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An apparatus for measuring the rate of diffusion of gases through porous solids at elevated pressures 1959

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AN APPARATUS FOR MEASURING THE RATE OF DIFFUSION OF GASES THROUGH POROUS SOLIDS AT ELEVATED PRESSURES by AGNES YU-WEN HAH B . S c , (China) U n i v e r s i t y of Taiwan, 1955 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of CHEMICAL ENGINEERING We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1959 ( i ) ABSTRACT An apparatus u t i l i z i n g a constant pressure f l o w system was developed f o r measuring the e f f e c t o f pressure on the d i f f u s i o n r a t e s , and t h e r e f o r e d i f f u s i o n c o e f f i c i e n t s , of b i n a r y gas mixtures p a s s i n g through porous s o l i d s . Hydrogen and n i t r o g e n were employed f o r t e s t i n g ceramic porous s o l i d s at room temperature, w i t h v a r i o u s pressures from 1 t o 14.6 atmospheres a b s o l u t e . The valu e s obtained f o r the products o f the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t s and absolute pressures were s u b s t a n t i a l l y c o n s t ant, w i t h a maximum d e v i a t i o n of +5%» I t seemed t h a t the d i f f u s i o n r a t e of hydrogen i n c r e a s e d w i t h p r e s s u r e , w h i l e t h a t of n i t r o g e n decreased. At atmospheric pressure the r a t i o of d i f f u s i o n r a t e s (^%2^U2^ w a s i n good agreement w i t h the t h e o r e t i c a l v a l ue proposed by d i f f u s i o n r a t i o i n c r e a s e d w i t h p r e s s u r e . This behavior might be due to some degree o f f o r c e d f l o w present i n the d i f f u s i o n p r o c e s s , although i t was not p o s s i b l e t o determine a cause f o r such a f l o w . T h i s apparatus i s s u i t a b l e f o r the study of d i f f u s i o n r a t e s i n the t r a n s i t i o n r e g i o n , between Knudsen and o r d i n a r y d i f f u s i o n , by simply changing pressure and hence the mean f r e e path of the gases i n v o l v e d . Forced f l o w would not be a f a c t o r i n t h i s r e g i o n . However, the experimental In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of 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 f o r reference and study. I f u r t h e r agree that permission f o r extensive 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 . I t 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 gain s h a l l not be allowed without my w r i t t e n permission. Department of The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date ( i i ) ACKNOWLEDGEMENT The author wishes t o express her g r a t i t u d e t o I m p e r i a l O i l L t d . and the N a t i o n a l Research C o u n c i l f o r f i n a n c i a l a s s i s t a n c e d u r i n g the p e r i o d i n which the re s e a r c h was conducted, and a l s o t o Mr. R. Muelchen f o r the c o n s t r u c t i o n of the d i f f u s i o n c e l l . I n p a r t i c u l a r , the author expresses her s i n c e r e thanks to Dr. D. S. S c o t t under whose s u p e r v i s i o n the res e a r c h was conducted. ( i i i ) NOMENCLATURE C r o s s - s e c t i o n a l area of porous sample Mo l e c u l a r species Mole f r a c t i o n of A i n A stream, B stream M o l e c u l a r c o n c e n t r a t i o n s o f A, B T o t a l M o l e c u l a r c o n c e n t r a t i o n D i f f u s i o n c o e f f i c i e n t of system A-B Bulk ( o r d i n a r y ) d i f f u s i o n c o e f f i c i e n t E f f e c t i v e d i f f u s i o n c o e f f i c i e n t Knudsen d i f f u s i o n c o e f f i c i e n t True o r d i n a r y d i f f u s i o n c o e f f i c i e n t Mole f r a c t i o n s of hydrogen i n hydrogen stream, i n n i t r o g e n stream. Boltzman Constant RTL A constant equal t o A Molecule weights of A, B D i f f u s i o n r a t e s , i n moles per u n i t time Log mean o f 1^ and Ng Absolute pressure P a r t i a l p r e s s u r e s Pore r a d i u s Temperature L i n e a r v e l o c i t i e s o f A, B Mean molecular v e l o c i t y Rates o f d i f f u s i o n i n mis per u n i t time ( i v ) X W , X W Flow r a t e s of hydrogen, n i t r o g e n t o 1 1 a d i f f u s i o n c e l l YH, YN O u t l e t f l o w r a t e s o f hydrogen, n i t r o g e n from the d i f f u s i o n c e l l A p r o p o r t i o n a l i t y f a c t o r of i n t e r d i f f u s i o n ^'flB Maximum energy o f a t t r a c t i o n between AB C o l l i s i o n I n t e g r a l (TI C o l l i s i o n diameter f o r the u n l i k e molecules A and B 0 P o r o s i t y C. C f i X e D e n s i t i e s (v) TABLE OF CONTENTS Page I n t r o d u c t i o n 1 Theory 3 A. D i f f u s i o n Mechanisms i n Porous S o l i d s 3 B. Counter D i f f u s i o n of Gases at Constant T o t a l pressure .. 7 C. Measurement o f D i f f u s i o n Rates 11 Apparatus 15 A. D i f f u s i o n Apparatus. . 15 B. M o d i f i c a t i o n o f Thermal C o n d u c t i v i t y C e l l s 17 C. D i f f u s i o n C e l l 19 D. Porous Sample 20 Experimental Procedures 22 A. C a l i b r a t i o n of Test Gauge 22 B. C a l i b r a t i o n of Flow Meters 22 C. C a l i b r a t i o n of Thermal D o n d u c t i v i t y C e l l s . 26 D. Measurement o f E f f e c t i v e D i f f u s i o n C o e f f i c i e n t o f Porous S o l i d and Rates o f D i f f u s i o n at v a r i o u s p r e s s u r e s 28 R e s u l t s 30 Experimental E r r o r s 39 A. Measurement of Gas Composition 39 B. Measurement of D i f f u s i o n Rates 39 D i s c u s s i o n 41 ( v i ) Page Conclusions and Recommendations 51 BIBLIOGRAPHY 52 APPENDIX ... 54 ( v i i ) LIST OF ILLUSTRATIONS IN TEXT Figure Page 1. Apparatus f o r Measurement of D i f f u s i o n Rates. 16a 2. M o d i f i c a t i o n of Thermal C o n d u c t i v i t y C e l l 17a 3. W i r i n g Diagram o f Thermal C o n d u c t i v i t y C e l l 17b 4. D i f f u s i o n C e l l Cross S e c t i o n s t o Shown Arrangement of- Gas Duct 19a 4a I s o m e t r i c Sketch o f D i f f u s i o n C e l l showing gas duct arrangement 19b 5. D i f f u s i o n C e l l - s i d e view 19c 6. D i f f u s i o n C e l l - top view 19<1 7. C a l i b r a t i o n P l o t of M o d i f i e d No. 1 Thermal C o n d u c t i v i t y C e l l , M i l l i v o l t VS%:N2>. 2?a 8. C a l i b r a t i o n P l o t o f M o d i f i e d No. 2 Thermal C o n d u c t i v i t y C e l l , M i l l i v o l t YS"% H2.Y?,. 2?b 9. D i f f u s i o n R e s u l t s f o r Sample 2, Arrangement I , De.P VS;. P..... 38a 10. D i f f u s i o n R e s u l t s f o r Sample 2, Arrangement I , R a t i o o f D i f f u s i o n Rates YB\ Absolute Pressure... 38b 11. D i f f u s i o n R e s u l t s f o r Sample 3 , Arrangement I , De.P YBi, P.. 38c 12. D i f f u s i o n R e s u l t s f o r Sample 2, Arrangement I I , De.p V*S- P 38d 13. D i f f u s i o n R e s u l t s f o r Sample 2, Arrangement I I I w i t h 1/4" B a f f l e s , De.P V.S;. P 38e 13a D i f f u s i o n R e s u l t s f o r Sample 2, Arrangement I I I w i t h 7/8" B a f f l e s , De.P V.S . P 38f ( v i i i ) F igure Page 14. P l o t of EL a g a i n s t N./NB at Constant Log Mean d i f f u s i o n Rate f o r Sample 01-A, Arrangement I . (Experimental N. va l u e s a d j u s t e d t o A r b i t r a r y Ordinate Scale) 48a IN APPENDIX 15. E f f e c t o f Flow Rate on Thermal C o n d u c t i v i t y C e l l Response, For 0.22% of N i t r o g e n i n Hydrogen Stream at 200 ohm 66a 16. C a l i b r a t i o n P l o t - Flowmeter 202-1. Sapphire F l o a t , f o r hydrogen at 70 F 66b 17. C a l i b r a t i o n P l o t - Flowmeter 202-1. Sapphire F l o a t , f o r N i t r o g e n at 70 F 66c 18. C a l i b r a t i o n P l o t - Flowmeter 203-1* Sapphire F l o a t , f o r hydrogen a t 70 F 66d 19. C a l i b r a t i o n P l o t - Flowmeter 203-1 Sapphire F l o a t , f o r Hydrogen a t 70 F and. 7*8 atms absolute 66e 20. C a l i b r a t i o n P l o t - Flowmeter 203-2, S t e e l F l o a t , f o r N i t r o g e n at 70 F and 7.8 atms a b s o l u t e 66f 21. C a l i b r a t i o n P l o t f o r No. 1 Thermal C o n d u c t i v i t y c e l l v b e f o r e M o d i f i c a t i o n . . . . 66g 22. C a l i b r a t i o n P l o t f o r No. 2 Thermal C o n d u c t i v i t y c e l l before M o d i f i c a t i o n . . . . 66h ( i x ) LIST OF TABLES IN TEXT Table Page 1. C h a r a c t e r i s t i c s of Porous S o l i d Sample... 21 2. C a l i b r a t i o n of Test Gauge 23 3. R e s u l t s at 1 Atmosphere 34- 4. Average R e s u l t s f o r Sample 2, Arrangement I and v a r i o u s pressures 36 5. Average R e s u l t s f o r Sample 3» Arrangement I and v a r i o u s pressures 37 6. Average R e s u l t s f o r Sample 2, Arrangement I I and v a r i o u s p r e s s u r e s 37 7. D i f f u s i o n R e s u l t s o f I n d i v i d u a l Runs f o r Sample 2, Arrangement I I I w i t h 1/4" B a f f l e s 38 7a. Average R e s u l t s f o r Sample 2, Arrangement I I I w i t h 7/8" B a f f l e s and Va r i o u s Pressures 38 7b. E f f e c t of Flow V e l o c i t y 45 7c. E f f e c t o f C e l l Arrangement 46 IN APPENDIX 4a. D i f f u s i o n R e s u l t s o f I n d i v i d u a l Runs f o r Sample 2, Arrangement 1 58 5a. D i f f u s i o n R e s u l t s o f I n d i v i d u a l Runs f o r Sample 3 , Arrangement I . . 61 6a. D i f f u s i o n R e s u l t s of I n d i v i d u a l Runs f o r Sample 2, Arrangement I I 62 7d. D i f f u s i o n R e s u l t s of I n d i v i d u a l Runs f o r Sample 2, Arrangement I I I 63 8. R a t i o of Equal Pressure D i f f u s i o n Rates f o r P a i r s of Gases 64 00 Table Page 9. C a l c u l a t e d C a l i b r a t i o n r e s u l t s f o r 203-1 hydrogen and 203-2 n i t r o g e n flowmeters 65 10. Examples of complete recorded d a t a f o r D i f f u s i o n Puns. • < 66 1 INTRODUCTION I t was d e s i r e d t o develop an apparatus t h a t would a l l o w measurements t o be made of the e f f e c t of pressure on the d i f f u s i o n r a t e s , and t h e r e f o r e d i f f u s i o n c o e f f i c i e n t s , of b i n a r y gas mixtures p a s s i n g through porous s o l i d s . A constant pressure f l o w system o p e r a t i n g i n the steady s t a t e w i t h counter d i f f u s i o n o f the two gases was p r e f e r r e d f o r s e v e r a l reasons. These reasons w i l l be d i s c u s s e d i n more d e t a i l l a t e r , but b r i e f l y they may be s t a t e d a s , (1) The m a j o r i t y of i n d u s t r i a l processes i n which gas-porous s o l i d c o n t a c t i n g i s i n v o l v e d operate at e s s e n t i a l l y constant t o t a l pressure w i t h a counter d i f f u s i o n process o c c u r r i n g , and t h e r e f o r e , i t might be worth w h i l e t o simulate t h i s type of b e h a v i o r , i f i t can c o n v e n i e n t l y be done. (2) By v a r y i n g the pressure the mean f r e e path of the gas mixture can be r e a d i l y changed over wide ranges. This would a l l o w the t r a n s i t i o n r e g i o n between Knudsen and o r d i n a r y molecular d i f f u s i o n t o be explored more e a s i l y , and a l l o w s e v e r a l r e l a t i o n s h i p s proposed f o r d i f f u s i o n r a t e s i n t h i s r e g i o n t o be checked. (3) Some aspects of counter d i f f u s i o n under constant t o t a l pressure c o u l d be i n v e s t i g a t e d at other than 1 atm. absolute pressure. (4) I f the pressure range covered c o u l d be made s u f f i c i e n t l y l a r g e , the v a r i a t i o n of the o r d i n a r y d i f f u s i o n 2 c o e f f i c i e n t w i t h pressure c o u l d be measured by a new method. A v a r i e t y o f porous s o l i d s would probably be r e q u i r e d t o achieve a l l of these o b j e c t i v e s . However, a s u i t a b l e porous s o l i d can u s u a l l y be found f o r any s p e c i f i c purpose. A d e s c r i p t i o n of an apparatus of the above type i s g i v e n i n t h i s t h e s i s , t o g e ther w i t h f a i r l y e x t e n s i v e t e s t s of i t s performance, u s i n g nitrogen-hydrogen mixtures as the t e s t b i n a r y p a i r . These gases were s e l e c t e d because of t h e i r i d e a l n a t u r e , and the ease of a n a l y s i s by thermal c o n d u c t i v i t y c e l l s . At 20°C, i d e a l behavior i s obtained f o r both gases at pressures up t o 60 atm. The apparatus was c o n s t r u c t e d f o r a maximum pressure of 300 p s i a . , but was a c t u a l l y operated t o a maximum pressure of o n l y 200 p s i a . a t 20°G. With replacement of flowmeters, the apparatus was capable- o f b e i n g used t o 1200 p s i . Some improvements i n e i t h e r measuring technique or d i f f u s i o n c e l l d e s i g n appear t o be necessary i f the apparatus i s t o operate i n a s i m p l e r ; and more p r e c i s e manner. However, accurate and reproducible . r r e s u l t s can be obtained by t h i s method, as demonstrated by the r e s u l t s of d i f f u s i o n measurements. 3 THEORY A. D i f f u s i o n Mechanisms in' Porous S o l i d s The d i f f u s i o n c o e f f i c i e n t s of gases at h i g h e r pressures are d e s i r a b l e to- know because of the i n c r e a s e i n importance of h i g h pressure c a t a l y t i c r e a c t i o n s . I t i s w e l l known t h a t d i r e c t measurements of the d i f f u s i o n o f gases through porous substances~ can o f t e n p r o v i d e v a l u a b l e i n f o r m a t i o n on the r a t e and the mechanism o f the processes t a k i n g p l a c e . D i f f u s i o n of a component of a gaseous mixture through a porous s o l i d may proceed by f o u r p o s s i b l e mechanisms of t r a n s p o r t , namely b u l k d i f f u s i o n , i . e . mean f r e e path of gas molecules i s l e s s t h a n pore s i z e ; Knudsen d i f f u s i o n , i . e . , mean f r e e path o f gas molecules i s g r e a t e r than pore s i z e ; s u r f a c e d i f f u s i o n i n a mobile adsorbed l a y e r , and f o r c e d f l o w i n pores due t o the presence of a t o t a l pressure d i f f e r e n c e . I n g e n e r a l , the t r a n s p o r t o f gas molecules through a porous s o l i d , due to b u l k d i f f u s i o n or Knudsen d i f f u s i o n ; or t o b o t h , i s of the most i n t e r e s t i n t h i s work. The other two mechanisms may be e l i m i n a t e d from the experiments i f the d i f f u s i o n i s c a r r i e d out w e l l above the c r i t i c a l temperature of the gas components, and i n the absence o f any t o t a l pressure d i f f e r e n c e . Prom a broad m e c h a n i s t i c stand p o i n t , molecules are t r a n s p o r t e d i n t o the i n n e r pore s t r u c t u r e of a s o l i d by 4 t h e i r random k i n e t i c motions. I f there were no " r e s i s t a n c e " t o t h i s t r a n s p o r t , molecules c o u l d d i f f u s e i n t o and through a porous s o l i d w i t h v e l o c i t i e s approaching the average molecular v e l o c i t y . Ihe a c t u a l r a t e of d i f f u s i o n i s many orders of magnitude slower than t h i s due t o two causes: (a) c o l l i s i o n s w i t h pore w a l l s , and (b) c o l l i s i o n s w i t h other molecules. I t i s c l e a r t h a t Enudsen d i f f u s i o n happens when the r e s i s t a n c e i s caused by molecular c o l l i s i o n s w i t h pore w a l l s , i . e . pore s i z e i s approximately t e n times l e s s than the means f r e e path. I n . t h i s i n s t a n c e , the d i f f u s i o n o f a p a r t i c u l a r molecular s p e c i e s at 1 atmosphere i n s m a l l pores (e. g. l e s s than 400 & diameter) i s independent of the presence or absence of other types of molecules, and depends o n l y on the p a r t i a l pressure g r a d i e n t of t h a t ( D ( 2 ) p a r t i c u l a r s p e c i e s . I t has been shown t h a t the Khudsen d i f f u s i o n c o e f f i c i e n t , D̂ ., f o r a molecular s p e c i e s i n a pore i s a f u n c t i o n of pore s i z e and the mean molecul a r v e l o c i t y , i . e . DK = T r v (1) where v i s the average molecular v e l o c i t y , and r i s the pore r a d i u s . For b u l k d i f f u s i o n i n a pore, the mean f r e e path X i s much s m a l l e r than the pore s i z e , and a molecule w i t h i n the pore s t r u c t u r e w i l l c o l l i d e w i t h other molecules f a r more o f t e n than w i t h the pore w a l l . Hence, the b u l k 5 d i f f u s i o n c o e f f i c i e n t Dg w i l l be independent of the pore s i z e and w i l l have the value of the o r d i n a r y d i f f u s i o n c o e f f i c i e n t D^. The simple k i n e t i c theory g i v e s the f o l l o w i n g approximate formula f o r the d i f f u s i o n c o e f f i c i e n t f o r a mixture o f two gases of s i m i l a r mass and molecular diameter, where v . Q- t°7 (3) A ir<rxCT (T = molecular diameter = t o t a l c o n c e n t r a t i o n i n molecules per C.C. v = average molecular v e l o c i t y X - mean f r e e path of gas (2) Wheeler v ' has presented s e v e r a l s e m i e m p i r i c a l , o v e r - a l l equations f o r the d i f f u s i o n c o e f f i c i e n t i n the t r a n s i t i o n r e g i o n between o r d i n a r y and Knudsen d i f f u s i o n , one such equation, f o r example, i s 1 _ ijr D = J v X (1 - e x ) (4) Th i s e q u a t i o n has the p r o p e r t y of g i v i n g equation (1) when r i s l e s s than and of g i v i n g equation (2) when r i s much g r e a t e r than X . The p h y s i c a l problem i s concerned w i t h r e l a t i v e p r o b a b i l i t y of a molecule s t r i k i n g the pore w a l l vs. s t r i k i n g a second molecule. I n equ a t i o n (4) the bracketed e x p r e s s i o n i s e x a c t l y the p r o b a b i l i t y t h a t a molecule w i l l have a c o l l i s i o n w i t h a second molecule before t r a v e l l i n g a d i s t a n c e equal t o the pore diameter. As f a r as can be determined, none of these equations f o r the 6 t r a n s i t i o n r e g i o n have ever been checked by any e x p e r i - mental data. These equations (1) (2) and (4) cannot be used at present f o r c a l c u l a t i n g the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t , but o n l y give a q u a l i t a t i v e e x p l a n a t i o n of the mechanism of gas d i f f u s i o n through porous s o l i d . T h e r e f o r e , f o r a porous s o l i d the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t ( l O , which may be made up of c o n t r i b u t i o n s mainly from the d i s c u s s e d two mechanisms, can o n l y be obtained by means o f experimental measurements. The e f f e c t i v e d i f f u s i o n c o e f f i c i e n t (D ) i s alwaysy s m a l l e r i n value than the t r u e b u l k d i f f u s i o n c o e f f i c i e n t (D^) because of the p o r o s i t y , pore geometry e t c . o f the porous s o l i d as s t a t e d by P e t e r s e n v > / and Cox v J . The r a t i o of D g and i s d e f i n e d as the d i f f u s i o n r a t i o f o r a c e r t a i n porous s o l i d , and i s constant f o r any gas p a i r i f there i s no s u r f a c e d i f f u s i o n or f o r c e d f l o w present. I t should be p o s s i b l e t o s e l e c t a porous s o l i d , a gas p a i r , and a s e t of c o n d i t i o n s o f temperature and pressure i n order t o study the process of b u l k d i f f u s i o n a l o n e , or Knudsen d i f f u s i o n a l o n e , or a combination of the two i n the t r a n s i t i o n zone. I n p a r t i c u l a r , as the mean f r e e path v a r i e s i n v e r s e l y as the molecular c o n c e n t r a t i o n , and t h e r e f o r e absolute p r e s s u r e , one of the e a s i e s t ways to o b t a i n v a r i a t i o n i n d i f f u s i v e b ehavior might be t o measure d i f f u s i o n r a t e s at v a r y i n g p r e s s u r e s . 7 B. Counter D i f f u s i o n o f Gases at Constant T o t a l Pressure The theory of d i f f u s i o n r a t e s i n gases was developed as a p a r t of the k i n e t i c t h e o r y , and i s due p r i n c i p a l l y t o M a x w e l l ^ ) and t o S t e f a n ^ ) , w i t h l a t e r important c o n t r i b u t i o n s from 0. E. Meyer(7\ S u t h e r l a n d ^ ) , L a n g e v i n ^ \ Chapman^ 1 0 \ Enskog^ 1 1*^, and J e a n s ^ ^ ^ i B r i e f l y , f o r a b i n a r y s o l u t i o n of substances A and B which i s not of uniform composition, there w i l l be an i n t e r - d i f f u s i o n of the substances which can be d e s c r i b e d i n terms of the l i n e a r v e l o c i t i e s of movement of A and B. I t i s assumed t h a t the drop i n c o n c e n t r a t i o n of substance A, -^-C^, which a c t s as a d r i v i n g f o r c e f o r the movement of A, i s p r o p o r t i o n a l t o the r e l a t i v e l i n e a r v e l o c i t y of A w i t h r e s p e c t t o B, u"A - U B ; t o the molecular c o n c e n t r a t i o n s of the two substances, C^ and C B; and t o the d i s t a n c e dL through which the d i f f u s i o n occurs. M a t h e m a t i c a l l y , t h i s g i v e s the well-known Maxwell eq u a t i o n , - a c A = p c A c B ( u A - U B ) dL (5) where jS i s a p r o p o r t i o n a l i t y f a c t o r o f i n t e r d i f f u s i o n . T h i s b a s i c equation can now be t r e a t e d to d e s c r i b e the v a r i o u s s i t u a t i o n s which may a r i s e . I n the case of gases, c - f C - i (6) and f d e n s i t y M molecular weight 8 Equation (5) then "becomes, u s i n g (6) and the i d e a l gas law, B e f i n e N'as the number of moles of gas d i f f u s i n g per t i m e , per u n i t area i n a d i r e c t i o n p e r p e n d i c u l a r t o t h a t of the d i f f u s i o n . N = &J (8) M Applying the i d e a l - g a s law, then - c f f t - ^rCNlp B- N 6 f A ) d L (9) Since p = pA + pB (10) - d p A = -j^p- (NUP- NAPA - NBPA) d L ( I D Let P A B - ^ j> So t h a t - d p A - ' - r T ^ F (NAP- N AP A - N 8PA) dL (12) • A B > For a steady s t a t e d i f f u s i o n , the t o t a l p r e s s u r e , P, i s co n s t a n t , so are the d i f f u s i o n r a t e s , N. and H L . A o I n t e g r a t i n g Equation (12) f o r counter d i f f u s i o n of A and B, i . e. and Ng having opposite s i g n s , then where the s u b s c r i p t s 1, 2, r e f e r t o the ends of the d i f f u s i o n path. Eqmv: - '( 'IJX^as, d e r i v e d by SherWood and P i g f o r d v but i t s use depends on knowledge of the r e l a t i o n between and Ng. For gases d i f f u s i n g through a porous s o l i d , the 9 D^g obtained from E q u a t i o n (13) i s the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t f o r the s p e c i f i c gas p a i r and porous s o l i d . Since NA - N a = N A ( 1 - P V and -Pgr — N R T V ' Then NART at P = 1 atm. (15) Here V| i s the d i f f u s i o n r a t e of A, i n mis per sec. at 1 atm and d i f f u s i o n temperature T. Since Yj^ , the volume d i f f u s e d , i s not u s u a l l y measured at the d i f f u s i o n temperature, but some temperature T s ^ > a temperature c o r r e c t i o n must be i n c l u d e d . VA VA Tf s t d and p^ /P = Ag,mole f r a c t i o n of A i n B stream, P A /P = A^mole f r a c t i o n of A i n A stream. 1 / S u b s t i t u t i n g these r e l a t i o n s h i p s i n equation (13) and r e a r r a n g i n g v«(T-M-fe>P--%-) D P = •- - n - - • - MA J (16) 1 - ( I - TIT) A NA A Hoogschagen^ 1^ has shown e x p e r i m e n t a l l y t h a t f o r both Enudsen and o r d i n a r y steady s t a t e counter d i f f u s i o n at one atmosphere, ^ i s a constant i n a constant t o t a l pressure system, and f o l l o w s the r e l a t i o n s h i p , 10 NA/~MA" + HtfrU = 0 (17) or N 6 ^ / MA , =̂  / (18) where i s the molecular weight of species A, Mg i s the molecular weight of species B. T h i s equation was d e r i v e d by Hoogschagen from the Knudsen^" 1"^ formula f o r Knudsen d i f f u s i o n . I n the case of o r d i n a r y d i f f u s i o n , t h i s d e r i v a t i o n was based on an impulse balance f o r the two d i f f u s i n g s p e c i e s , and i n v o l v i n g s e v e r a l s i m p l i f y i n g assumptions. Although t h i s t h e o r e t i c a l estimate i s o n l y an approximation, the experimental r e s u l t s f o r the r a t i o of the d i f f u s i o n r a t e s f o r He-0 2, N 2-0 2, G 0 2 - 0 2 / 1 ^ ^ H 2 - H 2 ^ and ̂ - K H ^ 1 ^ systems at atmospheric pressure (data are shown i n the Appendix, Table 8) are i n good agreement w i t h t h i s t h e o r e t i c a l approach. I t would be d e s i r a b l e t o t e s t E q u a t i o n (18) at hig h e r p r e s s u r e s . 11 G. Measurement o f D i f f u s i o n Rates Two main techniques have been used i n the past t o measure d i f f u s i o n r a t e s , and from t h i s i n f o r m a t i o n , t o c a l c u l a t e d i f f u s i o n c o e f f i c i e n t s . These methods, which have been c a l l e d the Loschmidt m e t h o d ^ ^ , and the S t e f a n method,are bo t h unsteady s t a t e experiments. The Loschmidt method i s based on the use o f two chambers, each f i l l e d w i t h a d i f f e r e n t gas, which are connected together i n some way (by the use of a s l i d e , v a l v e , e t c . ) . The d i f f u s i o n r a t e can be c a l c u l a t e d from the change i n c o n c e n t r a t i o n i n the chambers w i t h t i m e r , and from the dimensions' o f the apparatus. A number o f v a r i a t i o n s of t h i s , type have been used, at v a r i o u s times. N e a r l y a l l work on d i f f u s i o n i n dense gases at h i g h pressures has been c a r r i e d out i n t h i s type o f c e l l . I n the l a t t e r case, a porous p l u g was u s u a l l y used t o separate the chambers, and c o n c e n t r a t i o n changes were f o l l o w e d by means of r a d i o a c t i v e t r a c e r s . The s e l f - d i f f u s i o n c o e f f i c i e n t s or b i n a r y d i f f u s i o n c o e f f i c i e n t at e l e v a t e d pressures measured i n t h i s way has been r e p o r t e d f o r N 2-C0 2 C O g - C H ^ 2 ^ , and G G ^ - C j H g ^ 2 ^ . P r o p e r l y speaking, a t r a c e r technique g i v e s at l e a s t a two component m i x t u r e , and s e l f - d i f f u s i o n c o e f f i c i e n t s measured by t h i s method are r e a l l y close, approximations. S i m i l a r l y , mixtures c o n t a i n i n g t r a c e r s , and t r e a t e d as b i n a r y 12 m i x t u r e s , are r e a l l y t e r n a r y m i x t u r e s . I n many cases there have been a wide disagreement among d i f f e r e n t i n v e s t i g a t o r s concerning the e f f e c t of pressure on the d i f f u s i o n c o e f f i c i e n t . The S t e f a n method i s based on the e v a p o r a t i o n o f l i q u i d s from narrow tubes i n t o a f l o w i n g gas stream. One of the components must be i n the l i q u i d phase, and i t i s l i m i t e d , t h e r e f o r e , t o f a i r l y narrow ranges o f temperature and pressure f o r any one system. T h i s has (26),(27),(28), been used by o n l y Sage and coworkers, :t v ;. - - fcVw . t o measure the e f f e c t of pressure on d i f f u s i o n . For n-heptane and n-hexane i n b i n a r y mixtures w i t h methane, ethane and propane i t was found tthat pressure had a s i g n i f i c a n t i n f l u e n c e on the d i f f u s i o n r a t e even at pressures below 60 p s i a , the maximum used. A constant pressure f l o w system was used by Wicke (29^ and K a l l e n b a c h v " o r i g i n a l l y t o study counter d i f f u s i o n , p a r t i c u l a r l y when surface f l o w occurred. W e i s z ^ 0 ^ and Cox v ' l a t e r used m o d i f i c a t i o n s o f the method t o study e f f e c t i v e d i f u s i v i t i e s of porous s o l i d s , and i n the l a t t e r case, t o a l s o measure d i f f u s i o n c o e f f i c i e n t s at e l e v a t e d temperatures. A p p a r e n t l y , a steady s t a t e f l o w system has not been used p r e v i o u s t o t h i s work t o measure the e f f e c t o f pressure on the d i f f u s i o n c o e f f i c i e n t . A l l c o r r e l a t i o n s which have been presented f o r the c a l c u l a t i o n o f the b i n a r y d i f f u s i o n c o e f f i c i e n t assume 13 t h a t i t v a r i e s i n v e r s e l y with, the p r e s s u r e , at l e a s t f o r ( 5 ) , (8 ) , ( 3 D , ( 3 2 ) , (33) i d e a l gases / v w , . • ^ -r. J * For dense gases, (11), (33) the Enskog t h e o r y , ' .., ; .: which t r e a t s the molecules as r i g i d spheres, has "been used t o p r e d i c t b e h a v i o r of the d i f f u s i o n c o e f f i c i e n t as pressure v a r i e s . Perhaps the b e s t present c o r r e l a t i o n f o r the b u l k d i f f u s i o n c o e f f i c i e n t of i d e a l gases i s t h a t of H i r s c h f e l d e r e t . a l . (33). DA 6 = 0 . 0 0 2 6 * 8 0 ( 5 l S - ( T ^ i * ) - ] where = d i f f u s i o n c o e f f i c i e n t i n cm sec P = pressure i n atmospheres T = temperature i n °E kr AB ~ € A 6 k-; = Boltzman constant M :A,MB = M o l e c u l a r weight of species A and B (S^gi-^3- = M o l e c u l a r p o t e n t i a l energy parameters c h a r a c t e r i s t i c of A-B i n t e r a c t i o n i n A and °E, r e s p e c t i v e l y . I t i s w e l l known t h a t f o r i d e a l gases the molecular parameters, 0" and £ , are a f u n c t i o n of temperature on l y . Therefore at constant temperature, Equation (19) may be w r i t t e n i n the form: D^g = Constant x 1 , or 7 D^gP = Constant 1 4 For an i d e a l system, t h i s would he the expected r e s u l t from d i f f u s i o n r a t e measurements through porous s o l i d s i f the pore s i z e of the s o l i d i s l a r g e enough to e l i m i n a t e Enudsen d i f f u s i o n . For the - system, t h i s r e l a t i o n s h i p should h o l d at 20°C f o r pressures up to 60 atms. 15 APPARATUS A. D i f f u s i o n Apparatus The apparatus f o r measuring the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t a t hi g h e r p ressures was s i m i l a r i n p r i n c i p l e t o t h a t used by K. E. Cox f o r the i n v e s t i g a t i o n o f the temperature dependence of the d i f f u s i o n c o e f f i c i e n t . A d i f f e r e n t means of o b t a i n i n g pressure balance between the two s i d e s of the porous sample, and m o d i f i c a t i o n o f the thermal c o n d u c t i v i t y c e l l s were noteworthy changes. The apparatus, as shown i n F i g u r e 1, c o n s i s t e d of two gas t r a i n s , one f o r hydrogen, and the other f o r n i t r o g e n , which l e d the two gases t o opposite f a c e s o f the c y l i n d r i c a l porous s o l i d sample. The hydrogen used was standard commercial grade (99*8%), and the n i t r o g e n was premium q u a l i t y (99»85%)» Both were s u p p l i e d by the Canadian L i q u i d A i r Company. Now c o n s i d e r the. hydrogen gas stream i n d e t a i l . The gas from the storage c y l i n d e r f i r s t was passed through a pressure r e g u l a t o r , and reduced to the d e s i r e d p r e s s u r e , before passing through a s t e e l pipe d r y e r (1" p i p e , 24 in c h e s l o n g , packed w i t h anhydrous c a l c i u m s u l f a t e ^ ) . For s m a l l f l o w r a t e s of gas, l e s s than 100 m i l l i l i t e r per minute, a 6 f o o t long s t e e l c a p i l l a r y , 0.015 i n c h i n s i d e diameter, was i n s e r t e d before the d r y e r . T his c a p i l l a r y p r o v i d e d a back pressure o f approximately 10 pounds per square i n c h to 16 smooth out the f l o w . The hydrogen, a f t e r d r y i n g , was metered i n a b a l l f l o a t g l a s s flowmeter (Matheson types 202, 203 and 204), and was then conducted i n t o one s i d e of the d i f f u s i o n c e l l where i t contacted the face o f the c y l i n d r i c a l porous sample. The n i t r o g e n stream f o l l o w e d the same sequence as the hydrogen. A f t e r f l o w i n g out of the d i f f u s i o n c e l l , the two gas streams, one mainly hydrogen," the other mainly n i t r o g e n , were j o i n e d t o two branches of a tee and r e l e a s e d by a s i n g l e pressure r e g u l a t o r to the atmosphere. P a r t o f the gas, about 60 m i l l i l i t e r s p e r minute, was taken as sample from each stream before the j o i n . Each gas sample was r e g u l a t e d by a s m a l l Ermeto needle v a l v e , and then passed t o the m o d i f i e d thermal c o n d u c t i v i t y c e l l f o r a n a l y s i s . The d i f f e r e n t i a l p r e ssures between the top and bottom chambers of the d i f f u s i o n c e l l were measured on an i n c l i n e d draught gauge (Hays, 12 i n c h s c a l e , range 0 - 1 . 0 i n c h w a t e r ) . The absolute pressure o f the gas i n the system was measured by an accurate t e s t gauge of 300 p s i g s c a l e , and c o u l d be read w i t h an accuracy o f 0.2 p s i . For pressures l e s s than 5 p s i g . a mercury manometer was used i n s t e a d o f the t e s t gauge. Since the apparatus was Resigned f o r measuring the d i f f u s i o n r a t e s at e l e v a t e d p r e s s u r e s , a l l equipment used under h i g h p r e s s u r e , was assembled and connected by FLOWMETER PRESSURE CAPILLARY REGULATOR DIFFUSION C E L L P i c p m s 1* Appa*a!»*' f o r S ^ a u m i e t i t o f Mfimttm Bmm 17 3/8" standard stainless steel tubing and Brmeto type f i t t i n g s . A l l equipment was tested to a pressure of at least 300 ps i . B. Modification of Thermal Conductivity Cells. (T-C Cell) The thermal conductivity c e l l s employed were two Gow- Mac, Model WIS, recorder type, with four filament chambers for each c e l l . These c e l l s were of the "diffusion type" with the filaments being located i n a diffusion passage. This construction was supposed to make the c e l l response independent of gas flow rate. As shown i n the Appendix, Figure 15 > this was true only i f the flow was above 100 mis per minute, at lower flows the c e l l was very sensitive to flow rate. If the d i f f e r e n t i a l pressure between the two sides of porous sample was to be adequately controlled by mixing the two streams after sampling, then the gas sample could be only a small part of the outlet flow (about 300-500 mis per min. each). The m i l l i v o l t output apparently was a single function of gas composition i n the Gow-Mac c e l l s only i f the gas pressure, as well as the flow rate was maintained constant a l l the time. From this point of view, the T-C c e l l s were modified to give a constant flow rate and pressure over the filaments even i f the gas sample rate varied. As shown i n Figure 2, this was achieved by "leaking" a fraction of the sample over the filament and out through a capillary. A constant flow TO RECORDER T H E R M A L CONDUCTIVITY C E L L f WATER BATH F i g u r e 2. M o d i f i c a t i o n o f Thermal C o n d u c t i v i t y C e l l 2 2 OHM RESISTOR — ' W / w w w — 12 OHM RESISTOR ZERO ADJUST 2 OHM POT VVWVNA- • TO # - RECORDER TO , POTENTIOMETER -DECADE RESISTOR -+ TO # RECORDER • TO POTENTIOMETER Z T 6 VOLT F i g u r e 3. W i r i n g Diagram of Thermal C o n d u c t i v i t y c e l l s cr 18 r a t e was a t t a i n e d through, the c a p i l l a r y by keeping the sample f l o w under a constant pressure by b u b b l i n g i t out through a water b a t h maintained at a constant l e v e l . For each sample or r e f e r e n c e f i l a m e n t chamber, a c a p i l l a r y 1 1/2 i n c h long and 0.013 i n c h i n s i d e diameter welded t o a 1/4- i n c h pipe p l u g was screwed i n t o the b r a s s b l o c k o f the T-C c e l l . A hole was d r i l l e d t o j o i n the f i l a m e n t chamber t o the p l u g and hence c a p i l l a r y . The pressures o f sample gas were maintained at 2 i n c h e s water head f o r n i t r o g e n and 1 i n c h f o r hydrogen. T h i s arrangement worked v e r y w e l l , g i v i n g r e p r o d u c i b l e readings f o r b o t h streams, without having t o r e g u l a t e the sample f l o w except i n a q u a l i f e i a t i v e sense so t h a t about the same r a t e o f b u b b l i n g was used at a l l t i m e s . The w i r i n g diagram f o r the thermal c o n d u c t i v i t y c e l l i s shown i n Figure 3» A Y a r i a n A s s o c i a t e s G-10 r e c o r d e r as w e l l as a Leeds and Northrup P o r t a b l e p r e c i s i o n Potentiometer were used t o measure the output m i l l i v o l t s from the thermal c o n d u c t i v i t y c e l l b r i d g e . The f i l a m e n t c u r r e n t was p r o v i d e d by a 6 v o l t storage b a t t e r y . One v o l t m e t e r and two milliammeters were connected i n the w i r i n g system to i n d i c a t e the v o l t a g e s and m i l l i a m p e r e s r e s p e c t i v e l y f o r the f i l a m e n t c u r r e n t s of the two c e l l s . For the d e t e c t i o n o f N 2 i n hydrogen, a f i l a m e n t c u r r e n t o f 280 ma was used, and f o r d e t e c t i n g H 2 i n n i t r o g e n 124 ma. A l s o a decade r e s i s t o r was used f o r r e g u l a t i n g 19 the output m i l l i v o l t signal of each thermal conductivity c e l l to the potentiometer or the Varian recorder. C. Diffusion C e l l The diffusion c e l l was a c y l i n d r i c a l bomb 6 inches high and 4 inches i n diameter as shown i n Figure 4, 5 and 6. It consisted, essentially, of two c y l i n d r i c a l pieces, the top one 2.5 inches high and the bottom one 3*5 inches high, each machined from mild steel bar stock. The inside sample chamber diameter was 1 3/32 inches which was just the diameter of the porous sample when covered with a Gooch rubber sleeve. This sample chamber was 1 1/2 inches deep i n the top half and 2 1/2 inches deep i n the bottom half. In the top half, were six v e r t i c a l holes of 7/16 inch diameter d r i l l e d for placing socket head cap screws. The upper piece also had three gas ducts 3/16 inch i n diameter, used as a gas entrance, a gas outlet, and a connection to the d i f f e r e n t i a l draught gauge. Two of the ducts were d r i l l e d from the lower face of the top piece v e r t i c a l l y up into the solid and turned a 90 degree angle to the end of the chamber, as shown i n Figure 4. One duct entered along the axis of the sample chamber through a small extension, 1/2 inch deep and 1/4 inch i n diameter which was machined further into the steel from the end of the sample chamber. The face of the bottom piece had two grooves machined i n i t . The inner one was for a standard high PLAN VIEW OF BOTTOM PIECE SECTION B - B GAS DUCT DETAIL 6 HOLES 16 FOR SOCKET HEAD CAP SCREWS SECTION C - C GAS DUCT DETAIL SECTION A - A BOTH CELL PIECE FIGURE 4 D I F F U S I O N C E L L 4" F i g u r e 4 a. I s o m e t r i c S k e t c h of D i f f u s i o n C e l l , Showing Gas Duct Arrangement 19c F i g u r e 5. D i f f u s i o n C e l l - S i d e View 19d F i g u r e 6. D i f f u s i o n C e l l - Top View 20 pressure 0 - r i n g which c o u l d h o l d the porous sample i n a proper p o s i t i o n . I n the outer groove was placeddan 0 - r i n g f o r s e a l i n g the two h a l v e s o f the c e l l from leakage. There were a l s o s i x holes of 7/16 i n c h diameter f o r the cap screws. The gas d u c t s , which were i d e n t i c a l i n the top and bottom s e c t i o n s , were s e a l e d by s m a l l o - r i n g s . D. Porous samples The porous samples used i n t h i s study were the S e l a s OJ and 01 s u p p l i e d by the Selas C o r p o r a t i o n o f America i n the form of rods o f approximately 1 i n c h d i a m e t e r and 6 inches l e n g t h . Samples 03-A and 03-B, named No. 1 and No. 2 were cut from the same rod (Number 03-3) w i t h l e n g t h s approximately 2 inches and 1 1/4 i n c h e s , r e s p e c t i v e l y . Sample 01-A, named No. 3»was cut i n t o a 2 i n c h c y l i n d e r from a longer rod (Number 01-1). The two end faces of a sample were machined to smoothness. From the manufacturer's l i t e r a t u r e and from other w o r k ^ ^ the S e l a s samples were known t o be microporous s y n t h e t i c ceramic rod,, used p r i m a r i l y as b a c t e r i o l o g i c a l f i l t e r s ? The S e l a s 01 has a much g r e a t e r p o r o s i t y , and a l a r g e r pore s i z e , than the 03 grade. The c h a r a c t e r i s t i c s of the samples are g i v e n i n Table 1. TABLE I C h a r a c t e r i s t i c s of Sample Jo. Selas.No Length . L, cm X - s e c t i o n a l Area,A.cm^ P o r o s i t y @ Pore Size Average Microns This work Cox's work 1 03-A 5.019 5.376 0.286 a 1.31 a 10.66 / 11.40 2 03-B 3.157 5.376 0.286 1.31 12.86 11.40 3 01-A 5.065 5.391 0.590 b 4.5 b 3.97 2.61 Data f o r P o r o s i t y and Pore S i z e were taken from Cox's work. a. For Sample 03-2 b. For Sample 01-1 EXPERIMENTAL PROCEDURES A. C a l i b r a t i o n of Test Gauge The t e s t gauge used f o r i n d i c a t i n g the t o t a l pressure i n the d i f f u s i o n c e l l was c a l i b r a t e d w i t h an A s h c r o f t gauge t e s t e r . The r e s u l t s , as shown i n Table 2 showed t h a t most of the r e a d i n g s were v e r y a c c u r a t e , and the maximum d e v i a t i o n was o n l y 0 . 3 p s i g . B. C a l i b r a t i o n of flowmeters The c a l i b r a t i o n o f the Matheson U n i v e r s a l flowmeters ( s i z e s 202, 203 and 2C4) c o u l d be c a l c u l a t e d by knowing the s p e c i f i c g r a v i t y and V i s c o s i t y o f the gas under the c o n d i t i o n s of fl o w . Other methods, such as r i s i n g soap bubble method and a wet t e s t meter were a l s o used t o check the c a l i b r a t i o n . Since the c a l i b r a t i o n c u r v e s , showing tube read i n g a g a i n s t f l o w r a t e , f o r each f l o w meter are a f u n c t i o n of temperature, pressure and gas p r o p e r t i e s , each f l o w meter had t o be c a l i b r a t e d f o r the e n t i r e range of working c o n d i t i o n s . The f l o w r a t e s were expressed i n terms o f m i l l i m e t e r s per minute (or mls/min) at standard c o n d i t i o n s , i . e . 70°F (21.1°G) and atmospheric p r e s s u r e . The two 204 flowmeters, used f o r c a l i b r a t i n g the thermal c o n d u c t i v i t y c e l l s , gave a f l o w r a t e r a n g i n g from 100 to 5000 mls/min, and were simply c a l i b r a t e d by the Matheson c a l c u l a t i n g method. C o x ^ ^ checked these flowmeters by u s i n g a wet t e s t meter, and proved t h a t TABLE 2 C a l i b r a t i o n of Test Gauge Standard Gauge Pressure Pressure D e v i a t i o n p s i g p s i g p s i g 5.0 5.0 0 10.0 10.3 +0.3 15.0 15.2 +0.2 20.0 20.0 0 25.0 25.0 0 30.0 30.0 0 50.0 50.0 0 75.0 75.2 +0.2 100.0 100.0 0 125.0 125.0 0 150.0 149.7 -0.3 200.0* 200.0 0 these c a l c u l a t e d c a l i b r a t i o n s were accurate enough t o apply without f u r t h e r experimental measurements. But the two 202 flowmeters, w i t h f l o w r a t e s r a n g i n g from 5 t o 100 mls/min, had t o be c a l i b r a t e d by the r i s i n g soap bubble meter. The c a l i b r a t i o n curves obtained from the Matheson c a l c u l a t i o n , a n d the r i s i n g soap bubble meter are shown i n the appendix, F i g u r e s 16 and 17. E v i d e n t l y , the Matheson c a l i b r a t i o n f o r the 202 flowmeter, had a d i s c r e p a n c y of 20 -50%, and was not recommended. For d i f f u s i o n r u n s , flowmeter 203-1 was employed f o r the hydrogen stream and flowmeter 203-2 f o r n i t r o g e n (A sapphire f l o a t was used i f the l a s t number i s 1, and a s t e e l f l o a t when the l a s t number i s 2 ) . Both were c a l i b r a t e d by the Matheson c a l c u l a t i n g method, and a l s o by use of the wet t e s t meter at room temperature under v a r i o u s p r e s s u r e s of 1.068, 1.2, 1.34, 1.68, 2.02, 3.04, 4.376, 6 U , 7«8, 9 . 5 , 11.2 and 14.6 atmospheres. S e v e r a l c a l i b r a t i o n curves are shown i n the Appendix, F i g u r e s 18, 19 and 20. I t appeared t h a t , f o r the n i t r o g e n stream, the Matheson r e s u l t s have a p o s i t i v e d i s c r e p a n c y of the order of 1-5% from t h a t o f the wet t e s t meter. U s u a l l y the magnitude of the d i s c r e p a n c i e s i n c r e a s e d w i t h pressure and had an average d e v i a t i o n o f +4%. For hydrogen f l o w , the d i s c r e p a n c i e s were even worse (up t o 10 or 20%)t and more i r r e g u l a r . Therefore* the c a l i b r a t i o n r e s u l t s from the wet t e s t meter were 25 accepted f o r measuring the f l o w r a t e s i n the d i f f u s i o n runs. I t was estimated t h a t these wet t e s t meter c a l i b r a - t i o n s were accurate to 1%. Although the average temperature was about 2 1 GC, i t v a r i e d d u r i n g experiments from 2 0 ° - 2 5°C. T h e r e f o r e , the f l o w r a t e obtained from the c a l i b r a t i o n curves should be c o r r e c t e d f o r temperature t o the working c o n d i t i o n . A l s o , as mentioned b e f o r e , the pressure gauge might g i v e 0 . 3 p s i g e r r o r s i n r eadings. The e r r o r i n r e c o r d i n g temperatures and t o t a l p ressures would a f f e c t the c a l i b r a t i o n of the flowmeters. The magnitude of t h i s e f f e c t c o u l d be estimated from the Matheson c a l c u l a t i o n s , because, although the Matheson c a l c u l a t i o n was not s a t i s - f a c t o r y at e l e v a t e d p r e s s u r e s , the c a l c u l a t e d c a l i b r a t i o n curves u s u a l l y were p a r a l l e l and p r o p o r t i o n a l t o those o f the wet t e s t meter. As shown i n the Appendix, Table 9» the c a l i b r a t i o n s o f hydrogen flowmeter ( 2 0 3 - 1 ) and n i t r o g e n flowmeter ( 2 0 3 - 2 ) were a l l c a l c u l a t e d a t s i x c o n d i t i o n s : 70°]?, 150 p s i g ; 70°F, 15 p s i g , e t c . I t was found t h a t the e f f e c t of 5°F i n temperature or 0 . 3 p s i g i n pressure on the f l o w r a t e was of the order o f about 1%. This, proved t h a t the p o s s i b l e e r r o r i n r e c o r d i n g experimental temperatures and p r e s s u r e s , i . e. l e s s than 0.5°F and 0 . 3 p s i g , would not a f f e c t the c a l i b r a t i o n s o f the flowmeters s i g n i f i c a n t l y . 26 C. C a l i b r a t i o n o f the Thermal C o n d u c t i v i t y C e l l s (T-C C e l l s ) Before m o d i f i c a t i o n , the two thermal c o n d u c t i v i t y c e l l s were c a l i b r a t e d i n the same manner as t h a t d e s c r i b e d by C o x ^ . Ho. 1 T-C c e l l was c a l i b r a t e d f o r d e t e c t i n g the percentage of n i t r o g e n i n the hydrogen stream. A constant f l o w of pure hydrogen gas was taken from a gas c y l i n d e r t o the r e f e r e n c e s i d e as r e f e r e n c e gas. Ho. 2 T-C c e l l was used f o r d e t e c t i n g the percentage o f hydrogen i n n i t r o g e n , and pure n i t r o g e n was used as r e f e r e n c e gas. The c a l i - b r a t i o n r e s u l t s , m i l l i v o l t s a g a i n s t composition o f gas m i x t u r e , are shown i n the Appendix, F i g u r e s 21 and 22. Since the thermal c o n d u c t i v i t y of hydrogen i s about seven times t h a t of n i t r o g e n , the Ho. 2 T-C c e l l i s more s e n s i t i v e than Ho. 1. U s u a l l y the Ho. 1 T-C c e l l took about two hours t o warm up and a t t a i n a steady zero p o i n t due t o the p a r t i c u l a r b e h a v i o r of hydrogen. The other c e l l would r e a c h i t s steady zero p o i n t w i t h i n 30 minutes. The c a l i b r a t i o n procedure o f the m o d i f i e d T-C c e l l s i s s t a t e d b r i e f l y as f o l l o w s : (1); S t a r t pure r e f e r e n c e gas through both paths of the c e l l at a f l o w r a t e of 60-65 mls/min (measured at standard s t a t e ) f o r each. Approximately 30 mls/min o f the gas was evolved from the two c a p i l l a r i e s and the r e s t of i t , 30-35 mls/min, bubbled out under a one i n c h water head f o r the Ho. 1 T-C c e l l and a two i n c h head f o r the Ho. 2 T-C c e l l . 27 (2) The c e l l s were now switched on. A f t e r w a i t i n g a few minutes u n t i l the c e l l was f r e e o f a i r , the f i l a m e n t c u r r e n t was adj u s t e d t o 280 m i l l i a m p e r s f o r No. 1 c e l l and 124 f o r No. 2 c e l l . (3) The 2 ohm pot att a c h e d t o the c e l l was r e g u l a t e d u n t i l a s t r a i g h t zero l i n e was obtained on the re c o r d e r c h a r t . Thus the zero p o i n t of the c e l l was determined. ( 4 ) With the re f e r e n c e gas run n i n g as b e f o r e , a gas mixture of known composition was passed through the sample path. The mixture was made by t a k i n g the two gas streams, hydrogen and n i t r o g e n a t constant known f l o w r a t e s i n t o a tee branch mixer. Although the mixture might have a very h i g h f l o w r a t e o n l y about 60-65 mls/min of i t was taken i n t o the c e l l f o r a n a l y s i s . The composition o f the mixture "was? c a l c u l a t e d from the known f l o w r a t e s . (5) The output m i l l i v o l t s were measured on the potentiometer a f t e r a constant r e a d i n g had been obtained on the m i l l i v o l t r e c o r d e r . The s e n s i t i v i t y c o n t r o l r e s i s t o r was set at 900 ohms f o r No. 1 T-C c e l l , and 100 ohms f o r No. 2 c e l l . I n t h i s way a s e r i e s of p o i n t s , mole f r a c t i o n (percentage of gas by volume) a g a i n s t m i l l i v o l t s were obtained w i t h h i g h accuracy. The c a l i b r a t i o n results are shown i n F i g u r e s 7 and 8. F i g u r e 7. C a l i b r a t i o n p l o t of M o d i f i e d No-1 Thermal C o n d u c t i v i t y C e l l 27b V O L % H 2 F i g u r e 8. C a l i b r a t i o n p l o t o f M o d i f i e d NO.,2 Thermal C o n d u c t i v i t y C e l l 28 During t he o p e r a t i o n s , i t was found t h a t more a t t e n t i o n had t o be p a i d t o the zero p o i n t o f No. 1 c e l l i n which hydrogen was used as r e f e r e n c e . D. Measurement o f the E f f e c t i v e D i f f u s i o n C o e f f i c i e n t o f Porous S o l i d s and Rate o f D i f f u s i o n at V a r i o u s P r e s s u r e s . Runs at v a r i o u s p r e s s u r e s , from 1.068 t o 14.6 atmospheres, were a l l done i n the same manner. To s t a r t a r un the apparatus was assembled and t e s t e d t o be sure i t was f r e e of leakage. The thermal c o n d u c t i v i t y c e l l s were then switched on f o r warming and z e r o i n g over a two hour p e r i o d . The gas pressure r e g u l a t o r s and needle v a l v e s were then set t o give steady flowmeter rea d i n g s at the r e q u i r e d f l o w r a t e s and pr e s s u r e s . The o p e r a t i n g c o n d i t i o n s of the d i f f u s i o n runs c o u l d be e a s i l y a d j u s t e d to the r e q u i r e d ones by t u r n i n g needle v a l v e s 1 or 2 and the o u t l e t reducing v a l v e . The d r a f t gauge was s e t t o zero d i f f e r e n t i a l pressure across the porous s o l i d by a d j u s t i n g the needle v a l v e which was p l a c e d i n the n i t r o g e n l i n e between the d i f f u s i o n bomb and the tee j o i n t to the o u t l e t r e g u l a t o r . When c o n d i t i o n s were steady, a constant r e a d i n g was obtained on the c o n d u c t i v i t y c e l l r e c o r d i n g c h a r t . The output m i l l i v o l t s of the two T-C c e l l s were then a c c u r a t e l y measured on the potentiometer connected i n p a r a l l e l w i t h the r e c o r d e r . 29 For each, run the f o l l o w i n g d a t a were recorded: Date of r u n Run.number Number of sample Flowmeter numbers, flowmeter r e a d i n g s and f l o w r a t e s f o r hydrogen and n i t r o g e n gas Absolute pressure Ambient temperature Output m i l l i v o l t s of the two T-C c e l l s From these d a t a i t was p o s s i b l e t o c a l c u l a t e the gas compositions a f t e r d i f f u s i o n , and thus the r a t e s o f hydrogen and n i t r o g e n d i f f u s i o n ( i n m i l l i l i t e r s per minute per square centimeter o f the sample a r e a ) . From the r a t e s o f d i f f u s i o n the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t , D . f o r the sample t e s t e d was c a l c u l a t e d , e Complete recorded data f o r s e v e r a l runs (Table 10) and a sample c a l c u l a t i o n are g i v e n i n the Appendix. 30 RESULTS The r a t e s of d i f f u s i o n of the gas p a i r , hydrogen and n i t r o g e n were measured at a temperature o f 20°-25°C f o r t o t a l p r e ssures from 1 t o 14-.6 atms a b s o l u t e , and w i t h d i f f e r e n t arrangements of the gas ducts i n the d i f f u s i o n bomb. I n arrangement I , the pressure tap was l o c a t e d opposite t o the gas o u t l e t and the gas was conducted i n t o each d i f f u s i o n chamber from the s m a l l e x t e n s i o n as shown i n Figu r e 4 and 4a. I n arrangement I I , the pressure tap was now the p r e v i o u s gas i n l e t , so t h e gas i n l e t and o u t l e t now became opposite t o each o t h e r . For arrangement I I I , gas ducts were used i n the same way as i n arrangement I I , but a t h i c k paper b a f f l e 1/4 or 7/8 i n c h h i g h was i n s e r t e d v e r t i c a l l y between the i n l e t and o u t l e t taps and c o i n c i d e d w i t h a diameter o f each chamber. T h e r e f o r e , the gas which came i n t o the d i f f u s i o n chamber must f l o w over the b a f f l e and be w e l l mixed before going out o f the c e l l . G e n e r a l l y , the d i f f u s i o n r e s u l t s are expressed i n terms o f V H r a t e o f d i f f u s i o n of hydrogen through a sample, mls/min (at 21°G and 1 atm) VJJ r a t e of d i f f u s i o n of n i t r o g e n through a sample mls/min (at 21°C and 1 atm) v H w - r a t i o of r a t e s o f d i f f u s i o n , dimensionless. De.P the product o f e f f e c t i v e d i f f u s i o n c o e f f i c i e n t and pressure (cm /sec)(atm) 31 For convenience i n comparison, the r a t e s o f d i f f u s i o n and the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t s were a l l c o r r e c t e d t o the corresponding v a l u e s at standard room temperature, i . e. 21.1°C (70°F). The temperature dependence of the d i f f u s i o n c o e f f i c i e n t was c a l c u l a t e d from the H i r s c h f e l d e r e t . a l . equation ( 1 9 ) . The d i f f u s i o n c o e f f i c i e n t f o r H 2 ~ ^ 2 l n c r e a s e s about 0.5% w i t h an i n c r e a s e of 1 GC i n temperature. The r e s u l t s o f d i f f u s i o n runs at one atmosphere are shown i n Table 3» The v a l u e s of i n d i v i d u a l runs and t h e i r averages are a l l t a b u l a t e d . The r a t i o of the d i f f u s i o n r a t e s o f hydrogen f o r sample 2 and 1, as shown by the 10-57 f i r s t two s e t s of r e s u l t s , i s 7*0 = 1 . 5 2 , , which i s i n good agreement w i t h the i n v e r s e r a t i o of the two sample 5.019 l e n g t h s , i . e. 3 .175 = 1»59« The e r r o r of 4.4% might be caused by i n a c c u r a c i e s i n the flowmeter c a l i b r a t i o n s f o r Run B1-B4 o f sample 1, or by minor d i f f e r e n c e s i n the two samples although they were cut from the same r o d . Therefore, e f f e c t i v e d i f f u s i o n c o e f f i c i e n t s c a l c u l a t e d , were taken t o be independent o f sample l e n g t h . For sample 1, i n the s t e e l bomb, (Runs B1-B4) the r a t i o s of the r a t e s o f d i f f u s i o n f o r hydrogen and n i t r o g e n gas are c l o s e enough t o the t h e o r e t i c a l v a l u e of 3 . 7 4 - a t one atmosphere t o c o n f i r m the absence of any a p p r e c i a b l e f o r c e d f l o w . At 1.068 atmospheres, the r a t i o s f o r sample 2 and 3 are h i g h e r than 3.74-, and l i e i n the range of 32 3.8 t o 4.0. The r a t i o s of d i f f u s i o n r a t e s f o r Young's and K i s s ' s c e l l are i n good agreement w i t h one another having v a l u e s of 3.87 and 3.84 r e s p e c t i v e l y at 1.068 atmospheres. The c e l l constant of K i s s ' s c e l l (which used the same porous sample as t h a t i n Gox's work) determined from these data checks w i t h t h a t of Cox. The temperature dependence o f ('35') the gas p a i r KH^-Hg i n v e s t i g a t e d by Y o u n g w ^ y has been found t o agree w i t h t h a t obtained by K i s s v , although Young used a d i f f e r e n t porous, sample w i t h the c e l l constant determined from Runs 48, 49 and 50. R e s u l t s f o r h i g h e r pressures are presented here i n three s e r i e s . S e r i e s I : Sample 2 was t e s t e d w i t h arrangement I and gas fl o w r a t e s r a n g i n g from 200-1600 mis per minute. The average r e s u l t s are shown i n t a b l e 4. For i n d i v i d u a l r u n s , the r e s u l t s are shown i n Appendix, Table 4 a. The D .P product, and r a t i o of d i f f u s i o n r a t e s a g a i n s t absolute pressure are p l o t t e d i n F i g u r e s 9 and 10. S e r i e s I I ; T h i s set o f experiments was intended t o show the e f f e c t of pore s i z e o f the s o l i d , i f any, as sample 3 has n e a r l y 4 times the pore diameter and twice the p o r o s i t y of sample 2. The average d i f f u s i o n r e s u l t s f o r sample 3(01-A) w i t h arrangement I and v a r i o u s pressures are shown i n Table 5 and F i g u r e 11. I t can be seen t h a t the D g.P product does not v a r y w i t h p r e s s u r e . 33 Series III: These measurements were carried out to investigate the effect of c e l l arrangement. The average diffusion results for sample 2 with c e l l arrangement II and III are shown i n Tables 6, 7 and 7a, and i n Figures 12, 13 and 13a respectively. The D_.P products of sample 2 with arrangement III (Table 7d i n the Appendix) have a standard deviation of 2.35% with a corresponding mean deviation of 1.84%. The average results given for each series were obtained by averaging a l l the diffusion runs made, which varied i n number from 2 to 6 at each set of conditions. TABLE 3 D i f f u s i o n R esults at one Atmosphere and 21.1°C (1) Sample I , Arrangement I , Nitrogen i n the top chamber Run v No. H V N V H V N De. P atm at 21.1°C P B l 6.928 B2 7.039 B3 7QQ%9 B4 6.990 1.963 1.920 1.795 1.869 3.53 3.67 3.92 3.74 .0617 .0622 .0611 .0617 1 1 1 1 Average 7.0 1.887 3.71 .0618 (2) Sample 2, Arrangement I , Nitrogen i n the top chamber 4 10.72 5 10.43 6 10.43 10 10.75 11 10.36 12 10.73 (3.74)* It t l 11 II II .0590 .0582 .0583 .0594 .0574 .0591 1.068 1.068 1.068 1.068 1.068 1.068 Average 10.57 .0584 (3) Sample 2, Arrangement I, Hydrogen i n the top chamber 73 10.22 74 10.22 75 10.10 2.542 2.620 2.646 4.015 3.904 3.820 .0574 .0562 .0588 1.068 i t 11 Average 10.18 2.609 3.913 .0574 (4) Sample 3, Arrangement I , Hydrogen i n the top chamber 93 • 24.90 94 22.66 95 22.72 5.055 4.787 5.984 4 .925?* 4.70'""'"" 3.80 .2028 .1907 .2134 1.068 1.068 1.068 Average 23.43 5.275 .2025 (5) K i s s ' s d i f f u s i o n c e l l (same as Cox's) Sample 03-2 10.01 10.02 2.653 2.660 3.92 3.76 1.068 1.068 Average 10.01 2.657 3.84 TABLE 3 (cont'd) Run No. V H % V H V N atm P (6) Young's d i f f u s i o n c e l l , Sample 015 40 21.40 5.576 3.840 1.068 49 20.84 5.300 3.932 1.068 50 20.52 5.338 3.844 1.068 Average 20.92 5.405 3.87 ""Assumed value = '""High hydrogen r a t e . 36 .TABLE 4 Ser i e s I Average D i f f u s i o n R e s u l t s at Elevated Pressure Sample 2 Arrangement I Pressures De.Prp . atm V H V H V N j. at 21°C Note 1.068 10.57 (3.74) 1 (.0584) 1.20 11.08 (4.05) (.0598) 1.34 11.18 2.572 4 . 4 2 .0599 1.681 11.55 ( 4 . 4 6 ) ( . 0 6 1 5 ) 2.02 11.89 2 . 5 6 4 4.673 .0614 2.71 12.21 (4.82) (.0632) 3.04 12.37 2.615 4.83 .0649 4 . 3 7 6 12.77 2.470 5 . 0 1 9 .0633 6.1 12.92 2.511 5 . 14 .0638 7.8 13.01 2.583 5.03 .0647 9.503 13 . 6 9 * 2.691 5.09 .0648 11.204 13.42 2.553 5.343 .0633 14.605 13.85 2.544 5.434 .0644 6.1 12.71 2.418 5 . 2 4 .0640 (B>>in top) "Very h i g h flow r a t e of n i t r o g e n (800-1200 mls/min) ^•Results I n parentheses based on i n t e r p o l a t e d values f o r r a t i o of d i f f u s i o n r a t e s . TABLE 5 S e r i e s I I • Average D i f f u s i o n R e s u l t s f o r Sample 31-A Arrangement I Pressure atm.abs. V H De. P at 21.1°C 1.068 . 23.09 5.275 4.49 .2025 1.34 25.1 5.046 4.91 .2085 1.68 25.67 4.67 5.51 .2051 3.04 27.5 4.48 6.26 .2033 TABLE 6 S e r i e s I I I Average D i f f u s i o n R e s u l t s f o r Sample Z'i-Z Arrangement I I Pressure v" H V V — De. P H N V N 1.34 10.41 2.175 4.788 .0538 2.02 11.17 1.965 5.668 .0533 3.04 11.32 1.953 5.798 .0537 4.376 11.35 1.955 5.804 .0539 11.204 11.99 1.683 7.142 .0531 38 TABLE 7 R e s u l t s f o r Sample 2, Arrangement I I I w i t h 1/4" B a f f l e s Run No. V H % V H %̂ De.P 21.1°C P atm Trm °® 117 10.74 2.461 4.364 .0572 1.2 70 118 10.81 2.425 4.458 .0570 1.2 70 1 1 9 11.32 2.412 4.71 .0583 1.68 71 120 11.43 2.345 4.873 .0581 3.04 71 122 11.65 2.377 4.901 .0598 3.04 71 123 11.85 2.288 5.18 .0585 4.376 71 124 12.03 2.031 5.923 .0575 4.376 71 126 11.72 1.903 6.159 .0593 11.204 TABLE 7a Average D i f f u s i o n R e s u l t s f o r Sample 2Z Arrangement I I I , w i t h 7/8" b a f f l e P r e s s u r e V H V N V H % De.P 21.1°G 1.34 2.02 3.04 4.376 7.80 11.204 11.33 11.71 11.61 11.59 11.51 11.67 2.455 2.55 2.45 2.441 2.317 2.330 4.617 4.607 4.747 4.749 4.970 4.954 .0581 .0604 .0595 .0584 .0574 .0579 0.07 0.06 o -I 0 o n o ' j O t Figure 9« D i f f u s i o r Arrangeme L Results i nt I . De. or Sample P VSi p — 0 2 4 6 8 10 12 14 16 ABSOLUTE P R E S S U R E , A T M 6 0.2 D e P 0.1 •n O Q— 1 ^ KJ——^— ^ / • 0 I 2 3 4 A B S O L U T E P R E S S U R E , ATM 03 F i g u r e 11, D i f f u s i o n R e s u l t s f o r Sample 3, Arrangement I , De. P VS. P ° 0 . 0 7 0 . 0 5 F i g u r e 12. D i f f u s i o A rranges n R e s u l t s ent I I , De f o r Sample .P VS. P -o-< n r o 0 2 4 6 8 10 12 14 16 A B S O L U T E P R E S S U R E , A T M 0 . 0 7 0 0 6 P 0 . 0 5 o o CD  o F i g u r e 13 , D i f f u s i o ] Arrangem< 1/4 Baf; l R e s u l t s : mt I I I wi : i e s , Be.P 'or Sample VS. P 0 2 4 6 8 10 12 14 16 A B S O L U T E P R E S S U R E , A T M 0 . 0 7 0 . 0 6 P o o G O O F i g u r e 13a D i f f u s i o n Arrangeme 7/8 B a f f R e s u l t s f tit I I I w i t l e s De.P V or Sample h s. p 0 2 4 6 8 10 12 14 |6 A B S O L U T E P R E S S U R E , A T M 39 EXPERIMENTAL ERRORS (A) Measurement of Gas Composition The c a l i b r a t i o n p l o t s f o r the m o d i f i e d thermal c o n d u c t i v i t y c e l l s were used i n the c a l c u l a t i o n of the d i f f u s i o n r a t e s . Both of the c a l i b r a t i o n p l o t s , f o r hydrogen and n i t r o g e n a n a l y s i s , were estimated t o give the compositions of the streams a f t e r d i f f u s i o n w i t h a maximum e r r o r of + 2.5% and an average e r r o r of l e s s than 1%. The main v a r i a b l e s were the accurate c o n t r o l and measurement o f the q u a n t i t i e s o f the two gas streams t h a t made up the mixture of known composition f o r c a l i b r a t i o n purposes. F i g u r e s 16 and 1 7 , i n the Appendix, show t h a t the sma l l e r streams c o u l d be metered w i t h an accuracy o f about +1.2% ( i . e. w i t h i n + 0 . 2 ml/min.). The e l e c t r i c a l measuring c i r c u i t and the instruments used w i t h i t were f e l t t o have a much s m a l l e r e r r o r . (B) Measurement of D i f f u s i o n Rates P o s s i b l e e r r o r s i n the d i f f u s i o n r a t e v a l u e s were provid e d by the i n a c c u r a c i e s i n measurement o f f l o w r a t e s and c a l i b r a t i o n s of the thermal c o n d u c t i v i t y c e l l s . I n a d d i t i o n t o these, f o r c e d f l o w , due t o unbalanced d i f f e r e n - t i a l pressure across the porous sample, and the e f f e c t of d i f f u s i o n bomb geometry and pressure tap l o c a t i o n , a l s o played v a r i a b l e r o l e s i n a f f e c t i n g v a l u e s of d i f f u s i o n r a t e s . 40 I t was f e l t t h a t the measurement o f f l o w r a t e s (200-1000 mls/min) f o r d i f f u s i o n runs at v a r i o u s pressures might have a maximum e r r o r of + 2%, which was the sum of the e r r o r s from flowmeter c a l i b r a t i o n c u r v e s , experimental temperature and pressure, measurements,and r e a d i n g the b a l l f l o a t i n the g l a s s t u b i n g . The corresponding average e r r o r was estimated t o be +1% ( i . e. 2-10 mls/min.). As mentioned b e f o r e , d u r i n g d i f f u s i o n r u n s , the readings o f the d i f f e r e n t i a l d r a f t gauge were maintained at the zero p o s i t i o n w i t h an accuracy of 0.005 i n c h of water, which should have g i v e n n e g l i g i b l e f o r c e d f l o w ; f-,f. However, i t i s p o s s i b l e t h a t f o r c e d f l o w e x i s t e d , and cou l d cause a p p r e c i a b l e e r r o r s . T h i s aspect i s d i s c u s s e d i n the next s e c t i o n . I f t h i s e f f e c t does not s e r i o u s l y a f f e c t the value o f the d i f f u s i o n c o e f f i c i e n t c a l c u l a t e d , as seems t o be the case, then the maximum e r r o r i n determining the v a l u e of d i f f u s i o n c o e f f i c i e n t should be about 5%, w i t h a probable average e r r o r o f 3%. The experimental d a t a appear t o conform t o t h i s e s timate. 41 DISCUSSION The most notable f e a t u r e s of the r e s u l t s obtained i n t h i s work are the v a r i a t i o n i n the r a t i o of the two d i f f u s i o n r a t e s , and the constantcy o f the D .j? product, as the t o t a l pressure i n c r e a s e d . T h i s l a t t e r e f f e c t was expected, and was observed i n most of the runs made. I t a l s o seemed l o g i c a l t o suppose t h a t the r a t i o of the d i f f u s i o n r a t e s would remain c o n s t a n t , although there i s no c l e a r t h e o r e t i c a l reason e i t h e r f o r or a g a i n s t such a s u p p o s i t i o n , as p o i n t e d out by Hoogschagen v . I t i s not l i k e l y t h a t the b e h a v i o r observed f o r the d i f f u s i o n r a t i o v a l u e s was due t o any of the more obvious p o s s i b l e sources o f experimental e r r o r . For example, flowmeter c a l i b r a t i o n s under pressure were c a r r i e d out u s i n g the same f l o w system, and w i t h a l l connections the same, as i n subsequent d i f f u s i o n runs. The c a l i - b r a t i o n o f the thermal c o n d u c t i v i t y c e l l s was independent of pressure e f f e c t s , as the c e l l s operated under a constant s m a l l pressure at a l l times. On s e v e r a l occasions the system was checked f o r l e a k s by l e a v i n g i t at: 100 -psi; :.r ;. w i t h i n l e t and o u t l e t v a l v e s c l o s e d . An hour or more was always r e q u i r e d b e f o r e even 5 p s i drop i n pressure occurred. Hence, there i s no p o s s i b i l i t y of e r r o r s o c c u r r i n g due t o leakage. The d r a f t gauge which showed the pressure d i f f e r e n t i a l between the sample f a c e s was l o c a t e d at the same l e v e l as the sample, 42 t o a v o i d e r r o r s caused by gas d e n s i t y d i f f e r e n c e s i n manometer l i n e s . As p o i n t e d out i n the pre v i o u s s e c t i o n the u s u a l experimental e r r o r s expected would not have caused a maximum e r r o r o f more than 5% of the D .P product. As a matter o f f a c t , t h i s i s about the range of e r r o r a c t u a l l y found f o r d u p l i c a t e runs. I t should be p o i n t e d out a l s o t h a t runs made at one atmosphere t o t a l pressure conformed t o e x p e c t a t i o n s . The r a t i o o f d i f f u s i o n r a t e s was about as expected. Only a s m a l l d i f f e r e n c e . i n r e s u l t s was obtained by i n t e r c h a n g i n g the two gases throughout the system, and a change i n sample l e n g t h d i d not a f f e c t r e s u l t s s i g n i f i c a n t l y . Using t he g l a s s c e l l employed by Cox v and the same porous sample, the same value o f e f f e c t i v e d i f f u s i v i t y was obtained as t h a t r e p o r t e d by Cox. I n the case of Young's c e l l , (of tne same type as t h a t o f Cox) a d i f f e r e n t porous sample was used, as w e l l as a d i f f e r e n t d i f f e r e n t i a l gauge, again w i t h s a t i s f a c t o r y r e s u l t s . Therefore, i t must be concluded, t h a t at 1 atm. pressure and room temperature, no s e r i o u s e r r o r s i n measurements e x i s t e d , and tha t b u l k d i f f u s i o n o n l y was o c c u r r i n g through the s o l i d sample. With the e x c e p t i o n o f the runs i n S e r i e s I , below 3 atms p r e s s u r e , the v a r i a t i o n of the e f f e c t i v e d i f f u s i o n 4-3 coefficient with pressure was precisely as expected i.e. the D e»P product remained constant. However, the rather large changes i n the ratios of the diffusion rates as pressure increased was not expected. Furthermore, the value of this ratio did not appear to be a function of pressure only, but also to some degree depended on the velocity of flow i n the diffusion c e l l , the direction of the flow path, and the location of the d i f f e r e n t i a l pressure taps. This would seem to lead to the conclusion that some amount of forced flow was occurring through the sample, i n addition to diffusive flow. Table 7b presents some data on individual runs i n which flow velocities were varied. In Series I, using Sample 03-B, i t was only at the highest pressures that flow rate seemed to have a definite effect on the diffusion ratio (although this effect was usually small). For Sample 01-A, the effect of flow rate was noticeable, but this was to be expected, as the permeability of this sample was nearly 30 times as great as that for the 03-B solid. Runs using the 03-B sample with a baffled flow path to promote mixing did not show any effect due to velocity. Variations i n these cases (Series III) could well be due to normal experimental error. Data are shown i n Table 7c, for runs using nearly the same flow rates, at two pressures, and with varying c e l l arrangements. The effect of poor mixing i n the gas space above the sample i s evident from the low value of 44- D .P, and the h i g h d i f f u s i o n r a t i o i . obtained f o r arrangement I I ( i n l e t and o u t l e t d i a m e t r i c a l l y o p p o s i t e ) . Por a g i v e n geometric usage of the d i f f u s i o n c e l l , a constant v a l u e f o r the Dg*!1 product was obtained. T h i s was t r u e f o r two w i d e l y d i f f e r e n t porous samples, as w e l l as f o r d i f f e r e n t c e l l arrangements. I t was a l s o t r u e if tfehethgas-vmixinge:d-i&;J&;Q$ -Vchange-greatly-.l, and whether f o r c e d f l o w c o u l d be expected t o occur r e a d i l y or not. A q u a l i t a t i v e e x p l a n a t i o n can be o f f e r e d f o r the constancy/ o f the D g.P product even though the r e l a t i v e r a t e s of hydrogen and n i t r o g e n d i f f u s i o n are v a r y i n g . I n t h i s work, the c o n c e n t r a t i o n s o f the two streams a f t e r d i f f u s i o n were very low, t h a t i s , of the order of 1% - 5%. Therefore i n the d i f f u s i o n e q uation a p p l i c a b l e (equation 13 and 16), the q u a n t i t i e s A^ and Ag are approximately 0 and 1 r e s p e c t i v e l y . The e q u a t i o n can then be w r i t t e n , D . p _ f-SIk) A ( N< - N s ) A „ NA-MI (2i) S P A In A . ' K |„-gj. 1-(!-•£> A. ETL where K i s a numerical constant equal t o A . The f u n c t i o n - N-g/ i s the l o g a r i t h m i c average r a t e of d i f f u s i o n of both gases. Hence, i f t h i s q u a n t i t y remains c o n s t a n t , then the D .P product w i l l a l s o 45 TABLE ?b E f f e c t o f Plow V e l o c i t y N2 Plow Hg PlOw v H Run mls/min mls/min % P No. s t d s t d De. P atm 35 445 212 4.81 .0648 3.04 37 423 342 4.84 .O644 3.04 65 605 575 5.14 .0638 14.61 69 800 322 5.48 .O642 14.61 70 1198 443 5.68 .0651 14.61 93 414 517 4.93 .203 1.068 94 237 523 4.74 .191 1.068 95 268 284 3.30 .213 1.068 131 440 519 4.90 .0579 11.2 132 576 820 5.15 .0571 11.2 133 574 828 5.03 .0580 11.2 134 339 446 4.59 .0573 3.04 135 480 220 4.91 .0622 3.04 Remarks Sample 03-B Arrangement I Sample 01-A Arrangement 1 Sample 03-B Arrangement 3 7/8" b a f f l e 46 TABLE 7c E f f e c t of C e l l Arrangement N2 Plow Hp Plow . _ — . v H Run mls/min mls/min P C e l l No. sjtd s td V N De. P atm Arrangement 103 378 340 5.62 .0526 2.02 03-B A r r . I I 119 381 355 4.71 .0583 " 03-B A r r . I l l 1/4 B a f f l e 138 371 327 4.64 .0602 » 03-B A r r . I l l 7/8 B a f f l e 56 358 382 4.64 .0612 " 03-B A r r . I 116 475 456 7.60 .0515 11.2 03-B A r r . I I . 126 481 604 6.16 .0593 " 03-B A r r . I l l I/4" B a f f l e 131 440 519 4.90 .0579 11 03-B A r r . I l l 7/8 B a f f l e 68 620 648 5.14 .0632 " 03-B A r r . I 4-7 remain constant. I f f o r c e d f l o w of one component e.g. A, i s o c c u r r i n g , then the t o t a l r a t e of f l o w of A, N^, must i n c r e a s e . I f the t o t a l average f l o w of both gases i s t o remain constant, as d e f i n e d above, then the r a t e o f f l o w of B must n e c e s s a r i l y decrease as t h a t of A i n c r e a s e s . P r o v i d i n g the f o r c e d f l o w of one component i s not too l a r g e a f r a c t i o n of the t o t a l f l o w , i t a p p a r e n t l y tends to cause a decrease i n the dineVfe'^ve r a t e of the second component such t h a t the average mean f l o w i s not s e r i o u s l y a f f e c t e d . Obviously t h e r e i s a l i m i t beyond which t h i s a p p a r e n t l y f o r t u i t o u s phenomena c o u l d not be expected to occur, e. g. when the f o r c e d f l o w becomes too great. An i n s p e c t i o n of the data f o r i n d i v i d u a l runs shows th a t an i n c r e a s e i n the d i f f u s i o n r a t e of hydrogen d i d indeed cause a decrease i n the n i t r o g e n d i f f u s e d . The .exception t o t h i s g e n e r a l o b s e r v a t i o n can be found i n the runs r e p o r t e d as S e r i e s I . Here the experimental accuracy, p a r t i c u l a r l y f o r the n i t r o g e n a n a l y s i s , i s not as h i g h as i n other runs. The r e s u l t s ' of t h i s s e r i e s show, an apparent i n c r e a s e o f about 10% i n the D .P product w i t h pressure below 3.0 atms, which appeaps t o be due t o the f a c t t h a t the hydrogen d i f f u s i o n r a t e i n c r e a s e d w i t h l i t t l e or no corresponding decrease i n n i t r o g e n d i f f u s i o n r a t e . I n a l l other s e t s of runs, u s i n g e i t h e r d i f f e r e n t s o l i d s , o r d i f f e r e n t choices f o r c e l l c onnections, i t was g e n e r a l l y 48 t r u e t h a t as the amount of hydrogen d i f f u s e d i n c r e a s e d , the n i t r o g e n f l o w decreased. The u s u a l amount of i n c r e a s e i n the d i f f u s i o n r a t e of hydrogen over the e n t i r e pressure range was about 10%-30%, and the decrease of n i t r o g e n about 5-25%, depending on the c o n d i t i o n s used. The d a t a f o r sample 01-A are p l o t t e d i n Figure;.; 14.which a l s o shows a p l o t o f the v a l u e s of and N^/Ng which would giv e the same l o g mean average f l o w as t h a t observed when f o r c e d f l o w was absent. I t can be seen t h a t , e x p e r i m e n t a l l y , the d a t a does v a r y i n such a way as to g i v e a constant average f l o w , as indeed i t must, s i n c e D .P i s a l s o constant i n these runs. I t i s i n t e r e s t i n g t o note some data taken by Cox v J to demonstrate t h a t f o r c e d f l o w was absent i n h i s work. His r e s u l t s show t h a t the i n c r e a s e i n hydrogen d i f f u s i o n r a t e due t o a pressure head was almost the same as the decrease i n d i f f u s i o n r a t e when hydrogen was d i f f u s i n g a g a i n s t the same pressure head e. g. at +0.2 i n c h water the r a t e i n c r e a s e d 9.0%, a t -0.2 i n c h of water, i t devreased 10.2%. T h i s confirms the e x p l a n a t i o n g i v e n above f o r the c o n s t a n t l y of the I>e.P product, even though the q u a n t i t i e s d i f f u s e d may v a r y , or i n s p i t e of some degree of f o r c e d f l o w . No r e a l l y s a t i s f a c t o r y e x p l a n a t i o n can be o f f e r e d f o r the apparent e x i s t e n c e o f f o r c e d f l o w i n t h i s apparatus. Undoubtedly i n some of the runs done e.g. w i t h Sample 01-A, 7 A EXPERIMENTAL DATA FOR SAMPLE 0 I - A 8 0 12 14 F i g u r e 14. P l o t of f o r Sample 01-A, N A / N B N« a g a i n s t N A/Ng a t Co n s t a n t Log Arrangement 1. ( E x p e r i m e n t a l N to A r b i t a r y O r d i n a t e S c a l e ) . A Mean D i f f u s i o n Rate v a l u e s a d j u s t e d oo 49 or w i t h Arrangement I I , e i t h e r f o r c e d f l o w , or end r e s i s t a n c e due t o poor m i x i n g , e x i s t e d . Evidence f o r f o r c e d f l o w i n other r u n s , was i n d i r e c t . C a l c u l a t i o n s f o r fbrced f l o w i n the 03-B sample u s i n g e x p e r i m e n t a l l y determined p e r m e a b i l i t i e s and Darcy's law i n d i c a t e t h a t 1 p s i d i f f e r e n t i a l i s r e q u i r e d t o cause a f o r c e d f l o w o f 1 ml of hydrogen per minute. Any p o s s i b l e impact pressures can be shown to be of the order of 0.01" water. The p o s s i b i l i t y a l s o remains t h a t the d i f f u s i o n r a t i o i s , i n f a c t , a f u n c t i o n o f pressure. The o b s e r v a t i o n t h a t a complete r e v e r s a l of the system ( i . e. simply s w i t c h i n g the two gas c y l i n d e r s ) g i v e s p r a c t i c a l l y i d e n t i c a l r e s u l t s e i t h e r way, cannot e a s i l y be e x p l a i n e d on the b a s i s o f f o r c e d flow. I t w i l l be necessary to modify the d i f f u s i o n c e l l , and perhaps the d i f f e r e n t i a l d r a f t gauge arrangements^ before the s i t u a t i o n can be c l a r i f i e d . However, the apparatus can be used s u c c e s s f u l l y i n i t s present form f o r some purposes. I n i n v e s t i g a t i n g the t r a n s i t i o n r e g i o n between Knudsen and o r d i n a r y d i f f u s i o n , f o r c e d f l o w i s u s u a l l y a minor f a c t o r because of the very f i n e pore s i z e s involved,and t h e r e f o r e a s m a l l pressure unbalance i s of l i t t l e consequence. When f o r c e d flow i s present as a mechanism of t r a n s f e r i n a d d i t i o n to d i f f u s i v e f l o w , i t has been assumed t h a t the two can simply be added. However, i n view of the r e s u l t s obtained i n t h i s work, t h i s would no longer be necessary 50 as long as the f l o w i s l a r g e l y d i f f u s i v e i n nature. P a r t i c u l a r l y i n the f i e l d o f r e a c t i o n s i n porous s o l i d s t h i s might present a s i m p l i f i c a t i o n , s i n c e H^/Hg i s known from s t o i c h o i m e t r i c r e l a t i o n s . I f there i s an i n c r e a s e or decrease i n volume on r e a c t i o n , t h e n some degree of f o r c e d f l o w e x i s t s through the porous s o l i d i n order t h a t N^/Ng may have the necessary v a l u e . Knowing t h i s v a l u e , and the e f f e c t i v e d i f f u s i v i t y of the s o l i d , i t should be p o s s i b l e t o c a l c u l a t e the r a t e of the d i f f u s i v e process f o r a b i n a r y system of known k i n e t i c s , u s i n g the d i f f u s i o n e quation,only. 51 CONCLUSIONS AND RECOMMENDATIONS The present d i f f u s i o n c e l l and d i f f e r e n t i a l pressure measuring system should be m o d i f i e d i n such a way as t o giv e good gas space mixing and true s t a t i c pressure r e a d i n g a t the s o l i d sample f a c e s . The apparatus appears t o be most s u i t a b l e f o r v a r y i n g the mean f r e e path o f d i f f u s i n g gas systems by the a p p l i c a t i o n o f pre s s u r e . T h i s a l l o w s the nature of the d i f f u s i o n mechanism o c c u r r i n g i n a porous s o l i d t o be v a r i e d e a s i l y . Even i f f o r c e d flow were completely e l i m i n a t e d , the method i s not p a r t i c u l a r l y s u i t a b l e f o r measuring the v a r i a t i o n of the .P product w i t h absolute p r e s s u r e . T h i s i s due t o the n e c e s s i t y f o r m u l t i p l e ranges and c a l i b r a t i o n s of flowmeters. A s u b s t i t u t e f o r the type of flowmeter used here would s i m p l i f y experimental work. Some reason should be found f o r the n e c e s s i t y of t h r o t t l i n g the n i t r o g e n o u t l e t l i n e to achieve pressure balance i n the c e l l , when, i n the o r y , i t i s the hydrogen l i n e which should r e q u i r e t h r o t t l i n g . 52 BIBLIOGRAPHY (1) Kennard, E. 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A., 12, 56, 533 (1911). (12) Jeans, J . H. "The Dynamical Theory of Gases" 3rd Ed. Cambridge U n i v e r s i t y P r e s s , N. Y., 307 (1921). (13) Lewis, W. K., and K. C. Chang, Trans. Am. I n s t . Chem. Engrs., 21, 127 (1928). (14) Sherwood, T. K., and R. L. P i g f o r d , " A b s o r p t i o n and E x t r a c t i o n " 2nd Ed., McGraw-Hill,-New York, (1952). (15) Hoogschagen, J . , Ind. Eng. Chem., 4£, 906 (1955). (16) Khudsen, M., Ann. P h y s i k , 28, 75 (1909). (17) K i s s , M., B. A. S c Thesis i n Chemical E n g i n e e r i n g , U n i v e r s i t y of B r i t i s h Columbia, 0-959). (18) Loschmidt, I n t e r n a t i o n a l C r i t i c a l T ables, V o l . 5, (1928), p. 62, McGraw-Hill, New York. 53 (19) M i f f l i n , T. R. and C. 0 . Bennett, J . Chem. Phys., 22, 975 ( 1 9 5 8 ) . (20) Becker, V o g e l l , and Zigan, Z. N a t u r f o r s c h , 8 a , 686 ( 1 9 5 3 ) . (21) O'Hearn, H. A. and J . L. M a r t i n , Ihd Eng. Chem. 2081 ( 1 9 5 5 ) . (22) Timmerhaus., K. 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J o u r n a l 4 , 137 ( 1 9 5 8 ) . (34) H i r s c h f e l d e r , J . 0 . , C u r t i s s , C. P. and B i r d , R. B., "Molecular Theory of Gases a n d - L i q u i d " W i l e y , N.Y., ( 1 9 5 4 ) . (35) Young, M. June., P r i v a t e Communication t o Dr. D. S. S c o t t , Department of Chemical E n g i n e e r i n g , U n i v e r s i t y of B r i t i s h Columbia, ( 1 9 5 9 ) . APPENDIX Sample C a l c u l a t i o n E f f e c t i v e D i f f u s i o n C o e f f i c i e n t and D i f f u s i o n R a t i o Run 37. Data recorded as below Sample Selas 03-B Length L 3.157 cm Average Cross S e c t i o n a l Area, A 5.376 cm' Temperature, T° K 294° Absolute Pressure, P. atm 3.04 atm Nitrogen flow r a t e , i n l e t , X N 423 Si£ std, Hydrogen f l o w r a t e , i n l e t , X„ 342 " 11 ' n M.V. on No. 1 T-C c e l l 7.309 M.V. M.V. on No. 2 T-C c e l l 26.15 M.V. N i t r o g e n % i n o u t l e t Hg. N ^ 0.785$ Hydrogen % i n o u t l e t N g. iy6 2.915$ C a l c u l a t i o n : By means o f a m a t e r i a l b a l a n c e , based on c o n s t a n t p r e s s u r e . We c a n c a l c u l a t e the o u t l e t f l o w r a t e o f hydrogen and n i t r o g e n , i . e . Y and Y . T h e r e f o r e tine volume r a t e o f H N hydrogen (V^) and n i t r o g e n (V^) d i f f u s e d a r e the p r o d u c t s o f Y N * H N ^ Y H * r e 3 P e c t i v e l y « N Y (N H X H Where N T. H % N. H I<H. H V H V. N C u t l e t n i t r o g e n f l o w r a t e mls/min s t d . O u t l e t hydrogen f l o w r a t e mls/min s t d . Mole f r a c t i o n o f n i t r o g e n i n o u t l e t n i t r o g e n stream, Mole f r a c t i o n o f hydrogen i n o u t l e t " " Mole f r a c t i o n of n i t r o g e n i n o u t l e t hydrogen " Mole f r a c t i o n o f hydrogen i n o u t l e t 11 11 Rate o f d i f f u s i o n o f hydrogen mls/min s t d . Rate of d i f f u s i o n of n i t r o g e n mls/min s t d . A m a t e r i a l b a l a n c e over the system g i v e s * • * X H " Y N + Y H Y . N + Y . N H H N N iH (2) X f l - H )-X .H H N N N S o l v e (1) and (2) f o r Y and Y , we have Y H N H H H - o r Y. _ H H N H. N H I H T T - N_ (^) (3) H Y r T = X T + X - Y (4 N N H H V H = Y • H (5 V.T = Y • N (6 N H H F o r r u n 37, s u b s t i t u t e the known v a l u e i n t o e q u a t i o n (4), (5) and (6) ,^02915 342 - 423 \ 97085 ; Thus Y n = ' ! (.02915x = 332 ral/min. H .99215 - .00785 .97085' Y N = 433 ml/min. V_ = 12.62 ml/min. H = 2.606 ml/min. VH — = r a t i o o f d i f f u s i o n = 4.84 We c a n now a p p l y e q u a t i o n (16) d e r i v e d f r o m t h e Sherwood and P i g f o r d e q u a t i o n and c a l c u l a t e t h e Ma x w e l l d i f f u s i o n c o e f f i c i e n t . L e t hydrogen be component A. Then N/HH5) Ln — ' ) — ( i NM3 _L_ A ( I - l - 0 ^rm ~ Room temperature, 294° T s t d = = 294.1° K (70°P) L = = 3.157 cm A = = 5.376 2 cm' % . H H 2 " : 1 - % V H = 0.7934 % " .02915 " mole f r a c t i o n H H = .99215 mole f r a c t i o n V H „ = 12.62 mis per min. 12.62 1 (1) 60 3.157 (0.7934) 5.376 D e , P = m 1 - 0.7934 (.02915) 1 - 0.7934 (.99215) .0980 = 1.521 2 cm' De. P = O.O644 sec, (atm). where P 57 3.04 atm. Dm. P = 0.7657 at 294.1°K. 58 TABLE 4a D i f f u s i o n R e s u l t s 'of I n d i v i d u a l Runs f o r Sample 2 Arrangement I Run No. V H N V H V N at 21.1°C De. F P,atm Trm °C 4 5 6 10 11 12 10.72 10.43 10.43 10.75 10.36 10.73 (3.74)* it tt tt n it .0590 .0582 .0583 .0594 .0574 .0591 1.068 u tt tt it it 22 tt tt tt 23 23 Average 10.57 .0584 7 8 9 11.27 10.97 11.00 (4.05) it it (.0610) (.0595) (.0595) 1.2 it » 22 22 22 Average 11.08 .0598 13 14 52 53 54 11.09 11.15 11.21 11.38 11.39 2.605 2.633 2.473 (4.21) (4.21) 4.310 4.322 4.606 (.0589 (.0595 .0601 .0605 .0590 1.34 tt it tt tt 23.5 it 22 22 22 Average 11.18 2.572 4.42 .0599 15 16 17 18 11.36 11.37 11.88 11.60 (4 .46) tt it tt (.0695) (.0607) (.0629) (.0618) 1.681 tt tt » 19.5 » tt tt Average 11.55 (.0615) 19 20 21 55 56 57 72 11.50 11.89 11.70 12.03 11.83 12.12 12.17 2.592 2.549 2.507 2.606 (4.645) it it 4.641 4.641 4.834 4.671 (.0604) (.0632) (.0611) .0620 .0612 .0613 .0606 2.02 19.8 II it 22 22 22 20.4 Average 11.89 2.564 4.673 .0614 TABLE 4a (cont'd) V V V Run No. H N N De. P P. atm Trm 22 11.46 (4.82) (.0585) 2.71 20.4 23 12.60 » (.0655) it it 24 12.58 ii (.0651) tt tt Average 12.21 (.0632) 25 11.64 (4.865) (.0603) 3.04 20.4 26 12.60 (4.965) .0640 tt 20.4 36 12.62 2.623 4.81 .0651 tt 20.5 37 12.62 2.606 4.84 .0646 it 20.5 Average 12.37 2.615 4.83 .0649 27 13.13 (5.02) (.0681) 4.376 19 28 12.20 n (.. 0628) tt 19 29 11.90 ii (.0615) tt 19 30 13.55 H (.0685) tt 19.2 41 12.805 2.800 4.573 .0666 tt 20.8 42 12.645 2.165 5.840 .0604 tt 20.8 43 13.00 2.445 5*330 .0628 it 20.8 Average 12.77 2.470 5.019 .0633 38 13.1 2.551 5.13 .0650 6.1 20.8 39 12.84 2.482 5.17 .0632 tt 20.8 40 12.81 2.499 5.13 .0632 it 20.8 Average 12.92 2.511 5.14 .0638 44 13.18 2.481 5.31 .0639 7.8 20.4 45 13.16 2.581 5.10 .0655 » tt 46 12.65 2.693 4.69 .0650 tt it 47 13.03 2.579 5*02 .0645 tt tt Average 13.01 2.583 5.03 .0647 58 14.04 2.724 5.154 .0661 9.503 21.4 59 13.62 2.714 5.017 .0648 » 22 60 13.40 2.633 5.089 .0634 tt 22 Average 13.69 2.691 5.09 .0648 TABLE 4a ( c o n t ' d ) 60 Run No. V H V N V N De. P P atm Trm °C 61 62 63 64 68 13.36 13.69 13.26 13.32 13.46 2.548 2.490 2.508 2.594 2.618 5.243 5.498 5.287 5.135 5.141 .0634 .0629 .0624 .0631 .0645 11.204 n » ti ti 23 11 11 21.5 20 Average 13.42 2.553 5.343 .0633 65 69 70 71 13.30 13.76 14.14 14.23 2.588 2.51 2.489 2.567 5.139 5.482 5.681 5.543 .0630 .0642 ;0646 .0655 14.605 i» it u 21.5 20 20.4 20.4 Average 13.86 2.544 5.434 .0644 rf V a l u e s i n p a r a n t h e s e s i n t e r p o l a t e d . 61 TABLE 5a D i f f u s i o n R esults of I n d i v i d u a l Runs f o r Sample 3 Arrangement I Run No. Pressure atm V H V N V H % De. P at 21°C 93 94 95 1.068 tt tt 24.9 22.66 22.72 5.055 4.787 5.984 4.925 4.74 3.80 .2028 .1907 .2134 Average 23.09 5.275 4.49 .2025 91 92 1.34 n 24.80 25.4 5.125 4.967 4.84 4.97 .2065 .2105 Average 25.1 5.046 4.91 .2085 87 88 89 90 1.681 tt tt tt 25.65 25.73 27.23 27.00 4.83 4.81 4.685 4.41 5.33 5.35 5.82 6.12 .2046 .2043 .2060 .2055 Average 25.65 4.67 5.51 .2051 83 84 3.04 3.04 27.6 27.4 4.095 4.75 6.75 5.77 .1965 .2100 Average 27.5 4.43 6.26 .2033 TABLE 6a 62 D i f f u s i o n R e s u l t s of I n d i v i d u a l Runs f o r Sample 2 Arrang ement I I Run No. VH % V H *M De.P at 21.1°C Pressure atm Note 100 10.276 101 10.48 102 10.478 2.104 2.19 2.232 4.884 4.785 4.694 (.05267) .0543 (.0546) 1.338 1.34 1.34 0.1 nH2<N 2* Average 10.41 2.175 4.788, .0538 103 11.15 104 11.143 105 11.25 106 10.95 107 11.15 108 11.18 1.985 1.979 2.047 1.951 1.933 1.900 5.617 5.631 5.496 5.610 5.768 5.884 (0.0526) 1.0536 (0.0547) (0.0528 (0.053D 0.0532 2.02 2.02 2.015 2.08 2.035 2.02 0.03"H2>N2 Average 11.17 1.965 5.668 0.0533 109 11.33 110 11.31 1.953 1.952 5.801 5.794 (,.0537) .05365 ,3.04 3.04 0.05"H2>N2 Average 11.32 1.953 5.798 4 .0537 111 11.35 112 11.35 1.950 1.961 5.821 5.787 .05385 (.0540) 4.376 4.376 .06"H2>N2 Average 11.35 1.955 5.804 .0539 114 12.10 115 11.87 116 11.99 1.696 1.775 1.577 7.137 6.687 7.603 (.0532) .0545 .0515 11.204 11.204 11.204 .08"H2>N2 Average 11.99 1.683 7.142 .0531 ^Pressure of the hydrogen side was 0.1" water; gr e a t e r , than ..that of the n i t r o g e n s i d e . .( ) Values w i t h i n t h i s bracket allowed an experimental e r r o r e i t h e r i n d i f f e r e n t i a l pressure or i n t o t a l pressure. '63 TABLE 7d D i f f u s i o n R e s u l t s of I n d i v i d u a l Runs f o r Sample 2 Arrangement I I I (with 7/8" v e r t i c a l b a f f l e ) Run T r — D e . P Pressure No. H Ĵ N VN at 21.1°C absolute Note 140 11.35 2.463 4.608 y 0.0583 • 1.34 141 11.32 2.447 4.626 0.0579 " 142 (11.26) (2.462) (4.574) (0.0572) " .11 , ,H 20H 2<N 2 Average 11.33 2.455 4.617 0.0581 138 11.60 2.499 4.643 .0597 2.02 139 11.89 2*601 4.571 .0611 " Average 11.71 ,2.55 4.607 .0604 134 11.055 2.41 4.587 .0570 3.04 135 12.17 /2.48 4.907 .0619 , 11 Average 11.61 2.45 4.747 .0595 136 11.59 2.415 4.799 .0589 4.376 137 11.598 2*468 4.699 .0575 " Average 11.594 2.441 4.747 .0584 143 11.45 2.299 4.980 .0569 7.8 144 (11.585H2.335) (4.960) (.0578) 7.79 Average 11.507 2.315 4.970 .0574 127 11.70 2.467 4.743 .0590 11.204 129 (11.463) (2.335) (4.909) (.0585) " ,09"H ?0H p<N 9 130 11.65 2.332 4.996 .0583 " 131 11.52 2.350 4.902 .0576 " 132 I I . 6 4 2.262 5.146 .0570 11 133 11.73 2.333 5.028 .0578 Average 11.67 2.330 4.954 .0579 TABLE 8 R a t i o o f E q u a l P r e s s u r e D i f f u s i o n R a t e s f o r P a i r s of Gases, 1 atm Gases D i f f u s i o n R a t i o Observed T h e o r e t i c a l f r o m eq.(18) Helium-oxygen^ 3.03 2.66 2.54 2.83 N i t r o g e n - o x y g e n , 1.09 1.07 1.07 Carbon dioxide-oxygen-^ 0.89 0.80 0.85 Hydrogen-ni t r o g e n ^ 3.44 4.03 3.75 3.742 1. D a t a f r o m Hoogschagen. (15) 2. Data f r o m Cox. (4) 65 TABLE 9 C a l c u l a t e d C a l i b r a t i o n R e s u l t s f o r Plow Meters Gas. Mis 70°F Flow Rate min 1 atm No. o f Tube 70°F 75°F 70°F Flowmeter Reading 150 p s i g 150 p s i g 150 p s i g 203-1 3 167 166.9 167.9 4 284.7 284.5 286.1 5 454.5 454.2 455.5 6 669 671.4 673.7 7 877.8 877.1 878.1 203-2 7 503.7 501.4 502 .0 8 597.3 592.8 595.0 10 788.7 784.4 786.7 12 1003.8 999.9 1001.7 70°F 75 °F 70°F 15 p s i g 15 p s i g 15.3 p s i g 203-1 7 177.6 176.3 178 .9 8 241.5 239.1 243.6 10 371.2 369.1 374.9 12 600.8 595.8 605 .9 14 730.3 725.4 736 203-2 8 193.3 193.2 196 .7 10 264.4 262.9 267.4 12 339.3 337.9 342.7 14 432.5 429 436.4 16 520.3 517.2 524 H 2 N 2 H2 N 2 TABLE 10 Example o f Complete Recorded D a t a f o r Runs (Arrangement I ) Sa mp le  Wo . Run No. P atm P l o r Rate 21°C, N i t r o g e n i n l e t mls/min. 1 atm Hydrogen No. 2 i n l e t M.V. E2% i n N 2 No. 1 M.V. N2# i n H2 % V H % De. P 2 52 1.34 324.6 274.5 30.02 3.365 11.2 7.343 0.980 2.605 4.30 .0606 it 53 1.34 382 275.5 26.11 2.912 11.38 9.100 0.987 2.633 4.32 .0614 tt 54 1.34 330 319 30.02 3.364 11.39 7.343 0.797 2.473 4.61 .0612 2 36 3.04 411.7 305 26.85 2.993 12.62 8.379 .889 2.623 4.81 .0651 u 37 3.04 423 342 26.15 2.915 12.62 7.309 .785 2.606 4.84 .O646 2 41 4.376 512 331 22.0 2.447 12.805 8.064 .875 2.800 4.57 .0666 it 42 4.376 458 256 24.23 2.695 12.645 8.196 .889 2.165 5.84 .0604 II 43 ti 566 606 20.23 2.253 13.000 3.785 .411 2.445 5.33 .0628 II 65 14.605 605 515 19.08 2.136 13.30 4.723 0.513 2.588 5.139 .0630 tt 69 ti 800 322 15.15 1.687 13.76 7.445 0.808 2.51 5.482 .0642 II 70 ti 1197.5 443 10.45 1.170 14.14 5.325 0.577 2.489 5.681 .0646 it 71 II 1670 470 7.55 0.845 14.23 5.166 0.560 2.567 5.543 .0655 3 u 87 1.681 374 515 58.2 6.515 25.65 9.125 .9775 4.825 5.325 .2046 88 ti 376 506 58.0 6.485 25.73 9.249 .99 4.81 5.35 .2043 tt 89 it 557 720 41.96 4.700 27.23 6.225 .671 4.685 5.82 .2060 it 90 it 556.5 630 41.67 4.670 27.00 6.76 .727 4.41 6.12 .2055 5 FLOW R A T E , mls/min CTl P F i g u r e 1( >. C a l i b r a " ; i o n P l o t - Flowmetei • 202-1, Sapphir* j F l o a t , f ( >r Hydroger 1 a t 70°F • y / Q SOAP B U B B L E METER I.I A T M ^ SOAP B U B B L E METER 1.0 A T M % C A L C U L A T E D I.I A T M / / { / 0 5 10 15 2 0 25 30 35 4 0 F L O W R A T E , mls/min std 5.0 4.5 4.0 o z a UJ A O a: UJ £ 3.0 2.5 2.0 / / // /Figure 1' PI 01 Sap] Nita r C a l l b r a t : /meter 202- >hire Ploa- •ogen a t •"](. .on P l o t - •1 ; f o r )°P - Q SOAP, B U B B L E METER I.I A T M © SOAP B U B B L E METER 1.0 A T M # C A L C U L A T E D 1.1 A T M 0 0 15 F L O W 2 0 R A T E , 25 3 0 mls/min std 35 14 13 12 C3 z < LLI OC UJ CD 3 I I Figure 18 Flow Sapp Hydr . G a l i b r a t neter 203- hir e F l o a t ogen at 70 ion P l o t - 1, , f o r op O WET T E S T METER I.C © C A L C U L A T E D I.C • C A L C U L A T E D I.C )68 A T M )68 A T M ) A T M 10 8 100 2 0 0 3 0 0 FLOW RATE , mls/min 4 0 0 5 0 0 std 3 0 0 4 0 0 FLOW 5 0 0 RATE , 6 0 0 7 0 0 mls/min std CTi CD  66g PERCENT OF NITROGEN F i g u r e 21. C a l i b r a t i o n . P l o t f o r No. 1. Thermal C o n d u c t i v i t y C e l l b e f o r e M o d i f i c a t i o n 66h 0 I 2 3 4 5 6 PERCENT OF HYDROGEN F i g u r e 22. C a l i b r a t i o n P l o t f o r No. 2, Thermal C o n d u c t i v i t y C e l l b e f o r e M o d i f i c a t i o n

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