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UBC Theses and Dissertations

An apparatus for measuring the rate of diffusion of gases through porous solids at elevated pressures Han, Agnes Yu-Wen 1959-12-31

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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.Sc,  ( C h i n a ) U n i v e r s i t y o f T a i w a n , 1955  A THESIS SUBMITTED I N PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n t h e Department of CHEMICAL ENGINEERING  We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 1 9 5 9  (i)  ABSTRACT An a p p a r a t u s u t i l i z i n g a c o n s t a n t p r e s s u r e  flow  s y s t e m was d e v e l o p e d f o r m e a s u r i n g t h e e f f e c t o f p r e s s u r e on t h e 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 o f b i n a r y gas m i x t u r e s  coefficients,  passing 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 c e r a m i c porous s o l i d s a t room t e m p e r a t u r e , w i t h v a r i o u s pressures  f r o m 1 t o 14.6 atmospheres a b s o l u t e .  obtained f o r the products  of the e f f e c t i v e  c o e f f i c i e n t s and a b s o l u t e p r e s s u r e s were c o n s t a n t , w i t h a maximum d e v i a t i o n o f +5%»  diffusion substantially 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 while that o f n i t r o g e n decreased. pressure  The v a l u e s  pressure,  At atmospheric  t h e r a t i o o f 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 t h e t h e o r e t i c a l v a l u e p r o p o s e d b y However, t h e e x p e r i m e n t a l d i f f u s i o n r a t i o increased with pressure.  This  behavior  m i g h t be due t o some degree o f f o r c e d f l o w p r e s e n t  i n the  d i f f u s i o n p r o c e s s , a l t h o u g h i t was n o t p o s s i b l e t o d e t e r m i n e a cause f o r s u c h a f l o w . This apparatus i s s u i t a b l e  f o r t h e study o f d i f f u s i o n  r a t e s i n t h e 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 t h e mean f r e e p a t h o f t h e gases i n v o l v e d . w o u l d n o t be a f a c t o r i n t h i s r e g i o n .  and hence  Forced  flow  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  the r e q u i r e m e n t s f o r an advanced degree at the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  freely  a v a i l a b l e f o r r e f e r e n c e and  agree t h a t p e r m i s s i o n f o r e x t e n s i v e f o r s c h o l a r l y purposes may  study.  I further  c o p y i n g of t h i s  be g r a n t e d by t h e Head of  Department or by h i s r e p r e s e n t a t i v e s .  g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n  The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date  my  I t i s understood  t h a t c o p y i n g or p u b l i c a t i o n o f t h i s t h e s i s f o r  Department of  thesis  financial  permission.  (ii)  ACKNOWLEDGEMENT  The a u t h o r w i s h e s t o e x p r e s s h e r 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 t h e N a t i o n a l R e s e a r c h C o u n c i l f o r f i n a n c i a l assistance during the p e r i o d i n which t h e r e s e a r c h was c o n d u c t e d , and a l s o t o Mr. R. M u e l c h e n f o r the c o n s t r u c t i o n o f t h e d i f f u s i o n  cell.  I n p a r t i c u l a r , the author expresses h e r sincere t h a n k s t o D r . D. S. S c o t t under whose s u p e r v i s i o n t h e r e s e a r c h was c o n d u c t e d .  (iii) NOMENCLATURE C r o s s - s e c t i o n a l a r e a o f porous sample Molecular species Mole f r a c t i o n o f A i n A s t r e a m , B s t r e a m 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 Total Molecular concentration D i f f u s i o n c o e f f i c i e n t o f system A-B Bulk (ordinary) d i f f u s i o n Effective diffusion  coefficient  coefficient  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  coefficient  Mole f r a c t i o n s o f h y d r o g e n i n h y d r o g e n s t r e a m , i n n i t r o g e n stream. Boltzman  Constant  A constant equal t o  RTL A  M o l e c u l e w e i g h t s o f A, B D i f f u s i o n r a t e s , i n moles p e r u n i t  time  Log mean o f 1^ and Ng Absolute pressure P a r t i a l pressures 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 m o l e c u l a r  velocity  Rates o f d i f f u s i o n i n mis per u n i t  time  (iv) X ,X W 11  W  a  YH, YN  Flow r a t e s o f h y d r o g e n , n i t r o g e n t o diffusion cell Outlet  f l o w r a t e s o f hydrogen,  nitrogen  from the d i f f u s i o n c e l l A proportionality factor of interdiffusion ^'flB  Maximum energy o f a t t r a c t i o n b e t w e e n AB  (TI  Collision Integral 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 C. C f i X e  Porosity Densities  (v) TABLE OF CONTENTS Page Introduction  1  Theory  3  A.  D i f f u s i o n Mechanisms i n P o r o u s S o l i d s  B.  C o u n t e r D i f f u s i o n o f Gases a t C o n s t a n t Total pressure  C.  3 ..  Measurement o f D i f f u s i o n R a t e s  7 11 15  Apparatus  15  A.  D i f f u s i o n Apparatus.  .  B.  Modification  C.  Diffusion Cell  19  D.  P o r o u s Sample  20  o f Thermal C o n d u c t i v i t y  Cells  Experimental Procedures  17  22  A.  C a l i b r a t i o n o f T e s t Gauge  22  B.  C a l i b r a t i o n o f Flow Meters  22  C.  C a l i b r a t i o n o f 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 P o r o u s S o l i d and R a t e s o f D i f f u s i o n at various pressures  28  Results  30  Experimental Errors  39  A.  Measurement o f Gas C o m p o s i t i o n  39  B.  Measurement o f D i f f u s i o n R a t e s  39  Discussion  41  (vi)  C o n c l u s i o n s and Recommendations  52  BIBLIOGRAPHY APPENDIX  Page 51  ...  54  (vii) LIST OF ILLUSTRATIONS IN TEXT Figure 1.  Page A p p a r a t u s f o r Measurement o f D i f f u s i o n Rates.  16a  2.  Modification  3.  W i r i n g Diagram o f Thermal C o n d u c t i v i t y Cell D i f f u s i o n C e l l C r o s s S e c t i o n s t o Shown Arrangement of- Gas Duct  4. 4a  o f Thermal C o n d u c t i v i t y  Isometric Sketch of D i f f u s i o n  Cell  17a 17b 19a  Cell  showing gas d u c t arrangement  19b  5.  D i f f u s i o n C e l l - side view  19c  6. 7.  D i f f u s i o n C e l l - top view 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. 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>.  19<1 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  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 R a t e s YB\ A b s o l u t e P r e s s u r e . . .  38b  10.  11. 12. 13.  13a  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  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  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  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  (viii) Figure 14.  Page P l o t o f EL a g a i n s t N./N at Constant Log Mean d i f f u s i o n R a t e f o r Sample 01-A, Arrangement I . (Experimental N. v a 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) B  48a  I N APPENDIX 15.  E f f e c t o f F l o w Rate on T h e r m a l C o n d u c t i v i t y C e l l Response, F o r 0.22% o f N i t r o g e n i n Hydrogen S t r e a m a t 200 ohm  66a  C a l i b r a t i o n P l o t - Flowmeter 202-1. S a p p h i r e F l o a t , f o r h y d r o g e n a t 70 F  66b  C a l i b r a t i o n P l o t - Flowmeter 202-1. S a p p h i r e F l o a t , f o r N i t r o g e n a t 70 F  66c  C a l i b r a t i o n P l o t - Flowmeter 203-1* S a p p h i r e F l o a t , f o r h y d r o g e n a t 70 F  66d  C a l i b r a t i o n P l o t - Flowmeter 203-1 S a p p h i r e F l o a t , f o r Hydrogen a t 70 F and. 7*8 atms a b s o l u t e  66e  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 a t 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 Conductivity cellvbefore Modification....  66g  22.  C a l i b r a t i o n P l o t f o r No. 2 Thermal Conductivity c e l l before M o d i f i c a t i o n . . . .  66h  16. 17. 18. 19.  20.  (ix) LIST OF TABLES I N TEXT Table  Page  1.  C h a r a c t e r i s t i c s o f P o r o u s S o l i d Sample...  21  2.  C a l i b r a t i o n o f T e s t Gauge  23  3.  R e s u l t s a t 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 p r e s s u r e s  36  Average R e s u l t s f o r Sample 3» Arrangement I and v a r i o u s p r e s s u r e s  37  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  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  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 Various Pressures  38  7b.  E f f e c t o f 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  5. 6. 7.  7a.  IN APPENDIX 4a. 5a. 6a. 7d. 8.  Diffusion Sample 2, Diffusion Sample 3, Diffusion Sample 2,  R e s u l t s o f I n d i v i d u a l Runs f o r Arrangement 1 R e s u l t s o f I n d i v i d u a l Runs f o r Arrangement I . . R e s u l t s o f I n d i v i d u a l Runs f o r Arrangement I I  58 61 62  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  63  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 o f Gases  64  00 Table 9.  10.  Page Calculated Calibration results f o r 203-1 h y d r o g e n and 203-2 n i t r o g e n flowmeters  65  Examples o f c o m p l e t e r e c o r d e d 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 d e v e l o p a n a p p a r a t u s t h a t would a l l o w measurements t o be made o f t h e e f f e c t o f p r e s s u r e  on t h e  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 , o f b i n a r y gas m i x t u r e s p a s s i n g t h r o u g h p o r o u s s o l i d s . constant  pressure  A  f l o w system o p e r a t i n g i n t h e s t e a d y  state  w i t h c o u n t e r d i f f u s i o n o f t h e two g a s e s was p r e f e r r e d f o r s e v e r a l reasons.  These r e a s o n s 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 , b u t b r i e f l y t h e y may be s t a t e d a s , (1) The m a j o r i t y o f i n d u s t r i a l p r o c e s s e s  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 essentially  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 w o r t h w h i l e t o s i m u l a t e t h i s t y p e o f b e h a v i o r , i f i t c a n c o n v e n i e n t l y be done. (2) By v a r y i n g t h e p r e s s u r e t h e mean f r e e p a t h o f t h e gas m i x t u r e  c a n be r e a d i l y changed o v e r wide r a n g e s .  T h i s w o u l d a l l o w t h e 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 m o l e c u l a r  d i f f u s i o n t o be e x p l o r e d 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 p r o p o s e d 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 c h e c k e d . (3) Some a s p e c t s o f c o u n t e r d i f f u s i o n u n d e r t o t a l pressure absolute  constant  c o u l d be i n v e s t i g a t e d a t o t h e r t h a n 1 atm.  pressure.  (4) I f t h e p r e s s u r e r a n g e c o v e r e d  c o u l d be made  s u f f i c i e n t l y large, the v a r i a t i o n of the ordinary  diffusion  2  c o e f f i c i e n t w i t h p r e s s u r e c o u l d be measured by a  new  method. A v a r i e t y o f p o r o u s s o l i d s w o u l d p r o b a b l y be r e q u i r e d to achieve a l l of these o b j e c t i v e s .  However, a  suitable  p o r o u s s o l i d c a n u s u a l l y be f o u n d 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 o f an a p p a r a t u s o f t h e above t y p e i s given i n t h i s t h e s i s , together with f a i r l y extensive tests of i t s performance,  using nitrogen-hydrogen mixtures  the t e s t b i n a r y p a i r .  These g a s e s were s e l e c t e d b e c a u s e  o f t h e i r i d e a l n a t u r e , and t h e ease o f a n a l y s i s b y conductivity for  cells.  a p p a r a t u s was  o f 300 p s i a . , b u t was  thermal  A t 20°C, i d e a l b e h a v i o r i s o b t a i n e d  b o t h g a s e s a t p r e s s u r e s up t o 60 The  as  atm.  c o n s t r u c t e d f o r a maximum p r e s s u r e a c t u a l l y o p e r a t e d t o a maximum  p r e s s u r e o f o n l y 200 p s i a . a t 20°G. f l o w m e t e r s , t h e a p p a r a t u s was  With replacement  capable- o f b e i n g u s e d  of  to  1200 p s i . Some improvements i n e i t h e r m e a s u r i n g  technique  or  d i f f u s i o n c e l l d e s i g n a p p e a r t o be n e c e s s a r y i f t h e a p p a r a t u s i s t o o p e r a t e i n a s i m p l e r ; and more p r e c i s e manner.  However, a c c u r a t e and r e p r o d u c i b l e . r r e s u l t s  be o b t a i n e d by t h i s method, as d e m o n s t r a t e d o f d i f f u s i o n measurements.  can  by t h e r e s u l t s  3  THEORY A.  D i f f u s i o n Mechanisms in' Porous  Solids  The d i f f u s i o n c o e f f i c i e n t s o f g a s e s a t h i g h e r p r e s s u r e s a r e d e s i r a b l e to- know because  of the increase  i n importance of h i g h p r e s s u r e c a t a l y t i c r e a c t i o n s .  It  i s w e l l known t h a t d i r e c t measurements o f t h e 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 t h e r a t e and t h e mechanism o f t h e processes taking place. D i f f u s i o n o f a component o f a gaseous m i x t u r e t h r o u g h a p o r o u s s o l i d may  p r o c e e d b y f o u r p o s s i b l e mechanisms o f  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 p a t h o f gas m o l e c u l e s 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 p a t h o f gas molecules i s g r e a t e r t h a n pore s i z e ; s u r f a c e d i f f u s i o n i n a m o b i l e a d s o r b e d l a y e r , and f o r c e d f l o w i n p o r e s due t o t h e p r e s e n c e o f 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 , t h e t r a n s p o r t o f gas m o l e c u l e s t h r o u g h a porous s o l i d , due t o b u l k d i f f u s i o n o r Knudsen d i f f u s i o n ; o r t o b o t h , i s o f t h e most i n t e r e s t i n t h i s work.  The  o t h e r two mechanisms may be e l i m i n a t e d f r o m t h e e x p e r i m e n t s 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 t h e  critical  t e m p e r a t u r e o f the gas components, and i n t h e absence  of  any t o t a l p r e s s u r e d i f f e r e n c e . Prom a b r o a d m e c h a n i s t i c s t a n d p o i n t , m o l e c u l e s a r e 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 m o t i o n s .  I f t h e r e 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 , m o l e c u l e s c o u l d d i f f u s e i n t o and t h r o u g h a porous s o l i d w i t h v e l o c i t i e s a p p r o a c h i n g t h e average m o l e c u l a r v e l o c i t y . Ihe a c t u a l r a t e o f d i f f u s i o n i s many o r d e r s o f magnitude s l o w e r t h a n t h i s due t o two c a u s e s : ( 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 t h e r e s i s t a n c e i s caused b y m o l e c u l a r c o l l i s i o n s w i t h p o r e w a l l s , i . e . pore s i z e i s approximately t e n times l e s s than t h e means f r e e p a t h .  In.this instance, the d i f f u s i o n of a  p a r t i c u l a r m o l e c u l a r s p e c i e s a t 1 atmosphere i n s m a l l p o r e s ( e . g. l e s s t h a n 400 & d i a m e t e r ) i s i n d e p e n d e n t  o f the  p r e s e n c e o r absence o f o t h e r t y p e s o f m o l e c u l e s , and depends o n l y on t h e p a r t i a l p r e s s u r e g r a d i e n t o f t h a t (D(2)  p a r t i c u l a r species.  I t h a s b e e n shown t h a t t h e Khudsen  d i f f u s i o n c o e f f i c i e n t , D^., f o r a m o l e c u l a r s p e c i e s i n a p o r e i s a f u n c t i o n o f p o r e s i z e and t h e mean m o l e c u l a r velocity, i.e. DK  =  T  r  v  (1)  where v i s t h e average m o l e c u l a r v e l o c i t y , and r i s t h e pore r a d i u s . F o r b u l k d i f f u s i o n i n a p o r e , t h e mean f r e e p a t h i s much s m a l l e r t h a n t h e p o r e s i z e , and a m o l e c u l e  X  within  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 o t h e r molecules f a r more o f t e n t h a n w i t h t h e pore w a l l .  Hence, t h e 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 t h e v a l u e o f t h e 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^. following  The s i m p l e k i n e t i c t h e o r y g i v e s t h e  approximate  formula f o r the d i f f u s i o n  coefficient  f o r a m i x t u r e o f two g a s e s o f s i m i l a r mass and m o l e c u l a r diameter, where v  .  Q- t°7  (3)  ir<r C x  A  T  (T  = molecular  diameter  = t o t a l c o n c e n t r a t i o n i n m o l e c u l e s p e r C.C. v  = average m o l e c u l a r  velocity  X  - mean f r e e p a t h o f 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 s u c h e q u a t i o n , f o r example, i s 1 _ ijr D = J v X (1 - e ) (4) x  This equation has the p r o p e r t y o f g i v i n g r i s l e s s than greater than X  and o f g i v i n g .  vs.  e q u a t i o n ( 2 ) when r i s much  The p h y s i c a l p r o b l e m  relative probability  o f a molecule  s t r i k i n g a second m o l e c u l e .  e q u a t i o n ( 1 ) when  i s concerned  with  s t r i k i n g t h e pore  wall  I n equation (4) the  bracketed expression i s exactly the p r o b a b i l i t y  that a  m o l e c u l e w i l l have a c o l l i s i o n w i t h a second m o l e c u l e t r a v e l l i n g a d i s t a n c e e q u a l t o t h e pore d i a m e t e r .  before  As f a r  as c a n be d e t e r m i n e d , none o f t h e s e e q u a t i o n s f o r t h e  6  t r a n s i t i o n r e g i o n have e v e r b e e n c h e c k e d b y any e x p e r i mental data. These e q u a t i o n s  ( 1 ) ( 2 ) and ( 4 ) cannot be u s e d a t  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 but only give a q u a l i t a t i v e  coefficient,  e x p l a n a t i o n o f t h e mechanism o f  gas d i f f u s i o n t h r o u g h p o r o u s s o l i d . Therefore, f o r a porous s o l i d t h e e f f e c t i v e coefficient  (lO,  diffusion  w h i c h may be made up o f c o n t r i b u t i o n s  m a i n l y f r o m t h e d i s c u s s e d two mechanisms, c a n o n l y be o b t a i n e d b y means o f e x p e r i m e n t a l measurements.  The  (D ) i s alwaysy s m a l l e r i n  effective diffusion coefficient  value than the true 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  o f t h e p o r o s i t y , p o r e geometry e t c . o f t h e p o r o u s s o l i d as s t a t e d by P e t e r s e n  v > /  and C o x  v  J  .  The r a t i o o f D  g  and  i s d e f i n e d as t h e 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 p o r o u s  solid,  and i s c o n s t a n t f o r any g a s p a i r i f t h e r e i s no s u r f a c e d i f f u s i o n or forced flow present. I t s h o u l d be p o s s i b l e t o s e l e c t  a p o r o u s s o l i d , a gas  p a i r , and a s e t o f c o n d i t i o n s o f t e m p e r a t u r e  and p r e s s u r e  i n order t o study the process o f b u l k d i f f u s i o n alone, o r Knudsen d i f f u s i o n a l o n e , o r a c o m b i n a t i o n o f t h e two i n t h e t r a n s i t i o n zone. I n p a r t i c u l a r , as t h e mean f r e e p a t h v a r i e s  inversely  as t h e m o l e c u l a r c o n c e n t r a t i o n , and t h e r e f o r e a b s o l u t e p r e s s u r e , one o f t h e e a s i e s t ways t o 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 e h a v i o r m i g h t be t o measure d i f f u s i o n r a t e s a t varying pressures.  7  B.  C o u n t e r D i f f u s i o n o f Gases a t C o n s t a n t T o t a l P r e s s u r e The  t h e o r y o f d i f f u s i o n r a t e s i n g a s e s was d e v e l o p e d  as a p a r t o f t h e 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 f r o m 0. E. M e y e r ( 7 \ S u t h e r l a n d ^ ) , Langevin^\  Chapman^ \ 10  E n s k o g ^ * ^ , and J e a n s ^ ^ ^ i 11  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 o f s u b s t a n c e s A and B w h i c h i s n o t o f u n i f o r m c o m p o s i t i o n , t h e r e w i l l be a n i n t e r d i f f u s i o n o f t h e s u b s t a n c e s w h i c h c a n be d e s c r i b e d i n terms o f t h e l i n e a r v e l o c i t i e s o f movement o f A and B. I t i s assumed t h a t t h e d r o p i n c o n c e n t r a t i o n o f s u b s t a n c e A, -^-C^, w h i c h a c t s as a d r i v i n g f o r c e f o r t h e movement o f A, i s p r o p o r t i o n a l t o t h e r e l a t i v e  linear  v e l o c i t y o f A w i t h r e s p e c t t o B, u" - U ; t o t h e A  molecular  B  c o n c e n t r a t i o n s o f t h e two s u b s t a n c e s ,  C^ and  C ; and t o t h e d i s t a n c e dL t h r o u g h w h i c h t h e d i f f u s i o n B  occurs.  M a t h e m a t i c a l l y , t h i s gives t h e well-known  Maxwell  equation,  - 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 e q u a t i o n c a n now be t r e a t e d t o d e s c r i b e t h e v a r i o u s s i t u a t i o n s w h i c h may a r i s e . I n t h e case o f g a s e s , c -  f  - i f density M molecular  (6)  C  and  weight  8  E q u a t i o n (5) t h e n "becomes, u s i n g (6) and t h e i d e a l gas l a w ,  B e f i n e N'as t h e number o f moles o f gas d i f f u s i n g per time, per u n i t area  i n a direction perpendicular to  that of the d i f f u s i o n . N =  &J M Applying t h e i d e a l - g a s l a w , t h e n  ^rCNlp -  -cfft-  B  p =  Since  -dp Let  P  A B  A  N f )dL  p + p A  6  (10)  B  NAPA - NBPA) d L  (ID  ^ j>  - d p A - ' - r T ^ F (NAP•AB >  So t h a t  (9)  A  = -j^p- (NUP-  (8)  N P - N PA) dL A  A  8  (12)  F o r a s t e a d y s t a t e d i f f u s i o n , t h e t o t a l p r e s s u r e , P, i s c o n s t a n t , so a r e t h e 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 E q u a t i o n (12) f o r c o u n t e r d i f f u s i o n o f A and B, i . e.  and Ng h a v i n g o p p o s i t e s i g n s , t h e n  where t h e s u b s c r i p t s 1, 2, r e f e r t o t h e ends o f t h e d i f f u s i o n path. Pigford  v  Eqmv: -'('IJX^as, d e r i v e d b y SherWood and  b u t i t s use depends on knowledge o f t h e  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 o b t a i n e d f r o m E q u a t i o n (13) i s t h e e f f e c t i v e  diffusion  c o e f f i c i e n t f o r t h e s p e c i f i c gas p a i r and porous NA -  Since  Na=  N  solid.  ( 1 -  A  P V  -Pgr —  and  N R T  V'  N RT  Then  at P =  A  1 atm.  (15)  Here V | i s t h e d i f f u s i o n r a t e o f A, i n m i s p e r s e c . a t 1 atm and d i f f u s i o n t e m p e r a t u r e T. S i n c e Yj^ , t h e volume d i f f u s e d ,  i s not usually  measured  a t t h e d i f f u s i o n t e m p e r a t u r e , b u t some t e m p e r a t u r e a temperature c o r r e c t i o n A A Tf std V  T s  ^>  must be i n c l u d e d .  V  and p ^ /P = Ag,mole f r a c t i o n o f A i n B s t r e a m , P  /P = A^mole f r a c t i o n o f A i n A s t r e a m .  A  1  /  Substituting  these r e l a t i o n s h i p s  i n e q u a t i o n (13) and  rearranging  D  P =  v«(T-M-fe>P--%-) •- - n - - • MA J 1  -  ( I-  TIT) NA  (16)  AA  H o o g s c h a g e n ^ ^ h a s shown e x p e r i m e n t a l l y t h a t f o r b o t h 1  Enudsen and o r d i n a r y s t e a d y s t a t e atmosphere, ^  c o u n t e r d i f f u s i o n a t one  i s a constant i n a constant t o t a l pressure  s y s t e m , and f o l l o w s t h e r e l a t i o n s h i p ,  10  +  NA/~MA"  HtfrU  =  0  (17)  or N  ^  6  / MA  ,  =^ / where  (18)  i s t h e m o l e c u l a r weight  o f s p e c i e s A,  Mg i s t h e m o l e c u l a r w e i g h t  o f s p e c i e s B.  T h i s e q u a t i o n was d e r i v e d b y Hoogschagen f r o m t h e Knudsen^" "^ f o r m u l a f o r Knudsen d i f f u s i o n . 1  I n t h e case o f o r d i n a r y d i f f u s i o n , t h i s  derivation  was b a s e d on a n i m p u l s e b a l a n c e f o r t h e 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  several simplifying  assumptions.  Although t h i s t h e o r e t i c a l estimate i s only 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 , N - 0 , 2  H - H ^ and ^ - K H ^ ^ 1  2  2  2  2  G0 -0 / ^^ 1  2  systems a t a t m o s p h e r i c  2  pressure  ( d a t a a r e shown i n t h e A p p e n d i x , T a b l e 8 ) a r e 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 ( 1 8 ) a t higher pressures.  11  G.  Measurement o f D i f f u s i o n R a t e s Two m a i n t e c h n i q u e s  have been u s e d i n t h e p a s t t o  measure d i f f u s i o n r a t e s , and f r o m t h i s i n f o r m a t i o n , t o calculate diffusion coefficients.  These methods, w h i c h  have b e e n c a l l e d t h e L o s c h m i d t m e t h o d ^ ^ , and t h e S t e f a n method,are b o t h u n s t e a d y s t a t e e x p e r i m e n t s .  The  L o s c h m i d t method i s b a s e d on t h e u s e 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 g a s , w h i c h a r e c o n n e c t e d t o g e t h e r i n some way ( b y t h e u s e o f 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 c a n be c a l c u l a t e d f r o m t h e change i n c o n c e n t r a t i o n i n t h e chambers w i t h t i m e r , and f r o m t h e dimensions' o f t h e apparatus.  A number o f v a r i a t i o n s o f  t h i s , t y p e have been u s e d , a t v a r i o u s t i m e s .  Nearly a l l  work o n d i f f u s i o n i n dense g a s e s a t h i g h p r e s s u r e s h a s b e e n c a r r i e d out i n t h i s t y p e o f c e l l .  I nthe l a t t e r  c a s e , a p o r o u s p l u g was u s u a l l y u s e d t o s e p a r a t e t h e 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 b y means o f 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 orbinary d i f f u s i o n c o e f f i c i e n t at elevated p r e s s u r e s measured i n t h i s way h a s been r e p o r t e d f o r N -C0 2  COg-CH^ ^, 2  and G G ^ - C j H g ^ ^ .  t r a c e r technique  2  2  P r o p e r l y speaking, a  g i v e s a t 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 b y t h i s method a r e r e a l l y c l o s e , a p p r o x i m a t i o n s . mixtures  Similarly,  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 a s b i n a r y  12  mixtures, are r e a l l y ternary mixtures.  I n many c a s e s  t h e r e have b e e n a wide d i s a g r e e m e n t among d i f f e r e n t investigators diffusion The  concerning the e f f e c t  o f p r e s s u r e on t h e  coefficient. S t e f a n method i s b a s e d on t h e 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 o f t h e components must be i n t h e l i q u i d p h a s e , 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 p r e s s u r e f o r any one system.  T h i s has  (26),(27),(28), b e e n u s e d b y o n l y Sage and c o w o r k e r s , t o measure t h e e f f e c t  :  t  v  ;. - -  o f p r e s s u r e on d i f f u s i o n .  Vw  fc  .  For  n-heptane and n-hexane i n b i n a r y m i x t u r e s w i t h methane, ethane and propane i t was found tthat p r e s s u r e had a s i g n i f i c a n t i n f l u e n c e on t h e d i f f u s i o n r a t e e v e n a t p r e s s u r e s b e l o w 60 p s i a , t h e maximum u s e d . A c o n s t a n t p r e s s u r e f l o w s y s t e m was u s e d b y 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  p a r t i c u l a r l y when s u r f a c e f l o w o c c u r r e d . Cox  v  diffusion,  W e i s z ^ ^ and 0  ' l a t e r u s e d m o d i f i c a t i o n s o f t h e method t o s t u d y  e f f e c t i v e d i f u s i v i t i e s o f p o r o u s s o l i d s , and i n t h e l a t t e r c a s e , 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 a t elevated temperatures.  Apparently, a steady s t a t e f l o w  system h a s n o t b e e n u s e d p r e v i o u s t o t h i s work t o measure t h e e f f e c t o f p r e s s u r e on t h e d i f f u s i o n A l l correlations calculation  coefficient.  w h i c h have been p r e s e n t e d f o r t h e  o f t h e 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  that i t varies  inversely  (8),  (5),  i d e a l gases / v  with, the p r e s s u r e , at l e a s t f o r  (3D, w  ;  (33)  (33)  (11),  the Enskog t h e o r y , ' ..,  (32),  , . • ^ -r. J *  .:  F o r dense g a s e s ,  which t r e a t s the molecules  as r i g i d s p h e r e s , has "been used t o p r e d i c t  behavior of the  d i f f u s i o n c o e f f i c i e n t as p r e s s u r e v a r i e s . Perhaps t h e b e s t p r e s e n t c o r r e l a t i o n f o r t h 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 o f i d e a l gases i s t h a t o f Hirschfelder  D  A6  e t . a l . (33).  0.0026*80  =  where  (5lS-  (T^i*)-]  = 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  = p r e s s u r e i n atmospheres  T  = t e m p e r a t u r e i n °E kr ~ €  AB  A 6  k-  = Boltzman constant  ;  M: ,M A  B  (S^gi-^ 3  = M o l e c u l a r w e i g h t o f s p e c i e s A and B = Molecular potential characteristic °E,  energy  parameters  o f A-B i n t e r a c t i o n  i n A and  respectively.  I t i s w e l l known t h a t f o r i d e a l gases t h e m o l e c u l a r p a r a m e t e r s , 0" and £ , a r e a f u n c t i o n o f temperature only.  Therefore a t constant temperature,  E q u a t i o n (19) may be w r i t t e n  i n the form:  D^g  = Constant x 1 , or  D^gP  = Constant  7  14  For  a n i d e a l system, t h i s w o u l d he t h e e x p e c t e d r e s u l t  from  d i f f u s i o n r a t e measurements t h r o u g h porous s o l i d s i f t h e pore s i z e o f t h e s o l i d i s l a r g e enough t o e l i m i n a t e Enudsen diffusion.  For t h e  -  system, t h i s r e l a t i o n s h i p  h o l d a t 20°C f o r p r e s s u r e s up t o 60 atms.  should  15  APPARATUS A.  D i f f u s i o n Apparatus The a p p a r a t u s f o r m e a s u r i n g t h e e f f e c t i v e  diffusion  c o e f f i c i e n t a t h i g h e r p r e s s u r e s was s i m i l a r i n p r i n c i p l e to  t h a t u s e d by K. E. Cox f o r t h e i n v e s t i g a t i o n o f t h e  t e m p e r a t u r e dependence o f t h e 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 o f o b t a i n i n g p r e s s u r e b a l a n c e b e t w e e n the  two s i d e s o f t h e p o r o u s sample, and m o d i f i c a t i o n o f  the  t h e r m a l c o n d u c t i v i t y c e l l s were n o t e w o r t h y changes. The a p p a r a t u s , a s shown i n F i g u r e 1, c o n s i s t e d o f  two gas t r a i n s , one f o r h y d r o g e n , and t h e o t h e r f o r n i t r o g e n , w h i c h l e d t h e two g a s e s t o o p p o s i t e f a c e s o f the  c y l i n d r i c a l p o r o u s s o l i d sample.  The h y d r o g e n u s e d  was s t a n d a r d c o m m e r c i a l grade (99*8%), and t h e n i t r o g e n was premium q u a l i t y (99»85%)»  B o t h were s u p p l i e d b y t h e  C a n a d i a n L i q u i d A i r Company. Now c o n s i d e r the. h y d r o g e n gas s t r e a m i n d e t a i l . The gas f r o m t h e s t o r a g e c y l i n d e r f i r s t was p a s s e d t h r o u g h a p r e s s u r e r e g u l a t o r , and r e d u c e d t o t h e desired pressure, before passing through a s t e e l pipe d r y e r ( 1 " p i p e , 24 i n c h e s l o n g , p a c k e d w i t h anhydrous calcium sulfate^).  For small flow rates of gas, l e s s  t h a n 100 m i l l i l i t e r p e r m i n u t e , a 6 f o o t l o n g  steel  c a p i l l a r y , 0.015 i n c h i n s i d e d i a m e t e r , was i n s e r t e d before the dryer.  This c a p i l l a r y provided a back  p r e s s u r e o f a p p r o x i m a t e l y 10 pounds p e r square i n c h t o  16  smooth o u t t h e f l o w .  The h y d r o g e n , 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 f l o w m e t e r (Matheson t y p e s 202, 203 and 2 0 4 ) , and was t h e n c o n d u c t e d i n t o one  side  o f t h e d i f f u s i o n c e l l where i t c o n t a c t e d t h e f a c e o f t h e c y l i n d r i c a l p o r o u s sample.  The n i t r o g e n s t r e a m f o l l o w e d  the  same sequence as t h e h y d r o g e n .  A f t e r f l o w i n g out o f  the  d i f f u s i o n c e l l , t h e two gas s t r e a m s , one m a i n l y  hydrogen," t h e o t h e r m a i n l y n i t r o g e n , were j o i n e d t o two b r a n c h e s o f a tee  and r e l e a s e d by a s i n g l e p r e s s u r e  r e g u l a t o r t o t h e atmosphere.  P a r t o f t h e g a s , about  60  m i l l i l i t e r s p e r m i n u t e , was t a k e n as sample f r o m e a c h stream b e f o r e the j o i n .  E a c h gas sample was  regulated  by a s m a l l Ermeto n e e d l e v a l v e , and t h e n p a s s e d t o the modified thermal conductivity c e l l f o r analysis. The d i f f e r e n t i a l p r e s s u r e s between t h e t o p and b o t t o m chambers o f t h e 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 d r a u g h t gauge (Hays, 12 i n c h s c a l e , range 0-1.0  inch water).  The a b s o l u t e p r e s s u r e o f t h e gas i n t h e s y s t e m was measured by an a c c u r a t e t e s t gauge o f 300 p s i g 0.2 p s i .  and c o u l d be r e a d w i t h an a c c u r a c y o f  scale, For  p r e s s u r e s l e s s t h a n 5 p s i g . a m e r c u r y manometer was used i n s t e a d o f t h e t e s t gauge. S i n c e t h e a p p a r a t u s was Resigned  f o r measuring  the  d i f f u s i o n r a t e s a t 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 c o n n e c t e d b y  FLOWMETER  PRESSURE REGULATOR  CAPILLARY DIFFUSION CELL Picpms  1*  Appa*a!»*' f o r S ^ a u m i e t i t o f Mfimttm Bmm  17  3/8"  standard s t a i n l e s s s t e e l tubing and Brmeto type  fittings.  A l l equipment was tested to a pressure of  at l e a s t 300 p s i . B.  M o d i f i c a t i o n of Thermal Conductivity C e l l s . (T-C C e l l ) 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 " d i f f u s i o n type"  with the filaments being located i n a d i f f u s i o n passage. This c o n s t r u c t i o n was supposed to make the c e l l independent  of gas flow r a t e .  response  As shown i n the Appendix,  Figure 15 > t h i s was true only i f the flow was above 100 mis per minute, at lower flows the c e l l was very s e n s i t i v e to flow r a t e . I f 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 c o n t r o l l e d by mixing the two streams a f t e r 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 f u n c t i o n of gas composition i n the Gow-Mac c e l l s only i f the gas pressure, as w e l l as the flow r a t e was maintained constant a l l the time.  From t h i s 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 v a r i e d .  As shown i n Figure 2, t h i s was  achieved by "leaking" a f r a c t i o n of the sample over the filament and out through a c a p i l l a r y .  A constant flow  TO RECORDER  THERMAL  CONDUCTIVITY  CELL f  WATER 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  BATH Cell  2 2 OHM RESISTOR — ' W / w w w — 12 OHM RESISTOR ZERO ADJUST 2 OHM P O T  Z T  -DECADE  VVWVNA-  •  TO #- RESISTOR RECORDER  TO , POTENTIOMETER Figure  6 VOLT  -+  TO # RECORDER  • TO POTENTIOMETER 3.  W i r i n g Diagram o f Thermal C o n d u c t i v i t y  cells  cr  18  r a t e was  a t t a i n e d through, t h e c a p i l l a r y b y k e e p i n g  the  sample f l o w u n d e r a c o n s t a n t p r e s s u r e b y b u b b l i n g i t out t h r o u g h a w a t e r b a t h m a i n t a i n e d  at a constant  level.  F o r e a c h sample o r 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 l o n g and 0.013  inch inside  diameter  welded t o a 1/4- i n c h p i p e p l u g was  screwed i n t o t h e  b l o c k o f t h e T-C  d r i l l e d t o j o i n the  cell.  A h o l e was  f i l a m e n t chamber t o t h e p l u g and hence c a p i l l a r y . p r e s s u r e s o f sample gas were m a i n t a i n e d  brass  The  at 2 inches water  head f o r n i t r o g e n and 1 i n c h f o r h y d r o g e n . 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 e x c e p t i n a q u a l i f e i a t i v e sense so t h a t about t h e same r a t e o f b u b b l i n g was u s e d a t a l l t i m e s . The w i r i n g d i a g r a m f o r t h e t h e r m a l c o n d u c t i v i t y c e l l i s shown i n F i g u r e 3»  A Y a r i a n A s s o c i a t e s G-10  as w e l l as a Leeds and N o r t h r u p Potentiometer  Portable precision  were u s e d t o measure t h e o u t p u t  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 . c u r r e n t was  recorder  millivolts  The  filament  provided 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 m i l l i a m m e t e r s were c o n n e c t e d i n t h e w i r i n g s y s t e m t o i n d i c a t e the v o l t a g e s and  milliamperes  r e s p e c t i v e l y f o r t h e f i l a m e n t c u r r e n t s o f t h e two For the d e t e c t i o n o f N o f 280 ma was 124 ma.  2  cells.  i n hydrogen, a f i l a m e n t c u r r e n t  u s e d , and f o r d e t e c t i n g H  A l s o a decade r e s i s t o r was  2  i n nitrogen  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 s i g n a l of each thermal c o n d u c t i v i t y c e l l to the potentiometer or the Varian recorder. C.  Diffusion Cell The d i f f u s i o n 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.  I t consisted, e s s e n t i a l l y , 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 s t e e l bar stock. chamber diameter was  1 3/32  The inside sample  inches which was  just the  diameter of the porous sample when covered with a Gooch rubber sleeve.  This sample chamber was  i n the top h a l f and 2 1/2  1 1/2  inches deep  inches deep i n the bottom  half. In the top h a l f , were s i x v e r t i c a l holes of  7/16  inch diameter d r i l l e d f o r 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 o u t l e t , 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 i n t o the s o l i d 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 s t e e l 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  f o r a standard high  PLAN  VIEW  OF B O T T O M  PIECE  SECTION GAS  B-B  DUCT  DETAIL  6 HOLES 16 FOR SOCKET HEAD CAP SCREWS  SECTION GAS  SECTION BOTH  A -A  CELL  PIECE  FIGURE 4  D I F F U S I O N  C E L L  DUCT  C-C DETAIL  4"  Figure  4 a.  Isometric Sketch of D i f f u s i o n C e l l , Duct Arrangement  Showing  Gas  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 V i e w  20  p r e s s u r e 0 - r i n g w h i c h c o u l d h o l d t h e p o r o u s sample i n a proper p o s i t i o n .  I n t h e o u t e r groove was  placeddan  0 - r i n g f o r s e a l i n g t h e two h a l v e s o f t h e c e l l leakage. diameter  There were a l s o s i x h o l e s o f 7/16 f o r t h e cap s c r e w s .  The  from  inch  gas d u c t s , w h i c h were  i d e n t i c a l i n t h e t o p and b o t t o m s e c t i o n s , were s e a l e d by small o-rings. D.  P o r o u s samples The p o r o u s samples u s e d i n t h i s s t u d y were t h e S e l a s  OJ and 01 s u p p l i e d b y t h e S e l a s C o r p o r a t i o n o f A m e r i c a i n the f o r m o f r o d s o f a p p r o x i m a t e l y 1 i n c h d i a m e t e r inches length. No.  Samples 03-A  and 03-B,  named No.  2 were c u t f r o m the same r o d (Number 03-3)  l e n g t h s a p p r o x i m a t e l y 2 i n c h e s and 1 1/4 respectively.  Sample 01-A,  named No.  and 1  6  and  with  inches,  3»was c u t i n t o  2 i n c h c y l i n d e r f r o m a l o n g e r r o d (Number 0 1 - 1 ) .  a  The  two end f a c e s o f a sample were machined t o smoothness. From the m a n u f a c t u r e r ' s  l i t e r a t u r e and f r o m o t h e r w o r k ^ ^  t h e S e l a s samples were known t o be m i c r o p o r o u s  synthetic  c e r a m i c r o d , , u s e d 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  filters?  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 p o r e s i z e , t h a n t h e 03 g r a d e . samples a r e g i v e n i n T a b l e  1.  The  c h a r a c t e r i s t i c s of the  TABLE I C h a r a c t e r i s t i c s o f Sample  Jo.  Selas.No  Length . L, cm  1  03-A  5.019  5.376  0.286  2  03-B  3.157  5.376  0.286  3  01-A  5.065  5.391  0.590  X-sectional Area,A.cm^  Porosity @  Pore S i z e Average Microns  T h i s work  Cox's work  10.66 /  11.40  1.31  12.86  11.40  4.5  3.97  2.61  a  1.31  b  b  a  D a t a f o r P o r o s i t y and Pore S i z e were t a k e n from Cox's work. a.  F o r Sample 03-2  b.  F o r Sample 01-1  EXPERIMENTAL PROCEDURES A.  C a l i b r a t i o n o f T e s t Gauge The  t e s t gauge u s e d f o r i n d i c a t i n g t h e t o t a l p r e s s u r e  i n t h e 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 a n 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 T a b l e 2 showed  t h a t most o f t h e r e a d i n g s were v e r y a c c u r a t e , and t h e 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 o f flowmeters The  c a l i b r a t i o n o f t h e Matheson U n i v e r s a l  flowmeters  ( s i z e s 2 0 2 , 203 and 2C4) c o u l d be c a l c u l a t e d b y 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 t h e gas u n d e r t h e  conditions  of flow.  b u b b l e method  O t h e r methods, s u c h a s r i s i n g  soap  and a wet t e s t m e t e r were a l s o u s e d t o  check t h e c a l i b r a t i o n .  Since the c a l i b r a t i o n curves,  showing t u b e r e a d i n g a g a i n s t f l o w r a t e , f o r e a c h f l o w meter a r e a f u n c t i o n properties,  o f t e m p e r a t u r e , p r e s s u r e and g a s  e a c h f l o w meter h a d t o be c a l i b r a t e d f o r  t h e e n t i r e range o f w o r k i n g c o n d i t i o n s . were e x p r e s s e d i n terms o f m i l l i m e t e r s (or mls/min) a t standard c o n d i t i o n s , and  The f l o w  rates  per minute  i . e . 70°F (21.1°G)  atmospheric pressure. The  two 204 f l o w m e t e r s , u s e d f o r c a l i b r a t i n g t h e  thermal conductivity  c e l l s , gave a f l o w r a t e  ranging  f r o m 100 t o 5000 m l s / m i n , and were s i m p l y c a l i b r a t e d b y the Matheson c a l c u l a t i n g method.  C o x ^ ^ checked these  f l o w m e t e r s b y u s i n g a wet t e s t m e t e r , and p r o v e d  that  TABLE 2 C a l i b r a t i o n o f T e s t Gauge  Standard Pressure psig  Gauge Pressure psig  Deviation psig  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  200.0*  200.0  -0.3 0  t h e s e c a l c u l a t e d c a l i b r a t i o n s were a c c u r a t e enough t o a p p l y w i t h o u t f u r t h e r e x p e r i m e n t a l measurements.  But  t h e two 202 f l o w m e t e r s , w i t h f l o w r a t e s r a n g i n g f r o m 5 t o 100 m l s / m i n , had t o be c a l i b r a t e d b y t h e r i s i n g bubble meter.  The  soap  c a l i b r a t i o n c u r v e s o b t a i n e d f r o m the  Matheson c a l c u l a t i o n , a n d t h e r i s i n g soap b u b b l e m e t e r a r e shown i n t h e a p p e n d i x ,  F i g u r e s 16 and 17.  Evidently,  t h e Matheson c a l i b r a t i o n f o r t h e 202 f l o w m e t e r , d i s c r e p a n c y o f 2 0 - 5 0 % , and was  a  n o t recommended.  For d i f f u s i o n r u n s , flowmeter  203-1  f o r t h e h y d r o g e n s t r e a m and f l o w m e t e r (A s a p p h i r e f l o a t was  had  was  employed  203-2 f o r n i t r o g e n  u s e d i f t h e l a s t number i s 1,  a s t e e l f l o a t when t h e l a s t number i s 2 ) .  and  B o t h were  c a l i b r a t e d b y t h e Matheson c a l c u l a t i n g method, and a l s o by use o f t h e wet t e s t m e t e r a t room t e m p e r a t u r e v a r i o u s p r e s s u r e s o f 1.068, 1.2, 4.376, 6 U , 7«8,  9.5,  11.2  1.34,  and 14.6  1.68,  under  2.02,  atmospheres.  3.04, Several  c a l i b r a t i o n c u r v e s a r e shown i n t h e A p p e n d i x , F i g u r e s 18, 19 and 20.  I t a p p e a r e d t h a t , f o r the n i t r o g e n  s t r e a m , t h e Matheson r e s u l t s have a p o s i t i v e o f t h e o r d e r o f 1-5%  discrepancy  f r o m t h a t o f t h e wet t e s t m e t e r .  U s u a l l y t h e magnitude o f t h e 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 p r e s s u r e and had an average d e v i a t i o n o f +4%.  For  h y d r o g e n f l o w , t h e d i s c r e p a n c i e s were e v e n worse (up t o 10 o r 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 f r o m 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  e s t i m a t e d t h a t t h e s e wet t e s t m e t e r c a l i b r a -  t i o n s were a c c u r a t e t o  1%.  A l t h o u g h t h e a v e r a g e t e m p e r a t u r e was about 2 1 C , i t G  v a r i e d d u r i n g experiments from 20°-25°C.  T h e r e f o r e , the  f l o w r a t e o b t a i n e d f r o m t h e c a l i b r a t i o n c u r v e s s h o u l d 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 , t h e p r e s s u r e gauge might g i v e 0.3 p s i g e r r o r s i n readings.  The e r r o r i n r e c o r d i n g  t e m p e r a t u r e s and t o t a l p r e s s u r e s would a f f e c t t h e c a l i b r a t i o n o f the f l o w m e t e r s .  The magnitude o f t h i s  e f f e c t c o u l d be e s t i m a t e d f r o m t h e Matheson c a l c u l a t i o n s , b e c a u s e , a l t h o u g h t h e M a t h e s o n c a l c u l a t i o n was n o t  satis-  f a c t o r y at elevated 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 c u r v e s u s u a l l y were p a r a l l e l and t o t h o s e o f t h e wet t e s t meter.  proportional  As shown i n t h e  A p p e n d i x , T a b l e 9» t h e c a l i b r a t i o n s o f h y d r o g e n ( 2 0 3 - 1 ) and n i t r o g e n f l o w m e t e r  ( 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 15 p s i g , e t c .  I t was  flowmeter  p s i g ; 70°F,  f o u n d t h a t t h e e f f e c t o f 5°F i n  t e m p e r a t u r e o r 0 . 3 p s i g i n p r e s s u r e on t h e f l o w r a t e o f t h e o r d e r o f about 1%.  This, p r o v e d t h a t t h e 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 pressures, i .  was  and  e. l e s s t h a n 0.5°F and 0 . 3 p s i g , w o u l d  a f f e c t the c a l i b r a t i o n s o f the flowmeters  not  significantly.  26  C.  C a l i b r a t i o n o f t h e Thermal C o n d u c t i v i t y C e l l s (T-C  Cells)  B e f o r e m o d i f i c a t i o n , t h e two t h e r m a l 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 t h e 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 t h e  percentage o f n i t r o g e n i n the hydrogen stream.  A constant  f l o w o f p u r e h y d r o g e n gas was t a k e n f r o m 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 g a s .  Ho. 2 T-C  cell  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 u s e d a s r e f e r e n c e gas.  The  cali-  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 c o m p o s i t i o n o f gas m i x t u r e , a r e shown i n t h e A p p e n d i x , F i g u r e s 21 and 22. S i n c e t h e t h e r m a l c o n d u c t i v i t y o f h y d r o g e n i s about s e v e n t i m e s t h a t o f n i t r o g e n , t h e Ho. 2 T-C s e n s i t i v e t h a n Ho. 1.  U s u a l l y t h e Ho. 1 T-C  c e l l i s more c e l l took  about two h o u r s t o warm up and a t t a i n a s t e a d y z e r o p o i n t due t o t h e p a r t i c u l a r b e h a v i o r o f h y d r o g e n .  The o t h e r  c e l l would r e a c h i t s s t e a d y z e r o p o i n t w i t h i n 30 m i n u t e s . The c a l i b r a t i o n p r o c e d u r e o f t h e m o d i f i e d T-C  cells  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 p u r e r e f e r e n c e gas the  c e l l a t a f l o w r a t e o f 60-65 m l s / m i n (measured a t  standard s t a t e ) f o r each. the of  through both paths of  A p p r o x i m a t e l y 30 m l s / m i n o f  gas was e v o l v e d f r o m t h e two c a p i l l a r i e s and t h e r e s t i t , 30-35 m l s / m i n , b u b b l e d out u n d e r a one i n c h w a t e r  head f o r t h e Ho. 1 T-C Ho. 2 T-C  cell.  c e l l and a two i n c h head f o r t h e  27  (2)  The c e l l s were now s w i t c h e d on. A f t e r w a i t i n g a  few m i n u t e s u n t i l t h e c e l l was f r e e o f a i r , t h e f i l a m e n t c u r r e n t was a d j 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 p o t a t t a c h e d t o t h e 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 z e r o l i n e was o b t a i n e d o n t h e recorder chart.  Thus t h e z e r o p o i n t o f t h e c e l l was  determined. (4)  W i t h t h e r e f e r e n c e gas r u n n i n g as b e f o r e , a  gas m i x t u r e  o f known c o m p o s i t i o n was p a s s e d t h r o u g h t h e  sample p a t h .  The m i x t u r e was made b y t a k i n g t h e two gas  s t r e a m s , h y d r o g e n and n i t r o g e n a t c o n s t a n t known f l o w r a t e s i n t o a t e e branch mixer.  Although t h e mixture  might have a v e r y h i g h f l o w r a t e o n l y about 60-65 m l s / m i n o f i t was t a k e n i n t o t h e c e l l f o r a n a l y s i s . The c o m p o s i t i o n o f t h e m i x t u r e "was? c a l c u l a t e d f r o m t h e known flow rates. (5)  The o u t p u t m i l l i v o l t s were measured on t h e  potentiometer  a f t e r a c o n s t a n t r e a d i n g had b e e n o b t a i n e d  on t h e 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 s e t a t 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 . In  t h i s way a s e r i e s o f p o i n t s , mole f r a c t i o n  (percentage  o f g a s b y 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. shown i n F i g u r e s 7 and 8.  The c a l i b r a t i o n r e s u l t s a r e  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 Thermal C o n d u c t i v i t y C e l l  No-1  27b  VOL  %  H  2  F i g u r e 8. C a l i b r a t i o n p l o t of Modified Thermal C o n d u c t i v i t y C e l l  NO.,2  28  D u r i n g t h e o p e r a t i o n s , i t was f o u n d t h a t more a t t e n t i o n h a d t o b e p a i d t o t h e z e r o p o i n t o f No. 1 c e l l i n w h i c h h y d r o g e n was u s e d a s r e f e r e n c e . D.  Measurement o f t h e 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 P o r o u s S o l i d s and R a t e o f D i f f u s i o n a t V a r i o u s Pressures. Runs a t v a r i o u s p r e s s u r e s , f r o m 1.068 t o 14.6  a t m o s p h e r e s , were a l l done i n t h e same manner.  To s t a r t  a r u n t h e a p p a r a t u s was assembled and t e s t e d t o be s u r e i t was f r e e o f l e a k a g e . were t h e n s w i t c h e d hour p e r i o d .  The t h e r m a l  conductivity cells  on f o r warming and z e r o i n g o v e r a two  The gas p r e s s u r e  r e g u l a t o r s and n e e d l e  v a l v e s were t h e n s e t t o g i v e s t e a d y f l o w m e t e r a t t h e r e q u i r e d f l o w r a t e s and p r e s s u r e s .  readings  The o p e r a t i n g  c o n d i t i o n s o f t h e d i f f u s i o n r u n s c o u l d be e a s i l y a d j u s t e d t o t h e r e q u i r e d ones b y t u r n i n g n e e d l e v a l v e s 1 o r 2 and t h e o u t l e t r e d u c i n g v a l v e .  The d r a f t gauge  was s e t t o z e r o d i f f e r e n t i a l p r e s s u r e  across t h e porous  s o l i d b y a d j u s t i n g t h e n e e d l e v a l v e w h i c h was p l a c e d i n the n i t r o g e n l i n e between t h e d i f f u s i o n bomb and t h e t e e j o i n t t o 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 s t e a d y , obtained  a constant  r e a d i n g was  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  o u t p u t m i l l i v o l t s o f t h e two T-C c e l l s were t h e n a c c u r a t e l y measured o n t h e p o t e n t i o m e t e r p a r a l l e l with the recorder.  connected i n  29  F o r each, r u n t h e f o l l o w i n g d a t a were r e c o r d e d : Date o f r u n Run.number Number o f sample Flowmeter numbers, f l o w m e t e r r e a d i n g s and r a t e s f o r h y d r o g e n and n i t r o g e n gas Absolute Ambient  flow  pressure temperature  Output m i l l i v o l t s o f t h e two T-C From t h e s e d a t a i t was  cells  p o s s i b l e t o c a l c u l a t e the  gas  c o m p o s i t i o n s a f t e r d i f f u s i o n , and t h u s t h e r a t e s o f h y d r o g e n 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  m i n u t e p e r square c e n t i m e t e r o f t h e sample a r e a ) . 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  From  diffusion  c o e f f i c i e n t , D e . f o r t h e sample t e s t e d was  calculated,  Complete r e c o r d e d d a t a f o r s e v e r a l r u n s ( T a b l e 10) a sample c a l c u l a t i o n a r e g i v e n i n t h e A p p e n d i x .  and  30  RESULTS The r a t e s o f d i f f u s i o n o f t h e gas p a i r , h y d r o g e n and n i t r o g e n were measured a t a t e m p e r a t u r e o f 2 0 ° - 2 5 ° C f o r t o t a l p r e s s u r e s f r o m 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 o f t h e gas d u c t s i n t h e d i f f u s i o n bomb.  I n arrangement I , t h e p r e s s u r e t a p was l o c a t e d  o p p o s i t e t o t h e gas o u t l e t and t h e g a s was c o n d u c t e d i n t o each d i f f u s i o n chamber f r o m t h e s m a l l e x t e n s i o n a s shown i n F i g u r e 4 and 4 a .  I n arrangement I I , t h e p r e s s u r e  t a p was now t h e p r e v i o u s gas i n l e t , so t h e g a s i n l e t and o u t l e t now became o p p o s i t e t o e a c h o t h e r .  F o r arrangement  I I I , gas d u c t s were used i n t h e same way as i n arrangement I I , b u t a t h i c k p a p e r b a f f l e 1/4 o r 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 t h e i n l e t and o u t l e t t a p s and c o i n c i d e d w i t h a d i a m e t e r o f each chamber.  Therefore, the  gas w h i c h came i n t o t h e d i f f u s i o n chamber must f l o w o v e r the b a f f l e and be w e l l mixed b e f o r e g o i n g o u t o f t h e c e l l . Generally, 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 o f h y d r o g e n t h r o u g h a sample, m l s / m i n ( a t 21°G and 1 atm)  VJJ  r a t e o f d i f f u s i o n o f n i t r o g e n t h r o u g h a sample m l s / m i n ( a t 21°C and 1 atm)  v  H  w-  r a t i o o f r a t e s o f d i f f u s i o n , dimensionless.  De.P t h e p r o d u c t 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 p r e s s u r e (cm / s e c ) ( a t m )  31  For  c o n v e n i e n c e i n c o m p a r i s o n , t h e 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 t h e c o r r e s p o n d i n g v a l u e s a t s t a n d a r d room t e m p e r a t u r e , i.  e. 21.1°C (70°F).  The t e m p e r a t u r e dependence o f t h e  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 f r o m t h e H i r s c h f e l d e r et. a l . equation (19). H  2~^2 l  n c r e a s e s  The d i f f u s i o n c o e f f i c i e n t f o r  about 0.5% w i t h a n i n c r e a s e o f 1 C  in  G  temperature. The r e s u l t s o f d i f f u s i o n r u n s a t one atmosphere shown i n T a b l e 3»  are  The v a l u e s o f i n d i v i d u a l r u n s 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 o f t h e d i f f u s i o n  r a t e s o f h y d r o g e n f o r sample 2 and 1, a s shown b y t h e 10-57  f i r s t two s e t s o f r e s u l t s , i s  7*0  = 1.52,, which i s i n  good agreement w i t h t h e i n v e r s e r a t i o o f t h e two 5.019 l e n g t h s , i . e. 3.175  = 1»59«  sample  The e r r o r o f 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,  o r b y m i n o r d i f f e r e n c e s i n t h e two  samples a l t h o u g h t h e y were c u t f r o m t h e 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  calculated,  were t a k e n t o be i n d e p e n d e n t o f sample l e n g t h .  For  sample 1, i n t h e s t e e l bomb, (Runs B1-B4) t h e r a t i o s o f the r a t e s o f d i f f u s i o n f o r h y d r o g e n and n i t r o g e n gas a r e c l o s e enough t o t h e t h e o r e t i c a l v a l u e o f one atmosphere forced flow.  3 . 7 4 - a t  t o c o n f i r m t h e absence o f any a p p r e c i a b l e A t 1.068  atmospheres, t h e r a t i o s f o r sample  2 and 3 a r e h i g h e r t h a n 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 o f 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 a r e i n good agreement w i t h one a n o t h e r h a v i n g o f 3.87 and 3.84 r e s p e c t i v e l y a t 1.068 atmospheres. c e l l constant of K i s s ' s c e l l  The  ( w h i c h u s e d t h e same p o r o u s  sample as t h a t i n Gox's work) d e t e r m i n e d f r o m t h e s e c h e c k s w i t h t h a t o f Cox.  values  data  The t e m p e r a t u r e dependence o f  ('35') t h e gas p a i r KH^-Hg i n v e s t i g a t e d b y Y o u n g ^ w  found t o agree w i t h t h a t obtained by K i s s  y  has been , although  v  Young u s e d a d i f f e r e n t porous, sample w i t h t h e c e l l c o n s t a n t d e t e r m i n e d f r o m Runs 4 8 , 49 and 50. Results f o r higher pressures are presented three  here i n  series. Series I :  Sample 2 was t e s t e d w i t h arrangement I  and gas f l o w r a t e s r a n g i n g f r o m 200-1600 m i s p e r m i n u t e . The  a v e r a g e r e s u l t s a r e shown i n t a b l e 4.  For i n d i v i d u a l  r u n s , t h e r e s u l t s a r e shown i n A p p e n d i x , T a b l e 4 a. D .P p r o d u c t ,  The  and r a t i o o f d i f f u s i o n r a t e s a g a i n s t  a b s o l u t e p r e s s u r e a r e p l o t t e d i n F i g u r e s 9 and 10. Series I I ;  T h i s s e t o f e x p e r i m e n t s was i n t e n d e d t o  show t h e e f f e c t o f p o r e s i z e o f t h e s o l i d , i f a n y , as sample 3 h a s n e a r l y 4 t i m e s t h e p o r e d i a m e t e r and t w i c e t h e p o r o s i t y o f sample 2. for  The a v e r a g e d i f f u s i o n r e s u l t s  sample 3(01-A) w i t h arrangement I and v a r i o u s  p r e s s u r e s a r e shown i n T a b l e s e e n t h a t t h e D .P p r o d u c t g  5 and F i g u r e 11.  does n o t v a r y w i t h  I t c a n be pressure.  33  Series I I I :  These measurements were c a r r i e d out to  investigate the e f f e c t of c e l l arrangement.  The average  d i f f u s i o n r e s u l t s f o r sample 2 with c e l l arrangement I I and I I I are shown i n Tables 6, 7 and 7a, and i n Figures 12, 13 and 13a r e s p e c t i v e l y .  The D_.P products of sample  2 with arrangement I I I (Table 7d i n the Appendix) have a standard deviation of 2.35% with a corresponding mean d e v i a t i o n of 1.84%. The average r e s u l t s given f o r each s e r i e s were obtained by averaging a l l the d i f f u s i o n runs made, which v a r i e d i n number from 2 to 6 at each set of conditions.  TABLE 3 D i f f u s i o n R e s u l t s a t one Atmosphere and 21.1°C (1)  Sample I , Arrangement I , N i t r o g e n i n t h e t o p chamber  Run No.  v  Bl B2  6.928 7.039  B3  B4 Average (2)  H  7QQ%9  6.990 7.0  V  N  1.963 1.920 1.795 1.869 1.887  10.72 10.43 6 10.43 10 10.75 11 10.36 12 10.73 Average 10.57  10.22 10.22 10.10 10.18  N  3.53 3.67 3.92 3.74 3.71  De. P a t 21.1°C .0617 .0622 .0611 .0617 .0618  atm P 1 1 1 1  (3.74)* It tl 11 II II  .0590 .0582 .0583 .0594 .0574 .0591 .0584  1.068 1.068 1.068 1.068 1.068 1.068  2.542 2.620 2.646  2.609  4.015 3.904 3.820 3.913  .0574 .0562 .0588  1.068 it  11  .0574  Sample 3, Arrangement I , Hydrogen i n the t o p chamber  93 • 24.90 94 22.66 95 22.72 Average 23.43 (5)  V  Sample 2, Arrangement I , Hydrogen i n the t o p chamber  73 74 75 Average (4)  H  Sample 2, Arrangement I , N i t r o g e n i n the t o p chamber  4 5  (3)  V  5.055 4.787 5.984 5.275  Kiss's diffusion  10.01 10.02 Average 10.01  4.925?* 4.70'""'"" 3.80  .2028 .1907 .2134 .2025  1.068 1.068 1.068  c e l l (same as Cox's) Sample 03-2  2.653 2.660  3.92 3.76  2.657  3.84  1.068 1.068  TABLE 3 ( c o n t ' d )  Run No. (6)  V  H  %  V  H  V  N  atm P  Young's d i f f u s i o n c e l l , Sample 015  40 49 50  21.40  20.84 20.52  5.300 5.338  3.932  Average  20.92  5.405  3.87  5.576  ""Assumed v a l u e = '""High hydrogen r a t e .  3.840 3.844  1.068 1.068 1.068  36  .TABLE 4 Series I Average D i f f u s i o n R e s u l t s a t E l e v a t e d  Pressure  Sample 2 Arrangement I Pressures . atm  V  H  V  H  V  De.Prp j. a t 21°C  N  1.068  10.57  (3.74)  1.20  11.08  (4.05)  (.0598)  1.34  11.18  4.42  .0599  1.681  11.55  (4.46)  (.0615)  2.02  11.89  2.71  12.21  3.04  12.37  4.376  2.572  2.564  1  Note  (.0584)  4.673  .0614  (4.82)  (.0632)  2.615  4.83  .0649  12.77  2.470  5.019  .0633  6.1  12.92  2.511  5.14  .0638  7.8  13.01  2.583  5.03  .0647  9.503  13.69*  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  5.24  .0640  (B>>in t o p )  "Very h i g h f l o w r a t e of n i t r o g e n (800-1200 mls/min) ^•Results I n p a r e n t h e s e s based on i n t e r p o l a t e d v a l u e s f o r of d i f f u s i o n r a t e s .  ratio  TABLE 5 Series 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  V  De. P  H  atm.abs.  a t 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 Series 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  N  "H — N  De. P  v  V  H  V  V  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, A r r a n g e m e n t I I I w i t h 1/4"  V  R u n No.  V  %  H  2.461 2.425 2.412 2.345 2.377 2.288 2.031 1.903  10.74 10.81 11.32 11.43 11.65 11.85  117  118 119  120 122 123 124 126  12.03 11.72  H  De.P  %^  21.1°C  4.364 4.458 4.71 4.873 4.901 5.18 5.923 6.159  .0572 .0570 .0583 .0581 .0598 .0585 .0575 .0593  Baffles  P atm  1.2 1.2 1.68 3.04 3.04  4.376 4.376  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  A r r a n g e m e n t I I I , w i t h 7/8" b a f f l e  V  Pressure  1.34 2.02 3.04 4.376 7.80 11.204  V  H  11.33 11.71 11.61 11.59 11.51 11.67  V  N  2.455 2.55 2.45 2.441 2.317 2.330  H  %  4.617 4.607 4.747 4.749 4.970 4.954  De.P  21.1°G .0581 .0604 .0595 .0584 .0574 .0579  Trm ° ®  70 70 71 71 71 71 71  0.07  o  o  t  0.06  -I  'j  o  0  n  O  F i g u r e 9« D i f f u s i o r L R e s u l t s i or Sample Arrangeme n t I . De. P V S i p  — 0  2  4  6 ABSOLUTE  8 PRESSURE,  10  12 ATM  14  16  6  • O Q— n  0.2  D  e  1  KJ——^—  ^ ^/  P •  0.1  0  I  2 ABSOLUTE  PRESSURE,  3  4  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, A r r a n g e m e n t I , De. P VS. P  °  0.07  Figure  -o-<  12.  n  D i f f u s i o n R e s u l t s f o r Sample A r r a n g e s e n t I I , De .P VS. P  o  r  0.05  0  2  4  6 ABSOLUTE  8  10  PRESSURE ,  12 ATM  14  16  0.07  o  006 CD  P  o o Figure  13 , D i f f u s i o ]l R e s u l t s :'or Sample Arrangem< m t I I I w i 1/4 Baf; : i e s , B e . P VS. P  0.05  0  2  4  6 ABSOLUTE  8  10  PRESSURE ,  12 ATM  14  16  0.07  0.06  o  P  o  G  O  O Figure  0  2  4  6 ABSOLUTE  8  13a D i f f u s i o n R e s u l t s f o r Sample A r r a n g e m e tit I I I w i t h 7/8 B a f f l e s De.P V s. p  10  PRESSURE ,  12 ATM  14  |6  39  EXPERIMENTAL ERRORS (A)  Measurement o f Gas C o m p o s i t i o n The c a l i b r a t i o n p l o t s f o r t h e m o d i f i e d t h e r m a l  c o n d u c t i v i t y c e l l s were u s e d i n t h e c a l c u l a t i o n o f t h e diffusion rates. B o t h o f t h e c a l i b r a t i o n p l o t s , f o r h y d r o g e n and nitrogen  a n a l y s i s , were e s t i m a t e d t o g i v e t h e c o m p o s i t i o n s  o f t h e s t r e a m s 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 o f + 2 . 5 % and a n average e r r o r o f l e s s t h a n 1%. The main v a r i a b l e s were t h e a c c u r a t e c o n t r o l and measurement o f t h e q u a n t i t i e s o f t h e two gas s t r e a m s t h a t made up t h e m i x t u r e o f known c o m p o s i t i o n f o r c a l i b r a t i o n purposes. Figures smaller  16 and 1 7 , i n t h e A p p e n d i x , show t h a t t h e  s t r e a m s c o u l d be metered w i t h an a c c u r a c y o f  about +1.2% ( i . e. w i t h i n + 0 . 2 m l / m i n . ) . The e l e c t r i c a l m e a s u r i n g c i r c u i t and t h e i n s t r u m e n t s u s e d w i t h i t were f e l t t o have a much s m a l l e r  error.  (B) Measurement o f D i f f u s i o n R a t e s P o s s i b l e e r r o r s i n t h e d i f f u s i o n r a t e v a l u e s were provided by the inaccuracies and  i n measurement o f f l o w  c a l i b r a t i o n s o f the thermal c o n d u c t i v i t y c e l l s .  rates In  a d d i t i o n t o t h e s e , f o r c e d f l o w , due t o u n b a l a n c e d d i f f e r e n t i a l p r e s s u r e a c r o s s t h e porous sample, and t h e e f f e c t o f d i f f u s i o n bomb geometry and p r e s s u r e t a p 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 values of d i f f u s i o n rates.  40  I t was f e l t t h a t t h e measurement o f f l o w r a t e s (200-1000 m l s / m i n ) f o r d i f f u s i o n r u n s a t v a r i o u s p r e s s u r e s m i g h t have a maximum e r r o r o f + 2%, w h i c h was t h e sum o f the e r r o r s from flowmeter temperature  c a l i b r a t i o n curves,  experimental  and p r e s s u r e , measurements,and r e a d i n g t h e  b a l l f l o a t i n the glass tubing.  The c o r r e s p o n d i n g  average  e r r o r was e s t i m a t e d t o be +1% ( i . e. 2-10 m l s / m i n . ) . As m e n t i o n e d 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 , t h e r e a d i n g s o f t h e d i f f e r e n t i a l d r a f t gauge were  maintained  a t t h e z e r o p o s i t i o n w i t h a n a c c u r a c y o f 0.005 i n c h o f w a t e r , w h i c h s h o u l d 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 c o u l d cause a p p r e c i a b l e e r r o r s . i n t h e next  This aspect i s d i s c u s s e d  section.  I f t h i s e f f e c t does n o t s e r i o u s l y a f f e c t t h e v a l u e o f t h e 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 , a s seems t o be t h e c a s e , t h e n t h e maximum e r r o r i n d e t e r m i n i n g t h e v a l u e o f d i f f u s i o n c o e f f i c i e n t s h o u l d be about 5%, w i t h a p r o b a b l e average e r r o r o f 3%.  The e x p e r i m e n t a l d a t a appear t o  conform t o t h i s e s t i m a t e .  41  DISCUSSION The most n o t a b l e f e a t u r e s o f t h e r e s u l t s o b t a i n e d i n t h i s work a r e t h e v a r i a t i o n i n t h e r a t i o o f t h e  two  d i f f u s i o n r a t e s , and t h e c o n s t a n t c y o f t h e D .j? p r o d u c t , as t h e t o t a l p r e s s u r e i n c r e a s e d . e x p e c t e d , and was  This l a t t e r effect  was  o b s e r v e d i n most o f t h e r u n s made.  It  a l s o seemed l o g i c a l t o suppose t h a t t h e r a t i o o f t h e 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 r e a s o n e i t h e r f o r o r 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 b y H o o g s c h a g e n  .  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 o f t h e more p o s s i b l e sources of experimental e r r o r .  obvious  F o r example,  f l o w m e t e r c a l i b r a t i o n s under p r e s s u r e were c a r r i e d  out  u s i n g t h e same f l o w s y s t e m , and w i t h a l l c o n n e c t i o n s t h e same, as i n subsequent d i f f u s i o n r u n s .  The  b r a t i o n o f t h e t h e r m a l c o n d u c t i v i t y c e l l s was  caliindependent  o f p r e s s u r e e f f e c t s , as t h e c e l l s o p e r a t e d under a constant s m a l l pressure at a l l times. o c c a s i o n s t h e system was a t : 100  checked  On s e v e r a l  f o r l e a k s by l e a v i n g i t  - p s i ; :.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 . ;  hour o r more was  An  always r e q u i r e d b e f o r e even 5 p s i d r o p  i n pressure occurred.  Hence, t h e r e i s no  o f e r r o r s o c c u r r i n g due t o l e a k a g e .  possibility  The d r a f t gauge  w h i c h showed t h e p r e s s u r e d i f f e r e n t i a l between t h e sample f a c e s was  l o c a t e d a t the same l e v e l as t h e sample,  42 t o a v o i d e r r o r s caused b y 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 t h e p r e v i o u s experimental  section the usual  e r r o r s e x p e c t e d w o u l d n o t have c a u s e d a  maximum e r r o r o f more t h a n 5% o f t h e D .P p r o d u c t .  As  a m a t t e r o f f a c t , t h i s i s about t h e range o f 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 s h o u l d be p o i n t e d o u t a l s o t h a t r u n s made a t one  atmosphere t o t a l p r e s s u r e  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 a s e x p e c t e d .  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 o b t a i n e d b y i n t e r c h a n g i n g t h e two g a s e s t h r o u g h o u t t h e s y s t e m , and a change i n sample l e n g t h d i d n o t a f f e c t r e s u l t s significantly. U s i n g t h e g l a s s c e l l employed b y C o x  v  and t h e  same p o r o u s sample, t h e same v a l u e o f e f f e c t i v e d i f f u s i v i t y was o b t a i n e d Young's c e l l ,  as t h a t r e p o r t e d b y Cox.  I n the case o f  ( o f t n e same t y p e as t h a t o f Cox) a  d i f f e r e n t p o r o u s sample was u s e d , a s 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, a g a i n 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 c o n c l u d e d , t h a t a t 1 atm. p r e s s u r e  and room t e m p e r a t u r e , 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 t h a 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 t h r o u g h t h e 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 , t h e v a r i a t i o n o f t h e e f f e c t i v e d i f f u s i o n  4-3  c o e f f i c i e n t with pressure was p r e c i s e l y as expected i . e . the D » P product remained constant.  However, the rather  e  large changes i n the r a t i o s of the d i f f u s i o n r a t e s as pressure increased was not expected.  Furthermore, the  value of t h i s r a t i o d i d not appear to be a f u n c t i o n of pressure only, but also to some degree depended on the v e l o c i t y of flow i n the d i f f u s i o n c e l l , the d i r e c t i o n of the flow path, and the l o c a t i o n 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 a d d i t i o n to d i f f u s i v e flow. Table 7b presents some data on i n d i v i d u a l runs i n which flow v e l o c i t i e s were v a r i e d . Sample 03-B,  In Series I, using  i t was only at the highest pressures that  flow rate seemed to have a d e f i n i t e e f f e c t on the d i f f u s i o n r a t i o (although t h i s e f f e c t was u s u a l l y small). For Sample 01-A, but t h i s was  the e f f e c t of flow r a t e was n o t i c e a b l e ,  to be expected, as the permeability of t h i s  sample was nearly 30 times as great as that f o r the solid.  Runs using the 03-B  03-B  sample with a b a f f l e d flow  path to promote mixing d i d not show any e f f e c t due to velocity.  V a r i a t i o n s i n these cases (Series I I I ) could  well be due to normal experimental  error.  Data are shown i n Table 7c, f o r runs using nearly the same flow r a t e s , at two pressures, and with varying c e l l arrangements.  The e f f e c t of poor mixing i n the gas  space above the sample i s evident from the low value of  44-  D .P, and t h e h i g h d i f f u s i o n r a t i o i . o b t a i n e d 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 ) . P o r a g i v e n g e o m e t r i c usage o f the d i f f u s i o n c e l l , a c o n s t a n t v a l u e f o r t h e Dg*!  1  was  p r o d u c t was  obtained.  This  t r u e f o r two w i d e l y d i f f e r e n t p o r o u s s a m p l e s , as w e l l  as f o r d i f f e r e n t c e l l arrangements. tfehethgas-vmixinge:d-i&;J&;Q$  I t was  a l s o t r u e if  -Vchange-greatly-.l, and w h e t h e r  f o r c e d f l o w c o u l d be e x p e c t e d t o o c c u r r e a d i l y o r n o t . A q u a l i t a t i v e e x p l a n a t i o n c a n be o f f e r e d f o r t h e c o n s t a n c y / o f the D .P  product even though the r e l a t i v e  g  r a t e s o f h y d r o g e n and n i t r o g e n d i f f u s i o n a r e 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 t h e two  streams  a f t e r d i f f u s i o n were v e r y l o w , t h a t i s , o f t h e o r d e r o f 1% - 5%.  T h e r e f o r e i n the d i f f u s i o n e q u a t i o n a p p l i c a b l e  ( e q u a t i o n 13 and 1 6 ) , the q u a n t i t i e s A^ and Ag a p p r o x i m a t e l y 0 and 1 r e s p e c t i v e l y . t h e n be  D  The e q u a t i o n c a n  written,  . p _ S P  f-SIk) A  A  In  ( N<  -  Ns)  A. '  function  A  „  - N-g/  i s  the  NA-MI  |„-gj.  K  1-(!-•£> A.  where K i s a n u m e r i c a l c o n s t a n t e q u a l t o The  are  ETL A  (2i)  .  logarithmic  average r a t e o f d i f f u s i o n o f b o t h g a s e s .  Hence, i f t h i s  q u a n t i t y r e m a i n s c o n s t a n t , t h e n t h e D .P p r o d u c t w i l l a l s o  45  TABLE ? b Effect  N2 P l o w mls/min std  Hg PlOw mls/min std  35  445  212  37  423  65  Run No.  o f Plow  v  Velocity  H  %  De. P  P atm  4.81  .0648  3.04  342  4.84  .O644  3.04  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  S a m p l e 03-B Arrangement I  Sample 01-A Arrangement 1  Sample 03-B Arrangement 3 7/8"  baffle  46  TABLE 7c E f f e c t of C e l l Arrangement  N2 Plow .  Hp Plow _—.  v  H  Run No.  mls/min sjtd  mls/min std  103  378  340  5.62  .0526  2.02  119  381  355  4.71  .0583  "  138  371  327  4.64  .0602  »  56  358  382  4.64  .0612  "  116  475  456  7.60  .0515  126  481  604  6.16  .0593  131  440  519  4.90  .0579  68  620  648  5.14  .0632  V  N  De. P  P atm  11.2 " 11  "  Cell Arrangement 03-B A r r . I I 03-B A r r . I l l 1/4 B a f f l e 03-B A r r . I l l 7/8 B a f f l e 03-B A r r . I 03-B A r r . I I . 03-B A r r . I l l I/4" B a f f l e 03-B A r r . I l l 7/8 Baffle 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.  i s o c c u r r i n g , t h e n t h e t o t a l r a t e o f f l o w o f A, N^, increase.  A,  must  I f t h e t o t a l average f l o w o f b o t h g a s e s i s t o  r e m a i n c o n s t a n t , as d e f i n e d above, t h e n t h e r a t e o f  flow  o f B must n e c e s s a r i l y d e c r e a s e as t h a t o f 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 o f one  component i s n o t  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 apparently  tends  t o cause a d e c r e a s e i n t h e dineVfe'^ve r a t e of t h e  second  component s u c h t h a t t h e average mean f l o w i s n o t seriously affected.  O b v i o u s l y t h e r e i s a l i m i t beyond  w h i c h 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 n o t  be  e x p e c t e d t o o c c u r , e. g. when t h e f o r c e d f l o w becomes too  great. An i n s p e c t i o n o f t h e d a t a f o r i n d i v i d u a l r u n s shows  t h a t an i n c r e a s e i n t h e d i f f u s i o n r a t e o f h y d r o g e n d i d i n d e e d cause a d e c r e a s e i n t h e n i t r o g e n d i f f u s e d .  The  . e x c e p t i o n t o t h i s g e n e r a l o b s e r v a t i o n c a n be f o u n d i n t h e r u n s r e p o r t e d as S e r i e s I .  Here t h e e x p e r i m e n t a l  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 n o t as h i g h i n other runs.  The  r e s u l t s ' o f t h i s s e r i e s show, an a p p a r e n t  i n c r e a s e o f about 10% i n t h e D .P p r o d u c t b e l o w 3.0  atms, w h i c h appeaps t o be due  with  pressure  t o the f a c t t h a t  the h y d r o g e n 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 corresponding  as  decrease i n n i t r o g e n d i f f u s i o n r a t e .  or  no In a l l  other sets of runs, using e i t h e r d i f f e r e n t s o l i d s , or d i f f e r e n t choices f o r c e l l connections,  i t was  generally  48  t r u e t h a t as t h e amount o f h y d r o g e n 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 d e c r e a s e d .  The  u s u a l amount o f 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 t h e d e c r e a s e o f n i t r o g e n  about 5-25%, d e p e n d i n g on t h e c o n d i t i o n s u s e d . f o r sample 01-A  The  data  a r e p l o t t e d i n Figure;.; 14.which a l s o  shows a p l o t o f t h e v a l u e s o f  and N^/Ng  which would  g i v e t h e same l o g mean average f l o w as t h a t o b s e r v e d when f o r c e d f l o w was  absent.  I t can be s e e n t h a t , e x p e r i m e n t a l l y ,  t h e d a t a does v a r y i n s u c h a way  as t o g i v e a  constant  average f l o w , as i n d e e d 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 n o t e some d a t a t a k e n by C o x t o d e m o n s t r a t e t h a t f o r c e d f l o w was  v  J  a b s e n t i n h i s work.  H i s r e s u l t s show t h a t t h e i n c r e a s e i n h y d r o g e n d i f f u s i o n r a t e due  t o a p r e s s u r e head was  a l m o s t t h e same as  the  d e c r e a s e i n d i f f u s i o n r a t e when h y d r o g e n was  diffusing  a g a i n s t the same p r e s s u r e head e. g. a t +0.2  i n c h water  t h e r a t e i n c r e a s e d 9.0%, d e v r e a s e d 10.2%.  a t -0.2  i n c h of water, i t  T h i s confirms the e x p l a n a t i o n  given  above f o r t h e c o n s t a n t l y o f t h e I> .P p r o d u c t , e v e n t h o u g h e  t h e q u a n t i t i e s d i f f u s e d may  v a r y , o r i n s p i t e o f some  degree o f 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 U n d o u b t e d l y i n some o f t h e r u n s done e.g.  apparatus.  w i t h Sample  01-A,  7  A EXPERIMENTAL DATA SAMPLE 0 I - A  8  N /N A  0  12  FOR  14  B  F i g u r e 14. P l o t o f N« a g a i n s t N / N g a t C o n s t a n t L o g Mean D i f f u s i o n R a t e (Experimental N values adjusted f o r Sample 01-A, A r r a n g e m e n t 1. A to A r b i t a r y Ordinate S c a l e ) . A  oo  49 o r w i t h Arrangement I I , r e s i s t a n c e due  e i t h e r f o r c e d f l o w , or  t o poor m i x i n g , e x i s t e d .  f o r c e d f l o w i n o t h e r r u n s , was f o r f b r c e d f l o w i n the 03-B  indirect.  sample u s i n g  end  Evidence f o r Calculations experimentally  d e t e r m i n e d p e r m e a b i l i t i e s and D a r c y ' 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 1 ml o f h y d r o g e n per m i n u t e . pressures The  Any  of  p o s s i b l e impact  can be shown t o be o f t h e o r d e r o f 0.01" w a t e r .  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 of pressure.  The  c o m p l e t e r e v e r s a l o f t h e system ( i . the two  observation that  e. s i m p l y  a  switching  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, forced flow.  cannot e a s i l y be e x p l a i n e d on t h e b a s i s I t w i l l be n e c e s s a r y t o m o d i f y t h e  of  diffusion  c e l l , and p e r h a p s t h e d i f f e r e n t i a l d r a f t gauge arrangements^ b e f o r e t h e s i t u a t i o n can be  clarified.  However, t h e a p p a r a t u s can be u s e d s u c c e s s f u l l y i n i t s present  f o r m f o r some p u r p o s e s .  t r a n s i t i o n r e g i o n between Knudsen and  I n i n v e s t i g a t i n g the ordinary  diffusion,  f o r c e d f l o w i s u s u a l l y a m i n o r f a c t o r because o f t h e f i n e pore s i z e s involved,and unbalance i s of l i t t l e  therefore a small  very  pressure  consequence.  When f o r c e d f l o w i s p r e s e n t  as a mechanism o f t r a n s f e r  i n a d d i t i o n t o d i f f u s i v e f l o w , i t has b e e n assumed t h a t t h e two obtained  c a n s i m p l y be added.  However, i n v i e w o f t h e r e s u l t s  i n t h i s work, t h i s would no l o n g e r be  necessary  50  as l o n g as t h e f l o w i s l a r g e l y d i f f u s i v e i n n a t u r e . 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  solids  t h i s m i g h t p r e s e n t 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 f r o m 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 o r d e c r e a s e i n volume on r e a c t i o n , t h e n some degree o f f o r c e d f l o w e x i s t s t h r o u g h t h e p o r o u s s o l i d i n o r d e r t h a t N^/Ng may have t h e n e c e s s a r y  value.  Knowing  t h i s v a l u e , and t h e e f f e c t i v e d i f f u s i v i t y o f t h e s o l i d , i t s h o u l d be p o s s i b l e t o c a l c u l a t e t h e r a t e o f t h e d i f f u s i v e process  f o r a b i n a r y s y s t e m o f known k i n e t i c s , u s i n g t h e  diffusion  equation,only.  51  CONCLUSIONS AND RECOMMENDATIONS The p r e s e n t 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 p r e s s u r e m e a s u r i n g s y s t e m s h o u l d be m o d i f i e d i n such a way  a s t o g i v e good gas space m i x i n g and t r u e s t a t i c  p r e s s u r e r e a d i n g a t t h e s o l i d sample f a c e s . The  apparatus  a p p e a r s t o be most s u i t a b l e  for varying  t h e mean f r e e p a t h o f d i f f u s i n g gas systems b y t h e application  o f pressure.  This allows the nature o f the  d i f f u s i o n mechanism o c c u r r i n g i n a p o r o u s s o l i d t o be varied easily.  E v e n i f f o r c e d f l o w were c o m p l e t e l y  e l i m i n a t e d , t h e method i s n o t p a r t i c u l a r l y s u i t a b l e f o r measuring t h e v a r i a t i o n o f t h e pressure.  .P p r o d u c t w i t h a b s o l u t e  T h i s i s due t o t h e n e c e s s i t y f o r m u l t i p l e  r a n g e s and c a l i b r a t i o n s o f f l o w m e t e r s . A substitute  f o r t h e type o f flowmeter  would s i m p l i f y e x p e r i m e n t a l work.  used here  Some r e a s o n s h o u l d be  found f o r t h e n e c e s s i t y o f t h r o t t l i n g t h e n i t r o g e n o u t l e t l i n e t o a c h i e v e p r e s s u r e b a l a n c e i n t h e c e l l , when, i n t h e o r y , i t i s the hydrogen l i n e which should r e q u i r e throttling.  52  BIBLIOGRAPHY (1)  K e n n a r d , E. H., " K i n e t i c Theory- o f Gases" M c G r a w - H i l l , New York,.73-74 (1943). -  (2)  W h e e l e r , A., "Advances i n C a t a l y s i s " Academic V o l . 3 261-267 (1951).  (3)  P e t e r s e n , E. E.,  (4)  Cox, K. E., M. A. S c . T h e s i s . " D i f f u s i o n o f Gases" i n Chemical E n g i n e e r i n g , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1959-  (5)  M a x w e l l , J . C., " S c i e n t i f i c P a p e r s " , Cambridge  Press,  A. I . Ch. E. J o u r n a l , 4 343 (1958).  U n i v e r s i t y P r e s s , New Y o r k , 2  57  (1890).  (6)  S t e f a n , J . , Ann. P h y s . , 4 1 , 725  (7)  Meyer, 0 . E., " K i n e t i c T h e o r y o f g a s e s " , Longmans, R o b e r t s and G r e e n , London,  (8)  S u t h e l a n d , W.,  (1890).  (1899).  p h i l . Mag., 3 8 , 1(1894).  (9)  L a n g e v i n , I . , J . Am. Chem. S o c , 37, 426 (1915) J . Am. Chem. S o c , 3 8 , 2221-2295 (1916). (10) Chapman, S., and T. C. C o w l i n g , " M a t h e m a t i c a l Theory o f Non-Uniform Gases", Cambridge U n i v e r s i t y P r e s s , New Y o r k , 1939(11) E n s k o g , D., P h y s i k . A., 12, 56, 533 (1911). (12) J e a n s , J . H. "The D y n a m i c a l T h e o r y o f Gases" 3rd E d . Cambridge U n i v e r s i t y P r e s s , N. Y., 307 (1921). (13) L e w i s , W. K., and K. C. Chang, T r a n s . Am. I n s t . Chem. E n g r s . , 2 1 , 127 ( 1 9 2 8 ) . (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 E d . , McGraw-Hill,-New Y o r k , (1952). (15) Hoogschagen, J . , I n d . Eng. Chem., 4£, 906 (1955). (16) Khudsen, M., Ann. P h y s i k , 2 8 , 75 (17)  (1909).  K i s s , M., B. A. S c T h e s i s i n C h e m i c a l E n g i n e e r i n g ,  U n i v e r s i t y o f B r i t i s h C o l u m b i a , 0-959). (18) L o s c h m i d t , I n t e r n a t i o n a l C r i t i c a l T a b l e s , V o l . 5, (1928), p. 6 2 , M c G r a w - H i l l , New Y o r k .  53  (19)  M i f f l i n , T. R. and C. 0 . B e n n e t t , 22,  975  J . Chem. P h y s . ,  (1958).  (20) B e c k e r , V o g e l l , and Z i g a n , Z. N a t u r f o r s c h , 8 a , 686  (21)  (1953).  O'Hearn, H. A. and J . L. M a r t i n , Ihd Eng.  Chem.  (1955).  2081  (22) Timmerhaus., K. D. and H. G. D r i c k a m e r , J . Chem. P h y s . 20,  (23)  981-4  (1952).  .  J e f f r i e s , Q. R. and H. G. D r i c k a m e r , J . Chem. P h y s . , 21,  1358  (1953)  -  (24) J e f f r i e s , Q. R. and H. G. D r i c k a m e r , J . Chem. P h y s . , 22,  (25)  436  (1954)  Chou, C. H. and J . L. M a r t i n , I n g . E n g . Chem. , 4_2, 758  (1957).  (26) C a r m i c h a e l , L. T., B. H. Sage, and W. N. L a c e y , I n d . Eng. Chem. ,- 4 £ , 2205 ( 1 9 5 5 ) . (27)  C a r m i c h a e l , L. T. , B. H. Sage, A.. I . Ch. E . J o u r n a l , 2,  273  (1956).  (28) C a r m i c h a e l , L. T., B. H. Sage, and W. N. L a c e y , A. I . Ch. E. J o u r n a l , 1, 3 8 5 ( 1 9 5 5 ) . (29) W i c k e , E. and R. K a l l e n b a c h , K o l l o i d Z., 9 7 , 135 (1941).  (30) W e i s z , P. B., Z. P h y s . Chem., 11 Band, H e f t 1 / 2 , 1, (1957). (31)  A r n o l d , J . H., I n d . & Eng.  Chem., 2 2 ,  1091  (1930).  G i l l i l a n d , E. R., I n d . & Eng. Chem., 2 6 , 681 ( 1 9 3 4 ) . (33) S l a t t e r y , J . C. and R. B. B i r d , A. I . Ch. E. J o u r n a l  (32)  4,  137  (1958).  (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., " M o l e c u l a r T h e o r y o f Gases a n d - L i q u i d " W i l e y , N.Y., (1954).  (35) Young, M. J u n e . , P r i v a t e Communication t o D r . D. S. S c o t t , Department o f C h e m i c a l E n g i n e e r i n g , U n i v e r s i t y o f B r i t i s h Columbia, (1959).  APPENDIX  Sample  Calculation  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  Run 37.  Data recorded  Ratio  as below  Sample Length L Average Cross S e c t i o n a l A r e a , A Temperature, T° K A b s o l u t e P r e s s u r e , P. atm Nitrogen flow rate, i n l e t , X  S e l a s 03-B 3.157 cm 5.376 cm'  Hydrogen f l o w r a t e ,  342  294°  3.04 atm 423 Si£ s t d ,  N  i n l e t , X„ n M.V. o n No. 1 T-C c e l l M.V. o n No. 2 T-C c e l l N i t r o g e n % i n o u t l e t Hg. N ^ Hydrogen % i n o u t l e t N . g  "  11  7.309  26.15  '  M.V. M.V.  0.785$ 2.915$  iy6  Calculation: By means o f a m a t e r i a l pressure.  We c a n c a l c u l a t e  and n i t r o g e n ,  hydrogen Y  N*  H  N^  i.e.Y  Y  H*  the outlet flow rate  and Y . H N  ( V ^ ) and n i t r o g e n r e 3  P  b a l a n c e , based on c o n s t a n t  T h e r e f o r e tine v o l u m e r a t e o f  (V^) d i f f u s e d  e c t i v e l  y«  o f hydrogen  are the products of  Y  N  X  (N  H  H  Where N T. H  Cutlet nitrogen flow rate  mls/min s t d .  Outlet hydrogen flow 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  %  Mole f r a c t i o n o f h y d r o g e n 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  N. H  I<H.  Mole f r a c t i o n o f h y d r o g e n i n o u t l e t  H  V  stream,  H  11  11  Rate of d i f f u s i o n of 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 .  V.  N  "  A m a t e r i a l balance over the system gives *•  *  Y.N H Solve  X  H  H  "  Y  N  +  Y H  + Y . N N N  (1)  and  (2) f o r Y H  o r Y. _ H  H H  H  TT  N - N_  (2) X f l - H )-X .H H N N N  iH and Y , we h a v e N  Y H  H  H-  H.  N I( ^ ) H  (3)  Y V  rT  N  = X  T  N  + X  H  - Y  (4  H  = Y • H  H  (5  V. = Y • N N H H  (6  T  F o r r u n 37, s u b s t i t u t e  t h e 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 \ 9 7 0 8 5 = ' .02915x = .99215 - .00785 .97085' ;  Thus  Y  n H  Y  332  !  (  N  V_ H  H —  ral/min.  =  433  ml/min.  =  12.62  ml/min.  =  2.606  =  4.84  ml/min.  V  = r a t i o of d i f f u s i o n  We c a n now a p p l y e q u a t i o n Pigford  (16) d e r i v e d f r o m t h e S h e r w o o d and  e q u a t i o n and c a l c u l a t e t h e M a x w e l l d i f f u s i o n  coefficient. L e t h y d r o g e n be component  A.  Then  N/HH5) — ' )  Ln  —  (I-  l-  0  ( i  _L_ NM  3  A  57 ~ Room t e m p e r a t u r e , 294°  ^rm T  s t d == 294.1° K (70°P) L  cm  == 3.157  2 cm'  A == 5.376  % .: 1 H  H  "  2  % " H V  D  e  ,  P  =  H  -  % V  H  .02915 "  = .99215  H„ =  12.62  = 0.7934  mole f r a c t i o n mole f r a c t i o n mis p e r m i n .  1 3.157 12.62 (1) 60 (0.7934) 5.376 m 1 - 0.7934 (.02915) 1 - 0.7934 (.99215) .0980 = 1.521  2 cm' De. P = O.O644 s e c , (atm). where P Dm. P = 0.7657 a t 294.1°K.  3.04 atm.  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  (3.74)*  Average  10.72 10.43 10.43 10.75 10.36 10.73 10.57  7 8 9 Average  11.27 10.97 11.00 11.08  (4.05)  13 14  11.09 11.15 11.21 11.38 11.39 11.18  4 5 6 10 11 12  52  53 54 Average  it tt tt n it  a t 21.1°C P,atm De. F .0590 .0582 .0583 .0594 .0574 .0591 .0584  1.068 u tt tt it it  Trm °C 22 tt tt tt  23 23  (.0610) (.0595) (.0595) .0598  1.2 it  22 22 22  (.0589 (.0595 .0601 .0605 .0590  1.34  2.605 2.633 2.473  (4.21) (4.21) 4.310 4.322 4.606  tt it tt tt  23.5 it 22 22 22  2.572  4.42  .0599  (4.46)  (.0695) (.0607) (.0629) (.0618)  1.681  19.5  »  tt tt  it it  15 16 17 18 Average  11.36 11.37 11.88 11.60  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  4.641 4.641 4.834 4.671  (.0604) (.0632) (.0611) .0620 .0612 .0613 .0606  Average  11.89  2.564  4.673  .0614  tt it tt  »  tt tt  »  (.0615)  11.55 (4.645) it it  2.02  19.8 II  it 22 22 22  20.4  TABLE 4a (cont'd)  Run No. 22 23  24 Average 25 26 36 37 Average 27 28 29 30 41  V  H  V  N  11.46 12.60 12.58  V  N  13.13 12.20 11.90 13.55 12.805 12.645 13.00  Trm  (.0585) (.0655) (.0651) (.0632)  2.71  20.4  (4.865) (4.965) 4.81 4.84 4.83  (.0603) .0640 .0651 .0646 .0649  3.04  20.4 20.4 20.5 20.5  (5.02)  (.0681) (.. 0628) (.0615) (.0685) .0666 .0604 .0628 .0633  4.376  19 19 19 19.2 20.8 20.8 20.8  »ii  2.623 2.606 2.615  P. atm  (4.82)  12.21 11.64 12.60 12.62 12.62 12.37  De. P  n ii H  it tt  tt tt it  tt tt tt tt tt it  it tt  12.77  2.800 2.165 2.445 2.470  4.573 5.840 5*330 5.019  38 39 40 Average  13.1 12.84 12.81 12.92  2.551 2.482 2.499 2.511  5.13 5.17  .0650 .0632 .0632 .0638  6.1 tt it  20.8 20.8 20.8  44 45 46 47 Average  13.18 13.16 12.65 13.03 13.01  2.481 2.581 2.693 2.579 2.583  5.31  .0639 .0655 .0650 .0645 .0647  7.8  20.4  58 59 60 Average  14.04 13.62 13.40  2.724 2.714 2.633 2.691  .0661 .0648 .0634 .0648  9.503  42  43 Average  13.69  5.13 5.14 5.10 4.69 5*02 5.03 5.154 5.017 5.089 5.09  »tt  tt  »tt  tt it tt  21.4 22 22  60 TABLE 4a  V R u n No.  61 62  63 64  68  Average  65 69 70 71 Average  rf  V H  N  V  N  (cont'd)  De. P  P atm  11.204  13.36 13.69 13.26 13.32 13.46 13.42  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  2.553  5.343  .0633  13.30 13.76 14.14 14.23 13.86  2.588 2.51 2.489 2.567  5.139 5.482 5.681 5.543  2.544  5.434  .0630 .0642 ;0646 .0655 .0644  Values i n parantheses  interpolated.  n  »  ti ti  14.605 i» it u  Trm °C  23  11 11  21.5 20  21.5 20 20.4 20.4  61 TABLE 5a 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 3 Arrangement I  Run No.  Pressure atm  93 94 95 Average  1.068  91 92 Average  1.34  87 88 89 90  tt tt  n  1.681 tt tt tt  Average 83 84 Average  3.04 3.04  H % V  V  H  V  N  De. P a t 21°C  4.925 4.74 3.80 4.49  .2028 .1907 .2134 .2025  4.84 4.97  .2065 .2105  25.1  5.125 4.967 5.046  4.91  .2085  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  25.65  4.67  5.51  .2051  27.6 27.4  4.095 4.75  6.75 5.77  .1965 .2100  27.5  4.43  6.26  .2033  24.9 22.66 22.72 23.09  5.055 4.787 5.984  24.80 25.4  5.275  .2043  .2060 .2055  62 TABLE 6a 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 A r r a n g ement I I  Run No. 100 101 102  V  V  H  10.276 10.48 10.478  %  H  *M  De.P a t 21.1°C  Pressure atm  Note  2.104 2.19 2.232 2.175  4.884 4.785 4.694 4.788,  (.05267) .0543 (.0546) .0538  1.338 1.34 1.34  103 11.15 104 11.143 105 11.25 106 10.95 107 11.15 108 11.18 Average 11.17  1.985 1.979 2.047 1.951 1.933 1.900  5.617 5.631 5.496 5.610 5.768 5.884 5.668  (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"H >N  2  109 11.33 110 11.31 Average 11.32  1.953 1.952  5.801 5.794 5.798  (,.0537) .05365  ,3.04 3.04  0.05"H >N  2  111 11.35 112 11.35 Average 11.35  1.950 1.961  114 115 116  Average 10.41  12.10 11.87 11.99  Average 11.99  1.965  1.953  4  0.1 H2<N * n  2  2  0.0533 2  .0537 .05385 (.0540)  1.955  5.821 5.787 5.804  1.696 1.775 1.577  7.137 6.687 7.603  (.0532) .0545 .0515  1.683  7.142  .0531  4.376 4.376  .06"H >N  2  .08"H >N  2  2  .0539 11.204 11.204 11.204  2  ^ P r e s s u r e o f t h e hydrogen s i d e was 0.1" water; g r e a t e r , t h a n ..that o f the n i t r o g e n s i d e . .( ) V a l u e s w i t h i n t h i s b r a c k e t a l l o w e d an e x p e r i m e n t a l 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 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 7/8" v e r t i c a l b a f f l e )  Run No.  —  Tr  H  J^N  140 11.35 2.463 141 11.32 2.447 142 (11.26) (2.462) Average 11.33 2.455  V  N  4.608 4.626 (4.574) 4.617  De.P  Pressure  a t 21.1°C  absolute  y  1.34 " "  0.0583 • 0.0579 (0.0572) 0.0581  2.499 2*601  4.643 4.571  .0597 .0611  ,2.55  4.607  .0604  134 11.055 2.41 135 12.17 /2.48 Average 11.61 2.45  4.587 4.907 4.747  .0570 .0619 .0595  136 11.59 2.415 137 11.598 2*468 Average 11.594 2.441  4.799 4.699 4.747  .0589 .0575 .0584  4.376 "  4.980 (4.960)  .0569 (.0578)  7.8 7.79  4.970  .0574  4.743 (4.909) 4.996 4.902 5.146 5.028  .0590 (.0585) .0583 .0576 .0570 .0578  4.954  .0579  138 139  11.60 11.89  Average 11.71  143 144  11.45 2.299 (11.585H2.335)  Average 11.507 2.315 127 129 130 131 132 133  11.70 2.467 (11.463) (2.335) 11.65 2.332 11.52 2.350 II.64 2.262 11.73 2.333  Average 11.67  2.330  Note  .11 H 0H <N  2  ,09"H 0H <N  9  ,,  2  2  2.02 " 3.04 ,  11  11.204 " " " 11  ?  p  TABLE 8 Ratio  of Equal Pressure D i f f u s i o n Rates f o r P a i r s of Gases,  1 atm  Diffusion Observed  Gases  Ratio  Theoretical from  eq.(18)  Helium-oxygen^  3.03 2.66 2.54  2.83  Nitrogen-oxygen ,  1.09 1.07  1.07  Carbon dioxide-oxygen-^  0.89 0.80  0.85  Hydrogen-ni trogen^  3.44 4.03 3.75  3.742  1. D a t a f r o m H o o g s c h a g e n . (15) 2. D a t a 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  Gas. H  N  H  2  2  2  N  2  No. o f Flowmeter  Tube Reading  203-1  3 4 5 6 7  203-2  7 8 10 12  Meters  Mis 70°F F l o w R a t e m i n 1 atm 70°F 70°F 75°F 150 p s i g 150 p s i g 150 p s i g 284.7 454.5 669 877.8  166.9 284.5 454.2 671.4 877.1  167.9 286.1 455.5 673.7 878.1  503.7 597.3 788.7 1003.8  501.4 592.8 784.4 999.9  502.0 595.0 786.7 1001.7  167  70°F 15 p s i g  75 °F 15 p s i g  70°F 15.3 p s i g  203-1  7 8 10 12 14  177.6 241.5 371.2 600.8 730.3  176.3 239.1 369.1 595.8 725.4  178.9 243.6 374.9 605.9 736  203-2  8 10 12  193.3 264.4 339.3 432.5 520.3  193.2 262.9 337.9 429 517.2  196.7 267.4 342.7 436.4 524  14 16  TABLE 10 E x a m p l e o f C o m p l e t e R e c o r d e d D a t a f o r Runs ( A r r a n g e m e n t I )  Sample Wo.  P l o r Rate mls/min. 21°C, 1 a t m Run No.  P atm  Nitrogen inlet  2 it tt  52 53 54  1.34 1.34 1.34  324.6 382 330  274.5 275.5 319  30.02 26.11 30.02  3.365 2.912 3.364  2 u  36 37  3.04 3.04  411.7 423  305 342  26.85 26.15  2 it  41 42 43  4.376 4.376 ti  512 458 566  331 256 606  II  65 14.605 ti 69 70 ti II 71  605 800 1197.5 1670  1.681 ti it it  374 376 557 556.5  II  tt II  it 3 u tt it  87 88 89 90  E%  V  H  No. 1 M.V.  2# i n H2  11.2 11.38 11.39  7.343 9.100 7.343  0.980 0.987 0.797  2.605 2.633 2.473  4.30 4.32 4.61  .0606 .0614 .0612  2.993 2.915  12.62 12.62  8.379 7.309  .889 .785  2.623 2.606  4.81 4.84  .0651 .O646  22.0 24.23 20.23  2.447 2.695 2.253  12.805 8.064 12.645 8.196 13.000 3.785  .875 .889 .411  2.800 2.165 2.445  4.57 5.84 5.33  .0666 .0604 .0628  515 322 443 470  19.08 15.15 10.45 7.55  2.136 1.687 1.170 0.845  13.30 13.76 14.14 14.23  4.723 7.445 5.325 5.166  0.513 0.808 0.577 0.560  2.588 2.51 2.489 2.567  5.139 5.482 5.681 5.543  .0630 .0642 .0646 .0655  515 506 720 630  58.2 58.0 41.96 41.67  6.515 6.485 4.700 4.670  25.65 25.73 27.23 27.00  9.125 9.249 6.225 6.76  .9775 .99 .671 .727  4.825 4.81 4.685 4.41  5.325 5.35 5.82 6.12  .2046 .2043 .2060 .2055  H y d r o g e n No. 2 inlet M.V.  2  in  N  2  N  %  %  De. P  5  FLOW  RATE,  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 - F l o w m e t e i • 2 0 2 - 1 , S a p p h i r * j F l o a t , f (>r Hydroger 1 a t 70°F  /  0  5  10  Q  SOAP B U B B L E  ^  I.I A T M SOAP BUBBLE METER  % CALCULATED  / / { / 15  20  FLOW  RATE ,  •y  25 mls/min  30 std  METER  1.0  ATM  I.I  ATM  35  40  5.0  / /  4.5  //  /Figure  1' r C a l l b r a t : .on P l o t P I 01/meter 202- •1 Sap]>hire P l o a - ; f o r N i t a •ogen a t •"](.)°P  4.0  o z a UJ  A  O  a:  SOAP, B U B B L E METER I.I ATM © SOAP B U B B L E M E T E R 1.0 ATM # CALCULATED 1.1 ATM  Q  -  UJ  £  3.0  2.5  2.0  0  0  15 FLOW  20 RATE ,  25 mls/min  30 std  35  14  13  12  F i g u r e 18 . G a l i b r a ti o n P l o t Flow n e t e r 203- 1, Sapp h i r e F l o a t , f o r Hydr ogen a t 70op  C3  z < LLI  OC  UJ CD 3  II  10  8  100  200 FLOW  O  WET T E S T METER  I.C)68  © •  CALCULATED CALCULATED  I.C)68 A T M I.C) ATM  300 RATE , mls/min  400 std  ATM  500  300  500  400 FLOW  RATE ,  600 mls/min  std  700 CTi CD  66g  P E R C E N T OF F i g u r e 21.  NITROGEN  C a l i b r a t i o n . P l o t f o r No. 1. T h e r m a l C e l l before Modification  Conductivity  66h  0  I  2  3  P E R C E N T OF  4  5  6  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, T h e r m a l C o n d u c t i v i t y before Modification  Cell  

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