8840 0.1718 Go 0596 6.QO0QE-•04 0.0900 2 317. 7. 3.8 71E -03 0 o9400 0 . 1 3 8 2 Go0822 5.5945E- 08 0.0554 2390. 0.9148 0 . 5 1 3 6 0 . 1 1 1 3 1.294 OoOOlO 2 574. 36772 0»9490 0.0734 0.0247 6 . O 0 0 0 E - 04 Oo1009 23 28. 6.5892E -03 Go 9730 G o0568 0 . 0 . 3 5 0 6 . 0 . 1 7 3 E - 08 Go 0596 2170. 0„ 9622 0.4836 0. 0492 1 . 2 . 3 1 0.0004 2240. 36772 0o9490 0.0973 0.0247 6 . 0 0 0 0 E - •04 0.1009 2328. 6.5892E -03 0.973 0 0.0812 0.0350 6 . 0 1 7 3 E - 08 0.0596 2170. 0.9622 0.4836 0. 0492 1.231 0.0004 2240. 36776 0o6890 0*3277 0 . 1 7 3 9 6.CO0OE- 04 0.0717 5 053, :9.2749E -03 0.8340 0.2464 0.2214 4 . 5 . 2 8 7 E -•08 0.0448 3263. Oo7667 0.5590 0. 2727 1.544 0.G027 3988. 36 776 0o6890 0.3394 0 . 1 7 3 9 6.0000E- 04 0.0717 5 053. 9. 2749E -03 0 o8340 0.2595 0.2214 4.5287E- 08 0.0448 3263o 0.7667 0.5590 0. 2727 1.544 0.0027 3 983o 36776 0o6890 0.3290 0 . 1 . 7 3 9 6 . 0 0 0 0 E - •04 0.0717 5053. 9.2749E -03 Oo 8340 0.2478 0.2214 4. 5 . 2 8 7 E -•08 0.0448 3263o 0.7667 0o5590 0.2727 1.544 0.0027 3988. 36776 0.6890 0.30 97 0.1739 6.0Q00E- 04 0.0717 5 053. 9.2749E -03 0.8340 0. 2262 0. 2214 4.528 7E-08 0.0448 3 263. 0.7667 0 . 5 . 5 9 0 0.2727 1.544 0 . 0 0 2 7 3988. 36777 0. 8300 0.1844 0.0929 6.0000E- 04 0.0800 3302. 8.3040E -03 0.9150 Oo 1367 0 . 1 2 5 3 5.2869E- 08 G.0523 2572o 0.8767 0.5465 0.1649 1 . 3 . 5 1 0.0015 2878. 36777 0. 8300 0.2035 0.0929 6.G00QE- 04 0.0800 3302. 8.3G40E--03 0o9150 Go 1569 0.1253 5.2869E- 08 0.0523 2572, 0.8767 0.5465 G.1649 1 . 3 . 5 1 0.0015 2878. 36 777 0.8300 0.2208 0. 0929 6.00Q0E- 04 0. 0800 3 302. 8.3040e -03 0.9150 0.1752 0.1253 5 . 2 8 6 9 E - 08 0.0523 2572. 0. 8767 0. 5465 0.1649 1 . 3 5 1 0.0015 2878. 36778 0.8840 0 . 1 1 3 7 0.0596 6.0000E- 04 0. 0900 2817. 7.3871E -03 0o9400 0.0777 0.0822 5 05945E- 08 0 . 0 5 5 4 2390. 0.9148 0.5136 0, 1113 1.294 0.0010 2 5 74. 36778 0.8840 0.1372 0.0596 6.0GG0E-04 0. 0900 2817, . . 7 . 3 8 7 1 E--03 0.9400 0.1022 0.0822 5.5945E-08 0.0554 2390. 0.9148 0.5136 0.1113 1.294 0.0010 2574. 36778 0.8840 0.1465 0.0596 6.0000E- 04 0.0900 2 817. 7.3871E--03 0. 9400 0.1119 0 . 0 8 2 2 5.5945E-08 0.0554 2390. 0. 9148 0.5136 Oo1113 1.294 0.0010 2574, 36 779 0.9490 0 . 1 . 1 6 3 Go0247 6 0 O O O O E - 04 0 . 1 0 0 9 2328. 6. 5892E- 03 0. 973 0 Q.1005 0 . 0 . 3 5 0 6.0173E-08 0.0596 2170. 0.9622 0.4836 0.0492 1. 231 0.0004 2240. 266. N2 , N< CH3)3 , 2o020 MICRON 0 o PARTICLES {CONTINUED),, RUN YINTI EPEXP EPMO QINT FILMR REI MTC TYPE YINTO EPCORR EPSW PLM KN REO YINTLM EMT EPMA ULM UR RELM 36779 0,9490 0.0894 0.0247 6.0000E- 04 0.1009 2328. 6. 5892E -03 0.973 0 0. 0731 0.0350 6.0173E-•08 0.0596 2170. 0.9622 0.4836 0.0492 1. 231 0. 0004 2240. 36779 0.9490 0.0464 0.0247 6.0000E- 04 0.1009 2328. 6.5892E -03 0.9730 0. 0294 0. 0350 6.0173E-•08 0. 0596 2170. 0.9622 0.4836 0.0492 1.231 0.0004 2240. 36 797 0. 6390 0,2798 0.1739 6.0000E-•04 0.0717 5053. 9.2749E -03 0.8340 0. 192 7 0.2214 4.5287E- 08 0.044 8 3263. 0.7667 0,55 90 0,2727 1.544 0,0027 3 988, 3 6797 0. 6890 0,302 9 0.1739 6.0000E-•04 0.0717 5 053. 9. 2749 E - 0 3 0.8340 0.2186 0.2214 4. 5287E- 08 0. 044 8 3263. 0.7667 0.5590 0.2727 1.544 0.0027 3 988. 3 6 797 0.6890 0.28 67 0, 1739 6. OOOOE-•04 0.0717 5053. 9.2749E -03 0.8340 0.2004 0,2214 4. 5287E- 08 0.0448 3263. 0.7667 0.559Q 0.2727 1.544 0.0027 3983, 36798 0.7780 0.2587 0, 1229 6. OOOOE-04 0.076 5 3855. 8,6912E -03 0.8870 0.1999 0.1622 4.9955E- 08 0.0495 2792. 0. 8374 0.5535 0.2080 1,414 0.0019 3231. 36798 0. 7780 0.2618 0.1229 6.G000E- 04 0.0765 3 855. 8.6912E -03 0.8870 0,2033 0,1622 4.9955E-•08 0.049 5 2792. 0. 8374 0.5535 0,2080 1.414 0.0019 3231. 36798 0.7780 0,2501 0.1229 6.0000E- 04 0. 0765 3855. 8.6912E -03 0.8870 0.1907 0,1622 4.9955E- 08 0.0495 2792. 0. 8374 0. 5535 0,2080 1.414 0,0019 3231. 3 6799 0.8300 0.1970 0.0929 6.Q000E- 04 0,0800 3302. 8. 3040E -03 0.9150 0. 15 00 0.1253 5.2869E-•08 0.0523 2572. 0.8767 0, 5465 0,1649 1.351 0. 0015 2878. 36799 0.8300 0,1975 0.0929 6.0G00E- 04 0.0800 3302. 8.3040E -03 0.915 0 0.15 06 0. 1253 5.2869E- 08 0.0523 2572. 0.8767 0,5465 0. 1649 1.351 0. 0015 2 878. 3 6799 0. 8300 0.1745 0.0929 6.0000E- 04 0.0800 3 302. 8.3040E -03 0.9150 0. 1262 0, 1253 5.2869E- 08 0.0523 2572. 0.8767 0.5465 0.1649 1.351 0,0015 2878. 36300 0. 8840 0.1602 0.0596 6.0000E- 04 0,0900 2317. 7.3871E -03 0.9400 0. 1261 0,0822 5.5945E- 08 0,0554 2390. 0.9148 0,5136 0,1113 1,294 0.0010 2574. 36800 0. 8840 0.1588 0,0596 6.000QE-04 0.0900 2817. 7.3871E - 0 3 0. 9400 0.1247 0,0822 5. 5945E-08 0. 0554 2390, 0.9148 0.5136 0.1113 1.294 0.0010 2574. 36800 0.8840 0. 1708 0. 0596 6. 00005-04 0,0900 2817. 7.3871E -03 0.9400 0.1371 0.0822 5.5945E- 08 0.0554 23 90. 0.9148 0.5136 0.1113 1.294 0.0010 2574. 37051 0.9490 0. 1151 0.0247 6.0000E- 04 0.1009 2328. 6.5892E -03 0.9730 0.0993 0.0350 6.0173E- 08 0.0596 2170, 0.9622 0.4836 0. 0492 1.231 0.0004 2240. 37051 0.9490 0.0680 0.0247 6. GOOOE-04 0. 1009 2328. 6.5892E -03 0.9730 0.0514 0.0350 6.0173E- 08 0.0596 2170. 0.9622 0.4836 0. 0492 1.231 0.0004 2240. 26 7. N 2 , N ( C H 3 ) 3 , 2 . 0 2 0 M I C R O N D . P A R T I C L E S ( C O N T I N U E D ) . R U N Y I N T I E P E X P E P M O Q I N T F I L M R R E I M T C T Y P E Y I N T O E P C D R R E P S W P L M K N R E O Y I N T L M E M T E P M A U L M U R R E L M 3 7 0 5 1 0 . 9 4 9 0 0 . 0 4 4 5 0 . 0 2 4 7 6 . 0 0 0 0 E - 0 4 0 . 1 0 0 9 2 3 2 8 , 6 . 5 8 9 2 E - 0 3 0 . 9 7 3 0 0 . 0 2 7 4 0 . 0 3 5 0 6 . 0 1 7 3 E - 0 8 0 . 0 5 9 6 2 1 7 0 . 0 . 9 6 2 2 0 . 4 8 3 6 0 . 0 4 9 2 1 . 2 3 1 0 . 0 0 0 4 2 2 4 0 . 3 7 0 5 1 0 . 9 4 9 0 0 . 1 0 6 7 0 . 0 2 4 7 6 . 0 0 0 0 E - 0 4 0 . 1 0 0 9 2 3 2 8 . 6 . 5 8 9 2 E - 0 3 0 . 9 7 3 0 0 . 0 9 0 7 0 . 0 3 5 0 6 . 0 1 7 3 E - 0 8 0 , 0 5 9 6 2 1 7 0 . 0 . 9 6 2 2 0 . 4 8 3 6 0 . 0 4 9 2 1 . 2 3 1 0 . 0 0 0 4 2 2 4 0 . 3 7 0 5 1 0 . 9 4 9 0 0 . 1 0 5 7 0 . 0 2 4 7 6 . 0 0 0 0 E - 0 4 0 . 1 0 0 9 2 3 2 8 . 6 . 5 8 9 2 E - 0 3 0 . 9 7 3 0 0 . 0 8 9 7 0 . 0 3 5 0 6 . 0 1 7 3 E - 0 8 0 . 0 5 9 6 2 1 7 0 , 0 . 9 6 2 2 0 . 4 8 3 6 0 . 0 4 9 2 1 . 2 3 1 0 . 0 0 0 4 2 2 4 0 , 268. TABLE XXVIII DATA FOR N2 t N(CH3)3 , 5. 700 MICRON DIAMETER PARTICLES. * * $ * * # ^ ^ ^ * ^ * * * * ^ ^ ^ $ ^ ^ ^ * ^ ^ ^ $ ^ ^ * * ^ ^ * * ^ C 4 E * 4 : * 4 C $ * ^ * * * * * * * * * * * * * * * * * INERT GAS FLOW RATE CONSTANT IN ALL RUNS. INLET TEMP. (DEG. K) 293.0 , PRESSURE (ATM.) 1.000 CALIBRATION CORRECTION: COUNT/TRUE COUNT INLET: 1.0000 + 0.0 #YINTI + 0.0 #YTRNI/YIM TI OUTLET: 1.0000 + 0.0 *YINTQ + 0.0 * YTRNO/Y INTO GAS N2 {INERT) N(CH3)3 (TRANSFERRED) MOLEC, WEIGHT (G/GMOLE) DENSITY (KG/M**3) VISCOSITY (KG/M/SEC) MEAN FREE PATH (M) V0LUME**(l/3) (M/GMOLE**(1/3)) 28.02 1,165 1.7480E-05 6.3900E-08 3. 1190E-02 59.11 2.510 7. 5300E-06 1.880QE-08 4. 5360E-02 DIFFUSI VI TY (M**2/SEC) 8.4411E-06 RUN YINTI EPEXP EPMO QINT FILMR REI MTC TYPE YINTO EPCORR EPSW P L M KN REO YINTLM EMT EPMA ULM UR RELM 3 7052 0. 6890 0.2316 0.1739 6.OOOOE-04 0.0717 5053. 9.2749E -03 0.8340 0.2316 0.2214 4.5287E-08 0.0159 3 263. 0.7667 0.5590 0.2727 1.544 0.0027 3988. 37052 0.6890 0.2876 0.1739 6.0000E-04 0.0717 5053. 9.2749E -0 3 0,8340 0.2876 0. 2214 4. 5287E-08 0. 0159 3263. 0.7667 0.5590 0.2727 1,544 0.0027 3988. 37052 0.6890 0.2761 0. 1739 6.OOOOE-04 0.0717 5053. 9.2749E -03 0.8340 0.2761 0.2214 4,5287E-08 0.0159 3263. 0. 7667 0, 5590 0.2727 1,544 0.0027 3988. 37053 0.7780 0. 0947 0.1229 6,0000E-04 0.076 5 3855. 8.6912E -03 0,8870 0,0947 0.1622 4o995 5E-08 0.0175 2792. 0. 8374 0. 5535 0.2080 1.414 0.0019 3231. 37053 0.7780 0.1837 0.1229 6.0000E-04 0. 0765 3 855. 8.6912E -03 0.8870 0,1837 0.1622 4.9955E-08 0.0175 2792. 0. 8374 0.5535 0. 2080 1.414 0.0019 3231. 37053 0,7780 0,2624 0.1229 6.0000E-04 0.0765 38550 8. 6912E -03 0. 8870 0,2624 0.1622 4.9955E-08 0.0175 2792. 0. 83 74 0,55 35 0.2080 1.414 0.0019 3231, 37054 0.8300 0.0782 0.0,929 6.000QE-04 0.0800 3302. 8.3040E -03 0. 9150 0. 0782 0.1253 5.2869E-08 0.0186 2572. 0,8767 0,5465 0.1649 1.351 0.0015 2878. 37054 0.83 00 0,2796 0.0929 6.0000E-•04 0.0800 3302. 8.3040E -03 0.9150 0,2796 0. 1253 5. 2869E-08 0.0186 2572. 0.8767 0,5465 0.1649 1.351 0.0015 2878. 37055 0. 8840 0,1306 0. 0596 6.0000E-04 0.0900 2817. 7.3871E -03 0.9400 0. 1306 0.0822 5. 5945E-08 0.0196 2390. 0.9148 0,5136 0.1113 1.294 0.0010 2 574. 269 . A p p e n d i x E STATISTICAL ANALYSIS E . 1 G e n e r a l P o s i t i o n o f D a t a F o r e v e r y s e t o f d a t a , t h e mean o f f s e t o f t h e e x p e r i -m e n t a l r e s u l t s f r o m t h e p r e d i c t i o n s o f e a c h o f t h e t h r e e t h e o r e t i -c a l m o d e l s was c a l c u l a t e d . T h e mean o f f s e t i s t h e a v e r a g e o f a l l t h e d i f f e r e n c e s b e t w e e n t h e e x p e r i m e n t a l a n d t h e o r e t i c a l f r a c t i o n a l e f f i c i e n c i e s . T h e s t a n d a r d d e v i a t i o n o f t h e s e d i f f e r e n c e s was a l s o c a l c u l a t e d , a n d was u s e d t o d e t e r m i n e t h e s i g n i f i c a n c e o f t h e o f f s e t a t t h e 90% a n d 95% c o n f i d e n c e l e v e l s u s i n g t h e s t a t i s t i c a l t - t e s t . T h e c a l c u l a t i o n was d o n e b y c o m p u t e r u s i n g t h e p r o g r a m UBC SFRP ( L e , ( 1 9 7 5 ) ) . E . 2 T r a n s i t i o n R e g i m e B e h a v i o u r a n d I n e r t i a l D e p o s i t i o n No s i m p l e t e s t t o d e t e c t t r a n s i t i o n r e g i m e b e h a v i o u r c o u l d b e d e v i s e d . A t r a n s i t i o n r e g i m e m o d e l f o r p a r t i c l e r e m o v a l was t h e r e f o r e c r e a t e d , a n d u s e d i n t h e t e s t s . I n o r d e r t o c o n s t r u c t t h e m o d e l i t was p o s t u l a t e d t h a t i f p a r t i c l e b e h a v i o u r f e l l i n t o t h e t r a n s i t i o n r e g i m e , t h e n t h e 2 7 0 . p a r t i c l e v e l o c i t y w o u l d b e g i v e n b y V p = f V S W + ( 1 " f ) V M A ' w h e r e v ^ a n d v g w a r e t h e mean m a s s v e l o c i t y a n d S c h m i t t a n d W a l d m a n n ' s v e l o c i t y r e s p e c t i v e l y , a n d f i s a p a r a m e t e r o f o r d e r 1 o r s m a l l e r . I t i s s t r a i g h t f o r w a r d t o d e r i v e t h e c o r r e s p o n d i n g e x p r e s s i o n f o r p a r t i c l e r e m o v a l e f f i c i e n c y , u s i n g t h e f i l m t h e o r y a p p r o a c h ( s e e W h i t m o r e a n d M e i s e n , ( 1 9 7 3 ) ) , t o y i e l d w h e r e e T R i s t h e t r a n s i t i o n r e g i m e e f f i c i e n c y . ( T h e c o r r e s p o n d i n g d e r i v a t i o n f o r t h e g e n e r a l t h e o r y i s n o t o b v i o u s , a n d may n o t b e p o s s i b l e . ) B y m e a n s o f t h e b i n o m i a l e x p r e s s i o n , i t c a n b e s h o w n t h a t t h i s e x p r e s s i o n c a n b e a p p r o x i m a t e d b y £ T R = f e S W + ( 1 " f ) e M A w h e r e a n d e g w a r e s m a l l ( e ^ , £ g W << 1 ) . I t was f o u n d t h a t t h i s l i n e a r i s e d r e s u l t a g r e e d w i t h t h e m o r e a c c u r a t e e x p r e s s i o n t o w i t h i n 0 . 0 1 f r a c t i o n a l e f f i c i e n c y u n i t s f o r t h e v a l u e s o f e MA a n d e s w c o r r e s p o n d i n g t o e x p e r i m e n t a l c o n d i t i o n s i n t h i s w o r k . T h e s i m p l e e q u a t i o n was t h e r e f o r e s a t i s f a c t o r y f o r u s e i n t h e a n a l y s i s . I f t h e p a r t i c l e s a r e i n t h e t r a n s i t i o n r e g i m e , t h e n t h e p a r a m e t e r f w i l l b e a f u n c t i o n o f K n u d s e n n u m b e r . O v e r a 271. s m a l l range of Knudsen number v a l u e s , the r e l a t i o n s h i p can be regarded as l i n e a r , so t h a t f = A + B Kn , r r ' where A r and B r are c o n s t a n t s . I t f o l l o w s t h a t £TR = V £ S W " £MA> + B r ( £ S W " £MA ) K n + £MA ' I f i n e r t i a l d e p o s i t i o n i s a l s o important, the e f f i -c i e n c y w i l l depend on the stop p i n g d i s t a n c e parameter, S (see Chapter 6). The dependence can be assumed to be l i n e a r over the range o f t h i s parameter encountered i n the experimental work. Hence, the f i n a l e x p r e s s i o n f o r p a r t i c l e removal e f f i -c i e n c y becomes: E = A ( - £„„,) + B ( e „ 7 - e,,JKn + C S + E , . , . p r SW MA r SW MA r MA The t e s t s f o r both t r a n s i t i o n regime behaviour and i n e r t i a l d e p o s i t i o n i n v o l v e d attempting t o c o r r e l a t e the e x p e r i -mental values f o r E ^ w i t h the corresp o n d i n g values of (£g^ ~ ' Kn, and S, u s i n g the previous e q u a t i o n . The values o f the l a t t e r three v a r i a b l e s were based on the measured experimental c o n d i t i o n s (see Appendix C). The t e s t s were made on each i n d i v i d u a l data s e t , and on each s e t of grouped data (see Chapter 6 ) . The c o r r e l a t i o n was sought u s i n g a stepwise r e g r e s s i o n a n a l y s i s . In the a n a l y s i s , v a r i a b l e s are d i s c a r d e d as not s i g n i -f i c a n t i f the v a r i a n c e a t t r i b u t a b l e to them i s not s i g n i f i c a n t l y 272. d i f f e r e n t f r o m t h e r e s i d u a l v a r i a n c e a t t r i b u t a b l e t o r a n d o m s c a t t e r i n t h e d a t a . T h e s i g n i f i c a n c e l e v e l i s d e t e r m i n e d b y m e a n s o f t h e F - t e s t . T h e a n a l y s i s was made u s i n g s i g n i f i c a n c e l e v e l s o f 90% ( s i g n i f i c a n t ) a n d 95% ( h i g h l y s i g n i f i c a n t ) . T h e c a l c u l a t i o n was d o n e b y c o m p u t e r u s i n g t h e p r o g r a m p r e v i o u s l y m e n t i o n e d . T h e r e s u l t s o f t h e s e t e s t s d i d n o t c o n f i r m t h e h y p o -t h e s i s t h a t t h e d a t a i n d i c a t e d t r a n s i t i o n r e g i m e b e h a v i o u r . W h e r e t h e c o e f f i c i e n t s A r a n d B r w e r e f o u n d t o b e s i g n i f i c a n t , i t was c l e a r f r o m t h e i r v a l u e s t h a t t h e c o r r e l a t i o n was d u e n o t t o K n u d s e n n u m b e r , b u t t o o t h e r c a u s e s , p r o b a b l y s y s t e m a t i c e r r o r s i n t h e d a t a . L a r g e v a l u e s o f t h e s e c o e f f i c i e n t s i m p l y t h a t t r a n s i t i o n b e h a v i o u r i s c o n f i n e d t o a v e r y s m a l l K n u d s e n n u m b e r r a n g e , w h i c h i s n o t r e a l i s t i c . P a r t i c u l a r l y f o r t h e u n g r o u p e d d a t a , t h e r e was a s t r o n g i n t e r - c o r r e l a t i o n b e t w e e n t h e two v a r i a b l e s (e„ r 7 - e„„,) a n d SW MA ( e g w - e ^ ) K n . T h i s a r o s e b e c a u s e t h e v a r i a t i o n o f t h e K n u d s e n n u m b e r w i t h i n o n e s e t o f d a t a was n o r m a l l y s m a l l . W h e r e t h e s u p p o s e d l y i n d e p e n d e n t v a r i a b l e s i n a r e g r e s s i o n a n a l y s i s a r e a c t u a l l y i n t e r d e p e n d e n t , a s i n t h i s c a s e , t h e r e g r e s s i o n m e t h o d may h a v e d i f f i c u l t y i n c o r r e c t l y a t t r i b u t i n g a n y c o r r e l a t i o n t o t h e a p p r o p r i a t e v a r i a b l e . T h e v a l u e s o b t a i n e d f o r A r a n d B r m i g h t t h e r e f o r e r e f l e c t t h i s p r o b l e m r a t h e r t h a n s y s t e m a t i c e r r o r s . When t h e K n u d s e n n u m b e r r a n g e i s s m a l l , t h e i n f l u e n c e o f v a r i a t i o n i n K n u d s e n n u m b e r o n t h e r e m o v a l e f f i c i e n c y s h o u l d b e n e g l i g i b l e . T h i s v a r i a t i o n c a n b e n e g l e c t e d b y d i s c a r d i n g t h e t e r m B r ^ e s w ~ e M A ^ K n ^ r o r n t ^ i e a n a l y s i s - f f t h e c o r r e l a t i o n w i t h 273. (£g w - £ M A ) were s t i l l found t o be s i g n i f i c a n t , t h i s would s u b s t a n -t i a t e t h e h y p o t h e s i s o f t r a n s i t i o n b e h a v i o u r , and i n d i c a t e t h a t the p r e v i o u s u n r e a l i s t i c v a l u e s o f A r and B r were due t o i n t e r -c o r r e l a t i o n o f v a r i a b l e s . When t h e s e t e s t s were made, the c o r r e l a t i o n w i t h ( e g w - Ejy^) was found t o be g e n e r a l l y n o t s i g n i f i c a n t . I t was t h e r e f o r e c o n c l u d e d t h a t t r a n s i t i o n regime b e h a v i o u r c o u l d n o t be s t a t i s t i c a l l y d e m o n s t r a t e d , p r o b a b l y because o f t h e pre s e n c e o f s y s t e m a t i c e r r o r s i n t h e d a t a . T h i s does n o t mean,however, t h a t t r a n s i t i o n b e h a v i o u r was n o t i n e f f e c t , s i n c e the p o s s i b l e s y s t e m a t i c e r r o r s , as l i s t e d i n T a b l e IV, are much l a r g e r t h a n i s n e c e s s a r y t o confound the s t a t i s t i c a l a n a l y s i s . A l s o , i t i s p o s s i b l e , though n o t p r o b a b l e , t h a t the t r a n s i t i o n regime model was n o t a c c u r a t e enough f o r use i n t h e s e t e s t s . F o r some s e t s o f d a t a , the c o r r e l a t i o n w i t h t h e s t o p p i n g d i s t a n c e parameter was s i g n i f i c a n t , t y p i c a l l y i n d i c a t i n g an i n e r t i a l l o s s f o r 1 ym p a r t i c l e s i n t h e o r d e r o f 0.5% a t a Reynolds number o f 1000. T h i s was h i g h e r t h a n e x p e c t e d , b u t n o t o b v i o u s l y u n r e a l i s t i c . A t t h e same,time, the c o r r e l a t i o n w i t h s t o p p i n g d i s t a n c e was n e g a t i v e i n a few c a s e s , which was c l e a r l y i m p o s s i b l e . I t i s t h e r e f o r e c o n c l u d e d t h a t s y s t e m a t i c e r r o r s were i n t e r f e r i n g w i t h t h i s t e s t , b u t t h a t i n e r t i a l l o s s e s must i n any case have been v e r y s m a l l . 

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