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Effect of transverse vibration upon the rate of sublimation from horizontal cylinders Sugano, Yuzuru 1967

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E F F E C T OF TRANSVERSE  VIBRATION UPON  THE RATE OF SUBLIMATION FROM HORIZONTAL  CYLINDERS  by  YUZURU B.Eng.j  SUGANO  Kyoto U n i v e r s i t y ,  A THESIS SUBMITTED  1965  IN PARTIAL FULFILMENT OF  THE REQUIREMENTS  FOR THE DEGREE  OF  MASTER OF APPLIED SCIENCE  in  t h e Department of  CHEMICAL  We  accept  ' required  this  ENGINEERING  thesis  as conforming t o the  standard  THE UNIVERSITY OF B R I T I S H M a r c h , 1967  COLUMBIA  In  presenting  for  an a d v a n c e d  tiiat  the  study thesis  agree  that  of  this  of  thesis  for  may be g r a n t e d  for  Chemical E n g i n e e r i n g Columbia  It  of  British for  the  Columbia,  I  reference  and  extensive by  requirements  copying  gain  of  agree  this  t h e Head o f my  is understood  financial  permission.  A p r i l 7, 1967.  of  available  permission  representatives  his  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a Date  freely  or  by  fulfilment  University  purposes  my w r i t t e n  Department  the  scholarly  publication  without  at  in p a r t i a l  s h a l l make i t  I further for  thesis  degree  Library  Department or  this  shall  that not  be  copying allowed  i  ABSTRACT  The  e f f e c t o f v i b r a t i o n upon the r a t e of  from h o r i z o n t a l c i r c u l a r c y l i n d e r s has in several investigations. c o r r e l a t i o n has  sublimation  been s t u d i e d  However, no  previously  satisfactory overall  been o b t a i n e d up t o the p r e s e n t t i m e .  I n the p r e s e n t i n v e s t i g a t i o n , d a t a have been o b t a i n e d f o r mass t r a n s f e r from n a p h t h a l e n e t o a i r and  phenol to a i r  f o r h o r i z o n t a l c y l i n d e r s v i b r a t e d v e r t i c a l l y o v e r a wide range of Reynolds number.  I t i s shown t h a t t h e s e d a t a and  the  data of a l l previous i n v e s t i g a t i o n s , i n c l u d i n g l i q u i d  systems,  l i e on o r near a s i n g l e smooth curve p r o v i d e d t h a t an  appro-  p r i a t e system o f c o o r d i n a t e s i s s e l e c t e d . R e y n o l d s number and the  Further,  f o r high  h i g h Schmidt number, the d a t a approach  t h e o r e t i c a l e q u a t i o n of Jameson d e r i v e d  using  boundary-  layer theory. The  a u t h o r has  for sublimation  can  found t h a t the mass t r a n s f e r c o e f f i c i e n t  be i n c r e a s e d  which p r e v a i l s f o r the  by a f a c t o r of 30 o v e r t h a t  stationary  (non-yibrating)  For mass t r a n s f e r t o gaseous media o n l y , the  following  r e l a t i o n i s p r o p o s e d , h a v i n g an average d e v i a t i o n Sh = 0.261  Sc  1 / 3  This equation i s believed range of the v a r i a b l e s  :  Rev°-  7 1 7  ( H/d  ) ' 0  case. cor-  of±17 % :  2 3 3  t o be v a l i d over the  following  ii  Diameter :  0.07  Frequency :  100  Amplitude (double) :  0.05  V i b r a t i o n a l Reynolds number :  9  R a t i o of amplitude to diameter  0.2  -  -  1.1 7000  -  4.0  2000 -  5.7  cm RPM  cm  iii  ACKNOWLEDGEMENT  I wish t o thank Dr. D.A. Ratkowsky o f the Department of Chemical E n g i n e e r i n g  o f the U n i v e r s i t y o f B r i t i s h  Columbia  f o r h i s guidance and time i n h e l p i n g t o c a r r y out t h i s p r o j e c t . I wish a l s o t o thank Mr. R. Muelchen staff, particularly t h e i r cooperation  Mr. J . Baranowski  and the workshop  and Mr. F. Maltby f o r  i n c o n s t r u c t i n g the a p p a r a t u s .  I wish a l s o t o thank the N a t i o n a l Research C o u n c i l o f Canada f o r f i n a n c i a l a s s i s t a n c e , and the Department o f Chemical Engineering  o f the U n i v e r s i t y o f B r i t i s h Columbia f o r a d d i t i o n a l  support.  Yuzuru  Sugano  iv  TABLE OF CONTENTS Page LITERATURE SURVEY  1  INTRODUCTION TO PRESENT INVESTIGATION  5  THEORETICAL FOUNDATION  6  1.  S t r e t c h e d - F i l m Concept o f L e m l i c h  6  2..  Boundary-layer  8  S o l u t i o n o f Jameson  APPARATUS  14  A.  General  B.  Detailed  '  14 14  1.  Test s e c t i o n  14  2.  Amplitude  19  3.  Frequency  19  4.  Carbon-coated  5.  Temperature  20  6.  T o t a l pressure  20  wall  20  21  EXPERIMENTAL 1.  Sample C y l i n d e r C o a t i n g  21  2.  O p e r a t i o n o f Experiment  22  3.  P r o c e s s i n g o f Data  25  ."'RESULTS DISCUSSION  . 22  ' \.  33  CONCLUSIONS  51  FURTHER CONSIDERATIONS  53  V  Page LITERATURE  56  CITED  58  NOMENCLATURE  APPENDIX I .  Detailed  illustrative  calculations  A- 1  1.  S i n u s o i d a l motion  A- 1  2.  The f u n c t i o n  A- 1  3.  C a l c u l a t i o n o f mass t r a n s f e r c o e f f i c i e n t  APPENDIX I I .  o f the carbon-coated w a l l  Property o f m a t e r i a l s  A- 5  used i n the A- 8  experiment 1.  Naphthalene  A- 8  2.  Phenol  A- 8 A-10  APPENDIX I I I . C a l c u l a t i o n s 1.  Use o f d i g i t a l  2.  Sample c a l c u l a t i o n s  3.  Stationary  H.  Least-squares method  APPENDIX IV.  computer ';  mass t r a n s f e r c o e f f i c i e n t  O r i g i n a l data  A-10 A-10 A-ll A-13 A-19  vi  LIST OF TABLES Page 1.  Comparison between some p r e v i o u s  investigations 4  w i t h r e g a r d t o mass t r a n s f e r 2.  R e s u l t s of t h e p r e s e n t i n v e s t i g a t i o n f o r 26  naphthalene 3.  R e s u l t s of the p r e s e n t i n v e s t i g a t i o n f o r 29  phenol 4.  Gaseous system d a t a o f the p r e v i o u s a.  investigations  Naphthalene i n t o a i r , d a t a o f Rao  and 30  co-workers b.  c. 5.  Naphthalene and d-camphor i n t o a i r , d a t a of. L e m l i c h and Levy  30  Naphthalene i n t o ' a i r , d a t a o f Goh  30  L i q u i d system d a t a o f the p r e v i o u s a.  investigations  Benzoic a c i d i n t o g l y c e r o l - w a t e r , 31  d a t a o f Jameson b.  Benzoic a c i d i n t o water, data of 31  Rao and co-workers c.  E l e c t r o l y t i c redox  reaction,  d a t a o f Rao and co-workers  32  vii  LIST OF FIGURES Page 1.  Film considerations  7  2.  C u r v i l i n e a r c o - o r d i n a t e system  9  3.  Apparatus  4.  D e t a i l e d f i g u r e of t e s t  5.  Data o f L e m l i c h and Levy and o f Goh on t h e  15 section  17  34  c o - o r d i n a t e s o f k/k' v s . Res 6.  E f f e c t i v e surface area of v i b r a t i n g  7.  Data o f L e m l i c h and Levy and o f Goh on t h e \ p c o - o r d i n a t e s o f k / k ' - l v s . Rev(A/A')  8.  Comparison o f t h e p r e s e n t d a t a w i t h t h e p r e v i o u s  cylinder  3  36-b  works on t h e c o - o r d i n a t e s employed by L e m l i c h and Levy  "•  ';  37  i  9.  Comparison o f the p r e s e n t d a t a w i t h the p r e v i o u s works on t h e c o - o r d i n a t e s employed by K n i g h t  10.  Comparison o f e x p e r i m e n t a l r e s u l t s w i t h the Jameson t h e o r e t i c a l  11.  e x p e r i m e n t a l e q u a t i o n ( 1 9 ) o f Rao and co-workers 12.  Comparison o f the p r e s e n t n a p h t h a l e n e d a t a with equation  13.  (20)  Comparison o f the p r e s e n t n a p h t h a l e n e d a t a with equation  (21)  38  41  equation  Comparison o f e x p e r i m e n t a l r e s u l t s w i t h t h e  6-A  44  48  49  Comparison of v a r i o u s e x p e r i m e n t a l with equation  data  (22)  P a t t e r n of s t r e a m - l i n e s i n the neighbourhood of  an o s c i l l a t i n g  circular  \  cylinder  1  LITERATURE SURVEY The nomena has  e f f e c t of v i b r a t i o n or p u l s a t i o n on t r a n s p o r t been r e c e i v i n g i n c r e a s e d  However much of t h i s a t t e n t i o n has c o n v e c t i v e systems, that an  work t h a t has  augment n a t u r a l But  i n recent  been d i r e c t e d towards  been c a r r i e d out  c o n v e c t i o n has  mass t r a n s f e r i n v o l v i n g the of the  earliest  generally  i n the  o b t a i n e d d.n i n c r e a s e  to 500  % by  subjecting  already  attempt  been i n heat  to  transfer.  i n convective  case of v i b r a t i n g s u r f a c e s  as  s i g n i f i c a n t studies  heat  of the  t r a n s f e r problem appears to be t h a t of M a r t i n e l l i and who  forced  i n i t i a t i o n of v i b r a t i o n ;  there have been a number of i n v e s t i g a t i o n s  One  years.  i s , systems i n which t h e r e i s  imposed mean flow p r i o r to the  Most of the  attention  phe-  i n the  well.  Boelter^  heat t r a n s f e r c o e f f i c i e n t of  a 2 cm.,diameter, e l e c t r i c a l l y  up  heated,  c y l i n d e r to a v e r t i c a l s i n u s o i d a l v i b r a t i o n i n water at  freq-  (17) u e n c i e s up  to 40 c y c l e s per  second.  Lemlich  e f f e c t of v i b r a t i o n i n a i r on n a t u r a l from c y l i n d r i c a l wires of 0.3 of 39 to 122 ease i n the  c y c l e s per  cm.  second.  studied  c o n v e c t i v e heat  diameter i n a i r at He  obtained up  the  transfer frequencies  to 300, % i n c r -  heat t r a n s f e r c o e f f i c i e n t .  Deaver, Penny and  Jefferson  c o n s i d e r e d heat  v  from an o s c i l l a t i n g h o r i z o n t a l wire to water and  transfer  were able  c o r r e l a t e t h e i r r e s u l t s , with some s u c c e s s , by the  to  simple  expedient of forming d i m e n s i o n l e s s groups s i m i l a r to those used i n c o r r e l a t i o n s f o r combined f r e e and steady flow past a c y l i n d e r .  forced  Fand and  Kaye  c o n v e c t i o n .in . studied  t r a n s f e r of heat to a i r from a h o r i z o n t a l sound f i e l d  the  normal  2  t o the a x i s o f the c y l i n d e r .  S i m i l a r work was  AnanAnantanarayanan and Ramachandran^  and Van  reported  by  der Hegge Z i j n e n  (30) (29) Tsui  v  '' v i b r a t e d h o r i z o n t a l l y a v e r t i c a l heated p l a t e  i n n a t u r a l c o n v e c t i o n t o a i r and o b t a i n e d i n c r e a s e s i n the c o e f f i c i e n t o f up t o 124 12 8) S h i n e a l s o  %.  In an i n t e r f e r o m e t r i c s t u d y ,  v i b r a t e d a v e r t i c a l p l a t e i n a i r and  i n c r e a s e s of up t o 40 %. v  Kalashnikov  and  obtained  Chernicken^^  found g r e a t l y i n c r e a s e d heat t r a n s f e r f o r a h e a t e r v i b r a t e d a t 1.7  t o 26.7  c y c l e s p e r second i n v a r i o u s l i q u i d s .  Considerable  improvement has a l s o been r e p o r t e d w i t h the use of sound or ultrasound.  However, a l t h o u g h  s i m i l a r i n some ways, v i b r a t i n g  the f l u i d w i t h sound i s not q u i t e the same as d i r e c t l y the s u r f a c e i t s e l f .  vibrating  W i t h sound any a l t e r a t i o n of the boundary  l a y e r comes from w i t h o u t ; w i t h s u r f a c e v i b r a t i o n i t i n i t i a t e s from w i t h i n .  Furthermore f o r most work w i t h sound the  placement amplitude  dis-  i s r e l a t i v e l y s m a l l , while with a v i b r a t i n g  s u r f a c e i t can e a s i l y exceed the d i a m e t e r of the body. T a b l e 1. shows a comparison between some p r e v i o u s i n (12) v e s t i g a t i o n s w i t h r e g a r d t o mass t r a n s f e r . t r a n s f e r r a t e s of benzoic  Jameson  studied  v  a c i d to glycerol-water mixtures  and  o b t a i n e d v a l u e s up t o 28 t i m e s h i g h e r than those due (18)  to free  convection alone.  effect  L e m l i c h and Levy^  ' s t u d i e d the  of v e r t i c a l v i b r a t i o n upon mass t r a n s f e r by s u b l i m a t i o n from s m a l l h o r i z o n t a l c y l i n d e r s of naphthalene and d-camphor t o a i r a t room t e m p e r a t u r e at f r e q u e n c i e s o f 20 t o 118 c y c l e s per second. They o b t a i n e d i n c r e a s e s of up t o 660 % i n the  3  mass t r a n s f e r  coefficient.  A similar  investigation  h a s been  , who v i b r a t e d  a c y l i n d r i c a l sample i n a v e r t i c a l  (8) made by Goh sinusoidal rule,  motion  from  a sample c r a d l e a t t h e end o f a  and o b t a i n e d t r a n s f e r  a s t h o s e due t o f r e e  r a t e s o f up t o f i v e t i m e s a s h i g h  convection alone.  K n i g h t and Ratkowsky  have a t t e m p t e d  the d a t a o f G o h ^ and t h e d a t a o f L e m l i c h and It not  will  steel  to  correlate  Levy^ ^. 1  be shown l a t e r i n t h i s t h e s i s t h a t t h e i r p r o p o s a l i s (2 ^ ) ( 2 4 ) ( 2 5 )  adequate.  mass t r a n s f e r  R a o , R a j u a n d Rao^  J  ;  v  D  ' have  investigated  u s i n g b o t h l i q u i d and gas as t h e f l u i d  T h e y have a l s o p r e s e n t e d  an e x p e r i m e n t a l e q u a t i o n  both kinds o f systems.  Another  similar  medium.  correlating  investigation  h a s been  made by F i k l i s t o v a n d A k s e l r u d ^ ^ ^ , who made a o s c i l l a t i n g 7  motion  of the s o l i d p a r t i c l e s  i n t h e system  o b t a i n e d a n i n c r e a s e i n t h e mass t r a n s f e r to  to  5.65  experiments  However a l l o f t h e a b o v e - c i t e d  have been c o n d u c t e d  numbers a n d t h e r e s u l t i n g  i n a limited  equations  are very  range o f Reynolds dissimilar.  i t r e m a i n s t o o b t a i n an e x p e r i m e n t a l e q u a t i o n  covers t h e l a r g e range o f Reynolds gas  o f up  o f 0.2 t o 0.4 cm a n d l i n e a r v e l o c i t i e s o f 1.1  cm p e r s e c o n d .  Therefore  coefficient  f o r f r e q u e n c i e s o f 3 t o 36 c y c l e s p e r s e c o n d ,  10 t i m e s  amplitudes  CaSO^-H^O a n d  systems.  which  numbers i n b o t h l i q u i d a n d  T a b l e 1.  C o m p a r i s o n b e t w e e n some p r e v i o u s  investigations  w i t h r e g a r d t o mass t r a n s f e r .  author (ref.) (year)  material  Lemlich naphthalene o r d-camphor & Levy into (18) air (1961) Goh (8) (1963) Rao, Raj u, & Rao (23) (24) (25) (1963) (1965)  naphthalene into air benzoic acid into water electrolytic redox r e a c t i o n in pottasium f e r r i - and ferrocyanide naphthalene into air  d i a . o f double sample ampl. cm cm 0 .07  0 .046  i  \  0 .19  Rev  e q u a t i o n  rpm 1200 "  i  7080  3  S  —-, = 0.117  0.12  S  S  01-  100  0.23  0.8  0.253  0.189  1.090  i  3 6000 100  s  s 100  1500 1200  7000 50  0.19  7.66  7080  7000  0.21 $ 1.1  0.30  100  J  I  20 / 190  0.37  S 1.1  1500 3.9 0.1122 30  J  5  1  1  100  50  0.2  300  4  7000  2000  4.0  S  b e  J i - 1 = 0.021 R e v C ^ ) proposed by KrTigri-l &. !?atkt>«wsky 1  J  0.3278 <>  Kes  s  3 .722 0.46  i  =0.038  80  0 .07  J  Res  K  —  J ameson b e n z o i c a c i d i n t o g l y c e r o l 1.10 (12) (1964) - w a t e r m i x t u r e PRESENT n a p h t h a l e n e RESEARCH o r p h e n o l into a i r  0 .766  freq.  1  Sh-0-73O Exp. r e s u l t s  S  /  J  R e  4  C - F / '  are 5 o ~ i o o  Vii^her  'Hia?) - K i i s -f-heo refcica.1 e q u a t i o n  .  5  INTRODUCTION TO  PRESENT INVESTIGATION  I n t h e p r e s e n t i n v e s t i g a t i o n , n a p h t h a l e n e has c h o s e n as t h e s u b l i m a t i o n m a t e r i a l and m e n t a l d a t a have b e e n o b t a i n e d .  considerable  been  experi-  Afterwards the experimental  d a t a a r e compared w i t h t h e p r e v i o u s d a t a o r w i t h t h e d a t a u s i n g p h e n o l o b t a i n e d by t h i s a u t h o r i n l a t e r . e x p e r i m e n t s . The  r e a s o n why  n a p h t h a l e n e has been u s e d i s t h a t i t i s e a s y  t o compare t h e p r e s e n t i n v e s t i g a t i o n w i t h a l l o f t h e p r e v i o u s i n v e s t i g a t i o n s where n a p h t h a l e n e has been e m p l o y e d . naphthalene i s e a s i l y d e a l t w i t h , s i n c e i t i s not  ,  dangerous  except f o r i t s c o m b u s t i b i l i t y .  dangerous  t o use because  a Schmidt  number o f a b o u t  chemically  Phenol i s quite  o f i t s c h e m i c a l n a t u r e , but i t g i v e s 1.8  n a p h t h a l e n e , w h i c h i s 2.56. n o l i s 40.1  Besides,  which i s d i f f e r e n t  from t h a t  Since the m e l t i n g point  of  o f phe-  °C, i t i s e a s y t o make s a m p l e c o a t i n g s and p r o v i d e s  a means f o r t e s t i n g any p r o p o s e d c o r r e l a t i o n w h i c h t h e S c h m i d t number.  The  p i s t o n type of o s c i l l a t o r  s i n c e i t g i v e s more s t a b i l i t y a wire o s c i l l a t o r does.  contains i s used  i n f r e q u e n c y and a m p l i t u d e t h a n  I t was  d e s i g n e d t o s t u d y as h i g h a  r a n g e o f R e y n o l d s number, a s l a r g e a r a n g e o f d i a m e t e r , as l a r g e a.range as  o f a m p l i t u d e and as l a r g e a r a n g e o f f r e q u e n c y  possible. The  about  r a n g e o f v i b r a t i o n a l R e y n o l d s number o b t a i n e d  4 t o 2000 w h i c h was' more t h a n 10 t i m e s as l a r g e a s  o b t a i n e d i n p r e v i o u s i n v e s t i g a t i o n s w i t h gaseous  media.  was that  6  THEORETICAL FOUNDATION  No  p e r f e c t t h e o r y o f t h e t r a n s p o r t o f mass and  f r o m an o s c i l l a t i n g  c y l i n d e r has  b e e n p r o p o s e d up  to  heat  the  (17) present.  However L e m l i c h  has  o f t r a n s p o r t by means o f t h e  e x p l a i n e d the  "stretched-film"  mechanism  concept.  (12) Jameson^  has  d e r i v e d an e q u a t i o n w i t h some a s s u m p t i o n s  using boundary-layer 1.  theory.  S t r e t c h e d - F i l m Concept of Lemlich  suggests  Lemlich^  that there e x i s t s  1 7  ^  a stretched-film  around the o s c i l l a t i n g path of the c y l i n d e r . to apply t h i s transfer. It  concept  With  The if  evidence  f o r mass t r a n s f e r a s w e l l a s  film  surrounds  i n B r a t h e r than  c a r r i e s the f i l m  has  attempted  for  heat  r e g a r d t o t h e p h y s i c a l p i c t u r e , see F i g . 1.  i s argued t h a t the  as r e p r e s e n t e d  He  b a c k and  to support  the wire c a r r i e s  the e n t i r e v i b r a t i n g  t h a t the v i b r a t i n g  f o r t h w i t h i t as  this  cylinder  shown i n  A.  contention i s two-fold.  i t s f i l m b a c k and  First,  f o r t h , t h e r e would  s o m e t h i n g o f a v e c t o r summation o f v e l o c i t i e s  at r i g h t  the r i s i n g  c u r r e n t as  w o u l d n e v e r be  than the v e r t i c a l i n s t a n t s at both On  T h i s v e c t o r sum  current i t s e l f  and,  except  convection  f o r the  c r e s t s o f t h e a n g l e , w o u l d a l w a y s be  t h e o t h e r hand, t h e v e c t o r summation f o r a  moving wire would r e s u l t  i n a net  be  angles  b e t w e e n t h e h o r i z o n t a l l y m o v i n g w i r e and shown i n C.  path  less  two greater.  vertically  a d d i t i o n h a l f the time  and  7  B.  . Stretched  Film  D.  Fig.  1  Film  considerations  Flat  Plate  8  in a cancelling subtraction the  no  difference  z o n t a l and  less than that could  be  other h a l f .  b a c k and  c o n s i d e r e d t o be  the  as  instead  o f mass t r a n s f e r , he  between the  plane  z o n t a l l y or v e r t i c a l l y . l o s s from both surfaces than that  stretched-film  c o u r s e , do concept.  i t s favour.  of the usual  defined,  the  d e f i n i t i o n of the  b a s e d on  the  transfer  other  vibrated  variables to a i r h o r i -  convective i s only  represent rigorous  However t h e y do  heat  4 %  of a h o r i z o n t a l p l a t e .  higher  These  proof of  constitute  this  evidence  " s t r e t c h e d - f i l m " R e y n o l d s number p a r a m e t e r i s ' . t a k e n t o be  double amplitude, i n place of length  Boundary-layer Solution Jameson d e r i v e d  function  not  i t s film  a similar correlation  of a v e r t i c a l p l a t e  length  the  was  Lemlich.  B.  total natural  Thus, i n the  d i a m e t e r and  2.  The  from both surfaces  arguments, of  w h i c h he  in  hori-  Instead i t i s  c o n v e c t i v e heat  found that  surface  carry  i n A.  h e a t t r a n s f e r c o e f f i c i e n t and  e x i s t e d , whether the  e f f e c t of  wire could  indicated  When L e m l i c h i n v e s t i g a t e d  vertical  experiments of  manner i n d i c a t e d  stretched  Thus  for horizontal vibration.  v e r t i c a l v i b r a t i o n i n the  f o r t h i n the  for  found between the  Therefore i t i s u n l i k e l y that  in  the  average e f f e c t i v e v e l o c i t y over a c y c l e  v i b r a t i o n w o u l d be But  during  the  sum  the  parameter, i . e . diameter  only.  (12) of Jameson '  a t h e o r e t i c a l e q u a t i o n from a  stream  (27) boundary l a y e r theory of S c h l i c h t i n g • '  9  This  stream f u n c t i o n  c o n s i s t s o f a s t e a d y component a n d a  n o n - s t e a d y component. the  steady part  that  o f the stream f u n c t i o n , that  t h e mechanism o f t h e t r a n s p o r t  cylinder i s that.of This  J a m e s o n ' s a n a l y s i s i s made o n l y  will  small  only  from t h e o s c i l l a t i n g  when t h e t i m e o f o s c i l l a t i o n  when c o m p a r e d w i t h  means t h a t  flow.  i s very  the c h a r a c t e r i s t i c d i f f u s i o n time  t h e s t e a d y f l o w mechanism w i l l  m i d t number  i s , he assumed  t r a n s f e r i n t o the steady streaming  be v a l i d  on  i s large.  a p p l y when t h e S c h -  The b o u n d a r y l a y e r  approximation  (26) is  valid  only  when R e y n o l d s number i s v e r y  T h e r e f o r e Jameson's e q u a t i o n i s a p p l i c a b l e  large only  when b o t h  S c h m i d t number a n d R e y n o l d s number a r e l a r g e . H i s e q u a t i o n i s d e r i v e d / i n t h e f o l l o w i n g way. e q u a t i o n f o r mass t r a n s f e r i n t o t h e t w o - d i m e n s i o n a l  The  steady  boundary l a y e r i s :  LL 21 3x + with  boundary  X  =0  V 9c  =D  (1)  conditions  0= 0  ^ = 00 ,  C-0  V = 0 ,  c-c*  Fig.  2.  Curvilinear Co-ordinate  system.  10  Very will  c l o s e t o t h e body, t h e v e l o c i t y  be n e g l i g i b l e  Then, e q u a t i o n  so t h a t t h e t e r m  component TJ  may be n e g l e c t e d .  (1) s i m p l i f i e s t o 2  3 X ~ Using  X=  U  3 ^  (2)  YQ J e q u a t i o n  (2)  becomes  by c a r r y i n g o u t a mass b a l a n c e  along a streamline of value  S i n c e t h e v e l o c i t y g r a d i e n t may be assumed c o n s t a n t particular  Q,  t h e v e l o c i t y may be w r i t t e n  unit  f o r any  U=J$y  J& i s t h e v e l o c i t y g r a d i e n t . . Then a s t r e a m  ^  , where  function per  l e n g t h o f c y l i n d e r may be d e f i n e d a s  o I f the t h i c k n e s s of the imagined w h i c h a l l t h e mass t r a n s f e r o c c u r s = y^\  and  2  , where  ^/^—A  '  boundary l a y e r i n  i s ^ , t h e n y,= E  3  u a t i o n  ~jSA  m a v  t  n  e  n  b e  written si,  To t r a n s f o r m t h i s e q u a t i o n i n t o a t r a c t a b l e ^^0=  ^/j^j^ is  ^5  where  ^  i s a function of  zero at $ — 0  •  Then  ^ 2 ^ ^  form, $  one l e t s o n l y and  11  with  boundary  conditions  Y= i  c = o  0.  where the  ,  i s the saturation concentration  surface  of the  This variable equation  dS  with  2  solid.  equation i s solved  S = Y/0 (6)  of the solute at  by t h e i n t r o d u c t i o n o f a  new  > since the s u b s t i t u t i o n reduces  / j  t o the r e a d i l y solvable  form  3DdS  (  boundary  conditions  S = 0 ,  C-  C*  S = oo ,  c-  0  7  )  The s o l u t i o n o f t h e e q u a t i o n i s  •C  is  or  d  e  S  0  -  /dC\  This  C*  •  method o f s o l u t i o n i s i l l u s t r a t e d  i n Mickley,  12  Sherwood and R e e d  (21)  v  .  The d e n o m i n a t o r may be e x p r e s s e d  t e r m s o f t h e gamma f u n c t i o n [""(i).  /dc l  }  _ _  dS S=o  For  /Z  r(i)  calculation  concentration  yields  ( <\V) C* 3D  j  E v a l u a t i o n a t S=0  gradient  o f t h e mass t r a n s f e r  rate, the  i s needed a t t h e w a l l , w h i c h i s r e a d i l y  shown t o be (2SL)  = ± ( i £ )  -  An o v e r a l l mass t r a n s f e r  3  /  3  c  *  0~  Vz  c o e f f i c i e n t may be d e f i n e d a s  •6.  (9) Using it  the relations  i s found  d0/^Q  = "T/^ ^  3  and  ]^ ~~2 h  that  3  where  (10) For  in  the v e l o c i t y  w i t h only the steady  gradient j $ , that i s  p a r t o f j£  being  considered  13  Jf,  Now J a m e s o n e v a l u a t e d Schlichting's  i n (10)  The i n t e g r a l may be c a l c u l a t e d give a value K = 0.5165"  o f 1.198.  d  2/3  n*  by u s e o f t h e gamma  0.750  function  Then  a . 2/5  or r e a r r a n g i n g i n dimensionless  Re* S * ( a / r / ' *  or r e w r i t i n g t h e equation this  Then  fan®  Substituting  5d=  function) using  s o l u t i o n b a s e d on b o u n d a r y l a y e r t h e o r y .  >«=  to  (stream  form, *  (  I D  i n terms o f t h e q u a n t i t i e s used i n  thesis,  :/(>  S^o.qieRe'K^H/d)'  The c o e f f i c i e n t , 0 . 7 ^ 6 , r e p o r t e d i n r e f e r e n c e (12) is i n error.  14  APPARATUS A.  General The a p p a r a t u s u s e d  The c y l i n d r i c a l a perspex used  i s a s i m p l e one a s shown i n F i g . 3 .  sample v i b r a t e s v e r t i c a l l y  w a l l coated with a c t i v a t e d  t o avoid the effect  p r e s e n t i n t h e room.  c a r b o n , t h e box b e i n g  of convection c u r r e n t s which are  V i b r a t i o n I s t r a n s m i t t e d by means o f  a s h a f t c o u p l e d t o an a i r - d r i v e n motor o b t a i n a wider range w i t h an e l e c t r i c  **  B.  , chosen  o f f r e q u e n c i e s than would  i n order t o  be a v a i l a b l e  motor.  1 ft.  • *  i n a box , h a v i n g  X 1. f t .  X 1 ft.  made o f p e r s p e x  s i z e - 2 GB, 14000 RPM. , 1 ^ l b s , 5|f-" l o n g , T h o r Power C o . - L t d . U.S.A.  Detailed 1.  Test  section  As shown i n F i g . 4, t h e o s c i l l a t i n g rods normal  to i t .  s h a f t h a s two  A s a m p l e i s a t t a c h e d t o one o f t h e m .  The o t h e r r o d c a n s e r v e ..as a c o u n t e r b a l a n c e t o m i n i m i z e p o s s i b l e extraneous v i b r a t i o n s .  O r i g i n a l l y , i t was t h o u g h t  t h a t two r u n s c o u l d be t a k e n s i m u l t a n e o u s l y e m p l o y i n g  both  r o d s , a n d t h e t o t a l mass t r a n s f e r r e p o r t e d a s t h e a v e r a g e o f t h e two r u n s . in this box,  way.  an a v e r a g e  However i t d i d n o t p r o v e  f e a s i b l e t o operate  The s a m p l e r o d i s l o c a t e d a t t h e c e n t r e o f t h e d i s t a n c e o f 15 cm. f r o m t h e w a l l s .  15  Fig.  3.  Apparatus.  16  Key  t o F i g . 3.  1.  Cap  2.  Perspex  3.  Ventilation  4.  Plastic  5. •  Air-driven  6.  Frequency  7.  Pressure reducing valve  8.  Instrument a i r compressor  9.  Thermometer  wall  protector motor control valve  10.  Sample  11.  Vibrating  rod  12.  Activated  carbon  13.  Crank  14.  Turning  15.  Connector  16.  Strobo-scope  cylinder  shaft wheel  18  Key t o F i g . 4.  1.  Sample  cylinder.  2.  Rod  3.  I n t e r n a l • v i b r a t i n g shaft '  4.  Activated  5.  Bottom  6.  Seal  7.  Shaft  8.  External v i b r a t i n g shaft  9.  Vibration  carbon  plate  supporter  stabilizer  10.  Screw  11.  Shaft  12.  Crank  13.  P l a t e f i x e r No.  1  14.  P l a t e f i x e r No.  2  15.  Turning  16.  Travelling plate  17.  Vibration  supporter shaft  wheel  transmission  ( A l l u n i t s are i n m i l l i m e t e r s )  19  2.  Amplitude As  shown i n P i g . 4 , a t r a v e l l i n g p l a t e  w i t h two screws motor. can  on a t u r n i n g wheel c o n n e c t e d  Thus any double  be o b t a i n e d .  microscope  amplitude  The a m p l i t u d e  c a n be f i x e d  to the air-driven  i n .the r a n g e  up t o 5 cm  i s measured w i t h a t r a v e l l i n g  by o b s e r v i n g t h e u p p e r a n d l o w e r c r e s t s o f t h e  r o d on v i b r a t i o n . V e r n i e r M i c r o s c o p e No. 13, I n s t r u m e n t No. 14387, The P r e c i s i o n T o o l a n d I n s t r u m e n t Co. L t d . , ENGLAND.  *  3.  Frequency \  The  frequency  o f t h e v i b r a t i o n i s c o n t r o l l e d by  r e g u l a t i n g t h e p r e s s u r e s u p p l i e d t o t h e motor from t h e i n s t r u ment-air  compressor  located  Engineering Building. strobo-scop.e t u r n i n g wheel.  i n t h e basement o f t h e C h e m i c a l  The f r e q u e n c y  i s measured w i t h a  by o b s e r v i n g t h e f l a s h l i g h t To m i n i m i z e  pressure reducing valve  r e f l e c t i n g on t h e  the a i r pressure deviation, a  i sinstalled  a t the compressor.  T h u s t h e f r e q u e n c y c a n be c o n t r o l l e d w i t h i n a f e w p e r c e n t o f its  value throughout  an o p e r a t i o n .  A steady s i n u s o i d a l motion  o f t h e sample i s o b t a i n e d  (see appendix I - l ) . * M o d e l 116A, I n p u t 115 V, 600 t o 15000 RPM. R.H. N i c h o l s L t d . , CANADA. **  C l a s s t y p e #ASG 3 , Form X, s w i t c h o p e n s ' a t 100 l b s / i n c l o s e s a t 80 l b s / i n D. S q u a r e C o . L t d . , U.S.A. 2  2  20  4.  Carbon-coated The  about  Wall  four inner  s u r f a c e s o f t h e box a r e c o v e r e d  20 grams o f a c t i v a t e d  carbon  which adsorbs  (or p h e n o l ) , keeping the vapor p r e s s u r e i n s i d e gibly *  small  (see appendix  L o t No.  5.  naphthalene  t h e box  negli-  1-2).  1.2241, J . T . B a k e r  C h e m i c a l Co.,  U.S.A.  Temperature The  thermometer  temperature  i n s i d e t h e box  w h i c h has been c a l i b r a t e d  a s t a n d a r d thermometer. since  with  such a c o n t r o l would  No  i s measured u s i n g by c o m p a r i n g  temperature  i t with  c o n t r o l i s attempted  t e n d t o cause e d d i e s i n the a i r .  However i f t h e t e m p e r a t u r e has v a r i e d more t h a n 0.2  °C  t h e o p e r a t i o n , t h e e x p e r i m e n t a l r u n i s s t o p p e d and t h e  during results  i  discarded.  6.  Total Pressure A t m o s p h e r i c p r e s s u r e i s m e a s u r e d by t h e  l o c a t e d on t h e t h i r d Building.  a  barometer  f l o o r of the Chemical E n g i n e e r i n g  EXPERIMENTAL In' t h i s outlined,  section  the experimental  and t h e method o f a t t a i n i n g  presented,  these  along with the experimental  Experiments  o b j e c t i v e s are  procedure.  were s e t up t o o b t a i n d a t a  compared w i t h p r e v i o u s work and t o f i n d between t h e mass t r a n s f e r Therefore  1.  up t o a t e m p e r a t u r e The c y l i n d e r  steel.  This cylinder  and o t h e r  were  slightly  t o be c o a t e d  correlation  variables.  employed.  placed  i n a bath  cooled  cylinder  material,  T h i s procedure surface  was t h e n  of a cylinder  ends  blade  to give a  of salt  q u i c k l y plunged  i n a thin, without  uniform  into  uniform  to sublimate  This  the molten removed.  c o a t i n g on t h e being  formed.  m a t e r i a l were c u t w i t h After  being  and i c e .  and q u i c k l y  large crystals  length.  h o u r s t o make t h e s u r f a c e Naphthalene Phenol  the melting  benzene, t h e v e s s e l i t s e l f  of the c y l i n d r i c a l  was a l l o w e d  , was  was made o f s t a i n l e s s  f o r a few s e c o n d s ,  results  Both  higher than  c o n t a i n i n g a mixture  held there  or phenol  was washed and c o o l e d by i m m e r s i n g i t  a vessel containing cold  * **  the proper  sample m a t e r i a l , n a p h t h a l e n e  point.  sample  w h i c h c o u l d be  Sample C y l i n d e r C o a t i n g  heated  few  coefficient  the f o l l o w i n g procedures  The  in  objectives Is  a razor  that the c y l i n d r i c a l  by n a t u r a l c o n v e c t i o n f o r a  smoother.  9 9 - 9 9 3 % p u r i t y , A l l i e d C h e m i c a l Co., U.S.A. 99-95 % p u r i t y , B r i t i s h D r u g Houses L t d . , ENGLAND  22  2.  Operation of  Experiment  The d i a m e t e r o f the c y l i n d r i c a l sample was measured w i t h a c a l i p e r , an average v a l u e b e i n g t a k e n from t h r e e p o i n t measurements. scale.  The  The l e n g t h o f the sample was measured by a sample was t h e n weighed on a b a l a n c e whose  r e a d i n g s were r e p r o d u c i b l e t o w i t h i n +0.0001 g. the sample was  After that  f i x e d t o the r o d i n s i d e the box.  When a  l a r g e d i a m e t e r sample was used i n a v i b r a t i o n w i t h a h i g h f r e q u e n c y and a l a r g e a m p l i t u d e , the same s i z e s t e e l was put on the o t h e r r o d t o h e l p c o u n t e r b a l a n c e the  cylinder sample.  Opening t h e v a l v e l e a d i n g t o the source o f compressed a i r , the v i b r a t i o n was  started.  w i t h a stop-watch.  The  Time o f o p e r a t i o n was  measured  f r e q u e n c y was o f t e n measured w i t h  j t h e s t r o b o - s c o p e t o check i t s c o n s t a n c y .  A f t e r about  30  minutes o f o p e r a t i o n , the sample was t a k e n out and weighed a g a i n and the weight d i f f e r e n c e was r e c o r d e d .  The a i r  t e m p e r a t u r e i n s i d e the box was a l s o measured by a thermometer. I f t h e f i n a l temperature d i f f e r e d from the i n i t i a l by more t h a n 0.2 3.  °C, the experiment was  temperature  rejected.  P r o c e s s i n g o f Data I n t h i s s u b s e c t i o n the-.procedures f o r c o l l e c t i n g  p r o c e s s i n g the d a t a are g i v e n .  and  The d a t a o b t a i n e d from a  s i n g l e e x p e r i m e n t a l r u n c o n s i s t e d o f an a i r temperature  T,  an a t m o s p h e r i c p r e s s u r e P, an average d i a m e t e r d, a sample  length  , a double  time t , a weight The  a m p l i t u d e .of o s c i l l a t i o n H,  d i f f e r e n c e W and  o b j e c t of the present  an o p e r a t i o n  an a v e r a g e f r e q u e n c y set of experiments  compare t h e p r e s e n t d a t a w i t h p r e v i o u s work and a proper  correlation.  Therefore  were a mass t r a n s f e r c o e f f i c i e n t , number, v i b r a t i o n a l R e y n o l d s  what had  to  t o be  f.  was  to  present  calculated  stretched-film  Reynolds  number, S c h m i d t number, S h e r w o o d  number and  the r a t i o of the double  amplitude  In  a l l c a l c u l a t i o n s i t was  assumed t h a t a i r i s an  i d e a l gas.  I t i s b e l i e v e d that t h i s assumption  cause a s i g n i f i c a n t The  to the  e r r o r i n t h e v a l u e s o f any  diameter.  does  of the  not factors  v a l u e s o f e a c h o f t h e c h a r a c t e r i s t i c s were o b t a i n e d  as  follows. (1)  Viscosity S i n c e the' v a p o r  p r e s s u r e o f sample m a t e r i a l I s v e r y  s m a l l compared w i t h t h a t o f a i r , t h e v i s c o s i t y  and  the d e n s i t  of  The  equation  for  fluid  employed i s t h a t of the a i r i t s e l f .  viscosity  / * -  (2)  i s i n 3 r d e d . , p.370 o f  ^ 7 0 . G * id'*  ref.(22).  ( ^ - J  ( 1 2 )  Density The  e q u a t i o n f o r d e n s i t y i s d e r i v e d from the  ideal-  gas lav;.  j,-  ,.  ,,o- ,(iip)(_E_) 3  2 W  (  j  /  C  B  , ,  ( 1 3 )  24 (3)  Diffusion The  coefficient  H i r s c h f e l d e r , B i r d , and  Spotz  f o r the e s t i m a t i o n of the d i f f u s i o n other than  P  ,  25  °C.  "  *  ^  (31)  coefficient  at  i s used temperatures  '  I„  Pr,\  method  (14) -Of.  where  -  B = (\o.i  -2.4.4 ^ / M , \  «/M  )*  t  >  1 0  l s  i n t e g r a l w h i c h i s a f u n c t i o n o f K T / £ , where  i s the  a  of molecular  interaction.  the c o l l i s i o n  diameter,  absolute temperature, are the m o l e c u l a r The  value of  6  >a  IZ  having  42 and  weights  of  represents  from the observed  ' P' ^  1 1  components,  62  and  respectively.  value of  a t 25°C, t h e c o l l i s i o n ,  the diameter  from Table  14-  ref.(22).  Mass t r a n s f e r The  o f t h e two  i s obtained  14-44  energy  K i s the Boltzmann constant, T i s the  been c a l c u l a t e d u s i n g v a l u e s o b t a i n e d  Table  (4)  I n the above e q u a t i o n ,  P i s t h e t o t a l p r e s s u r e , and  diffusion coefficient^ V  collision  t h e  coefficient  mass t r a n s f e r  coefficient  (cm/sec) i s g i v e n  as  p  t h e mass t r a n s f e r f l u x (g/cm  ).  The  (g/cm  s u r f a c e of the  i n the b u l k of the f l u i d . calculated  The  s o l i d and  from the vapor p r e s s u r e  bulk of the f l u i d  the  at the  i s t a k e n t o be  the  concentration  c o n c e n t r a t i o n at the  e v a l u a t e d at the wet-bulb temperature. i n the  force  d r i v i n g f o r c e i s the d i f f e r e n c e between  c o n c e n t r a t i o n at the  is  s e c ) d i v i d e d by d r i v i n g  surface  surface which i s  The  concentration  zero  (see appendix  1-3).  25  RESULTS In t h i s s e c t i o n the c a l c u l a t e d r e s u l t s of the data of the present i n v e s t i g a t i o n and the data of the p r e v i o u s workers, which are used  i n the D i s c u s s i o n  ( O r i g i n a l data are presented  1.  The A.  Present  The A.  Investigation  2.  Phenol Table  2.  i n appendix  Naphthalene Table  B.  3-  Previous  Investigations  Gaseous systems \ Table 4 . a, b, c  B.  s e c t i o n , are  Liquid  systems  Table 5. a, b, c  \  IV)  presented.  26  Table 2.  R e s u l t s o f the p r e s e n t i n v e s t i g a t i o n f o r naphthalene.  NO.  K/K"  A/A'  RES  REV  H/d  SC  •• SH  301 5.142 1.320 97.32 64 . 7 6 0 . 5 0 3 2 . 5 3 1 9.725 302 1.659 1.320 75.87 50 . 4 9 0 . 5 0 3 2 . 5 3 1 3.137 303 L.98 8 1.304 99.60 6 7 . 4 4 0 . 4 7 7 _2_. 5 2 7 3.923 304 3 . 135 1.296 121.23 8 2 . 7 5 0 . 4 6 5 2. 527 6.328 305 3 . 189 1.304 120.71 8 1 . 7 3 0 . 477 2 . 5 2 6 6.255 306 3.629 1.304 125.89 8 5 . 2 4 0 . 477 2 . 5 2 6 7.117 401 5.84 7 1.308 182.50 1 2 3 . 0 5 0 . 4 8 3 2 . 531 1 1 . 4 7 9 402 6.926 1.338 171.32 1 1 1 . 8 7 0 . 5 3 1 2 . 531 1 2 . 3 6 2 501 _5_.520__ 1.304 80.28 54 . 3 6 0 . 4 7 7 2 . 5 2 8 J J L . 0 7 5 . 502 5.232 1.312 78.89 5 2 . 9 6 0. 489 2 . 528 1 0 . 0 4 3 601 1.057 1.329 42 . 2 7 2 7 . 8 5 0. 517 2 . 524 2.102 602 2.318 1.331 7 8 . 79 51 . 8 3 0 . 5 2 0 2 . 5 2 4 4.586 701 3.076 1.363 8 1 . 9 9 52.22 0.570 2.531 5.676 702 3.252 1.304 137.27 92.87 0.478 2.528 7 . 1 1 0 703 3.-788 1.366 156.47 9 9 . 3 5 _P_. 3I_5_ _ 2 . 5 2 6 6 .829 801 4.29 1 1.332 ,182. 34 1 1 9 . 8 5 0 . 521 2.524 8 .482 802 1.783 1.351 54. 8 9 35 . 3 7 0 . 5 5 2 2 . 5 2 4 3 .329 1 10 1 2.943 1.380 71.03 4 4 . 4 7 0 . 59 7 2 . 5 2 5 5 .612 3.004 1102 1.370 79.66 5 0 . 4 0 0 . 581 2 . 5 2 4 5 .877 1 103 3.720 1.350 203.37 1 3 1 . 2 4 0. 550 2 . 5 2 5 7 .716 1104 1.618 1.369 50.64 3 2 . 0 7 0 . 57_9. 2 . 5 2 4 3 . 176 1201 1 .505 1.449 40.10 ! 2 3 . 5 2 0 . 705 2 . 5 2 0 2 .915 1301 2.956 1.633 144.21 7 2 . 2 9 0 . 995 2 . 5 2 0 5 .613 1302 6 .907 1.637 301.86 1 5 0 . 9 3 1 . 0 0 0 2 . 5 2 0 13 . 0 4 6 1303 2.922 1.642 127.90 63 . 7 0 1. 008 2 . 5 1 8 5 .440 1304 4.129 1.606 190.72 97 . 6 8 0 . 9 5 3 2 . 5 1 9 8 .141 1J05_ 1.438 1.609 65.37 3 3 . 4 0 J L - _9.57_ 2 . 5 1 9 2 .824 1801 8.727 3.246 1012.93 2 2 3 . 6 9 3 . 5 2 8 2 . 5 2 9 17 . 1 9 6 1401 4.756 1.625 89.96 45 . 3 9 0 . 9 8 2 2 . 5 2 0 9 . 143 1402 7.979 1.625 296.17 1 4 9 . 4 3 0 . 9 8 2 2 . 5 2 0 15 . 3 2 9 8.595 140 3 1.628 283.61 1 4 2 . 7 3 0 . 9 8 7 2 . 5 2 0 16 . 4 2 7 14 0 4 1 2 . 9 0 5 1.640 376.95 187 . 9 8 1. 005 2 . 5 2 0 24 . 2 1 6 _ _ 1 . 5 . Q 1 _ __9_.A9_6„ _ _ L . A 5 _ 9 _ _2.3_7.._6_4_ _ U . 6 _ . . 7 6 _ _ L . . 0 3 3 _ _ 2 . . 3 „ 2 2 _ JUL . 3 2 3 1502 1 0 . 4 9 2 1.616 277.71 1 4 1 . 1 9 0 . 967 2 . 5 2 2 20 . 4 7 7 1503 1 0 . 4 9 2 1.616 277.71 1 4 1 . 1 9 0 . 967 2 . 5 2 2 20 . 4 7 7 1504 5 .903 1.532 268.38 1 4 6 . 2 1 0 . 8 3 6 2 . 5 2 3 13 . 3 8 8 1505 7.116 1.628 216.30 1 0 8 . 8 6 0 . 9 8 7 2 . 5 2 4 13 . 6 7 9 1506 3.323 1.649 133.70 6 6 . 2 3 1. 019 2 . 5 2 4 6 .202 1507 1.596 1.650 54.42 2 6 . 9 2 JU 02.1_ _ 2 _ . 5 2 5 _ _ 2 _ . 9 7 6 1601 2.572 9.331 545.94 1 5 7 . 3 4 2 . 4 7 0 2 . 5 2 6 18 . 5 6 5 1602 4.990 2. 572 239.89 6 9 . 1 4 2 . 4 7 0 2 . 5 2 7 •' 9 . 9 3 4 160 3 7.675 2. 596 558.60 1 5 9 . 2 5 2 . 5 0 8 2 . 5 2 7 15 . 0 5 0 1604 8 . 5 16 2.626 630.59 1 7 7 . 4 6 2 . 5 5 4 2 . 5 2 7 16 . 4 2 0 1605 8 .494 2.617 542.53 1 5 3 . 2 5 2 . 5 4 0 2 . 5 2 7 16 . 4 6 4 . 1_70_1_ 7 . 7 5 4 3..218 8 6 . 6 1 JL: A 8 3 _ _2..5.2.6_ _1.5. . 3 2 9 388.32 1702 1 3 . 4 3 1 3.264 1374.64 3 0 1 . 7 3 3. 556 2. 526 26 . 0 0 9 1802 1 3 . 6 5 8 3.270 1146.59 2 5 1 . 1 6 3 . 565 2 . 5 2 9 26 . 6 3 4 1803 1 1 . 5 0 9 3.300 1059.69 2 2 9 . 7 6 3. 612 2 . 5 2 9 22 . 1 5 1 J  continued  !  27  NO.  A/A •  RES  teo^- 1 1 . 9 9 2 3 . 2 94 1 0 9 7 . 4 7 8.069 3.349 489.09 iaos 1901 _1 2. 3 . 2 4 6 1 3 5 4 . 4 1 1902 1 0 . 1 9 0 3.051 919.99 9.641 1903 3.070 971.36 2001 7 . 166 3.258 405.16 2002 7.616 3.276 523.53 2003 1 1 . 1 2 5 3.235 1143.10 _2.10.1__1.2_._3 5 9 4.334 1792.48 2102 8.290 4.342 1145.15 2103 1 6 . 9 5 9 4.393 1076.19 2104 6.155 4.437 465.79 2201 8.409 4.428 724.74 2202 9.151 4.472 970.06 2203 9.904 4.428 1170.21 2301 2.426 1.226 10.89 2302 1.384 1.229 21.68 2303 2.597 1.230 \ 36.65 2401 1.920 1.241 68.89 2402 1.388 1.227 53.51 .2,5 0.1 1...968 _1.2_35 6 5 ..4 5 6 5 . 96 2502 1.235 2 .07 2 2503 1.227 1 .65 2 6 1 . 16 1.237 7 5 . 69 2601 1 .522 2602 1.244 7 . 37 1 .465 2 603 1.247 1 .089 6 . 62 2702 2 .745 1 . 2 39 6 6 . 03 2 703 1.253 1 .938 5 6 . 60 2801 5 .52 8 1.921 1 8 5 . 67 4 . 193 2802 1.934 51 . 05 1.951 2803 6 .720 229.09 3 .594 1.348 290,1 4 0 3 . 76 5 .10 6 6 1 0 . 13 1.350 L_2902 4 1 1 . 15 • 3 0 0 1 10 . 9 6 5 1.898 ! 3002 10 . 5 7 7 1.909 4 2 3 . 38 ! 3101 1.350 2 .814 3 3 5 . 37 1.354 i 3102 3 .758 . 4 4 8 . 29 1 310 3 5 .512 1 . 3 50 6 2 9 . 57 3104 4 .995 1. 342 6 0 9 . 74 3105 1 . 344 1 .88 3 3 3 3 . 18 247.51 3106 1.346 1 .967 3107 4 .625 1.348 5 4 2 . 33 4 .807 1.346 6 1 4 . 40 3108 3109 3 .829 5 96.11 I. 346 . 6 5 9 _ 2 1 . 3 4 9 3 5 5 . 73 3110_ 2 5 6 . 69 3111 1 .675 1 . 350 6 .70 2 3112 8 1 1 . 82 1.350 3113 1.35 9 6 .732 8 4 3 . 94 3114 1.326 1 .486 2 6 2 . 55 .  ;  K/K •  :  REV 238.44 104.28 299 . 1 0 217.95 228.46 89 . 11 114.45 253.44 287.40 183.22 170.02 72.80 113.51 150.29 183.29 8.04 15.96 26.93 49.98 39.45 47 . 8 3 48 . 2 0 . 45.10  i  55.16 5 .33 4.77 48 . 0 1 40.49 75 . 8 6 20 . 7 0 91 . 8 4 260.95 393.63 170.58 174.33 216.37 288.19 406.32 396.68 216.24 160.30 350.63 397.93 38S . 2 1 229.03 165.60 523 . 5 7 539 . 5 7 173.69  I 1  H/d  SC  SH  3 . 603 2 . 5 2 6 2 2 . 9 9 4 3 . 690 2 . 5 2 6 1 5 . 1 2 2 3.528 2.527 27.803 3 . 221 2 . 5 2 7 2 1 . 8 8 4 3.252 2.526 20.482 3 . 547 2 . 5 2 8 1 4 . 0 2 4 3.574 2.528 14.788 3.510 2.528 21.998 5 . 2 3 7__2_._5 2 4 _ 2 4 . 7 6_5 5.250 2.524 16.559 5.330 2.528 33.807 5.398 2.528 12.114 5.385 2.532 16.737 5.455 2.532 17.981 5.385 2.531 19.648 0.354 2.531 4.907 0.359 2.530 2.762 0.361 2.530 5.155 0.378 2.529 3.612 0.356 2.529 2.773 0 . 3 6 8 2 . 529 3 . 78 6 0 . 3 6 8 2 . 528 3.982 0 . 356 2 . 528 3 .280 0 . 372 2 . 528 2 .899 0 . 3 8 4 2 . 528 2 .699 0 . 3 8 8 2 . 527 1.976 0 . 3 7 5 2 . 539 5 .368 0 . 398 2 . 537 3 .554 1 . 447 2 . 532 10 . 7 25 8.034 .1 . 4 6 7 2 . 532 1 . 4 9 5 2 . 531 12 . 6 0 2 0 . 5 4 7 2 . 533 18 . 4 7 2 0 . 5 5 0 2 . 532 26 ._05_8 1 . 4 1 0 2 . 528 21 . 6 4 1 1 . 4 2 9 2 . 5 2 8 20 . 6 3 5 0 . 5 5 0 2 . 530 14 . 3 9 7 0 . 556 2 . 529 18 . 8 7 7 0 . 549 2 . 529 28 . 0 6 1 0 . 5 3 7 2 . 529 26 . 0 1 4 0 . 5 4 1 2 . 527 9 .666 0 . 544 2 . 530 10 . 1 3 9 0 . 5 4 7 2 . 530 23 . 7 7 8 0 . 5 4 4 2 . 529 24 . 7 3 3 0 . 543 2 . 5 2 9 19 . 7 2 0 _ 0 . 54_8_ 2 . 53_0__13_.6J..2 8 .452 0 . 5 5 0 2 . 526 0 . 5 5 1 2 . 526 33 . 7 2 9 0 . 564 2 . 5 2 6 33 . 0 4 4 8 .058 0 . 5 1 2 2 . 526  continued  28  NO.  K/K«  3115 6 . 5 74 3201 5 . 920 __3_2_0_2___6_. 0 0 3 3203 5 . 129 3204 5 . 180 4 . 78 0 3 20 5 7 . 228 3206 3 2 0 7 11 . 0 7 7 __3.3.0 L ._1.6_. 17 7 ; 3 3 0 2 1 6 . 851 3 3 0 3 11 . 6 2 3 3304 1 5 . 99 5 : 3305 1 5 . 788 3 4 0 1 2 6 . 392 3.50 i __2_8. 7 2 9 3 5 0 2 30". 68 0 3503 2 1 . 472 3504 1 9 . 211 3505 1 9 . 485 3506 2 0 . 089 —35_Q7__25_. 0 3 0 :  A/A«  RES  REV  H/d  SC  SH  1 .347 061. 89 557 . 6 3 0 . 546 2 . 526 3 3 . 4 2 7 1 .617 7 9 0 . 05 401 . 19 0 . 9 6 9 2 . 5 2 4 2 9 . 6 6 1 1 .619 9 9 0 . 98 502 • A 9 _ _0_• 9_72__2.- _525__30_..008 554.63 1.622 2 8 0 . 5 4 0 . 9 7 7 2 . 528 2 6 . 037 671. 79 1 .623 339 . 4 7 0 . 9 7 9 2 . 528 2 6 . 211 1 .625 867. 5 4 437 . 7 3 0 . 982 2 . 526 2 3 . 9 8 4 1 . 6 2 5 1 5 4 3 . 11 778 . 6 0 0 . 9 8 2 2 . 527 3 6 . 291 1 . 6 2 5 .1878. 0 9 94 7 . 6 1 0 . 9 8 2 2 . 527 5 5 . 6 8 9 2 ...2.8 3__5 622.. 06_ _L864. •_33_.2 . _ Q i 6 _ _2.. 538 _86_. 68.1 = 2 . 2 8 6 4 8 9 4 . 32 1620 . 8 9 2 . 0 2 0 2 . 5 38 9 0 . 056 , 2 . 2 8 9 4 4 9 2 . 2 3 1484 . 8 0 2 . 0 2 5 2 . 535 61 . 345 2 . 2 9 6 4 8 1 1 . 97 1585 . 2 7 2 . 0 35 2 . 537 8 4 . 642 : 2 . 3 0 2 4 6 3 1 . 81 1520 . 8 7 2 . 0 4 5 2 . 5 3 7 8 3 . 074 4 . 5 7 8 3 8 9 0 . 33 587 . 7 0 5 . 6 2 0 2 . 537 5 0 . 5 8 4 : 4 . 6 0 7 .3564. 0 4 534 . 6 8 5 . 6 6 6 2 . 531 5 3 . 6 7 0 4 . 4 6 5 4 7 7 1 . 31 740 . 6 4 5 . 4 4 2 2 . 533 5 9 . 182 4 . 5 9 7 2 7 0 3 . 02 406 . 4 5 5 . 6 5 0 2 . 532 3 9 . 8 67 i 4 . 6 5 7' 2 8 1 5 . 01 417 . 3 8 5 . 7 4 4 2 . 531 3 4 . 9 1 7 . 4 . 3 9 3 2 6 2 2 . 95 4 1 4 . 3 7 5 . 330 2 . 5 2 9 3 8 . 540 I 4 . 4 6 5 2 9 5 6 . 38 458 . 9 1 5 . 4 4 2 2 . 529 3 8 . 9 1 6 * 4 . 5 4 9 3 9 8 7 . 25 6 0 6 . 5 1 5 . 5 7 4 2 . 529 4 7 . 3 0 8 i  ( i  29  Table,. 3 .  Results o f the present i n v e s t i g a t i o n f o r phenol.  NO.  SH  1 14.195 2 16.776 _3__1.1.._5.4_1_ 4 21.514 5 24.933 6 26.711 7 31.016 8 .9.68 8 __9_A4_..2_7.0_ .10 4 5 . 8 2 0  SC  REV  1.86 2 5 5 . 1.86 2 4 3 . -.L._06__1.24_. 1.86 2 7 8 . 1.86 304. 1.86 3 6 7 .  H/d  0.54 7 0.549 -0_..55_0_ 0.539 0.545 , 0. 545 6 0.550 1.86 3 7 2 , 1 0.550 1.86 199, J-..8AL6.8.2., J _ 4 . . . 2 . 2 3 _ j 1.86 5 8 8 , 7 4 . 2 6 5 I  30 NO'.  !  SH  SC  REV  H/d  Table 4-a.  Naphthalene  Into a i r , data o f Rao and 17.2 0.882 1 2 .:9 28 2.58 2 3.620 2.58 28.7 1.471 co-workers. 3__ 5.0 57._.2..58__40...2__2_.059_ 2.58 54.5 2.794 4 6.122 5 7.4 53 2.58 64.6 3.309 1 6 7.985 2.58 84.6 4.338 2.58 114.8 5.882 7 9.050 8 3.891 2.5 8 38.6 0.606 '.These v a l u e s are o b t a i n e d 9.__7.226._2.58.__ 89..9_ _1.. f-08_ from f i g . 1 o f r e f . ( 2 5 ) . 10 8.615 2.58 116.8 1.831 11 13.340 2.58 186.9 2.930 12 15.007 2.58 2'24.7 3.521 5. 132 2.58 3 9.3 0.391 13 14 9.72 3 2.58 145.6 1.449 .15. 12.694 2.58 _1.89_._2_ 1.884 16 15.665 2.58 254.7 2.536 17 7 .;226 2.58 60.7 0.380 18 11.116 2.5 8 179.7 1.127 19 17.786 2.58 337.0 2.113 1  N O'm 1 2 .3 4 5 6 7 8 9 10 .1:1  NO'.  SH  5.553 3.476 1.43J 6.27 2 2.2 98 5.746 4.117 2.873 1 . 191 2.440 4.200  SH  1 7.713 2 6.427 _3„,.5....6.9.3 4 5.142 5 4.958 6 3.673 7 2.-755  SC  REV  2. 5 8 2. 58 2_. 58 2. 5 8 2, 58 2, 58 2. 58 2, 58 _2 , 58 2, 58 2, 5 8  SC  H/d  .28.8 19.2 9.6 42.9 21.4 37.2 3 3.9 27.2 20.3 14.4 32.2  REV  Table 4-b.  Naphthalene  and d-camphor Into a i r ,  3.0 2.0 1.0 2.0 1.0 1.1 1.0 0.8 0.6 1.5 1.5  data o f L e m l i c h and Levy,  These v a l u e s are obtained from f i g . 2 o f r e f . ( 1 8 ) .  j Table 4-c.  H/d  Naphthalene  i n t o a i r , data o f Goh. 2.60 48.9 1.761 2.60 110.5 0.032 2. 6.0 95...1 ..0...1.56„ 2.6 0 36.4 1.032 2.60 25.7 1.525 2.60 16.6 1.787 • These v a l u e s are obtained 2.60 16.3 0.596 i from f i g . 1 and f i g . 3 1  of r e f . ( 1 6 ) .  31  NO.  SH  SC  REV  H/d  Table 5-a. Benzoic  acid  into glycerol-water, 1 267 . 3.23 1. 1 0. 196 2 485. 3.23 2.2 0.196 d a t a o f Jameson. 3 _566.._._3..23__.2 . 5__0...102_ 4 825 . 3.23 3.2 0.196 5 805. 3.23 4.3 0.102 6 10 15. 3.23 5.1 0.298 These v a l u e s a r e o b t a i n e d 7 871. 3.23 6.4 0. 102 8 1214. 3.23 7.0 0.196 from f i g . 3 o f r e f . ( 1 2 ) . _9„.1.0.6.7„.___ 3 . . . 2 3 _ _1XL..2__0.,_2.9„8 : 10 1772 . 3.23 9.5 0.196 11 1580. 3.23 22.3 0. 198 12 1562. 3.23 24.8 0.298 13 2407 . 3.23 47.7 0.198 ,  NO.  SH  SC  REV  H/rj  .1 0 3.33 897. 135. 2.400 2 112.45 897. 220. 2.400 3 163.95 __897. 400. 2.400 4 .236.2 8 8 97. 700. 2.400 5 27'3.41 897. 900. . 2.400 6 289.32 897. 1G00. 2.400 7 46 2.92 897. 2000. 2.400 8 617.22 897. 3200. 2.400 9 694.38 097. 4000. 2.400 .10 925.84 897. 6000. 2.400  T a b l e 5-b. B e n z o i c  acid  i n t o w a t e r , d a t a o f Rao and  co-workers.  from f i g . 5 o f r e f . ( 2 3 )  32  T a b l e 5-c. **  Sc  J * 10  889. 889. 889. 889. 889 . . 889. 889 J .  Electrolytic  Rao and c o - w o r k e r s .  Rev  6.17 12.7 222.8 4.70 19. 7 4 5 3.9 4 . 07 24.9 6 60. 7 29. 1 3f. 4 8 905.7 3.22 33.8 1135.0 3 . 0 1 . . ....39.1 1406.0 . 2.82 41.3 1584.9 089.1 2 . 69 46 . 2 1862.1 889 2 . 52 50.7 2177.7 889.2 . 37 54.9, 2511.9 889.: 2.26 5 7.9 2766.9 88 9.3 2 . 1 8 62.2 .. .3083.2 . 8 89.i 2 . 0 9 65.6 3396.3 889. 1.99 69.6 37 8 4 . 4 1025. 5.51 12.5 223.9 1025. 4.21 19. 3 451.9 1025. 3.20 30.2 929.0 1 0 2 5 . . . . 2 . 9 5 _ . . . 3 3 . 9 ...J 1 2 9 . 8 . . 1025.i 2 . 7 2 391. 1 14 1 5 . 8 1025. 2.58 1606.9 42.2 10 25.1 2 . 4 0 1949.8 47". 7 1025 . 2 . 31 51.8 2 2 0 2.9 1025. 2.14 2511.9 54.7 1025. 2 . 0 1 . . . ..-57.4..... . 2 8 0 5 . 4 . 1025. 1 . 95 61.8 3113.9 1.89 1025. 3451.4 66.2 1025. 1 . 82 38 1 0 . 7 70.3 1925. 4.55 8.6 121.6 1925.S 2 . 92 10.7 237 . 1 1 9 2 5 . 1 . 2 . 9 2 . _ ... 1.6.0.. . _...3 5 4 . 8. 19 25.1 2 .6.1 478.6 19.3 19 2 5.; 2 . .12 20.3 618.0 1925. 22.7 755. 1 1.95 1925. 1.91 26.6 899 . 5 19 2 5.1 2 . 03 995.4 31.3 1925. 1 .90 ..31.9 . 1 0 8 3 . 9 . ... 1925. 1.86 34.2 1188. 5 1.77 1925. 37 s.2 1355.2 1925. 1.58 15 2 4 . 1 37.3 1.57 1925. 41.3 1694.3 1925. 1.61 4 5.9 1840 . 8 1 . 5 7 . . ... 5 0 . 8 .20 8 9 . 3 . 1925. 2 2 3 9 . 3 . 76 7. 7 120.2 10.4 22 3 9 . 2 . 52 241.0 2 2 39.; 2 . 4 8 15. 1 3 5 6. 5 22 3 9 . . 2 . 2 4 18.4 479.7 2239. 1.91 20 . 0 613.8 2 2 3 9 . . 1 . 7 0 . . . . 2 1 . 8 . .. . . 7 . 4 9 . 9 2 2 3 9 . 1 . 67 2 5.5 89 3.3 997.7 2239. 1 .74 29.7 1061.7 22 3 9 . 1 . 6 2 29.5 1199 . 5 2 2 3 9 . 1. 60 32.8 2 2 3 9 . 1. 52 3 5.2 1355.2 2239. 1.35 36.2...... .1.5.6 3 . 1_ 2 2 3 9 . 1 . 36 17 2 9 . 8 40.2 2239 . 1.45 46.2 1862. 1 !  redox r e a c t i o n , d a t a from  Sh  •max. .  122. 188.0 190. 268.3 239. 323.7 280. 37 9 . 0 325. 4 2 4.3 3 7 6 . . _.....47 2 . 2 . 397. 501.4 444. 543.4 48 7 . 587.7 528. 631.2 557. 662.5 5,98. 699.3 630. 733.9 669. 774.7 .126. 197.6 195. 280.8 305. 402.6 342.._. 444.0 394. 497.0 425. 529.5 481.. 583.2 522. 619.9 552.. 662.0 57.9.._ 6.99...6_ 623. 737.6 66 8 . , 776.0 709. " * 8 1 5 . 4 107. 179.7 133. 25 0 . 9 307.0 19 9 . . _ 241. 356.5 252. 405. 1 283. 447.8 331. 48 8 . 7 389. 514.1 397....._ . . 5 3 6 . 5 . 426. 561.8 599.9 463.. 464. 636.2 513.. 670.8 571. 69 9 . 2 7.4 4 . 9.. 632. 187.9 101.. 136. 266.0 198.: 323.6 241. 375.4 42 4 . 6 262. 286... _ 469.3 3' 3 3 . 512.2 389. 541.3 386. 558.4 5 93.5 430. 460.. 630.9 473. __ 6.7.7.6_ 526. 712.8 604. 739.5  So* (H/d)'* rn i n. 123.4 ! 176.2 ! . 212.5 248.8 2 78.5 3 10.0_ 329.1 356.8 385.8 414.4 434.9 . n . 1 . These 4 5c 9  481.8  o b t a i n e d from  1™'^  184.3 264.3 291.5 326.3  n  values are  f i g . 5 of r e f . (24).  **  382*.9 407.0 434.6 4.59_..3__ 484.3 509.4 535.3 118.0 164.7 201.5 234.0 266.0 294.0 32 0 . 9 337. 5 3 52..2.._ 368.8 39 3 . 8 417.6 440.4 459.0 48 9.0..__ 123.4 174.7 2 12.4 246.4 278.7 308.1 336.3 3 5 5.4 366.6 389.7 414.2 4 4 4 . 8._ 46 7 . 9 * 485.5 :  J=(k/V)(Sc)  2 / 3  33  DISCUSSION The r e s u l t s o f t h e p r e s e n t  investigation are plotted  on v a r i o u s s y s t e m s o f c o o r d i n a t e s , t h e s e b e i n g s u g g e s t e d by the v a r i o u s attempts Prom t h e s e  graphs,  a t c o r r e l a t i o n by p r e v i o u s  investigators.  i t c a n t h e n be s e e n how c l o s e l y t h e r e l a t i o n -  s h i p s p r e v i o u s l y proposed  are able t o f i t the current data. (l8)  The p r o p o s e d shown i n F i g . 5 . applicable  c o r r e l a t i o n o f L e m l i c h a n d Levy  They have p r o p o s e d  that equation  f o r values o f t h e s t r e t c h e d - f i l m Reynolds  i s (15) i s number  g r e a t e r than 20. \  V  k' = O . I I 7 R  (15)  e s  T h i s c o r r e l a t i o n i s based upon t h e t r a n s f e r o f n a p h t h a l e n e (17) and  d-camphor t o a i r a t room t e m p e r a t u r e .  a l s o o b t a i n e d some d a t a f o r h e a t a r e a l s o shown i n F i g . 5 .  \C  0.8? ^  ^  0.038 Res  •  L e m l i c h and Levy have proposed  4. = 0.038 R  es  n  a  t r a n s f e r based upon t h e  1.13  (16)  6c  0.85  K  has  t r a n s f e r t o a i r and t h e s e  c o r r e l a t i o n f o r b o t h mass a n d h e a t above d a t a , v i z . ,  Lemlich  1.13  P  r x  / o\  However when Goh p r e s e n t e d h i s - e x p e r i m e n t a l d a t a o n t h e( 1 5 ) lower t h a n t h e d a t a o f L e m l i c h and Levy ( F i g . 5 ) . Knight v  same c o o r d i n a t e s , i t was f o u n d  t h a t h i s d a t a were  clearly  35  attempted like  t o e x p l a i n t h i s d i s c r e p a n c y , u s i n g an i d e a ,  t h a t o f L e m l i c h , r e s t s upon t h e s t r e t c h e d - f i l m  Knight reasoned  that the e f f e c t i v e  m i g h t be t h e s u r f a c e w h i c h  which  concept.  surface area f o r sublimation  forms t h e outermost  t h e v i b r a t i o n a l p a t h , t h a t i s A = ( i t d + 2H )X  boundary o f (see F i g . 6 ) .  (l6) K n i g h t and Ratkowsky left-hand  presented  an e q u a t i o n i n w h i c h t h e  s i d e i s r e p r e s e n t e d by k / k ' - l .  be a more r e a s o n a b l e  This appears t o  e x p r e s s i o n t o use than k/k', s i n c e i t  s a t i s f i e s t h e l i m i t i n g c o n d i t i o n t h a t when t h e r e i s no v i b r a tion  ( i . e . when R e v = 0 ) , t h e n £ - 1  Equation and  = (17)  k=k . 1  0.021 Rev C ~ f succeeds  ( i  )  somewhat  ( F i g . 7).  Comparison between t h e d a t a o f L e m l i c h and L e v y , and is  the present  .  i n c o r r e l a t i n g both the data o f Lemlich  L e v y a n d o f Goh, b u t t h e d a t a o f Goh a r e s t i l l  l o w e r by a f e w p e r c e n t  7  Goh,  i n v e s t i g a t i o n on k / k ' v e r s u s Res c o o r d i n a t e s  shown i n F i g . 8.  T h i s f i g u r e demonstrates  that the present  d a t a do n o t c o i n c i d e w i t h t h o s e  o f t h e p r e v i o u s s t u d i e s when  p l o t t e d on t h e s e  I t i s seen t h a t t h e samples  coordinates.  with the l a r g e r diameters  g i v e l o w e r v a l u e s o f k/k' a t t h e  same s t r e t c h e d - f i l m R e y n o l d s This characteristic  number. i s a l s o seen i n F i g . 9 which  e m p l o y s t h e same c o o r d i n a t e s a s u s e d by K n i g h t T h i s f a c t was n o t so r e a d i l y a p p a r e n t  and R a t k o w s k y .  when o n l y t h e d a t a o f  36-a  A = (it  F i g , 6. area of  d + 2H  ) £  E f f e c t i v e surface vibrating cylinder  36-b  F i g . 7. D a t a o f L e m l i c h and L e v y and o f Goh " c o - o r d i n a t e s o f ( k / k ' - l ) v s . Rev(A/A ') .  on t h e  r — r ~ T ~ T i II i r  k/k'  n n r  (1)  0.07 - 0.19 cm. d i a  L e m l i c h and  (2)  0.12 - 0.23  Goh< )  0  0.38  (approx.)  this  author  (naphthalene)  *  1.1  (approx.)  this  author  (naphthalene)  Levy  (18) 1 6  *" o  'o  10  L 10  ... I  o o  o  O  I I 1000  100  LO  Res F i g . 8. C o m p a r i s o n o f the p r e s e n t d a t a w i t h t h e p r e v i o u s works on c o - o r d i n a t e s employed by L e m l i c h and L e v y .  the  U ) 0.07  - 0.19  (2)  -  0.12  c m . d i a . L e m l i c h and Gohd6) 0.23  0  0I38(approx.)  X  1.1.(approx .)  Levy'' ^ 1  /  this  author(naphthalene)  this  author(naphthalene) 0  o  10  rH  -  /  /  1 s  /  / /  ///  —  X  °  o  o  o  o —  0  o 0  v*  O  o  / s  -  °°  0  /  °  * *  \  X s  1  /  / S  0  0  0  00  0  o o  0  X  o  o °  1  1111  X  1  I I I M i l l  100  1000 Rev(A/A ) 1  1  1  1  1 1 MM  10000  2  Fig. 9. Comparison o f the p r e s e n t d a t a w i t h t h e p r e v i o u s works on t h e c o - o r d i n a t e s e m p l o y e d by K n i g h t .  co  39  L e m l i c h and due  to the  slightly  L e v y and  t h a t o f Goh  f a c t t h a t the diameters  g r e a t e r than  readily  This i s  e m p l o y e d - b y Goh  that of Lemlich  a considerable overlap. diameters  were c o n s i d e r e d .  and  In the present  u s e d were much l a r g e r , and  were  L e v y , and  only  there  investigation,  was  the  t h e d i s a g r e e m e n t i s more  apparent. The  above o b s e r v a t i o n s  were i n c l u d e d i n t h e r e l a t i o n m i g h t be  suggest t h a t i f the  diameter  l e f t - h a n d side of the e q u a t i o n , the  improved.  mass t r a n s f e r c o e f f i c i e n t  Thus Sherwood number, t h a t i s  times  diameter  d i v i d e d by  diffusion  c o e f f i c i e n t m i g h t be u s e d a s t h e o r d i n a t e i n p l a c e o f A second reason  cor-  f o r c o n s i d e r i n g the  k/k'.  S h e r w o o d number i s t h a t (12)  it  appears i n the t h e o r e t i c a l equation  e q u a t i o n , d e r i v e d from boundary-layer to apply  o n l y when t h e t i m e  diffusion  when S c h m i d t number i s l a r g e .  layer approximation large^ should  . be  number a r e  ..  v  t h e o r y , may  of. o s c i l l a t i o n  compared w i t h a c h a r a c t e r i s t i c i.e.,  of Jameson  be  i s very  time  This  expected  small  of the  system,  Furthermore the  boundary-  a l s o r e q u i r e s t h a t t h e R e y n o l d s number  Therefore  Jameson's t h e o r e t i c a l  equation  a p p l i c a b l e o n l y when b o t h R e y n o l d s number and large.  T h i s e q u a t i o n , w r i t t e n i n terms of  Schmidt the  v i b r a t i o n a l R e y n o l d s number, i s  Sh=0.SI6Sc Rev (H/d) /5  2  l/e  be  (18)  40  J a m e s o n o b t a i n e d e x p e r i m e n t a l d a t a f o r mass t r a n s f e r f r o m a. h o r i z o n t a l benzoic mixture  acid cylinder o s c i l l a t i n g - v e r t i c a l l y  o f g l y c e r o l and  S c h m i d t number ( 3.23 moderate present of  up  water.  x 10'  These d a t a have v e r y l a r g e  ) but t h e R e y n o l d s  (up t o a b o u t 1 0 0 ) .  The  gaseous d a t a o b t a i n e d i n the  i n v e s t i g a t i o n are w i t h r e l a t i v e l y  Thus b o t h  assumptions  l a r g e Reynolds  s e t s o f d a t a seem t o s a t i s f y  upon which  number  d a t a and  o n l y one  Jameson's  L e m l i c h and  L e v y and  w i t h low Reynolds  o f Goh  A further  number a l l  The  data  of  f o r gaseous systems are a l l taken  number.  shown i n P i g . 10.  rests.  experimental  the present data f o r the h i g h e s t Reynolds  s l i g h t l y above t h e t h e o r e t i c a l e q u a t i o n .  of  of  the Jameson's t h e o r e t i c a l e q u a t i o n  T h e s e d a t a a r e a l l shown i n P i g . 10.  also  number i s o n l y  t o 2000 b u t w i t h a s m a l l S c h m i d t number o f t h e o r d e r  2.5.  lie  to a  T y p i c a l values of these data They l i e b e l o w t h e t h e o r e t i c a l  s e t o f e x p e r i m e n t a l data- has  been  (2 3) (2 4 ) ( 2 ")) '. T h e s e d a t a were  are line.  presented  1  by Ra.o,  R a j u and  by t h e s e w o r k e r s  Rao  v  0  K  obtained  K  i n three independent  sets of  experiment.  (23) The  first  s e t t h a t was  reported  d e a l s w i t h the e f f e c t  v  h o r i z o n t a l t r a n s v e r s e v i b r a t i o n on d i s s o l u t i o n o f acid  c y l i n d e r s i n t o water.  They d i f f e r  from  benzoic  Jameson's  experimental data w i t h respect to the f a c t t h a t the number i s s l i g h t l y l o w e r Reynolds  (range  from  810  number i s c o n s i d e r a b l y h i g h e r  A l s o J a m e s o n ' s c y l i n d e r was  vibrated  t o 984)  (range  of  Schmidt  but  from  in a vertical  the  80 t o 7 0 0 0 ) . direction.  D C-  R a o , R a j u and R a o , e l e c t r o l y t i c  redox  Rao, R a j u and R a o , b e n z o i c a c i d  into  reaction water  ( 2 i)  A  r  O  Rao, R a j u and Rao, n a p h t h a l e n e , I n t o a i r  o  The p r e s e n t d a t a o f n a p h t h a l e n e  X  The p r e s e n t d a t a o f p h e n o l i n t o a i r  Q  L e m l i c h and L e v y , n a p h t h a l e n e Goh, n a p h t h a l e n e  1000  (p? j  into  air  v  into a i r (18)  o r d-camphor i n t o a i r  X  (12)  Jameson, b e n z o i c a c i d  into glycerol-water  10  10.  '  100  W rig,  v  / 2  Sc  1 / 3  (K/d)  I  000  1 / 6  Comparison o f e x p e r i m e n t a l r e s u l t s Jameson t h e o r e t i c a l e q u a t i o n ( 1 8 ) ,  v i t h the  42  The  second  transfer  set of data  i n electrolytic  vibrating electrodes.  i s c o n c e r n e d w i t h t h e r a t e s o f mass redox r e a c t i o n s from Here, t h e Schmidt  horizontally  number r a n g e s  800 t o 2240 w h i l e t h e R e y n o l d s number r a n g e s f r o m l e s s 100 t o v a l u e s a s l a r g e a s 7 0 0 0 .  The t h i r d  from than  set of data  v  J  '  deals with h o r i z o n t a l l y v i b r a t i n g c y l i n d e r s of naphthalene to a i r , that was  but t h e range o f v a r i a b l e s i s n o t n e a r l y as g r e a t as  i n t h e p r e s e n t s t u d y , e . g . , t h e maximum R e y n o l d s l e s s than 190.  number  R a o , R a j u a n d Rao f o u n d t h a t a l l t h e s e  s e t s o f d a t a c o u l d be c o r r e l a t e d  by a s i n g l e e q u a t i o n , w h i c h ,  when w r i t t e n i n t e r m s o f - S h , ' S c - , a n d Rev becomes  Sh=0.+l S c ^ R e v It  i sdifficult  0 , 6  '  .  t o make a n e x a c t c o m p a r i s o n o f t h e e x p e r i m e n t a l  d a t a o f R a o , R a j u a n d Rao w i t h o t h e r p r o p o s e d  correlations  s i n c e t h e o r i g i n a l d a t a were n o t r e a d i l y a v a i l a b l e . if  (is)  However,  a n a t t e m p t i s made t o r e a d t h e d a t a f r o m g r a p h s t h a t  have p r e s e n t e d , a n d i f a n a v e r a g e v a l u e o f ( H/d )  they  i s employed,  then t y p i c a l approximate values o f t h e i r data f o r both t h e liquid  and gaseous systems  graph which r e s u l t s  c a n be a d d e d t o P i g . 1 0 .  The  i s a very i n t e r e s t i n g one.  I n s p e c t i o n o f F i g . 10 shows t h a t t h e d a t a o f R a o , R a j u and R a o , f o r h o r i z o n t a l l y v i b r a t e d to l i q u i d  c y l i n d e r s t r a n s f e r i n g mass  systems, l i e very close t o t h e . t h e o r e t i c a l equation  o f J a m e s o n , i . e . , E q u a t i o n (18) .  Since these data possess  43  both  c r i t e r i a u n d e r w h i c h t h e J a m e s o n ' e q u a t i o n may  t o be v a l i d , n a m e l y h i g h R e y n o l d s number and  high  number, t h e g e n e r a l a g r e e m e n t o f t h e d a t a and supports the  the v a l i d i t y  smooth c u r v e  equation  i n a l l previous study tend  This i l l u s t r a t e s  For lower  However, i t investi-  t o l i e on  t h a t c o u l d be d r a w n t h r o u g h  agreement o f a l l the e x p e r i m e n t a l effect  the  f i t i s n o t n e a r l y as g o o d .  g a t i o n s as w e l l a s i n t h e p r e s e n t  the data p o i n t s .  Schmidt  S c h m i d t number a n d / o r  does appear t h a t the d a t a o b t a i n e d  near a single  expected  of Jameson's t h e o r e t i c a l e q u a t i o n .  sets of data possessing lower  R e y n o l d s number, t h e  be  or a l l of  the approximate u n i v e r s a l  investigations  o f v i b r a t i o n u p o n mass t r a n s f e r  into  from s i n g l e  the  horizontal  c y l i n d e r s , d e s p i t e the f a c t t h a t the c o r r e l a t i o n s proposed each of the i n d i v i d u a l t o be t o t a l l y  i n v e s t i g a t o r s appear at f i r s t  disparate.  The  d i f f e r e n c e between the  p r o p o s e d c o r r e l a t i o n s i s e a s i l y e x p l a i n e d by t h e f a c t t h e i n d i v i d u a l c o r r e l a t i o n s have b e e n o b t a i n e d  glance various that  f o r a much  n a r r o w e r r a n g e o f t h e v a r i a b l e s t h a n t h a t shown by F i g . F u r t h e r , t h e d a t a o f Rao  and  c o - w o r k e r s were o b t a i n e d  h o r i z o n t a l v i b r a t i o n s , whereas the d a t a of a l l o t h e r gators apply to v e r t i c a l  The  c o o r d i n a t e s used here are  empirical relationship Equation  (19).  I t can  10.  for investi-  vibrations.  A second method o f p r e s e n t i n g a l l t h e r e s u l t s i n F i g . 11.  by  obtained be  by Rao,  Raju  suggested and  i s shown by  the  Rao, i . e . ,  seen t h a t t h e r e i s a g r e a t  deal  1  I MM  1  Rao, R a j u  and Rao, e l e c t r o l y t i c  redox  Rao, R a j u  and Rao, b e n z o i c  into  Rao, R a j u  and Rao, n a p h t h a l e n e  The p r e s e n t  data  The p r e s e n t  data of phenol  Lemlich  acid  into  of naphthalene  Goh, n a p h t h a l e n e  I n t o a i r (16)  Jameson, b e n z o i c  acid  viater^ 3) 2  a i r (25)  into a i r  100  o r d-camphor i n t o  ai  r  U8)  glycerol-water(12) O  <5  100  1 0  r  reaction(24)  into a i r  and L e v y , n a p h t h a l e n e into  rn  Mill  1000 Rev  Fig.  11.  Comparison  of experimental  experimental  equation  (19)  results  with the  o f Rao and  co-workers  45  more s c a t t e r h e r e t h a n i n F i g . 10. importance of i n c l u d i n g the term relation,  This demonstrates H/d  i n any p r o p o s e d  a s F i g . 11 d o e s n o t t a k e t h i s a d d i t i o n a l  l e s s group It  into  account.  would  be d e s i r a b l e t o be a b l e t o e x p r e s s t h e  c o v e r i n g t h e whole  range of the v a r i a b l e s .  h i m s e l f t o the d a t a o f gaseous  are three l i k e l y  Sh = Sh = The  proposed  0, [ 0 [ 0_ [ 2  systems o n l y , then the  chances  be o b t a i n e d . using  :  S c , Rev., 1+H/d S c , Rev,  A/A'  S c , Rev,  H/d  ]  (i)  ]  ( i i )  ]  ( i i i )  f u n c t i o n s are a l l g i v e n i n terms of d i m e n s i o n -  l e s s g r o u p s and an e x p o n e n t i a l r e l a t i o n s h i p  b e t w e e n Sherwood  number and t h e o t h e r d i m e n s i o n l e s s g r o u p s was Equation  restricts  ways o f e x p r e s s i n g t h e r e s u l t s ,  terms of the f o l l o w i n g k i n d  results  correlation  I f one  a r e more f a v o r a b l e t h a t a s i n g l e c o r r e l a t i o n may  Sh =  cor-  dimension-  p r e s e n t e d i n F i g . 10 by means o f a s i n g l e w o r k i n g  There  the  tried.  ( i ) i s s u g g e s t e d by t h e s t r e t c h e d - f i l m  concept,  s i n c e t h e s t r e t c h e d - f i l m R e y n o l d s n u m b e r , R e s , c a n be as t h e p r o d u c t o f  Rev  and  1+H/d.  Equation ( i i ) i s  s u g g e s t e d by t h e i d e a o f K n i g h t , and E q u a t i o n ( i i i ) Jameson's a n a l y s i s based upon boundary method o f l e a s t  written  by  layer theory.  The  squares i s used f o r f i n d i n g the exponent  t h e R e y n o l d s number and u p o n t h e r a t i o t o diameter (see appendix I I I - 4 ) .  The  upon  of double amplitude exponent  upon t h e  he S c h m i d t number was assumed t o be 1/3 r e t i c a l and e x p e r i m e n t a l evidence  a s t h e r e i s some t h e o -  for this value.  Besides  t h a t , t h e v a r i a t i o n o f S c h m i d t number i n t h e v a r i o u s g a s e o u s systems being c o r r e l a t e d  i sinsufficient  t o e s t a b l i s h i t s e x p o n e n t by l e a s t  f o r one t o be a b l e  squares  fitting.  It  seemed b e s t , t h e r e f o r e , t o f i x t h e v a l u e o f t h e e x p o n e n t a t 1/3,  arbitrarily  as suggested  by a n a l o g o u s  c o n v e c t i v e mass  H) t r a n s f e r processes The  .  c o r r e l a t i o n s o b t a i n e d by t h e - l e a s t - s q u a r e s p r o -  cedure, u s i n g only t h e data f o r naphthalene present  study a r e as follows', l/r  Sh = 0.187 Sh = 0.192  0.72G  Sc Rev I. /j  and  a r e shown g r a p h i c a l l y  The  equations  g i v e s t h e best  and  by P i g . 1 2 ,  (22) 13,  and 14, r e s p e c t i v e l y .  fit.  Thus i t i s found  that Equation  P i g . lh shows t h e e x p e r i m e n t a l  i  and  (22) data,  data, the present  d a t a , a n d some t y p i c a l v a l u e s o f t h e d a t a o f L e m l i c h  Levy, It  o f G o h , a n d o f Rao a n d c o - w o r k e r s i s proposed  satisfactory  that Equation  (22)  (gaseous  data only) .  should prove  enough t o s e r v e a s an e x p e r i m e n t a l  for the effect from  0.233  ( H / d )  i n c l u d e s t h e present naphthalene  phenol  (21)  ( A / A')  h a v e a n a v e r a g e d e v i a t i o n o f 20 %, 21 %  %, r e s p e c t i v e l y .  which  . (20)  0.443  0.717,  Sh - 0.261 S c R e v 5  0.37 3  ( 1+H/d.)  0.728  Sc Rev l/„  17  obtained i n the  t o be  correlation  o f v i b r a t i o n upon t h e s u b l i m a t i o n o f m a t e r i a l  horizontal circular  cylinders vibrated vertically to  47  gaseous media.  The f a c t  a l s o l i e near t h i s l i n e zontal  vibration  t h a t t h e d a t a o f Rao a n d c o - w o r k e r s  s u g g e s t s t h a t i t may a p p l y t o h o r i -  as w e l l .  T h i s e q u a t i o n c o v e r s a range o f  d i a m e t e r b e t w e e n 0.07 a n d 1.1 cm., f r e q u e n c i e s b e t w e e n 100 and  7000 RPM., d o u b l e  and  vibrational  addition H/d,  a m p l i t u d e s between 0.05 a n d 4.0 cm.,  Reynolds  the range  numbers b e t w e e n 9 a n d 2000.  o f the r a t i o o f double  i s b e t w e e n 0.2 a n d 5.7.  In  amplitude t o diameter,  48  10  100  1000 Rev  F i g . 12. Comparison of the present naphthalene with Equation (20).  data  49  Rev F i g . 13. Comparison of the present naphthalene v.'ith E q u a t i o n (21) .  data  50  100 o  o o  The  present  naphthalene  data  h e present phenol data Goh typical valuesd^) L e m l i c h and L e v y , t y p i c a l v a l u e s ( l 8 ) Rao, R a j u and Rao, t y p i c a l values^)  T  CM  -o  \ cn \  O CO.  5  1 0  Equation  10  100  1000 Rev  Pig.  14.  Comparison o f v a r i o u s e x p e r i m e n t a l  with Equation  (22) .  data  (22)  51  CONCLUSIONS  (1)  I t has been found t h a t a l l the p r e v i o u s e q u a t i o n s  t h a t have been p r e s e n t e d f o r the e f f e c t o f v i b r a t i o n upon s u b l i m a t i o n from h o r i z o n t a l c i r c u l a r c y l i n d e r s do not f i t the d a t a w e l l over a wide range o f Reynolds  number o r when  the d i a m e t e r o f the sample c y l i n d e r i s l a r g e .  (2)  When a l l o f the a v a i l a b l e e x p e r i m e n t a l d a t a f o r  both gaseous and l i q u i d  systems are p r e s e n t e d on the  o f c o o r d i n a t e s suggested (Pig.  by Jameson's t h e o r e t i c a l e q u a t i o n  1 0 ) , i t i s seen t h a t these d a t a l i e ( a p p r o x i m a t e l y ) on  a s i n g l e smooth curve o v e r t h e e n t i r e range o f number.  (3)  system  '  The  Reynolds  \  l i q u i d d a t a o f Rao, Raju and Rao h a v i n g h i g h  Schmidt.number and h i g h Reynolds  number seem t o f i t Jameson's  t h e o r e t i c a l equation f a i r l y c l o s e l y . t e n d t o approach  Even gaseous systems  Jameson's t h e o r e t i c a l e q u a t i o n i n the  limit  at t h e h i g h e r range o f Reynolds number, i . e . , t h e exponent o f the Reynolds  (4)  number approaches  1/2.  The maximum r a t i o o f the v i b r a t i o n a l mass t r a n s f e r  c o e f f i c i e n t t o the s t a t i o n a r y mass t r a n s f e r c o e f f i c i e n t o b t a i n e d i n the p r e s e n t r e s e a r c h i s about 30 compared w i t h  52  a maximum v a l u e o f 10 o b t a i n e d i n p r e v i o u s s t u d i e s .  (5) • I t i s proposed  t h a t t h e e q u a t i o n o f best f i t f o r  the e x i s t i n g d a t a f o r gaseous systems o n l y i s g i v e n by t h e f o l l o w i n g e q u a t i o n w i t h an average d e v i a t i o n o f 17 % . Sh = .0.261 Sc Rev°' ( H/d )°-»* /3  7,7  T h i s e q u a t i o n i s b e l i e v e d t o be v a l i d f o r v e r t i c a l  vibration  and perhaps a l s o f o r h o r i z o n t a l v i b r a t i o n over t h e f o l l o w i n g range o f t h e v a r i a b l e s : Diameter  0.07 - 1.1 cm. \  100 - 7000 RPM.  Frequency Amplitude  0.05 - 4.0 cm.  (double)  V i b r a t i o n a l Reynolds  number  R a t i o of amplitude t o diameter v  9. - 2000 0.2 - 5.7  53  FURTHER CONSIDERATIONS  The  m e c h a n i s m o f mass t r a n s f e r f r o m an  c y l i n d e r i s q u i t e complex. cylinder  i s not  layer theory  The  oscillating  flow p a t t e r n around  yet c l a r i f i e d .  According  of S c h l i c h t i n g , the  to the  the  boundary-  flow pattern along  the  (11) oscillating and  surface  various other  i s shown by  present  dusty  author  surroundings  A of F i g . 1 5 .  has  is initiated  a l s o made a v i b r a t i o n a l o p e r a t i o n  u s i n g c a r b o n powder.  I t was  of the  c y l i n d e r as  shown i n B o f F i g . 1 5 .  author  has  from second-hand p e r s o n a l  Richardson  side  However  this  communication  t h a t the  f l o w p a t t e r n i s more c o m p l e x ( s e e F i g . 1 5 C ) . i t would not  be  o f Brown U n i v e r s i t y i s  easy t o analyze  s o l v e the problem of t r a n s p o r t from the  e r i n a t h e o r e t i c a l way oscillating The h e a t and  u n t i l the  in  surface  P.  to  suggesting  the mechanism oscillating  and cylind-  stream f u n c t i o n around  the  cylinder i s clarified. mechanism o f s u b l i m a t i o n i n v o l v e s  mass t r a n s f e r .  which to evaluate  the  The  appropriate  simultaneous  temperature  s a t u r a t i o n c o n c e n t r a t i o n of the  i s the wet-bulb temperatune. t e m p e r a t u r e was  '  observed  t h a t Dr.  Therefore  D.  V J J  by a c o u s t i c a l means.  t h a t minute p a r t i c l e s of carbon s t i c k onto the  learned  West  workers a l s o report that a s i m i l a r p a t t e r n .  e x i s t s when t h e o s c i l l a t i o n The  curve  obtained  by  In t h i s calculation  study,  the  at vapor  wet-bulb  (see.appendix  1-3).  Fig.  15.  P a t t e r n of stream-lines i n the neighbourhood o f an o s c i l l a t i n g c i r c u l a r c y l i n d e r .  55  However, i n systems where t h e vapor p r e s s u r e  of the s o l i d i s  l a r g e , o r where t h e l a t e n t heat o f s u b l i m a t i o n i s l a r g e , i t would be a d v i s a b l e t o measure t h e temperature o f t h e s u r f a c e directly.  T h i s c o u l d be done by i n s t a l l i n g a thermocouple  i n t o the c y l i n d r i c a l  sample.  \  56  LITERATURE  CITED  1.  A n a n t a n a r a y a n a n R. and A. Ramachandran Mech. E n g r s . , 8_0, 1426 (1958)  : T a n s . Am.  2.  B a i l l e u l et (Auflage),  Ferdinand  a l . : "Active  (1953)  Kohle",p.4l,  Bennett C O . Transfer",  4.  D e a v e r F.K., W.R. Penney and T.B. J e f f e r s o n S o c . Mech. E n g r s . , 84C, 251 (1962)  5.  Fand R.M.  6.  7.  Enke  \  3.  83C, 133  Soc.  and  J . E . Myers : "Momentum, H e a t , and p.502, M c G r a w - H i l l (New Y o r k ) , (1962)  and  J . Kaye  : T r a n s . Am.  Soc.  Mass  : Trans.  Mech. E n g r s . ,  (1961)  F i k l i s t o v I.N. and G.A. Akselrud. : I n z h . - F i z . Akademie Nauk B e l o r u s s k . U.S.S.R., 7 ( 1 ) , 45 F i k l i s t o v I.N. and Politekn. Inst.,  G.A.  Akselrud  : Dokl.  Zh.,  (1964)  L'vovsk.  5(1-2), 104 (1963)  8.  Goh T.T. : B. S c . App. t h e s i s , U n i v . B r i s b a n e , A u s t r a l i a (1963)  9.  H i r s c h f e l d e r J.O., C F . C u r t i s s and R.B. B i r d : " M o l e c u l a r T h e o r y o f Gases and L i q u i d s " , pp.538-540, W i l e y , (New Y o r k ) (1954)  10.  Hodgman C D . , R.C West and "Handbook o f C h e m i s t r y and C h e m i c a l Rubber P u b l i s h i n g  11.  "International C r i t i c a l McGraw-Hill  (New  S.M. Selby : P h y s i c s " 37th e d . , ( C l e v e l a n d ) (1956)  Tables"  York)  Queensland,  vol  5.,  (1939) 19_, 793 (1964)  12.  Jameson G.J.  13.  Jost  14.  Kalashnikov  15.  Nauk. ( U . S . S . R . ) , 119, 735 (1958) Knight I . C : B. S c . App. t h e s i s , U n i v . B r i s b a n e , A u s t r a l i a (1964)  W.  Am.  : Chem. Eng.  Sci.,  : " D i f f u s i o n " Academic N.V.  and  V.I.  Press  Cherniken  Inc.  (New  : Doklady  York) Akad.  Queensland,  (I960)  \ \  5'7  16.  11,  K n i g h t I.C. and D.A. Ratkowsky : A.I.Ch.E.J., 370  (1965)  17.  L e m l i c h R. : I n d . Eng. Chem., 4_7_, 1175  (1955)  18.  L e m l i c h R. and M.R.  7,  19.  Mantell C L .  20.  M a r t i n e l l i R.C. and L.M.K. B o e l t e r : P r o c . F i f t h I n t e r n . Congr. App. Mech., p.578 ( 1 9 3 8 ) M i c k l e y H.S., T.K. Sherwood and C E . Reed : " A p p l i e d Mathematics i n Chemical E n g i n e e r i n g " , 2nd e d . , M c G r a w - H i l l (New York) ( 1 9 5 7 )  21.  Levy  : A.I.Ch.E.J.,  240 ( 1 9 6 1 )  : " A d s o r p t i o n 2nd e d . " ( 1 9 5 D  22.  P e r r y J.H. : "Chemical E n g i n e e r ' s Hand Book" 4 t h e d . , M c G r a w - H i l l (New York) (1964.)  23.  Rao K.S., G.J.V.J. Raj u\ and C.V. Rao : T r a n s . I n d i a n Chem. E n g r s . , 5 , 100 (I963)  24.  Rao K.S., G.J.V.J. R a j u and C.V. Rao : I n d i a n J . Tech.,  25.  Rao K.S., G.J.V.J. Raju and C.V. Rao : T r a n s . I n d i a n Chem. E n g r s . , 7 , 59 ( 1 9 6 5 )  26.  Rosenhead L. : "Laminar Boundary L a y e r s " Chap. V I I , Oxford Univ. P r e s s . (1963)  27.  3,  38  (1965)  S c h l i c h t i n g H. : "Boundary L a y e r Theory", 4 t h e d . , . Chap. 1 1 , M c G r a w - H i l l (New York) ( i 9 6 0 )  28.  Shine A . J . : Mech. Eng. 8 l , No. 1 0 , 95  29.  T s u i Y.T. : Ph. D. t h e s i s , Ohio S t a t e U n i v .  30.  Van d e r Hegge Z i j n e n B.G. 205  31. 32.  : A p p l . S c i . Res., A 7 ,  and C.Y. Lee : I n d . Eng.-Chem., 4 7 , No. 6 ,  (1955)  W e s t e r v e l t P . J . : J . A c o u s t i c a l Soc. Am., (1953)  33.  (1953)  (1958)  Wilke- C R . 1253  (1959)  West .G.D.  25., No. 1,  60  : P r o c . Phys. S o c , 64_, No. 378B, 483 ( 1 9 5 1 )  53  NOMENCLATURE  2  A  Effective  A'  Surface  a  Single  c  Concentration of material  g/cm  Saturation  g/cm  * c  s u r f a c e a r e a o f c y l i n d e r ( >Ld+2H)Jt. -  area o f c y l i n d e r amplitude  cm  %c\ X  2  cm  of oscillation  cm  concentration of material  3  2 . cm / s e c  D  Diffusion coefficient  d  Diameter o f c y l i n d e r  f  Frequency o f o s c i l l a t i o n  H  Double amplitude  h  Heat t r a n s f e r c o e f f i c i e n t  k  Mass t r a n s f e r  coefficient (vibrational)  cm/sec  k'  Mass t r a n s f e r  coefficient  cm/sec  SI  Length, o f c y l i n d e r  72  Circular  Nu  N u s s e l t number dh/X.  P  Atmospheric  P  V a p o r p r e s s u r e of. m a t e r i a l  P  r  Prandtl'  cm -1 sec  of oscillation  frequency  '.  cm" c a l / Ccm s e c  (stationary)  cm o f o s c i l l a t i o n 2^tf  pressure  number  mmHg mmHg  Cp/VX  V  Radius  of cylinder  Re  R e y n o l d s number b a s e d o n c i r c u l a r  Res  Stretched-film  Rev  V i b r a t i o n a l R e y n o l d s number 2fHd/x^  S  Surface  area  -1 sec  R e y n o l d s number  cm f r e q u e n c y 2nar/_>>  2fH(H+d)/^  2 cm  •59  Sc  Schmidt  Sh  number  If/D  . S h e r w o o d number  dk/D  T  Temperature  °K o r  t  Time  u.  V e l o c i t y component p a r a l l e l  vl"  V e l o c i t y component n o r m a l t o s o l i d  W  Weight  X  Displacement p a r a l l e l  $  Displacement normal to s o l i d  °C sec  to solid  surface  surface  cm/sec cm/sec  of m a t e r i a l sublimated  g  to solid  surface  cm  surface'  cm  i  greek l e t t e r s  :  J3  V e l o c i t y gradient  p  Gamma f u n c t i o n  X  Heat  S,A  of sublimation  Boundary  9  sec  ,  cal/g  layer thickness  cm  A n g u l a r d i s p l a c e m e n t from a x i s of o s c i l l a t i o n  Jj  Kinematic v i s c o s i t y  fi  Density  /V p  3  radian cm  /sec g/cm  Viscosity &  _ x  0i ' 0 2 ' 9*3  g/cmsec s  i  S  n  i  f  l  e  s  a  function  Stream f u n c t i o n ^  V a l u e o f ll  A.  Thermal  3  at outer  cm edge, o f b o u n d a r y  c o n d u c t i v i t y of a i r  layer  /sec  cm /sec 2  cal/cm°Csec  A-l  APPENDIX I Detailed  1.  calculations—  S i n u s o i d a l motion In  The  illustrative  the accompanying  present  apparatus  i  =  T>m  =  M  Therefore  <i  figure.  has  cm  .12  2.15  cm  i s l a r g e enough compared  with  p  the value  of  ( r-sinw>t  e q u a t i o n may  ) .  be r e w r i t t e n a s  Then  the  follows. Fig. I - l  Thus, the motion of the apparatus  2.  can  The  be  sample o b t a i n e d w i t h t h e  c o n s i d e r e d t o be  f u n c t i o n of the carbon  A d s o r p t i o n of naphthalene adsorption^ be  applied.  unit  time  sinusoidal.  coated or phenol  ^, so t h e L a n g m u i r t h e o r y ^ The  experimental  wall i s a Van  der  of adsorption  Waals can  r a t e o f a d s o r p t i o n i n mass o f m a t e r i a l p e r  i s g i v e n as  follows,  A-2  where  P  i s t h e vapor  pressure of material,  surface area o fcarbon, the temperature y(\  and  M  R  i s the molecular  S  i s the  weight,  i s t h e u n i v e r s a l gas c o n s t a n t .  c a n be o b t a i n e d i n u n i t s o f g / s e c by p r o p e r  u n i t s and c o n v e r s i o n f a c t o r s .  choice o f  When t h e r a t e o f s u b l i m a t i o n  i s equal t o the rate of adsorption, the e q u i l i b r i u m pressure  i n s i d e t h e box i s f i x e d .  naphthalene  9.82  as f o l l o w s .  x 10~  6  (actually the effective p  C  cm  T = 2 9 8 °K  p r e s s u r e i n t h e box i s  Then TH = 9 . 8 2 x l 0 ~  g/sec.  6  s u r f a c e a r e a i s c o n s i d e r e d t o be a s l i t t l e  •as t h e a r e a o f t h e w a l l c o v e r e d  5 x 10  with  The maximum r a t e o f s u b l i m a t i o n i s  g / s e c i n r u n No. 3 5 0 2 .  When t h e e f f e c t i v e  vapor-  U s i n g an experiment  as.an example, t h e vapor  calculated  T i s  with carbon,  S = 3 6 0 0 cm  s u r f a c e a r e a i s b e l i e v e d t o be M = 1 2 8 g/g-mole a n d  p e r gram o f carbon)'. a r e employed.  Then t h e e q u a t i o n t o f i n d  P i s :  P=™/?ERMT S u b s t i t u t i n g v a l u e s i n t o t h e above p =  q  ^  x | Q  "V2Tcx^.  36oo  O G y l 2 8  x2n  v  1 atm = 1 . 0 1 3 x 1 0 =  =  M  ™  Z  3  °  K  2  vg-mole/  p  T  )  \cm Sec V 3-mole °k§-ryiole / G  .....  J *  V  = | , z | x | Q ' ( - 3 . Vqtfrh/Z But  equation,  6  'Vaito cm sec*  (g/cmsec )  l-g'«lO-*JZj—  '  g  2  and 1 g = 1/128 (g-mole)  atm  0.34 I * I 0"'° *tw = 7 . 1 5 x 1 0  wmHg .  A-3  The  a b o v e c a l c u l a t i o n i s made n e g l e c t i n g t h e r a t e o f d e s o r p t i o n . ,  Then t h e . e q u i l i b r i u m v a p o r p r e s s u r e on t h e c a r b o n s h o u l d be o b t a i n e d i n o r d e r t o e x a m i n e w h e t h e r of  surface  t h e above v a l u e  v a p o r p r e s s u r e i n t h e box i s a p p r o p r i a t e o r n o t .  It i s  assumed t h a t t h e e q u i l i b r i u m v a p o r p r e s s u r e o f t h e a d s o r b e d m a t e r i a l obeys  the Freundlich e q u a t i o n ^ ^ f o r adsorption, 1  that i s , x = k P where x  1  /  n  i s the m a t e r i a l adsorbed  (cm ( N , T . P . ) / g  activated  c a r b o n ) a n d P i s t h e e q u i l i b r i u m p r e s s u r e (mmHg). is  insufficient  As t h e r e  d a t a f o r n a p h t h a l e n e , benzene i s adopted f o r (p)  the  purpose  o f o b t a i n i n g v a l u e s o f k and n  pressure equation  P = Naphthalene  .  The v a p o r  becomes,  (x/62.1)  5 , 3 1  i s a d s o r b e d e v e n more r e a d i l y t h a n b e n z e n e ,  naphthalene has a l a r g e r m o l e c u l a r weight, a h i g h e r t e m p e r a t u r e , and a l o w e r v o l a t i l i t y fore i ti s sufficient in  critical There-  t o u s e t h e above e q u a t i o n f o r b e n z e n e  p l a c e o f naphthalene as t h i s w i l l  more c o n s e r v a t i v e .  than benzene-has.  since  make t h e c a l c u l a t i o n  even  The c a r b o n w a l l i s r e n e w e d e v e r y t w e n t y  r u n s t o p r e v e n t t h e a d s o r b e d n a p h t h a l e n e f r o m a c c u m u l a t i n g on the  carbon s u r f a c e , which c o n s i s t s o f about  20 grams o f c a r b o n .  A-lJ  Fig.  1 - 2 .  Amount o f mass s u b l i m a t e d  with  time.  A-5  amount o f n a p h t h a l e n e t h a t i s a d s o r b e d i s a b o u t 0.1 g r a m s ,  The  which I s equivalent  t o 0.875 c c ( N . T . P . ) p e r 1 gram o f c a r b o n .  The  P = 7 x 1 0 ~ ^ mmHg.  equation  gives  suggests that the carbon s t i l l further adsorption  The a b o v e a r g u m e n t  has s u f f i c i e n t  and t h e r a t e o f d e s o r p t i p n  s m a l l c o m p a r e d w i t h .the r a t e o f a d s o r p t i o n . considered zero  that t h e vapor pressure  capacity  for  i s negligibly Thus i t may be  i n s i d e t h e box i s a l m o s t  compared w i t h t h e v a p o r p r e s s u r e  on t h e sample  surface  w h i c h i s a b o u t 0.08 mmHg. F u r t h e r , F i g . 1-2  shows t h a t t h e r e  i n the rate of sublimation with time,  i s no d i f f e r e n c e  even though t i m e s as  l a r g e a s 4 h o u r s were u s e d i n p r e l i m i n a r y s t u d i e s . been a c o n s i d e r a b l e  build-up  o f n a p h t h a l e n e i n s i d e t h e box  d u r i n g the time that i t takes decreasing  for  t o do a , c o m p l e t e r u n , t h e n a  r a t e o f s u b l i m a t i o n w o u l d have b e e n  These c o n s i d e r a t i o n s  seem t o j u s t i f y  3.  obtained.  taking the driving  s u b l i m a t i o n t o be t h e c o n c e n t r a t i o n  surface  Had t h e r e  force  o f vapor at the s o l i d  Itself.  C a l c u l a t i o n o f mass t r a n s f e r c o e f f i c i e n t The  vapor pressure  a t u r e , and i s d e r i v e d Clausius-Clapeyron then,  P  from l i t e r a t u r e values  equation.  Using  . .0(13.9169 - W . 9 / T )  c" = 0.002055138 P*/T different  o f m a t e r i a l i s a f u n c t i o n o f temper-  g/cm . 3  (11) (22)  using the  n a p h t h a l e n e a s a n example,,  ^  The s u r f a c e  temperature i s  from t h e a i r temperature and t h a t i s t h e s o - c a l l e d  A-6  wet-bulb temperature.  The e q u i l i b r i u m  equation f o r simul-  (22)  t a n e o u s mass and h e a t t r a n s f e r ^  ' is :  htT-.T ) = r k ( c * - c ) w  where  h i s heat t r a n s f e r c o e f f i c i e n t T  cal/°Ccm sec 2  i s wet-bulb temperature  °C  T i s a i r temperature  °C  ?J" i s h e a t o f s u b l i m a t i o n  cal/g  K i s . mass t r a n s f e r c o e f f i c i e n t c  i s saturation material  concentration  cm/sec of the  at the surface  c i s concentration  of the material  g/cm in a i r  w h i c h i s t a k e n t o be z e r o  g/cm  Then  T-T = \ r e * w  As m e n t i o n e d  i n the Discussion  Sh = Sc ' ^ ( R e v , We may w r i t e Nu  section,  H/d)  an a n a l o g o u s e a u a t i o n f o r heat =  P  ^ ( R e v ,  Therefore >3  H/d)  transfer,  3  A-7  where  D  i s t h e d i f f u s i o n c o e f f i c i e n t cm / s e c and  the  thermal conductivity  for  sublimation i s  where  D,X,  T a n d Y and c  Sc  and  P  o f a i r cal/cmsec°C.  is  The e q u a t i o n  a r e e v a l u a t e d a t t h e -temperature  a r e e v a l u a t e d a t t h e t e m p e r a t u r e Tw •  A t r i a l - a n d - e r r o r s o l u t i o n o f t h e above e q u a t i o n i s employed s and  c  i s obtained.  and t h e s o l i d  The t e m p e r a t u r e d i f f e r e n c e  s u r f a c e - I s f o u n d t o be a b o u t  n a p h t h a l e n e and about Using the value of c  0.07  between a i r °C f o r  0.25 °C f o r p h e n o l a t 20 °C. c a l c u l a t e d by t h e above p r o c e d u r e , t h e  mass t r a n s f e r c o e f f i c i e n t k i s o b t a i n e d by t h e f o l l o w i n g equation, k = W/Atc"  A-8  APPENDIX I I -Property o f m a t e r i a l s used  Naphthalene  ( 1 1  »P-  6 2 )  .  ( 2 2  i n the experiment  -P-I- > 5 5  M o l e c u l a r weight  128.17  Critical  temperature  T =  Critical  r  pressure  P = 39.2 a t m c  c  476.5 °C  M e l t i n g p o i n t a t 1 atm  T = 8 0 . 2 2 °C  B o i l i n g p o i n t as 1 atm  T = b  217.9  °C  Vapor p r e s s u r e t e m p e r a t u r e , °C  vapor p r e s s u r e ,  25  0.087  50  0.764  55  1.142  Combustible  P h e n o l  (ll,P.62)(22,p.3-56)  M o l e c u l a r weight  94.11  Critical  T = £  419.2 °C  C r i t i c a l pressure  P =  60.5 a t m  M e l t i n g p o i n t a t 1 atm ° B o i l i n g p o i n t a t 1 atm  T = 40.1 °C m o, T = 181.9 C  temperature  Vapor p r e s s u r e  c  b  mmH^  A-9  temperature,  C  v a p o r p r e s s u r e , mmHg  25  0.27  40.1  1.00  62 .5  5  Chemically  corrosive  .00  A-10  APPENDIX I I I Calculations  1.  Use o f d i g i t a l The  the  computer  IBM 7040 c o m p u t e r a t t h e C o m p u t i n g C e n t r e o f  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 was u s e d f o r a l l t h e  calculations. purpose  2.  T y p i c a l c o m p u t e r programmes u s e d  a r e p r e s e n t e d a t t h e end o f t h i s  f o r that  appendix.  Sample c a l c u l a t i o n s : Run No. 1302 N a p h t h a l e n e - A i r  Example  Experimental data : D a t e A u g . l / ' 6 6 s t a r t i n g a t 11:40 A i r temperature  AM  T = 2 7 - 9 °C  Atmospheric pressure  P = 7 5 9 - 7 mmHg  Diameter  d = 0 . 3 8 1 cm  of cylinder  L e n g t h o f c y l i n d e r % = 3 . 9 2 cm Double  amplitude  Frequency  H = 0 . 3 8 1 cm  of oscillation  f. = 4890 RPM = 8 1 . 5 s e c  Time o f o p e r a t i o n ,  t = 30.0 min  Weight o f m a t e r i a l  sublimated  Viscosity  and d e n s i t y  jj-. ( E q u a t i o n ( 1 2 ) ) J>  (Equation(13))  Rev -_25£L£. =  W = 0.0086  o f a i r a t 2 7 . 9 °C  = I.8383 x 10  _ Z <  = 1.1726 x 10~ 150  .9  3  g/cmsec g/cm  3  grams  A-ll  Res  ( 1+H/d  = Rev  k k'.  _ wt. wt.  301.9  ) =  subllmated/unlt time/unit area ( v i b r a t i o n a l ) sublimated/unit time/unit area ( s t a t i o n a r y )  = 6.9065 =1.0  H/d  = 1 + 2H/-ft d =  A/A'  1.637  D ( E q u a t i o n ( l 4 ) ) = 0.06220 c r n / s e c 2  Sc = y>/p  D = 2.5205  k = W/A'tc Sh = dk/D  3.  obtained  = 13.046  s t a t i o n a r y mass t r a n s f e r c o e f f i c i e n t , k',  from the equation W/A't  Therefore  =  k'  s u b l i m a t e d , A'  as f o l l o w s ,  = W/A'tc i s the  where W i s t h e w e i g h t o f m a t e r i a l surface area of c y l i n d e r , t i s the c  i s the  s u r f a c e of the m a t e r i a l .  h a v e been t a k e n k'  is  k'c*  o f s u b l i m a t i o n , and  at the runs  1-3)  S t a t i o n a r y mass t r a n s f e r c o e f f i c i e n t The  time  = 2.1298 cm/sec ( s e e a p p e n d i x  and  saturation concentration About twenty f i v e s t a t i o n a r y  the average value  o f . k ' i s employed.  = 0.30837 cm/sec  T h e r e I s no  significant  temperature over experiments.  change o f the v a l u e  the range of temperatures  o f k' used i n  with these  A-12  'Table  Stationary (average  mass t r a n s f e r c o e f f i c i e n t .*  diameter  O.38  cm)  TEMP PilTtS SUBL.RATL V A P . TIME K' •'G MMHG 9/cmVm. H H HG MIN. CM/SBC 0 25 .0 75 8 . 0 . 5 ...9.1 0 .0871 .31. .0 .28268 .. 25 .0 758 . 0 6 .04 0 .0871 60. 0 .28890 25 . 2 .7 5 8 . c 5 .85 c .0883 30.. 0 .27349 27 .0 75 5 .8 n .21 0 .1004 36 0. 0 .31289 27 .0 755 .8 8 .24 0 . 10 04 360. 0 .31404 2 5 ; 3 758 .0 7 . 15 0 .08 39 35. 0 .33047 26 i i .7 5 6 .6 7 .20 .0 .09 40 63.. 0 .30 3 82 26 L 756 .6 8 .81 0 .0940 65. 0 .3 7176 2 6 5. 5 75 9 .4 7. 51 0 .0968 420. 0 .30285 26 : 5 7 59. 4 7.51 0 . 09 68 4 5. G .30285 26 i 5 759 .4 6 .96 0 .09 68 63. 0 .28067 24 ; 4 759 .6 6 .01 0 .0836 20. 0 .30793 24 i.4 7 5.9 .6. .5.96 c . 08 36 35.... 0.305 37 24 . 5 7 59 . 6 6 .45 0 . 08 42 40. 0 .326 70 24 ;9 7 5 9 . 6 6 .73 0 .0865 45. 0 .32561 23 . 7 7 5 fi .5 5 . 60 0 . 0 7 9 9 60. 0 .31100 .24 i5. 7 56 . 5 6 .38 c .08 42 240. 0 .:32316 2 5 . 1 7 56 .'5 6 . 70 G . 08 7 7 130. 0 .31683 . .. 26 . 2 7 56 .7. . 6.66 0 .0947 120.. 0 .2 7786 . 25 ;9 .7 56 . 7 6 . 89 0 .0927 90. 0 .2 9742 26 . 3 7 56. 7 .80 0 . 09 5 4 90. 0 .280 51 26 , 3 7 5 e 30. 0.29701 1 .20 0 .09 54 23 i 2 75.5 . 0 5 .60 0 . 07 73 120. .0J32950 2 3 ^8 75 5 . G 5 . 86 C .08 04 25. 0 .32171 24 75 5 .0 5 • 87.. G .0825 140. G .3C775 . 24 » 5 75 6 .8 6 . 35 0 .08 42 60. 0 . 32164 7 5 6 6 .17 140:. .8 0 .0842 0 .31252 2.4. 5 24 . 3 75 6 .8 6•. 04 0 .08 30 60. 0 .31304 y  I  s  t:  »  «  f  c  data  f o r naphthalene  A-13  4.  method^ ' -95-99)  Least-squares Example  2 1  : Case  p p  Sh = ft ( S c , R e v , H / d )  As m e n t i o n e d i n t h e D i s c u s s i o n s e c t i o n , t h e e x p o n e n t o f Sc i s t a k e n t o be 1/3, a n d a n e x p o n e n t i a l r e l a t i o n s h i p is  assumed.  Sc'*  Therefore =  x Rev  y  t h e r e q u i r e d form ( H/d )  of equation i s :  z  where x , y a n d z a r e c o n s t a n t s t o be o b t a i n e d . Taking  t h e l o g a r i t h m o f both  s i d e s , t h e above  equation  becomes, l o  Putting  s  (-#Vs  >  Oc  A = l o g ( JLh_ Sc.  l o  =  s  x  +  y  lQ  s  R e v  +  z  lQ  s  (  H  /  d  )  ) , B = l o g R e v , C = l o g ( H/d ) a n d X = l o g x ,  3  the equation i s s i m p l i f i e d as f o l l o w s X + By + Cz = A F = ( X + B.y + C z - A. ) i=l  II  1  1  where N I s t h e number o f d a t a p o i n t s . to f i n d proper value.  Then t h e p r o b l e m i s  v a l u e s o f X, y a n d z t o g i v e F t h e minimum  T h e r e f o r e - ^ l , 5Il a n d ^E.  ~P  ax = H  d  1  s h o u l d be z e r o .  dz  ay  2( X + By + Cz - A ) = 0  |£  = Z I 2 ( X  |£  = I I 2( X + B y + Cz - A ) ( C ) =  Three simultaneous  + By + C z - A ) ( B )  equations  are obtained.  X*N  + yCB + zCC =U A  XHB  + yZIB +  z£BC=£!AB  XUC  + yUBC+  zCC =CAC  2  2  = 0 0  A-14  Using the  subroutine  1  SOLTN', a v a i l a b l e a t t h e U.B.C.  C o m p u t i n g C e n t r e , v a l u e s o f X, y, and Gauss e l i m i n a t i o n  method.  z are obtained  by  the  £UG'ANO ISN (r  0  *- * "~  r  ,r /  'r f p.  -  •  *~ A-  >  SOURCE  •  P  o  -  STATEMENT  FORTRAN  SOURCE LIST  A-15  SIBFTC THESIS C CALCULATION O F SC AND RE * C AIR NAPHTHALENE 1 * 100 READ 1 , N O , D A T E , T , P , D I A, WI D,AMP,TIME,DW,FRQ 3 1 ... FORMAT { 2X, I 4 , F 9 . 4 , 1X.F6. 2 , IX , F 6. 1, 1 X , F.5 . 2 , IX , F5 . 2 , IX , F6 . 3, 1X , F It IX,F7.4,lX,F6o0) • C DIA*.*MM FREQ**R.P.M. TIME**MIN 4 TK=T+273.16 5 * VlS=170.6.*.iO.**(-6. )*(TK/273.16)**0.768 6 R0H=1.2929*10.**(-3.)*(273.16/TK)*(P/760.0) VK=VIS/R0H . _ ;.. . 7 10 VEL=2.*AMP*FRQ/60. 11 RES=(D.IA/10.+AMP)*VEL/VK 12 REV=DIA/10.*VEL/VK 13 ARATI0=l.+2.*AMP/3. 141592/DI A*10. SUBSCRIPT! TO GAS 2TO SAMPLE C 14 .... WMi=28.97. 15 .WM2 = 128.17 16 E10K=97c0 17 T E20K=971.13 20 S. Rl=3.617 21 * R2=6.23 . , C .. .DIFFUSION COEFFICIENT ... 1 .. 22 * ROMOL=<l./WMl+l./WM2)**0.5 23 RAV=(Rl+R2)/2. 24 RSQ=RAV**2. 25 ROEOK=.CEiQK*E20K)**0.5 TKE=TK/ROEOK 26 * 27 256 .. . I F ( T K E - 1 . 0 ) i l , l l , 3 . . .__ ..... 30 "TT 3 \ IFi*TKE-2.0)12,12,-4 4 IF(TKE-3.0)13,13,14 31 32 * 11 CI=1.331*(0.3/TKE)**0.510643 GO TO 15 33 * 34 12 CI=0.7197*(l./TKE)**0.421669 35 * .. G O TO 15 . .. . : 36 13 CI=0.5373*12./TKE)**0.306517 37 4' GO TO 1.5 14 C1=0.4745*(3./TKE)**0.20 9053 40 41 15 8=(10.7-2.46*ROMOL)*0.0001 DG = B*TK**i:.5*ROM0L/{ P/760. )/RSQ/CI 42 . SC=VK/DG . . . 43 44 * CUSC=SC**<1.73.) 45 A0R=AMP/DIA*10. CUSQAR=A0R**(1./6,) 46 * CORRECT C P£RT=0„ 47 . . SCC = 10Co . . . ... _ . ..... ... . 50 R AM DA = 0.0192 *{ 398./ (TK-f-125. ) ) * ( T K / 2 7 3 . )**1.5/360. 51 TKK = TK 52 53 * 274 TK= TKK—PERT PP=10.**(13.9469-4544.9/TK) 54 Ce=.002'055138*PP/TK 5 5 .* 56 JLT W H E A T = - « 5 5 7 8 * ( T K - 2 7 3 . 1 6 ) +596..3 ... . HEAT=0.234*WHEAT 57 D6LT=DG/RAMDA*(SC/0.7)**0.33333*HEAT*CC 60 *  A-lG 5UGANQ  I  FORTRAN SOURCE  SN 61 62 63 64 67  # *  PERT=A8S(DELT) PERCE=ABS(SCC-CC)/CC SCC=CC IF{PERCE.GT.0„01) GG  V-  p- .  ''""NO  TO  THESIS  274  APK=DW/TIME/3.14159265/DI A*10./WID/60./CC K'=STAK STAK=0.30837 RAT IOK = A P K / S T A K S ' = R A T L G K - 1 . . ... U=REV*{ ARATI0).**2. SHERWOOD NUMBER SH=DIA/10.*APK/DG T E C = R E V * * 0 . 5 * S C * * 0 . 3 3 3 3 3 3 * { A M P / D I A * 1 0 . )**{ Z=SH/TEC Y=SH/SC**0.3 3 3 3 3 3 / A 0 R * * ( l . / 6 o ) SSH=DIA/10.*<APK-STAK)/DG SY=SSH/SC**0„333333/A0R**(1./6.) Z0NY=SH/REV**0.5/SC**0.3 33 3  * . 4V  75 76 77 100 101 102 103 104 105 106 107  >  LIST  .TK = T K - 2 7 3 . 1 6 . . . . . .  70 71 72 73 74  SOURCE  STATEMENT  1-/6.)  ZCNX=A0R**0.5 SQ=A0R**0.5 CSQ=1./SQ . . P-IN = S H / ( - S C * * 0 . 3 3 3 3 3 3 ) / ( 0 . 5 1 8 0 3 * S Q + 0 . 3 0 4 2 8 * 0 S Q ) HO UNI.T = P I N / R E V * * 0 . 5 111 TSAHEN=SH/((l./A0R)**0.5- •(A0R**0.5)*0.22)/SC**0.33333 C INDIAN 112 YY=SH/iCUSC 113 . SSS = SH/SC**0.333333/CUSQAR. 114 SPRE=2-.*3. 141592*REV PRINT2,N0,-RATIOK,ARATI0,RES,REV, AOR,SC,SH 115 * FORMAT(20X,14,2(1X,F6.3)ilX,F7.2,lX,F7.2t2(lX,F5.3),lX,F6.3) 1 16 * 2 117. * GO TO 1 0 0 STOP 120 * 1000 END _ , . 1 2 1 . * .. .  MESSAGES  FOR  ABOVE  ASSEMBLY  JR594  ...  S U G A N O  F O R T R A N  I S N  S O U R C E  0  $ I B F T C •4T  'r  r  1  •*  2  *  C  4  1 5 1 7  R E A D 2 , S H { T  2  t  21  f  ' >. >•  >  I F ( N O ( I ) . E Q . 1 3 ) G 0  *  1  .  C O N T I N U E .  3  D 0 9 9 9  2 4  X Y = 0 .  2 5  X S  2 6  Y S = 0 . W= 0 .  3 0  WX = 0 .  *  4 0  I F ( K I J „ E Q . 3 )  I)  3  D Y = A L Q G ( l < ,  J  ...  r A G R ( I  )  )  D Y = A L 0 G ( 1 . + A 0 R ( I ) * 2 . / 3 . 1 4 1 5 9 2 6 5 ) 1 * * 0 - 3 3 3 3 3 3 ) .  Y = Y + D Y  *  X Y  = X Y - s - D X * D Y  X S = X S + D X * * 2  +  Y S = Y S + D Y * * 2 W = W + D W .  W X = W X + D W * D X  .  ..  V g Y = W Y + D W * D Y  5 4  4  C O N T I N U E  5 6  P R 5  5 7  I N T S « X , Y , X Y , X  F O R M A T  S • Y  S,W,WX  ,  WY  (/ / 8 ( 2 X , E 1 3 o 7 ) / ' )  A ( 1 , 1 ) = R A S T  6 0  *  A ( 1 , 2 ) = X  6 2  A (  6 3  . .  .  1 , 3 ) = Y  . A ( 2 , 1 ) = X  6 4  A { 2 , 2 ) = X S A ( 2 , 3 ) = X Y  6 5  +  .  A ( 3 , 1 ) = Y  ...  . 6 7 -4-  A ( 3 , 2 ) = X Y  T  A ( 3 , 3 ) = Y S  •*  8 ( 2 ) = W X  *  C A L L  .  B(1)=W  7 1  B ( 3 ) = W Y  7 3  7 6  I ) , N 0 (  X = X + D X  5 3  7 5  A O R {  ... ..  DW = A L O G ( S H ( I ) / S C ( I ...  . 5 1  7 4  T O  ...  I F ( K I J „ E Q „ 2 )  5 2  ' f  = 1 , L A S T  D Y = A L 0 G ( A 0 R ( I ) )  7 2  t  .  3 5  7 0  I ) , R E V { I )  1 5 )  K I J = 1 , 3  3 4  6 6  I )  . '.  D X = A L 0 G ( R E V ( I ) )  6 1  ) , N 0 (  ..  3 3  4 7  >  I ) , A O R ( . I  WY = O o 0 0 4 1  4 5  ,  ) , R E V (  = 0 .  2 7  5 0  F ( H / D ) A O R (2 0 0 ) , N 0 ( 2 0 0 ) , A {3 , 3  Y = 0 .  4 3  >  A N O  X = 0 .  *  4 4  > >  R E V  L E N D = I  R A S T = L A S T  4 6  O F  , P L S (2 0 0 ) , R E V { 2 3 0 ) ,  I F ( N O ( I ) . E Q . 3 5 0 7 ) L A S T = I  2 1  3 2  I ), S C( I ) , P L S ( I  F O R M A T ! 5 ( 3 X . E 1 3 . 7 ) . 3 X „  3 1  _  E X P O N E N T S  0 0 )  • P R I N T 2 1 , S H ( I ) , S C ( I ) , P L S (  2 2  • p-  F O R  , S C ( 2  F 0 R M A T ( 5 E 1 3 . 7 , I 5 )  2 0  2 3  M E T H O D ( 2 0 0 )  0 0 1 1 = 1 , 3 0 0  1 2 .  A-17  1 ) , B ( 3 )  7 .  S Q U A R E S  D I M E N S I O N S ! - !  5 6  L I S T  K O T A E  L E A S T  3  0~  S O U R C E  S T A T E M E N T  .  .  S O L T . N (  A , B , 3 v 3 , D E T )  B ( 1 ) = E X P ( B ( 1 )  )  .  P R I N T 6 , B ( 1 ) , B ( 2 ) , B ( 3 ) , D E T  ..  . ..  A-18 .SUGANO . ISN  ~ SOURCE  77  •?*-  100 101  6  * 961  * fv  - - 1  ;  i  i i  i. - 0 -  i  |  NO  102 103 104 105 106 107 112 115 116 117 120 121 122 123 125 127 130  * •* * -r  *.  * * *  FORTRAN  SOURCE  LIST  KQTAE  STATEMENT  FORMAT ( 3 X , 3HB1 = ,-E13 - 7 , 3 X , 3HB2= , E 1 3 . 7 , 3 X , 3 H B 3 = , E 1 3 . 7 , 4 X , 4 H D E T = , E 1 3 . 17 ) PRINT961, FORMAT<2X,1HI,4X,2HM0,9X,2HSH,14X,2HSC,9X,3HH/0,6X 1,5X,8H**/REV**,7X,4HUNIT,8X 4HLEFT,7X,3HREV) .. U T O T = 0 .  ,10HSH/SO*l/3  t  DO 1 0 1 = 11 L E N D C=SH(I)/SC(I)**0.33333 D=C/REV(I )**B(2) E=C/AOR(I)**B(3) IF(KIJ.EQ.2) E=C/(1.+A0R(I))**B(3) . I F U I J . . E Q . 3) E = C / < l . + A Q R ( I ) * 2 . / 3 . 1 4 1 5 9 2 6 5 )**B( 3 ) U=E/REV< I ) . * * B ( 2 ) / B ( 1 ) S=I UT0T =UT0T + A L 0 G 1 0 ( E / B U ) ) * * 2 UABS=(UT0T/(S-3.))**0.5 PR I N T 1 1 , I , N O < I ) , S H < I ) , S C ( I ) , A O R ( I ) , C , D , U , E , R E V ( I> .. , U A B S 1 1 . . . : . . .. F O R M A T { l X , I 3 , 2 X , I 4 , 2 X E 1 3 . 7 , 2 X , £ 1 3 . 7 , 2 X , F 7 . 4 , 2 ( 2 X , E 1 3 . 7 ) , 2 X , F 3 . 5 1,3X,F9»4,2X,F9.3,3X,F9.3) CONTINUE 10 999 CONTINUE STOP 1000 END  MESSAGES  t  FOR  ABOVE  ASSEMBLY  A-19  APPENDIX  IV  O r i g i n a l data  Table  IV-1. O r i g i n a l data of naphthalene  Table  sublimation  into a i r .  IV-2. O r i g i n a l data of phenol  sublimation  into a i r .  Table I V - 1 . RUN MO.  O r i g i n a l data o f naphthalene  DATE MO.CY.H.M. DAY  ROOM TEMP. C  ATMOS. PRESS. MMHG  D I A . LENG. CM.  CM.  sublimation into a i r . DODL. AMPL. CM.  GPTN. TIME KIN.  MASS SUBL. GRAM  FREQ. RPM.  301 11 4 / 8 4 5 23-0 757.8 0.370 3.40 0.186 30,0 0.0031 4310. 302 7/ 4 / 942 23.0 757.8 0.370 3.40 0.186 30.0 0.0010 3360. . . 303. 7 / 4 / 1 0 1 9 . 2 4 . 5 7 5 7 . 8 . 0 - 3 9 0 . 3 . 4.0. 0 . 1 8 6 _ _ 3 0 . 0 0 . 0 0 1 5 4296. 304 7/ 4 / 1 1 1 9 24.9 757.8 0.400 3.75 0.186 30.0 0.0028 5152. ,305 7/ 4 / 1 5 2 9 25.4 757.7 0.390 3.70 0.186 30.0 0.0029 5235. 306 7/ 4 / 1 6 0 4 25.4 757.7 0.390 3.70 0.186 30.0 0.0033 5460. 401 7/ 5/1100 22.8 755.0 0.385 3.70 0.186 30.0 0.0039 7890. 402 7/ 5 / 1 1 0 0 22.8 755.0 0.350 3.70 0.186 30.0 0.0042 7890. 501 . 7 / 6/124.4 „ . 2 4 . 0 . 754-0._0.. 3 9 0 „ 3 . . 6 3 _ 0 . 1 8 6 . . . . 3 0 . 0 0 - 0 0 4 2 _ 3 4 7 0 . 502 7/ 6 / 1 2 4 4 24.0 754.0 0.380 3.65 0.186 30.0 0.0039 3470." 601 7/12/1425 26.3 753.6 0.400 3.73 0.207 30.0 0.0011 1580. 602 7/12/1500 26.3 753.6 0.398 3.73 0.207 30.0 0.0024 2955. 701 7 / 1 3 / 634 23.0 753.7 0.363 3.68 0.207 32.0 0.0021 3200. 702 7 / 1 3 / 740 24.0 753.7 0.433 3.70 0.207 .30.0 0 . 0 0 2 8 4800. 703 . 7 / 1 3 / 824.. . 2 5 . 2 . 7 5 3 . 7 . 0 . 3 6 . 0 . 3 - 6 8 . . . 0 . 2 0 . 7 . . . 3 3 . 0 _ _ 0 - 0 . 0 3 4 . _ 6 2 2 0 . '801 7 / 1 4 / 950 26.2 754.2 0.397 3.66 0.207 30.0 0.0043 6840. 802 7/14/1038 26.2 754.2 0-375 3.66 0.207 32.0 0.0018 2137. 110.1 7/25/1035 25 . 8 7 5 8 . 0 0 . 3 8 0 3 . 5 6 0 . 2 2 7 32.0 0.0028 2400. .1102 7/25/1299 26.2 758.0 0.391 3.28 0.227 35.0 0.0031 2650. 1103 7/25/1439 25.9 759.3 0.413 3.55 0.227 33.0 0.0040 6510. 1104 .. _ 7 / 2 5 / 1 5 1 4 . _ 26.3__7.5.9.._3_.0...392..3 .7.0__0.22 7_ _33 . 0 _ 0 . 0 0 1 8 . _ 1680.. 1201 7/28/1340 28.3 757.2 0.393 3.88 0.277 30.0 0.0020 1022. 1301 8/ 1/1104 2 7 . 9 759.7 0.383 3.92 0 . 3 8 1 30.0 0.0037 2330. 1302 8/ 1 / 1 1 3 9 27.9 759.7 0.381 3.92 0.381 30.0 0.0086 4890. 1303 8/ 1/1315 2 8 . 9 759.8 0.378 3.92 0.381 32-0 0.0043 2092. 1304 8/ 1/1354 28.8 759.8 0.400 3.88 0.381 30.5 0.0060 3030. 13G5 8 / . . 1 / 1 4 3 2.... 2 8 . 6. _ 7 5 9 . 8 . 0 . 398._3..88_ .0 . 3 8 1. ...30 . 0 _ 0 . 0 0 2 0 ._1040 . 1801 8 / 1 6 / 930 23.8 757.0 0.388 3.68 1.369 22.0 0.0048 1940. 1401 8/ 2/1050 2 7 . 9 759.2 0.388 3.64 0.331 30.0 0.0056 1445. 1402 8/ 2/1125 2 8 . 0 759.2 0.388 3.64 0.381 30.0 0.0095 4760. 1403 8/ 2/1224 28.0 759.2 0.386 3.79 0.381 30.0 0.0106 4570. 1404 8/ 2 / 1 4 4 3 28.0 759.2 0.379 3.75 0.381 13.0 0.0067 6130. _ .1501 ... .. 8 / . . 7 / 2 C 9 9 „ _ 2 7 _ . 0 . _ _ 7 5 5 . 0 . . . 0 . 3 6 8 _ 3 . 6 8 . 0 . 3 8 1 _ 3 0 . 0 _ . 0 . 0 0 9 7 . . . . 3 9 2 0 . . 1502 8/ 7/2135 2 7 . 1 755=0 0 . 3 9 4 3 . 1 4 0 . 3 8 1 30.0 0.0099 4430. 1503 8/ 7 / 2 2 0 9 27.1 755.0 0.394 3.14 0.381 30.0 0.0099 4430. 1504 8/ 7 / 2 2 4 6 26.5 755.0 0.456 3.49 0.331 30.0 0.0067 3950. 1505 8/ 7 / 2 3 2 4 2 6 . 3 755.0 0.386 3.55 0.331 30.0 0.0068 3470. 1506 8/ 7/2359 26.0 755.0 0.374 3.58 0.381 30.0 0.0030 2175. 1507 8/ 8/ 2 9 _ . _ 2 5 . 7 . . 7 5 5 . 0 . . 0 . . 3 7 3 _ _ 3 . 5 8 _ . 0 . . . 3 8 1 __54.0_. 0 . 0 0 2 5 885. 1601 8 / 3 / 220 25.0 755.0 0.396 3.74 0.978 31.0 0.0086 1890. 1602 8/ 8/ 250 24.9 755.0 0.396 3.74 0.978 30.0 0.0044 830. 1603 8 / 8 / 329 24.8 755.0 0.390 3.74 0.978 30.5 0.0067 1940. 1604 8/ 8/ 400 24.7 755.0 0,383 3.74 0.978 30.0 0.0071 2200. 1605 8/ 8 / 435 2 4 . 7 755.0 0.385 3.73 0.978 30.0 0.0071 1890. ... 1701 . . . . . 8 / 1 . 1 / 1 9 4 9 2 5 . 0 . 7 . 5 . 5 . 9 . . . 0 . 3 9 3 . 3 . 9 6 _ 1 _ . 369___ 3 5 . 5 _ 0 . 0 0 8 6 748 ._ 17C2 8/11/2030 25.0 755.9 0.385 3.95 1.369 10.0 0.0041 2660. 1802 8/16/1025 23.8 757.0 0.384 3.68 1.369 29.0 0.0098 2201. 1803 8/1671115 2 3 . 8 757.0 0.379 3.69 1.369 44.0 0.0124 2040.  continued  A-21  RUN NO.  DATE MO.CY.H.M. DAY  -  ROOM TEMP. C  ATMOS. PRESS.  DIA.  LENG.  DOB L. A n . , .  MMHG  CM.  CM.  CM.  OPTN. TIME  MASS SUBL.  FREQ.  MIN.  GRAM  RPM.  1804 8/16/1644 25 . 0 7 5 8 . 3 G. 3 8 0 3 . 6 7 1 . 369 14.0 0.004 7 2123. 180 5 8/ 1 6 / 2 3 5 7 25 . 0 7 5 9 . 1 0 . 371 3 . 6 5 I . 369 31.0 0.0068 950. 1901 8 7 1 7 / . 1 5 0 0_„. 2 4 . 8 . . 7 5 8 . 3 . 0 . 3 8 8 . _3 o 9.4 _1. _ ..3 69_. . . 3 0 . 0 . 0 . 0 1 2 8 _. 2 6 0 5 . 1902 8/17/1537 24 . 9 7 5 8 . 3 0 . 4 2 5 3 . 6 0 1 . 3 6 9 1734. 31.0 0.0096 1903 8 / 1 7 / 1 6 10 25 . 0 7 5 8 . 3 0 . 421 3 . 6 0 1 . 3 6 9 30.0 0.0088 1836. 8/18/1.00 2001 2 4 , 0 756 „ a 0., 3 8 6 3 . 7 0 1 . 369 3 0 . 0 0 . 00 5 5 778 . 2002 24 . 0 7 5 6 . 8 0 . 3 83 3 . 7 0 1 . 3 6 9 8/18/1131 30. 0 0.0058 1007 . 2C03 24 . 0 7 5 6 . 8 0 . 3 9 0 4 . 1 6 1 . 3 6 9 8/18/1320 30.0 0.0097 2190 . . .. 2 1 0 1 . . . 8 / 2 4 / 2 105 _.. 2 6 . 0 . . 7 5 6 . 0 . . 0 . 401 . 3 . 9 8 . .2 . 1 0 0 . 3 0 . 0 . 0 . 0 1 3 3 .1595 . 2102 8/24/2135 26 . 1 7 5 6 . 0 0 . 4 0 0 3 . 9 8 2 . 1 0 0 31.0 0.0093 1020 . 2103 8/25/1309 24 . 0 7 5 5 . 2 0 . 3 9 4 4 . 0 1 2 . 1 0 0 10.0 0.0048 950. 2104 8/25/1324 24 . 0 7 5 5 . 2 0 . 3 8 9 4 . 0 1 2 . 1 0 0 25.0 0.0043 412. 2201 8/30/1017 2 2 . 5 7 5 4 . . 1 0 . 390 3 . 9 1 . 100 30 . 0 0 . 0 0 5 8 636 . 2202 22 . 5 7 5 4 . 1 0 . 385 3 . 9 1 2 . 1 0 0 8 / 3 0 / 1 0 50 13.0 0.0027 853 . 2 2 0 3 .... . 8 / 3 0 / 1 1 1 0 2.3 . 0 7 5 4 . 1 „ 0 . 390.. . 4 . 16. 2 . 1 . 0 0 . _ _ 3 0 . 0 . . 0 . 0 0 7 7 . _ . . 1 0 3 0 . 2301 9/ 1/1100 23 . 0 7 5 9 . 1 G. 39 5 3 . 9 5 0 . 1 4 0 43.0 0.0026 665. 2302 9/ 1/1354 23 . 1 7 5 9 . 1 0 . 3 9 0 4 . 30 0 . 1 4 0 40.0 0.0015 1337 . 2 303 9/ 1/153 7 2 3 . 1 7 5 9 . 1 0 . 388 4 . 3 0 0 . 1 4 0 40.0 0.0028 2268. 2401 23 . 6 7 5 6 . 9 0 . 370 3 . 9 8 0 . 1 4 0 9/ 5/1048 62.0 0.0030 4440. 2402 9/ 6/1306 23 . 6 7 5 6 . 9 0 . 3 9 3 4 . 0 5 0 . 140 63.5 0.0024 3300. _ 2 5 0 1 . . _ 9 / _ _ 7 7 1137 .... 2 3 . 9 . 7 5 5 . 0 . 0 . 3 8 0 . . 3 . 9 0 . . 1.40 . . . 6 0 . 0 . . 0 . 0 0 3 1 41.55 . 2502 24 . 0 7 5 5 . 0 0 . 3 8 0 3 . 9 0 0 . 1 4 0 9/ 7/1241 60.0 0.0033 4190. 2503 9/ 7/1429 2 4 . 2 7 5 5 . 0 0 . 3 9 3 3 . 8 7 0 . 140 76.0 0.0035 3795 . 260 1 9/ 8 / 1 2 0 0 24 . 1 7 5 6 . 3 0 . 3 7 6 3 . 8 9 0 . 140 57.0 0.0023 4840 . 2602 9/ 9 / 1 2 0 0 24 . 3 7 5 4 . 9 0 . 3 65 3 . 9 3 0 . 1 4 0 433 . 77.0 0.0030 2 6 03 9/ 9 / 1 3 2 3 24 . 9 7 5 4 . 9 0 . 3 6 1 3 . 9 3 0 . 1 4 0 7 5 . 0 0 . 0 0 2 3 439 . . '.. .... 2 7 0 2 . 9 / 1 2 / 1 1 1 0 . 18 . 9 7 5 5 . 7 . 0 . 3 7 3 . . 3 . 1 6 . . ,0 . 140... _ 2 5 . 0 „ . 0 . 0 0 0 8 . _ 4 1 2 0 . . 2703 9/12/1305 19 . 8 7 5 5 . 7 0 . 352 3 . 9 4 0 . 140 57.5 0.0017 3702 . 2 2 . 5 7 5 4 . 4 0 . 3 8 0 3 . 2 1 0 . 5 50 2801 9/15/1330 60.0 0.0061 1665 . 2802 9/15/14.34 22 . 4 7 5 4 . 4 0 . 37 5 3 . 2 0 0 . 5 50 32.0 0.0024 460. 28 0 3 9/15/1510 22 . 8 7 5 4 . 4 0 . 368 3 . 2 0 0 . 5 5 0 34.0 0.0042 2085. 2901 9/ 1 6 / 1 2 2 0 22 . 0 7 5 3 . 0 1 . 0 0 5 4 . 12 0 . 5 5 0 34.0 0.0072 2163 . 2 9 0 2 . . . . 9 / 1 6 / 1 3 5 . 5 _ . . 22 . 3 . . . 7 . 5 3 . 0 . 1 . . COO. 3.. 9 5 . .0 ..5 50. _ _ . 3 5 . 0 . 0 . . 0 1 0 . 4 . . 3 2 8 5 . 24 . 3 7 5 6 . 9 0 . 390 3 . 7 0 0 . 5 5 0 3001 9/18/1320 30.0 0.0088 3675. 3002 24 . 1 7 5 6 . 9 0 . 3 8 5 3 . 7 0 0 . 5 5 0 9/18/1.399 31.5 0 .0086 38 0 0 . 23 . 1 7 5 9 . 0 1 . 0 0 0 3 . 7 7 0 . 5 5 0 3101 9/19/1309 24.5 0.0042 1800. 9/ 19/1847 23 . 9 7 5 6 . 9 0 . 9 9 0 3 . 7 7 0 . 5 5 0 3102 31.0 0.0077 2 440 . 3103 9/20/1050 23 . 8 7 5 8 . 1 1 . 0 0 1 4 . 31 0 . 5 5 0 30.5 0,0127 3395. 3104 9 / 2 0 / U 5 . 1 _ . . 2 3 . 8 . . 7 5 8 . 1 . _.1..024_ . 4 . 2 8 ..0.. . 5 5 0 . . . . 3 0 . 0 . 0 . 0 1 1 5 . 3 2 4 0 . 2 4 . 9 7 5 8 . 1 1 . 017 4 . 2 1 0 . 550 3105 9/20/1412 30.0 0.0048 1790. 3106 23 . 4 7 5 8 . 1 1 . O i l 4 . 2 1 0 . 5 5 0 9/20/1445 30.0 0.0042 1323. 3107 9/20/1620 23 . 1 7 5 0 . 1 1 . G06 4 . 2 0 0 . 5 5 0 38 . 0 0 . 0 1 2 0 2903. 3108 23 . 7 7 5 8 . 1 1 . O i l 4 . 2 0 0 . 5 5 0 9/20/1939 30.0 0.0106 3290. 3109 • 9 / 2 0 / 2 0 0 9 23 . 7 7 5 8 . 1 1 . 012 4 . 2 0 0 . 5 5 0 46.5 0.0131 3190 . 9 / 2 0 / 2 1 2 8 .. . 2 3 . 4 . . . 7 5 8 . . 1 _ 1 . 0 0 4 . . 4 . 2 0 0. . 5 5 0 . . . 3 2 . 0 . 0 . 0 0 6 0 ... 19 1 0 . . _ 3.1.10. 3111 9/21/1500 25 . 0 7 5 8 . 1 1 . GOO 4 . 3 0 0 , 5 5 0 32. 5 0.0047 1395. 25 . 2 7 5 8 . 1 0 . 9 9 9 4 . 2 0 0 . 5 5 0 9/21/1536 3112 31.0 0.0179 4420 . 25 . 3 7 5 8 . 1 0 . 975 4 . 3 1 0 . 5 5 0 3113 9 / 2 1/ 1 6 1 3 24 . 0 0 . 0 1 4 1 4670 . 3114 9/21/1650 25 . 0 7 5 8 . 1 1 . 0 7 5 4 . 2 1 0 . 5 5 0 40.0 0.0054 1361 .  continued  A-2 2  RUN NO.  .......  3115 3201 3202. 3203 3204 3205 3206 3207 3301 . 3 3 02 3303 3304 3305 3401 .. 3 5 0 1 3502 3.503 3504 .3505 3506 3507  DATE MO.CY.H.M. DAY  ROOM TEMP. C  9 / 2 1/ 1922 25.0 9/22/1039 26 . 0 9/22/1915 25.9. 9/23/1244 24.0 9/23/1328 24.2 9/23/1415 25.0 9 / 2 3 / 1 5 10 24.9 9/23/1545 2 4.7 1 0 / 1 1 / 1 2 2 4 . ...19 . 5 10/11/1253 19.6 10/1 1/1305 21.0 1 0 / 1 1 / 1436 19.9 10/11/1610 20.0 10/11/1614 19.9 10/18/1320 . 2 3 . 0 10/19/1244 22.0 22.1 10/19/1299 10/19/1340 22.8 10/24/1049 2 3.8 10/24/1130 23 . 8 10/24/1250 23.9  ATMOS. PRESS. MMHG 758.  1  752.0  7 52 . 0 757.8 757.8 757.8 757.8 757.8 .756.0 756.0 756,0 756.0 7 56.0 756. 0 75 8 . 8 747.5 747. 5 747.5 759.9 759.9 759.9..  DIA.  LENG •  CM.  CM.  1.008 1.008 .1.005 1.000 0.998 0.995 0.995 0.995 .1.02 6 1.024 1.021 1.016 1.011 0.368 0.36 5 0.380 0.366  4.21 4.25 4.25. 4.25 4.25 4.25 4.25 4.24 4.45 4.45 4.45 4 .45 4.45 3 . 60 4.00 3.55 3 . 86 3 , 86 3 . 80 3.80 3.80  0.360  0 . 388 0.380 0.371  DGBL . AMPL. CM.  OPTN . TIME MIN.  0 .550 30.0 0 .977 30.0 0 • 977_. . 4 3 . 0 31.5 0 .977 0 .977 37.0 0 .977 52.0 0 .977 30.0 0 .977' 15.0 . 2 .068 .19.0 2 .068 4.0 2 .068 30. 5 2 . 068 20.0 2 .068 3.0 2 .068 18.5 2 .06.8. .... 3 0 . 0 2 .068 9.0 2 .068 30.0 2 . 06 8 30.0 33.0 2 . 068 2 .068 31.5 2 .068 8.0  MASS SUBL. GRAM 0.0168  FREQ . RPM.  4660 . 1914. 0.0245 . 2403. 0.0123 1323. 1606 . 0.0149 0.0211 2 087 . 3710. 0.0182 0.0136 4510 . 0 . 0 1 4 9 _ 3 950 . . . ... 0.0033 3443. 0.0204 3190 . 0.0161 3400. 0.0024 3280. 0.0072 3480. . 0 . 0 2 0 1 . .3240 . 0.0053 4350. 0.0131 2480. 0.0125 2600. 0.0166 2 370. 0.0160 2680. .0.0050 3630. 0.0171  A-2 3  Table  IV-2.  RUN  NO. 1 2 . 3. 4 5 6 7 8 9 10  Original  data  o f phenol  sublimation  into a i r .  DATE ROOM . A T M O S . D I A . L E N G . DOBL . OPTN. MASS FREQ. MO.DY..H.M. T E M P . P R E S S . A M P L . TIME SUBL. DAY C MMHG CM. CM. C M . M I N . GRAM • R P M . 12/12/2205 20. 4 12/12/2330 20. 3 12/13/ 104 . 2 0 . 3 12/13/ 144 20. 2 12/15/2019 21 . 0 12/15/2122 21 . 2 12/ 1 5 / 2 2 2 5 21. 1 12/15/2335 21 . 0 12/23/1945 . 22. 2 12/23/2124 20. 1  75 3 . 2 1 . 0 0 5 4 . 10 0 . 550 16. 0 0. 7 5 3 . "J 1 . 002 4 . 10 0 . 550 13. 0 0. 7 5 3 . 2. . 1 . 0 0 0 . . 4 . 0 0 . .0 . 5 5.0_. . 1 6 . 0. . 0 . 7 5 3 . 2 1 . 020 3 . 70 0 . 550 15. 0 0. 7 5 2 . 3 1 . 0 1 0 3 . 60 0 . 550 14. 5 0. 7 5 2 . 3 1 . 010 3 . 60 0 . 550 14. 0 0. 7 5 2 . .3 1. 0 0 0 3 . 60 0 . 5 5 0 15. 0 0 . 7 5 2 . 3 I . 0 0 0 3 . 60 0 . 5 5 0 17. 0 0. . 7 5 4 . 2. . 1 - 0 3 0 ..3.. 7Q A . 3 5 0.... . 6 . 0 . 0 . 7 5 4 . 2 1 . 0 2 0 3 . 70 4 . 3 5 0 9. 0 0.  0121 2100. 2000. 0115 0095. 1030. 0152 2250 . 0180 2500 . 0190 3020. 0234 3090. 0082 1650 . 0 1 5 3 ^ ...1720. 0192 600.  

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