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An exploratory study of the mechanism of coalescence of drop pairs Cordero, Leopoldo J. Jr. 1970

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AN EXPLORATORY STUDY OF THE MECHANISM OF COALESCENCE OF DROP PAIRS  by  LEOPOLDO J . CORDERO, J R . B.  A  S„  s  University  o f S a n t o Tomas, I 9 6 3  THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  in  t h e Department of  CHEMICAL ENGINEERING  We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o the r e q u i r e d s t a n d a r d  THE  UNIVERSITY OF BRITISH COLUMBIA February, 1970  In  presenting  this  an a d v a n c e d  degree  the L i b r a r y  shall  I  further  for  scholarly  by h i s of  agree  this  written  thesis at  the U n i v e r s i t y  make i t  tha  for  of  of  Columbia,  British  available  by  gain  shall  of  Chemical  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, Canada  February  24.  1970  that  not  Engineering  Columbia  the  requirements  reference copying  of  I agree and this  copying  or  for that  study. thesis  t h e Head o f my D e p a r t m e n t  is understood  financial  for  for extensive  p u r p o s e s may be g r a n t e d It  fulfilment  permission.  Department  Date  freely  permission  representatives. thesis  in p a r t i a l  or  publication  be a l l o w e d w i t h o u t  my  ii  ABSTRACT  H i g h - s p e e d movie p h o t o g r a p h y in a liquid-liquid  extraction  column  of drop c o a l e s c e n c e  h a s been u s e d  to study  t h e mechanism o f c o a l e s c e n c e t a k i n g p l a c e between d r o p u n d e r g o i n g mass t r a n s f e r was  m a i n l y from the d i s p e r s e d  The that  of  density  of  s p r a y column  apparatus.  studied  t o the c o n t i n u o u s phase.  the d i s p e r s e d  of  of diffusion  direction  t h e c o n t i n u o u s phase o  of a g l a s s  cal  The  0  pairs  phase  The e x t r a c t i o n  was  less  system  square c r o s s - s e c t i o n and  than consisted  associated  Other main a c c e s s o r i e s i n c l u d e d a s c h l i e r e n  s y s t e m and a h i g h - s p e e d m o v i e  The  i n v e s t i g a t i o n was  lo  Visualization the u s e  of  the  the m o t i o n o f  of  camera»  carried  o u t i n two  ways:  t h e d i f f u s i o n p r o c e s s , by  schlieren  techniques, t o s t u d y  various materials  a t and n e a r t h e d r o p c o n t a c t  2o  opti-  Measurement o f c h a n g e s  occurring  area°  i n drop  shape  with  timeo  iii  TABLE OF CONTENTS  Page INTR ODUCT I ON  © O O © © 0 9 © © G O © « O © O O © » © © © © © © © © © © O © © © © O © O © O O Q O ©  THE OR Y UNDER STUDY  ©©©©©©©o©©©©oe©e©o©o©©eoe«©oo©e©©©©eo  Jj'ffiSlilM. XNAH|Y INVESTI GAT I ON  0 o e e © o © © © o © o © © e © « o © e © e * « o © o © e ©  X *7 1 3  A•  SCOp©  B •  PTOCQCLIU ©  • ©©©©©©©©••©©©©©•©©©©©©©©©©•©©©©©©©e©  1 3  MA IN INVESTIGATION  ©©©oo©o©©e«©o©©©ocoGSGc©eo©©«©«o©o©e©  20  A. PART X  ©©©9©©o©e©©o©©o©Q©©o©o©©©©©©o©se©©©©o©©o© 1  Attempted M o d i f i c a t i o n s SCHXiIEREN STUDIES  to Existing  Apparatus..  1 3  20  ©©©©©©©©o©©©o©oo©©©oo©oo©©©o©©  2 ^  ©©e©&©e©o©©©o9©«e©©o©9©©9©©o©©0©©o©©a©o&©  23  A©  SCOP©  B.  Some P h o t o g r a p h i c  EXPERIMENTAI* PROCEDURE  Considerations  25  .  ©©©©©©©©•©©•©©©©©©©•©©©©©©•©©©©©o  29  A.  MIBK-Acetic Acid-Water System..................  32  B*  MIBK™Wstsi* S y s t s m  3^  C.  Toluene-Acetic  RESULTS  A c i d - W a t e r System  ..............  ©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©a  DISCUSSION A.  ©©©©©©©©©©©©©©©o©©©©©©©©©©©©©  ©©oo©©©e©©©oo©©e©9©©e©©o©©©©o©©©©eo©9©©e©©o©©  Effect  o f K n i f e Edge O r i e n t a t i o n on IlH£L££© o e © © © © o © e © © o « © © « © o © © © © © o © © © © © © o  SChXi©I*©Tl  B.  Drop R o t a t i o n a n d C o n t i n u o u s Ph&s©  Solute  Suspension  D.  Forces  E.  Minimum A t t a i n a b l e  •PART I I  A*  AND  DROP  SCOP©  o f Drops a t Ends of N o z z l e s  Influencing  Interfacial Depth  3 3 ^  3 ^  i n the  ©©©©©©©©o©©©©©©©©©©©©©©©©©©©©©  C.  CONCLUSIONS  Diffusion  40  Activity  60  ........  62  .......  64  of F i e l d  RECOMMENDATIONS  66 6?  O © © © © © © © © © © © © © © © © © © © © © © © © © © ©  69  ee©©o©©oo©oo©©©©©©©©o©©©o©©©o©©©o©e©©©e©o  ^0  SHAPE  STUDIES  iv TABLE OF CONTENTS  (confdo) Page  B.  Some P h o t o g r a p h i c  Co  Preliminary  Considerations  © © © . © © . o © . © . © .  ?0  ••••••••«••••©©•••••  72  ©©©©©©0©©©©©©©©©©©©©©©©©©©©©©©©©©  90  Considerations  EXPERIMENTAL PROCEDURE A.  MIBK-Methanol-Water System  B.  Measurement o f P s e u d o - r a d i u s  Co  Statistical  RESULTS  Tests  « © © © © © © © © . ©.©«©©©©©© •©  .©•©  95  ©©©©©©©©©©©©o©©©©©©©©©©©©©©©© 1 0 0  ©©oo©©e©00©©o©o©©©©©©©©0©OOOQ©©0©d©©©©©©Q©00©0©©  A©  E x p e r i m e n t a l Huns  B.  P s e u d o - r a d i u s Measurement  C©  Statistics  DISCUSSION  90  oeeo«©©o©©««o©©©©©©©©©©ooo©©o  •••«••«•  105 105  •••••••* 1 1 2  ©©©©e©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©  l l 6  ©©©©©©©a©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©®©©  137  A.  Applicable  Photographic  B©  Interpretation  Co  Precision  o f Data  Problems  ©o©©©©©©©©©©©©©©©©©©©©©©  of" Drop A n a l y s i s  1^1*8  •©•©••••••••©•••©••• I 6 3 ©...©.. 1 6 9  CONCLUSIONS AND RECOMMENDATIONS III ITSR A TURB CI TB D  >.. * 1 3 7  «©©©  ©©©©©©©©©©©©©©a©©©©©©©©©©©©©©©©©©©©©©©©  17^  APPENDICES A.  Determination of Acetic Acid Concentration i n t h e D i s p e r s e d Phase • • © • • • © • • • • • • • • • • • • • • • • • A—1  B.  Determination in  of Methyl  t h e D i s p e r s e d Pha  C.  Calibration  D.  Room T e m p e r a t u r e  E.  Test  F.  Properties  S©  Alcohol  a « « » » 0 © a o e © © e © » © © © e © © © s e  o f the Timing L i g h t Fluctuations  f o r Significance of Various  Concentration  Generator  C-l  ©©».©o«.«.©©©©©<>«  of Linear Regression S u b s t a n c e s Used  13 " " l  D-l  .... E - l F-l  V  TABLE OF CONTENTS ( c o n t ' d o ) Page G.  D e r i v a t i o n of Equation f o r the Locus of P o i n t s Generated by a Moving Drop with Respect t o a S t a t i o n a r y Movie Camera  G-l  H.  Sample C a l c u l a t i o n Showing the R e l a t i o n s h i p between L i n h o f and Hycam Exposure S e t t i n g s e e « H-l  I  C a l c u l a t i o n of F i l m Frame Span i n Runs 18 and 19 f o r N e g l i g i b l e Drop Growth E f f e c t 0 0 0 . 0 I - l  a  Jo  Heat E f f e c t s Accompanying the Mixing of G l a c i a l A c e t i c A c i d i n t o Water a t Room TGHipGrSL t \H*© ©©©©©©•©©©©•©©©©©©©©©•©•©©©©•©•©•o J**"l  IC©  Ps©ud.o~i*o,ciixzs Efettst  Lo  Input and Sample Output of the L i b r a r y Program, "UBC LQF", f o r Run 19  M.  ©©o©©©©©©©©©©©©©©©©©©©©©©©©  Input and Sample Output of the M u l t i p l e R e g r e s s i o n Program f o r Run 19 Written by Kozak and Smith (^5) • • • • o * * * o * s o * « o * o o * *  L-l  * o * * o  M—1  vi  LIST  OF  TABLES  Table I.  Page E x p e r i m e n t a l Data f o r P a r t StlXCLle S  II. III. IV.  Ball  )  © . © • © « .  (R©f*«  ©.©.......©...©..D  ©©©©©©©©©©©•©©•©©eoeoo©©eo  Vllb.  Analysis Run  in  Run  © . . © . . . © . . o . © © .  Table of L e f t Table of Right  of V a r i a n c e  Table of L e f t  Table of Right  IXb.  Analysis  XI.  Table of Left  Analysis  Table of Right  19  (Extended)  109  XI*p XX8  XX9  X20  Drop  ©©©©©©©©a©©©©©©©©©©©©©©©©©©©  of Variance  9^  Drop  i n Run 19 (Ext©nd©d)  i n Run X.  of V a r i a n c e  93  Drop  i n Run X9 ©©©©©©*«©©©©©©©©©©©©©©©©©©©©©©*©©©©©©©© iXa.  89  Drop  ©©©©©©©©©©•©•©©©©©©©©©©©©•©©©©©©©©©©©©©  of Variance  85  Drop  ©©©©©©©©©©©©©©©©©©©©©©©©©©o©©©©©©©©©©©©  X9  Analysis  Times  33  Shape  ©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©a©©  of Variance  X8  Analysis  Coalescing  of Variance  i n Run 1 8 in  I I (Drop  ©©©©©©o©©ooooo©©©©©a©©©©©©o©©o©©©©©©©©©©  Drop H o l d i n g a n d Analysis  VHIb.  ^3 )  E x p e r i m e n t a l Data f o r P a r t  Vila.  Villa.  • « © « . . © » 9 . © o . . © . © o a © e o © « o © . . . . . © o  R e f r a c t i v e I n d e x - C o n c e n t r a t i o n Data of M e t h y l A l c o h o l a t 2 5 ° C ( R e f . 42) Exposure Factors f o r D i f f e r e n t S c a l e s of  StUdi© s ) VI.  (Schlieren  B e a r i n g E x p e r i m e n t a l Data  R.© p I * O C L \ l C f c V.  I  X2X  Drop  ©©a..©©©©©.©©.©.©©©©©©©©.©©©  122  A G e n e r a l Form o f Anova T a b l e . • . . • . . • « • • • • • • • • • • 1 2 3 Drop D i v i d i n g  L i n e s whose X-Y  Relationships  Coi*i*©spond t o Z s r o SXop© © a © © © © © © © © © © © © © © * © © © © © © © X23 XII.  Predictive  E q u a t i o n s and  by t h e M u l t i p l e A—1«  Titration  B—1o  Refractive  C—1.  Timing Light  Data  R  2  Values Obtained  R e g r e s s i o n Program  .............. 1 3 0  ©©•©©«*.©.©..©..©©©.•.•©©•••«©©©.©  Index Data a t 2 0 ° C Calibration  A—2  ...................  B—3  ........................  C—2  vii LIST OF  TABLES(cont'd.)  Table  Page  D-l.  Temperature  F l u c t u a t i o n s i n Two  E-l.  Various P r o p e r t i e s of D i f f e r e n t a t 2 0 ^ C where A p p l i c a b l e  J-l.  Ch. E. Rooms .... D - 3 Substances  . . . . * o o » o . . o . . . . . . . . • • « •  Heats of S o l u t i o n of A c e t i c Acid-Water Q.'fc 1 8 © 3 ^ C  ( R s f • tyTL )  F—2  System  o©«0«e©o®oo«©»«ooo®©o««o©©«»©  J""2  ....... K - 2  K-l.  Pseudo-radius Data of L e f t Drop i n Run 18  K-2.  Pseudo-radius Data of Right Drop i n Run 18 ...... K - 3  K-3.  Pseudo-radius Data of L e f t Drop i n Run 19  K-J+  e  Pseudo-radius Data of R i g h t Drop i n Run 19  .......  K-4  ......  K-5  viii LIST OF FIGURES Figure lo 2ao  2b.  3»  Page Ternary composition diagram w i t h s u r f a c e t e n s i o n as parameter (19) . . © . . a © . . . . . . . .  .  T r a n s f e r of m a t e r i a l from the d i s p e r s e d phase t o the continuous phase f o r a system of the type c o r r e s p o n d i n g t o Figure 1 ( 1 9 )  8  9  T r a n s f e r of m a t e r i a l from the continuous phase t o the d i s p e r s e d phase f o r a system of the type c o r r e s p o n d i n g t o Figure 1 ( 1 9 ) . . . . . 1 2 Schematic flow diagram of the e x t r a c t i o n SyStSffi  ©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©©ft  4-.  S c h l i e r e n arrangement  5.  Photographic views of the apparatus.  13  used i n the experiments .. 1 7  (Corresponds t o Figure 4 © )  18  6©  E x t r a c t i o n system  O . O O O O O O » . O . O . O . . Q « . « « O » O . O O O O  7*  Extraction  ooe.«oo9«o9ooo.oo.o.o»«o.oo.«.  21  8.  The r e g i o n of i l l u m i n a t i o n i n a c o n v e n t i o n a l s c h l i e r e n system ( 3 9 ) • • • • • • • • • • • • • • • • • • » • • • • » • •  27  9-13° 1^4—17o  column  21  S c h l i e r e n photographs of v a r i o u s drop p a i r s .... ^8 S c h l i e r e n photographs of v a r i o u s drop p a i r s «...  52  18.  L i g h t bundle - k n i f e edge arrangement i n th© Tosplsi* msttoocL ( 2 2 ) ©©©©©©©©©©©©©©©©©©©©©a©© 3 3  19»  Image f o r m a t i o n , f o r a p a r t i c u l a r case, i n a s c h l i e r e n system (Toepler method) .........  20.  Basic photographic arrangement  58  used f o r  drop shs.p© stucli©s ©©©©©©©©©©©©©a©©©©©©©©©©©©©©© 7 ^ 21.  Conventional photograph of drop p a i r i n r u n 1 5 » o  22.  S i m p l i f i e d path of l i g h t r a y p a s s i n g between  23°  E f f e c t of i r r a d i a t i o n and h a l a t i o n on  dl*OpS  UHIDSICIC© cL  ••©©©•©oe©e©«oo9«©©«e©©eo©©d©e©e©e©G©o Jf i l n i  (^f*3 )  ©©•«©•©©••©•©©©©©©©•©«••©©©©©  79  7^ 78  ix LIST OF FIGURES (cont'd.) Figure 24.  Page E f f e c t of i r r a d i a t i o n as shown i n photographs of b a l l b e a r i n g s i n contact w i t h each other  79  25»  V-block mount f o r s t e e l b e a r i n g experiments ....  81  26.  Photographic arrangement f o r s t e e l b e a r i n g experiments and drop shape s t u d i e s ............. B l o c k i n g of a l i g h t ray due t o b a l l misalignment . . . . « « . © » . . . . . . . o . . . . . . . . . . . « « » » • . .  27• 28.  84  Impression of "waist" between two s o l i d spheres due to i r r a d i a t i o n caused by OV©]?© XjpO SHI*©  29o  83  ©©•©••©••©©•©•©©©©©©•©©©©©•••©••©©©  CuS-coated b a l l b e a r i n g s a t a d i s t a n c e of s e p a r a t i o n of 0 . 0 0 1 5 i n . . . . . . . . . . . . . . . . . . . . . . . . .  30.  L o c a t i o n s of v a r i o u s d i v i d i n g l i n e s and r e f e r e n c e p o i n t s f o r drops b e i n g measured  31.  Impression of h o r i z o n t a l of r e s i d u a l v s . time  (44)  8^1"  87  98  "band" f o r p l o t . . . . . . . . . . . . . . . . . . . . . .  102  32.  P a r t i a l view of c o a l e s c i n g MIBK drops  33•  Photograph from r u n 18 showing b l u r r e d g r a i n y  34.  images a t c e n t r a l a r e a of the p i c t u r e .......... 114 Photograph from r u n 1 9 showing b l u r r e d g r a i n y images a t the l e f t and r i g h t side of the piCtUI*©  35»  11 ^  R e s i d u a l v s . o b s e r v a t i o n no. (and frame no.) with no unexplained v a r i a t i o n . (Corresponds tO  36.  •©©•••©•©•©©©©©•©©©©©•©©•©•©©©©©•©©•©©©©  107  Fi££U3T©  31  0  )  • Q « « 0 O 6 O 0 o e o o o e o * 0 « o e e o o « e o e * o e o e  R e s i d u a l v s . o b s e r v a t i o n no. (and frame no.) with unexplained v & r i & t i o n © • • © • • © • © o * © © © © © © * © «  12(7  128  37•  Equations f i t t e d and behaviour observed over 0 - 1 5 0 f i l m frames i n r u n 18  131  38.  Equations f i t t e d and behaviour observed over 0 - 1 0 0 f i l m frames i n run 1 9  132  39.  Equations f i t t e d , and behaviour observed over 0 - 2 0 2 f i l m frames i n r u n 1 9 (extended) ...  133  X  L I S T OP FIGURES ( c o n t ' d o ) Figure 40.  41.  Page P l o t of pseudo-radius v s . o b s e r v a t i o n no. (and frame n o . ) f o r v a r i o u s d i v i d i n g l i n e s o f t h e l e f t d r o p i n r u n 19 . . . . . . . . . . . . . . . . . . . . .  134  P l o t of pseudo-radius v s . observation no. (and frame n o . ) f o r v a r i o u s d i v i d i n g l i n e s of the r i g h t drop i n r u n 1 9 • •  135  42.  Sketch f o r the d e r i v a t i o n of Eq.  43.  L o c u s o f P(Xfl,  Yd) f o r two s p h e r i c a l r a d i i  44.  S k e t c h showing  t h e image o f a p o i n t  i n w a t e r when v i e w e d  (10)  . . . . . . . . . .  ..... 140  located  from a i r  45.  I s o s o l u t e l i n e s b e t w e e n two d r o p s a t a n  46.  E q u a t i o n s f i t t e d over 0 - 2 0 2 f i l m frames and b e h a v i o u r observed over 0^-100 f i l m frames, i n r u n 1 9 ..................oooao.......  47*  139  145  152  Change i n d r o p shape i n r u n 1 9 a s t h e t i m e of c o a l e s c e n c e approaches, averaged f o r the two d r o p s . (Total magnification of Y ©C[U«3,lS  •)  ooa*oeoe««o*o*«oooo*«oaea»eeee«e«9»  B-l.  R e f r a c t i v e i n d i c e s of s o l u t i o n s of methyl a l c o h o l i n MIBK-saturated water (20°C)  J-l.  S k e t c h showing s o l u t e c o n c e n t r a t i o n l a y e r Q, rOUHCL 6£tCh drOJ) o o o o e e o a e o a a o a e a a o a a e e a a t a a e e e e  3.60  B-4 <X~6  xi  ACKNOWLEDGEMENTS  The  a u t h o r wishes  t o D r . S t u a r t D. C a v e r s , undertaken,  u n d e r whose g u i d a n c e  f o r h i s continual  tance, and h e l p f u l of t h i s  t o express h i s s i n c e r e  criticisms  appreciation  this  s t u d y was  encouragement, v a l u a b l e a s s i s extended  throughout  the course  project.  He a c k n o w l e d g e s w i t h s p e c i a l g r a t i t u d e  the help o f  D r . James S. F o r s y t h , whose a d v i c e , comments, a n d s u g g e s t i o n s are  i n every p a r t  of this  thesis,  particularly  i n i t s second  portion.  There  a r e many o t h e r p e o p l e who a s s i s t e d  ways a n d i t i s i m p o s s i b l e t o c i t e a u t h o r wishes  N a t i o n a l Research  t o thank  support.  The  to a l l .  jointly  Dr. Cavers  C o u n c i l o f Canada, f o r p r o v i d i n g  a s s i s t a n c e , a n d The U n i v e r s i t y additional  e v e r y one o f them.  t o acknowledge h i s debt  He a l s o w i s h e s  i nvarious  of B r i t i s h  and the financial  Columbia, f o r  1 INTRODUCTION  "On C e r t a i n Surfaces aptly in  Curious  o f Wine a n d o t h e r  Motions Observable a t the  Alcoholic Liquors",  c h o s e n by James Thomson f o r h i s f a s c i n a t i n g a c c o u n t  1855  correct  of surface explanation  sion e f f e c t s .  movements..  riments  T h i s was p r o b a b l y  H i s f i n d i n g s were n e v e r n o t i c e d u n t i l  on s u r f a c e  t e d phenomena were a l l c a u s e d by l o c a l tension.  puted p r i o r i t y ing  o f these  that a r e caused  (2), the Marangoni  although r e l a t e d surface  the departure  by  extension  interface.  v a r i a t i o n s of i n t e r f a c i a l  i n t u r n by d i f f e r e n c e s i n c o m p o s i t i o n  The s e c o n d i s t h e c o n j u g a t e  is  dilational  later  f i n d i n g s w h i c h have come  i s movement i n a f l u i d  m o t i o n l s c a u s e d by l o c a l  temperature.  dis-  the Marangoni e f f e c t s (2).  e f f e c t s a r e "...two d i s t i n c t first  differences of i n t e r -  t h e r e a s o n why M a r a n g o n i  Q u o t i n g S t e r n l l n g and S c r i v e n  The  the r e p o r -  o f van d e r Mensbrugghe' s f i n d i n g , ' the r e s u l t -  f o r Thomson's e a r l i e r  t o be c a l l e d  expe-  When I t a l i a n p h y s i c i s t C a r l o M a r a n g o n i  p u b l i c i t y was p r o b a b l y  took c r e d i t  ten-  van der  i n 1869 a r e v i e w o f a l l e a r l i e r  movements a n d e s t a b l i s h e d t h a t  (1)  the f i r s t  o f t h e phenomena r e l a t e d t o s u r f a c e  Mensbrugghe p u b l i s h e d  facial  was t h e t i t l e  from e q u i l i b r i u m t e n s i o n  The tension or  of the f i r s t : that  i t  i s produced  or c o n t r a c t i o n o f an i n t e r f a c e , that  deformation".  effects.  i s , by  2 During  15  the l a s t  y e a r s , a number o f t e r n a r y s y s -  tems have b e e n f o u n d  whose i n t e r f a c e s were d i s t u r b e d d u r i n g  mass t r a n s f e r  of the  o f one  components.  t u r b u l e n c e , a s many w o r k e r s a g r e e , of The  interfacial  t w o - f i l m model o f Whitman  transfer  i n r e g i o n s c l o s e t o the  ternary and  diffusion.  interface,  pictured  a  serene  liquid  extraction,  t o the  t h e o r y , as  typified  g o i n g mass t r a n s f e r .  Sigwart  this  by  out,  the  and  Ward a n d  s p o n t a n e o u s and Nassenstein  on p e n d e n t d r o p s ,  (5,  p h o t o g r a p h s o f the  Although  6,  the  and  ivity, trolled  eruptions regions  two-film in  some  theory  liquid-  c o n f u s i n g and  disorderly  phases of systems under(4)  were the  interfacial  reported similar  f o r the  first  turbulence, findings  system carbon  obtained excellent  to  tetra-  schlieren  phenomena.  t h e r e were d i s o r g a n i z e d movements a s  of ordered  c o u l d be  by  that with  surrounding  i n the above-mentioned e x p e r i m e n t a l  appearance  found  place  exceptions  Brooks  7)  tra-  t h e r e were  localized  particularly  c h l o r i d e - a c e t i c acid-water,  out  the  o f some u n e q u i l i b r a t e d l i q u i d  notice  t o take  a c c o m p a n i e d by  Although  i t turned  effects.  t h a t assumed s o l u t e  p r o c e s s d u r i n g mass t r a n s f e r as  variations  c o n t r a d i c t e d the  i t was  while  were a g i t a t e d s p o n t a n e o u s l y .  to l o c a l  interface  s y s t e m s , mass t r a n s f e r was  spasms i n t h e  state  (3)  Indeed,  interfacial  of the Marangoni  phenomenon q u i c k l y  ditional  pure m o l e c u l a r  i s due  t e n s i o n , t h a t i s , one  e x i s t e n c e of t h i s  This  flows,  achieved  o b s e r v a t i o n s , some  i . e . , organized  interfacial  f o r s h o r t p e r i o d s of time  c o n d i t i o n s a s r e p o r t e d by  pointed  Sigwart  and  under  Nassenstein  actcon(6).  3 They d i r e c t e d solution  a  towards a  tetrachloride and  j e t of flat  from the  disorganized  tained  d e p e n d e d on  I t was  not,  and  interface water  (9)  of  side*  of  how  was  ethyl but  By  that,  partially i n the the  were i n t u r n of  the  surface  the  active  typical  ciency  has  the  Sternling  so  and  acid  less  Sternling  theoretical  Westwater  the  This (10)  criteria  the  who  one  since  surface  and  reacid-  were the  movement  effect during  coalescence.  for larger  i n the  effi-  interfacial  It i s , therefore,  phase  neces-  other at  then to a v o i d  the  coalescence  c o a l e s c e n c e would r e s u l t area.  beha-  acid-  f r o m the  of  valid,  s e a r c h f o r maximum  in striving  this,  Apart  ana-  concept  completely  ease  math-  interfacial  activity.  interfacial  f o r mass t r a n s f e r .  drops a f t e r formation  transfer.  instability  experience  to p r e d i c t  column,  ob-  They f o r m u l a t e d a  Scriven  process a f f e c t s  to achieve  b i g g e r d r o p s and  r e s u l t they  considerable  i n t o water.  always r e s u l t e d  as  produced  system e t h y l a c e t a t e - a c e t i c  sary to e f f e c t i v e l y disperse outset  isobutanol  system g l y c o l - a c e t i c  contaminants,  extraction  areas a v a i l a b l e  any  either  of  water-carbon  i m a g i n a t i v e work of  O r e l l and  transfer  mass t r a n s f e r  In a  case  related  water, with a c i d  the  of n i t r i c  interfacial by  i n water  contacting  (8) l i k e w i s e  turbulence.  insufficient  the  system  show, t h r o u g h h y d r o d y n a m i c  organized  acetate,  viour  the  t h e r e was  interfacial  or  verified  ported  direction  some s y s t e m s may  turbulence  the  organized flows;  the  that  e m a t i c a l model t o lysis,  or  however, u n t i l  Scriven  treatment  of  sodium c h l o r i d e  w a t e r p h a s e s , B e r g and. B a l d w i n  either  of  saturated  in  4  Johnson that  and B l i s s  (11) a s e a r l y a s 1946 p o i n t e d o u t  i n a s p r a y e x t r a c t i o n column, mass t r a n s f e r was h i g h e r  when t h e s o l u t e  i n a ternary  c o n t i n u o u s phase Zuiderweg  s y s t e m was t r a n s f e r r e d  t o t h e drops©  Smith  (13) probably supplied  (12) a n d G r o o t h u i s and  t h e answer©  was s o , t h e y r e a s o n e d t h a t due t o l o c a l tension,  assist  the coalescence o f drops, depending  can e i t h e r  this  of i n t e r -  i n h i b i t or  upon t h e d i r e c t i o n  transfer©  Mahajan in  solute  As t o why  variations  facial  of  a diffusing  from the  (14) was, p e r h a p s ,  the f i r s t  to report  the coalescence of drops a t a plane i n t e r f a c e ,  on r e a c h i n g t h e phase  boundary  but r e s t a t the i n t e r f a c e McRoberts  do n o t c o a l e s c e  f o r some time©  other workers,  instantaneously  interface©  coalescing  Prom r e s u l t s o f  t h e r e i s e v i d e n c e on d i s a g r e e m e n t  measurements f o r i d e n t i c a l  drops©  the drops  Cockbain and  ( 1 5 ) measured the r e s t - t i m e s o f such  drops a t a plane l i q u i d - l i q u i d  A significant  of rest-time scatter  f o u n d whose r e s t - t i m e m a g n i t u d e may depend on many like size,  temperature,  contamination, i n t e r f a c i a l  g e o m e t r i c shape  o f the i n t e r f a c e ,  c o s i t i e s and d e n s i t i e s . proposed  that  interfacial  d r a i n a g e and, t h e r e f o r e ,  tension,  drop vis-  (16), among  t u r b u l e n c e brought about  was  factors  and the system  J e f f r e y s a n d Lawson  short rest-time  that  others,  accelerated  f o r benzene d r o p s i n  an aqueous c o n t i n u o u s Phase w i t h a c e t o n e a s t h e t r a n s f e r r i n g solute© using  Gillespie  Taylor's  and R i d e a l  (17) gave a t h e o r y f o r r e s t - t i m e  treatment of the approach  of p a r a l l e l  flat  discs  5  separated  by  fluid©  experimental unable tive  results©  of the  continuous  explain  this  i t i s now  well for Picknett  their (18) were  proposed an  film  and  known t h a t the  i n two  alterna-  coalescence©  phenomenon i s s t i l l  trated  on  the  coalescence  case©  the  study  drainage  elements©  followed  t h e u n d e r l y i n g mechanism not  fully  understood© has  of d r o p s a t a p l a n e Although  of the  perhaps because  involved i n keeping  present  coales-  the  been  s t u d y was  a pair  instituted  Much  interface  same g e n e r a l  coalescence  to  concen-  mentioned above a p p l i e s a l s o t o the  detailed  b e e n neglected©  the  in this field  between p a i r s o f d r o p s .  quence o f e v e n t s  general  stages, namely:  which separates  the c o n s i d e r a b l e r e s e a r c h  ties  E l t o n and  c o n c l u s i o n , , and  takes place  f i l m rupture  not  accounted  semi-theoretical expression  cence p r o c e s s  of  However©  to confirm t h i s  Although  by  This theory  and se-  latter  of drop p a i r s  of the e x p e r i m e n t a l  has  difficul-  o f moving d r o p s together©  to provide  some o f t h e  The  missing  information.  A t t e n t i o n was for  coalescence  w h i c h was and  in a  (13)°  other.  together at w i l l controlled©  Smith The  c a u s i n g drops to form f a c i n g each  (12)  latter  f r o m two  and  mass  Independently  transfer by  Groothuis  i n v e s t i g a t e d coalescence capillary  by  t u b e s whose e n d s were  In t h i s manner, the d r o p s were f o r c e d  so c l o s e n e s s  Smith,  t o t h e h y p o t h e t i c a l mechanism  t e r n a r y system undergoing  p r o p o s e d by  Zuiderweg  given  Caswell,  of approach  c o u l d be  Larson,  Cavers  and  easily  (19)  provided  6  experimental coalescence both  i n f o r m a t i o n as of free  liquid  groups of workers  coalescence facial  was  due  of  near  i s then  Investigations  the d r o p  the  used  G r o o t h u i s and  theory.  liquid  brief,  s o l u t e on t h e phases.  The  inter-  resulting  produced  interface.  of t h i s work t o c a r r y out  to provide evidence,  Zuiderweg  (13)  was  r e c o r d s of the  photography u t i l i z i n g  s c h l i e r e n and  of a  A n o z z l e arrangement  hope o f o b t a i n i n g v i s u a l high-speed  In  of  t h a t , i n many i n s t a n c e s ,  the purpose  i n order  support by  i n a column.  to the e f f e c t two  or d i f f i c u l t y  surface t e n s i o n , they e x p l a i n e d ,  movements a t and  It  drops  suggested  t e n s i o n between t h e  imbalances  t o the ease  ordinary p i c t o r i a l  i f any,  similar s e t up.  to  to that In  coalescence  the phenomena,  o p t i c a l methods s u c h t e c h n i q u e s were  used.  as  7 THEORY UNDER STUDY  The  hypothetical  c o a l e s c e n c e mechanism p e r h a p s i s  b e s t e x p l a i n e d by q u o t i n g Smith e t a l  "The difficulty  mechanism p r o p o s e d  tension  o f two l i q u i d s o  They f o u n d ,  f o r example,  two-phase m i x t u r e : The s o r t  of a solute  tension that  water,  the ease or  i n many e x p e r i m e n t a l on t h e i n t e r f a c i a l  Murphy. L a s t o v i c a ,  have m e a s u r e d i n t e r f a c i a l  tension.  to explain  of coalescence observed  c a s e s d e p e n d s on t h e e f f e c t  (19):  i n such  a n d F a l l i s (20)  ternary  the a d d i t i o n  systems.  of acetone  toluene, lowered  of behaviour o r d i n a r i l y  t o the  the i n t e r f a c i a l encountered i s  shown i n F i g . 1 where t h e t i e l i n e s r e p r e s e n t c o e x i s t i n g phases a t v a r i o u s i n t e r f a c i a l where t h e i n t e r f a c i a l  "On the  t e n s i o n decreases from a t o e."  the b a s i s  of F i g . 1 the h y p o t h e s i s t o e x p l a i n  coalescence of drops  i s then the f o l l o w i n g .  d r o p s a s shown i n F i g . 2. 1 and approach through  solvent  These  consist  C o n s i d e r two  of solvent  A of F i g .  one a n o t h e r a s i n F i g . 2a d u r i n g t h e i r B o f F i g . 1.  r a t e d w i t h component  Assume t h a t  o f the drops and i n t o  solute  i s saturated,  C of F i g . 1 i s t r a n s f e r r i n g  the c o n t i n u o u s phase.  B between t h e d r o p s r e c e i v e s  motion  the drops a r e satu-  B, t h a t t h e c o n t i n u o u s phase  w i t h component A, a n d t h a t out  t e n s i o n s a , b , c, d, a n d e  solute  The s o l v e n t  from both d r o p s .  more, a n y m i x i n g p r o c e s s g e n e r a l t h r o u g h o u t  Further-  the continuous  Figure  1.  Ternary composition diagram with s u r f a c e  t e n s i o n as parameter  (19).  9  DIRECTION OF INTERFAGAL MOVEMENT  DIRECTION OF CIRCULATION IN DROP  Figure  2a.  DIRECTION OF DROP MOVEMENT  ZONE OF HIGH SOLUTE CONCENTRATION  T r a n s f e r o f m a t e r i a l from t h e d i s p e r s e d phase t o the c o n t i n u o u s phase f o r a system o f the type corresponding to Figure 1 ( 1 9 ) „  10  phase w i l l  be somewhat i n h i b i t e d  the d r o p s i s concerned because somewhat by t h e d r o p s  "The  i s that  the drops.  the o t h e r drop  t h a n i n r e g i o n s more remote  because  H i n F i g . 2a).  H.  o f the i n t e r f a c e  H.  drop w i l l  result  The u n b a l a n c e d  force  less  approach  w o u l d be e x p e c t e d  f o r material  transfer  the r e m a i n d e r  c o n c e n t r a t i o n s on b o t h  interfacial  tensions near t e n s i o n around  of the i n t e r f a c e  and the s h r i n k i n g  o f the drops.  G t h a n :they a r e n e a r  interfacial  i n stretching  of drop approach,  Streaming  o u t o f t h e zone o f d r o p a p p r o a c h  also,  a c i r c u l a t o r y movement  will  f r o m t h e d r a g a s s o c i a t e d w i t h t h e movement  the drop i n t e r f a c e  both  resulting  of the i n t e r f a c e .  bring fresh  to continue the process.  this  behaviour."  around  be p r o m o t e d a n d ,  solute to  When t h e l a s t ,  o f B b e t w e e n t h e d r o p s b r e a k s down t h e d r o p s 2a i l l u s t r a t e s  each  o f c o n t i n u o u s phase  o f drop f l u i d ,  c i r c u l a t i o n w i t h i n the drop w i l l  G  i n t h e zone  o f the i n t e r f a c e s  fluid  Fig.  slightly  (e.g., a t G i n F i g . 2a)  are higher near  F i g . 1 then i m p l i e s lower  layer  than i t w i l l i n  t h e s o l u t e b u i l d u p between t h e d r o p s . "  than near  The  bet-  W i t h i n each o f the  This r e s u l t  "Thus, i n F i g . 2a s o l u t e sides  concentration  f r o m t h e zone o f c l o s e  o f the r e d u c e d d r i v i n g  following  being protected  c o n c e n t r a t i o n s should decrease  i n the r e g i o n f a c i n g  (e.g., l o c a t i o n s  the s o l u t e  t e n d t o r i s e more q u i c k l y  the r e m a i n i n g r e g i o n s a r o u n d drops the solute  of t h i s region  between  themselves;  result  ween t h e d r o p s w i l l  as f a r as the region  coalesce.  11  "On  the  solute  other  i s being  hand, when t h e  but  the  the  dispersed  2b,  b o t h draw s o l u t e f r o m the  t r a n s f e r r e d from the  p h a s e , when two  ween them, and,  with mixing  lower  solute  concentration  cable  on  s i d e s of the  the  approacho high  In t h i s c a s e ,  i n the  takes  place  'contact'  trated  i n F i g . 2b.  transfer'  f o r the  zone and  It should s o l u t e as  be  are  drag  pulls  vice  versa',  and  vice  versa',  s i n c e w h e t h e r component A i s w a t e r and  B an  organic  solvent,  organic  solvent,  as  i t a p p l i e s i n connection  hypothesis  to  to continuous  'water p h a s e t o o r g a n i c  o r component B w a t e r a n d  i s immaterial  t o the  drop  more illus-  'direction  this  not  appli-  comparatively  forced apart  noted that  'dispersed  a  of the i n t e r f a c e  Frictional  these  drops,  zone o f  is  Pigo  p h a s e bet*=  than t h a t  the  tension  spreading  zone.  r e f e r s to  there  to  shown i n  i n h i b i t e d between the  d r o p s remote from  same,  continuous  l a y e r of continuous  soon r e s u l t s  d r o p s and  i s the  drops approach as  interfacial  towards t h i s  w a t e r between t h e  system  of  with  phase  phase  or  or  component  component A  argument."  an  DIRECTION OF DROP MOVEMENT  MOVEMENT  Figure  2b,  CONCENTRATION  T r a n s f e r o f m a t e r i a l from the continuous phase t o the d i s p e r s e d system o f the type corresponding t o F i g u r e 1 (19)«  phase f o r a  13  PRELIMINARY  A.  INVESTIGATION  Scope  The duce t h e  p r e l i m i n a r y i n v e s t i g a t i o n was  behaviour reported  by  Smith e t a l  s y s t e m MIBK-* a c e t i c a c i d - w a t e r . * * drops dispersed to water, cu.  that at  f t . soln.),  that  coalescence  with  the  at  the  with  their  the f o r MIBK  occurred  operation  (0.068 l b . m o l e s  w i t h i n the  i n t e r f a c e was the  o f 8$w  rapid.) still  occurred  and  column,  and  Familiarization motion p i c t u r e  at this  stage.  Procedure  Preparation  of the  a d d i n g a m e a s u r e d amount o f ganic  tilled  dispersed  phase was  case,  a b o u t 8$w  w a t e r was  allowed  * Methyl  by  mixture,  f o r several minutes.  w h i c h was The  or-  concentration,  (0.068 l b . m o l e s / c u . f t . s o l n . ) .  then added to the  to stand  done  s o l u t e , a c e t i c - a c i d , t o the  s o l v e n t , MIBK, t o make a d e s i r e d s o l u t e  in this  and  for  (They r e p o r t e d ,  solute concentration  coalescence  (19)  repro-  a c e t i c a c i d t r a n s f e r f r o m MIBK  s c h l i e r e n e q u i p m e n t and  c a m e r a s , and  B.  i n water with  meant t o  Dis-  shaken,  procedure  was  i s o b u t y l ketone.  ** When t h e c o n s t i t u e n t s o f a t e r n a r y s y s t e m a r e g i v e n i n t h e p r e s e n t t h e s i s , t h e s e c o n d s u b s t a n c e m e n t i o n e d i s the s o l u t e w h i c h i s t r a n s f e r r e d between p h a s e s c o n s i s t i n g m a i n l y o f the o t h e r two substances.  14 repeated  until  a thin layer  of water remained v i s i b l e  s a t u r a t i o n o f t h e MIBK p h a s e w i t h w a t e r was i n s u r e d o the  c o n c e n t r a t i o n of the s o l u t e i n the organic  was l e s s solute  than  t h e c a l c u l a t e d amount b e c a u s e  t o the t h i n l a y e r  continuous distilled above,  w a t e r w i t h MlBKo  system. nozzle, and  some t r a n s f e r o f for.  S i m i l a r procedure  3 i s a schematic  The l i g h t e r  was u s e d a s  d i s p e r s e d phase f l o w e d  were t h o s e  MIBK.  f l o w d i a g r a m f o r t h e whole  a t the bottom o f t h e square  column used  designed  through  g l a s s column. by S e l b y  a glass Both  (21).  t o the d i s p e r s e d phase.  served a s feed and discharge Saran  f i t t i n g s were u s e d  tanks.  column w i t h  the f l o w of each  line  ( F i g . 3)«  filling  phase t o about  volume a n d m a i n t a i n i n g t h a t l e v e l of a weir  polyethylene  Polyethylene  r u n was b e g u n by p a r t i a l l y  the continuous  the e l e v a t i o n  (built  3/k  by s u i t a b l e  by S e l b y  needle  phase.  the g l a s s  o f the column's adjustment  valves that control  work was c a r r i e d  of  (21)) i n the d i s c h a r g e started  the flow t o the  nozzle.  All  jars  t u b i n g and  F l o w o f t h e d i s p e r s e d phase was t h e n  by a d j u s t i n g t h e n e e d l e  counter-  f o r p i p i n g and Teflon-packed  v a l v e s were p r o v i d e d t o c o n t r o l  The  Two-gallon  nozzle  Continuous  phase f l o w e n t e r e d a t t h e t o p o f t h e column a n d was current  The  by s h a k i n g and s a t u r a t i n g t h e  t o i n s u r e s a t u r a t i o n o f t h e water phase w i t h  Fig.  Hence,  s o l v e n t , MIBK,  o f w a t e r was n o t a c c o u n t e d  p h a s e was p r e p a r e d  Thus  0  o u t a t room  temperature  0  15  FEED (ORGANIC SOLV-)  FEED (WATER)  VENT  GLASS COLUMN  r DISCHARGE  DISCHARGE  F i g u r e 3«  Schematic  flow diagram  of the e x t r a c t i o n system.  16 The with  Hycam camera i n p l a c e "A"  under t o p i c ment and tilted ally  that  focus from  o f Ml it©  points  and  dicular  focus  piece  sition  source,  Obviously,  be  i t .  equal  test  To  direction  section, T  cancel t o Ml can  be  rays  edge was  point  (K,  the l i g h t i f the  changed u n i f o r m l y  light  beam.  the . source method  upward and  The was  the the  i n the  be  checked  path  and  i n two  light  test  by  perpendi-  positions  circles  at  are  tilted  equal  to0^°  the  k n i f e edge was adjusted  cut  r  ^  the a e  holding  paper's  the  moved  this viewing across  so t h a t t h e  i n h a l f as sensitivity  po-  rectilinear  in  image  the  f o r both  d e f l e c t i o n s c a u s e d by  section.  in  by  The  i l l u m i n a t i o n on  posi-  perpen-  was  noting  —  both  rays  beam were  bundle.  T h i s gave e q u a l ray  the  reflected  horizontal position at  approximately  downward l i g h t  gradients  as  light  k n i f e edge was  (22).  was  beam and  of the  so t h a t  reduce  ( t h e g l a s s c o l u m n ) , was  M2  was  physicto  determined approximately  l o c a t e d i n the  i n F i g . 4)  were  can  placed  t h a t Q2  light  Ml,  then l o c a t e d at  coma, m i r r o r so  (22)  further  adjust-  small as  t h a n 10°  rays  i n diameter  o f paper i n the  knife  Toepler  of these  as  o f p a p e r i n the l i g h t  f o r minimum s i z e  screen  was  L, was  n e a r M2»  described  parabolic mirror,  event, l e s s  T h i s p a p e r was  o f m i r r o r M2  a piece  index  light  (also Fig. 5  i n t o proper  t h a t i t s w a l l s f a c i n g the l i g h t  to  opposite  i n any  parallelism  The  so  The  00'.  should  tioned  follows:  S) and put  so t h a t c o l l i m a t e d l i g h t  The  Parallel.  of  as  The  to l i n e  n e a r Ml  screen,  i t s o f f s e t a n g l e , (9i»  holding a f l a t cular  of  "DISCUSSION", was  p o s s i b l e and,  aberrationso  the  of  focussed  so  shown i n F i g - k  s c h l i e r e n system  In f o c u s s i n g ,  refractive i t should  F i g u r e 4„  S c h l i e r e n arrangement  used  i n the  experiments.  17a  Key  to Figure  K  L o c a t i o n of k n i f e  L  Light  M  l»  M  2  4  edge.  s o u r c e <,  Schlieren mirrors  S  Viewing  T  Test  f  F o c a l l e n g t h o f s c h l i e r e n m i r r o r s , M]_ and  p  Distance  of t e s t  q  Distance  of viewing  01'  O2  screen*  .  0  section.  Offset  section  to mirror,  M2°  M2.  screen to mirror,  M2.  angles.  * These p i e c e s o f equipment comprise the A e r o l a b S c h l i e r e n S y s t e m , i n c l u d i n g t h e k n i f e edge a s s e m b l y ( l o c a t e d a t K) w h i c h i s n o t shown h e r e . L i s a PEK h i g h - p r e s s u r e m e r c u r y a r c lamp w i t h a 0.012x0.012 i n . s o u r c e . M i a n d M2 a r e 6 - i n . p a r a b o l i c f i r s t - s u r f a c e mirrors having 4 8 - i n . f o c a l l e n g t h each. S i s a screen constructed of sandblasted plastic. The k n i f e edge a s s e m b l y c o n s i s t s o f a n a d j u s t a b l e r e c t i l i n e a r k n i f e edge and a u n i v e r s a l l y - m o u n t e d m i r r o r w h i c h c o u l d be u s e d t o r e f l e c t t h e image t o a convenient l o c a t i o n f o r S i f d e s i r e d .  Figure  5.  Photographic views of the apparatus.  (Corresponds  to Figure  4}  19 be r i o t e d figure,  t h a t the dimensions may  be  of  "p" and  changed as l o n g as  "q", a s  i n the  the l e n s e q u a t i o n  above  is  satis-  fied: 1/p  + 1/q  (1)  = 1/f  where p = d i s t a n c e o f t e s t  section  q = d i s t a n c e of viewing f = focal The  schlieren  length of  image was  For photographs, later,  the  state with uniform photographs of drop Polaroid  Type  f o r the  55  focussed  the  spray  as k n i f e  a  coalescence  volved.  P/N,  Proper  factory  film  the  results,  i t was  more r i g i d modified  by  containers.  (19)  was  decided  screen,  t o be  S.  described  reached  a  screen.  steady  interface  level,  Films used  T r l - X Pan,  and  were Ilford  factors  m a g n i f i c a t i o n , s h u t t e r speed, photographic  conditions  c o n t r a s t and  on the  of  and in-  quality  f i l m were f o u n d  combinations  verified,  and,  to continue  the  mm.  0  of  t o be  the  satis-  settings.  Fur-  took p l a c e f o r c o n d i t i o n s r e p o r t e d  column frame and improving  M2  Kodak T r i - X R e v e r s a l f o r the  attempted  thermore, that coalescence Smith e t a l  Pan,  mm©  i n p l a c e o f the  constant  overall  image a s r e c o r d e d first  Ml and  e x p o s u r e depends on many  edge s e t t i n g ,  f o r the  used  Kodak P l u s - X  Nevertheless,  schlieren  0  the v i e w i n g  were t a k e n .  i s a f u n c t i o n o f the p a r t i c u l a r  by  on  c o l u m n had  d r o p l e t s and  L i n h o f camera, and  Hycam camera. such  schlieren mirrors  L i n h o f or Hycam camera,  soon as  mm.  screen;, t o m i r r o r , M2,  e a c h w i t h l e n s removed, was  As  FP3  t o m i r r o r , M2,  with  the  with  promising  i n v e s t i g a t i o n with  the e n t i r e  p i p i n g and  these  extraction  a  system  providing leak-proof  20  MAIN  A.  INVESTIGATION  Attempted M o d i f i c a t i o n s t o E x i s t i n g Apparatus  I t was n e c e s s a r y frame t o s u p p o r t shown i n F i g o  6.  so t h a t  This i s  t h e p o s i t i o n o f t h e column  direction  ( F i g . 7)»  The  were b e n t t o make b o t h e n d s f a c e e a c h  e i t h e r h o r i z o n t a l l y or v e r t i c a l l y , piping  and s t a b l e  The column r e m a i n e d t h e same, b u t p r o v i s i o n s  i n the v e r t i c a l  spray n o z z l e s  a more r i g i d  t h e e x t r a c t i o n column, s e c u r e l y . .  were made i n t h e f r a m e adjustable  to design  system consisted, of n y l o n  was  glass other,  a s d e s i r e d . ( F i g . 7)»  t u b i n g and. f i t t i n g s  The  except  f o r p o r t i o n s l e a d i n g t o the d i s c h a r g e  t a n k s w h i c h were  poly-  ethylene  The n y l o n  being  tubing with  Saran f i t t i n g s .  u s e d was f o u n d t o be q u i t e r i g i d straighten portions lengths  so t h a t  o f i t by i n s e r t i n g  t h e new  nylon.  QVF p i p e  For supply  were p r o v i d e d lene  flow  tanks,  a t b o t h ends w i t h  jars with  receiver  tight-fitting  tanks.  I t was f o u n d  w e i r by a c o n t r o l v a l u e .  n a t i n g a g e n t s t h a t may l i q u i d s being that  i t was n e c e s s a r y  alter  shape was r e t a i n e d , b y t h e s e c t i o n s were u s e d .  These  Polyethy-  were r e t a i n e d t o s e r v e  convenient  to replace  the  To i n s u r e a g a i n s t a n y the surface  studied, appropriate  only polyethylene,  the combination  f l a n g e s and b o l t s .  lids  to  through i t s u i t a b l e  o f g l a s s t u b i n g and t h e n immersing  i n a hot water bath u n t i l  tubing  over-  contami-  p r o p e r t i e s o f the  precautions  Saran, n y l o n ,  as  stainless  316), T e f l o n , Tygon, and. g l a s s were a l l o w e d  were t a k e n so steel  (Type  t o come i n c o n -  22  tact  with the a p p r o p r i a t e l i q u i d s -  gram o f t h e system  remained  The s c h e m a t i c  flow  dia-  t h e same a s i n F i g . 3 e x c e p t f o r  t h e m o d i f i c a t i o n s n o t e d above t o t h e s p r a y n o z z l e s a n d t o t h e means o f I n t e r f a c e  control.  Up t o t h i s p o i n t  i n the investigations, d i s p e r s e d  phase f l o w e d by g r a v i t y a t a c o n s t a n t r a t e n e e d l e v a l v e s , one l o c a t e d n e a r in  t a k i n g a photograph,  nozzle  tips  (Fig. 6).  due t o mass t r a n s f e r l e f t  i n t h e wake o f d r o p s  The movement o f t h e s e  i n t h e c o n t i n u o u s p h a s e medium was o b s e r v e d  v e r y much s l o w e r t h a n t h e movement o f t h e s o l u t e ring  from  patterns, In  fact,  due  t h e oncoming d r o p s w h i c h l i k e w i s e so t h a t  one c a n be d i s t i n g u i s h e d  t o t h e mass t r a n s f e r l e f t  An  it  was t h e n  injector  s e t up.  was h o p e d t h a t d r o p  rate  the other. that  were  i n t h e wake o f p r e v i o u s l y d e -  system  consisting  By means o f t h e s y r i n g e ' s p l u n g e r , g r o w t h c o u l d be c o n t r o l l e d  i n producing pairs o f growth.  o f a hypodermic  end o f t h e d i s p e r s e d phase  means o f t h e p l u n g e r o f t h e s y r i n g e . arose  schlieren  c a n be c o n s i d e r e d n e g l i g i b l e .  syringe attached to the i n l e t line  from  t o be  transfer-  formed  t h e e x t e n t o f t h e movement o f s c h l i e r e  tached drops  Thus,  s c h l i e r e . * were e v e r - p r e s e n t n e a r t h e  t h a t were p r e v i o u s l y r e l e a s e d . schliere  each n o z z l e  r e g u l a t e d b y two  of drops  However,  a t w i l l by  difficulties  of roughly equal volumetric  Somehow, t h e r e was u n e q u a l  friction  loss i n  * O p t i c a l i n h o m o g e n e i t i e s i n a n o t h e r w i s e o p t i c a l l y homogen e o u s medium, used here instead of the commonly accepted form "schlieren".  23  the  lines  l e a d i n g to each g l a s s n o z z l e ,  defective needle valves phase f l o w . set-up  was  t h a t were u s e d t o r e g u l a t e  After futile discarded  p o s s i b l y due  attempts  i n favour  of  to c o r r e c t t h i s , the  to  dispersed the  o l d arrangement.  whole  24  PART I  SCHLIEREN  STUDIES  25  PART I  A.  SCHLIEREN STUDIES  Scope  High-speed photography optical  s y s t e m was  utilized  c o u p l e d with the  to f i n d  o u t i f t h e r e were  movements a t o r n e a r t h e d r o p i n t e r f a c e understanding  possible  l a r g e number o f p a r a m e t e r s , was  The  t o the  Fundamental  arrangement, made.  any  to contribute  o f t h e c o a l e s c e n c e mechanism.  s t u d i e s of the s i m p l e s t  schlieren  avoiding  c o l u m n was  opera-  ted w i t h a stagnant c o n t i n u o u s phase,  thereby reducing  d i s t u r b a n c e made by u n n e c e s s a r y f l u i d  f l o w w i t h i n the  tion  column.  acetic  B.  The  s y s t e m s M I B K - a c e t i c a c i d - w a t e r and  a c i d - w a t e r were u s e d  of p i c t u r e  extractoluene-  i n the e x p e r i m e n t s .  photography,  as i n any  t e c h n i q u e s used t o i l l u m i n a t e  photographed.  The  problem  thousandth o f a second The  commercial except  p h o t o g r a p h y may  that  much g r e a t e r result  or l e s s ,  same b a s i c r u l e s  the i n t e n s i t y  be  the  fields  concerns subject  o f o b t a i n i n g enough  becomes more i m p o r t a n t when t h e e x p o s u r e  graphy.  other  t a k i n g , among t h e p h o t o g r a p h e r ' s c h i e f  the l i g h t i n g  t o be  one  the  Some P h o t o g r a p h i c C o n s i d e r a t i o n s  In t e c h n i c a l  are  a  times involved  followed  used  i n ordinary  i n h i g h - s p e e d work  required  i s usually very  t h a n i n most o t h e r a r e a s o f a p p l i c a t i o n .  of t h i s ,  the  scientific  are  a s i n h i g h - s p e e d photo**  of l i g h t i n g  of l i g h t  light  h i g h - s p e e d movie  As  a  photographer  26  i s o f t e n f a c e d with the problem o f r e q u i r i n g high continuous  lighting.  intensity  L i k e the commercial photographer, the  s c i e n t i f i c worker i s i n t e r e s t e d a l s o i n the c o n t r o l of l i g h t and  shadow t o o b t a i n h i g h image q u a l i t y and, t h e r e f o r e , an  a c c u r a t e photographic  r e c o r d of the s u b j e c t i n q u e s t i o n .  In many i n s t a n c e s , the s c i e n t i f i c photographer may f i n d i t convenient  to s a c r i f i c e a e s t h e t i c values  i n order t o use the  most d i r e c t methods p o s s i b l e i n o b t a i n i n g maximum  information  out of a p i c t u r e j u s t as food may be served without,  so t o  speak, the "trimmings".  The  4 x 5 i n . L i n h o f Super Technika  V camera, Ch.  E. 23450 and the 16mm x 400 f t . Hycam high-speed camera (Model K20S4E), Ch. E . 2355. with l e n s e s removed were subst i t u t e d f o r the viewing  screen i n the s c h l i e r e n runs.,  Proper exposure was found by t r i a l a t the s t a r t due  t o the unusual type of o p t i c a l system employed  (Fig. 8).  Lenses, i n s t e a d of m i r r o r s , are shown i n t h i s f i g u r e f o r convenience.  With no l e n s aperture  i n v o l v e d i n the s c h l i e r e n  arrangement, i t i s p o s s i b l e t o determine an e q u i v a l e n t to t h i s a p e r t u r e present  value  i n the m i r r o r system which can be  used and taken as l e n s aperture  f o r use with the L e i t z  s i x - L l i g h t meter (Ch. E . 2267). v a l e n t t o t h a t of a l e n s a p e r t u r e ,  To o b t a i n t h i s value  Microequi-  the k n i f e edge s e t t i n g and  IMAGE PLANE  Figure  8„  The r e g i o n o f i l l u m i n a t i o n  i n a conventional  FILM PLANE  s c h l i e r e n system  (39)»  27a  Key  L-|_o  L<2  P P  8  a f]_  Schlieren  f£  on  the  image  A point  on  the  film  Focal  plane. plane  Height  corresponding  to  P.  angle.  lengths  of s c h l i e r e n  respectively, h  8  lenses.  A point  Divergence 9  to Figure  of l i g h t  source.  lenses,  L]_ and  L2,  28 magnification these  two  o f the  f a c t o r s a c t the  camera t o p a r t l y  First by  trialo  aperture on ASA  control  s y s t e m must "be c o n s i d e r e d  same way  determination  No.),  a film  of an  was  read  on  i n run 1 ,  o f 200  film  replaced fps,frames  corresponded  to a  multiplying  600  the  being  product  pps  by  per  2.5»  the  of 2.0  a  lens based,  (formerly  of 15.8  the p r o p e r  The  sec.  was  found  All  movie f i l m s were p r o c e s s e d  white f i l m s Leitz  to provide  Films,  Ltd., except  where n o t e d  some600  otherwise.  by  ratio, (23)° 9  this  meter.  reliable  resuits.  by  was  sec. obtained  s h u t t e r speed  a c c o r d i n g to the  above p r o c e d u r e  for  camera s p e e d o f  o f b l a c k and  The  For  exposure  ( p i c t u r e s per  o f the  called  and  shutter duration-period  the r e c i p r o c a l  f/no.  done  meter r e a d i n g .  s h u t t e r speed o f 1/1500  A l l o w i n g f o r t h e wide l a t i t u d e gave r o u g h l y a n  light  pps  sec).  0  T h i s v a l u e was  USASI No.  (daylight),  camera speed, o f 600  film  obtained,  f o r a l i g h t meter r e a d i n g  o f USASI No.  the  e q u i v a l e n t f / n o . was  f r o m the m e t e r .  camera s h u t t e r s p e e d , and  obtained at a times  falling  Once a p r o p e r l y e x p o s e d f i l m was value  since  as a diaphragm a c t s i n a  the l i g h t  t h e known a p p r o p r i a t e d a t a :  example©  pps  schlieren  Trans-Canada  29 EXPERIMENTAL PROCEDURE  Upon c a l i p e r e x a m i n a t i o n •was f o u n d used  t h a t i t s w a l l s were n o t e x a c t l y p a r a l l e l  i n s c h l i e r e n experiments,  along  the e n t i r e  of t h i s  experimentso way, hamper since  were  the c o r r e c t  cing  and n o t q u a n t i t a t i v e  imper-  i n no  o f the p r e s e n t analysis  i n the e n s u i n g experiments,  work  i s involved.,  the s t r i a t i o n s  edge was s e t v e r t i c a l l y  and t h e r e  t h a t were e v i d e n t i n t h e p i c t u r e s  s i n c e o n l y a s m a l l a r e a was o c c u p i e d  by the c o a l e s -  dropso  experiments  column u n d e r c e r t a i n coalescence  c o n s i s t e d of running  extraction  t o study  c o n d i t i o n s and  pleted,  a l l equipment  the spray photographing  t h e mechanism«  As soon a s the. n e c e s s a r y  m o d i f i c a t i o n s were com-  i n contact with  r o u g h l y washed o u t w i t h MIBK. were  Of s e v e r a l o t h e r  d e f e c t s would,  interpretation  o n l y a few o f t h e s e  The  drop  t h a t these  o n l y when t h e k n i f e  obtained  travelling  s o r t were r e t a i n e d f o r use i n t h e p r e s e n t  qualitative  appeared  striations  a n d , when  o n l y t h e ones s h o w i n g t h e l e a s t  I t was f e l t  As was o b s e r v e d  showed  l e n g t h o f t h e column„  columns a v a i l a b l e , fections  o f t h e g l a s s column, i t  soaked i n c o n c e n t r a t e d  t h e f l u i d . s was t h o -  The 1 / 4 - i n .  nitric  S.S. n e e d l e  valves  a c i d , o v e r n i g h t and t h e n  rinsed  i n running water b e f o r e b e i n g  soaked a g a i n  remove  organic and i n o r g a n i c i m p u r i t i e s .  i n MIBK t o  E x t r a c a r e was  taken  30 t o i n s u r e t h a t no c o n t a m i n a t i o n , active  nature,  continuous those  was p r e s e n t  phase  especially  i n the system.  f e e d s were p r e p a r e d  d e s c r i b e d i n the s e c t i o n ,  of a surfaceThe d i s p e r s e d a n d  by methods s i m i l a r t o  "Preliminary Investigation".  Measurement o f l i q u i d s was done b y g r a d u a t e . phase was t h e n  poured  into  r u n was s t a r t e d b y f i l l i n g tinuous l i q u i d to c l e a r  along  rod.  effort rate  t o shake t h o s e  on f i l m  t h a t were  them o f f w i t h a  a t the proper  drop  flow  moment.  s i n c e t h i s was n o t b e l i e v e d t o be i m p o r t a n t . "CD" was u s e d  to indicate  from  t h e moment a p r e v i o u s l y c o a l e s c e d d r o p  from  the n o z z l e s t o the onset  No flow  However,  the time  taken  was r e l e a s e d  of coalescence  o f a new  drop  CD i s d e p e n d e n t , among o t h e r t h i n g s , upon t h e d i s t a n c e  between t h e two n o z z l e  tips.  To d e t e r m i n e sent  clinging  was made t o measure e x a c t l y t h e d i s p e r s e d p h a s e  a quantity called  pair.  the con-  trapped w i t h i n .  As soon a s t h i s was done, l i q u i d  s t a r t e d and r e c o r d e d  The  s t a n d i n g f o r a few m i n u t e s  the w a l l s o f the c o n t a i n e r by swiping  stirring was  t h e g l a s s column w i t h  of t i n y a i r bubbles  Sometimes i t was n e c e s s a r y  liquid  i t s r e s p e c t i v e f e e d tank.  w h i c h t h e n was l e f t  the l i q u i d  Each  i n the feed,  the c o n c e n t r a t i o n of a c e t i c  s a m p l e s were t i t r a t e d , w i t h  0.1 N s o d i u m h y d r o x i d e from  time  acid  phthalate  elsewhere  t o time  solution,  (24).  The t i t r a t i n g  (24) and w i l l  carbonate-free  whose s t r e n g t h was  against a standard  solution procedures  n o t be r e p e a t e d  here.  acid, p r e -  checked  of potassium a r e mentioned By a n u n f o r -  3 1 tunate for  o v e r s i g h t , measurements o f a c e t i c a c i d  the  earlier  m i n e d by on  the  titration,  preparation  priate  runs,  liquids  exact  but  of coalescence  The  reported  due  of  runs reported phase  difficulty  was  n e c e s s a r i l y the  the  presence  the  the  partly  of p r e c e d i n g  or continuous  the  actual  obser-  time p i c t u r e s  always l e s s  t h a n what  t h e s i s s t a r t e d with  of d e t e r m i n i n g  no  taking  i n t h a t phase h a s  because first  the  the  not  been  true  drop p a i r  value  due  studied  p a i r f o r m e d when a r u n  solute concentration  I n the  t o mass t r a n s f e r b e c a u s e  was  phase of  pairs.  t o m o d i f y , whenever  necessary,  e x t r a c t i o n column w i t h  phase or both  n e c e s s i t y of h a n d l i n g  place  t i m e a t w h i c h p h o t o g r a p h s were  drop  convenient  method o f c h a r g i n g  persed  very  t h e r e f o r e , the  I t was  taking  before the  of  superfluous  i n t o w h i c h mass t r a n s f e r was  This d i f f i c u l t y arose  s o l u t e was  was  in this  taken.  receiving  Hence a t  solute concentration to the  and  appro-  titration...  c o n c e n t r a t i o n a t the  s t a r t e d and,  a c t u a l l y be  nozzles  of t h i s  not  may  i s made.  as a r e s u l t  i n the  place.  saturation.  solute concentration  All  graduate  Determination  d r o p s emerge f r o m the  solute  a p p r o x i m a t e d by  b e c a u s e mass t r a n s f e r i s a l r e a d y  reported  deter-  to i n s u r e mutual  as  was  were n o t  a d d i t i o n of  solute concentrations  were t a k e n ,  7,  o f t h e m i x t u r e n e g l e c t i n g the  case,  vation  to run  were s i m p l y  i n any the  1  from run  concentration  h e a v y and  i n order bulky  to  the  dis-  eliminate  containers,  such  3 2  as  t h e QVF f e e d t a n k s , whenever t h e i r c o n t e n t s have t o be  emptied,  c l e a n e d , and/or f l u s h e d , t o accomodate  l i q u i d mixtures..  The e x t r a c t i o n  different  column a n d i t s n o z z l e  a s s e m b l y were t h o r o u g h l y washed i n t a p w a t e r , r i n s e d i n distilled  w a t e r , and t h e n a i r - d r i e d  whenever t h e f e e d  p o s i t i o n or e i t h e r the d i s p e r s e d or the continuous was c h a n g e d  i n the experiments©  c a r r i e d each  phase t o t h e e x t r a c t i o n  new m a t e r i a l o f t h e same k i n d . and  The o r i g i n a l  continuous  site  mixture  was r e p l a c e d w i t h  Afterwards,  was b e i n g u s e d  phase  t u b i n g which  the d i s p e r s e d  phase l i n e s were t h o r o u g h l y f l u s h e d  whatever l i q u i d  com-  with  f o r each r e s p e c t i v e  line.  All  experiments  were made a t room  temperature©  T e m p e r a t u r e d e v i a t i o n s i n t h e room were f o u n d reasonable  l i m i t s under  schlieren  Operating data f o r a l l the runs  A©  MIBK-Acetic  1)  Nozzle  Acid-Water  Tips Oriented  to vary within  c o n d i t i o n s (Appendix  c a n be f o u n d  i n Table I .  System  Horizontally  T h i s a r r a n g e m e n t o f t h e g l a s s n o z z l e s was to  that  tion all  of Groothuis and Zuiderweg  ( 1 3 ) i n their  similar  investiga-  o f t h e c o a l e s c e n c e mechanism a s m e n t i o n e d earlier© the runs  knife  i n this  D).  section  edge was a r b i t r a r i l y  except  as otherwise  s e t t o c u t the l i g h t  For  s t a t e d , the rays horizon-  Tabla I .  Experimental Eteta f o r Part  Solute Concentration. DirecDisNozzle Cont. persed t i o n of i n 3 x lb.moles Run ou.ft.soln. Orientation Transfer No. Solute Phase Phase 1 2 3  A c e t i c Mater Aold II  it  4  II  5  _  6  Acetlo Acid  7  II  II II II 9) I. * •t II  II  II  II  II  9 10  »  11  »  12  „  13  n  14  II  _ _»* D -*C  it ti II  68  Horizontal  68  II  68 68  »  19  8  MIBK  *  II  II II II It it M t  Ttilusne  Leltz Film Light L i g h t Source Knife Edge (USASI No., Me t e r Current Rdg. d a y l i g h t ) Camera Setting Rdg., amp. 4. 00 - 4 . 2 5 H o r i z o n t a l  11  4.80 - 5 . 00  n  4.75  II  5 . 3 0 - 6.00  II  5.30 - 5.50  - 5 .  0  T r l - X Rev. (200)  0  T r l - X Rev. (200)  17.7  11  16.7  5.00  ti  52.62  >i  5.20 - 5 . 5 0 Vertical  11  5 . 2 0 - 5 . 5 0 Horizontal  II  n  56.45  Vortloal  54.82  -  5.20 - 5 . 5 0 Vertical  9.43  -  5.75  6.28  II  6. 20 51.96  11  5 . 5 0 - 6 . 5 0 Horizontal  9.43  Bl II  16.5  - 5.50  - 6.50  "  16.25 16.2  n  ti  15.8  4X Pan. Neg.(500)  52.62  II  II  Studies)  C -<*»D  II  j)  I (Schlieren  5.50 - 6 . 5 0  11  4.00  11  4.00  11  •1  'Unsaturated Phase (Rooohlnl's m i x t u r e ) . **"D" stands f o r dispersed phase and "C" f o r continuous phase (see Table V a l s o ) . " " T h e s e a r e s h u t t e r speed v a l u e s . In seoonds.  Timing Film Ught MagnifiFreq. , cation plp/seo.  Hyoam  600  10  0.798  11  1200  100  0.798  11  2500  100  0.790  11  2000  10O  O.788  2000  100  O.786  2000  100  O.786  >t M It  2000  100  0.786  16.7  II  2000  100  O.78O  16.7  II  2000  100  O.766  17.5  II  2000  100  0.780  2000  100  O.78O  2000  100  0.765  I6.5  It II tl  17.5 17.5  II  T r l - X Jfen»  16.0  Linhof  16.0  it  (320)  Camera Frame Speed, PPS  It  0.765  250 1 250  -  0.765  3^ tally  so t h a t  only density gradients  t i o n were o b s e r v e d  ( 2 2 ) . The  i n the v e r t i c a l  d i s p e r s e d phase  ( 0 . 0 6 8l b . moles/cu. f t . soln.) a c e t i c t r a n s f e r was in and  section  from the d i s p e r s e d  (a) b e l o w .  R o c c h i n i d e s c r i b e d under  Solute  Transferring  Run sal  film  1 was  (USASI No.  (b) t o f o l l o w .  The  from  adjusting  the v a r i a b l e  s p e e d was  meter  resistor  5 ° ° amps.  ration,  practised lamp  t h i s may  s p e e d and  o f the l i g h t  t h e amperage above t h e i d e a l  of the mercury  of  Hycam m o v i e  increased  Rever-  that  hence  reading  film  shorter  o f 1 5 . 8 t o 1 6 . 2 5 by  on t h e c o n t r o l  panel from  This procedure of c u r r e n t range  increasing  of 4 . 0 - 4 . 5  s h o r t e n s the  However, i f u s e d  n o t m a t t e r much.  the  s o u r c e was c o r r e s p o n d i n g  normally as t h i s  (25)»  to 1 2 0 0  of coalescence.  somewhat t o o low e x p o s u r e  from a l i g h t  s h o u l d n o t be  (b)  Drops  to a higher shutter  4 . 2 5 amps, t o a b o u t  phase  2 0 0 , daylight).  exposure, the i n t e n s i t y increased  acid  used, t h r o u g h o u t .  t o slow down t h e m o t i o n a t t h e i n s t a n t  r e c e i v e d , due  8%m  to that  t a k e n a t 6 0 0 p p s w i t h Kodak T r i - X  To compensate f o r t h e  ly  reversed, i n s e c t i o n similar  For run 2 , the s h u t t e r pps  i n MIBK a n d  c o m p o s i t i o n was  camera w i t h the l e n s removed was  a)  about  t o the c o n t i n u o u s water  T r a n s f e r was  t h e c o n t i n u o u s phase  acid  was  direc-  ( 2 5 )  life  f o r a short  du-  35 3 was  Run at  a  still  h i g h e r camera frame  would occur  at this  p e r a g e c o u l d be  An  was  probably  not  immediately  Kodak f i l m with was  an  as  was  In-  f i l m s was  con-  lamp l i f e , HPS  available  a t the  used, t h i s o f 500  drop v e l o c i t y tance  time  time  the  was  increased.  b)  Solute  previous  (daylight).  verse  runs,  T r a n s f e r r i n g to  phase.  direction, The  t o 3»3  t h i s make  was  Another  Panchromatic  Negative  L i g h t source  amperage  h e l d down t o 2 0 0 0  7»  Velocity  of dispersed  i n c r e a s e d from 1 . 7  sec..-  By  by m a i n t a i n i n g  decreasing the  t i p s a s r u n 3»  t o the  onset  of  pps  same the  sec, the dis-  real  coalescence  Drops  s o l u t e was  i . e . , from the  continuous  daylight)  of i n q u i r y .  film.  so t h a t CD was  from drop approach  6 and  am-  5»0.  a t the n o z z l e and  In r u n s  kX  camera s p e e d was  reduced  800,  (USASI No.  of s e p a r a t i o n between n o z z l e interval  of f a s t e r  a s Kodak b r a n d s b u t  u s i n g Kodak T r i - X R e v e r s a l  i n a l l the  time  use  Negative  suitable  For run 4,  as  speed u n l e s s the  naturally  still.  USASI No.  p h a s e f l o w was  Underexposure  i n c r e a s e d t o a much h i g h e r v a l u e  again h e l d to about  while  speed.  coalescence  source  Ilford  frame  to observe  light  stead of s a c r i f i c i n g sidered.  made a t 2500 pps  phase was  t r a n s f e r r e d i n the  continuous not  t o the  re-  dispersed  s a t u r a t e d with  main  com-  36 ponent  o f the d i s p e r s e d  composition phases  p h a s e , a n d was p r e p a r e d  of Rocchini's  mixture to avoid  t o have t h e  separation of  (26): 1.29/&* 9J.6k%w 5»07^w  MIBK Water Acetic  acid. (26) t o prevent m i s t i n g of  The  u s e o f t h i s m i x t u r e was f o u n d  the  c o n t i n u o u s w a t e r phase upon t r a n s f e r o f a c e t i c a c i d  that phase. Rocchini the  This misting  phenomenon was a t t r i b u t e d by  t o the i n f l u e n c e  mutual  from  of a solute  a n d / o r t e m p e r a t u r e on  s o l u b i l i t y between two p a r t l y m i s c i b l e  solvents.  W i t h o u t t h e use o f t h e above m i x t u r e , upon e x t r a c t i o n o f the  a c e t i c a c i d from the MIBK-saturated. water phase, a  amount o f k e t o n e w i l l  come o u t o f s o l u t i o n .  For r u n s 6 and 7,  a l l lines leading  t i o n c o l u m n were d e t a c h e d a n d t h a t l i n e p e r s e d phase was s e a l e d containing  t h e c o n t i n u o u s p h a s e was d r a i n e d  the dispersed  c o n t i n u o u s phase.  a s s e m b l y so  The d i s p e r s e d  QVF  MIBK-saturated water used as phase i n runs 6 and 7  larly  consisted  o f MIBK a n d w a t e r , e x c e p t  being  saturated  a n d t h e m a i n component  was p o s s i b l e w i t h  and the l i n e  was now s u p p l i e d b y t h a t  contained  now MIBK a n d , t h e r e f o r e ,  The QVF t a n k  joined t o the nozzle  phase f l o w  tank which p r e v i o u s l y  t o the extrac-  c a r r y i n g the d i s -  f o r t h e time b e i n g .  c o n n e c t e d f r o m i t was t h e n that  small  that  the l i q u i d  of dispersed  no c o n t a m i n a t i o n by a t h i r d  t h e above a r r a n g e m e n t .  simi-  phase was liquid  Continuous phase  37 charging this  o f t h e column was b a t c h w i s e  column, t h r o u g h  one o f t h e o p e n i n g s  with R o c c h i n i • s mixture was t h e n t i g h t l y unnecessary  and was done by  i n the top o f i t ,  contained i n a b o t t l e .  closed, b y a n y l o n f i t t i n g  vapour  filling  The c o l u m n  t o prevent any  leakage.  Runs 6 and 7 were a g a i n  s h o t a t 2000 p p s ; l i g h t  m e t e r r e a d i n g s were a l l l6»5 c o r r e s p o n d i n g t o an amperage of about Both  5°2 a s read, f r o m  r u n s were i d e n t i c a l  the l i g h t except  edge was s e t h o r i z o n t a l l y w h i l e to a v e r t i c a l  position  the h o r i z o n t a l in  so t h a t  that  source  the e f f e c t  panel.  i n r u n 6, t h e k n i f e  i n r u n 7» t h i s was c h a n g e d i n run 7 density gradients i n  d i r e c t i o n were o b s e r v e d .  order t o observe  control  T h i s change was made  o f the k n i f e  edge p o s i t i o n on  the  o b s e r v a t i o n s o f d e n s i t y g r a d i e n t s between t h e d r o p s .  2)  Nozzle  Tips Oriented  The  g l a s s n o z z l e s were b e n t  were f a c i n g e a c h cence ancy  Vertically  other v e r t i c a l l y  so t h a t  t h e two t i p s  i n order to study  coales-  when t h e d r o p s were one on t o p o f t h e o t h e r and b u o y f o r c e s were a c t i n g  compared  i n a different  t o when t h e t i p s were o r i e n t e d  Only gated: from liquid  on t h e d r o p s  one d i r e c t i o n  t h e MIBK d r o p s  phase p i p i n g  system  of solute  manner  horizontally.  t r a n s f e r was  investi-  t o the continuous water phase. was r e f i t t e d  to i t s original  The  posi-  3 8 tion was  a s i n r u n s 1 , 2 , 3 » and  from drops to the c o n t i n u o u s phase.  ( r u n s 8 and  1 1 ) and v e r t i c a l  of the k n i f e w i t h about dispersed  The  MIBK p h a s e .  acetic acid  from  t h a t used  bulence  orientations  9 were  concentration i n r u n s 8 and  and h e n c e ,  r u n s 1 0 and  i n the  1 1 were  repli-  due  i n r u n s 1 0 and  1 1 was  reduced  9 t o decrease I n t e r f a c i a l  t o the r e l a t i v e l y  a high  driving  force  high  acid.  tur-  solute  con-  present within  system.  The throughout.  Hycam camera w i t h t h e l e n s removed was Other r e l e v a n t  d a t a c a n be  used  found i n Table I.  MIBK-Water S y s t e m *  In r u n 5 ° a b i n a r y  s y s t e m was  used, w i t h o u t  a c i d b e i n g p r e s e n t , w i t h a c o n t i n u o u s phase  of pure  and a d i s p e r s e d p h a s e  o f w a t e r - s a t u r a t e d MIBK.  in  the e f f e c t  and  replicates  f t . soln. acetic acid  Similarly,  also  horizontal  0 . 0 0 9 l b . moles/cu. f t . soln. a c e t i c  ( 9 ) o T h i s was  centration,  B.  Runs 8 and  0 . 0 5 l b . moles/cu.  transfer  Both  ( r u n s 9 and 1 0 )  edge were u s e d .  c a t e s , w i t h about  the  4 when the s o l u t e  order t o determine 7°  In e a c h o f t h e s e two  u s e d and mass t r a n s f e r acetic  acid  was  transferred  * Run 5 » i n v o l v i n g r u n s 6 and 7 °  water  T h i s was  o f MIBK t r a n s f e r  i n two  was  d i r e c t i o n s a t once  f r o m the c o n t i n u o u s phase  t h e MIBK-water s y s t e m , was  done  i n runs 6  runs, Rocchini's mixture  occurred  acetic  -  t o the  performed before  39  drops and, s i m u l t a n e o u s l y , nuous water phase. saturation  MIBK f r o m t h e d r o p s t o t h e c o n t i -  This last  of the phases.  t r a n s f e r was due t o m u t u a l u n -  Since  r u n 5 had a pure water  t i n u o u s phase, and s i n c e i n R o c c h i n i ' s c o n t i n u o u s  con-  mixture,  t h e r e was some MIBK, t h e mass t r a n s f e r r a t e i n r u n 5 was e x pected, t o be h i g h e r the  larger  than  those  MIBK c o n c e n t r a t i o n d r i v i n g  Usual a c e t i c a c i d was  procedures  liquid  but then  were o b s e r v e d  phase bing nylon  found  reached  up t h r o u g h  one  the t i p of the disturbances  observed.  by water from  These  schliere  the continuous  the g l a s s t u b i n g - n y l o n t u -  T h i s p r o b l e m was c o r r e c t e d b y r e p l a c i n g t h e worn  Run 5 was r e p e a t e d was f i l m e d a t 2000 p p s w i t h  knife  were  t o be c a u s e d  t u b i n g i n the a f f e c t e d  responding  " c a p s u l e s " o f im-  However, o p t i c a l  t h a t somehow s e e p e d t h r o u g h joint.  tiny  w h i c h could, e i t h e r be due t o d e n s i t y o r c o n c e n -  t r a t i o n d i f f e r e n c e s or both, were l a t e r  t o i n s u r e t h a t no  t o be t r a v e l l i n g  when t h e s e  n o z z l e , no d r o p s were f o r m e d . schliere,  f o r c e i n r u n 5°  present.  o f t h e two g l a s s n o z z l e s .  or  6 and. 7 b e c a u s e o f  were u n d e r t a k e n  Run 5 was s t a r t e d miscible  of runs  to a light  source  glass-nylon  with light  the t i g h t  connections.  m e t e r r e a d i n g o f 16.7  amperage  edge was s e t h o r i z o n t a l l y .  joint.  o f a b o u t 5°5°  The  It cor-  40 C.  Toluene  At with  - Acetic Acid  this  a solvent  was u s e d  since  stage,  surface  two s o l v e n t s a r e compared  i n t h e MIBK r u n s ,  tension  Toluene  and the d e n s i t y  i n A p p e n d i x Fo  t o take p i c t u r e s w i t h only»  t h e ones w i t h  t i p s were among t h e b e s t  series  of runs.  the v e r t i c a l l y - o r i e n t e d  e x p o s e d p i c t u r e s i n t h e whole  By f o l l o w i n g s i m i l a r e x p o s u r e  i t was f e l t  a close  the n o z z l e  The r e a s o n f o r t h i s was b e -  nozzle  toluene,  t h e MIBK  t e n s i o n and d e n s i t y .  The s u r f a c e  0  oriented v e r t i c a l l y  cause  to replace  i t h a s s a t i s f a c t o r y p r o p e r t i e s , and s i n c e i t  I t was d e c i d e d tips  System  i t was d e c i d e d  of higher  was r e a d i l y a v a i l a b l e of these  - Water  comparison could  settings f o r p o s s i b l y be  achieved©  B a t c h w i s e p r o c e d u r e s were u s e d . to the corresponding runs.  The QVF f e e d  was n o t u s e d out  p r o c e d u r e s f o r the MIBK-acetic tank which  i n order  supplied  t o prevent  b y a 250  ml° l e v e l l i n g  t h e t o p by a cork  clamps a t t a c h e d  contamination  g l a s s bulb  frame.  The n e e d l e v a l v e s  placed  by screw-type p i n c h  w e l l when u s e d w i t h  that  since  phase washing  T h i s t a n k was  t h a t was c o v e r e d  wrapped i n aluminium f o i l  t o one o f t h e p o s t s  acid-water  the dispersed  a h e a v y t a n k a s t h e a b o v e i s cumbersome.  replaced at  These were s i m i l a r  a n d h e l d by  o f t h e e x t r a c t i o n column  c o n t r o l l e d drop flow  were r e -  c l a m p s t h a t worked s u r p r i s i n g l y  the f l e x i b l e  Tygon t u b i n g .  A l l lines  41 t h a t had been i n c o n t a c t with MIBK were removed and r e p l a c e d with n y l o n t u b i n g except f o r the d i s p e r s e d phase l i n e which was  made up of Tygon, some p o l y e t h y l e n e tubing, and n y l o n  fittings. connected  Part of the d i s c h a r g e l i n e which was  immediately  t o the bottom of the square g l a s s column was a l s o  r e p l a c e d with f r e s h tubingo  T h i s ensured a g a i n s t any MIBK,  which might have been l e f t over from p r e v i o u s runs, i t s way back t o the g l a s s column and contaminating sent c o n t e n t s .  finding i t s pre-  Drop flow once more was made continuous.  The flow was g r a v i t y - p r o d u c e d , and was r e g u l a t e d by t u r n i n g the screws i n the p i n c h clamps which c o n s t r i c t l i q u i d through  the f l e x i b l e  Tygon l i n e .  flow  A l l runs i n v o l v i n g toluene  were made with the k n i f e edge c u t t i n g o f f l i g h t r a y s h o r i In r u n 12, the d i s p e r s e d toluene phase contained  zontally. acetic acid  (6.28  x 10  phases were mutually other. was 6»5o not  l b . moles/ cu. f t . s o l n . ) , and both  s a t u r a t e d with the main component of the  Camera speed was 2000 pps and the l i g h t meter r e a d i n g  1?.5 corresponding t o a l i g h t  source amperage of about  Drop coalescence was narrowly missed and the r u n was repeated.  P i c t u r e s of runs 13 and 14 were taken with the Linhof camera (lens removed).  The d i s p e r s e d toluene phase  contained 6.2 x 10"" ^ l b . moles/cu. f t . s o l n . and 51.96 x 10"" 3 l b . moles/cu. f t . s o l n . of a c e t i c a c i d i n runs 13 and 14, respectively.  Other e x t r a c t i o n c o n d i t i o n s were i d e n t i c a l t o  those of r u n 12.  The camera s h u t t e r speed was s e t a t 1/250  42  seco w i t h to for  f / 4 o 5  both  source  the "aperture" opening when l e n s i s a t t a c h e d ) « runs with a l i g h t  amperage  The All  of  a t i t s widest Light  (corresponding  v a l u e s were t h e same  meter r e a d i n g o f I60O and a  light  4 o 0 o  continuous  p h a s e was t o l u e n e - s a t u r a t e d watero  o t h e r d a t a a r e t o be f o u n d  i n Table  L  ^3 RESULTS  Still tools  and  i n r e c o r d i n g drop  occurrences inherent record  such as  the  i s taken  of the  coalescence  phenomena..  in real  confuse  the  and  viewer  drop  by d e t e r m i n i n g  coalescence  o p t i c s what v i s u a l  when a  photographic be  F o r example, a  movie  v i e w e d i n s l o w m o t i o n on  sbhliere  the n e c c e s a r y coalescence the a c t u a l  a  seen  with  by  coalescence  6,  the  drop  (and a l s o where n o t e d  (The  Except  of  occupied  coalesce  under  start  At h i g h e r camera  of drop  coalescence otherwise) t o be  o n l y one  only a f r a c t i o n  was due  resupply drop  speeds  of the  total  g r o w t h t o coalescence© not recorded to poor  performed  comments p r e s e n t e d  of  schlieren  hoped t h a t the  i n r u n 1,  attempted©  s y n c h r o n i z a t i o n w h i c h had  the  the d e n s i t y g r a d i e n t s c o u l d  information©  p e r r u n was  3 and  t h e use  I t was  of  t h e mechanism  c h a n g e s o c c u r when d r o p s  caused  i n v o l v e d from  the purpose  i n f o r m a t i o n on  i n f l u e n c e o f mass transfer©  In r u n s  Human e r r o r  However, t h i s must  p o i n t e d out e a r l i e r , to provide  time  high-speed  a c c u s t o m e d t o movements  p r e s e n t work was  sulting  important  time©  As was  the  o f drops»  c o n s i d e r a b l e caution©  a t c o n s i d e r a b l e speed  s c r e e n can  extremely  phenomena, p a r t i c u l a r l y  i n o b s e r v a t i o n i s o f t e n reduced  approached with taken  movie photography a r e  in this  on  film  camera-process  manually..  section with  regard  44 t o movement o f m a t e r i a l s film,  and  not  f r o m the  Interfacial rized and  by  the  sharp the  presence  picture  was  viewed  further  slow down the  analysis  the  of drop  In r u n of  focus.  in  the  on  t o be  was  of  Knife  be  Edge  The  picture  exhibited  was  the  run of  at  screen, a  1  a as  i t  was  faster rate  picture  for  to  closer  I t was  knife  This  which  on  drop a t  left  the  called,  the  This  hand  amount o f  layer  this  "Effect  Image".  side  left  and  believed  edge o r i e n t a t i o n a n d heading,  that  both  drops  was  here-  also  surrounded  difference  Schlieren  "the  (from  noticed  of  out  pronounced  ( F i g . 9)<>  l a t e r under the  Orientation  slightly  picture  upper halves  quiescent.  smaller  the  lower h a l v e s  the  t o be  much more  of  present  the  the  discussed  a  of  observation  the  appeared  r i g h t drop").  ( 3 0 ) was  with  ( f r o m h e r e o n t o be son,  operated  r i g h t hand s i d e  "the  necessarily  will  on  movements w i t h i n  a dark border to  associated  effect  i n slow m o t i o n  2 , the  l i g h t e r shade on  t o be  film  motion.  the  called,  characte-  c o a l e s c e n c e s w e r e n o t e d and  I n t e r f a c i a l turbulence  drop a t  not  four  i n the  the  movie  thesiso)  i n both drops  evident  camera must be  diffusional layer  a  (8)  turbulence  About  that  in  shown i n t h i s  of e d d i e s prevented  interfaceo  drops as  prints  v i o l e n t movements was  evident  a  were drawn f r o m v i e w i n g the  of  drop"),  the  picture  for  interfacial  some  rea-  turbulence.  :  45 Probably,  this behaviour represented a reduction  concentration driving ing  force  or t o a slower r a t e  owing t o e i t h e r  i n solute  incomplete mix-  of drop f o r m a t i o n .  A c c o r d i n g t o the  f o r m e r r e a s o n i n g , t h e m i x t u r e p r e s e n t i n the l e f t leaner  i n the a c i d  t h a n what i t w o u l d  Thus,  a lower d r i v i n g  latter,  a decay  in interfacial  reduction  of the  interface  dividing  phase It the  interesting  to note just  the  -  5°°»  outside  while  tension  t o the  a c r o s s the continuous changes. schliere  The  the drop  in  left slightly  b e h a v i o u r was  ob-  use  o f Kodak 4 x P a n c h r o m a t i c  Negative  (USASI  d a y l i g h t ) i n r u n 3 t o compensate f o r a h i g h e r camera  In run 2.  i n moderate  o v e r e x p o s u r e and  The  schliere  were  r u n was  reduced  i n the r i g h t motion.  drop,  contrast.  more c l e a r l y  s e e n t o be m o v i n g  i n the c o u n t e r c l o c k w i s e d i r e c t i o n around  clockwise  F o r the  t h e p e r i p h e r y o f the  t o move a r o u n d  However, s c h l i e r e movement i n t h i s  tently  f r o m the  at-  intermittent.  speed, r e s u l t e d  than  difference  movement o f t h e  i n a counterclockwise d i r e c t i o n .  The  result.  o c c u r r e d due  interfacial  T h e s e s c h l i e r e appeared  s e r v e d t o be  No.  activity  concentration  to smaller  p r e p a r a t i o n was  would  t h e d i s p e r s e d phase  c o n t i n u o u s phase  drop. and  solute  giving rise  was  force  was  n o r m a l l y be when com-  p l e t e m i x i n g d u r i n g t h e d i s p e r s e d phase tained.  drop  intermit-  the l e f t  the c o r r e s p o n d i n g s c h l i e r e  shown  drop  exhibited  46 Run 4 showed d i f f u s i o n a l lar  t o those r e p o r t e d i n d e s c r i b i n g  s h o u l d be n o t e d  that  such l a y e r s  3, a l t h o u g h t o a l e s s e r movement was  observed  t o be  with  complete  lence.  absence  Also,  projection  appeared  observed  the r e s u l t s  i n the form  i n the b i n a r y  phase, the l i q u i d  interfacial  of a s i n g l e  illustrates  turbulence.  layer  However, movement o f  the drops b u t  t h a t were  i n appearance.  the k n i f e  i n r u n 6 the v e r t i c a l  d i e n t s were v i s u a l i z e d , ponents  dis-  p r e s e n t , took p l a c e i n v a r i o u s  same e x t r a c t i o n  i n run 6 except that  While  was  almost  P i g . 10  this.  I n r u n 7» as  i n r u n 6 where  T h e r e were no e r u p t i o n s a r o u n d  to a d i f f u s i o n a l  Coalescence  o f the i n t e r f a c e  s i m p l y d i s t u r b a n c e s o f v e r y low i n t e n s i t y similar  horn-like  the continuous t o the d i s p e r s e d  i n the v i c i n i t y  although s l i g h t l y  directions.  turbu-  system.  from  t u r b e d due t o i n t e r f a c i a l schliere,  of s c h l i e r e  l a y e r was a g a i n o b s e r v e d f o r r u n 5  on t h e t o p o f e a c h d r o p .  transferred  i n run 2 ( i t  varied.  In the use o f R o c c h i n i ' s m i x t u r e s o l u t e was  simi-  i n r u n s 1 and  The d i r e c t i o n  o f any n o t i c e a b l e  schliere  i n both drops  occurred a l s o  extent).  A diffusional  was  layers  (Fig'.. 1 1 ) .  c o n d i t i o n s were  edge was  used  set v e r t i c a l l y .  components o f t h e d e n s i t y  i n r u n 7 i t was  the h o r i z o n t a l  gracom-  Note t h e d i f f e r i n g r e g i o n s o f d e c r e a s e d .  47 and  increased  illuminations  compared w i t h r u n 7 » to  8  A g a i n , the  f a v o u r m o v i n g i n any  The so t h a t  i n F i g s . 1 0 and schliere  particular  n o z z l e s were now  positioned  stages of drop growth.  ditions,  or pendent  i n shape  schliere the  around  lower drop.  directions cillation  d i f f u s i o n was appeared peared in  the drop.  The to  slightly  right  u s e d and t h a t  acetic  portion  i n various  a c i d appeared  of the p i c t u r e .  a n d was  and  o r no m i x i n g  ap-  taking  o f the  film.  o f r u n 9 were s i m i l a r a vertical  the d r o p s appeared The  drop,  distributed  schliere  due  knife  t o be t o the  t o be m o v i n g downward a t t h e Whether t h i s was  settling  s i m p l y movements owing t o c o n v e c t i o n c u r r e n t s p r e s e n t a t e d by  or o s -  solute  f o r the d u r a t i o n  being that  (Fig. 1 3 ) .  around  For the lower  diffused  ( F i g . 1 2 ) with l i t t l e  out of f o c u s  diffusing  The  i n the c o n t i n u o u s f l u i d  run 8 , the only d i f f e r e n c e  dis-  the drop boundary  photographic conditions  edge s e t t i n g was  and  However, p e n d u l u m - l i k e m o t i o n  p l a c e w i t h the c o n t i n u o u s p h a s e ,  con-  were o b s e r v e d a l s o  not u n i f o r m a l l around  pattern  Fig.  Under these  intermittent,  l e s s near the n o z z l e t i p .  a unique  i n run  o b s e r v e d t o be  observed i n the lower drop.  suspended  vertically  c l o c k w i s e movement o f the  Schliere  T h e i r m o t i o n was  once a g a i n . was  d r o p was  w i t h accompanying  observed  to top contact.  1 2 shows the. l a t e r  torted  were n o t  direction..  t h e d r o p s were m a k i n g b o t t o m  the u p p e r  1 1 when r u n 6 i s  the p r e v i o u s drops d e t a c h i n g and  rising  up  the  or  crecolumn  Figures 9 - 1 3 . Schlieren photographs  of various drop p a i r s .  49 and/or movements generated  by the drop i n t e r f a c e was  i n v o l v e d i n t a k i n g 100 f t o  t a i n , because of the b r i e f time f i l m , which comprises  not c e r -  the run, approximately  3 secso  of  In a d d i -  t i o n , because of the l i m i t e d camera viewing a r e a , the e n t i r e s o l u t e f l o w p a t t e r n was  difficult  to d i s t i n g u i s h o  No n o t i c e -  able amount of motion by the s c h l i e r e or drop o s c i l l a t i o n observed  f o r e i t h e r of the two  f a c i a l turbulence was  absent  drops i n the p i c t u r e o  was  Inter-  i n the l e f t - h a n d p a r t of the l o -  wer drop l o c a t e d near the n o z z l e t i p .  The absence of t h i s  turbulence i s shown i n F i g . 1 3 °  Runs 10 and 11 were c a r r i e d out a t low  concentra-  t i o n of s o l u t e i n the d i s p e r s e d phase (9«43 x 10** ^ lbo moles/ cuo  fto  soln ) 0  0  Under these c o n d i t i o n s , d i s t o r t i o n of drop  shape, i n t e r f a c i a l a c t i v i t y , and  o s c i l l a t i o n were very much  l e s s than f o r h i g h e r c o n c e n t r a t i o n s . absent  from the p i c t u r e s o b t a i n e d  t e r f a c e was  almost  O s c i l l a t i o n was  virtually  ( F i g s . 14 and 1 5 ) °  t u r b u l e n t - f r e e and  The i n -  the l o c a t i o n of the  dif-  f u s i o n a l l a y e r , which depends upon the k n i f e edge o r i e n t a t i o n , was  c l e a r l y shown owing to l e s s e r i n t e r f a c i a l a c t i v i t y  i n p r e v i o u s runs.  D i r e c t i o n of movement of the  than  schliere  was  in various directions.  Due  to the h i g h e r i n t e r f a c i a l t e n s i o n value of  toluene compared to MIBK (Appendix F ) , with toluene  compri-  s i n g the main component of the d i s p e r s e d phase i n run i n s t e a d of MIBK, the drops were observed  12  to be b i g g e r i n  50 size.  After  remained  one  c o a l e s c e n c e , the r e s u l t i n g  a t t a c h e d t o t h e u p p e r nozzle<>  l o w e r n o z z l e was  similar  taken as r u n 12.  edge was  i n the two  appeared  r u n s as would  Another drop from  be  The  light  expected.  due  m a i n l y to the weight  pendent  d r o p b e a r i n g down on i t .  tions near which  smooth i n t e r f a c e  or evidence of l a r g e  and  was  Laminar  t h a n the  movement was  Run  i n various  13  was  schlieren  in  i n the form  and 1 1 .  that  stronger a c t i v i t y  bounding  t o f l o w by d e n s i t y drops). with  Run  13  of run  A g a i n , the  of run 12. camera.  would  earlier,  12  schliere  Photographs  In r u n 1 3 ,  Goltz  be e n c o u n t e r e d  of the drop out of which currents  (i.e.,  The  the  evident  pendent  (30)  suggested  i n the the  stronger  interface  solute  tended  the lower p a r t s of both  showed, r e s u l t s w h i c h  this expectation.  sur-  oscilla-  o f s m a l l e r u p t i o n s was  As m e n t i o n e d  that part  was  patterns present  the lower p a r t s of both drops p a r t i c u l a r l y (Fig. 16).  upper,  directions.  a repetition  drop  layer  concentration l e v e l  were t a k e n by means o f t h e L i n h o f surface a c t i v i t y  the  (30)  diffusion  t h e r e were no d r o p  t o t h a t r u n s 10  similar  drops  o f t h e h e a v i e r and b i g g e r  scale  t h e d r o p s a t the s o l u t e  12,  p a t t e r n s were  Both  observed, i n t h e f o r m o f a q u i e s c e n t d i f f u s i o n a l rounding a  the  pendent  of close approach during  s t a g e , the l o w e r d r o p b e i n g f l a t t e r  perhaps  still  ( I n b o t h r u n s 1 1 and  set h o r i z o n t a l l y o )  t o f l a t t e n a t t h e zone  rest-time  drop  made t o c o a l e s c e w i t h t h i s b i g g e r  d r o p and. t h i s was the k n i f e  large  seem-  photographs  t o be  i n accord  showed a b i g g e r v i e w -  51 a r e a t h a n t h o s e f o r r u n 12„ and. i n r u n 1J  ing  coming f r o m t h e l o w e r d r o p downward  c o u l d be s e e n t o a p p e a r  solute  ximately  6 x 10~3 i  ximately  52 x 1 0 " 3  interfacial  c o n c e n t r a t i o n was D  o  moles/cu.  mass  increased accordingly  (Fig. 17).  the  r u n s t a k e n t o g e t h e r were s t u d y o f two d r o p s  conditions.  cated drop r o t a t i o n  On t h e o t h e r h a n d , i t may  to confirm  drop  of the s o r t  t o be s t i f f  initially  immerse p o r t i o n s  them.  and  be t h a t t h e  d e s c r i b e d by G o l t z  indi-  (30).  suggestive of  rotation.  The n y l o n t u b i n g u s e d found  (13)  o b s e r v e d i n some o f t h e r u n s  The b e h a v i o u r o b s e r v e d i n r u n 8 was e s p e c i a l l y  to  found a t or  h y p o t h e s i s p r o p o s e d by G r o o t h u i s a n d Z u l d e r w e g  movement o f t h e s c h l i e r e  attempts  However, a l t h o u g h a l a r g e  i n t h e zone o f d r o p a p p r o a c h  (12).  The  coalescing  o f f i l m s were e x a m i n e d , no b e h a v i o u r was  a l s o by Smith  appro-  i n r u n 13 t o a p p r o i n r u n 14.  present a general visual  near the i n t e r f a c e  from  f t . soln.  transfer  u n d e r mass t r a n s f e r  increased  f t . soln.  l b . moles/cu.  activity  All  number  flowing  a l o n g the lower n o z z l e ' s lengtho  The  to  the solute  S  of t h i s  The n y l o n f i t t i n g s  after a period  of time.  i n most o f t h e l i n e s  were  a n d i t was n e c e s s a r y a t t i m e s i n hot water  i n order to straighten  were a l s o f o u n d t o become Influence  c h a n g e s was assumed n e g l i g i b l e  o f ambient  brittle  temperature  c o n s i d e r i n g t h a t maximum room  Figures  14 - 1 ? .  Schlieren photographs of various drop p a i r s .  53 temperature the  short period  of ambient the of  f l u c t u a t i o n s during  density the  umn o  of time  a i r density gradient  involved  changes  was  s c h l i e r e n systems  e a c h r u n were v e r y i n each filming.,  was  relatively was  small f o r Influence  likewise neglected smallo  confined  within  The  depth  since of  the s q u a r e  field col-  5^ DISCUSSION  A°  Effect  of  Knife  Edge  Runs 6 t o 11 In r u n s 6,  8,  and  used,  i n r u n s 7»  light  patterns  8,  and  knife (31)  10  and  edge.  11, 9»  show the  and  10,  provide s a  further  of k n i f e  knife  i n each p a i r  8 of  Schlieren  to  the  the  of  orientation.,  The  of  runs(7 and  6,  9  effect  and  of  S a w i s t o w s k l and  the  was  different  different positions  p a p e r by  example  Image  edge p o s i t i o n  a v e r t i c a l one.  were due  Figure  on  effect  a horizontal  observed 11)  Orientation  the  Goltz  of k n i f e  edge  position.  If  i n the  g r a d i e n t normal to be  deflected  in  the  This d e f l e c t i o n  the of  the  light  field this  results point  the  light  rays,  light  r a y s may  techniques, In  source  the  varies  be one  illumination  the  view of  the  The  of  the  second  image o f  the  light  of l i g h t  rays  schlieren source  of  called  of  schlieren  image  cross-sectional  f o c a l plane  one  deflection  s c r e e « . C o n s i d e r F i g . 18. bundle  travels.  displacement  i n the  of  will  changes  light  the  p a r t i c u l a r point  change o f  with  used being  t h i s method, the  index  rays  o b s e r v e d by  c o r r e s p o n d i n g to  through a  the  viewing  (Fig. 4).  on  the  is a refractive  speed of l i g h t  (22).  the  in a  of  there  the  t h r o u g h the M2  of  passing  path  the  schlieren  image o f  section  i n d e x o f a medium where t h e  T o e p l e r method  the  a  the  because  refractive  a number o f  test  of  This passing  mirror,  i s square  and  is  55  NOTE:  b = h  INITIAL IMAGE OF SOURCE  Figure  18.  L i g h t b u n d l e - k n i f e edge T o e p l e r method ( 2 2 ) .  arrangement  i n the  56 an  opaque k n i f e edge  edge i s a d j u s t e d tion, off  18o  disturbance  i n the t e s t  sec-  decrease  uniformly.  shown i n F<igo  p a r t o f t h e image on  o r i n c r e a s e a c c o r d i n g t o whether  i s t o w a r d s o r away f r o m t h e k n i f e e d g e .  p l a c e m e n t o f t h e image o f t h e s o u r c e  parallel  t h e r e f o r e , be s e t p e r p e n d i c u l a r t o t h e d i r e c t i o n  in  order  index  observed,  effect.  Regions that a r e evenly photograph correspond  must,  i n which  o r d e n s i t y g r a d i e n t s a r e t o be  t o o b t a i n the s c h l i e r e n  illuminated i n a  schlieren  t o zero density gradient.  From t h e f o l l o w i n g r e l a t i o n s f o r  two-dimensional  flow (22):  where  £)^j~y  =  total and  L Tfo  -  angular  light  d e f l e c t i o n s i n the X  ^directions respectively.  width  Dis-  t o the k n i f e  edge p r o d u c e s no e f f e c t a t t h e s c r e e n , a n d t h i s edge  the r e f r a c t i v e  i s cut  i s i n t r o d u c e d , p a r t o f t h e image  I l l u m i n a t i o n o f the c o r r e s p o n d i n g  the d e f l e c t i o n  The  i s reduced  may be d i s p l a c e d t o a p o s i t i o n  screen w i l l  o f M2.  f r o m t h e image o f t h e s o u r c e  so t h a t i l l u m i n a t i o n on t h e s c r e e n  of the source  plane  so t h a t f o r n o d i s t u r b a n c e s  part of the l i g h t  When a n o p t i c a l  the  i s placed, a t t h e f o c a l  of test  = refractive section.  section.  index  of a i r surrounding  test  5 7 7jt it  _ refractive  i s seen t h a t l i g h t  refractive density.  index For  gradient,  the  direction the  direction  that its  the  For  run  The  of these  light  to  On  rays  illustration  the  almost  other or  the  i s opposite  the  vertical  to  d e f l e c t i o n of l i g h t components passing  each drop but  the  hand, t h e  parallel  tail  vertical  of the  deflected  downwards  tones are  produced.  of the  By p o s i t i o n i n g t h e  components o f ( F i g . 19)»  the l i g h t an  passing  are  represent  density gradient setting  t h a t the  remains undisturbed.  to  drop, r e s p e c t i v e l y .  t o the k n i f e edge  path  close  ( F i g . 19).  of drop approach  so  so  i n s t e a d of m i r r o r s  a r r o w h e a d and  direction  (3))o  those  d e f l e c t e d upwards  l o w e r b o u n d a r i e s o f the  completely  ( 2 ) and  d e f l e c t e d downwards w h i l e  purposes, l e n s e s  of  i s t o w a r d the p o s i t i v e  (equations  outside  component  drop boundary p a r t i c u l a r l y a t  the  higher  system  that  some p o r t i o n o f the  off  the  of a c e t i c a c i d  so  gradient  of  of  example, a h o r i z o n t a l k n i f e edge  i t s lower r e g i o n are  u p p e r and  region  index  ( A p p e n d i x F)  index  6 as an  shown i n t h i s f i g u r e and the  refractive  of water  refractive  upper r e g i o n are  close  the  direction  r u n s i n v o l v i n g the  employed, t o o b s e r v e  this gradient. directions  i n the  section.  o f mass t r a n s f e r .  Taking s e t t i n g was  in test  i . e . , t o w a r d the  experimental  than t h a t of the  of i n t e r e s t  d e f l e c t i o n s are  MIBK-acetic acid-water, is greater  index  light  the  rays  image o f v a r i o u s  at  zone  here  k n i f e edge t o r a y s which  is  cut  are light  Some d e n s i t y g r a d i e n t s , w h i c h a r e  not  D E F L E C T E D  LIGHT  Figure  19.  Image f o r m a t i o n ,  f o ra particular  case,  RAYS  i n a schlieren  system (Toepler  method)„  59 e x p e c t e d t o be e d g e , may second rays can  visualized  schlieren mirror,  a c t as a can  circular  affect  the  From t h e edge c a n the  be  M2,  oriented  other,  section  stop  given  so a s  example,  owing t o the  may  direction  From t h e  The  when t h e flow,  arise  results  knowledge of the the  and be  i m a g e s o f the vertical  the  s e v e r a l forms of  workers  (33,  34)  the  about  When d e n s i t y  gradients  i t i s desired to rotated  study  and  successive  t o make s u c h a n  p i c t u r e s with taken  i n the  two  adjustment  simultaneously i t seems s a f e direction  test  for  comparithat  suffices  to  s e c t i o n o f the  other,  knife  t o say  t h a t f o r m s two  and. t h e  one  give  present  separate  image  indicating  horizontal density  s t o p have b e e n u s e d by light  Otherwise,  different  i s referred to reference  to render  knife  information  section simultaneously,  reader  mirror  image.  or i s r e p r o d u c i b l e .  For a device  density gradients  gradients, more,  test  light  phenomenon i n v o l v e d I s , f o r  d e f l e c t i o n i n one  study.  final  t i m e l a g between  obtained,  conditions prevailing  experimental  and  the  conditions,and,  k n i f e edge i s s i m p l y  edge o r i e n t a t i o n s s h o u l d son.  proper  direction.  knife  Thus, t h i s  considerations,  time r e q u i r e d  steady-state  complications  the  of  a l l o f the  (22).  to provide  i n any  the  significant  inability  i l l u m i n a t i o n i n the  another p i c t u r e taken.  i s not  the  test  have b e e n s t u d i e d i n one them i n the  to  p o s i t i o n of the  to c o l l e c t  foregoing  density gradient  pictures  t o the  sometimes a p p e a r due  r e f r a c t e d , i n the  thus,  due  32.  Further-  different  deflections visible.  6 0 B.  Drop R o t a t i o n a n d S o l u t e D i f f u s i o n  Goltz and  thought  the  nozzle.  ( 3 0 ) observed r o t a t i o n  t h i s motion  Bakker, hand, contended  was i n i t i a t e d  van Buytenen,  a n d Beek  t e n s i o n which  A c c o r d i n g t o them, suppose  interfacial  impinges  then the i n t e r f a c i a l  i s richer  within  continuously  i n solute  the drop forced  like  drop,  B since  i s entrained,  i n the d i r e c t i o n  momentum o f t h e i n c o m i n g l i q u i d i s disturbed  the incoming l i q u i d i s o f A.  The d r o p  starts  i n one d i r e c t i o n . o f drop  a n d a n i r r e g u l a r movement  results.  ( 3 6 ) observed  of drop formation.  They  growth  that the  r o t a t i o n depended on:  rate  i n the drop.  i s so g r e a t  G a r n e r , Nut t, a n d M o h t a d i  1.  the incoming  t o move f r o m A t o B a n d a s t h e  o u t , however, t h a t a t v e r y h i g h r a t e s  rotation  the incoming  a t a n a r e a A,  than the l i q u i d  r o t a t i n g and m a i n t a i n s a c i r c u l a t i o n found  the s o l u t e lowers the  t e n s i o n a t A becomes l o w e r t h a n a t  T h i s causes the i n t e r f a c e liquid  the undisturbed  on t h e i n t e r f a c e  some o t h e r a r e a i n t h e i n t e r f a c e liquid  ( 3 5 ) on t h e o t h e r  causes the i n t e r f a c e  t e n s i o n and i f i n a pendent  d i s p e r s e d phase  drop  by i m p e r f e c t i o n s i n  move f r o m t h e a f f e c t e d a r e a t o w a r d s  regions.  the  of an upright  Phase  t h a t d r o p r o t a t i o n was due t o l o c a l i z e d  lowering of i n t e r f a c i a l to  i n the Continuous  that  6 1 2.  concentration  3»  nature of the l i q u i d s .  They s t u d i e d p e n d e n t  drops o f n i t r o b e n z e n e , chlorobenzene,  carbon t e t r a c h l o r i d e ,  and c h l o r o f o r m c o n t a i n i n g , a s s o l u t e s ,  acetone, e t h y l a l c o h o l , hol.  of s o l u t e .  methyl  The c o n t i n u o u s phase  alcohol,  was w a t e r .  and i s o p r o p y l  The c o n c e n t r a t i o n o f  s o l u t e v a r i e d b e t w e e n 2 a n d 30 p e r c e n t . the a d d i t i o n and  of a s u r f a c e - a c t i v e agent  the d i r e c t i o n  t h e zone direction  o f r o t a t i o n depended  run 8 appeared  All  t o agree with t h e i r  the above-mentioned  as t o whether t h e i r  the v a l i d i t y  rotation  on t h e p o s i t i o n o f the drop.  The  drop d i s t o r t i o n i n  findings.  workers  gave no  indication  e x p l a n a t i o n s f o r drop r o t a t i o n apply t o  drops of any n o z z l e o r i e n t a t i o n . check  They f o u n d o u t t h a t  suppressed  of concentration gradient within o f r o t a t i o n and accompanying  alco-  of their  No a t t e m p t was made t o  r e a s o n i n g s , b u t , i f one a c c e p t s  Bakker  e t a l ' s explanation,  pected  t o c o n t i n u e i n t h e same d i r e c t i o n a s l o n g a s t h e a f -  f e c t e d a r e a , which in  then drop r o t a t i o n  has a lower  t h e same p o s i t i o n  interfacial  i n the drop.  each other and t r a n s f e r r i n g  solute  facial  schliere  remains  t o t h e s u r r o u n d i n g medium, of t h i s  affected  the r e g i o n o f drop approach p r o v i d e d the i n t e r -  tension  The  tension,  F o r two d r o p s a p p r o a c h i n g  r o t a t i o n may be d i s t u r b e d due t o t h e s h i f t a r e a towards  c a n be e x -  i s lower i n the l a t t e r  region.  I n t e r m i t t e n t n a t u r e o f t h e movements o f t h e  around  t h e d r o p s a s o b s e r v e d i n some o f t h e r u n s  6 2 (and the  p r e s u m a b l y t r i g g e r e d by d r o p r o t a t i o n ) may i n t e r f a c e a f f e c t e d by l o w e r  interfacial  imply  tension  that  d i dnot  r e m a i n i n t h e same p o s i t i o n i n t h e d r o p a t a l l t i m e s . occurrence  o f d r o p r o t a t i o n may have a d i s t u r b i n g ,  controlling, the in  e f f e c t on i n t e r f a c i a l  sort of i n t e r f a c i a l the theory  o f Smith  m i g h t be g r o s s l y  movement  pictures  travelling  still  ( 1 2 ) and G r o o t h u i s and Zuiderweg ( 1 3 )  showed t h e d i f f u s i n g s o l u t e  t h a t was  the nozzle's  shown w h e r e a s i n t h e c i n e viewing f i e l d  camera. these  believed  the  of solute  movements was  o f f e r e d by t h e o p t i c s  the s o l u t e  Linhof clearly  o f t h e Hycam  the s o l u t e  The downward p a t t e r n  c o n t i n u o u s phase  Due t o t h e l a r g e  f i l m s t h i s was n o t so o w i n g t o a  due t o t h e a b s e n c e  which prevented  orientation,  m o v i n g downwards a n d  length.  I t was i n t e r e s t i n g t o n o t e  two r u n s .  nozzle  o b t a i n e d w i t h t h e use o f t h e  camera, t h e p a t t e r n  limited  contemplated  affected.  alongside  picture area  i f not  therefore  s t r e t c h i n g and s h r i n k i n g  In r u n s 1 3 a n d 14 w i t h v e r t i c a l the  and  The  behaviour i n  of flow of solute  of appreciable  mixing  from d i s p e r s i n g  was  forces  efficiently in  thereby c r e a t i n g l o c a l i z e d high  solute  c o n c e n t r a t i on.  C.  S u s p e n s i o n o f Drops a t Ends o f N o z z l e s .  Coalescence industry,  involves  of l i q u i d  drops i n free  drop p a i r s as encountered i n travel.  In t h i s s i t u a t i o n ,  6 3 d r o p s c a n come i n t o c o n t a c t a t a n y c o n c e i v a b l e a n g l e w h i l e travelling  a l o n g t h e column..  is difficult  the  s u s p e n s i o n o f d r o p s a t t h e ends o f n o z z l e s p e r h a p s  involved.  of studying  and to d u p l i c a t e  i n free  vel  r e a s o n a b l e way  to control  S i n c e drop c o n t a c t  c o a l e s c e n c e under  H o r i z o n t a l and v e r t i c a l  used t o simulate s i d e - t o - s i d e  tra-  i n experiments, is a  the c i r c u m s t a n c e s  n o z z l e o r i e n t a t i o n s were  and t o p - t o - b o t t o m c o n t a c t s r e s -  pectively.  I n t h i s work, t h e f o r c e s a c t i n g upon l i q u i d in free tal  t r a v e l were n o t e n t i r e l y  procedure  Frictional  force  i s absent  i n d u c e movement i n t h e i n t e r f a c e circulation.  nozzles,  i n t e r f a c i a l movement may  c a s e due t o l o c a l l y causes d i f f e r e n t  For drops  altered  occur during free  travel,  lances  the  respect  drop  but i n t h i s  tension  or other oscillation  but i s induced i n a d r o p s , where t h e  different oscillations  (once a g a i n ) f r o m  ( 3 5 ,3 6 ) .  n a t u r e of o s c i l l a t i o n and d r o p  two c a s e s  lation  tension  Drag  a t t h e ends o f  occur also,  n o t from drag, b u t r a t h e r  i n interfacial  damental  suspended  Furthermore, drop  way f r o m what i t i s f o r p e n d e n t may a r i s e ,  falling  and r e s u l t a n t  interfacial  from drag.  or  i n t h e p r e s e n t work.  internal  may  experimen-  ( s u s p e n s i o n o f drops a t the ends o f n o z z l e s ) .  d r a g , f o r example, a c t s on r i s i n g  drops and t h i s may  d u p l i c a t e d , i n the  drops  This d i f f e r i n g  fun-  s u r f a c e movement i n  ( s u s p e n d e d a n d f r e e d r o p s ) may  a n d s u r f a c e movement h a v i n g d i f f e r i n g t o c o a l e s c e n c e i n t h e two c a s e s .  imba-  result  in oscil-  importances with  64 D.  Forces Influencing  Interfacial  In t h e i n v e s t i g a t i o n changes  i n refractive  schlieren©  of ternary l i q u i d  systems,  i n d e x c a n be c a u s e d by c h a n g e s  c e n t r a t i o n or i n temperature by  Activity  which,  No h e a t - r e l e a s i n g  i n con- .  i n turn, are v i s u a l i z e d  chemical reaction  is in-  volved  i n t h e p r e s e n t work a n d i n t e r f a c i a l  activity  is ini-  tiated  s i m p l y by f o r c e s o f h e a t a n d / o r mass transfer©  (Heat  f o r c e s a r e , o f c o u r s e , t h o s e due t o h e a t o f s o l u t i o n . ) interpret which  the s c h l i e r e n r e s u l t  i t i s necessary to determine  o f t h e s e two p r o c e s s e s i s o p e r a t i v e  tem u n d e r  consideration  distinguishable  since  i n the t e r n a r y  schlieren.  ficult  t o separate the heat e f f e c t  effect  as heat of s o l u t i o n d u r i n g e x t r a c t i o n  vorced  f r o m mass t r a n s f e r b e c a u s e  solutions tice,  only.  both temperature  f r o m t h e mass  transfer  c a n n o t be d i -  one c a u s e s t h e o t h e r u n l e s s ,  s y s t e m t h a t was u s e d c o n s i s t e d  tension  could,  In p r a c -  a n d c o m p o s i t i o n f o r a n y mass t r a n s f e r  dampened, o r a r r e s t e d ,  depending  of i d e a l  t h e r e f o r e , be a f f e c t e d by  cess and, consequently, i n t e r f a c i a l  two  It i s dif-  (The s y s t e m u s e d was n o t i d e a l . )  interfacial  sys-  h e a t a n d mass t r a n s f e r a r e i n -  from each o t h e r under  of c o u r s e , the t e r n a r y  To  pro-  a c t i v i t y may be p r o m o t e d ,  on t h e manner i n w h i c h t h e  e f f e c t s are put together.  In t h e p r e s e n t work, i t was f o u n d t h a t of the t e r n a r y acetic acid  the i n t e r f a c e  s y s t e m was l e s s d i s t u r b e d when t h e d i r e c t i o n o f  t r a n s f e r was f r o m t h e a q u e o u s t o the d i s p e r s e d  65 MIBK p h a s e t h a n when s o l u t e difference the f a c t  i n interfacial  t r a n s f e r was r e v e r s e d .  This  a c t i v i t y was e v i d e n t l n y s p i t e o f  that f o rboth d i r e c t i o n s  of transfer,  e f f e c t s a r e o f t h e same m a g n i t u d e .  the heat  In a d d i t i o n ,  the heat  e f f e c t s accompanying the m i x i n g o f a c e t i c a c i d w i t h were c a l c u l a t e d temperature acid  (Appendix  increase  J ) and found  o f about  t o a c o n t i n u o u s water  t o produce  a maximum  0.14°C f o r t r a n s f e r  of a c e t i c  p h a s e f r o m a n MIBK d r o p where  t h e c o n c e n t r a t i o n was 56.45 x 10~^ l b . m o l e s / c u . T h i s temperature various  effect  other ternary  activity  systems  t o be s e n s i t i v e  index gradient r e s u l t i n g this  considerations,  a l o n e does n o t cause  f t . soln.  i s s m a l l compared w i t h t h a t o f which  do n o t e x h i b i t  and, b e s i d e s , the s c h l i e r e n  not b e l i e v e d  water  system  interfacial  p r e s e n t l y used i s  enough t o d e t e c t t h e r e f r a c t i v e  from  such a t e m p e r a t u r e  i t i s concluded that heat  rise.  Prom  of mixing  i n t e r f a c i a l a c t i v i t y and i s n o t b e l i e v e d  t o be t h e c o n t r o l l i n g f a c t o r c o n c e n t r a t i o n l e v e l s used.  i n t h e phenomena, a t the s o l u t e Comparison  o f heat  effects  a c c o m p a n y i n g t h e m i x i n g o f t h e two s o l v e n t s , MIBK a n d w a t e r , and  those f o r a c e t i c a c i d  result  i n similar  c o n c l u s i o n s t o those mentioned  as o f t h i s w r i t i n g , literature latter  i n water/MIBK would p r o b a b l y  no s u f f i c i e n t  t o make a n y h e a t e f f e c t  systems.  d a t a were f o u n d comparisons  above b u t , i n the  f o r these  66 Eo  Minimum A t t a i n a b l e Depth of F i e l d  The depth of f i e l d  of the c o n v e n t i o n a l  schlieren  system b e i n g used, which has f i x e d f o c a l l e n g t h m i r r o r s , i s a f u n c t i o n of the s i z e of the l i g h t  source  i n F i g . 8, the l i g h t r a y s p a s s i n g through  (39)»  As shown  the t e s t s e c t i o n  are not p e r f e c t l y p a r a l l e l owing to the f i n i t e l i g h t  source  and because the divergence a n g l e , a, i s r e l a t e d to the source h e i g h t , h, and f o c a l l e n g t h , f , by the  equation  a = h f  One  (4)  can see t h a t only when the angle, a, i s inc.  creased i s i t p o s s i b l e to i n c r e a s e the angle a t P by reduce the depth of f i e l d .  and  1  there-  Since the divergence angle,  i s constant a l o n g the l e n g t h bounded by L1L2,  the  a,  present  setup i s c h a r a c t e r i z e d by a s i n g l e value of the depth of field.  T h i s was  measured to be approximately  2-in.  There-  f o r e , a c o n s i d e r a b l e r e g i o n of d i s t u r b a n c e s on e i t h e r side of the o b j e c t plane and t h e o r e t i c a l l y encompassing the e n t i r e column width w i l l appear i n sharp focus a t the image or f i l m plane, making i t d i f f i c u l t to d i s t i n g u i s h the planes i n the column where the v a r i o u s d e n s i t y g r a d i e n t s occur. l a p s c o u l d account  These  f o r the over-abundance of s c h l i e r e seen i n  the f i l m s and c o n f u s i o n , due  to s u p e r i m p o s i t i o n of images, as  to whether the d e s i r e d r e g i o n to be v i s u a l i z e d i s being served a t a l l .  over-  Depth of f i e l d can be reduced  the use of m u l t i p l e k n i f e edges  (40).  ob~  c o n s i d e r a b l y by  67 CONCLUSIONS AND RECOMMENDATIONS  S c h l i e r e movements near the drop i n t e r f a c e were observed i n some runs.  These movements were those of the  continuous phase f l u i d  h i g h l y concentrated with r e s p e c t t o  a c e t i c a c i d solute*  For r u n 8, t h i s behaviour was b e l i e v e d  to be c h a r a c t e r i s t i c of drop rotation.. a f f e c t e d runs, i t was d i f f i c u l t movements, l e t alone determine t r i g g e r e d by motion  In the r e s t of the  t o p i n p o i n t what caused  whether these movements were  i n the i n t e r f a c e i t s e l f ,  due t o mixing or other p r o c e s s e s a t t r i b u t a b l e  or were p u r e l y to d i f f u s i o n .  However, the i n t e r f a c i a l d i s t u r b a n c e p r e d i c t e d by Smith and Groothuis and Zuiderweg s t r e t c h i n g and s h r i n k i n g  such  (12)  (13) i n the form of i n t e r f a c i a l  (Marangoni  e f f e c t ) , and accompanying  streaming of the continuous phase, were not observed i n any of  the runs examined.  I t i s suggested t h a t u s i n g a d i f f e r e n t t e r n a r y s y s tem that would produce  s t r o n g e r i n t e r f a c i a l movements, and  a l s o t h e i r conjugate, more pronounced sweeping of the a d j a cent continuous phase, might provide the necessary answer. However, a search f o r such a system was not made i n t h i s work. In a d d i t i o n , i t i s suggested t h a t the s c h l i e r e n depth of f i e l d be reduced  (40) f o r b e t t e r i n t e r p r e t a t i o n of the coalescence  mechanism.* However, the equipment needed i s e x t e n s i v e (40) and w i l l  r e q u i r e c o n s i d e r a b l e time and e f f o r t to assemble.  It i s f e l t  that study should be focussed. a l s o on a more imme-  68 diate  problem  time p r i o r  o f u n d e r s t a n d i n g how  to coalescence.  photography would would of  be u s e d .  The  c r i b e s work a l o n g t h e l i n e s  shape  changes  with  In s u c h work, o r d i n a r y p i c t o r i a l Measurements o f d r o p  show any d r o p d i s t o r t i o n  i n t e r f a c i a l tension.  drop  resulting  second p a r t of t h i s l a s t  dimensions  from l o c a l l o w e r i n g of t h i s  thesis  proposal.  des-  6 9  PART I I  DROP SHAPE STUDIES  7 0  PART I I  A.  STUDIES  Scope  Work was pattern of  DROP SHAPE  initiated  of the drops as they  t o study the g e n e r a l  shape  c o a l e s c e d under the i n f l u e n c e  mass t r a n s f e r o  High-speed, rial  photography  t e c h n i q u e s were u s e d ,  r a t i o n "being s i m i l a r  u t i l i z i n g ordinary picto-  e x t r a c t i o n procedures  t o those  i n the previous  and  prepa-  schlieren  work .  B.  Some P h o t o g r a p h i c  Liquid tively  d r o p s w i t h i n a l i q u i d medium  weak i n p i c t u r e  refractive simple  Considerations  indices..  solution  a r e compara-  c o n t r a s t due t o s m a l l d i f f e r e n c e s i n  The u s e o f d y e s a p p a r e n t l y p r o v i d e s a  t o the problem  of producing high c o n t r a s t  but u n f o r t u n a t e l y i t i s always d o u b t f u l whether are not surface a c t i v e . is  A reasonable a l t e r n a t i v e  the proper use of l i g h t i n g  able picture Amberkar bubble useful.  contrast.  effects  dyes  to dyes  t o a c h i e v e an a c c e p t -  K i n t n e r , Horton,  Graumann, a n d  (41) p r e s e n t e d v a r i o u s p h o t o g r a p h i c  and drop  such  i n v e s t i g a t i o n t h a t were f o u n d  techniques i n t o be v e r y  7 1 A d i f f u s e r was u s e d f o r most o f t h e r u n s , t o p r o vide uniform i l l u m i n a t i o n .  This consisted  of e i t h e r a  single  s h e e t o f t r a c i n g p a p e r o r a g r o u n d g l a s s , w h i c h e v e r was more suitable of the  f o r the p a r t i c u l a r  problem.  To m i n i m i z e  t h e image c a u s e d b y shadows a n d r e f l e c t i o n s test  section,  with the l i g h t  t h e camera l e n s  source.  distortion  occurring i n  s h o u l d be p r o p e r l y  aligned  S l i g h t m o d i f i c a t i o n s were made  from  time t o t i m e , t o o b t a i n the b e s t r e s u l t s f o r a s p e c i f i c a p lication.  Because employed,  c o n v e n t i o n a l p h o t o g r a p h i c m e t h o d s were  the use o f an exposure meter  to obtain  the c o r r e c t  e x p o s u r e was w e l l - a d a p t e d f o r most s i t u a t i o n s u s i n g light  f o rbacklighting.  light  s o u r c e was u s e d  light  d i s t r i b u t i o n p r e s e n t gave  and  ( a s one done on o c c a s i o n ) ,  and e r r o r .  I n some c a s e s , t h e f i l m  the poor l i g h t i n g  t h e uneven  exposure  readings,  speed was t o o s l o w  conditions available,  good e x p o s u r e was s t i l l due  incorrect  naked  i t was f o u n d c o n v e n i e n t t o d e t e r m i n e p r o p e r e x p o s u r e b y  trial for  On t h e o t h e r hand, when a  diffused  but, fortunately,  o b t a i n e d f o r b l a c k and w h i t e  t o t h e i r wide l a t i t u d e s  films  of exposure.  Except f o r those of r u n 1 5 , p r o c e s s i n g and p r i n t i n g of  a l l t h e f i l m s were done i n t h e d e p a r t m e n t ' s  mostly  Ilford  developers, ing  papers.  chemicals, p a r t i c u l a r l y  the I D - 1 1  d a r k room  using  and I D - 2 0  I F - 1 3 a n d I F - 1 5 h a r d e n e r - f i x e r s , a n d Kodak S t a n d a r d p h o t o f i n i s h i n g p r o c e d u r e s were  print-  followed  72 a n d n e e d n o t be m e n t i o n e d  here.  t i m e s i n f i l m p r o c e s s i n g was f i l m m a t e r i a l and. t r e a t i n g i n the d e v e l o p i n g was  obtained.  C.  Preliminary  done by c u t t i n g  solution until  and t r a n s m i s s i o n  MIBK-Acetic Acid-Water  The t e s t  ( r u n 15)  was  ponent  t o the e f f e c t s of l i g h t ,  film  column  In the a c t u a l  involved  have  f r o m one  chemical  40 mm.  used p r e v i o u s l y  irradiation.  x 40 in all  s o u r c e was  the u s u a l  mm. the  e x p e r i m e n t a l work, t h i s r u n w h i c h was  previously  Hence t h e r e was  des-  sheet  com-  no c o n t a m i from  t o a n o t h e r , a p r o c e d u r e which f o l l o w e d r u n 12.  g l a s s n o z z l e s were o r i e n t e d , h o r i z o n t a l l y a single  These  of refraction,,  and f i l m  the u s u a l  been n e c e s s a r y h a d r u n 15  d i f f u s e r was  involved  images.  n a t i o n p r o b l e m o f t h e s o r t w h i c h c o u l d have a r i s e n  would  density  t h e use o f t o l u e n e a s a m a i n  of the d i s p e r s e d phase.  switching  times  System  done b e f o r e r u n 12,  c r i b e d and which  the a p p r o p r i a t e  of non-schlieren  s e c t i o n was  square g l a s s e x t r a c t i o n s c h l i e r e n runs.  immersion  and p h o t o g r a p h i c problems  d i f f i c u l t i e s are a t t r i b u t a b l e  1)  of the  Considerations  the p r o p e r i n t e r p r e t a t i o n  reflection,  development  strips  them f o r d i f f e r e n t  There a r e o p t i c a l in  Determination of  i n r u n 15  of t r a c i n g paper.  The  The  and t h e light  PEK h i g h - p r e s s u r e m e r c u r y a r c lamp u s e d  73 in  the p r e v i o u s s c h l i e r e n r u n s .  constructed  to contain  A c a r d b o a r d box  the d i f f u s e r and  s e c t i o n from a l l extraneous l i g h t directly  upon t h e f i e l d  lamp.  E i g . 20  Run  was  15  with Tri-X f i l m .  of i n t e r e s t  The  r u n was  (attached it  was  c a n be  16.0  a c h i e v e d by  f/l.9. that  spotmeter,  when d i r e c t e d  barrel,  A  2359,  widest  due  was  effective  o n l y a b o u t f/3-5  lens although  confirmed  t o the The  read a l i g h t - l e v e l  inherent  Pentax number o f  spot i n the  e x t e n s i o n t u b e added  c o l o u r temperature However:*-, i t was  hoping that  would  The  slower f i l m  of l i g h t  object.  t o the  lens  that to a  the f i l m i s  d e c i d e d t o r u n t h e camera a t o f t h e b l a c k and  stop i n underexposure.  procedure to a r r i v e  i s described f u l l y  Light".  s p e e d due  a t which  t h e wide l a t i t u d e  t a k e c a r e o f one  2600 p p s  Diffused  i n a drop  T h i s v a l u e does n o t a l l o w f o r an a l l o w a n c e  being used.  of  f r o m t h e MIBK  Dim. C o s m i c a r  was  pps  t h e camera s p e e d c o r r e s p o n d e d t o a v a l u e o f a b o u t  different  seconds.  t h e 75  towards an a p p r o p r i a t e mm.  5000  Hycam r e p r e s e n t a t i v e  must be g i v e n t o a c c o u n t f o r a  film  MIBK-Acetic  o f t h e Hycam c a m e r a .  Ch. E .  a n d w i t h a 45  2600 p p s .  5000 pps  The  the l i m i t a t i o n  characteristics  A t f/3.5  concentration  t o t h e Hycam c a m e r a ) was  t h i s and e x p l a i n e d  1°/21°  falls  comes f r o m t h e a r c  photographed a t  l b . moles/cu. f t . soln.  r a t e d up t o  optical  and  T r a n s f e r o f a c e t i c acid, was  d r o p s t o w a t e r , where t h e a c i d  that  test  shows t h e e x p e r i m e n t a l p h o t o g r a p h i c s e t - u p .  system.  53.52 x 10""^  the  except t h a t which  t h e o n l y e x p e r i m e n t made w i t h t h e  Acid-Water  aperture  shield  was  white  CD was  5  a t t h e camera s p e e d v a l u e  under  the heading,  "Procedure,  74  -o-  MERCURY ARC LAMP  DIFFUSER SQUARE GLASS COLUMN DROPS HOLLOW SQUARE CYLINDRICAL BOX (BLACKENED INTERIOR)  MOVIE  Figure  20.  CAMERA  B a s i c p h o t o g r a p h i c arrangement shape s t u d i e s .  used  f o r drop  75 I t was s u s p e c t e d t h a t  the dark b l o t c h  b e t w e e n t h e two d r o p s a t t h e zone was n o t a l i q u i d p u r e l y an o p t i c a l reflection,  and t r a n s m i s s i o n .  each other with a c e t i c t h e c o n t i n u o u s phase resulting  acid-rich  drop approach water  phase  transferring  outside from  and t r a n s m i s s i o n  destination  which  film  o r even  since  arrive,  in  partly by  Thus,  light  rays are refracted  ray entering  the h i g h  case, the f i l m  the i n t e n s i t y  o f such l i g h t  of the o r i g i n a l  being scattered  of refraction,  sketch  rays i s dimi-  irradiation  light  occurs since l i g h t  ( F i g . 23) i s n a t u r a l l y  halide  may  actually  elsewhere.  falling  scattered within  p a s s e d on t h r o u g h t h e e m u l s i o n .  irradiation.  concen-  i n s i d e the  i s p a r t l y a b s o r b e d by t h e s i l v e r h a l i d e  the s i l v e r  Indices  i s r e d u c e d t o z e r o b e f o r e r e a c h i n g t h e camera  the r e s t  emulsion  turn  i n the r e f r a c t i v e  s t e p s b e f o r e i t can r e a c h i t s  i s , f o rthis  only a portion  Film film  continuous  I t i s h i g h l y probable from the s i m p l i f i e d  of F i g . 2 2 , that nished  o f t h e pure  ( F i g . 2 2 ) i s s c a t t e r e d by a s e r i e s  zone  reflection,  camera.  index of the  t h e d r o p s a t t h e zone o f  that  light  approach  from these drops t o  the r e f r a c t i v e  and water.  A single  refraction,  As t h e two MIBK d r o p s  (Fig. 21), liquid  t h e two d r o p s b u t  on b y l i g h t  owing t o a d i f f e r e n c e  that region.  tration  acid  i s different  between a c e t i c a c i d in  brought  ( F i g . 21)  o f drop approach  bridge or "waist" j o i n i n g effect  located  i t and  g r a i n s and  The l i g h t  absorbed  g r a i n s accounts f o r the e f f e c t  I t s conjugate, h a l a t i o n ,  on a  called  o c c u r s when t h e l i g h t  76  77 (MIBK) > 77 (ACETIC ACID) > D  D  ^(WATER)  FROM LIGHT S O U R C E MIBK-sat'd  Figure  22,  Simplified drops o  path of l i g h t  WATER  ray passing  PHASE  between two  77 which  passed  on t h r o u g h t h e e m u l s i o n r e a c h e s t h e f i l m  (Figo  2 3 ) a n d may  pass through  t o the e m u l s i o n t o produce effect  i s called  halation  a s the Kodak T r i - X ,  a  the base  image e f f e c t o  secondary  so t h a t h a l a t i o n o t h e r hand, can  f o r example,  i n the  case of a c o n t r a s t y  of c o a l e s c i n g dropso  t a i n e d when p a r a l l e l  light  Irradiation  its best  emulsion  still  t h i c k and grainy..  i l l u s t r a t e d , i n F i g . 24a  for illuminationo  This  (cuprous  s u l f i d e - c o a t e d ) i n c o n t a c t w i t h each  Uncoated  spheres a l s o  Details  on e x p e r i m e n t s  2)  Steel  Bearing  showed t h e same r e s u l t  a darkening e f f e c t  from each  and  impression i s spheres o t h e r i n air©  as  i n Figo  24bo  spheres a r e g i v e n below,  Experiments  In o r d e r t o determine  dertaken wherein  "waist"  i s overexposed  taken u s i n g s o l i d  dealing with  a  i s ob-  impression of a  d r o p s , p r o v i d e d the f i l m  i s rather  such as  silhouette  r a y s are used  an  nil.,  encountered,  subject  Such a  can produce  be  such  light-  is practically  on t h e  back  This  However, most modern f i l m s  0  Irradiation,  between t h e two  reflected  come w i t h a b a c k i n g made o f a  absorbing material  silhouette  o r be  base  whether r e f r a c t i o n  produces  between the d r o p s , an e x p e r i m e n t  two  was  un-  s p h e r e s were h e l d a t c o n v e n i e n t d i s t a n c e s  o t h e r w i t h a i r between.  By  t h i s procedure,  density  g r a d i e n t s c o n c e n t r a t e d i n the c r i t i c a l  zone b e t w e e n t h e  spheres a r e e l i m i n a t e d and  effects  the a d v e r s e  of  refraction  RAYS OF LIGHT FROM SMALL BRIGHT OBJECT  Figure  23„  Effect  of i r r a d i a t i o n  and h a l a t i o n on u n b a c k e d f i l m  (43).  79  F i g u r e 24.  E f f e c t of i r r a d i a t i o n as shown i n photographs of b a l l bearings i n c o n t a c t with each o t h e r .  80 c a n be  ignored.  substance of  was  used  c o u r s e , was  The  To d e c r e a s e  reflection, a  t o coat the  spheres.  light-absorbing  Light transmission,  absent.  s p h e r e s were  steel ball  bearings, 5 / 3 2 - i n .  diameter  and a c c u r a t e t o w i t h i n  ximately  t h e c u r v a t u r e o f t h e p a r t s o f the d r o p s  run 1 5 »  These b e a r i n g s were mounted on a p a i r  V-blocks held The  together at both  0 . 0 0 1 - i n .  ends by  b l o c k s were c o v e r e d w i t h p a p e r  to produce  a non-reflecting  These had  surface.  Perspex  rubber bands  The  (Fig.2 5 ) °  felt  pen  b l o c k s were  ink  de-  to enable  between the b a l l s  t o measure t h e i r d i s t a n c e o f s e p a r a t i o n .  of cuprous  bearings. fate  The  solution.  cleaned b a l l s  steel  copper  ball  the f r e e  sulfide  coating  and  found  of t h i s  t o be  were f i r s t  was  passed  Cu  from  w h i c h d e p o s i t e d on t h e  R e a c t i o n with hydrogen The  applied  to the dipped  sulfide  sulfide  reasonably  steel  ball  i n copper  placed in a  iron  the  (coming  sulfate  test iron  from  the  solution  b l a c k cuprous  examined under a  sul-  Since  s u r f a c e of the  produced  was  slipped  o v e r them.  i n the a c t i v i t y s e r i e s ,  bearing) reduced  metal  was  They were t h e n removed and  tube where h y d r o g e n i s above  sulfide  gauge t o be  in  signed with s l o t s  A coating  a feeler  appro-  studied  of  b l a c k e n e d by  in  to  balls. sulfide.  microscope  even.  P i c t u r e s were t a k e n f o r two  different  ditions.  Parallel light  r a y s were u s e d  and,  lighting,  t h e l a t t e r f o r most o f t h e work and  lighting  also, the  con-  diffused former  only  Figure  25.  V - b l o c k mount f o r s t e e l b e a r i n g e x p e r i m e n t s .  82 f o r purposes  of comparison.  The  photographic  c o n d i t i o n s i s shown i n F i g o  lighting  26.  b a l l s a t d i s t a n c e s o f s e p a r a t i o n o f 0, 0o0025 i n s . were t a k e n , b o t h A  75  mm.  e x t e n s i o n tube was  cuprous  Pictures  0.0015,  sulfide  of  Alignment optical  axis  of the  tube  tube,  attachment  was  obvious  t h a t any  separations,  p a s s p e r p e n d i c u l a r t o the  done by m a k i n g  thermore, rays are  these requirements collimated,  have p a s s e d  inclination  the  correct  posed. (Table I I ) .  false 24a  picture 24b).  to cover part of a  ball Fur-  when the the  bundle  exposure.  of a The  At f i r s t  a few  were f o u n d  t o be  Samples o f t h e s e p i c t u r e s  of i r r a d i a t i o n ,  and  It i s  light  normal  that  should  e x p e r i m e n t a t i o n were i n v o l v e d i n  were made w i t h T r i - X R e v e r s a l b u t  effect  common  ( F i g . 27)°  from  of the l i g h t  the  through.  Some g u e s s w o r k a n d determining  blocking  apply e s p e c i a l l y  s i n c e any  angle would cut o f f a p o r t i o n  spheres.  e s p e c i a l l y at small  to l i g h t  which  also.  system  could result  of  t o o b t a i n the  system  misalignment,  bare.  lens  o f the  a x i s o f t h e b a l l s midway b e t w e e n t h e two  and  c o a t e d and  same m a g n i f i c a t i o n a s most o f t h e r u n s b e i n g s t u d i e d were f i l m e d u s i n g a 75 mm.  steel  0.002,  a t t a c h e d t o the Cosmicar  o f t h e 45 mm.  t h e Hycam camera i n s t e a d  set-up f o r both  due  to overexposure,  " w a i s t " between the lighted  o f the b a l l  "waist" at that  areas  silhouette  s p o t where  and  the b a l l s  overex-  show how  the  can produce  steel  i n both  pictures  balls  a  (Figs.  figures increased left  the  impression  touched  ( F i g . 28).  83  NOTE : 1. MAKE F=f (FOCAL LENGTH OF SCHLIEREN MIRROR) TO OBTAIN PARALLEL LIGHT (AS SHOWN BELOW). 2. INSERT DIFFUSER IN FRONT OF V-BLOCK FACING MIRROR TO OBTAIN DIFFUSED LIGHT AND MAKE F > f TO CONVERGE LIGHT SHOULD INCREASED LIGHT INTENSITY BE DESIRED.  LIGHT SOURCE  SCHLIEREN MIRROR  Figure  26.  P h o t o g r a p h i c arrangement for. s t e e l b e a r i n g e x p e r i m e n t s and d r o p shape s t u d i e s .  84  COMMON AXIS  F i g u r e 27.  B l o c k i n g of a l i g h t ray due t o b a l l misalignment.  PROPERLY EXPOSED BALL OUTLINE  F i g u r e 28.  OVEREXPOSED BALL OUTLINE  Impression of " w a i s t " between two s o l i d spheres due to i r r a d i a t i o n caused by overexposure.  Table  Steal Lighting Bearing Condition Dia.,In. Coating  5_  Dlatanoa Separation, In.  Data  L e l t z Light Film L i g h t Source (USASI No.. Meter Current d a y l i g h t ) Rdg. Bdg.,amp.  P.ln.  Camera Frame Speed, Camera pps  CuO  0, 0.0015, Trl-X 0.002, 0.003, Rev. (200) 0.006  16.7  4.0  48  Hyoam  10  CuS  0, 0.0015, Fine-Grain 0.002, 0.0025 Dupl. Pos.  17.3  5.0  48  Hyoam  25  0, 0.0015, 0.002. 0.003  Trl-X Bev. (200)  16.8  4.0  48  Hyoam  10  0, 0.0015, Fine-Grain 0.002, 0.0025 Dupl. Pos.  17.3  5.0  48  Hyoam  25  CUS  0, 0.0015  Fine-Grain Dupl. Pos.  18.5  3.7  52  None  0, 0.0015  Fine-Grain Dupl. Pos.  18.5  3.7  52  32  None  32  I I . B a l l Bearing Ezparlmantal  Refer t o Plg.Zft. **Thls ooatlng w a s ' f i r s t used p r i o r t o switching to the b e t t e r CuS c o a t i n g .  Timing E x t . Light Tube Freq., Length, Film plp/seo. mm. Eiposure  10  Lens Aperture  75  overexposed  f/16  75  oorreot  r/3-5  75  overexposed  f/11  75  oorreot  f/3.5  Hyoam  75  oorreot  f/3.5  Hycam  75  correct  f/3.5  10  86 A film the  of  slower emulsion  Kodak F i n e  Grain  duplicating film  w h i c h has  fine  this film  detail,  separated  by  The  any  "waist" of the  2 9 a and i n run index  of  gradient,  MIBK t o  by  w o u l d be  solute the  the  show no  main r e a s o n ability  to  be  for  record  steel  balls  with  Photographic  this data  appreciable  this  to the  selecting a  steel  r e s u l t s are  "waist"  due  two  evidence balls  for  s t u d i e d r e g a r d l e s s of  Some o f the  eliminated  From t h e find a  The  satisfactory.  image d i s t o r t i o n  S e l e c t i o n of a  high r e s o l u t i o n .  P i c t u r e s obtained  separation  Therefore,  and  very  e s s e n t i a l i n p i c t u r e s of  1 5 c o u l d l a r g e l y be  its effect  i t has  obtained  obtained.  gradient  was  i t i s b e l i e v e d to  o r d a r k b l o t c h between t h e  w o u l d a l s o be  3)  that  very  results  2 9 b .  This  II.  distances  perspective  this  t o be  g r a i n and  g i v e n but  a mere 0 . 0 0 1 5 i n .  shown i n T a b l e  of a  fine  (daylight).  was  w h i c h was  f i l m were f o u n d are  not  USASI 5 0 o r l e s s  employing  then t r i e d .  D u p l i c a t i n g Positive,, a b l u e - s e n s i t i v e  I t s e m u l s i o n s p e e d was around  speed, was  given  in Figs.  or dark b l o t c h  observed  presence  of a  s u i t a b l e solute to  due  to t h i s  or, a t l e a s t ,  the  optical  reduced  refractive eliminate effect  to a point  that  negligible.  Suitable  Solute  foregoing results,  i t was  desirable  such t h a t , upon i t s t r a n s f e r from the  continuous  p r e v i o u s l y used, the  water phases a t  refractive  index  the  to  dispersed  concentrations  gradient  obtained  in  (a) .  Figure  2 9 .  Diffused light  CuS-coated b a l l b e a r i n g s a t a d i s t a n c e  (b).  Parallel  of s e p a r a t i o n  light  of 0 . 0 0 1 5 i n .  88 the a r e a o f drop approach neglected.  To  satisfy  w o u l d be  the above c r i t e r i o n ,  be n e e d e d w i t h a r e f r a c t i v e to  that  M e t h y l a l c o h o l was  requirement.  The methyl  III,  i t had  the added  over the  advantages  i f one  p l o t s %w  It i s obvious  from  7^  s o l u t i o n w i t h methanol c o n c e n t r a t i o n as  the r e s u l t i n g  c u r v e w i l l have a v e r y s m a l l s l o p e  c o n c e n t r a t i o n range  Furthermore,  25°C  these  c o n c e n t r a t i o n of methanol v s .  o f 0.0  the t h i r d  t o 2l.?$w.  The  i s , therefore, component e f f e c t  i s 1.33232.  the r e f r a c t i v e That  i n d e x of methyl  of MIBK-saturated  refractive  practically  t o s a t u r a t e t h e c o n t i n u o u s w a t e r phase i n the  work.  (the  this  a l c o h o l / w a t e r s o l u t i o n s a t 25°C i s shown i n T a b l e  negligible, neglecting  at  to  index-concentration relationship,  index g r a d i e n t w i t h i n t h i s range,  used  continuous  available.  refractive  methanol/water  abscissa,  would  or n e a r l y so,  t o come c l o s e  o b t a i n e d f r o m r e f e r e n c e 42.  data that of  found  Furthermore,  being readily  for  index i d e n t i c a l  be  a solute  of MIBK-sat'd water which s e r v e d as the  phase.  of  s m a l l enough t o  o f t h e MIBK actual alcohol  water a t  25°C  c o n t i n u o u s p h a s e ) i s 1.3346 by Abbe r e f r a c t o m e t e r  measurement.  These r e f r a c t i v e  t o g e t h e r than i s the r e f r a c t i v e same t e m p e r a t u r e  (1.3715)•  i n d i c e s a r e much  closer  index of a c e t i c a c i d a t  the  8 9  Table  III.  R e f r a c t i v e Index - C o n c e n t r a t i o n o f M e t h y l A l c o h o l a t 2 5 ° C (Bef. r Methanol  7? ° 25  %  OoO  1 . 3 3 2 3 2  21o7  1 . 3 3 8 2 3  3 7 . 6 6  1 . 3 4 0 9 0  5 2 o 2 2  1 . 3 4 1 6 3  5 ^ 2 3  1 . 3 4 1 6 3  6 4 . 3 5  1 . 3 4 0 6 5  6 8 o 2 0  1 . 3 3 9 8 4  8 0 . 4 4  1 . 3 3 6 6 3  8 6 . 2 7  1 o 3 3 5 0 5  9 2 . 4 8  1 o 3 3 1 9 3  1 0 0 . 0 0  1 0 2 7 7 3  2 5 Max.  7\p  =  1 . 3 4 1 7 0  a t $w M e t h a n o l  =  5 3 ^  Data 4 2 )  9 0 EXPERIMENTAL PROCEDURE  A.  MIBK-Methanol-Water  The  e x t r a c t i o n procedures  of the  previous  to the  difficulty  solute  i s used,  new  nylon  System  were i d e n t i c a l  runs u s i n g a c e t i c a c i d  as  the  tubing.  As  i n the  toluene  was  runs,  those  solute<>  of p r e v e n t i n g contamination  the d i s p e r s e d phase l i n e  to  when a  Due new  replaced  with  a levelling  bulb  once a g a i n r e p l a c e d the  QVF  tank i n the p r e v i o u s  involving acetic  The  d i s p e r s e d phase p i p i n g s y s t e m  sufficiently  acido  vapour t i g h t .  r e p l a c e d w i t h new prevent square ving  light  The  0  t o produce  t h a t used  i n the  steel  similarly aligned.  1 )  Collimated Light  Run diffuser.  o f the  contents  o r towards the  This  parallel, set-up  bearing experiments  1 6 was  performed u s i n g p a r a l l e l  Methyl  a l c o h o l was  MIBK p h a s e where the a c i d c u . f t . s o l n . t o the  to the mo-  light  or d i v e r g i n g  was  the  same  in Fig. 2 6  and  light  with  rays  t r a n s f e r r e d from the  c o n c e n t r a t i o n was  continuous  of  was  was  arrangement u t i l i z e d  converging,  r a y s w h i c h e v e r were n e e d e d .  was  no  lighting  s c h l i e r e n m i r r o r away f r o m  i n order  line  same m a t e r i a l i n o r d e r  p o s s i b l e contamination  g l a s s column  the  source  as  any  experiments  P a r t of the d i s c h a r g e  t u b i n g of the  •  dispersed  0 . 0 0 3 9 l b . moles/  water phase, b o t h  phases,  of  9 1 c o u r s e , b e i n g m u t u a l l y s a t u r a t e d w i t h t h e main component the  other.  A film  w i t h 7 5 mm. at  extension  t a k e n by  t h e Hycam camera a t $000 p p s  tube a t t a c h e d  an a p e r t u r e o p e n i n g of f / 3 . 5 «  resulting decided but  was  f r o m t h e use  to t r y a f i l m  s l o w e r t h a n 4X  Panchromatic  light).  An LLN  Due  slightly  parallel  reading  2 )  light  (light-level  cutting loss,  because  spotmeter  resulted  number) r e a d i n g  of 2 5 0 (day-  o f 1 6 . 8 was  when i t was  w i t h the l i g h t  t h e Kodak  placed  across  s o u r c e ammeter  4 . 0 amps.  g l a s s was  chosen over t r a c i n g paper as  the t r a c i n g  p a p e r was  by 1 LLN more t h a n t h e g r o u n d scale.  Use  g l a s s on  of the ground g l a s s  down e x p o s u r e by a b o u t film,  5 0 0 , daylight),  was  Kodak 4X used.  an a c c e p t a b l e exposure  5 stops.  failed  e x p o s u r e was  scale,  To make up f o r t h i s (USASI  several attempts to  when u s i n g  trial  t e s t s were t h e n made by t h e L i n h o f  when t h e c o r r e c t  the  diffuser  Panchromatic Negative At f i r s t ,  the  f o u n d t o c u t down t h e  i n a d e c r e a s e o f 5 LLN a s r e a d on t h e P e n t a x  a fast  Exposure  Reversal  Light  intensity  Pentax  reduction  T h i s was  N e g a t i v e w i t h a USASI No.  beam o f l i g h t  Ground diffuser  than T r i - X  Negative.  f l u c t u a t i n g between 3 « 6 a n d  Diffused  t o the l i g h t  faster  o b t a i n e d by t h e L e i t z e x p o s u r e m e t e r the  t o the Cosmicar l e n s s e t  o f t h e 7 5 nmi» e x t e n s i o n t u b e , i t was  Panchromatic  Double-X  of  and  still  No. obtain  error. camera  and  obtained, appropriate conversions  ( A p p e n d i x H) were made t o t r a n s l a t e  the  Linhof  camera  92 settings the  t o e q u i v a l e n t Hycam v a l u e s  same c o r r e c t  In to  those  lized  r u n 17  the e x t r a c t i o n  r e d u c t i o n of i l l u m i n a t i o n  d i s t a n c e was  a 6 i n . diameter slightly in. to  and  7/16  and  a t f/3'5  camera frame tube  was  and  speed  3  IV, r e p r o d u c e d convenient expressed  with  to  from "...  in focal  (column 3)°  sufficient  image and  using  of about  300  In o r d e r  converge from a  form  was  Pentax spotmeter  3,6  amps.  The  T h i s tube  when a 150  lens  c u t down the  mm.  1/2 due  read aper-  readings corresponded pps  a  minor axes of  elliptical  The  to  to a  extension  exposure  by  stops.  To a r r i v e  duction  a l l these  being used.  approximately  of  The  source,  uti-  smaller area having  shape h a v i n g m a j o r and  the mercury a r c  was  mirror-light  t o make the l i g h t  i n . respectively.  similar  light  occurred.  schlieren  c r o s s - s e c t i o n to a  elliptical  t u r e was  of  altered  the  inherent oblique aberration.  12.82  c o n d i t i o n s were  However, s i n c e d i f f u s e d  compensate f o r t h i s d e c r e a s e , source  at  exposure.  o f r u n 16.  here,  i n order to a r r i v e  a t t h e above c o n c l u s i o n , c o n s i d e r  Table  r e f e r e n c e 43.  i t is  first  find  lengths The  accuracy  original.  To use  either  by  can  visual  from  or the  extension  scale  f r e q u e n t l y be comparison  Exposure times  the a p p r o p r i a t e f a c t o r  table,  the b e l l o w s  (column 2),  latter  this  can  5»  °r  repro-  estimated  o f the  t h e n be  columns 4,  of  lengths  found 6".  by Use  columns 5 or 6 n e c e s s i t a t e s a r e f e r e n c e exposure based  on  Table IV.  (1) Object Distance  Exposure F a c t o r s f o r D i f f e r e n t S c a l e s of Reproduction  (2) Bellows Extension  (u)  (v)  CO  f  2f  (3) L i n e a r Scale of Reproduction (m = v / f - 1)  (4) Marked f-number must be M u l t i p l i e d by  (5) or Exposure Indicated f o r Object a t must be Multiplied by*  (Ref. 43)  (6)  or Exposure Indicated f o r Same-size Reproduction must be Mult i p l i e d by  (1 + m)  (1 + m )  0  x 1  x 1  l-l/8f  1/8  x 1-1/8  x 1-1/4  X  l-l/4f  1/4  x 1-1/4  x 1-1/2  X 3/8  l-l/2f  1/2  x 1-1/2  x  l-3/4f  3/4  x  1-3A  x  2f 2-l/2f  1  (Same-size)  x  2  1-1/2  x  2-1/2  3f  2  x  4f  3  x 4  5f  4  x  3 5  exposure f a c t o r s i n columns 5 and 6 are p r a c t i c a l  2  2-1/4  3  ((1  + m) /4) 2  X 1/4  X  5/16 1/2  X 3/4  x 4  X 1  x 6  X 1-1/2  9  X 2-1/4  x  x 16  X 4  25  X 6  x  approximations.  94 lens focussed at i n f i n i t y  (column 5)  l e n g t h s away ^column  S i n c e no r e l i a b l e  been by  established  t h e use  t o be use  to q u i c k l y determine  of a l i g h t m e t e r  t h e most p r a c t i c a l  o f a 150  valent IV,  6).  to use.  3f  length  a p p e a r s i n column  For the c u r r e n t  column  marked f-number must be m u l t i p l i e d goes back  following film  t o the Pentax  correspond  3°5  f o r f / n o , one  t o a frame  t e n s i o n tube  taken i n t o  ting  o f a b o u t 100 i s equivalent  consideration,  3  p p s , f o r frame  speed.  f/3°5  to  and a b o u t  i n table same  that pps.  I f one  sets  the  500  for  these v a l u e s With  a n d a new  the  ex-  f/no« corrected  T h i s exposure  300  row  the  o f 3°  the a c t u a l  f/10.5  by  o r Jf  reading,  900  giving  s h o u l d be m u l t i p l i e d value  speed of about  i s equi-  s c a l e s and  finds  the  lens  4 shows t h a t  for light  found  problem,  On t h e  by a f a c t o r  spotmeter  c o m b i n a t i o n o f 12.82  speed, and  mm.  o f the l e n s . 2,  focal  exposure  4 was  nim° e x t e n s i o n t u b e w i t h t h e 75  " f " b e i n g the f o c a l  now  the c o r r e c t  o f 225  two  method h a s y e t  i n t h i s work, c o l u m n  to a t o t a l bellows extension  i n which  or a t an o b j e c t  p p s by l a w  set-  of r e -  ciprocity.  The  frame  s p e e d o f 300  slow f o r the purpose chance  and  film  b u t i t was  the r u n a t  4500  p p s o b t a i n e d above  d e c i d e d , anyway, t o t a k e a pps.  p e c t e d t o produce an underexposure less  than the c o r r e c t  were d e v e l o p e d i n ID-11 on  t h e n e g a t i v e was  T h i s p r o c e d u r e was  ex-  corresponding to 4 stops  f/no. s e t t i n g . and,  i s too  A number o f t e s t  surprisingly,  strips  an a c c e p t a b l e image  o b t a i n e d a t a development  time  o f 8 min.  95 40 s e c .  A p p r o p r i a t e p i c t u r e s were p r i n t e d on I l f o r d No. 5  bromide paper.  I t should be noted here t h a t the n o z z l e  disappeared from the camera f i e l d  of view due to a h i g h  m a g n i f i c a t i o n obtained w i t h the use of the 150 tube.  tips  mm.  extension  The disappearance of the n o z z l e t i p s and, hence, of  the known n o z z l e diameter r e s u l t e d i n the absence of a convenient l i n e a r scale f o r use as r e f e r e n c e i n t h i s r u n .  In run 18, o n l y 75 mm.  l e n g t h of e x t e n s i o n tube  was used and the camera speed was  increased to  5000  pps.  Methyl a l c o h o l c o n c e n t r a t i o n i n the d i s p e r s e d phase  0.0020 l b . moles/cu.  was  f t . soln.  Run 19 was a g a i n s i m i l a r to run 18 except t h a t the methanol  c o n c e n t r a t i o n i n each drop i s h i g h e r (0.088 l b .  moles/cu. f t . s o l n . ) was used.  T r i - X R e v e r s a l f i l m was  used  here since 4X Panchromatic Negative f i l m was not a v a i l a b l e and i n order t o compensate somewhat f o r the slower f i l m speed, the l i g h t  source amperage was  A d d i t i o n a l d a t a on a l l  B.  Measurement of  i n c r e a s e d to 5»5  amps.  the runs are shown i n Table V.  Pseudo-Radius  To determine the shape p a t t e r n of a drop as i t c o a l e s c e s w i t h another, the changes i n shape of the drop must be measured.  T a b l e V.  Run  No.  Experimental Data f o r Part  1 5  Solute Conto Phase D i s p e r s e d Phase Direction of Transfer S o l u t e cone., 1 0 3 x lbomole/cuoft. soln. Nozzle O r i e n t a t i o n L i g h t Source Current R e a d i n g , amp. F i l m (USASI No., daylight) L i g h t Meter Reading Diffuser  i spositioned  Studies)  18  1 6  1 7  Methanol Water MIBK D—> C  Methanol Water MIBK D —> C  Methanol Water MIBK D—»C  Methanol Water MIBK D—>C  5 3 - 5 2  3 o 9 0  4 . 2 1  1 . 9 5  8 7 . 7 8  Horizontal 5 . 5 - 6.0  Horizontal  Horizontal 3.6  Horizontal 3o6  Horizontal  4  Acetic Water MIBK D—>C  Acid  -  3.6  4X PanchroT r i - X Rever- Double-X matic ( 5 0 0 ) sal ( 2 0 0 ) ( 2 5 0 ) 16.5 (Leitz) 1 6 . 8 (Leitz) 12.82 (Pentax) S i n g l e S h e e t None Ground of T r a c i n g Glass Paper 1 3_ (circle)  Size of Major Axis, i n . Light 4 Image on Minor 3_ (circle) Diffuser* Axis, i n . Hycam Camera Camera Frame Speed,pps 5 0 0 0 Lens A p e r t u r e f / 3 . 5 E x t e n s i o n Tube 4 5 L e n g t h , mm. Timing L i g h t Frequency, 1 0 0 pip/sec0 Film Magnification 0 . 9 3 Lighting Condition Diffused *Diffuser  I I (Drop Shape  1 9  5 ° 5  4X Panchro- T r i - X Revermatic ( 5 0 0 ) sal ( 2 0 0 ) 12.82 1 3 0 9 (Pentax) (Pentax) Ground Ground Glass Glass 1  1  2  2  2  h  h  h  4 5 0 0  5 0 0 0  5 0 0 0  f / 3 ° 5  f / 3 . 5  f / 3 . 5  f / 3 . 5  7 5  1 5 0  7 5 -  7 5  1 0 0  1 0 0  1 0 0  1 0 0  1 . 3 3  2 . 3 3  1 . 3 3  1 . 3 3  Parallel  Diffused  Diffused  Diffused  Hycam 5 0 0 0  a s shown i n F i g .  2 0 .  Hycam  Hycam  Hycam  97 P r e l i m i n a r y work was a n d 19.  carried  o u t on r u n s 15.  P i c t u r e s were c h o s e n f r o m t h e e n t i r e  length  i n a g i v e n r u n so t h a t a f i x e d number o f f r a m e s between each p i c t u r e the p i c t u r e s  o r frame  on t h e 16  means o f t h e f i l m darkroom  onto a  cation.  The  mm.  fixed  movie  ( p o i n t s P*  and  traced  by  P"  reference  each n o z z l e  These  of the n o z z l e  tips  The  P"  divided  sectors.  The  into  were m e a s u r e d f r o m p o i n t s each t r a c i n g .  The  plotted against  (Fig. 3 0 ) . radial P'  distances  time.  These  were  tracing from  which  corners of  i n determining  E a c h d r o p was  l i n e s bounding  drop  points  two  t i p shown i n e a c h t r a c i n g were u s e d o f P» and  magnifi-  each  f o r every  p o i n t s were l o c a t e d .  the l o c a t i o n  by  department's  inside  i n F i g . JO).  c o n s i s t e n t l y a t t h e same l o c a t i o n  two  purposes,  hand.  points located  a c c o r d i n g to the set p o s i t i o n these  For t r a c i n g  i n the  film  intervened  s h e e t o f p a p e r a t a p p r o x i m a t e l y 24X  image t h e n was  of  s t r i p were p r o j e c t e d  enlarger available  Fixed reference were c h o s e n  studied.  18,  then  the  sectors  t o P" t o t h e d r o p p e r i p h e r y f o r obtained f o r each l i n e  were  d i s t a n c e s were c a l l e d ,  "pseudo-  radii".  The r e f e r e n c e p o i n t s originating w h i c h was locate  P*  and  f r o m them were a c t u a l l y  superimposed  t h e s e two  P" and  the r a d i a l  drawn on a m a s t e r  on e a c h t r a c i n g  A master  s h e e t made o f p a p e r w i t h p o l a r  prepared  f o r each o f the l e f t  and  sheet  t o be m e a s u r e d .  p o i n t s t h e f o l l o w i n g p r o c e d u r e was  drops.  To  followed.  coordinate l i n e s  the r i g h t  lines  was  Consider  98  LEGEND 1-70° 6 2 - I00 7 3 - !30 8 ~ 4 - I45 9 5 - 155 10 11-280 Q  o  0  Figure  30„  170° 185. I95 220 250 Q o  Locations of various d i v i d i n g l i n e s p o i n t s f o r drops b e i n g measured„  and  reference  99 the  master  Point  s h e e t t o be  P" f i r s t  was  p r e p a r e d f o r the r i g h t  chosen  two  tracing,  a t the p o i n t  points,, P" and  dinate  paper  o r i g i n and P o i n t s A, nozzle  X,  o r master  of c o n t a c t  C, and  D  earlier» reference  The  location  t r a c i n g , was  o f P'  set i n position  the  origin  superimposed  so t h a t X.  P',  master  P o i n t s A,  B,  The  and l i n e  sheet as  coor-  a t the  two  additional  sheet f o r the  t h e same  first  Point  left  not  P' was  This  s h e e t was until  sheet  marked  this  line  on  paper  of the now  of  sample  master  the 1 0 ° - l i n e  X on t h e 1 0 ° - l l n e ,  was  second  adjusted,  0°,  originating  o  n  from p o i n t  These  c o r n e r s o f the  c o o r d i n a t e sheet and  passed through p o i n t  maintaining point  P" was  on  P" b u t depended on the p o s i t i o n  on the t r a c i n g .  on the f i r s t  drops.  P o i n t P' was  on the d r o p , u s i n g  o f the s e c o n d  located  c o o r d i n a t e paper©  The m a s t e r  determined as f o l l o w s .  was  first  that  on the  points.  the  t o the p o l a r  t i p s ) t h e n were marked on t h e m a s t e r  l o c a t e d a r b i t r a r i l y a s was  sheet  o f t h e two  (comprising a l l four  contained similar  P".  X a l s o was  s h e e t i n s u c h a way  a l o n g the 1 7 0 ° - l i n e  X was B,  Point  t h e n were t r a n s f e r r e d  r e f e r e n c e s as mentioned drop  drop.  30)o  (Figo  on a sample t r a c i n g a t a b o u t  c e n t r a l a r e a i n the r i g h t this  drop  180  , originating  from p o i n t  P"  one  single  lineo  C, and D t h e n were marked on t h e  second  sheet©  s h e e t , o v e r l a p p e d and  formed  T h e r e were e l e v e n r a d i a l the  right  drop,  starting  the  280°-line©  the  same number o f r a d i a l  or d i v i d i n g  from an a n g l e of 70°  Symmetry r e q u i r e d  that  l i n e s and  lines  drawn f o r  and e n d i n g a t  the l e f t  t h a t each  of the  drop a l s o  of these  be named a c c o r d i n g t o e a c h c o r r e s p o n d i n g m i r r o r  image  have  lines (Figo  30)©  100 In r e p o r t i n g the f i n a l data on runs 18 and 19, t r a c i n g s were r e p l a c e d by photographic  p r i n t s which are  r a t e r e p r o d u c t i o n s of the n e g a t i v e imageso  Likewise,  p o l a r c o o r d i n a t e paper, used as master sheet:., was be too t h i c k to c l e a r l y see through  the accu-  the  found  i t so t h a t i t was  to  replaced  by t r a c i n g paper, t r a n s f e r r i n g a l l the a p p r o p r i a t e p o i n t s and lineso  Co  The drops measured were those  Statistical  The in  of runs 18 and  19=  Tests  observed  dependence of one v a r i a b l e upon  t h i s case the pseudo-radius(Y)  upon time  (X), was  another,  initially  c o n s i d e r e d to be a s t r a i g h t - l i n e r e l a t i o n s h i p ; the equation such l i n e was l a t i o n was  obtained by the method of l e a s t  squares.  done on an IBM 7044 e l e c t r o n i c d i g i t a l  u s i n g the l i b r a r y subroutine, "UBC  LQP",  of  Calcu-  computer  f o r l e a s t squares f i t  (Appendix L)»  The l i n e a r model was of  regression©  This was  then t e s t e d f o r s i g n i f i c a n c e  done by a t - t e s t of the n u l l hypo-  t h e s i s that the true value of the slope parameter of the model, ^9/  , was  zero  (Appendix E ) .  In other words, a t - t e s t  c a r r i e d out t o examine the confidence i n t e r v a l b i l i t y l e v e l used) i n order to see lies  to  i f the value of  i n the I n t e r v a l t h a t i n c l u d e s z e r o .  hypothesis, H  0  :j9/=  (at the  was probaor slope  I f so, then the n u l l  0, c o u l d not be r e j e c t e d and  i t suffices  say that the r e s u l t c o u l d be accepted but only on the b a s i s  1 0 1  of the observed d a t a of data evidence thesis  and  evidence  of unexplained v a r i a t i o n h y p o t h e s i s was  or zero,  of the r e s i d u a l s .  a g a i n s t t i m e and  any  The  residual,  time  from  found  used  f o r a n IBM  7 0 4 4  program uses  T h i s p r o g r a m was  the backward e l i m i n a t i o n  e l i m i n a t e d one  exponent a t a m  ordinate,  was  the i m p r e s s i o n of analyzed  t o be  inadequate, the  "best"  p o l y n o m i a l models  i n FortranlV  Data P r o c e s s i n g System.  regression equation of a predetermined  is  as  an  w r i t t e n by Kozak and  of Forestry  (where m i s s e t a t a v a l u e o f 4 )  regression  to s e l e c t  r e g r e s s i o n e q u a t i o n among t h e d i f f e r e n t  o f t h e U.B.C. F a c u l t y  i n the  s e q u e n c e p l o t method ( 4 4 ) .  r e g r e s s i o n p r o g r a m was  t h a t were u s e d .  by  rejected  done by  ( F i g . 3 1 ) was  Where t h e l i n e a r m o d e l was  (45)  either  T h i s was  deviation  "band" o f r e s i d u a l s  a c c o r d i n g to the g r a p h i c a l  a multiple  hypo-  determined  i . e . , where t h e s l o p e s o f t h e  l i n e s were e i t h e r n o n - z e r o  a horizontal  set  0  d a t a where t h e n u l l  or not r e j e c t e d ,  plotted  i n another  a d e q u a c y o f t h e l i n e a r m o d e l was  c h e c k i n g o u t f o r any  examination  w e l l happen t h a t  i s found which i s c o n t r a r y t o the n u l l  so r e j e c t i t  The  observed  I t may  0  This  language  particular  technique wherein  a  f o r m as shown b e l o w  i s computed a n d time.  Smith  the X  variable  1 0 2  TIME  Figure 3 1 o  I m p r e s s i o n o f h o r i z o n t a l "band" f o r p l o t r e s i d u a l v s . time ( 4 4 ) .  of  103 This  i s done by  bution  calculating  of each independent  included  where  i n the  Sb^  =  was  variable  with  s e l e c t s the  independent the  time.  power o f  possible  combination  comprise  this  t o the  i ~  i s eliminated  i s r e p e a t e d m i n u s one  and  of t h e  model.  variables  correlation  a l l the  (powers of  coefficient  independent  that  T h e n the  c a l c u l a t e s equations three  variable  continues u n t i l  the t o t a l  independent  Y,  power  variable.  This process  three  dependent v a r i a b l e ,  proX)  with  the  f o r a l l the  variables  that  set.  T h i s p r o g r a m was of v a r i o u s polynomial  by a d d i n g  i —  smallest variance r a t i o  w h i c h have t h e h i g h e s t s i m p l e  the  f o r the  corresponding  whole p r o c e s s  d e l e t e d each  course,  the  0  variable.  v a r i a b l e s are e l i m i n a t e d from gram  i H L power o f  2,.. ,m)  s t a n d a r d d e v i a t i o n of the r e g r e s s i o n  of the  The  i = 1,  variable,  independent  coefficient  first.  f o r the  = regression coefficient the  (X , where  contri-  equation.  independent  The  variable  Fj, = v a r i a n c e r a t i o  bi  the v a r i a n c e r a t i o n o f the  models w i t h  improvement  a new  term  useful  i n the  f o r comparing the that of a l i n e a r  adequacy one.  p r e s e n t model must be  t o the model would produce  one  some r e a l  Of wheresig=  104 nificance  and  not  s i m p l y due  t o the  p a r a m e t e r s i n t h e model i s g e t t i n g (the  the v a r i a b l e s  then  select  from  i s to t r y every  chosen a l l the  b e l i e v e d t o be  electronic  very  computers  (X*„  of  saturation point  important  and  still  (46).  statistical  useful  variables  of a n a l y s i s .  However, p e r s o n a l  m)  i s available  of  and  T h i s method  the  use  of in  i n r e t a i n i n g a l l the (powers o f X) This b e l i e f  data  is  shared i n the  experience  s i n c e no  f o r doing  i n the  runs used  judgement a n d  i n e v a l u a t i n g the  procedure  ....  obtained.  on t h e l a r g e number o f t r i a l  essential  "best"  so t h a t i t i s hoped t h e method u s e d  equation a t a l l stages  method  thus  2,  time-consuming even w i t h  significant  Kozak b a s e d  the  p o s s i b l e combination  where 1 = 1,  equations  t h e p r e s e n t work c o u l d p r o v e  by  close to  t h e b e s t method o f s e l e c t i n g  regression equation  is  t h a t t h e number  number o f o b s e r v a t i o n s ) .  Probably  all  fact  unique  this.  are  105 RESULTS  Ao  E x p e r i m e n t a l Runs  In a l l t h e r u n s where o r d i n a r y  photographs  taken w i t h o u t the use of s c h l i e r e n o p t i c s , adequate intensity  remained  f u s e r was u s e d . of  4500  to  a p r o b l e m e x c e p t i n r u n 16  Contributing  5000  pps  (2=5  f a c t o r s were h i g h  t i m e s more p p s t h a n f o r t h e s c h l i e r e n  blems,  t h e f i l m s o b t a i n e d m o s t l y were u n d e r e x p o s e d  paper  theless,  or I l f o r d  rejected  As a r e s u l t o f t h e s e p r o -  emulsions used.  loss i n contrast,  (Kodak P-5  B5-1P)»  lighter  background.  reduced  to a large  run  light  on h a r d  r u n s were, n e v e r -  i n r u n 16  resulted  in a  silhouetted against  i n the photographs  a t t h e zone  16 was p r o p e r l y  The  Several  e x t e n t the dark b l o t c h  used as s o l u t e ,  defined  To compensate f o r t h e r e -  The u s e o f m e t h y l a l c o h o l  i n t h i s research  were w e l l  spite  due t o g r o s s u n d e r e x p o s u r e .  p r e d o m i n a n t l y d a r k image o f t h e d r o p  methyl a l c o h o l  in  t h e p i c t u r e s were p r i n t e d  The u s e o f p a r a l l e l  ticed  dif-  camera s p e e d s  and the use of a d i f f u s e r .  sulting  light  where no  runs),  of the f a s t e r f i l m  were  a  f o r solute  t h a t was  first  o f r u n 15<>  the i n t e r f a c i a l  no-  With  boundaries  of drop approach.  Like  run  15,  exposed.  s t a g e s o f c o a l e s c e n c e were o b s e r v e d a s  As t h e two o p p o s i n g d r o p s met, t h e s u c c e s s i o n  follows:  of events  that  106 followed  showed t h a t  l y but appeared  the drops d i d n o t c o a l e s c e i n s t a n t a n e o u s -  t o r e s t a t the i n t e r f a c e  they c o a l e s c e d , a l i q u i d  " b r i d g e " o r "neck"  shape was i n s t a n t a n e o u s l y 32)o  This  liquid The  formed  from both drops u n t i l  collapse  to unite  " b r i d g e " o r "neck" r a p i d l y  depletion  of f l u i d  f o r some t i m e .  of c y l i n d r i c a l  t h e two d r o p s  grew i n s i z e ,  o n l y one b i g g e r d r o p  remained.  from b o t h drops a c c o u n t e d f o r t h e i r of the  Before the onset o f c o a l e s c e n c e , the dark (Fig. 21),  in run 1 5 steel b a l l  a c c o r d i n g t o the r e s u l t s  e x p e r i m e n t s was n o t b e l i e v e d  of coalescence w i t h the appearance  blotch  of the previous  t o be t h e b e g i n n i n g  of a l i q u i d  "bridge" or  "neck" b e t w e e n two o p p o s i n g d r o p s b u t s i m p l y a n o p t i c a l nomenon a s s o c i a t e d w i t h t h e p r e s e n c e dients.  For practical  purposes,  of refractive  total  elimination  d a r k b l o t c h was n o t o b t a i n e d a f t e r u s i n g m e t h y l though  i t appeared  and 19 m e n t i o n e d  from the photographs  i n this  section  d a r k b l o t c h was d i m i n i s h e d . pearance  of a dark b l o t c h  drops and the s t a r t "holding time". in literature  ( 4 7 ) „ which  gra-  of this  alcohol a l 17,  t h e appearance  18,  of a  The time between t h e f i r s t a p separates the  o f c o a l e s c e n c e was measured,,and  T h i s time  i s almost i s defined  similar  called  to "rest  t o be t h e t i m e  and the s t a r t  a d r o p w i t h i t s common p h a s e . the appearance  that  phe-  index  of funs 16,  i n t h e space which  e l a p s e s between t h e a r r i v a l  cause  (Pigo  drawing  and i n c r e a s e d both the diameter and l e n g t h  "bridge".  When  time"  which  of coalescence of  The two d e f i n i t i o n s  d i f f e r be-  o f a d a r k b l o t c h b e t w e e n t h e two d r o p s  d o e s n o t n e c e s s a r i l y mean t h e a r r i v a l  or meeting  o f two i n -  107  Figure 3 2 .  P a r t i a l view of c o a l e s c i n g MIBK drops.  108  terfaceso  "Coalescence time" was  taken to be the time b e t ~  ween the onset of coalescence characterized, by the formation of the l i q u i d of  initial  " b r i d g e " and. the e v e n t u a l formation  one l a r g e r drop, completing the coalescence process<>  Run 16 u t i l i z e d the p a r a l l e l l i g h t i n g  arrangement  and a methyl a l c o h o l c o n c e n t r a t i o n of 0 0039 l b o moles/cuo o  fto  solno  i n the d i s p e r s e d phase.  than that of run 15°  T h i s c o n c e n t r a t i o n i s lower  The h o l d i n g time was  frame-by-frame a n a l y s i s of the c i n e f i l m , times l a r g e r than i n run 15  to be r o u g h l y 40  of course, a d i f f e r e n t  Other r e l e v a n t data on runs 15-19  inclusive,  solute.  are found i n  V.  In run 17, ratio  through  (Table VI) which u t i l i z e d the d i f -  f u s e d l i g h t i n g arrangement and,  Table  found,  m a g n i f i c a t i o n , which i s taken t o be the  of f i l m image s i z e  to o b j e c t s i z e , was measured to be  approximately equal to 2:\due to the use of a 150 mm. s i o n tube.  exten-  The two n o z z l e t i p s were out of view as seen i n  the cine f i l m because  of t h i s m a g n i f i c a t i o n . H o l d i n g time  was  8 times l e s s  VI).  found t o be about  D i f f u s e d l i g h t was  p a r a l l e l l i g h t was  used.  than t h a t i n run 16  (Table  used i n t h i s run whereas i n run  16,  A very s l i g h t darkening a t the zone  of drop approach was n o t i c e d as the two drops met  each o t h e r .  The n o z z l e t i p s a g a i n were seen i n runs 18 and where only the 75 nmi. e x t e n s i o n tube was  used.  19  109  Table Run  VI.  No.  Drop H o l d i n g a n d C o a l e s c e n c e H o l d i n g Time,  sec.  Times  Coalescence  Time, s e c .  1 5  O0OO39  0.014-9  1 6  O.I67  0.0142  1 7  0  18  O . I 3 6 5  0.0114  1 9  0 . 0 2 5 6  0 . 0 1 3 8  .  0  2  1  0 . 0 1 3 2  110 The h o l d i n g times obtained, f o r a l l the runs cont a i n i n g methanol show t h a t there was  no c o n s i s t e n c y with  res-  pect to h o l d i n g times among them (Table V I ) , p a r t i c u l a r l y between runs 1 7 and 18 where the e x t r a c t i o n c o n d i t i o n s were about the same but whose h o l d i n g times d i f f e r by 55 %°  Runs  G  1 7 and 19 gave c l o s e v a l u e s although  t h e i r solute  t i o n s were not the same (Table V I ) .  Likewise,  concentra-  runs 16 and  18  gave c l o s e v a l u e s of h o l d i n g time with about the same s o l u t e c o n c e n t r a t i o n but whose l i g h t i n g arrangements were d i f f e r e n t . It must be emphasized here t h a t the v a r i a t i o n i n h o l d i n g times obtained must be t r e a t e d with c a u t i o n since t h i s process s t a t i s t i c a l i n nature  and  the number of o b s e r v a t i o n s ,  t h i n g , are too small to make any the r e s u l t s obtained may  conclusions.  is  for  one  Nevertheless,  suggest t h a t there are other f a c t o r s  a s i d e from s o l u t e c o n c e n t r a t i o n , l i g h t i n g arrangement,  and  m a g n i f i c a t i o n which c o u l d i n f l u e n c e and/or c o n t r o l h o l d i n g times.  Brown and who  Hanson (48) mentioned a number of workers  reported a s i g n i f i c a n t  spread  of r e s t times f o r i d e n t i c a l  drops i n the same system but as y e t , they cannot agree on what causes t h i s c o n s i d e r a b l e magnitude may  scatter.  depend on any  They b e l i e v e d r e s t time  or a l l of the f o l l o w i n g :  tem-  p e r a t u r e , drop s i z e , the geometric shape of the i n t e r f a c e , the degree of p u r i t y of the components, t h e i r v i s c o s i t i e s d e n s i t i e s , the i n t e r f a c i a l t e n s i o n , and shock.  the occurrences  Since, by d e f i n i t i o n , r e s t time can  and  of  influence holding  Ill time  p r e s u m a b l y any s c a t t e r  s  flected  the  Coalescence  f o r a l l runs  time  i s shown i n T a b l e V I .  f o r runs  study  15-19  inclusive,  i n this  were o b t a i n e d .  the s i g n i f i c a n c e  During  of the l i q u i d  i t with  (as shown a t P, Q, R, a n d S i n F i g . 32).  n - b u t y l benzoate drops  An right  drop  data  since  "bridge", that  appeared  t o cave i n  T h i s phenomenon  shown by K i n t n e r  (49)  was  o f two  c o a l e s c i n g i n water.  interesting  i n F i g . 34,  No f u r t h e r a t -  project.  the drop  t o t h a t i n photographs  s e c t i o n of  of these  of t h i s  the formation  c a n be r e -  Close values of coalescence  i s o u t s i d e the scope  r e g i o n which connected  similar  results  shown i n T a b l e V I .  tempt was made t o s t u d y any  time  i n the f i n d i n g s  thesis  time  in rest  sidelight  consisting  o f r u n 19 was t h a t t h e of water-saturated  MIBK  w i t h a m e t h a n o l c o n c e n t r a t i o n o f 0.088 l b . m o l e s / c u . f t . s o l n . , was f o g g e d  by e x t r e m e l y  working with  similar  fine  d r o p l e t s of water.  Rocchinl  s o l v e n t s , w a t e r a n d MIBK, a t t r i b u t e d  (26), this  m i s t i n g phenomenon t o t h e i n f l u e n c e o f a s o l u t e a n d / o r temperature  on t h e m u t u a l  solvents, seen  i n this  solubility  b e t w e e n two p a r t l y m i s c i b l e  c a s e , w a t e r a n d MIBK.  t h a t f o g g i n g was n o t u n i f o r m  are darker of emulsion  than  the r e s t  i n the r i g h t  but appeared  o f the drop drop  From F i g . 34*-  contents.  i t is  i n patches The  which,  formation  showed t h a t , a t t h e t i m e  the f u n  was f i l m e d , s e p a r a t i o n o f p h a s e s had o c c u r r e d i n t h e r i g h t  112 drop. out  Upon v i e w i n g t h e movie f i l m ,  the event p r i o r  inside  to coalescence that  the drop appeared  direction,,  This  t o be  emulsion patches present.  a l s o might not  be  be  throughmaterial  i n the c l o c k w i s e  made v i s i b l e  by  the  dark  I t i s reasonable to expect  i n t e r f a c i a l movement a l s o .  circulating.  observed  observed  the l i q u i d  circulating  c i r c u l a t i o n was  b e h a v i o u r t o Induce  i t was  The  left  However, s u c h c i r c u l a t i o n  i n the l e f t  drop  because  this drop  could  of the absence  of  emulsification.  B.  Pseudo-Radius  The and  v a r i o u s p s e u d o - r a d i i of the drops  r u n 19 were m e a s u r e d i n t h i s  purposes, level  effect  c o n c e n t r a t i o n used  determined  on d r o p  It  employed.  was  This  t r a c i n g and  For  whether s o l u t e  s h a p e as a p a i r  comparison  plotted  e r r o r was  easily  Therefore, i t  c o n c e n t r a t i o n has  of drop  against  different  convenience,  scatter resulted  t i m e when hand t r a c i n g attributed  to  t h e m e t r i c s c a l e was  m a g n i f i c a t i o n «= 24x  was  adopted,  = 24x)  was  as was  inaccuracies  used  Minimum l e n g t h d i s c e r n i b l e  (total magnification  any  coalesces.  c o r r e c t e d by u s i n g p h o t o g r a p h i c p r i n t s  the p s e u d o - r a d i i .  photographs  f o r each.  found that unnecessary  p s e u d o - r a d i u s was  ring  study f o r  i n run- 18  both runs b e i n g s i m i l a r except f o r the  of solute  c o u l d be  in  Measurement  instead.  i n measu-  i n the  0 . 0 5 cm.  (A  total  f o r i l l u s t r a t i o n purposes,  in  113 Figs.  33  and  34  T h e r e f o r e , i n a s p h e r e , a change  volume c o r r e s p o n d i n g t o a l i t t l e  less  t h a n 0.05  i n r a d i u s would pass u n d e t e c t e d under  i n drop  cm.  change  t h e p r e s e n t measurement  procedure.  Measurements o f d r o p p s e u d o - r a d i i i n s u c c e s s i v e  film  had  frames  which  t o "be r e s t r i c t e d  t h e p s e u d o - r a d i u s change  photographs  t o e l i m i n a t e any  1390  and  i t was 800  r u n s 18 a n d  estimated  frames  0.05  In p r a c t i c e , the e n t i r e inertia also,  and  solely  dispersed on w h i c h  distortion.  any  because accuracy  changes v a r y  was  of t h i s e f f e c t  e f f e c t s may change,  imbalance  the  interfere i n the  c o n s i d e r e d because that  tended  over  arise  a c c o m p a n y i n g mass  surface  as  the  o f the  drop  t o bulge t e m p o r a r i l y  i m p e r f e c t i o n s i n the g l a s s  o f the itself  (e.g.,  o p t i c a l d i s t o r t i o n a l t h o u g h the  was  c o n s i d e r e d t o be m i n i m a l .  o f b u o y a n c y and a l s o  o f t h e a b o v e frame  about  t o some e x t e n t , t o  N o n - p a r a l l e l i s m of the w a l l s  contribute  of the e f f e c t  to increase  o r volume  tension  impinged  g l a s s column a n d  magnitude  These  phase f l o w s i n t o the d r o p ,  s t r i a t l o n s ) may  of  p s e u d o - r a d i u s c h a n g e s t h a t may  inertial'-effeet  this material  growth.  photographs.  t o b u o y a n c y and,  to i n t e r f a c i a l An  i n the  i n the  of coalescence) f o r  drop pseudo-radius  due  to i t s v e l o c i t y .  square  cm.  over  substituted for  were r e q u i r e d  t o drop growth  to determine  transfer.  due  optical  i n addition  effort due  interface  t o drop  cm.  I ) t h a t a span  t o the onset  19 r e s p e c t i v e l y ,  r a d i u s u n i f o r m l y by  due  of frames  t h a n 0.05  s p h e r e s were  (Appendix  (prior  span  i s less  effect  Assuming a p p r o p r i a t e l y - s i z e d the drop,  to a  t o the  Mostly  inherent i n -  span e s t i m a t e owing t o t h e assump-  114  Figure 3 4 .  Photograph from run 1 9 showing b l u r r e d g r a i n y a t t h e l e f t and r i g h t s i d e o f t h e p i c t u r e .  Images  115 tion and  of a  sphere,  the a c t u a l  c o n s i d e r e d t o be  {prior  t o the  respectively, these f i l m spherical  spans  t h a t were  f o r r u n s 18  Conservative figures  onset  studied and  were 101  o f c o a l e s c e n c e ) f o r r u n s 18  and  corresponded  r a d i u s o f 0.004 cm.  o f 151  19  and  were t h e r e f o r e a d o p t e d  assumed, o f c o u r s e , facial  spans  drop growth-free  treated with caution. frames  frame  for analysis.  Each  19  of  t o a u n i f o r m i n c r e a s e i n the i n the photographs.  that within  these  t e n s i o n - i n d u c e d shape changes,  film  It i s  frame  i f any,  spans  inter-  w o u l d be  sig-  n i f i c a n t l y evident.  The  frame  span b e i n g c o n s i d e r e d was  t w e n t y - s i x p a r t s each At the end was  of each  tion  of f i l m  Table  successive film  K-3  K-3,  202.  and  frames  and  K-4  into account, No.  c o n t a i n i n g an e q u a l number o f interval  measured a l o n g each d i v i d i n g l i n e  b l e s K - l , K-2,  K-4  over the  o f r u n 19,  starting  from  t h e d i s c u s s i o n o f r u n 19, F o r any  t a k e n f o r each  span  considered.  six additional frame No. frames  g i v e n frame,  19  showed s l i g h t l y  picture t h i s was  ( F i g s . 33 due  and  frames.  and 19°  Ta-  distribu-  Note t h a t  frames  in  were  taken  and. e n d i n g on  frame  are i n c o r p o r a t e d i n be  called,  "run  o n l y one measurement  t h a t was  A l a r g e number o f p r i n t e d and  101  into  pseudo-radius  i n r u n s 18  t h i s run w i l l  pseudo-radius  the  i n A p p e n d i x K show the  When t h e s e a d d i t i o n a l  (extended)".  divided  19 was  considered.  photographs  of runs  18  blurred, spots i n c e r t a i n a r e a s of 34).  t o the presence  At f i r s t ,  i t was  thought  of a h i g h r e f r a c t i v e  the  that  index g r a -  1 1 6 dient material  i n these  l o c a t i o n s (see  e v e r , upon c l o s e r e x a m i n a t i o n , enlarger  carrier  cess  not  was  s u r f a c e was due  t o two  f o r the  holding not  lying  possible 1.  2.  the  i t was  discovered  f i l m negative  i n the  negative  so t h a t  i n one  flat  plane.  use  with  3 5 mm.  films,  h o l d the  1 6 mm.  negative  negative  the n e g a t i v e between two  carrier,  to  was  was  was  held  the  printing the  pro-  negative be  meant f o r  too l a r g e  entirely  that  carrier  negative one  plane  or p a r t s to  i n f l u e n c e of heat.  or p a r t s  was of  another When  happened between f o c u s s i n g and the p r i n t  flat.  so d e s i g n e d  in this  to  open f r a m e s so t h a t t h e r e  "jump" f r o m  under the  w h i c h was  carrier  tendency f o r the  it  that  reasons:  negative  a  How-  T h i s problem c o u l d  The  The  "DISCUSSION") .  this  exposing,  o f i t went out  of  focus. By  stopping  blurring  C.  down the  c o u l d be  to i n c r e a s e depth  of  field,  minimized.  Statistics  The 18  enlarger lens  and  Vila,  a n a l y s i s of v a r i a n c e  1 9 I n t e r p r e t e d by Vllb,  To  Villa,  the  VHIb,  facilitate  IXa  linear and  (ANOVA) t a b l e s f o r model a r e  shown i n  runs Tables  IXb.  understanding  of the  t e r m s shown i n  117 Table  Vila.  Dividing Line  Analysis of Variance  Source  Table  of Left  D e g r e e s Sum o f Square s of Freedom x l O -  6  70°  Total(corre cted) R e g r e s s i o n (b^) Re s i d u a l  25 1 24  29.073  100°  Total(corrected) Regression ( b i ) Re s i d u a l  25 1 24  10.463 2.6546 7.8086  130°  Total(corrected) Regression ( b i ) Residual  25  8.0248  145°  Total(corrected ) R e g r e s s i o n (b]_) Residual  25  155°  T o t a l (corrected.) Regression ( b i ) Residual  25  185°  Total(corrected) Regression ( b i ) Residual  25  195°  Total(corrected) Regression ( b i ) Residual  25  220°  Total(corrected) Regression ( b i ) Residual  25  250  Total(corrected) Regression ( b i ) Residual  25  13.398  280°  Total(corrected) Regression ( b i ) Residual  25  28.230 1.0468 27.183  9  1 24  1 24 1 24 1 24  1 24  1 24 1 24 1 24  37.434 8.3613  0.84307  7.1818  17.153  1.3949  15.758 27.095  0.13465 26.960  5.0506  0.002465.0481 12.474  1.2633  11.210  9.1354  1.4381 7.6973  3.4659 9.9326  Drop i n Run 18  Mean Square x 10~°  Calculated t-value  8.3613 1.2114  -2.6272  2.6546  -2.8564  0.84307  -I.6785  1.3949  -1.4576  0.32536  0.29924  O.65658  0.13465 1.12333  0.3462  0.00246-  0.1082  1.2633  1.6445  1.4381  2.1176  0.21034 0.46708  0.3207 . 3.4659 0.41386  2.8939  1.0468 1.1326  0.9614  1 1 8  Table  Vllbo  Dividing Line  Analysis of Variance  Source  Degrees of Freedom  Table  ofRight  Sum o f Square s x10-6  Drop  Mean Square x 1 0 - 6  Total(corrected) Regression ( b l ) Re s i d u a l  25  1 4 o 9 5 1  2 4  I 4 c 7 7 2  0 . 6 1 5 5  Total(corrected) Regression ( b l ) Residual  25  19.925 809664  8.9664  2 4  10.959  0.4566  25  1 0 . 4 0 0  130°  Total(corrected) Regression ( b l ) Residual  1450  Total(corrected) Regression ( b l ) Re s i d u a l  25 2 4  10.535  155°  Total(corrected) Regression ( b l ) Residual  25  28.636  185°  Total(corrected) Regression ( b l ) Residual  25  Total(corrected) Regression ( b l ) Re s i d u a l  25  1 0 . 4 2 8  2 4  1 0 . 2 4 3  Total(corrected) Regression ( b l ) Residual  25  21.973  2 4  21.952  25  39.494  2 4  3 8 . 2 4 6  2 5  1 8 . 8 2 0  2 4  17.974  70° 1 0 0 °  195° 2 2 0 °  250°  Total(corrected) Regression ( b l ) Residual  2 8 0 °  Total(corrected) Regression ( b l ) Residual  1  1  1  2 4  1  1  2 4  1  2 4  1  1  1  1  O0I7856  2o7669  7»633  O.I7856  2.7669  i n Run 1 8  Calculal t-vali  -0.539  -4.431  -2.950  0 . 3 1 8 0  21.972 1 1 . 4 3 7  11.437 O.43896  -5.104  6.3362  6.3362  13»809 0.69351 13.116  0.69351 0.5465  -1.126  0.18537 0.42679  -0.659  22.300  0.18537  0.92917  0.02053: 0.02053;  1 . 2 4 7 7  0 . 8 4 5 5 3 .  - 2 . 6 1 1  -O0I5O  0.9147  1 . 2 4 7 7  O0885  1.5936  0.84553 0.7489  1 . 0 6 2  1 1 9  ["able V l l l a o  Dividing Line  A n a l y s i s of Variance  Source  Degrees of Freedom  Table of L e f t  Sum o f Square s x 1 0 - 6  Drop i n Run  Mean Square x  10~  6  Total(corrected) Regression ( b i ) Residual  25  Total(corrected) Regression ( b i ) Re s i d u a l  25  Total(corrected) Regression ( b i ) Residual  25 24  1 2 . 5 4 7  Total(corrected) Regression ( b l ) Residual  25  430546  1  I80O72  24  2 5 . 4 7 4  155°  Total(corrected) Regression ( b i ) Re s i d u a l  25  29.558 130444 16O114  Total(corrected) R e g r e s s i o n (b]_) Re s i d u a l  1 2  8 o 7 1 3 1  1 7 0 °  1  5 . 3 2 6 3  5 . 3 2 6 3  1 1  3.3868  O . 3 0 7 8 9  Total(corrected) Regression ( b i ) Residual  25  7.1816  Total(corrected) Regression ( b i ) Re s i d u a l  25  Total(corrected) R e g r e s s i o n (b]_) Residual  25  7 0 °  1 0 0 °  130O  145°  1 8 5 °  1 9 5 °  2 2 0 °  2 5 0 °  Total(corrected) R e g r e s s i o n (b]_) Residual  1  24  1  24  1  1  24  1  24  1  24  1  2 2 . 9 3 7  0,28601 2 2 o 6 5 1  31=931 13*350 1 8 , 5 8 0  -O.55O  0 . 9 4 3 7 9  13.350  - 4 . 1 5 3  0 . 7 7 4 1 7  23.506  - 6 . 7 0 5  0 . 5 2 2 7 9  1 8 . 0 7 2  - 4 . 1 2 6  1.0614  13.444  - 4 . 4 7 5  0 . 6 7 1 4  0 o 6 l 7 3 2  0 . 6 1 7 3 2  6 , 5 6 4 3  0 . 2 7 3 5  - 4 . 1 5 9  - 1 . 5 0 2  15.873 1 , 2 8 6 7 1 4 O 5 8 6  1 . 2 8 6 7  - 1 . 4 5 5  0 . 6 0 7 7 5  2 8 , 7 2 6  10,145 1 8 , 5 8 0  25  1 4 , 9 6 3  24  0,28601  3 6 . 0 5 3  23.506  24  1  Calcula t-val'  10.145  3 . 6 2 0  0 . 7 7 4 1 7  6,0101  6 . 0 1 0 1  8 o 9 5 3 3  0 . 3 7 3 0 5  4.014  120 Table  Vlllbo  Dividing Line  Analysis  of V a r i a n c e  Source  Degrees of Freedom  Table  of Right  Drop i n Run 1 9  Sum o f Squares x 10-6  Mean Square x10-6  9 = 1 9 6 7 0o12447 9.0722  0.12447 O . 3 7 8 O I  0 . 5 7 4  I 0 6 7 8 8 0.60358  - 1 . 6 6 8  Calculated t-value  100°  Total(corrected) Regression (bi) Residual  25 1 24  130°  Total(corrected) Regression (bl) Residual  25  I 6 . I 6 5 1 . 6 7 8 8 14.486  145°  Total(corrected) Regression (bl) Residual  25 1 24  15.885 4.8791 11.006  4.8791 O . 4 5 8 5 8  - 3 . 2 6 2  155°  Total(c orre cted) Regression (b^) Residual  25  16.641 3.8719 12.769  3.8719 0.53204  -2.698  170°  Total(corrected) Regression (b]_) Residual  1 2 1 1 1  6 . 2 2 5 9 0 . 2 3 8 6 4 5 . 9 8 7 3  0 . 2 3 8 6 4 0 . 5 4 4 3  - 0 . 6 6 2  1 8 5 °  Total(corrected) Regression (bl) Residual  25 1 24  2 . 6 1 9 9 0 . 1 3 4 7 7 2 . 4 8 5 1  0 . 1 3 4 7 7  -1.141  25  9.1804  1 9 5 °  Total(corrected) R e g r e s s i on (bi) Residual  1 24  0.23032 8.9501  250°  Total(corrected) Regression (b^) Residual  25 1 24  280°  Total(corrected) Regression (bx) Residual  25  1 24  1 24  1 24  0.1035 0.23032  O.786  5.0119 0.41601 4.5959  0.41601 0 . 1 9 1 5  1 . 4 7 4  2 . 6 2 5 1 0.23852 2 . 3 8 6 6  0 . 2 3 8 5 2 0.0994  1.5^9  0 . 3 7 2 9  1 2 1  Table  IXa. A n a l y s i s o f Variance Run 1 9 ( E x t e n d e d )  Dividing Line  7 0 °  100°  1 3 0 °  145°  1 5 5 °  1 7 0 °  185°  Source  T o t a l (corre c t e d) Regression ( b i ) Residual Total(corrected) Regression ( b l ) Residual Total(corrected) Regression ( b l ) Residual Total(corrected) Regression ( b i ) Residual Total(corrected) Regression ( b l ) Residual Total(corrected) Regression ( b l ) Residual Total(corrected) Regression ( b i ) Residual  195°  Total(corrected) Regression ( b l ) Residual  220°  Total(corrected) Regression ( b l ) Residual  250O  280°  Total(corrected) Regression ( b i ) Residual Total(corrected) Regression ( b l ) Residual  Degrees of Freedom  Table  of Left  Sum o f Square s x 1 0 " °  Drop i n  Mean Square x 10-6  Calculated t-value  24.133  - 4 . 9 3 2  5 3 o 8 9 2  31  1  24.133  3 0  29.759  31  82.084 60.884  3 0  2 1 o 2 0 0  31  9 0 o l l 5  30  15=641  3 1  8 7 o 4 6 0  1  1  1  3 0  31  1  7 4 . 4 7 4  5 4 . 9 5 1 3 2 . 5 0 9  24.192  18  16.467  1  31  1  3 0  5 . 3 6 2 3 1 1 . 1 0 5  52.542 32.324  0.29873  3 0  20.218  31  47.766  1  3 0  - 7 . 1 2 1  1 . 0 8 3 6  1 7 . 6 0 6  - 4 . 6 7 2  0 . 8 0 6 4  5 . 3 6 2 3  - 2 . 8 6 5  0 . 6 5 3 2  O . 3 1 5 8 6  31  31  5 4 . 9 5 1  9 . 4 7 5 9  25=317  3 0  - 1 1 . 9 5 2  0 . 5 2 1 3 7  0 . 0 0 0 1 2  3 0  1  7 4 . 4 7 4  0 . 0 0 0 1 2  2 5 . 6 1 6  1  - 9 . 2 8 2  O.7067  9 . 4 7 6 1  3 1  1  60.884  41.798 1 7 . 6 0 6  3 0  17  0 . 9 9 1 9 7  34.286  0.29873 0.8439 3 2 . 3 2 4  0 . 5 9 5  6 . 9 2 6  0 . 6 7 3 9  3 4 . 2 8 6  13.480  0 . 4 4 9 3  16.819 7.5895  7.5895  9 . 2 2 9 5  0 . 0 2 0  O . 3 0 7 6 5  8 . 7 3 5  4 . 9 6 7  1 2 2  Table  I X b o  Dividing Line  100O  130  0  1 4 5 °  155°  Source Total(corrected) Regression (bl) Residual  250  0  3 0  0 . 4 0 6 6 7  0.40667  9 c 1 4 1 7  0 . 3 0 4 7  2 6 . 9 7 8  1  1 4 . 5 4 2  3 0  1 2 . 4 3 5  31  4 1 . 8 1 8  Total(corrected) Regression (bl) Residual  Total(corrected) Regression (b^) Residual Total(corrected) Regression ( b l ) Residual  1 3 0  0 . 4 1 8 2 7  15.748  2 7 c 2 9 5  3 0  1 4 . 5 2 3  1 8  1 8 . 1 4 7  1  1 0 . 6 0 3  1 7  7 . 5 4 4  31  4 1 . 0 1 1  1  2 9 o 8 5 4  3 0  1 1 . 1 5 7  31  4 2 . 7 9 6  1  2 2 . 0 4 3  3 0  2 0 . 7 5 3  31  3 0 . 8 8 6  1  1 8 . 8 9 9  3 0  1 1 . 9 8 6  31  1 5 o 8 6 l  1  5 o 3 1 3  3 0  1 0 . 5 4 8  1 3 0  Calculated t-value  L 1 5 5  I60I67  1  31  x  Mean Square 1 0 ~ 6  9 o 5 4 8 3  31  Total(corrected) Regression ( b l ) Residual  2 2 0 °  1  Sum o f Squares x 1 0 - 6  Total(corrected) Regression ( b i ) Residual  Total(corrected) Regression ( b l ) Residual  1 9 5 °  31  o f R i g h t Drop i n  31  Total(corrected) Regression ( b j ) Residual  1 8 5 °  Degrees of Freedom  Table  Total(corrected) Regression ( b i ) Residual  Total(corrected) Regression (b^) Residual  1 7 0 °  2 8 0 °  A n a l y s i s of Variance Run 1 9 ( E x t e n d e d )  0 . 4 1 8 2 7  - 0 . 8 9 3  0 . 5 2 4 9  1 4 . 5 4 2  - 5 . 9 2 3  0 . 4 1 4 5  2 7 . 2 9 5  - 7 . 5 0 9  0 . 4 8 4 1  1 0 . 6 0 3  - 4 . 8 8 8  0.44376 2 9 . 8 5 4  - 8 . 9 6 0  0 . 3 7 1 9  2 2 . 0 4 3  - 5 . 6 4 5  0 . 6 9 1 7 7  1 8 . 8 9 9  - 6 . 8 7 8  0 . 3 9 9 5  5 » 3 1 3  - 3 . 8 8 7  O . 3 5 1 6  703861 0 . 5 4 4 7 2  0 . 5 4 4 7 2  6 . 8 4 1 4  0 . 2 2 8 0 5  )  - 1 . 5 4 6  1 2 3 these  tables,  understood  some e x p l a n a t i o n s a r e i n order..  that  Sum o f s q u a r e s a b o u t t h e mean I n e q u a t i o n form £(Yi  - Y)  where  I t i s commonly  2  =  _  Sum o f s q u a r e s about r e g r e s s i o n  t h i s c a n be e x p r e s s e d  £(Yi - Y i ) + 2  Yi = i ~  +  Sum o f s q u a r e s due t o r e g r e s s i o n  as f o l l o w s :  £(Yi - Y ) , 2  i = i , 2,  0 00  ,n  (?)  o b s e r v a t i o n o f the dependent v a r i a b l e s the  pseudo-radius ° Y  = mean o f Y.  A  Y i =• p r e d i c t e d v a l u e Corresponding dom  to Eq  0  of Y f o r a given X (time).  ( 7 ) , the s p l i t  of the degrees  ( 4 4 ) is (n-1) =  (n-2)  + 1  (  where n = no» o f s e t s o f o b s e r v a t i o n s O O O O 9  U s i n g Eqso tional is  of f r e e -  ( X^l 9  ( X i , Y]_), (Xg,  8  )  ^2^°  l£tl ) o  ( 7 ) and ( 8 ) and employing  alternative  forms f o r the e x p r e s s i o n s o f E q ,  computa-  ( 7 ) an. ANOVA  table  c o n s t r u c t e d i n the f o l l o w i n g form: Table  X.  A General  Form o f ANOVA  Degrees o f  About mean ( t o t a l , c o r r e c t e d f o r mean) Regression  1  n - 2  2  Mean  (EYi)  2  n «  b  About r e g r e s s i o n (residual)  Sum o f  „  n - 1  Table,  l LxiYi -  (£xi)(£Yi)"  by s u b t r a c t i o n  MS n S  2  R  124 where b i  o f s l o p e p a r a m e t e r o f t h e m o d e l , j8j  = estimate  X]_  = i t h o b s e r v a t i o n o f the independent  .  variable,  time. S  = mean s q u a r e  about r e g r e s s i o n ( a l s o c a l l e d the  "sample v a r i a n c e " ) . = mean s q u a r e  MSJJ  The or  due t o r e g r e s s i o n .  "Mean S q u a r e " c o l u m n i s o b t a i n e d by d i v i d i n g e a c h "SS" Sum o f S q u a r e s e n t r y b y i t s c o r r e s p o n d i n g  dom.  Note t h a t t h e e n t r i e s  i n t h e ANOVA  inclusive.  However, t h e d i f f e r e n c e  for brevity  i n the l a t t e r .  shown i n A p p e n d i x E .  absolute t-table  t-values with (44) h a v i n g  percentage  =  Tables V i l a  - IXb,  i s o n l y due t o c o n t r a c t i o n ,  Additional  r e l a t e d equations  used  C o m p a r i s o n s made o f t h e c a l c u l a t e d  t h e a p p r o p r i a t e t ( n - 2 , 1-iOO  (n-2) degrees  from a  o f freedom and (1-iOO  points of a t - d i s t r i b u t i o n  d i v i d i n g l i n e s have  of f r e e -  i n t h i s t a b l e u n d e r t h e .'^Source"  c o l u m n a r e worded d i f f e r e n t l y  are  degrees  showed w h i c h  s l o p e s where t h e n u l l  drop  hypothesis,  Ho:^9/  0, c o u l d n o t be r e j e c t e d .  The 100(1 used The  -Ot)%  t e s t was a t w o - s i d e d  confidence  level.  was 0.01 t o o b t a i n r e s u l t s various dividing lines  t(24,  0.995) = 2.797»  test  conducted  The l e v e l  o f s i g n i f i c a n c e , OC ,  t h a t were 99%  corresponding  i . e . , corresponding  a t the  significant.  t o |t| l e s s  than  t o no d e p e n d e n c y  r e l a t i o n s h i p between v a r i a b l e s X a n d Y ( z e r o s l o p e ) , a r e shown i n T a b l e hypothesis  XI.  I n o t h e r words, f o r t h e s e l i n e s ,  c o u l d n o t be r e j e c t e d .  the n u l l  Table Run No.  XI.  Drop D i v i d i n g Lines whose X-Y R e l a t i o n s h i p s Correspond to Zero Slope  Confidence Level Drop  99$  99*9$  Left  130°,145°,155°.185°,195°.280°,220°,70°  L.H.S.* p l u s  Right  70°,185 ,195 .220 ,250 ,280 ,155°  L.H.S.* p l u s  130°  Left  70°,185°,195°.280o**  L.H.S.* p l u s  220  Right  70°**,100°,130°,170°,185°,195° 220°,250°,280°,155°  L.H.S.* p l u s 145  Left  185°,195 .170  Right  70°,100°,130°,280°  o  O  O  o  o  * L e f t hand side entry under confidence l e v e l of 99^» * * D i v i d i n g l i n e s along which no pseudo-radius changes were a c t u a l l y  measured.  100° 250° 8  126 T h e r e were a few null  h y p o t h e s i s was  dence l e v e l was  One  t h e 99$  z e r o a t the  i s f a c e d w i t h the  to r e j e c t  the n u l l  evidence thesis,  decision  that  merely  predictor, the  selected  b u t a b o u t two suggestion dient that  times  observed  the  of those  hypothesis,  99%  Wetz  t-value  (44)  H  Q  linear  at  investiga-  i s no  strong In  this  considered,  of zero  similar  i n Table  who  regarded  XI.  suggested as  satis-  should exceed  p o i n t of the  not  t-distribution, pointo  This  p r e s e n t work a s a c u r r e n t e x p e l i n e a r equations :fy=  confidence l e v e l  f o r a l l remaining  J.M.  s e l e c t e d percentage  serves o n l y i n the  the n u l l  since there  s h o u l d be  percentage  f o r assessment  t e d a t the rule  the  that further  o f the l i n e s l i s t e d  i n f l u e n c e d by  or  f o r these d i v i d i n g l i n e s  t o assume a v a l u e  i n o r d e r t h a t an e q u a t i o n  factory  of whether t o r e j e c t  l i n e s were n o n e t h e l e s s  purposes,  model  (Table  h y p o t h e s i s c o u l d be r e j e c t e d .  t o t h a t a s s i g n e d t o the r e s t T h i s d e c i s i o n was  s l o p e o f the l i n e a r  It i s felt  slope of these  for a l l practical  the confi-  99»9$ c o n f i d e n c e l e v e l  are warranted  t h a t the n u l l the  the  hypothesis  confidence l e v e l .  t i o n s of these l i n e s  l i n e s where  s t r o n g l y r e j e c t e d , a t t h e 99$  for this lines,  t e s t e d t o be  XI). not  and  not  other d i v i d i n g  and  0,  was  not  where the  strongly rejec-  i s n o t meant t o be  equations  test  embodied  in  the  this  t h e s i So  Figs.  35  o b s e r v a t i o n number of unexplained  and  36  show t y p i c a l  p l o t s of r e s i d u a l  (time) showing the absence and  variation  i n the l i n e a r model,  vs.  presence  respectively.  >0-2  faO CO  o oo ooo  +  a H as -p o oo  ooooo  —  OOOOO --0-I < ZD Q UJ -0-2  o  o  ooooo  OO  o  -0-3 26 24 22 20 18 - 16 14 12 10 8 OBSERVATION NO- (X) L 138 i i i i 54i _ 42 30 18 150 126 11i4 102 90i 78i 66 FRAME NO- PRECEDING COALESCENCE Figure  35.  R e s i d u a l v s . o b s e r v a t i o n n o . (and frame no.) w i t h no u n e x p l a i n e d v a r i a t i o n . (Corresponds t o F i g u r e 3 1 . )  821  1 2 9 The line  pseudo-radius  1 7 0 ° results  data  do n o t a p p e a r  i n A p p e n d i x K show  i n r u n 18 s i n c e no measurement  c o u l d be t a k e n due t o t h e a p p e a r a n c e 19» measurement o f t h e l i n e same r e a s o n .  of a dark b l o t c h .  a t 1 7 0 ° was i n c o m p l e t e  i n plots  (X) was adopted, f o r t h e sake shown, f o r e x a m p l e ,  Predictive  of pseudo-radius  of convenience.  i n Appendix  In r u n  f o r the  The u s e o f o b s e r v a t i o n numbers i n s t e a d  v a l u e s a s the a b s c i s s a  is  that  of time  (Y) v s . t i m e  The c o n v e r s i o n  K.  e q u a t i o n s o b t a i n e d by t h e m u l t i p l e  r e g r e s s i o n program f o r those d i v i d i n g  l i n e s whose X-Y  t i o n s h i p s were f o u n d  s l o p e a r e shown i n  Table values  XII.  t o have n o n - z e r o  rela-  These e q u a t i o n s w o u l d , o f c o u r s e , n o t a p p l y t o  o f X o u t s i d e the a p p l i c a b l e  range.  The m u l t i p l e  2 coefficient  o f d e t e r m i n a t i o n , R , shown i n t h i s  table i s  defined: SS due t o r e g r e s s i o n T o t a l SS, c o r r e c t e d f o r mean T h i s term measures the p r o p o r t i o n o f t o t a l v a r i a t i o n R  2  _  —  t h e mean, Y, e x p l a i n e d by t h e r e g r e s s i o n ? R more f u l l y  i n a later  Figs.  topic  under  about  i s explained  "DISCUSSION".  3 7 . 3 8 , a n d 39 show t h e v a r i o u s l o c a t i o n s o f  t h e r e g i o n s i n t h e d r o p where p s e u d o - r a d i u s observed.  2  /Q \  Figs.  40 a n d 41  show t h e f i t t e d  r a d i u s v s . o b s e r v a t i o n number f o r r u n 1 9 . showing the p l o t s  c h a n g e s were plots  of pseudo-  The r e a s o n f o r n o t  f o r r u n 18 a r e e x p l a i n e d u n d e r t h e h e a d i n g ,  "DISCUSSION, I n t e r p r e t a t i o n  of Data".  Table  Xllo  Run No.  P r e d i c t i v e E q u a t i o n s and R  Drop  Dividing Line  0.13136  II  18  Predictive  ii  100°  0.13426  Right 145° 70°  Left  19  (Extended )  Right  Values  Y = 0.11246  0.12735  Obtained  by the M u l t i p l e  R e g r e s s i o n Program  Equation  R  0 . 1 5 8 2 5 X + 2.97346X  2  +  0 . 2 9 1 4 7 X - 55°5509X  2  -  10.4601x3  2  0.5481 + 2727.54x  3  -  41525» OX * 2  0.6300  0.5591  +  310 4036x3  100°  Y =  130°  Y = 0.12930  145°  Y = 0.12346  155°  Y = 0.12108 - 0.07686X + 1 3 3 . 0 1 5 X ^  0.5997  220°  Y = 0.09895 +  0 . 0 5 3 1 5 X  0.6157  250°  Y = 0.10486 +  2 . 2 0 1 1 7 X  280°  Y =  145°  Y = 0.12638 - 3.78106X  155°  Y = 0.12486 -  170°  Y =  185°  Y = 0.11473 +  195°  Y =  220°  Y = 0 . 1 1 0 1 4 - 0.09673X + 7 . 7 2 3 3 4 X  250°  Y =  0.12656  0.11890 0.11310 0.11660  - 3*10448x  -  -  2  3.73441X  2  +  3907336x3  0.8488  3.77947X  2  + 42.7179x3  0.7027  - 21.5726x3  2  0 . 0 9 2 7 3 X  + 6.68294X 2  2  0.7442  155.609X + L:2 0 8 . 3 0 X 3  + 105.629X 3  1  *  842.380X^  0.7049 0.5746  0.04884X  006543  0.04578X  0o5844  2.33950X  2  - 115o786x  - O.II538X + 1 0 . 5 6 5 4 X  -  0.7747  0 . 0 7 0 1 9 X + 6.68546X  3  + 1035°81X^  2  •-  2  •-  2  293o319x3 +2 2 2 5 o 6 3 X ^  0.9082 0.7841  192.583x3 + 1306.01X^ 0.9323 •- 176.423x3 + 1 2 7 9 o 7 1 X ^ 0 . 6 5 7 5  131  F i g u r e 37«  Equations f i t t e d and behaviour observed over 0 - 1 5 0 f i l m frames i n run 18.  LEGEND 1 2 3 4 5  Figure 3 8 .  -  70° 6 - 170° 100. 7 - 185° I30 8 - 195° !45 9 - 220 155 10 - 2 5 0 II - 280° 0  0  E q u a t i o n s f i t t e d and b e h a v i o u r 0 - 1 0 0 f i l m frames i n r u n 1 9 .  o  observed  over  1 3 3  LEGEND t  2 3 4 5  Figure  39°  -  70° 6 - 170° 100 7 - I85 !30 8 - I95 I45 9 - 220 155 10 - 250 11-280 o  Q  o  Q  Q  o  E q u a t i o n s f i t t e d and b e h a v i o u r o b s e r v e d 0 - 2 0 2 f i l m frames i n r u n 1 9 ( e x t e n d e d ) „  over  o - — DIVIDING LINE e  6 9  —  II  II  ADDITIONAL  70° 100°  •  •n  13 5h  -o  €  130  —  n  II  130°  —  II  II  145°  —  II  II  155°  —  II  II  170°  —  II  II  185°  —  II  II  195°  —  II  II  220°  —  n  u  250°  It  280°  —  II  SCALE  J  0  0006  sec.  NOTE LINES 170? 185* AND 195° NOT SHOWN COMPLETELY. THESE ARE PARALLEL TO THE ABSCISSA AT THE VALUES INDICATED. :  LEFT  DROP  666©6©©©©©6  ©  X (VI  cn <  a  UJ  < n - 12 Oh  e> < < io 11-51-  t>  ooo  oo  ooo ooo  oo  CM  oo  oo-  oo  ooo  o  o  CO  Q < tr  i  o  O 10 5h UJ CO a.  IOOF  32  31  30  202  185  168  F i g u r e 40.  29  28  27  151  134  Tl7  OBSERVATION  FRAME  NO  NO-  26  100  22  18  8*  68  (X )  PRECEDING  52  36  20  COALESCENCE  Pseudo-radius v s . o b s e r v a t i o n no. (and frame no.) f o r v a r i o u s of the l e f t drop i n run 19.  dividing  s 4  o  6  CD H  O  o  OJ  IN)  ro  GO  OJ  I0  2  PSEUDO-RADIUS (Y) 9 cn  x  ft  (TOTAL  MAGNIFICATION  EQUALS  ro 6  24 x) OJ  6  cn  CD  ct  p< tr o CD i » P-  ct P-  ci  CO  -O  oi o  T| CD  _ 03  4 <1  o CO  H" O CO  13 t— ct . o 1  3  O  P.  >-b 4 SB B  CD  o  o 4 4 CO  P. (XJ.  m S2| z O '  OJ  *  co m  >  0D  n 3D  m o m o — o z o  z ™ o o  ro  >  CD  GO  o * O > m o> co o m z o rn  ro ro  GO  e6  I I I  •  3 c-o o - ©  i i i I i i I  9  I O ZD  < s  s s  ;  a  Co  i  ro  d  o  ro ro _ _ _ _ _ — — C O U l N l C C O S O I ^ U O ^ O O O cn cn o cn O o O o o o o e o e o o o o i\>  CD CO  © n  O X H  i ) :  5  n n n  n tt tt tt  O  TJ  GO CO O CO CO >  O H "0 m r m  H  m r z -< m  co > O  > I . ° o  co  _i m o m o  o  o z >  Ol m o  < o > o f- -o CO c (ft m > r o co aa 9  l  05  30 >  I-  00  o  °  — r~~  z o  m o r~ H  >  H  o m  p  o  w *  z  CO  o > r m  1 3 6 According to Table the  X-Y r e l a t i o n s h i p s  lines  consideredo  XI, f o r the l e f t  a l l showed z e r o  As w e l l ,  X-Y r e l a t i o n s h i p s  for  b o t h d i v i d i n g l i n e s were f i t t e d  as mentioned e a r l i e r .  were f o u n d  I n r u n 19  t o have z e r o  were f i t t e d , t o s e v e n  a l l b u t two o f slopes.  to polynomial  (extended)  the d i v i d i n g l i n e s measured i n the l e f t tions  o f them.  o f r u n 18,  slopes f o r a l l d i v i d i n g  f o r the r i g h t drop  the  drop  equations,  (Table X I ) ,  drop,  similar  the r i g h t drop,  linear.  two  out o f s e v e n  equations  These were t h e c o r r e l a t i o n s  l i n e s a t 1 5 5 ° a n d 1 ? 0 ° . No a t t e m p t of r u n 1 9 s i n c e the p r e d i c t i v e (extended) n a t u r a l l y apply, a range of X v a l u e s from  Input g r e s s i o n program  fitted  ( 4 5 ) from  output  well. were  was made t o f i t t h e d a t a  that  obtained f o r run 1 9 they are l i m i t e d to  2 6 t o 1 o b s e r v a t i o n numbers  a n d sample  equa-  f o r the l e n g t h s o f the  equations  except  for  However, f o r t h e l i n e  2 2 0 ° , a l i n e a r e q u a t i o n was f o u n d t o f i t r e a s o n a b l y In  Data  only.  data of the m u l t i p l e r e -  w h i c h t h e above p r e d i c t i v e  t i o n s were o b t a i n e d a r e shown i n A p p e n d i x  M.  equa-  1 3 7 DISCUSSION  A.  Applicable  1 )  Effect  of  i n drop  sizes, if  effect  of p e r s p e c t i v e  study i s well-known.  f o r example,  on p h o t o g r a p h i c images The  measurement o f d r o p  i s a f f e c t e d by t h i s  phenomenon i n t h a t  m e a s u r e m e n t s were made f r o m a p i c t u r e  situated and  Problems  Perspective  The used  Photographic  relatively  shape  t o the drop,  of the drop w i l l  t h e c a m e r a must be the t r u e  close  outline  n o t be  t a k e n by a  the t r u e  obtained.  p l a c e d a t an i n f i n i t e  3 0 0 mm.  focal  magnification l e n s was  l e n g t h l e n s ) was (Attachment  found  arrangement  o f 7 5 mm.  enlargement  of the  image o b t a i n e d by  o b t a i n e d w i t h t h e 7 5 mm. grainy picture s e t - u p was  of such a l e n s  a much l o w e r to telephoto  e x t e n s i o n tube. of the  a much g r a i n i e r p i c t u r e  than  l e n s plus extension tube.  i s h a r d t o t a k e measurements on,  adopted  (of  o b t a i n e d by u s i n g  t h e use  f o r t h e work d e s c r i b e d  a  sufficient.  o f an e x t e n s i o n tube  l e n s p l u s 7 5 mm.  o n l y produce  be  t o view  purposes,  t o produce  n o t p r a c t i c a l . ) t h a n what was  lens could  Theoretically,  o f the d r o p but- f o r p r a c t i c a l  In t h e p r e s e n t s t u d y , the use  dimension  distance  camera e q u i p p e d w i t h a t e l e p h o t o l e n s w i l l  camera  here.  the  an  Print  former that Since a latter  1 3 8 Resorting photography explained  t o the l e n s  - e x t e n s i o n tube  introduces a perspective  thus:  effect  space  both drops approach  focussed a t p o s i t i o n the l i n e  bisecting  the d r o p h o r i z o n the  tangential  point  each  i s a l o n g the Y^-axls,  other,  J  the distance-separating  or o u t l i n e ,  point  point  t h e two d r o p s ,  i n two-dimensions,  P(X^, " % ) . S i m i l a r l y , i s also  are symmetrical.  i s viewed a t  i s n o t shown  of t h e second  As t h e d r o p moves  coalescence w i t h the other drop, S-»0 and P-»S. the d r o p  outline  i s never viewed  a t a single  by t h e l e n s a t L t X ^ , 0 ) , w i t h r e s p e c t infinite  number  then  a corresponding  seen b u t t h i s  t h e second, d r o p a n d t h e p o s i t i o n  tangential  then, i f a l e n s i s  L(XJ , 0) a n d a l o n g t h e X ^ - a x i s , which i s  on t h e o t h e r d r o p  because  c a n be  ( F i g . 42 - e x a g g e r a t e d f o r c l a r i t y )  whose common a x i s w i t h a n o p p o s i n g d r o p that  which  I f one a s s u m e s t h e d r o p t o be a s p h e r e o f  a radius r i n free  and  system o f  toward  Therefore,  fixed plane,  t o time, but a t an  o f planes a s , i n two-dimensions,  at P(X , Y ) d  d  a n d a l o n g t h e a r c P S;.,  The tangential  locus  location  o f P(X^, Y ) , a s g e n e r a t e d from i t s d  to i t s final  position  shown i n F i g . 4-3 f o r two s p h e r i c a l in.  The f o r m e r d i a m e t e r s i z e  t h e maximum number 19  (Appendix  described  I).  i n this  EXPERIMENTS".  thesis  d i a m e t e r s , 0.108 a n d  i s t h e one u s e d  of successive The l a t t e r  (at the o r i g i n ) , i s  film  frames  i n calculating i n r u n s 18 a n d  l s the diameter of b a l l b e a r i n g s  under the heading,  The e q u a t i o n o f t h e l o c u s  c a l c u l a t e d and found t o b e :  O . I 5 6  "STEEL  BEARING  o f P ( X , Y ) was d  d  139  F i g u r e 42.  Sketch f o r the d e r i v a t i o n of E q ( 1 0 ) . o  140  141  where Y  d  = d i s t a n c e a t any time o f p o i n t optical axis  X  d  P from the  (X^-axis), i n .  = d i s t a n c e a t any time o f p o i n t  P from the  common a x i s o f t h e two s p h e r e s X^ = o b j e c t r  c o n j u g a t e , e q u a l s 5»09 i n .  = r a d i u s of sphere, i n .  Appendix  G shows how E q . (10) was o b t a i n e d .  X^->0.108/2  i n . and a s  X^-^0.156/2  e q u a t i o n s c o n t a i n e d r = 0.108/2 O.O78 X^ =  ( Y ^ - a x i s ) , in»  i n .respectively,  0.054, X^  = O.O78  I n P i g . 43, a s  i n . f o r c u r v e s whose  = 0.054 i n .  Y increases  and r =  Indefinitely;  a r e , t h e r e f o r e , asymptotes.  i n t e r s e c t i o n with the a x i s  i s a t (0,0)  since  0.156/2 =  the l i n e s The o n l y  the drops,  which  are r e p r e s e n t e d here a s spheres, c o a l e s c e a t t h i s p o i n t . f i n d i n g s a r e e a s i l y deduced it  was d i f f i c u l t  t h e maximum d r o p  from  0.002  in.  to  0  that appeared  i n t h e space between them,  frame n o . 202). The a p p l i c a b l e  s i n c e when Y  d  =  i n F i g . 43 c o v e r e d b y t h i s  Therefore, Y  span  of Y  0 the  r e p r e s e n t e d here as spheres, f i n a l l y area  i n r u n 18,  s e p a r a t i o n was t a k e n f r o m r u n 19 a s a b o u t  0.004 i n . ( i n f i l m  0.002  Since,  t o d i s t i n g u i s h t h e d i s t a n c e b e t w e e n d r o p s due  to the dark b l o t c h  mately  f r o m E q . (10).  These  d  d  i s approxi-  v a l u e s was t h e n  two d r o p s , w h i c h a r e  meet a n d c o a l e s c e .  The  span a n d i t s c o r r e s p o n d i n g X^  v a l u e s a r e s e e n t o be e x c e e d i n g l y s m a l l .  The present  consequence  situation,  of a steep perspective f o r the  brought about by a c l o s e  object-to-lens  142 distance, apparent  which  will  increase  d i s t a n c e o f drop  The  "be i n v e s t i g a t e d a r e :  presence  w o u l d be e x p e c t e d .  o f image b l u r d  c a n be d e t e c t e d by k n o w i n g  goes from 0 , 0 0 2 i n , t o 0 ,  than the depth  This  ( 1 0 ) t o be 0 . 0 0 0 0 1 8  of f i e l d  change i n  obviously greater than e i t h e r  of  X^ a n d , t h e r e f o r e ,  in.  from  The d e p t h  of f i e l d  o f the above quoted  changes  t h e a r c P S a t i t s maximum l e n g t h (when  Y ) i s a t the t a n g e n t i a l p o i n t ) , d  i s w i t h i n the r e g i o n  sharp f o c u s .  The  Increase i n each p s e u d o - r a d i u s a f f e c t e d  movement o f P, from  the t a n g e n t i a l  drops approach  o t h e r i s e q u a l t o ( r - CK).  each  ( 0 . 0 5 4 i n . and O . O 7 8  ible  l e n g t h o f 0 . 0 5 cm.  pseudo-radii  point  i n the photographs,  d i s t a n c e of drop  of P(X£,  Y ) from d  the opposing drop  1 . e.,  2Y  d  For both r  8  s  discern-  ( 0 . 0 1 9 7 i n . ) i n t h e measurement o f t h e  camera l e n s a t L(Xj_,, 0  distance  S, a s t h e two  Compared t o a minimum  t h e above v a l u e f o r ( r - CK)  i s u n d e t e c t a b l e by p r e s e n t m e a s u r i n g  The  towards  by t h e  i n . ) , t h e v a l u e o f ( r - CK) o b t a i n e d was  f o u n d t o be l e s s t h a n 0 . 0 0 1 i n .  in  blur  i n . f o r spheres o f r = 0 . 0 5 4 i n . , and  is  the  I f the  t h e n image  was c a l c u l a t e d  0 . 0 0 0 0 3 i n . f o r spheres of r = O . O 7 8  of  of  separation.  change o f X^ i s l a r g e r  P(X£,  blurring,  i n p s e u d o - r a d i u s , and f a u l t y assessment  by how much Xa c h a n g e s a s Y  Eq.  image  methods.  s e p a r a t i o n a s viewed  ) i s n o t the true  distance since the  i t s corresponding point  i s different  ¥ 2S0 ( F i g . 4 2 ) , e x c e p t ,  through  from the t r u e  (by symmetry)  distance,  o f c o u r s e , when b o t h  drops  143 touch  each other  ference  (when P(X-|. Y ) i s a t S)»  i s negligible p  radii  of the study  portant  study  o u t l i n e c a n be c a r r i e d above b u t i t i s f e l t  effect  of p e r s p e c t i v e  for it  that only  of perspective  out a l o n g  Besides,  the  similar  c a l c u l a t i o n s show t h e ( F i g . 42) t h a t  findings will o f the d r o p  that this  on t h e e n t i r e  t h e same l i n e s a s d e s -  that these  portions  seems h i g h l y p r o b a b l e  given  changes i n s i z e a r e im-  t o be so i n s i g n i f i c a n t  that  a l l the remaining  f o r both  considerations..  of the e f f e c t  c a n be c o n c l u d e d  zero  itself< >  cribed  it  practically  i s such  and n o t the s i z e  A drop  d  when d e d u c e d f r o m e a r l i e r  nature  dif-  b e c a u s e a r c P S a t i t s maximum l e n g t h ,  or a r c ( X , Y ) S , i s s t i l l d  However, t h i s  d  D  conclusion  be  obtained  Furthermore, will  be  valid  e v e n t h o u g h t h e a c t u a l d r o p s a r e n o t p e r f e c t l y spherical»  2)  Effect  of R e f r a c t i o n  In d i s c u s s i n g t h e e f f e c t  of p e r s p e c t i v e ,  sumed t h a t no d e n s i t y g r a d i e n t was p r e sent« was t o be c o n s i d e r e d , refraction  as i n the p r e s e n t  i t was a s -  If this  gradient  work, t h e e f f e c t  of  on t h e p o s i t i o n a n d s h a p e s o f t h e o b j e c t must be  consideredo  When a r a y o f l i g h t mitted  b y ) one medium p a s s e s  travelling  i n (ioe-.being  into another having  tical  properties i t s direction  light  ray enters normally),  i s changed  trans-  different  (except  I.e., the r a y i s bent.  op-  when t h e F i g . 44  144 shows how  an  observer  some o p t i c a l l y ly  point  a distance  fractive  a i r medium a t E v i e w s p o i n t  d e n s e medium, say,  sees an a p p a r e n t p o i n t  Therefore, at  i n an  0 will  water.  The  I i n s t e a d o f the  observer  real  index  f a c t o r o f -*= p r o v i d e d  the  actual-  image a t  a c t u a l l y a p p e a r c l o s e r t o the  i than i t a c t u a l l y i s a t distance  0 in  0  o  surface  o, by  a  re-  i n c i d e n t rays are  par-  ty axial,  w h i c h means t h a t  (5'0).  the normal passing  I f the  through p o i n t s  a d i r e c t i o n normal closer  t o the  distance the  the  surface w i l l  considered. water with  light  the  A light  that  i t will  having  a different  be  field,  as  the  concentration  borne  be  a c t u a l l y appear  0 with  ray w i l l  phase  i n m i n d t h a t F i g . 45  be  (MIBK-saturated methanol),  m e d i a i n the  (air).  order  index.  behave a s  that  named  To  complicate  sketch  continuously gradient  represents  in Fig.  i t enters  s o l u t e d i f f u s e s i s made up  or d e n s i t y  to  (51)«  surroundings  still  b e n t e a c h time  bent  respect  (the e x t r a c t i o n c o l u m n ) t o  i n the e x a g g e r a t e d  that a light ray w i l l  from  r e f r a c t i n g m e d i a must  the  three  object  refractive  r e g i o n w h e r e i n the  and  axis  i s viewed  o over  continuous  (glass),  p a s s f r o m the  camera l e n s .  gradient  of p o i n t  work, t h r e e  rays encounter these  except  the  0 will  the  with  1 than i t a c t u a l l y i s a t  to distance  the  object  d i s s o l v e d s o l u t e , a c e t i c a c i d or  The  rays  i . e . , the  at a distance  present  e x t r a c t i o n column  the  0,  small angle  i s located along  surface, point  equal  the  as  I and  These a r e the  make o n l y a  apparent depth  be  In the  can  observer  t o the  surface  o and  they  as  field. a map  a medium the  of a  matter, density  o f F i g . 45  so  9  i t passes  through  ( I t should o f the  44  be  density  1 4 5  Figure 4 4 .  S k e t c h s h o w i n g t h e image o f a p o i n t i n w a t e r when v i e w e d f r o m a i r .  located  146  Figure 4 5 »  Isosolute i n time.  lines  b e t w e e n two  drops a t an  instant  147 gradient in  a t an  instant  i n time.  degree  also  ferring figure which the  of r e f r a c t i o n  changed  interval  c a n be t o Figo  The  visual  simplifying  44  thinks  I f one  the d e n s i t y  gradient  of s o l u t e  be v i e w e d a t I , a n d a t any field,  changes radius  diffusion,  I will  imagines a  surface w i l l  in this  since  The  As  point  s y s t e m must f i r s t  the e n t i r e  be  the d e n s i t y  One  c a n o n l y assume d i s t o r t i o n  negligible gradient  and  camera  time©  I constantly pseudo-  d r o p image i s c o n i s not  g r a d i e n t map  obtained as a f u n c t i o n the  as  the d e p t h  extent of t h i s d i s t o r t i o n  work s i n c e  of  actually  varies with  i n i exceeds  appear b l u r r e d .  s u c h measurements a r e o u t s i d e  of the  of time  scope o f t h i s  project.  image b l u r e r r o r s  t o be index  due  t o the p r e s e n c e o f a  small r e f r a c t i v e  field  i n the neighbourhood  o f t h e d r o p s o b t a i n e d by  o f the methanol  solute.  Also,  procedures f o r pseudo-radius are not tect  i n each  o f t h e w a t e r medium  v a r y s i n c e 7^  and  use  the g l a s s  i f one  0 on t h e d r o p  c o u l d be a f f e c t e d  time  t h e s i t u a t i o n and r e -  i n p o s i t i o n w i t h t i m e , measurements of the  calculable entire  and  t i m e , t h e e x t e n t o f change point  over a f i n i t e  o f the a i r medium i n t h i s  i s zero and  i will  tinuously distorted.  the  effect  o b t a i n e d by 0  therefore,  r a y s being observed are  as r e p r e s e n t i n g both the a i r and  region  If,  of the l i g h t  with time.)  l e n s a t E, t h e n a p o i n t  the  concentrations  t h e p r e s e n t e x p e r i m e n t s change w i t h time a n d ,  the  of  However, t h e  changes  less  t h a n 0 . 0 5 cm.  the p r e s e n t measuring  sensitive  enough t o  de-  ( i n the photographs) o f which  above e f f e c t s a r e e x p e c t e d t o  contribute.  148 B.  I n t e r p r e t a t i o n of Data  Over the i n t e r v a l 3 2 S X S 2 6  i n F i g s . 40 and 41, any  dependency r e l a t i o n s h i p t h a t may show must be t r e a t e d with c a u t i o n s i n c e there a r e only s i x f i l m frames sampled f o r curve f i t t i n g over a p o p u l a t i o n of 1 0 2 f i l m frames, interval 2 6 > X > 1 , 1 0 0 frames,  whereas over the  which i s e q u i v a l e n t t o a p o p u l a t i o n of only  there a r e t w e n t y - s i x frames sampled.  sample s i z e i n the former p o p u l a t i o n w i l l ,  The s m a l l e r  t h e r e f o r e , provide  a r e g r e s s i o n equation l e s s u s e f u l f o r p r e d i c t i v e purposes w i l l be o b t a i n e d from the l a t t e r  than  sample.  Data over the I n t e r v a l 3 2 S X > 2 6  (corresponding t o  1 0 2 f i l m frames) was i n c l u d e d i n order t o supply a d d i t i o n a l i n f o r m a t i o n on r u n 19 w i t h i n the drop growth-free frames.  zone of 800  U n f o r t u n a t e l y , t h i s d e c i s i o n was made a f t e r  pseudo-radius  measurements on r u n 18 and no f u r t h e r a c t i o n was  taken f o r t h i s r u n t o match the a d d i t i o n a l treatment on r u n 1 9 « parts:  performing  performed  In t h i s s e c t i o n , r u n 1 9 w i l l be d i s c u s s e d i n two  One, f o r data over i n t e r v a l 2 6 ^ X 2 1  data over the i n t e r v a l r u n 19 over the f i r s t  3 2 > X > 1 .  and the other, f o r  Then r u n 18 i s compared with  of these i n t e r v a l s .  However, i n f i t t i n g  curves f o r r u n 1 9 , the r e g r e s s i o n equations were obtained d a t a over the i n t e r v a l 3 2 S X S 1  s i n c e these  n a t u r a l l y a p p l y t o the i n t e r v a l 2 6 > X ^ 1  from  same equations  except t h a t the value  of the equations may be somewhat r e s t r i c t e d w i t h i n the i n t e r v a l mentioned a s a l r e a d y noted. s u b j e c t w i l l be made l a t e r .  F u r t h e r remarks concerning  this  149 A n a l y z i n g the upper r e g i o n of the l e f t drop  (covered  by l i n e s 7 0 ° , 1 0 0 ° , and 1 3 0 ° ) i n run 1 9 ( F i g . 40) one can see t h a t , over the i n t e r v a l 2 6 > X > 1 , corresponding t o a time i n terval  o f from  0 o 0 3 4  sec. t o the onset of coalescence, the  curve o f l i n e 7 0 ° f l a t t e n s curves o f l i n e s  1 0 0 °  and I  out as X tends t o 1 . 3 0  0  However, the  slope upwards, but a l s o f l a t t e n  out over the l a s t f i v e o b s e r v a t i o n nos. before the onset of coalescence. sec.  In other words, between  0 . 0 3 4  sec. and  p r i o r t o the s t a r t o f coalescence the drop  appears  interface  t o reach upwards a t that segment or r e g i o n ( d e s c r i b e d  by p o i n t s of i n t e r s e c t i o n viding  0 . 0 0 5 4  and t h e i r v i c i n i t i e s ) where the d i -  l i n e s 1 0 0 ° and 1 3 0 ° i n t e r s e c t  the l a s t few s p l i t  Within  seconds (corresponding t o about the l a s t  f i v e o b s e r v a t i o n nos.) i t s motion.  the i n t e r f a c e .  the i n t e r f a c e  Likewise, from X =  2 6 ,  concerned 0 . 0 3 4  seems t o stop  sec. (from Appendix  K) t o the onset of coalescence, the r e g i o n of i n t e r f a c e c r o s s e d by l i n e 7 0 ° appears  t o have i t s outward movement  arrested.  There are no s i g n i f i c a n t changes observed  i n the  l e n g t h s of d i v i d i n g l i n e s b e l o n g i n g t o the upper r e g i o n of the r i g h t drop  i n run 19 ( F i g . 41).  In the lower r e g i o n (covered by d i v i d i n g l i n e s 2 5 0 ° ,  and 280°) of the l e f t drop line  i n run  the i n t e r v a l  2 6 > X > 1 ,  relationship  having a n e g a t i v e s l o p e .  2 2 0 °  1 9  2 2 0 ° ,  ( F i g . 40) over  i s r e p r e s e n t e d by a l i n e a r The curve of l i n e  i s l i k e w i s e shown t o slope downwards and then f l a t t e n out  2 5 0 °  1 5 0 towards X = 1 while  gradually rally  the curve  of l i n e  280° i s gene-  t a k e n t o have z e r o slope,, i m p l y i n g no d e p e n d e n c y  rela-  tionship.  In t h e lower (Fig.  26>X>1,  41) o v e r t h e i n t e r v a l  220° and  drop  the curves of l i n e s  Although both  curves appear  dependency" c o n c l u s i o n i s a r r i v e d a t a f t e r  the r e l a t i v e that  wavy, t h e considering  l a c k o f any a p p r e c i a b l e Y changes and o b s e r v i n g  t h e maximum r a n g e  lateral  i n run 1 9  2 5 0 ° c a n be c o n s i d e r e d t o have no o b s e r v e d d e p e n -  d e n c y o f Y upon Xo "no  r e g i o n of the r i g h t  direction,  o f movement  i e , 0  o  o f t h e wavy c u r v e  twice t h e i r amplitudes,  i n the  i s less  t h a n t h e measurement e r r o r  o r t h e minimum d i s c e r n i b l e  change  in  (0,05  0,0016  Y w h i c h c a n be m e a s u r e d  ft.  i n F i g . 4 1 ) , so t h a t  lines  220° and  the e q u a t i o n s f o r both c u r v e s of  2 5 0 ° a r e " f i t t e d t o the e r r o r s " only,  same c o n c l u s i o n a p p l i e s a l s o line  cm. o r a p p r o x i m a t e l y  280° i n the l e f t  shows no s i g n i f i c a n t  drop,)  t o the a n a l y s i s  (The  o f the curve of  L i n e 280° o f the r i g h t  drop  c h a n g e s i n t h e measurement o f i t s l e n g t h .  I t must be p o i n t e d o u t t h a t , w h e r e a s c e r t a i n m e n t s o f c u r v e s f o r v a r i o u s d i v i d i n g l i n e s a l s o may a  change i n Y, o r p s e u d o - r a d i u s ,  ximately  O0OOI6 f t . i n F i g s ,  o r t h e minimum d i s c e r n i b l e curves, e g,, that 0  in  for line  F i g , 41, show a d e f i n i t e  value.  less  t h a n O 0 O 5 cm  0  seg-  exhibit or appro-  40 a n d 41, t h e measurement  change  i n Y, s u c h  segments o f  1 4 5 ° o v e r the I n t e r v a l overall  error  2 6 > X > 1  t r e n d towards a h i g h e r Y  On t h e o t h e r hand, t h e o v e r a l l  t r e n d o f the curves  151 220°  for lines is  towards  ment f r o m of  and.  a fixed  250°  mentioned  i n the p r e c e d i n g paragraph  Y v a l u e , and i n these cases the d i s p l a c e -  t h i s v a l u e by t h e c u r v e s o v e r t h e s p e c i f i e d  X i s relatively  small.  Therefore, l i n e  145° i n t h i s  example c a n r e a s o n a b l y be c o n s i d e r e d t o i n d i c a t e relationship  behaviour of the lower r e g i o n s o f the drops can  interpreted physically  paragraphs back  i n a way  f o r the upper at  for  The same goes  example.)  d e s c r i b e d a s t h e "zone  t h e zone  by l i n e s  170°,  170°,  195°  220°  and  i n the l e f t  185°,  145° a n d 155°  26>X>5.  For  line  f o r the r e g i o n s of the drops  region  no s i g n i f i c a n t  r u n 19  a n d 280° a s shown i n P i g . 46,  r u n 19, t h e b e h a v i o u r o f t h e i n t e r f a c i a l  t e n s o u t , whereas t h a t  in  region  i n the  145°, 155°,  ding l i n e s  (The l o w e r d r o p  of drop approach",  o f drop approach  interval  are  given f i v e  as mentioned  curves f o r l i n e s the  to that  discussions.  For in  similar  regions.  220°, 250°,  includes l i n e s  succeeding  a dependency  o f Y upon X.  The be  range  At  changes  185°,  and  and 195° indicate  X«=5,  of l i n e  155°  i n F i g . 40.  The  a n upward t r e n d  over  145° f l a t -  c o n t i n u e s upward.  observed i n the l e n g t h s of  There divi-  195°.  the above-mentioned  region  c a n a g a i n be i n t e r p r e t e d of the r i g h t  i s described  the curve of l i n e  ( F i g . 41) o v e r t h e i n t e r v a l  250°  drop,  drop  of the r i g h t  26>XSl,  similarly  (also  drop  the curve of  t o those of l i n e s  shown i n F i g . 41).  1 5 2  LEGEND 1 2 3 4 5  F i g u r e 46„  Equations behaviour run 1 9 o  -  70° 6 - 170° I00„ 7 - 185° l30 8 - 195° 145. 9 - 2 2 0 155 10 - 2 5 0 II - 2 8 0 o  o  f i t t e d o v e r 0 - 2 0 2 f i l m f r a m e s and observed over 0 - 1 0 0 f i l m frames, i n  153 Thus, t h e r e seems t o be n o d e p e n d e n c y o f Y on X f o r l i n e 195° for  t h e X range  s p e c i f i e d above.  near having p o s i t i v e  slopes.  The c u r v e  an upward t r e n d a t t h e same time tion to level of l i n e  185° i s t a k e n t o have  are l i -  145° e x h i b i t s  showing a n o t i c e a b l e X = 1.  inclina-  The c u r v e  zero slope.  marks i n F i g . 46 show t h e v a r i o u s l o c a t i o n s on  interface  e x h i b i t i n g pseudo-radius  changes over t h e i n -  26>X>1 e x c e p t f o r l i n e 170° o f t h e r i g h t d r o p whose  terval  applicable results  interval  i s 26 2 r X > l 4 .  shown i n t h i s  figure  i s due t o t h e f a c t  that  segments o f c u r v e s f i t t e d  I t s h o u l d be n o t e d  are different  38 f o r t h e same r u n a n d o v e r rence  a n d 170°  of l i n e  o f f a s t h e c u r v e moves t o w a r d  The the  L i n e s 155°  from  those  t h e same i n t e r v a l .  This  F i g . 46 r e l a t e s  over a wider  diffe-  time p e r i o d  (corres(corres-  t o the i n t e r v a l  3 2 > X 2 l ) t h a n f o r F i g . 38  ponding  t o the i n t e r v a l  26>XSl).  As a r e s u l t ,  t r e n d was e s t a b l i s h e d  of F i g .  t o t h e 26>X>1  ponding  of a l o n g e r term  that the  the presence  t h a n c o u l d be shown i f  o n l y t w e n t y - s i x o b s e r v a t i o n n o s . were c o n s i d e r e d f o r c u r v e ting.  O b s e r v a t i o n s must be t a k e n o v e r a s u f f i c i e n t  v a l u e s o f the independent curve  variable,  range o f  X, so t h a t a n e m p i r i c a l  i s o b t a i n e d w i t h a shape a t a n y p o i n t w h i c h i s r e l i a b l e  for predictive an attempt  purposes.  Such a curve w i l l  i s made t o f i t d a t a t a k e n  ( F i g . 38) e s p e c i a l l y  riance  or repeated values i n " c l u s t e r s "  t h i s work).  n o t be o b t a i n e d i f  over a narrow range  values  stead  fit-  i f the data  show c o n s i d e r a b l e v a ( a s was t h e c a s e i n  T h e r e f o r e , F i g . 46 i s c o n s i d e r e d f r o m  o f F i g . 38 f o r s t u d i e s p e r t a i n i n g  of X  here  on i n -  t o the i n t e r v a l  262rX5L  154 Analysis  o f the i n t e r f a c i a l  l i n e s 70°, 1 0 0 ° , 130°, 145°, l i n e s 145°,  155°, 170°,  right  both  drop,  r e g i o n s d e s c r i b e d by  a n d 155°  i n the l e f t  I 8 5 , 195°, 2 2 0 ° , a n d 0  o f r u n 19, s u g g e s t s t h a t  250°  t o p r o g r e s s towards a h i g h e r value o f Y a s  o t h e r words, the i n t e r f a c e s at  those r e g i o n s d e s c r i b e d by the d i v i d i n g l i n e s However, c h a n g e s i n l i n e s  the l e f t  drop  the by  o f r u n 19 o v e r  opposite e f f e c t ,  magnitude further  o f the observed  investigation  For at  t h e same span  t o recede.  the p s e u d o - r a d i u s  show t h a t  appears  the lower  p a r t s o f the drops, and these took  c r e a s e a t two t e s t  left  drop  3 2 S X S 2 6 of  c u r v e s t h a t were o b t a i n e d  that  only the l e f t  t h e form  respect to experienced  of a pseudo-radius defrom the  and lower r e g i o n s of the t o those a s s o c i a t e d  with  discussion regarding the i n t e r v a l  f o r s i m i l a r behaviour drop.)  drop  One c o u l d s u r m i s e  t h e upper  (See a l s o e a r l i e r  the l e f t  (through which t h e  ( F i g . 4 6 ) . With  e x h i b i t e d movements s i m i l a r  buoyancy.  s m a l l so t h a t  o v e r t h e i n t e r v a l 26>X£;1,  locations.  preceding description  region described  t o i n c r e a s e a t some l o c a t i o n s i n  r e g i o n . o f both drops  changes,  just  i s necessary.  the upper  any  j u s t men-  seem t o show  trend i s r e l a t i v e l y  v a r i o u s t e s t l o c a t i o n s on t h e i n t e r f a c e pass)  t o bulge  F o r some o f t h e c u r v e s t h e  run 1 9 . the response  dividing lines  In  2 2 0 ° , 250°, a n d 280° i n  i . e . , the i n t e r f a c i a l  these l i n e s appear  concerned  X-»26.  o f both drops appear  tioned,,  i n the  o v e r t h e span  32SX>26, t h e t r e n d o f t h e segments o f t h e c u r v e s is  drop and  o f t h e upper  Accordingly, lines  and lower r e g i o n s  1 0 0 ° a n d 130° a r e  155 l e n g t h e n i n g whereas t h o s e ing,  o f buoyancyo  On  the  o t h e r hand, one  with considerable j u s t i f i c a t i o n c r e a s e s and  decreases  buoyancy b u t , dimensions  absence right  instead,  drop  of drop  o v e r the  interval  exhibit  a s s u m i n g no  o f the r i g h t  drop  32>X>26,  r a d i u s decrease  26 > X > 1  i f one  I n c r e a s e i n the  p s e u d o - r a d i i are e i t h e r  ly  f o r 3 2 ^ X S 1 , a mere 202  could, be  size  span  (whether  may  cannot  o f 800  be  in fact,  due  use the  divi-  over  inter-  of pseudo-  the l e n g t h s o f a l l  t o drop growth,  film  frames  drop-growth  t o t a l absence  be a c c o u n t e d  combination:  the  t o the  evidence  free  f o r by  o f any  frames.  i n F i g . 41  used In  i s about  volumetric  decreases  three f a c t o r s ,  The  especial-  have b e e n  o r d e r o f magnitude g r e a t e r than the average  radii  due  c o n s i d e r s a l l the  o f change o f p s e u d o - r a d i u s  The  (The  i n c r e a s i n g or remaining constant.  i n drop  growth r a t e .  offset  lower r e g i o n s of  o r 3 2 > X > 1 ) , no  increase  the r a t e  be  drop growth.  i n P i g . 41  i s p r e s e n t , and,  out of a p o s s i b l e  and  of  changes.)  however, t h a t  v a l s 26>X>1,  in  indicative  thereby o v e r l o o k i n g those r e g i o n s t h a t  pseudo-radius  Now,  fact,  i s not  of i n -  p o i n t s i n t h e s e r e g i o n s compared w i t h  zone o f d r o p a p p r o a c h ,  since  combination  distortion,.  changes i n the upper  measuring  ding l i n e s  the  could expect  o f some p a r t s o f a d r o p must n a t u r a l l y  o f any  of fewer  that  i n pseudo-radius  by d e c r e a s e s i n o t h e r p a r t s ,  an  decreas-  c o r r e s p o n d i n g t o the d r o p m o v i n g upwards u n d e r the i n -  fluence  may  220° and 250° a r e  of l i n e s  i n pseudo-  a c t i n g alone  or  156 1.  drop regions  e x h i b i t i n g decreases  r a d i u s were n o t 2.  considered, i n the  d r o p volume i n c r e a s e d due in  3°  the  system,  d r o p was  result  changes w i t h i n the sulted  in liquid  very  "spring"  r a p i d growth r a t e .  s y s t e m i s meant, n o t  suddenly increased,  of a decreased  to possible  oscillating.  ,'!spring" i n the  f l o w r a t e was  measurements,  and  Item 2 a n d / o r 3 c o u l d e x p l a i n the  By  i n pseudo-  pressure  but,  i n the  rather,  being  "squeezed  out"  the  that, as  dispersed  s y s t e m e n c l o s i n g the  that  phase  the  volume,  d i s p e r s e d phase  i n t o the  drops.  reThe  d i s p e r s e d phase p r e s s u r e  i n s i d e the  l i n e s l e a d i n g to the  nozzle  drop r a d i i  increased,  would f a l l  ship being,  for a  as  the  the  glass  relation-*  s p h e r i c a l drop,  (11) r where  A  = pressure  p  the  d i f f e r e n c e b e t w e e n the  continuous  dyne/cm. -  r  = drop r a d i u s ,  periphery within  interfacial  reduction  tension,  line.  ( P j ) , g i v e n byAP = P^  i n the  line,  creased  or,  duction  i n pressure  i f the  -  P^,  dyne/cm.  in interfacial  tension along  i n a lowering  Then, f o r example,  trapped  and  cm.  would a l s o r e s u l t  the  (Pg)  2  d  Similarly,  phase  drop  relatively  would a l l o w  the  of the  the  pressure  flexible,  tubing walls  drop  pressure  i f an a i r b u b b l e  t h i s would expand as  t u b i n g was  the  to  the  was der re-  contract  157 on  the l i q u i d  the  contents.  E i t h e r mechanism w o u l d r e s u l t  "squeezing out" of l i q u i d  therefore,  into  the d r o p s .  toward  ( I t s h o u l d be n o t e d  p r e s e n t work, n y l o n t u b i n g was than glass for  or metal  example,  used.  T h i s i s more  tubing, certainly,  t h e d r o p were o s c i l l a t i n g  c o u l d move i n a manner s u c h  r a d i u s as viewed  that  i n e l e v a t i o n was  the  as viewed  no  i n f o r m a t i o n on b e h a v i o u r  no  oscillations  for  r u n 18 frames  borne  r e s p e c t i v e l y were v i e w e d  t o time p r i o r  No  in  degree  F i g . kl  900;  up  due  the to  of run  19  i t will  o f 2000  (A t o t a l  i n these runs.) and  900  these frames  be  I t must prior  proportional exposed  (5000 p p s ) .  Therefore, with  i n c r e a s e i n drop oscillation.  and  frames  were  t o i t s s e t speed  p a t t e r n s were o b s e r v e d a l s o . of c e r t a i n t y ,  However,  i s a c e t i c a c i d ) and  here are not n e c e s s a r i l y  building  c o u l d n o t be  therefore,  (The number o f  about  o f 1500  the f i g u r e s  to coalescence since  the c a m e r a was  oscillation  a fair  pps.  solute  were p r o j e c t e d s i m i l a r l y .  i n mind t h a t  and,  pictures  o f t h e s e were m e a s u r e d . )  (where t h e  t o c o a l e s c e n c e mentioned  while  202  o n l y the f i n a l  f o r r u n 15  films  be  o f 16  at a projection rate  that  The  when t h e m o v i e f i l m  o b s e r v e d b e f o r e c o a l e s c e n c e was  The  1500  in plan.  i n plan i s available.  were a p p a r e n t  the  b a l a n c e d by a c o r r e s p o n d i n g  i n t h i s work were e l e v a t i o n v i e w s ,  recalled  than,  i n c r e a s e i n pseudo-  obtained  frames  so  ( f a c t o r 3 above),  i n pseudo-radius  viewed  i n the  flexible  b u t much l e s s  decrease  was  that  and,  rubber.)  If drop  the n o z z l e t i p s  in  size  noted  158 The Smith  (12) and G r o o t h u i s and Zuiderweg  (13)  h y p o t h e s i s p r e d i c t s t h a t , f o r s o l u t e t r a n s f e r r i n g out of the drops, the l o w e r i n g of the i n t e r f a c i a l t e n s i o n a t the zone of  drop approach would r e s u l t i n the s t r e t c h i n g of the i n t e r -  f a c e a t t h i s zone.  In a d d i t i o n , i t i s b e l i e v e d t h a t f o r the  p r e s e n t work, as water i s swept out from between the drops d u r i n g the p r o c e s s of c o a l e s c i n g  (solute t r a n s f e r out of the  d r o p s ) , and i n the absence of drop growth, r e a c h out toward one another t o f i l l  these drops may  the v o i d .  (The drops  cannot move f r e e l y , b e i n g a t t a c h e d t o the g l a s s tubes. ) A l s o , w i t h low i n t e r f a c i a l t e n s i o n a t the zone of drop approach, the drops may bulge toward one another because of weak surface f o r c e s . drop contents i n . ly,  ( I n t e r f a c i a l t e n s i o n tends t o h o l d  I f i n t e r f a c i a l t e n s i o n i s weakened l o c a l -  the drop should bulge a t t h a t p o i n t .  traction condition  For the same ex-  ( t r a n s f e r out of the drops) t h i s  mechanism may operate even i n the Smith  last  (12) case where the  drops were f r e e t o move about i n the continuous medium.)  The i n c i d e n c e of pseudo-radius changes i s l e s s among the  r e g i o n s examined i n the r i g h t drop than i n the l e f t  ( F i g s . 38, 39. and 46).  drop  T h i s behaviour may have a d i r e c t  b e a r i n g on the t o t a l l a c k of pseudo-radius decreases i n the r i g h t drop of r u n 19 (extended) ( F i g . 4 1 ) . Now, the l e f t and the  r i g h t drops would be expected b a s i c a l l y t o behave  larly  a t any g i v e n i n s t a n t  simi-  (although i t should be borne i n  mind that t h e r e was apparent e m u l s i f i c a t i o n i n the r i g h t drop i n r u n 19).  Thus, the s e t s of pseudo-radius data f o r the l e f t  159 and by  the r i g h t averaging  effects of  drops are e s s e n t i a l l y  duplicates.  them, i t i s p o s s i b l e t o m i n i m i z e  that can a r i s e  Therefore,  the " s t r a y "  i f o n l y t h e measurements made on one  the drops i s c o n s i d e r e d .  (Such  "stray" effects  e x a m p l e , be due t o t h e d i f f i c u l t y o f d e t e r m i n i n g radius differences. ) A Y ,  The a v e r a g e  increment  t h e n was p l o t t e d a g a i n s t d i v i d i n g l i n e  number s e r v i n g a s t h e p a r a m e t e r 170°  ( F i g . 47).  was n o t c o n s i d e r e d due t o i n c o m p l e t e  In d e t a i l , A Y ' (left  small  with  ( s e e F i g . 47).  AY'  from the r i g h t  were o b t a i n e d  Then t h e v a l u e line  obtained  (Dividing  F o r example,  data. )  f r o m F i g . 40  by s u b t r a c t i n g t h e p s e u d o -  i n dividing  pseudo-radius  and  0.1235  0.1235  a t a chosen  values of  d r o p by u s e o f F i g . 41. dividing  line  drop  f t . and  Adding O . O O 3 5  145° i n t h e l e f t  at observation nos.  f t . gives O . O O 3 5  2 equals  i s an average v a l u e , A Y i n F i g .  f t . respectively.  the r i g h t  0.1233  ft.  32 and 1  Subtracting Similarly,  0.1264 f t . and  f t . , giving  0.0031  drop are  0.1200  0.0031  ( F i g . 40),  0.1200 f t .  f t . from  values are  f t . as the d i f f e r e n c e .  f t . t o g e t h e r and d i v i d i n g  O.OO33 f t . ( A Y ) . T h i s value  of A Y i s then  t h e sum marked  t h e a b s c i s s a a t d i v i d i n g l i n e 145°,  t h e o b s e r v a t i o n n o . 1.  47.  i n d i v i d i n g l i n e 145°  ( F i g . 41), t h e c o r r e s p o n d i n g  down on F i g . 47 a l o n g for  Corresponding  f o r e a c h d r o p a t t h e same  The r e s u l t  the  by  line  a n d t h e same o b s e r v a t i o n number a r e a d d e d t o g e t h e r a n d  d i v i d e d by 2.  in  pseudo-  observation  r a d i u s a t o b s e r v a t i o n n o . 32 f r o m t h e p s e u d o - r a d i u s o b s e r v a t i o n , number  for  i n pseudo-radius,  v a l u e s were d e t e r m i n e d  drop) f o r each d i v i d i n g l i n e  can,  (Note t h a t t h e n u m e r i c a l  60  80  100  120  DROP  140  160  DIVIDING  180  LINE ,  200  deg.  220  240  F i g u r e 47 < > Change i n drop shape i n run 19 as the time of c o a l e s c e n c e approaches, f o r the two drops,, ( T o t a l m a g n i f i c a t i o n o f / \ Y equals 24x.)  260 averaged  280  161 v a l u e s quoted physical  h e r e a l l a r e 24  system  since  present  in Figs.  40,  average  change  graph one  the o n s e t indicates  another  41,  include  and  47.)  toward  least,  Smith  since  (12)  interesting  the mutual p a r a l l e l i s m a r e a d j a c e n t t o each the l e f t  41), e t c . s i d e by  drop  185°  are l i n e s  reasonable  behaviour 185°  and  terfacial able ment.  point  other.  195°  195°  Pass  due  and  195°» 39«  (13)  o f r u n 19  is  lines  130°,  and  46,  For t h i s  and  145°  and  so  then i t i s of these  two  reason,  the  i n t e r f a c e where  lines  the e n t i r e i n -  lines plus a  o u t s i d e the b o u n d a r i e s  G e n e r a l l y s p e a k i n g , one  at  f o r example, l i e  to include two  1  220° and 250° ( F i g .  p o i n t s i n the d r o p  side  155°»  t o a l o w e r i n g of  i n the v i c i n i t y  these  toward  Zuiderweg  i n the a n a l y s i s  extended  This  approach.  ( F i g . 41), l i n e s  c a n be  on e a c h  be  characteristics.  two  frames  consistent,  are approximately p a r a l l e l  segment bounded by  portion  well  i n s u c h f i g u r e s a s 38,  of those  202  145° and  G r o o t h u i s and  185°  the  each  r e a c h out  Thus, l i n e s 100°,  that l i n e s  similar  from  o f most c u r v e s whose d i v i d i n g  t o assume t h a t l i n e s  lines exhibit  t o be  zone o f d r o p  ( F i g . 40)  and  Given  side  indicates  a s the o b s e r v a t i o n n o .  i s found  the b u l g e may  t e n s i o n i n the  One  145°  and  the  o r d i n a t e of z e r o .  the drops p r o g r e s s i v e l y  This behaviour  interfacial  in  Thus F i g . 47  of c o a l e s c e n c e a t an that  w i t h the  hypothesis  of  the m a g n i f i c a t i o n f a c t o r  i n t h e r e g i o n d e s c r i b e d by l i n e s  reached.  sizes  coalescence, starting  reaching a high point at l i n e is  the a c t u a l  i n shape o f b o t h d r o p s a s t h e y a p p r o a c h  o t h e r and p r o c e e d before  they  times  reason*  of the  seg-  c a n r e a s o n a b l y speak o f a " r e -  162  gion"  or  "segment" i n s t e a d  pseudo-radius terfacial  of  changes might  " p o i n t s " where c e r t a i n  occur  "points" exhibiting  so l o n g a s  drop  the v a r i o u s i n -  such b e h a v i o u r  have one  common  movemento  All for  l i n e s 155°  the  right  the l a s t  the curves of P i g s . and  drop, few  2 2 0 ° i n the l e f t  appear  split  to approach  seconds  (within approximately w o r d s , the d r o p s  the l a s t  exhibit  no  The  drop, drops,  interval  26SXS1  i s encountered  in  r u n 19  ( F i g . 46  on  the r e s u l t s  range  o f X was  anticipated  as  f o r r u n 18  of a l l these  considered.  i n the e a r l i e r X =  difficulties,  t o e l a b o r a t e on  the r e s u l t s  c o m p a r i s o n , o f r u n 18  and  145°  the f a c t  In o t h e r their  be  quite  i n the  that  casts  f o r which  of  sig-  understood.  right  i n both over  the  different  of X i s extended  t o F i g . 38)  ( P i g . 37)  within  the p o i n t  measured l i n e s  when t h e r a n g e  compared  m e n t s were t a k e n b e y o n d  changes i n  b e h a v i o u r may  Also,  in  of coalescence.,  changes i n p s e u d o - r a d i u s  ( F i g . 37) •  behaviour  start  1 0 0 ° and  of twenty  155°  zero slope at l e a s t  f o r i t are not  only l i n e s  show s i g n i f i c a n t  f o r those  for line  Interfaces near  for this  however, t h e r e a s o n s  out of a p o s s i b l e  except  drop and  significant  coalescence.  In r u n 18,  41,  5 observation nos.).  o v e r much o f t h e i r reason  and  b e f o r e the  pseudo-radius  nificant;  40  some  o n l y the  as  doubt limited  T h i s u n f o r t u n a t e b e h a v i o u r was part 26  o f t h e work so t h a t no i n r u n 18.  neither  will  any  Therefore, attempt  o b t a i n e d f o r r u n 18,  r u n 19  be  not  measurebecause made  nor w i l l  any  be made w i t h r e s p e c t t o t h e  163 effect  of solute  c o n c e n t r a t i o n on p s e u d o - r a d i u s .  the p l o t s  o f the f i t t e d  the r i g h t  drop  Co  o f r u n 18 a r e n o t  P r e c i s i o n of Drop  The  over the  32 2 X S 1 .  from  the n e x t  24X).  obtained, a t a p r i n t  T h u s , the e r r o r  io.05  d r o p s was  cm.  not  t o be made. enlarging.  reduced,  The  on the  C u t t i n g down on since  the  cm.  (about  Y  va-  0.0016  i n length that  m a g n i f i c a t i o n of  could 0.05  approximately  a dividing  line  i s taken  the o u t l i n e  of  The  a result  of  the  picture  the m a g n i f i c a t i o n would not  size that  Another  of superimposing  o f the  printed  produce  image w o u l d  be  i t w o u l d become h a r d e r t o measure source  the master  of e r r o r r e s u l t s  r e f e r e n c e p o i n t s P'  and  P"  the that  (e.g., i n  s h e e t , must a l w a y s l i e  the c o r r e s p o n d i n g spots i n e v e r y p r i n t l i n e s a r e measured from  from  sheet over e v e r y p r i n t  w h i c h a r e drawn on the m a s t e r  dividing  values of  (Of c o u r s e , t h e v a l u e ,  i n measuring  w i t h the r e s u l t  39 )s  I n most  of these three  0.05  by  g r a i n y image p r i n t e d was  b e i n g measured.  Fig.  one  T h i s e r r o r arose because  changes i n i t .  process is  methods.  s h a r p enough t o e n a b l e more a c c u r a t e measurements  a better result  size  i n t h i s work a r e  Each  difference  be m e a s u r e d by p r e s e n t m e t h o d s .  t o be  shown.  pseudo-radius measuring  t h e minimum d i s c e r n i b l e  was  for  Analysis  interval  lues i s different  cm.,  14-5°  t h e main d a t a r e v e a l e d o n l y t h r e e d i s t i n c t  obtained  ft.)?  100° and  experimental e r r o r s involved  obtained mainly from cases,  curves f o r l i n e s  Likewise,  these  since  the l e n g t h s o f  points.  164 Blurred o f r u n s 18 the  and  19»  non-flatness  process. )  spots  The  as mentioned e a r l i e r . of  the  the n e g a t i v e  blurred  o f image o v e r t h e lap  e x i s t i n c e r t a i n a r e a s o f the  spots  during  affected regions.  mentioned e a r l i e r ,  determination, a b o u t the  R  2  , m e a s u r e s the  mean Y e x p l a i n e d  by  the  to l o s s of  sharpness  regions  over-  naturally affected.  multiple  "proportion  the  to  photoenlarging  When t h e s e  d r o p o u t l i n e , measurements a r e  As  (These were due the  contribute  prints  coefficient of  of  total variation  regression".  From E q .  (9),  2 values value  of R of,  explains  close  say, 90$  centage.  0.9  of  to u n i t y  are  means t h a t  the  total  However, t h e r e  therefore  the  desirable  regression  since  equation  a  obtained  v a r i a t i o n , when e x p r e s s e d a s i s a e s p e c i a l danger i n t h i s  a  per-  meaning  2 since R  can  of  properly  can  t h e n be  if a  we  be  c h o s e n which f i t s observation  third-order  0.9323° rived,  The  and  given  close  19,  values  Y at  model  c e r t a i n number since a  data exactly. four  such as  the  range  value  For  shows t h a t  compared t o t h a t that  t o the  the  R  2  model  example,  d i f f e r e n t values  of  Eq  3  (5)  where m =  In T a b l e  of R  f r o m a low  e q u a t i o n f o r w h i c h an  f o r example,  p r e d i c t o r as  not  employing a  XII  d i f f e r e n t p r e d i c t i v e equations for various  The  0.9323°  by  through a l l f o u r p o i n t s .  i n r u n s 18  included.  of  the  p o l y n o m i a l model  Passes e x a c t l y  lines  simply  s e l e c t e d c o e f f i c i e n t s ' i n the  have an  shows t h e  made u n i t y  which dividing  f o r each l i n e  i s also  o f 0.5481 t o a h i g h value  of  X,  0.5481 was  of de-  i t i s basically a less useful e q u a t i o n h a v i n g R^  equal  to  number o f p a r a m e t e r s i n e a c h model i s  saturation point  (i.e.,  the  number o f  obser-  165 A more complex m o d e l ,  vations). could  provide  an  other  adequate a l t e r n a t i v e  than  the  one  to obtain a  used,  higher  2 value  of R  , assuming,  s i o n p r o g r a m had modelo  able  determine  As  provided well,  i f the  a  the  variable,  (44).  By  this  c o u l d be  repetitions  i s incorrect, 2  made t o a s s e s s R  the d e p e n d e n t v a r i a b l e ,  X,  a t the  Y,  r e q u i r e d data are not  having  different  the  equations  "best  indepen-  v a r i a n c e , (f  of R  and  presented  the  i n the  i n v o l v e s the  residual  a s many a s 70  variables (including of which can  dent  present  polynomial  be  was  handled.  t h a t were c a l c u l a t e d  t h e method o f l e a s t  X.  work.  squares.  by  of  c o n s i d e r a t i o n of the  the  pro-  designed  transformed  s e l e c t e d as  the  problem a f o u r t h - o r d e r  independent v a r i a b l e  highest-ordered  of  predictive  i s primarily  c u l a t e d v a r i a b l e s ) any  one  just  i n this  v a r i a n c e g i v e n by  handle  In the  not  computer p r i n t o u t s o f  incidentally,  variable.  and  in  s e t " o f X t e r m s among an a r r a y  T h i s program,  by  o f the  the p r o p e r  gram.  equations  repeat  o r more  same v a l u e  available  for selecting  the m u l t i p l e r e g r e s s i o n program values  run  to  suffers  i . e . , two  of the  o f t h e measurement o f Y a t the  A criterion  mial with  or  , provided  same v a l u e  t o o b t a i n an e s t i m a t e  avail-  f o r "lack of f i t "  i s meant a g e n u i n e r e p e a t e d  However, the  the  test  from the  " r e p e a t measurements", when m e n t i o n e d anywhere  thesis,  equation  "best" equation  statistical  measurements, a r e a v a i l a b l e dent  t h a t the m u l t i p l e r e g r e s -  p o s t u l a t e d model  from l a c k of f i t , measurements o f  of course,  and  various  polynothe  polynomial  p r o g r a m were  I t i s the  cal-  depen^  chosen to provide  The  to  obtained  same method a s  that  166  u s e d by ly  the l i b r a r y  a p p l i e d on  subroutine,  selection  the  the  as  having  pointed  an  w h i c h was out  values  of p r o v i d i n g the  equation  of X terms.  of E r and  is finally  the most i m p o r t a n t  terms  previous-  earlier,  of v a r i o u s models or e q u a t i o n s  relative  s t u d i e d , and  As  advantage  from good p o s s i b l e c o m b i n a t i o n s tions,  LQF",  the l i n e a r model.  p a r t i c u l a r p r o g r a m has adequate  "UBC  information i s 1.  the  an  computed equa-  variance  s e l e c t e d t o be  are  considered  included.  F o r e a c h r e g r e s s i o n a n a l y s i s ( A p p e n d i x M), lowing  user  From t h e s e  of r e s i d u a l  this  the  fol-  provided:  code name o f t h e  v a r i a b l e s i n the  subset  for regression analysis, 2.  regression  3.  standard  coefficients,  d e v i a t i o n s o f the r e g r e s s i o n  coeffi-  cients, 4.  a variance in  the  ratio  ("F"  value)  f o r each X  equation,  5.  i n t e r c e p t (constant  6.  standard  e r r o r of  7.  residual  variance,  8.  multiple correlation  coefficient  9»  multiple coefficient  of d e t e r m i n a t i o n  10.  term  a variance regression, freedom.  ratio with  term),  estimate,  ("F" the  value)  (R), (R  ),  and  f o r the m u l t i p l e  appropriate  degrees  of  167 Some o f t h e s e error  ( i t e m 7-),  equation  among t h e  6 or  c o u l d be general  while  A criterion  obvious.  item  ( i t e m 6)  of estimate  variance  7 and  terms are i s the  the  standard  square r o o t  the  residual  relation  hypothesis  equal  9«  As.:.well,  the  or R  2  one  can  use  (multiple c o e f f i c i e n t extra  accounted  information  f o r by  term i s p r e f e r r e d  the  the  "best"  variance  e i t h e r of  about  the  "F"  regression  "F"  based  on 10)  (item  by  the  coefficients  (variance  proportion  gained  of  9 is  item  ratio  regression  of determination)  equation  instead  8 to  item  However, i n t e ' s t i n g t h e  that a l l p a r t i a l  to zero,  of  of  e a r l i e r m e n t i o n e d t o be  taken i n t o c o n s i d e r a t i o n .  are  o f the  The  f o r s e l e c t i o n of  l o t was  item  Interrelated.  (52).  Because  of  of  use  in multiple  ratio)  sum of R , 2  squares this  regression  analysis.  As  pointed  of observations, (n-1)  n,  powers of the  out  the  t h a t the  number o f  polynomial  model u n d e r  the  a d d i t i o n o f a new  the  number o f p a r a m e t e r s  polynomial  sets  t h a n the number of p o t e n t i a l  X v a r i a b l e i n the  (Eq. ( 5 ) ) . p always i n c r e a s e R until n and  given  i s much g r e a t e r  consideration  equals  earlier,  power o f X i n the  passes through a l l data  will model  points,  p R  can,  t h e r e f o r e , be  made u n i t y w i t h o u t a t t a i n i n g a f u n c t i o n a l  r e l a t i o n s h i p between v a r i a b l e s .  The  up  (5),  t o the  f o u r t h power o f X  considered  t o be  sufficient  relationship  provided  has  s e l e c t e d the  properly  wise, an  the  (Eq.  use  of a polynomial  where m =  4)  model  was  t o c l o s e l y approximate the e x i s t i n g  m o d e l i s a d e q u a t e and  the  program  "best" regression equation.  a l t e r n a t i v e model may  have t o be  used.  Other-  168 The as  t o what p a r t i c u l a r  appropriate provides R  procedure  (R  i s to f i n d  the b e s t  S  form o f the p o l y n o m i a l  model i s most  t h a t a r r a n g e m e n t whose a n a l y s i s  combination  0 . 5 ) a t the  variances  followed i n a r r i v i n g at a decision  lowest  (also c a l l e d  o f the  X terms h a v i n g  p o s s i b l e value the  of the  sample v a r i a n c e ) .  a  high  residual  1 6 9 CONCLUSIONS AND  RECOMMENDATIONS  In t h e p r e s e n t work, d r o p  pseudo-radius  changes  were m e a s u r e d a s a means o f a t t e m p t i n g t o t h r o w l i g h t c o a l e s c e n c e mechanism o f d r o p p a i r s before dergo  the  The  r a d i o s oover t h a t p o r t i o n  reach  out toward  one  interfacial  The  time  coalesce.  This  interval,  t e r i z e d by a n on t h e  The  interval the  was  was  as a r e s u l t  b e h a v i o u r was  c o v e r e d by time  of  generally  r u n 1 9 o v e r the X i n t e r v a l  this sults  consistent  theless, shape  the a u x i l i a r y  drops began t o  variations.  26  Over  movements c h a r a c -  T h i s was  over t h i s to y i e l d  drop.  carried an  out  auxiliary  interval.  For  conclusive re-  o b t a i n e d o v e r the o t h e r i n t e r v a l . data i n d i c a t e d  mea-  i n various locations  3 2 to 2 6 .  investigation  with  Zuiderweg ( 1 3 ) .  g r e a t e r i n the l e f t  r e a s o n , t h e d a t a were l e s s l i k e l y t h a n were t h o s e  part  locally  0 . 0 3 4 sec.  of i n t e r f a c i a l  of pseudo-radius  s t u d y and n o t a c o m p l e t e  pseudo-  o b s e r v a t i o n nos.  of about  un-  the drops t e n d to  Drop p s e u d o - r a d i u s measurements were a l s o in  to  c o n s i d e r e d i n t h i s work was  the m a g n i t u d e  interface  that  the Just  i n the upper  i n s t a n t when the two  to a t o t a l  increase  i n the  ( 1 2 ) and of G r o o t h u i s and  interval  to 1 , equivalent  indicate  forces.  s u r e d backward from  observed  of the i n t e r f a c e  another perhaps  t h e h y p o t h e s i s o f Smith  this  variations  zone o f d r o p a p p r o a c h  lowered  i n a s p r a y column.  o n s e t o f c o a l e s c e n c e , t h e d r o p s were f o u n d  shape c h a n g e s .  o f the  on  the presence  of  None-  drop  170  Additional  work must f i r s t  w h i c h i n v e s t i g a t i o n was be  taken  t o be  influencing fully in  firmly  the  understood.  done i n t h e  concentrated before  conclusive  observed  be  drop  the r e s u l t s  F o r example,  0  the  A l s o , i n view o f the  statistical  cates,  small changes  tion,  t o see  how  the  curves  say, a r e needed f o r each experiment.  c o u l d be 145°  tests  line the  t e s t e d between c u r v e s , of a drop  i n the  current research are 1.  o f the e f f e c t s  b u o y a n c y upon d r o p mass t r a n s f e r ,  ciently  covers  hypothetical Smith Such a  (12)  those  repli-  f o r the In a d d i -  framework o f  the  that  suffi-  entire  response  time  of  the  G r o o t h u i s and once a n d  constant with  f o r a l l , provide to a l l i n c i -  shape o t h e r  of the time  by  (13).  Zuiderweg  p r o p o s i t i o n w o u l d be densities  the  mechanism a d v a n c e d  e x e r t e d by mass t r a n s f e r o  e q u a l , and  and  the i n f l u e n c e  amount o f c o r r e c t i o n due  w h i c h the  growth  interval  coalescence  and  of drop  o v e r an  f o r c e s a f f e c t i n g drop  excellent for  those  shape, w i t h o u t  study would,  the r i g h t dental  trend,* 6  to  offered:  Determination  of  observed  the need  experiments.  f o l l o w i n g s u g g e s t i o n s w i t h i n the  yet  Then c o n s i s t e n c y  f o r example,  6 replicate  could  forces  shape v a r i a t i o n s a r e n o t  some o f t h e v a r i o u s p s e u d o - r a d i i m e a s u r e d , and  apply  area i n  Of  course,  t o use two  than  a  an  system  p h a s e s were  (i.e.,  when mass  * See e a r l i e r comments u n d e r T o p i c C, DISCUSSION on n e e d f o r t e s t i n g " l a c k o f f i t " f o r a n y assumed model t h a t may have a low value.  1 7 1 t r a n s f e r was  occurring),  the f o r c e s due system 2.  t o buoyancy.  w o u l d be  A study of drop over a in  time  so a s  hard  to  However, s u c h  shape b e h a v i o u r  interval  o f any  short-time study.  carried  longer than that  long-term  ments w h i c h m i g h t  to  used  used  interfacial  i n the  T h i s p r o p o s a l c a n be  move-  over  the  present  applied  to  the  r e m a i n i n g unmeasured p o r t i o n s o f the  films  concerned.  to  I t may  be n e c e s s a r y a l s o  v i s e a method o f d e t e r m i n i n g the e x a c t span  that  i s drop  than i s p o s s i b l e sphere  3.  on  determine  have b e e n m i s s e d  interval  f o r a drop  I t w o u l d be drop  calculation.  to determine optically  of  spheres  i n p l a c e of drops  so t h a t  the  remains  constant.  spheres  so a s t o p e r m i t  solid  should  the r e l e a s e  m a t e r i a l which c o u l d e n t e r each a bored passage.  refrac-  study c o u l d  t h e use  porous  the  ( i f at a l l )  by  be  how  c o n t i n u o u s phase i n  T h i s proposed  The  frame  of a  o f the e x i s t e n c e of a  out perhaps  de-  accurately  substitution  i n d e x g r a d i e n t i n the  carried  more  i n making the  shape i s d i s t o r t e d  t h e p r e s e n t work. be  the  interesting  as a consequence tive  growth-free by  a  find.  the p r e s e n t r e s e a r c h so a s  the f o r m  to eliminate  sphere  shape possibly of  solute  through  A l s o , measurements c o u l d be  made o f any by  the  c o n t r i b u t i o n to o p t i c a l  square g l a s s  parallelism (e.g., 4.  5»  of w a l l s  i n the  search  further  Zuiderweg  in  i n the  the  Smith  ( 1 3 ) ,  discussion.  interfacial to  ( 1 2 ) and  would  tension  the  theory  Groothuis  and  triggers interfacial  of t h i s  interfacial  present  motion.  system would h o p e f u l l y movements r e l a t i v e l y  work.  t h a t may  Then any  important  have p a s s e d u n d e t e c t e d  revealed.  Such a t e r n a r y  have p h y s i c a l p r o p e r t i e s particular work, a s ,  indeed,  the  The at  study other  determine This  of the  greater  i n some  experiments.  the  research  respects.  changes i n the  could  so f a r m i g h t  MIBK-methanol-water  e n t i r e drop  suggestion  the  behaviour  s u i t e d to  c r o s s - s e c t i o n s of the the  result  s y s t e m must  r e q u i r e m e n t s of the  system d i d , a t l e a s t  6.  non-  measuring e r r o r s ,  i n magnitude than those a t t a i n e d i n  be  of  imperfections  system t h a t  that, according  p r o p o s e d by  use  and  for a ternary  increase  Imbalance  The  and/or g l a s s  reading  outlined earlier  The  a result  striations).  Reduction as  column a s  distortion  shape  imply  pseudo-radius drop  to  characteristics.  further  complete  However, f u r t h e r s i m p l e  steps  1 7 3 c o u l d be in  taken  w i t h use  the p r e s e n t  provide along  study.  of the f i l m s These c o u l d be  f u r t h e r pseudo-radius  other d i v i d i n g  obtained  lines  used  to  measurements  than  those  measured  so f a r .  7.  Replacement as  of the n y l o n  tubing that  t h e d i s p e r s e d phase l i n e  material  (e.g.,  the p o s s i b i l i t y  stainless of  served  w i t h a more  steel) to  rigid  prevent  " s p r i n g i n e s s " i n the  system.  8.  The  study  of t e r n a r y systems w i t h  opposite d i r e c t i o n from  the  continuous  see w h e t h e r o r n o t consistent with earlier  9«  ( 1 2 ,  of  solute transfer, i . e . ,  t o t h e d i s p e r s e d phase the b e h a v i o u r  the  sizes  general  would  the h y p o t h e s i s r e f e r r e d  be to  1 3 ) .  A device f o r producing equal  the  metered drops  of  s i m u l t a n e o u s l y would r e s u l t improvement  of the  in  experiments.  to  174  LITERATURE  CITED  1.  Thomson, J . , P h i l , Mag., 10,' Ser. 4 , 3 3 0 ( 1 8 5 5 ) .  2.  S t e r n l i n g , C V . and S c r i v e n ,  3.  whitman, Chem. and Met. Eng., 2_9_, No. 4 , 146 ( 1 9 2 3 ) .  4.  Ward, F.H. and Brooks, L.H., Trans., Faraday S o c , 48, 1124  5»  L.E., Nature, 187. 186 (I960).  (1952).  Sigwart, K. and N a s s e n s t e i n , H., Naturwissenschaften, 42, 458 ( 1 9 5 5 ) .  6.  Sigwart, K. and N a s s e n s t e i n , H., Ver Deut. Ing. Z e i t . , 28, 453 ( 1 9 5 6 ) .  7.  N a s s e n s t e i n , H. and Kraus, W., 220  (1956).  Chem. Ing. Tech., 28,  8.  Berg, J.C. and Baldwin, D.C., Trend i n Eng., Univ. of Washington, 1£, No. 4, 1 3 ( 1 9 6 5 ) .  9»  S t e r n l i n g , C V . and S c r i v e n , J . , £, 514  (1959).  L.E., Am. I n s t . Chem. Engrs.  10. O r e l l , A. and Westwater, J.W., Am. I n s t . Chem. Engrs. J.,  8, 350 ( 1 9 6 2 ) .  11. Johnson, H.F. and B l i s s , H., Trans. Am. Engrs., 42, 3 3 I ( 1 9 4 6 ) .  1  I n s t . Chem.  12. Smith.,. A.R., B.A.Sc. t h e s i s , The U n i v e r s i t y of B r i t i s h Columbia, 1 9 5 8 . 13°  Groothuis, H. and Zuiderweg,  12,  288  (I960,).  F . J . , Chem. Eng. S c i . ,  14. Mahajan, L.D., P h i l . Mag., 10, 383 ( 1 9 3 0 ) . 15*  Cockbain, E.G. and McRoberts, T.S., J . C o l l o i d 440  S c i . , 8,  (.1953).  16. J e f f r e y s , G.V. and Lawson, G.B., Trans. I n s t . Chem. Engrs. (London), 4J., T294 ( I 9 6 5 ) . 17.  Gillespie, 173  T. and R i d e a l , E.K., Trans. Faraday S o c , £2,  (1956).  18. E l t o n , G.A.H. and P i c k n e t t , R.G., i n Schulman, J.H. (Ed.), Proceedings of 2nd I n t e r n a t i o n a l Congress on Surface A c t i v i t y , V o l I, p. 288, Butterworths, London, 1 9 5 7 .  175 19«  S m i t h , A.R., C a s w e l l , J . E . , L a r s o n , P.P. Can. J . Chem. Eng., 41, 150 (1963).  and  20.  Murphy, N.F., L a s t o v i c a , J . E . , a n d E n g . Chem., 4°_, IO35 (1957).  21.  S e l b y , W.J., B.A.Sc. t h e s i s , Columbia, 1964.  22.  H o l d e r , D.W. and N o r t h , R . J . , N o t e s on A p p l . - S c i . , No. 31, S c h l i e r e n M e t h o d s , p. 14, 5, 4, 38, Her M a j e s t y ' s S t a t i o n e r y O f f i c e , London, I963.  23.  H y z e r , W.G., Photography,  24.  S w i f t , E.H., A System o f C h e m i c a l A n a l y s i s f o r The Common E l e m e n t s , pp. 99-102, W.H. Freeman and Co., San F r a n c i s c o ,  Fallis,  University  of  Cavers,  J.G.,  S.D.,  2nd.  British  E n g i n e e r i n g and S c i e n t i f i c High-Speed p. 23, The M a c m i l l a n Company, New York,  I962.  1939. 25.  Manual o f O p e r a t i n g I n s t r u c t i o n s f o r A e r o l a b S y s t e m . Ch. E . 2320. November. 1965.  260  R o c c h i n l , R . J . , M.A.Sc. t h e s i s , Columbia, 1961.  27°  S t e c h e r , P.G. ( E d . ) , The Merck Index, p. 671, 1117. 8th E d i t i o n , M e r c k and Co., I n c . , N.J., 1968.  28.  C h e r o n i s and  29o  B r i t i s h Pharmacopoeia, P r e s s , London, 1948.  30.  Goltz,  31.  S a w i s t o w s k i , H. and G o l t z , ( L o n d o n ) , 41, 174 (1963).  32.  B a r r y , F.W.  33*  H o l d e r , D.W., Thomson, J . S . , and M a c p h a i l , D.C., Modern D e v e l o p m e n t s i n F l u i d D y n a m i c s - H i g h Speed F l o w . C h a p t e r X I , O x f o r d U n i v e r s i t y P r e s s , O x f o r d , 1953•  34.  Taylor,  H.G.  Bakker,  C.A.P., v a n  Buytenen,  Garner,  F.H.,  C.W.  35.  36.  364  Entrikin,  G.E.,  (1948).  J . Imp.  and  and  Chem. and  (1955).  Eng.  News,  of  22,  British 6,  2 0 08 (1955).  41-42, The  Pharmaceutical  Coll.  Chem. E n g .  Soc,  G.E.,  G.M.,  and  12,  Trans. Inst.  J . Aeronautical  Waldrum, J.M.,  Eng. S c i . , 21, 1039 (1966). 603  University  pp.  Edelman,  Nutt,  The  Schlieren  and  Mohtadi,  Chem. E n g r s . S c i . , 15.  Inst.,10,378(1933).  J . Sc. P.M.,  40 (1958/9).  Beek, W.J.,  M.F.,  Nature,  Cheiru,  175.  1 7 6  37°  Lewis, 3 2 5  38. 39»  49.  J.B.,  Trans. Inst.  Sherwood, T.K.  1030  Chem. E n g r s .  (1957)o  and  Wei,  J.C.,  Ind. Eng.  K a n t r o w i t z , A. and  1£, 311 (1950).  Trimpi,  R.L.,  K i n t n e r , R.C., H o r t o n , T . J . , and Chem. E n g . , 32., 235 ( 1 9 6 1 ) .  42.  International C r i t i c a l Co., New York, 1929 •  43.  Horder, 59, 67,  44.  D r a p e r , N.R. and S m i t h , H., p . 88, 15, 305, 6 4 , 2 8 , 11, New Y o r k , 1966.  46.  Chem.,  49,  Hauptmann, E . , p r i v a t e c o m m u n i c a t i o n w i t h Dr. S.D. Department o f C h e m i c a l E n g i n e e r i n g , The U n i v e r s i t y B r i t i s h C o l u m b i a , J a n . 26/67.  4lo  45.  3L»  (London),  ( 1 9 5 3 ) o  A. ( E d . ) , The I l f o r d 58, 68, 5th E d i t i o n ,  Kozak, A. and  438  Tables,  (1965)o  Smith,  Cavers, of  J . Aeronautical S c i . ,  Graumann, R.E.,  Can.  Vol V I I , McGraw-Hill  J.  Book  Manual o f P h o t o g r a p h y , p. 73, Ilford Limited, Ilford, 1958. Applied Regression Analysis, 19, John W i l e y & Sons, I n c . ,  J.H.G., The  Forestry  Chronicle, 4 1 ,  Kozak, A., P r o b l e m s i n M u l t i p l e R e g r e s s i o n A n a l y s i s , a mimeographed n o t e h a n d e d o u t i n F o r e s t r y 5 6 2 c o u r s e , F a c u l t y o f F o r e s t r y , The 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 , 1 9 6 9 *  47.  C h a r l e s G i E . and Mason, S.G. , J . C o l l o i d 2 3 6  4 8 .  S c i . , 15_,  ( I 9 6 0 ) .  Brown,A.H. a n d  Hanson,C., B r i t .  Drew, T.B., Hoopes, J.W., Chemical E n g i n e e r i n g , p. Y o r k , I963.  50.  H a l l i d a y , D. and R e s n i c k , R., P h y s i c s f o r S t u d e n t s o f S c i e n c e a n d E n g i n e e r i n g , p . 891, Combined E d i t i o n , J o h n W i l e y & Sons, I n c . , New York, i960.  52.  Kozak, A., University  V e r m e u l e n , T., Academic  2, 695 (1966).  49.  5 1 . Weber, R.L., White, M.W., P h y s i c s , p . 6 4 5 , 6 4 4 , 2nd New York, 1952.  and  Chem. Eng.,  88, Vol.4,  Advance i n P r e s s , New  and M a n n i n g , K.V., College E d i t i o n , M c G r a w - H i l l Book Co.,  R e s e a r c h N o t e s . F a c u l t y o f F o r e s t r y , The o f B r i t i s h C o l u m b i a , No. 57, A p r i l 1966.  177  53-  Timmermans, J o , P h y s i c o - c h e m i c a l C o n s t a n t s o f Pure O r g a n i c Compounds, p . 273. V o l I I , E l s e v i e r P u b l . Co., I n c . , Amsterdam, 195°» Ibid..  55»  p . 152,  Vol I.  P e r r y , J.H. ( E d . ) , C h e m i c a l E n g i n e e r s ' Handbook, p . 3 6 3 , 3rd E d i t i o n , M c G r a w - H i l l Book Co., New Y o r k , 1950.  5 6 . B r i n s m a d e , D.S. and B l i s s ,  Engrs.,  22., 679 (1943).  H.,  T r a n s . Am.  Inst.  Chem.  A  -  l  APPENDIX A Determination in  The  of A c e t i c  Acid  t h e D i s p e r s e d Phase  t i t r a t i n g procedures  concentration  Concentration  of a c e t i c a c i d  used  f o r determining  p r e s e n t i n the d i s p e r s e d phase  composed o f w a t e r - s a t u r a t e d MIBK were t h o s e These p r o c e d u r e s bonate-free  consist  of t i t r a t i n g  O o l N sodium h y d r o x i d e  nolphthalein indicator.  The  a n d n e e d n o t be m e n t i o n e d  The hydroxide xide was  each  t o be  be  the  determined  determined  true  i f two  easily  made i n d u s t r i a l l y  common  by  sodium  s t a n d a r d i z i n g the  hydro-  hydrophthalate.  The  normality  titrated.  The  been p r e s e n t ) .  by m i x i n g  100  added  end  to  single  point could  then  t h a n w o u l d have  (SDAG-1K m i x t u r e  g a l l o n s of dehydrated  a l c o h o l with 5 g a l l o n s of dehydrated  T i t r a t i o n data are  was  t o p r o v i d e a homogeneous,  ( o r much more e a s i l y  p h a s e s had  phe-  N.  sample  sample was  using  carbonate-free  A s u i t a b l e amount o f SDAG-1K m i x t u r e  phase a s  car-  here.  0.097  each ketone-dominated  (24).  sample w i t h  o p e r a t i n g methods a r e  s o l u t i o n a g a i n s t potassium calculated  of Swift  s o l u t i o n and  n o r m a l i t y o f the p r e p a r e d  s o l u t i o n was  the  methyl  alcohol.)  shown i n T a b l e A - l .  been  is  ethyl  A - 2  Table  A-l.  Volume o f SDAG-1K a d d e d , ml,  Titration  Data  Run No,  Volume o f Sample, ml.  Volume o f NaOH u s e d , m l .  8  5  25  46.78  46.63  0.10  0.09  9  5  25  45.40  45.30  0.09  0.09  10  15  25  23.46  23.60  0.17  0.16  11  15  25  23-46  23.60  0.17  0.16  12  15  50  15o73  15.80  0.20  0.20  13  15  50  15.50  15.60  0.20  0.20  14  5  75  43.00  43.20  0.20  0.20  15  5  25  44.17  44.40  0.10  0.10  For  Sample  For  Blank  1  B -  APPENDIX B Determination  of Methyl  in  Alcohol Concentration  the D i s p e r s e d Phase  M e t h a n o l c o n c e n t r a t i o n i n t h e w a t e r - s a t u r a t e d MIBK was  o b t a i n e d by r e l a t i n g  calibration refractive Cho  Eo  plot  through  d i r e c t l y from  the p o i n t s i n t h i s p l o t .  The  i n the c a l i b r a t i o n pipetted  and  i t was  flask  and  into  D i s t i l l e d w a t e r was  neous m i x t u r e  from  was  clear  m e t h a n o l was just  a b u r e t t e , drop  constantly until  that  the  was  Care  fitted  c o n c e n t r a t i o n of  plot  into  was  was  each  as f o l l o w s .  a thoroughly  A  cleaned  a new  then added i n t o by  drop, w h i l e  t h e homogeswirling  phase appeared.  When i t  s e p a r a t i o n of p h a s e s would p e r s i s t ,  added c a r e f u l l y  disappeared.  line  drawn  m i x e d a n e q u a l l y known volume  of m e t h a n o l .  the m i x t u r e  pre-  unknown  smooth l i n e  straight  me-  squares.  known amount o f MIBK was dried  the  method t o o b t a i n t h e e x a c t  t o be u s e d  the  supplied with  methanol composition of each  i s then determined  The  o f known  (The Abbe r e f r a c t o m e t e r was  a d j u s t e d a c c o r d i n g t o the i n s t r u c t i o n s The  A  o f t h e Abbe r e f r a c t o m e t e r ,  w a t e r - s a t u r a t e d MIBK sample  by t h e method o f l e a s t  sample  index to composition.  c o n s t r u c t e d by d e t e r m i n i n g  t h e use  concentration.  the i n s t r u m e n t . ) sample  through  of each  thyl alcohol viously  ( F i g . B - l ) was  index,  2 4 4 7 .  refractive  by b u r e t t e u n t i l t a k e n t o be  further  the water phase  s u r e t h a t no  excess  B - 2  methanol was mixture was  used.  W a t e r - s a t u r a t i o n of the MIBK-methanol  assumed to be reached a t t h i s p o i n t .  exact volume of each component t h a t was was  c a l c u l a t e d and expressed  i n wt.$.  added, the concentratkn The d e n s i t y of each  c o n s t i t u e n t i n the mixture a t room temperature obtained from l i t e r a t u r e  (27, 53.  55)«  Knowing the  (20°C) was  Discrepancies i n  d e n s i t y r e a d i n g s between a c t u a l room temperature  and  20°C  may  be avoided by o b t a i n i n g d i r e c t l y the mass of each c o n s t i t u e n t by the use of the a n a l y t i c a l balance. the present procedure,  The e r r o r s i n v o l v e d i n  however, are assumed t o be  i n s i g n i f i c a n t as f a r as present requirements  are  relatively concerned.  The r e f r a c t i v e index of each s o l u t i o n was triplicate.  read i n  The prisms of the r e f r a c t o m e t e r were cleaned  thoroughly with benzene and petroleum  e t h e r between r e a d i n g s .  Table B - l shows the r e f r a c t i v e index data f o r runs 16, 1 7 . 18, and 1 9 and f o r p r e p a r i n g F i g . B - l a t 20°C.  Since the methanol w i l l tend t o d i s t r i b u t e should a two-phase mixture taken t o ensure  itself  of water and MIBK r e s u l t , care  t h a t no s e p a r a t i o n of phases o c c u r r e d i n the  monophase samples.  The e n t i r e o p e r a t i o n of mixing the  solution  and measuring i t s r e f r a c t i v e index i n p r e p a r i n g F i g . B - l performed  was  was  a t the same s i t e t o a v o i d the p o s s i b i l i t y of sudden  room temperature  changes, i f any.  During the p e r i o d t h a t  the samples f o r runs 16, 17. 18, and 19 were t r a n s p o r t e d  B -  3  f r o m t h e e x t r a c t i o n a r e a i n room 218 t o room 328A where t h e r e f r a c t o m e t e r was s i t u a t e d , served d u r i n g differences  the e n t i r e  i n ambient  t h e r e were n o phase  r e l o c a t i o n processo  changes ob-  Measurement o f  temperature between the above-mentioned  rooms a n d t e m p e r a t u r e f l u c t u a t i o n s w i t h i n a g i v e n p e r i o d i n b o t h rooms  ( A p p e n d i x D - l ) i n d i c a t e no a p p a r e n t d i s c r e p a n c i e s  among r e a d i n g s t h a t  Table B - l .  Run No.  Weight Fraction Me t h a n o l  could  result.  Refractive  Index D a t a a t 20°C  Refractive  Index,  0 . 0 0 9 8 1 6  1 . 3 9 3 4  1 o 3 9 3 4  1 . 3 9 3 5  0.02446  1 . 3 9 2 6  1 . 3 9 2 6  1 . 3 9 2 6  *  0 . 0 3 8 8 0 2  1 . 3 9 1 4  1 . 3 9 1 4  1 . 3 9 1 4  *  0 . 0 5 2 9 9  1 . 3 9 0 6  1 . 3 9 0 6  1 . 3 9 0 6  *  0 . 0 6 6 8 9 9  l o 3 8 9 7  1 . 3 8 9 7  l o 3 8 9 7  *  0 . 0 8 0 7 2 8  I . 3 8 8 5  I . 3 8 8 5  I . 3 8 8 5  1 6  0 . 0 0 2 5  1.3940  1.3941  1.3940  1 7  0 . 0 0 2 7  1.3940  1 . 3 9 4 0  1 . 3 9 4 0  18  0 . 0 0 1 2 5  1.3941  1.3941  1.3941  1 9  0 . 0 5 6 2 5  l o 3 9 0 3  1 » 3 9 0 3  1 o 3 9 0 3  ^ C a l i b r a t i o n data f o r F i g . B - 2 .  1-3940  1-3930  o ~ x  1-3920  -  1-3910  UJ Q  UJ  > £  1-3900  £  1-3890  < or u_  1-3880  Figure B - l .  2 3 4 CONCENTRATION,  Refractive  indices  of solutions  5 wt  6 %  of methyl a l c o h o l  i n M I B K - s a t u r a t e d w a t e r (20 C).  C - 1  APPENDIX C Calibration  The  of the  timing l i g h t  t o mark r e g u l a r b l i p s the  outer  exact film TSI a  strip  camera  Digital  The  was  Ch.  were t a k e n e v e r y 10  Generator  Ch.  2 3 5 6 , was  E.  used  at prescribed frequencies along  corresponding  Frequency Meter  photo p i c k u p ,  was  of l i g h t  generator  Light  generator,  of t h e m o v i e f i l m  speed  strip.  Timing  i n order to determine t o any  given  segment  c a l i b r a t e d a g a i n s t the  (Model £ 6 0 ) ,  Ch.  the  of  Darcy/  2 5 7 3 . using  E.  2 5 2 3 . t o r e l a y the l i g h t b l i p s .  E.  sec. i n t e r v a l  t h a t the  the  timing  Data  generator  operating.  Calibration  data are  shown i n T a b l e  C-l.  From  these  d a t a , a p p r o p r i a t e c o r r e c t i o n s were made on a l l c a l c u l a -  tions  involving  in Appendix while  the  o f camera  I, t h e g e n e r a t o r  observed  r e a d i n g o f 117 obtained  the use  frequency  (Table C - l ) .  correct  frame  values.  For  frequency  was  was  t o have an  found  T h e r e f o r e , the  s h o u l d be m u l t i p l i e d  t o o b t a i n the  speed  s e t a t 100  camera  by a c a l i b r a t i o n  speed.  example, pips/sec.  average speed  factor  of  117 100  C - 2 Table C - l o Rated Frequency, ^\pip/sec Observa-^\ t i o n Number  Timing L i g h t  10  100  Calibration  1 0 0 0  Observed. Frequency,, p i p / s e c  1  808  1 1 6  1040  2  8o9  117  1039  3  8 c 8  117  1039  4  9 o 0  118  1039  5  9-1  117  1 0 3 9  6  808  1 1 6  1039  7  8o5  117  1038  8  8 . 7  117  1039  9  8 . 6  117  1038  10  8o5  116  1039  11  8 . 5  118  1039  12  8 . 6  117  1038  13  8 . 8  116  1039  14  9 . 0  116  1039  15  8 . 7  117  1038  D - 1  APPENDIX D Room Temperature F l u c t u a t i o n s  Measurements  of temperature f l u c t u a t i o n were taken  f o r two e n c l o s e d rooms i n the Chemical E n g i n e e r i n g b u i l d i n g on s e v e r a l o c c a s i o n s .  The purpose of these t e s t s were to  determine the magnitude of t h i s f l u c t u a t i o n f o r two l o c a t i o n s where experimental work was being undertaken,, and a l s o t o measure  the temperature d i f f e r e n c e between these two l o c a t i o n s  at i d e n t i c a l  times.  Temperature measurements March 2, 6, and 8, 1967.  were made i n room 218 on  The thermometer was l o c a t e d beside  the square column and i n s i d e the path of the c o l l i m a t e d r a y s with the s c h l i e r e n system arranged as i n F i g . 4.  light The  thermometer was l o c a t e d between the column and the s c h l i e r e n m i r r o r , M l . Temperature f l u c t u a t i o n data are shown i n Table D-l.  Another thermometer was used i n t a k i n g temperature r e a d i n g s simultaneously i n room 328A where the Abbe r e f r a c t o meter was s i t u a t e d .  This thermometer reads 0.06°F h i g h e r  than the one used i n room 218.  The data shown i n Table D - l  f o r the thermometer used i n room 328A a r e c o r r e c t e d v a l u e s . T h i s thermometer was p l a c e d above the l a b o r a t o r y bench on  D - 2  which the r e f r a c t o m e t e r working a r e a operator  to the r i g h t  The t h e r m o m e t e r was  of the instrument  above t h e  (with the  facing i t ) .  No a b s o l u t e obtained.  sat.  calibration  o f the thermometers  was  D Table  D-l.  Date March  2 ,  1967  "  8 : 2 5  P.m.  Room 218 67o75°F  i n Two Ch. E . Rooms  Room  328A  6 8 . 1 ° F  8 : 3 0  68.42  6 8 = 1  8 : 3 5  6 8 . 4 5  68.2  8:40  6 8 . 5 1  6 8 . 3  "  8 : 4 5  68.64  "  8 : 5 0  6 8 . 6 5  6 8 . 4 5  "  8 : 5 5  6 8 . 8  6 8 . 6  1 1  9 : 0 0  6 8 . 8  6 8 . 6  "  9 : 0 5  6 8 . 7 5  6 8 . 4 5  "  9 ^ 1 0  6 8 . 7 3  6^^1967  1 1 : 1 5  a.m.  6 8 . 2 5  68.48  6 8 . 5  69.14  1 1 : 2 0  6 8 . 5  "  1 1 : 2 5  6 8 . 6 8  6 9 . 6 3  "  1 1 : 3 0  6 8 . 8 8  6 9 . 2  " 1 1  March  Fluctuations  Time  "  .....Maroli.,  Temperature  3  6 9 . 4 3  1 1 : 3 5  6 8 . 9 5  6 9 . 8 7  11:40  6 9 . 0  6 9 . 8 6  "  1 1 : 4 5  6 9 . 0 3  "  1 1 : 5 0  6 9 . 0 2  70.04  "  1 1 : 5 5  6 9 . 0 2  7 0 . 1 5  "  1 2 : 0 0  69.18  7 0 . 0 6  7 O . O 3  7 0 . 9 7 7 0 . 9 7  8 ,  1 9 6 7  2 : 0 5  p.m.  7 0 . 2  2 : 1 0  7 0 . 0 5  "  2 : 1 5  7 0 . 0 9  "  2 : 2 0  6 9 . 9  7 1 . 2  "  2 : 2 5  7 0 . 2  7 1 . 2  "  2 : 3 0  7 0 = 0  7 1 . 1  "  2 : 3 5  6 9 . 9  7 1 . 0  "  2:40  6 9 . 7  "  2 : 4 5  6 9 . 5  2 : 5 0  6 9 . 9 5  71.08  70.82 70.81 7 0 . 7 5  E - 1  APPENDIX E Test  It  for Significance  i s assumed t h a t t h e r e a d e r  ting a straight squares"  of Linear Regression  line  i s f a m i l i a r with  by t h e e s t i m a t i o n p r o c e d u r e  of  fit-  "least  s o t h a t most o f t h e v a r i o u s e x e r c i s e s i n v o l v e d i n  t h i s method w i l l  We  n o t be mentioned<>  can write the estimates  o f t h e linear»  first-  o r d e r model t o be Y = b  Q  + b-L X  (E-l)  A  where  Y  = the p r e d i c t e d value the  X b  Q  pseudo-radius.  = observed  independent  = estimate  of intercept  the model, b i = estimate model s> Eq  0  o f Y f o r a g i v e n X„  b  0  Q  time  0  parameter of  «  of slope parameter of the o  ( E - l ) i s the p r e d i c t i v e  solutions f o r b  variable,  equation..  We  can a l s o w r i t e the  and b i ( 4 4 ) t o be  (E-2)  = Y - bi X  JT(Xi - X ) ( Y i - Y) bi  =  — £(Xi  i = 1, - X)  2  2,..,n  (E-3)  E  where  X, Y  = mean v a l u e s  - 2  of t h e X and Y v a r i a b l e s ,  respectively. Xi,  Yi= i t h observation  of the X and Y v a r i a b l e s ,  respectively, n  Eq.  (X^.  precision  We now t a c k l e t h e q u e s t i o n  c a n be a t t a c h e d  (Eq. E - l ) . Yi  I f we s q u a r e  o f what measure o f  to the estimate  Consider  o f the r e g r e s s i o n  the f o l l o w i n g i d e n t i t y :  - Y i = Y i - Y - ( Y i - Y) both (Yi  We c a n e x p r e s s  - (E-4) ;  s i d e s a n d sum f r o m i = 1 t o n, we  - Y)  =  2  (Yi- Y i )  2  +  (Yi- Y )  Sum o f s q u a r e s =  a b o u t t h e mean last  earlier ted tive  two p r e c e d i n g discussion.  a s "SS".)  obtain  (7)  2  E q . (7) i n words a s f o l l o w s :  Sum o f s q u a r e s  The  Y^),  ( E - l ) i s , t h e r e f o r e , s o l v a b l e once v a r i a b l e s Xj^ a n d Yj^  a r e known.  line  = no. of s e t s o f o b s e r v a t i o n s  Using  computational  Sum o f  squares  + about r e g r e s s i o n  due t o r e g r e s s i o n  e x p r e s s i o n s a r e a l s o mentioned  ("Sum o f s q u a r e s "  t e r m i s now  E q s . (7) a n d (8) and e m p l o y i n g  forms f o r the e x p r e s s i o n s  i n an  abbreviaalterna-  o f E q . (7) we  c a n w r i t e a more w o r k a b l e r e l a t i o n s h i p a s : SS a b o u t t h e mean ^Y^ ( c o r r e c t e d f o r mean) "  2  ~ (^Yl ) n  2  (E-5)  E  - 3  SS due to regression = b^ j £ Y i X i  (E-6)  ilxiillliij  -  We now test the null hypothesis that the slope parameter of the model, j9 , is equal to ^8j » whereiS^is a specified value which, in this case, is zero, against the alternative that JSj,, is different from ^0/ (usually stated "H : ^9/ = ^ versus K± :^9/ ) by calculating the "t" statistic as follows (44): /  0  o  0  0  t  =  (b - j8/o)[ p X j - X ) ]* 2  T  ( E  -  7 )  s where s = standard error of estimate (obtained from ANOVA table by taking the square root of the mean square about regression, s )o 2  absolute value of t is compared with t(n-2, 1iOO from a t-table (44) with (n-2) degrees of freedom - the number on which s is based, and at a level of significance, OC o o f OoOlo I f |t|««t(n-2, l-iOCh we could not reject the null hypothesis that^8/ is equal to j9/<>or that the slope of the linear, first-order model is equal to zero. The  2  p - 1  APPENDIX P Properties  of V a r i o u s  Sodium h y d r o x i d e agent grade Nichols grade  Chemical  Co., L t d . , M o n t r e a l .  The MIBK was  interest.  o  (5892o6 A ) .  Co., Edmonton.  index  acetic  values  reported i n this  values:  o f a medium i s i t s i n d e x  t i v e , when i t s i n d e x conditions.  a b s o l u t e , when t h e i n d e x referred  Since  the a b s o l u t e  of r e f r a c -  t o a vacuum, a n d r e l a -  to a i r , differ  to distinguish  index  f o rdry a i r l s  a n d so n e a r t o u n i t y , i t f o l -  lows t h a t , f o r a solid, or a l i q u i d ,  square  abso-  i s compared, t o t h a t o f d r y a i r a t s t a n -  1 . 0 0 0 2 9 1 8 f o r the sodium D l i n e  index r e l a t i v e  table  o f sodium  R e f r a c t i v e i n d i c e s c a n be g i v e n a s e i t h e r  tion  No r e f r a c t i v e  grade f u r n i s h e d  the wavelength of the D l i n e  or r e l a t i v e  The  Methyl  some p r o p e r t i e s o f g l a c i a l  lute  necessary  technical  MIBK, t o l u e n e , a n d w a t e r t h a t a r e o f  The r e f r a c t i v e  f o rlight-ihaving  from  Co., V a n c o u v e r .  F-l lists  a c i d , methyl a l c o h o l ,  the  a c e t i c a c i d were r e -  ( a b s o l u t e ) a n d t o l u e n e , were r e a g e n t  Table  dard  Used  (A.C.S. s p e c i f i c a t i o n ) and were o b t a i n e d  Fisher • S c i e n t i f i c  are  and g l a c i a l  s u p p l i e d by Canadian Chemical  alcohol by  Substances  the absolute  only  slightly  index, and and i t i s n o t  between them f o r p r e s e n t  purposes.  column i s made o f b s o r o s i l i c a t e g l a s s .  index value  c o u l d be f o u n d  i n the l i t e r a t u r e  F  Table  F-lo  - 2  Various Properties of D i f f e r e n t a t 2 0 ° C where A p p l i c a b l e .  Substance  Value  Property-  Glacial Acetic Acid  d e n s i t y , gmo/cc. r e f r a c t i v e index,7? f t m o l e c u l a r weight P  6O0O5  Methyl Alcohol  d e n s i t y , gm<»/cco r e f r a c t i v e index,7f~ molecular weight ™  0.7924 1=3292 3 2 0 04  density, MIBK  surface  Toluene  Dry A i r  for F-l.  gm./cc.  refractive surface  Crown Glass  1O3718  0.8007 1.396 dynes/cm. 2 3 . 9  index,7^0  tension,  refractive  0.8669 28.52  0.99998 1.333 dynes/cm. 7 2 o 8  index  r e f r a c t i v e index, (standard conditions)  this material,  0  index,7jp  tension,  and c r o w n g l a s s  Ref  c  1.049  d e n s i t y , gm./cc. surface t e n s i o n , dynes/cm density,  Water  gm./cco  refractive  Substances  27  27  53  5 4 27.  1.517  51  1.000292  51  i s shown i n s t e a d  5 5  i n Table  G - 1  APPENDIX G Derivation  of Equation  f o r the Locus of P o i n t s  a M o v i n g Drop w i t h R e s p e c t  Consider Figo of r a d i u s ,  r , having  k2°  i t s centre,  and moving a l o n g  the  tangential point,  can  be f o u n d by t h e r e l a t i o n  CL  = PL  2  i t s axis d  Substituting appropriate (Y  d  Since  + CK)  + (X )  2  CK = V r  •- Xd  towards Y  Camera  of ordinate,  = 0, the l o c u s of  d  to point  d  L ( X , 0) L  (H-l)  ;  t e r m s we  =  2  L  2  C, on t h e a x i s  P(X , Y ) , with respect  + CP  2  Movie  A s s u m i n g t h e d r o p t o be a s p h e r e  Y , d  to a Stationary  G e n e r a t e d by  Y  2 d  +  find  (Xd - X  L  )  + r  2  , inserting this relation  (H-lA)  2  i n t o Eq. (H-lA)  yields [(Y  d  +  r2 - X d ) 2  Y  d  2  (X )2]  +  l £  L  2  ^ X ?  Yd  [Y 2 d  Xd  2  + (Xd - X L ) ] + r 2 2  - Xd  Xn  -  Vr  2  X  L  X ) L  - Xd  2  (10)  1  H -  APPENDIX H Sample  C a l c u l a t i o n Showing the and  Hycam E x p o s u r e  Suppose a by  the  Linhof  j e c t and  correctly  still  N  L  =  1/125  sec,  =  11  f/11  u s e d was  or  film  The  object-to-lens distance,  the  black  and  U*L, was  VL,  was  11.625  Linhof  135  nmi°  (5°32 i n . ) .  l e n s was  camera  o b t a i n an  now  desire  (lens f o c a l  t o 5«7  equal  in.  and  The  length,  1+1=1 v  "L"  has  and  Hycam  a  10,5  obtained  ti*  9  speed  i n . and  The  f j j = 75  focal  sub-  and  rela-  o f USASI the  length  o r 2.95 doubling  object-to-lens  i s assumed t o be  125«  lens-toof  the  Hycam h i g h - s p e e d  mm.  while  c h a n g i n g the  However, f r o m t h e  u  time,  t o change t o t h e  illumination  f o r both Linhof  *Subscript  in.  e q u a l l y exposed n e g a t i v e  s p e e d t o USASI 250 UJJ,  was  c o a l e s c i n g drops as  w h i t e and  image d i s t a n c e ,  vie  Settings  f o l l o w i n g exposure  The  We  Linhof  NL:  tive aperture, L  Between  exposed n e g a t i v e  camera w i t h  y i e l d e d the  t  Relationship  mo-  i n . ) , to the  film  distance, constant  and  shots.  lens equation  (43). (H-l)  f  stands f o r Linhof  while  "H"  i s f o r Hycam,  H - 2  we  choose f i r s t  correspond relative in.  to find  Linhof  exposure  time  t o a change i n o b j e c t - t o - l e n s d i s t a n c e  aperture,  and the v a l u e  values  a new  N^,  constant.  L  take  o f f ^ r e m a i n s t h e same.  t o E q . ( H - l ) , we V  We now  setting to h o l d i n g the  U ( = Ug) =  Substituting  these  obtain  = 80.00 i n .  Given the e x p r e s s i o n  (43)  magnification, m = v - 1 f and  5«7  L  (H-2)  substituting, M  r  = 80.00 i n . - 1 = 14.00 5.32 i n .  A value Linhof  exposure  of  i s a l s o d e t e r m i n e d f o r the o r i g i n a l  settings.  M (old) = L  11.625  5.32 From r e f e r e n c e required  43  This  i n . - 1 = 1.19 «  1  in.  (see T a b l e  f o r t h e new  i s f o u n d t o be  IV' a l s o ) ,  set of Linhof  the exposure  time  s e t t i n g s i s g i v e n by the  equation t'(new) = t ( o l d ) x  provided  the m a g n i f i c a t i o n ,  ( M ( 0 1 d ) ) was e q u a l L  to  (1 + M(new) )  M,  to unity.  L  (H-3)  2  i n the o r i g i n a l We  setting  can t h e r e f o r e a p p l y  Eq.  (H-3)  yield 2 t(new) = 1 125  sec. x  (1 + 14.00)  4  = _1 2.22  sec.~ 1 sec. 2  3  H -  Since fast  t h e Hycam camera u s e s a f i l m whose (USASI 250),  by h a l f .  we must r e d u c e  Therefore,  f/11  at  speed  the exposure  t h e new L i n h o f e x p o s u r e  i s twice as time,  setting i s  1/4 s e c .  In o t h e r words,  i f we move t h e L i n h o f  in.  i n . we c o u l d e x p e c t t h e e x p o s u r e  t o U-^ = 5»7  camera f r o m U  s e c . t o 1/4  s e c , h o l d i n g the r e l a t i v e  constant.  F o r t h i s new o b j e c t - t o - l e n s d i s t a n c e , we  e q u i v a l e n t Hycam e x p o s u r e  exposed  setting  =  L  time  f r o m 1/125  the  t(new),  10.5 altered  aperture  t o o b t a i n an  determine identically  negative.  From E q .  (H-l), V  Vg  v  H  I f we choose Hycam l e n s t o  f/3»5»  corresponding  exposure  determining  =  i s given by:  1  1__ + _1_ = 5.7 i n .  H  2.95  in.  6.12  in.  t o s e t the r e l a t i v e  aperture  of the  i»e., a t i t s w i d e s t l e n s opening, the time  setting  i s c a l c u l a t e d by  t h e l i g h t - p a s s i n g power r a t i o  first  o f t h e Hycam  t o t h e L i n h o f l e n s , ^H, g i v e n by t h e r e l a t i o n  lens  (43)  (H-4)  H -  Substituting  appropriate  at  5 . 7  UH  =  UL  =  LH _ LL  Since ( 4 3 )  4  Hycam a n d L i n h o f  exposure  settings  in.,  1 1 x 80 in. _ 5.° ?-2 I n . p. 5 x 6.12 in 2 . 9 5 in.  =  I6?.j  =  5 1 9 o O  7 . 2 6  exposure time, t , i s r e l a t e d t o l i g h t - p a s s i n g  power, L,  by  *s =  H L l  tL  (H-5)  Substituting, tji =  sec. x  1 4"  Dividing ratio the  1 5 1 9 . 0  =  1  sec,  2 0 7 5  t h e denominator by 2 . 5 » t h e s h u t t e r  ( 2 3 ) , and taking  exposure  duration-period  the r e c i p r o c a l of the r e s u l t ,  t i m e , s e c , t o t h e camera s p e e d , p p s .  obtain = Co  The  equivalent f / 3 . 5  8 3 0  pps.  J  Hycam e x p o s u r e at  8 3 0  pps.  setting Is, therefore,  converts Thus, we  I - l  APPENDIX I Calculation  of F i l m  Frame Span i n Runs 18  Negligible  The O0O5  no.  of successive f i l m  which 0.05  cm.  The  drop, as  of s p h e r i c a l  frames  length  (Figs.  i n r u n s 18  pseudo-radius  33 a n d  a n d 19  was  34).  The  determined  i n the p s e u d o - r a d i u s by a n amounts  shown i n the same p r i n t s , was  shape h a v i n g a d i a m e t e r , d,  o f s e p a r a t i o n o f t h e two  33 a n d  o f the  (as i n F i g s .  s t a r t o f shape m e a s u r e m e n t s , w h i c h  distance  The  i n the p h o t o g r a p h s  w o u l d p r o v i d e a change  t o be the  cm.  for  Drop Growth E f f e c t  minimum d i s c e r n i b l e  was  and 19  assumed  o f 55 nim. a t  i s r o u g h l y o n e - h a l f the  n o z z l e t i p s i n both runs  '  34).  volume o f the  sphere, V  s  = ^ x 7T x ^ ^  m  m  J  = 87114.00mm  3  The  new  v o l u m e , V"sis> a f t e r a r a d i a l i n c r e a s e  V i = 4 x7Tx|5^inm + 0.5 3 \* s  of 0.05  cm.  is  mm)  J  = 91952.54mm  3  Av = v  S i  -  v  s  = 91952.54 - 87114.00 = 4838.54mm  3  The  time  t a k e n from  the i n s t a n t  a c o a l e s c e d drop detaches  b o t h n o z z l e t o t h e o n s e t o f c o a l e s c e n c e o f a new which  was  c a l l e d by  t h e term  "CD",  was  drop  m e a s u r e d t o be  from  pair, 7*5  sec.  1-2  This value rate, is  i s now  used t o c a l c u l a t e  F, a s s u m i n g  still  that  the d i s p e r s e d p h a s e  flow  t h e volume o f t h e s p h e r e a t t h i s  point  Vs.  = 1106  CCo seco  The p e r i o d , cm.  t , n e c e s s a r y to produce a r a d i a l  increase  of  O0O5  i s then  Av  t =  F  =  0.4  sec.  S t a r t i n g a t t h e o n s e t o f c o a l e s c e n c e a n d g o i n g "back i n t i m e until  t =  0 . 4 s e c , the e q u i v a l e n t  frame  span was e s t i m a t e d  t o be a b o u t 1 3 9 0 f r a m e s f o r r u n 18 a n d a b o u t 8 0 0 f r a m e s f o r r u n 1 9 which corresponded to an i n c r e a s e The  camera  speed v a r i e s  calculations including a and w i l l  involved  over these f i l m  i n obtaining  p r e s e n t e d below,  shown.  Similar  times f o r  r u n s 18 a n d 1 9 r e s p e c t i v e l y , speed f o r a range  The  instance,  computational procedures are spans.  l i 5 0 and 1 0 0 frame spans f o r  were d e t e r m i n e d .  of f i l m  values.  t e r m s i n one  however, f o r s h o r t e r frame  The e l a p s e d  camera  frame  these values are lengthy,  summation o f a b o u t f o r t y  n o t be  i n r a d i u s by 0 . 0 5 cm.  Variations i n  f r a m e s a r e shown  below.  1 - 3  Run 1 8 : Frame  Frame n o .  Camera s p e e d , p p s  span, frame  3860  0-8  8  3850  8-85  77  3825  85 - 123  38  3800  123 - 150  27 150  frames  Run 1 9 : Camera  Frame no o  speed, pps  2560  0 - 3  2550  3 -  Frame  span, frame  3  29  26  2500  29  -  54  25  24?5  54 -  78  24  2460  78 - 100  22  100  Average  camera  frames  s p e e d (Run 1 8 )  =JL(3860)  150  = 205.87  +  Z2J3850)  150  + __28(3825)  150  + 1976.33 + 968.99  = 3835.19 PPS  +  +  684.00  27  (3800)  150  1-4  Average  camera speed = _1_(2560) 100  (Run 1 9 ) + 26J2550) 100  +  21_(2500) 100  +  24_(24?5) 100  + 22 ( 2 4 6 0 ) 100 = 7608O + 663=00 + 6 2 5 . 0 0 + 594o00 +  54l»20  = 2 5 0 0 . 0 0 pps Elapsed time to cover frame no. 0 - 150  i n run 18  = 150 frames 3835.19 frames/seCo =  O0O39  sec.  E l a p s e d time to cover frame no. 0 - 100 i n run 19 = 100 frames 2 5 0 0 . 0 0 frames/sec. = 0.04 sec.  To o b t a i n the c o r r e s p o n d i n g change i n r a d i i f o r both runs, l e t us c o n s i d e r the e l a p s e d time of 0 . 0 3 9 sec. to a p p l y f o r both cases since the d i f f e r e n c e between the two very small.  A timing l i g h t c a l i b r a t i o n factor  times i s  (Appendix  C)  of 100 i s m u l t i p l i e d to t h i s v a l u e . 0 . 0 3 9 s e c , to give an 117 e l a p s e d time ( c o r r e c t e d ) of 0 . 0 3 4 sec. Volume i n c r e a s e = f l o w r a t e x e l a p s e d time , cc 0 , = 11.6 x O.O34 sec. = 0.4 cc.  (corrected.)  1-5  The new d i a m e t e r ,  d  1 0  c o r r e s p o n d i n g t o a volume  0o4 c c . i s o b t a i n e d f r o m  the r e l a t i o n  (87.114 + 0 . 4 ) c c . = di  3  7T d j 6  3  = 87.514 x 6 = 1 6 7 . 1 3 9 c c . 3.1416  d^ = 5°508 cm. Radius  increase of  change = d i - 5° 5 cm. 2  = 0.004 cm.  - 1  J  APPENDIX J Heat E f f e c t s  Accompanying into  the M i x i n g  Water a t Room  A heat of s o l u t i o n cial  acetic  acid  of G l a c i a l Acetic  Temperature  p r o d u c e d by the t r a n s f e r  below, h e a t s o f s o l u t i o n ,  vels, one in  of  are given,  f o rvarious acetic  acid  concentration l e s  acid.  r e f . 42, t h e a c i d  For lack  mentioned  of any d e f i n i t e  acid/cu.  f t . soln.  ft.  added t o  statement  l s assumed t o be g l a c i a l  acetic  O.OO76 l b . moles  From r e f . 5 6 , a n MIBK p h a s e c o n t a i n i n g  acetic  J - l (4-2)  Q, i n k i l o j o u l e s e v o l v e d /gm-mole  i s i n equilibrium  w i t h a water phase c o n t a i n i n g cu.  In Table  e x p r e s s e d a s t h e number o f m o l e s o f w a t e r , M ,  mole o f a c e t i c  acid.  of g l a -  f r o m t h e d i s p e r s e d MIBK p h a s e t o t h e c o n t i -  n u o u s w a t e r phase was d e t e r m i n e d a s f o l l o w s o  solute,  Acid  a t about 1 9 ° C  0 . 0 1 3 9 l b . moles o f a c e t i c  acid/  soln.  Let  u s assume t h a t  1.  The c o n t i n u o u s p h a s e i s i n i t i a l l y acetic  2.  the following  relationships  a c i d and c o n t a i n s water  The r a t e  of a c e t i c  with respect  mass t r a n s f e r  free of  only.  acid transfer  t o t i m e a n d no f r e s h  phase m a t e r i a l  hold:  i s uniform dispersed  f l o w s t o each drop d u r i n g the process.  J  3«  No m i x i n g during so  - 2  o c c u r s i n the continuous  the e n t i r e  that  period  the d i f f u s e d  solute  t o be c o n f i n e d w i t h i n drops 4.  only  Equilibrium  The o p p o s i n g other of  tration  at  * At !3o6°Co  of the  concentration<>  drops a r e s e p a r a t e d from  the s o l u t e  i n t h e c o n t i n u o u s phase  envelopes  the a f f e c t e d  c o n t i n u o u s phase  each  each  concen-  t o be t h e  space  (Figo J - l ) ;  i s a layer  which  d r o p a n d h a s a volume e q u a l t o  o f the d r o p which  Heats  acid  so a s t o e n a b l e  the a f f e c t e d  J - lo  the v i c i n i t y  b e t w e e n t h e two p h a s e s i s r e a c h e d  same t h r o u g h o u t  Table  c a n be c o n s i d e r e d  j u s t enough t o p r e v e n t any i n t e r m i x i n g  solute  that  transfer  0  with respect to a c e t i c 5»  of solute  phase  of s o l u t i o n  i t surrounds  (Figo J - l )  of a c e t i c acid-water  18O5°C ( 4 2 ) .  139  I0I2  197  lo53*  207  I0I5  411  lo37  00  1.90  system  0  J - 3  The maximum t e m p e r a t u r e r i s e  i n the continuous  p h a s e c a n be e x p e c t e d w i t h t h e u s e o f h i g h e s t a c e t i c c o n c e n t r a t i o n i n t h e d i s p e r s e d phase b e c a u s e u n d e r conditions and  into  9  maximum t r a n s f e r  of a c e t i c a c i d  t h e c o n t i n u o u s phase  acid  those  out o f the drops  c a n be o b t a i n e d .  Only a c i d  c o m p o s i t i o n s a c c u r a t e l y m e a s u r e d b y a n a l y t i c a l methods a r e c o n s i d e r e d , , a n d on t h i s b a s i s r u n 8 h a d t h e h i g h e s t phase a c e t i c a c i d tic  concentration:  a c i d / cu, f t o soln  calculated  The q u a n t i t y ,  D  x 10"  56°45  M , s  3  dispersed  l b o moles  ace-  f o r t h i s run i s  below.  Maximum a c e t i c a c i d  c o n c e n t r a t i o n i n t h e a q u e o u s phase  (from  d i s t r i b u t i o n data) =  56.45 x 1 0 ~ 3 l b . moles  cu. f t . s o l n . =  0.0139  x  (0.0139 + 0.0076)  3 6 . 4 - 9 x 10"" 3 l b . m o l e s / c u . f t . s o l n .  Volume o f a c e t i c a c i d  i n the aqueous p h a s e / c u . f t . s o l n .  = 36.49 x I P " l b m o l e s x 60.05 l b . / l b . (1.049 x 6 2 . 4 3 ) l b . / c u . f t . 3  0  = 3»35 x 1 0 "  2  cuo f t .  Volume o f c o r r e s p o n d i n g w a t e r / c u . f t . s o l n . tivity  o f volumes  (assuming a d d i -  hold)  = 1 . 0 - O.O335 = O.9665 c u . f t . Lb.  moles  mole  of corresponding water/cu. f t . soln.  = 0.9665 x 6 2 . 4 3 = 3 ° 3 5 18.02  ii -  M o l e s w a t e r a d d e d t o one mole solution  =  In Table M  g  =  91.73.  we We  (to produce a  of the continuous  3 5  l o o k f o r the v a l u e find  e v o l v e d / g m . mole  5 which i m p l i e s the l a y e r  t o be a b o u t 1  s o l u t e by e x t r a p o l a t i o n . o f 0.02  kilojoules We now  assume  that  c c , c o n f o r m i n g t o assumption  t h a t b o t h d r o p s have n o t y e t f u l l y  f r o m a s s u m p t i o n 6,  i n the c o n t i n u o u s  = (1 x 1000) x  but  grown, a n d  o f c o n t i n u o u s w a t e r phase i m m e d i a t e l y  it,  Heat e v o l v e d  of Q corresponding t o  t h i s v a l u e m i s s i n g from the t a b l e  t h e d r o p o c c u p i e s a volume  (36.49  x  h a s t h e same  Joules gm. mole a c i d  10"3)  = 1:.17  x 10"  volume.  phase x  463.6  gms.  lb.  l b . moles  -srO.02 c c . x c u . f t .  cu. f t . soln.  Weight  s  ' - = 91.73 36.49 x 10~J 3  J-l,  surrounding  to that  M  consideration)  c a n r e a s o n a b l y be c o n s i d e r e d  that  acetic acid,  of concentration equal  phase under  4  28317 c c ,  joules  2  of the c o n t i n u o u s  phase  *0.02 cu. f t . x 62.43 28317 = 20.00 x 10~ gm. 3  l b . x 453.6 gms. cu. f t .  lb.  J  Temperature  rise  =  - 5  i n the c o n t i n u o u s  phase/drop  1.17 x 1 0 ~ joules j o u l e s / c a l x 1 c a l / ( g m ° C ) x 20.00 x 10~3 2  4.184 = 0.14  °C  g  m  .  LAYERS  Figure  J-l.  S k e t c h showing  solute concentration  l a y e r around  each  drop.  K - 1  APPENDIX K Pseudo-radius  Data  The pseudo-radius data f o r runs 18 and 19 were measured o r i g i n a l l y  i n m e t r i c units„  The a s t e r i s k marks under column 170° show the f i l m frames where no pseudo-radius measurements were taken due t o the dark b l o t c h appearing between the drops, as mentioned earlier.  Table K - l .  P s e u d o - r a d i u s Data of L e f t  Time p r i o r ^Dividing Film to onset ^\Line Frame o f c o a l e s - Obser-" No. c e n c e . s e c c v a t i o n Nd>  70°  100°  130°  145°  D r o p i n Run  18  155°  185°  Pseudo-radius, (Measurements on the enlargement;  0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150  0 0.0013 0.0027 0.0040 0.0053 0.0067 0.0080 0.0093 0.0106 0.0120 0.0133 0.0146 0.0160 0.0173 0.0186 0.0201 0.0214 0.0228 0.0241 0.0255 0.0268 0.0283 0.0297 0.0310 0.0324 0.0337  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  170°  3.80 3o75 3.80 3.80 3.80 3.80 3.80 3.80 3.75 3.80 3.75 3.75 3.75 3.75 3.80 3.80 3o70 3.80 3c 70 3»70 3.80 3.80 3c75 3.75 3-75 3.70  4.30 £o35 4.30 4.35 4.40 £c35 4.30 4.35 4.35 4.35 4.30 4.35 4.40 4.35 4.30 4.35 4.30 4.35 4.30'- 4 . 3 5 4.30 4.35 4.30 4.35 4.30 4.35 4.3O 4.35 4.30 4.35 4.30 4.35 4.30 4.35 4.30 4.30 4.3O 4.35 4.30 4.35 4.30 £.35 4.30 4.35 4.3O 4.35 4.30 £c35 4.30 £.35 4.25 £.35  4.20 4.15 4.20 4.20 4.20 4.20 4.20 4.15 4.15 4.20 4.20 4.20 4.20 4.15 4.20 4.15 4.15 4.15 4.20 4.20 4.15 4.15 4.15 4.20 4.20 4.15  4.00 4.00 4.00 4.00 4.00 3.95 3.95 4.00 4.00 4.00 4.00 4.00 3.95 3.95 4.00 3.95 4.00 4.00 4.00 4.10 3o95 • 3o95 4.00 4.00 4.00 4.00  •a •a#  * * *  •a-  * * * # #  *  220O  50°  280°  3-55 3.50 3 = 50 3°55 3-50 3°55 3»55 3°55 3.55 3 = 55 3-55 3»55 3.55 3 = 55 3-55 3°55 3.60 3 = 55 3.55 3.55 3.55 3-55 3.60 3°55 3-55 3*55  4.35 4.30 4.30 4 = 35 4.25 4.30 4.3o 4.30 ^•35 4.30 4.35 4.35 4.35 4=35 4.35 4.30 4.35 4.30 4=35 4.30 4=30 4.25 4.35 4.35 4.35 4.35  2  cm.  magnification  *  195°  3.60 3«60 3.60 3.60 3.60 3.60 3.60 3»6o 3.60 3.60 3.60 3c55 3.60 3.55 3.60 3.60 3.60 3.60 3.60 3.60 3.60 3o60 3.60 3.60 3.60 3.60  =  3.45 3.45 3.45 3°50 3.45 3.45 3c45 3.45 3.50 3-^5 3.^5 3.45 3-^5 3.45 3-^5 3.^5 3 ^ 5 3.45 3.45 3.50 3.45 3.45 3.50 3.45 3.50 3.50  2kx)  3.35 3.35 3»35 3o35 3*35 3.35 3°35 3.35 3.35 3.35 3.35 3.35 3.35 3.35 3o35 3.35 3.40 3-35 3.40 3»35 3.40 3-35 3°35 3»35 3.40 3.35  tt , f\j  Table K - 2 . Pseudo-radius  Film Frame Noo  0 6 1 2  18 24 3 0 3 6  42 48 54  Time p r i o r t o onset of coalescence.sec.  0 0 o 0 0 1 3  0.0027 0.0040 0 . 0 0 5 3  0.0067 0.0080 0 , 0 0 9 3 0 . 0 1 0 6  0.0120  6 0  0 . 0 1 3 3  6 6  0.0146  7 2 7 8  84 9 0 9 6 1 0 2 1 0 8  114 1 2 0 1 2 6 1 3 2 1 3 8  144 1 5 0  0 . 0 1 6 0 0 . 0 1 7 3  0.0186 0.0201 0.0214 0.0228 0.0241  .Dividing  .Line Obser-^ v a t i o n No>  1 2 3  4 5 6 7  8  9  3.40 3.40 3.40 3.40 3 . 3 5  3.40 3.40 3.40 3 . 3 5  4 . 1 0  4 . 1 0  4 . 0 0  4 . 1 5  4 . 1 0  4 . 0 0  4 . 1 5  4 . 1 0  4 . 0 0  4 . 1 5  4 . 1 0  3 . 9 5  4 . 1 0  4 . 1 0  3 . 9 5  4 . 1 0  4 . 1 0  4 . 0 0  4 . 1 0  4 . 1 0  4 . 0 0  4 . 1 0  4 . 0 5  4 . 1 0  4 . 1 0 4 . 1 0  4 . 0 0  3 . 9 5  4 . 0 5  3 o 7 0 3 » 7 0  3.60  4 . 3 5  4 . 0 5  3 . 5 0  3 . 7 0  4.40  4 . 0 0  3 - 7 0  3 . 6 O  3 . 5 0  3 . 6 5  4 . 3 5  4 . 0 0  3 . 7 0  3 . 6 0  3 . 5 0  3 . 6 5  4 . 3 5  4 . 0 0  3 . 7 0  3 . 6 0  3 . 5 5  3 . 7 5  3 . 9 5  3.60  4 . 4 5  3 . 7 0  3 . 5 5  3 . 7 5  4 . 4 5  3 . 6 5  3 . 6 5  3 . 5 5  3 . 7 0  4.40  4 . 0 0  3 . 6 5  3.60  3 . 5 5  3 . 7 5  4 . 4 5  4 . 0 0  3 . 7 0  3 . 7 5  3 . 9 5  3 . 6 5  3 . 6 5  3 . 6 0  3 . 4 5  3 . 7 0  4.40 4.40  4 . 0 0  3 * 7 0  3 . 6 0  3 . 5 0  3 . 7 5  4 . 4 0  4 . 0 0  3 . 7 0  3 . 6 0  3 . 5 0  3 . 7 0  4 . 4 0  3 - 9 5  7 0  3 . 6 0  3 - 5 5  3 . 7 0  4 . 4 0  3 . 6 0  3 . 5 5  3 . 7 5  7 0  3 . 6 0  3 . 5 5  3 . 7 0  7 0  3 . 7 5  4 . 1 0  4 . 0 5  3 . 9 5  4 . 1 0  4 . 1 0  3 c 9 5  4 . 1 0  4 . 0 5  3 . 9 5  4 . 1 0  4 . 0 5  4 . 0 0  4 . 1 0  4 . 0 5  4 . 0 0  4 . 1 0  4 . 0 5  3 o 9 5  4 . 1 0  4 . 0 5  3 . 9 5 4 . 0 0  3 c 9 5  4 . 1 0  4 . 0 5  3 . 9 5  3 o 9 5  4 . 1 0  4 . 0 5  3 . 9 5  4 . 0 5  1 7  18 1 9  •35 3 . 3 5  3 . 9 0  0.0268 0.0283 0.0297  21  3 - 3 5  2 2  3.40 3.40  3 . 9 5  24  3 . 3 5  2 5  3«4o  2 3  2 6  3.40  3 . 9 5  3.60  3 . 5 0  7 0  3 . 6 0  3 . 5 5  3 . 7 0  7 0  3 . 6 5  3 . 5 5  3 . 7 0  3 . 6 5  3 . 5 5  4 . 4 0 4 . 4 0 4 . 4 0  4.40 4 . 4 0 4 . 4 0  3 . 5 0  3 . 6 5  3 c 7 0  3 - 5 5  3 . 7 5  4 . 0 0  3 . 7 0  3 . 6 0  3 . 5 0  3 . 6 5  4 . 0 0  3 . 7 0  3.60  3 - 5 °  3 . 7 °  3 . 9 5  3 . 7 0  3 . 6 0  3 . 5 °  3 - 7 5  3 . 6 5  3 . 6 0  3 . 5 0  3 . 7 0  4.40  3 . 6 5  3 . 6 0  3 . 7 °  4 . 4 0  4 . 0 5  4 . 1 0  4 . 1 0  3 . 9 5  4 . 1 0  4 . 0 5  3 . 9 0  4 . 1 0  4 . 0 5  4 . 1 0  4 . 0 5  4 . 1 0  4 . 0 0  3 c 9 5  6 5  3.60  3 c 9 5 4 . 0 0  3 . 9 5  •a-  3 . 5 5  3 . 9 5  3.40  0 . 0 3 3 7  4.40  3 . 6 5  3 . 9 5  1 6  2kx) 3 . 6 5  3 . 3 5  3 o 9 5  280c  3 . 5 0  1 2  ,40 ,40 ,40 ,40  2 5 0 °  3 . 5 0  1 1  3.40  =  c  3 . 6 0  4 . 0 5  1 5  ,  3.60  4 . 1 0  14  _  3 » 7 0  3 c 9 5  3 » 3 5  magnification  4 . 0 5  3.40  1 3  .  P s e u d o - r a d i u s , cm,  (Measurements on the enlargement;  4 . 1 0  1 0  i n Run 1 8  _  2 0  0.0324  o f R i g h t Drop  7 0 ° 100° 130° 145° 1 5 5 ° 170° 185° 195° 220  0 . 0 2 5 5  0 . 0 3 1 0  Data  4 . 0 0 3 . 9 5  3 . 5 °  4 . 4 0 4 . 4 0  4.40 4 . 4 5  Table K-3. Pseudo-radius Data of L e f t Drop In Run 19 Time p r i o r .Dividing Film to onset ^\Llne Frame of c o a l e s - ObserNo. cence.seo. v a t l o n NoV  0 4 8  12 16 20 24 28  32 36  40  44 48  52 56  60  64  68 72  76 80 84  88  92 96  100  117  134 151 168 185  202  0 0.0013 0.0027 0.0040  0.0054 0.0067 0.0080 0.0094  0.0109 0.0123  0.0137 0.0150 0.0164 0.0178 0.0193  0.0207  0.0221 0.0235 0.0249  0.0262 0.0278 0.0292  O.O306 0.0320 0.0333 0.0347 0.0412 0.0477 0.0538  0.0606 0.06?3  O0O736  1 2  3 4 5 6 7  8 9 10 11 12 13 14  15 16  17 18 19  20 21  22 23 24  25 26 27 28  29 30 31 32  70° 100° 130°  145°  155° 170° 185° 195°  Pseudo-radius, cm, (Measurements on t h e enlargement;  3.45 3.45 3.35 3.40 3.45 3.45 3.45 3.40 3.45 3.45 3.45 3.40 3.40 3.40 3.45 3.45 3.40 3.40 3.45 3.45 3.45 3.40 3.40 3.45 3.40 3.40 3.40 3.40  3.90 3.85 3.85 3.85 3.90 3.90 3.90 3.90 3.90 3.85 3.90 3.80  3.85 3-85 3.85 3-85 3.85 3.85 3.85 3.80 3.85 3.80 3.85 3.85 3.80 3.80  3.80  3.75 3.75 3.35 3.75 3»35 3.75 3*35 3»75 3«3Q  3.95 3.75 3.95 3.75 3.95 3.75 3.90 3.80 3.95 3.75 3.95 3.75 3.95 3.75 3.95 3-75 3.95 3.75 3.90 3.75 3.95 3.75 3.90 3.75 3.90 3.75 3.90 3.70 3.90 3-75 3.90 3.75 3-90 3.75 3.90 3.75 3.85 3.65 3.85 3.70 3.85 3-65 3.90 3.70 3.90 3.75 3.90 3.75 3.85 3.65 3-85 3-65 3.85 3-65 3.80 3.65 3.80 '3.60 3.80 3o65 3.80 3.65 3.80 3-65  magnification  3.65  3.70 3.70 3.70 3.70 3.65 3.65  # «  3.70  3.65 3.65 3.65 3.65 3.65 3.65 3.65 3.65  3.70 3.65  3.60  3.60  3.60  3.65 3.65 3.65  3.60 3.60 3.60  3.60  3.60 3.60  3.60 3*65  * * # 3.45 3.45 3.45 3.45 3.45 3.45 3.40 3.40 3.45 3.40 3.40 3.40 3.40 3-35 3.40 3.40 3.40 3.40 3*40  =  3.10 3.15 3.15 3*15 3.10 3.10 3.10 3.15 3.10 3.15 3.10 3.15 3.10 3.10 3.10 3.15 3.15 3.10 3.10 3.10 3.10 3.10 3.15 3.10 3.10 3.10 3.10 3.10 .25 3.10 .25 3.10 .25 .25 3.15 >30 3.20  3.25 3.30 30 25 25 25 25 3.25 3.25 3.25 3.25 3.25 3.25 3.25 3.25 3.25 3.30 3.25 3-25 3-25 3.25 3.25 3.25 3.25 3.25 3-25 3.25  220°  250°  280°  3.20 3.20 3.20 3.20 3.20 3.20 3.20 3.20 0 3<2 2 0 3<20 3. 25 3.20 3< 3 .20 3.20 3.20 3.25 3.20 3.20 3.25 3.25 3.25 3.25 3.25 3.20 3.25 3.30 3.30 3.25 3.30 3.30 3«30  3.85 3.85 3.85 3.85 3-85 3.85 3.85 3.85 3.85 3.85 3-85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.90 3.90 3.85 3.85 3.90 3o95  24x)  3.00 3.00 3.00 3.05 3.00 3.05 3.05 3.00 3.00 3.05 3.05 3.05 3.05 3.05 3.00 3.05 3.10 3.10 3.05 3.10 3.05 3.10 3.05 3.05 3.05 3.05 3.10 3.10 3.10 3.10 3.10 3ol5  Table K - 4 . Time p r i o r Film to onset Frame o f c o a l e s No. cence.sec.  P s e u d o - r a d i u s Data o f R i g h t Drop i n Run 1 9  Dividing Xine Observ a t i o n NcV  70° 100° 130°  4  8 12 16 20 24 28  32 36  40 44 48  52 56 60 64 68  72 76 80 84  88 92 96 100 117 134 151 168 185 202  0 0.0013 0.0027  1  0.0054 0.0067  5 6 7  0.0040  0.0080  0.0094 0.0109 0.0123 0.0137 0.0150 0.0164 0.0178 0.0193 0.0207 0.0221 0.0235 0.0249  0.0262 0.0278 0.0292  0.0306 0.0320 0.0333 0.0347 0.0412 0.0477  O.O538 0.0606 0.0673 0.0736  2  3  4  8 9  10 11 12  n  15 16 17 18 19 20 21 22 23 24  25 26 27 28 29  30 31 32  155°  170° 185°  Pseudo-radius, (Measurements  0  145°  3.25 3.25 3.25 3.25 3.25 3.25 3.25 3.25 3.25 •25 •25 •25 •25 25 3.25 3.25 3-25 3.25 3.25 3. 25 3. 25 3. 25 3- 25 3. 25 3- 25 3. 25 3«25 3- 25 3« 25 3« 25 3. 25 3« 25  3.75 3.75 3.75 3.75 3.75 3.75 3.75 3.70 3.70 3-75 3.75 3.75 3.70 3.75 3.75 3.70 3.75 3.75 3.75 3-75 3.75 3.75 3.75 3.75 3.75 3.75 3- 75 3. 75 3. 75 3. 75 3. 75 3< 75  on t h e enlargement;  3.90 3.90 3.90 3.90 3.90 3.95 3.95 3.95 3.90 3.90 3.90 3.90 3.85 3.90 3.90 3.90 3.85 3-90 3.90 3.90 3.85 3.90 3.90 3-90 3.90 3.90 3.90 3.90 3.90 3.90 3.90 3.90  3.85  3.85  3.85 3.85 3.85 3.85 3.85 3.85 3.85  3.80 3.80  3.80  260°  cm. magnification =  •  3.80  3.80  3.80 3.80 3.75 3.80  3.85 3.80 3.85 3.80 3.80 3.75 3.80 3.75  195° 220° 250°  #  3.85 3.80 3.60 3.85 3.80 3.60 3.80 3.75 3.60 3.80 3-75 3.60 3.85 3.80 3.60 3.80 3.75 3.55 3.05 3.80 3.60 3.85 3.80 3.60 3.80 3.75 3.55 3.80 3.75 3.55 3-85 3.80 3.60 3.80 3.75 3.60 3.80 3.75 3.6O 3.80 3.75 3.55 3.80 3.75 3.55 3.80 3.70 3.55 3.80 3.70 3.55 3.80 3.70 3.55 3.75 3.70 3.50  3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.45  3.50 3.50 3.50 3.50  3.45 3.45 3.40 3.40 3.40 3.40  3.45 3.45 3.45 3.45 3.45 3.40 3.40 3.40 3.45 3.45 3.45 3.45 3.45 3.45 3.45 3.45 3.45 3.45 3.45 3.45 3.45 3.40 3.45 3.45 3.45 3.45 3.40 3.40 3.35 3.35 3-35 3.35  24x)  3.35 3.35 3.35 3.35 3-35 3.35 3.35 3.35 3-35 3-35 3.35 3.35 3.35 3-35 3.35 3-35 3.35 3- 35 3- 35 3. 35 3. 35 3. 35  3-35 3-35 3.35 3-35 3-35 3-35 3.30 3.25 3.25 3-25  3.55 3-55 3.55 • 55 • 55 55 • 55 • 55 55  3-55 3.55 3-55 3-55 3.55 3-55 3-55 3.60 3.55 3-55 3.55 3.55 3.55 3.55 3.55 3.60 3.55 3-55 3.55 3.50 3.50 3.50 3.50  4.20 4.15 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.20 4.2 0 4.20 4.20 4.20 4.20 4.20 4.15 4.20 4.15 4.20  tt 1  L - l  Appendix I n p u t and  Sample "UBC  The line are  sample  7 0 ° o f the l e f t s e c o n d s and f e e t  L  Output of the L i b r a r y LQF",  f o r Run  o u t p u t on page drop.  19  L - 4 i s f o r the d i v i d i n g  The u n i t s  respectively.  Program,  o f the X and Y  variables  L PLEASE  RETURN  •> SJ'OB  16006  $P AGE  TO  THE  CHEMICAL  JOB  NUMBER  JOB  START  LEOPOLDO  ENGINEERING  16006 16HRS  - 2 BUILDING  CATEGORY F 25MIN  CORDERO  USER'S  NAME-  LEOPOLDO  V9M011  46.3SEC  CORDERO  USE OFF  JR.  30  '^FORTRAN  i.  C ^ 0  L E A S T SQUARES F I T FOR RUN 19 . . . .. DIMENSION X ( 2 0 0 ) , Y ( 2 0 0 ) , Y F ( 2 0 0 ) W ( 2 0 C ) E l ( 5 0 ) » E ? ( 5 0 ) iP(50 ) . R E S ( l F(200)»R(200)tYSUM(200)  1  ?  >  "-  s  3 4 5 6 7 10 11 12 13 14 15 16 17 20 21 22 23 « 24 25 26 27 30 31 32 33 34 35 36 37 40 41 42 43 44 45 46 47 50 51 52 53 54 55 56  .t-t p-  t  t  f  3 R E A D ( 5 , 1 ) N,MtNI 1 F0RMAT13I5) YSUM(1)=0. DO 39 1=1,5 39 P ( I ) = 0 . 0 2 FORMAT!13F6.2)  20  R E A D ( 5 , 2 ) ( F ( I ) ,R(I) ,I= 1,N) DO 18 1=1iN I F ( F ( I ) . L T . 3 . 0 ) GO TO 20 I F ( F ( I).GT.3 .0.AND.F(I) . L T . 2 9 . 0 ) GO TO 21 I F ( F ( I )..GT.29.0.AND.F( I ) . I T . 5 4 . 0 ) GO TO 2 2 I F ( F ( I ) ..GT. 5 4 . 0 . AND. F ( I ) . L T . 7 8 .GO 0 ) TO 23 I F ( F ( I ) . G T . 7 8 . 0 . A N D . F ( I ) . L T . 1 0 1 . ) GO TO 30 I F ( F ( I ) . E Q . 1 1 7 . ) GO TO 31 32 I F ( F ( I ) ..EQ. 1 3 4 . ) GO TO I F ( F ( I ) . E Q . 1 5 1 . ) GO TO 32 I F ( F ( D . . E Q . 1 6 8 . ) GO TO 34 I F ( F ( I ) . E Q . 1 8 5 . ) GO TO 35 I F I F I I ) . E Q . 2 0 2 . ) GO TO 36 X(I GO  )=F(I)/(2560.*1.17) TO 17  21  X( I ) = F { I ) / ( 2 5 5 0 . * 1 . 17) GO TO 17  22  X ( I ) = F ( I ) / ( 2 5 0 0 . * 1 . 17 ) GO TO 17  23  X ( I ) = F ( I ) / ( 2 4 7 5 . * 1 . 17 ) GO TO 17  30  X(I)=F{I)/(2460.*l.17) GO TO 17  31  X(I)=F(I)/(2430.*1.17) GO TO 17  32  X ( I ) = F ( I ) / ( 2 4 0 0 . * 1 . 17) GO TO 17  34  X ( I ) = F ( I ) / ( 2 3 7 0 . * 1 . 17) GO TO 17  35  X( I ) = F ( I ) / ( 2 3 5 0 . * 1 . 17) GO TO 17  36 X ( I ) = F ( I ) / ( 2 3 4 5 . * 1 . 1 7 ) 17 Y d )=R( I ) / 3 0 . 4 8 18 Y S U M ( 1 ) = Y S U M ( 1 ) + Y ( I ) YBAR=YSUM(1)/FLOAT(N) EXTERNAL AUX CALL L Q F ( X , Y , Y F , W , E 1 , E 2 , P , 0 . , N , M , NI» NO,EP,AUX ) I F ( N D . E O . O ) GO TO 3 WRITE(6,40)  L  57 60 61 62 63 64 65 66 67 70 71 72 73 74 75 76  F(.)RMAT(66II E S T I M A T E S OF ROOT MEAN SQUARE S T A T I S T I C A L CR •<0R I \l THE 1 PARAME TER S) W R I T E ( 6 , 5) ( E l ( I ) , 1 = 1 »M ) WRITE(6,4) 4 F 0 R M A T ( 6 0 H E S T I M A T E S OF ROOT MEAM SQUARE T O T A L ERROR IN THE PARAME ITERS) M) W R I T E ( 6 , 5 ) ( E 2 ( I ) ,1 = 1, 5 FORMAT(1X,OG15.5) WRITE(6,6) 6 FORMAT(88H V A L U E S OF X F I T T E D V A L U E S OF Y RESI V A L U E S OF Y Y-YBAR) 1DUALS Y BAR DO 7 I=1,N D I FF = Y{ I ) - Y B A R RES(I)=Y(I)-YF( I ) 7 W R I T E ( 6 , 5 ) X ( I ) , Y ( I ) , Y F ( I ) , R E S ( I )t Y B A R , D I F F WRITE(6,8 ) 8 FORMAT(1H1) GO TO 3 END  40  SIBFTC 77 j 100 10:1 102 103 104 , 105 106 107 !  - 3  THS5B F U N C T I O N AUX(P,.D,X,L) DIMENSION P ( 5 0 ) , D ( 5 0 ) D ( 1 ) = 1. AUX=P(1) DO 10 J = 2 , 5  o(j)=n(J-I)*x 10 AUX = AUX,+ P ( J )*D( J ) RETURN END GENTRY  L - 4  EXECUTION  I N T E R M E D I A T E E S T I M A T E S OF PARAMETERS 0.00000E-38 0.00000E-38 FINAL  ESTIMATES 0.11310  OF  PARAMETERS -0.45928E-01  NO  E S T I M A T E S OF ROOT MEAN SQUARE S T A T I S T I C A L ERROR IN THE PARAMETERS 0.29124 9.3490 E S T I M A T E S OF ROOT MEAN SQUARE T O T A L ERROR IN THE PARAMETERS 0.28971E-03 0.92999E-02 RESIDUALS F I T T E D V A L U E S OF Y V A L U E S OF X V A L U E S OF Y 0.93316E-04 0.00000E-38 0.11319 0. 1 1 3 1 0 0.11319 0. 1 1 3 0 3 0.15489E-03 0.13407E-02 0.10991 0.11297 0.26814E-02 -0 . 3 0 6 4 4 E - 0 2 0.4O221E-O2 0.11291 0.11155 -0.13624E-02 0.53628E-02 0.11319 0.11285 0 .33962E-03 0.67035E-02 0.11279 0.11319 0 .40119E-03 0.80442E-02 0.11319 0.11273 0.46277E-03 0.11155 0.11266 -0.11161E-02 0.93850E-02 0.11319 0.11259 0.10940E-01 0 .59577E-03 0.12308E-01 0.11253 0 .65858E-03 0.11319 0.11319 0.11247 0.13675E-01 0.72139E-03 0.11240 -3 . 8 5 6 2 2 E - 0 3 0.15043E-01 0.11155 0.16410E-01 0.11234 0.11155 -0 . 7 9 3 4 2 E - 0 3 0.11228 -0.73061F-03 0.17778E-01 0.11155 0.11319 0.19339E-01 0.1122 1 0 .98150E-03 0.11214 0 . 10449E-02 0.20720E-01 0.11319 0.22101E-01 0.11155 0. 1 1 2 0 8 -0 . 5 3 2 0 4 E - 0 3 0.11202 -0 . 4 6 8 6 0 E - 0 3 0.11155 0.23483E-01 0.11319 0.11195 0.24864E-01 0 .12353E-02 0.11319 0.11189 0.26245E-01 0 . 12987E-02 0. 1 1 3 1 9 0.11 182 0. 1 3 6 9 9 E - 0 2 0.27795E-01 0.11176 -0.20671E-03 0.29185E-01 0.11155 0.30575E-01 0.11169 0.11155 -0.14288E-03 0.11163 0.31964E-01 0 . 15614E-02 0.11319 0.33354E-01 0.11155 0.11156 -3.15221E-04 0.34744E-01 0.11150 0.48608E-04 0.11155 0.41152E-01 0.11155 0.11121 0.34293E-03 0.11090 3.64461E-03 0.11155 0.47721E-01 0.10991 -0.71776E-03 0.53775E-01 0.11063 0.10991 0.11031 -0.40493E-03 0.60586E-01 -0.97276E-04 0.10991 0.67285E-01 0.11001 0. 1 0 9 7 1 -3.14465E-02 0.73625E-01 0.10827  0  M  -  1  Appendix M Input and Sample Output of the M u l t i p l e f o r Run 19  The  W r i t t e n by Kozak and Smith  (The p r e d i c t i v e  equation  i s i n Table XII and i s shown g r a p h i c a l l y i n F i g . 40.)  Under the heading,  "Independent V a r i a b l e " ,  the terms X ( I ) ,  X1SQR, XICUB, and XIFOR -correspond t o X, X , 2  respectively length  (45)  sample output, s t a r t i n g on page M - 3 , i s f o r the  d i v i d i n g l i n e 7 0 ° of the l e f t drop. chosen  R e g r e s s i o n Program  i n the polynomial model.  (e.g., Y) i s f e e t , and f o r time  X, 3  and. X^  The u n i t used f o r (e.g., X),  seconds.  M  LEOPOLDO  CORDERO ISN 0 1 2 3 4 11  1  I 01HRS  2  FORTRAN  * * t  4  c c  *  * c  20 * 21 * 22 * 2 24 3 25 * 30 * 33 1 t C 35 * 36 * 37 40 * 41 6 43 * 5 46 * 47 *  NO M E S S A G E S F O R 46MIN 29.9SEC  SOURCE  LIST  STATEMENT  SIBFTC DATA MULTIPLE REGRESSION PROGRAM C  +  12 13 14 15  JR. SOURCE  -  (CODED BY A. KOZAK) FOR  RUN  S U B R O U T I N E DAT ( X , A V , P R O D , N R E A U , N R C W , N V A R , X M I u,XMAX) DIMENSION X ( 7 0 ) , AVI 7 0 ) , P R O D ( 7 0 , 7 0 ) , X M I N ( 7 0 ) , X M A X ( 7 0 ) DO 5 K = 1 , N K 0 W READ ( 5 , 4 ) (X( I ) , I = 1 , N R E A D ) FORMAT(2F15.7) X=VARIABLES TRANSFORMATIONS ENTERED HERE X(3)=X(1)*X(1) X(4)=X(3)*X(I) X(5 ) =X(4)*X(1) IF IK. N C I ) GO TO 3 F I N D M I N I M U M AND M A X I M U M V A L U E S DO 2 I = i , N V A R X M I N U )=X( I) X M A X ( I ) = X{ I ) DO 1 I=1,NVAR IF ( X ( I ) . L T . X M I N ( I ).) X . M I N I I ) = X ( I ) IF ( X ( I ) . G T . X M A X ( I ) ) X M A X I I )=.X( I ) CONTINUE C A L C U L A T E SUMS ( A V ) AND P R O D U C T S (PROD) DO 5 I=1,NVAR A V { I ) = A V ( I ),+ X( I ) DO 6 J = I , N V A R P R O D ( I , . J ) = P R O D ( I , J ) + X ( I ) *X { J ) P R C D ( J , I ).= P K C D ( I »J.). CONTINUE RETURN END  ABOVE  ASSEMBLY  19  M - 3  REGRESSION  ANALYSIS,  THE  DEPENDENT  VARIABLE  IS  Y  INDEPENDENT VARIABLE  REGRESSION C G E F F I C IENT  XII) X1SCR XICUB X1F0R  G.220321E-01 - 0 . 5 9 2 4 2 5 E OO - 0 . 140900E 02 0 . U 6 9 6 9 E 03  0,032 0.006 0.008 0.011  ANALYSIS,  THE  DEPENDENT  VARIABLE  R E G R E S S ION C O E F F I t IENT  STANDARD D L V I A I ION  VAR I A NCI": RA n n  0. 125438E-01 - 0 . 2 6 6 3 5 9 E 02 0.201370E 03  0.316670E-01 0 . 2 8 5 2 8 1 E 02 0.341854E 03  0,157 0,872 0,347  IS  C O N S T A N T TERM =; 0 . 112379E 00 S T A N D A R C ERROR OF E S T I M A T E = 0.915158E-03 RESIDUAL VARIANCE «= 0 . 8 375 1 4 E - 0 6 M U L T I P L E CORRELAT ICN C O E F F I C I E N T = 0.75152 R SQUARED = C.56479 VARIANCE RATIO =; 12.112 WITH 3 AND THE V A R I A B L E TO BE O M I T T E D I S = XI I )  REGRESSION  AN4LYSIS,  THE  DEPENDENT V A R I A B L E INDEPENDENT VARIABLE XICUB X1F0R  C O N S T A N T TERM =, 0.112516E 00 S T A N D A R D ERROR: O F E S T I M A T E = 0.901757E-03 RESIDUAL VARIANCE = 0.813165E-C6 MULTIPLE CORRELATION COEFFICIENT = 0.74990 R SQUARED >= C . 5 6 2 3 5  IS  D E G R E E S OF  FREEDOM  Y  INDEPENDENT VARIABLE X( I ) XICUB X1F0R  27  0.122970E 0.740929E 0.159574E 0.111150E  VARIANCE RATIO  00 01 03 OA  C O N S T A N T TERM ^ 0.112346E 00 STANDARD ERROR OF E S T I M A T E = 0.931841E-03 KESICUAL VARIANCE = 0.868327E-06 MULTIPLE CORRELATION COEFFICIENT = 0.75159 R SQUARED = 0.56489 VARIANCE RATIO =i 8.763 WITH 4 ANO T H E V A R I A B L E TO OE O M I T T E D I S = X1SGR  REGRESSION  STANDARD DEVIATION  28  D E G R E E S OF  FREEDOM  Y  REGRESSION COEFFICIENT -0.167328E 0.907656E  02 02  STANDARD D E V I AT ION 0.135402E 0.194341E  02 03  VAR ! ANCE RATIO 1.527 0.218  M -  VARIANCE RATIO = 18.631 THE V A R I A B L E TO BE OMITTED IS = REGRESSION  WITH X1FCR  4  2  A N A L Y S I S , THE DEPENDENT V A R I A B L E  AND  IS  REGRESSION COEFFICIENT - 0 . 1 0 4 6 0 1 E 02  REGRESSION  SELECTED  REGRESSION COEF.FIC IENT  STANDARD DEVIATION  VAR I A N C E  - G . 4 0 0 2 2 1 E 02 0 . 6 8 8 5 9 5 E 00 0. 2 8 6 1 U E 03  0 . 6 6 0 0 9 9 E 02 0 . 1 9 0 8 9 2 E 01 0 . 5 7 6 3 6 6 E 03  0,363 0,130 0.246  30  FOR A L L COMBINATIONS ARE = XICUB  0.169605E  VARIANCE RAT3U 33,036  DEGREES OF FREEDOM  XISQR  X1F0R  A N A L Y S I S , THE DEPENDENT V A R I A B L E I S INDEPENDENT VARIABLE XICUB XISQR X1F0R  CONSTANT TERM =. 0. 112433E 00 STANDARD ERROR OF ESTIMATE = 0.915593E-03 RESIDUAL VARIANCE = 0.8383UE-06 MULTIPLE CORRELATION C O E F F I C I E N T = 0.75125 R SQUARED = 0.56437 VARIANCE RATIO =i 12.092 WITH AND REGRESSION  STANDARD DEVIATION 01  CONSTANT TERM =; 0 . 1 1 2 4 6 2 E 00 STANDARD ERROR OF ESTIMATE = 0.B89928E-03 RESIDUAL VARIANCE * 0.791972E-06 MULTIPLE CORRELATION C O E F F I C I E N T = 0.74770 R SQUARED <= 0. 5 5 9 0 6 VARIANCE RATIO =. 38.036 WITH I AND THE V A R I A B L E RETAINED I S = XICUB THE V A R I A B L E S  DEGREES OF FREEDOM  Y  INDEPENDENT VARIABLE XICUB  29  28  RATIO  DEGREES OF FREEDOM  A N A L Y S I S , THE DEPENDENT V A R I A B L E I S INDEPENDENT VARIABLE XICUB X1SCR  CONSTANT TERM =, 0. 1 12520E 00 STANDARD ERROR OF ESTIMATE = C.903619E-03 RESIOUAL VARIANCE * 0.816527E-06 M U L T I P L E CORRELATION C O E F F I C I E N T = 0.74869  REGRESSION COEFFICIENT  STANDARD OEVIATION  VARIANCE RAT 5 0  - 0 . 7 5 9 2 1 4 E 01 -G.201739E 00  0 . 9 3 2 9 5 1 E 01 0 . 6 4 4 9 8 4 E 00  0,662 0,098  M -5  c  R SCUARED  =  C56C54 29  VARIANCE RATIO  =.  10.495  WITH  2  OEGREES OF FREEDOM  AND Y  ?  REGRESSION ANALYSIS.  THE DEPENDENT VARIABLE  IS  INOEPENDENT VARIABLE X1CUQ XIFOR CONSTANT TERM =s 0.112516E 00 STANDARD ERROR OF ESTIMATE = C.901757E-03 RESICUAL VARIANCE = 0.S13165E-06 MULTIPLE CORRELATION COEFFICIENT = 0.74990 R SQUARED = 0.56235 VARIANCE RATIO => 18.631 WITH 2 AND REGRESSICN ANALYSIS,  THE DEPENDENT VARIABLE  IS  INDEPENDENT VARIABLE  CONSTANT TERM =. 0 . 112553E 00 STANDARD ERROR OF' ESTIMATE = 0.905555E-03 RESIDUAL VARIANCE «= 0.820030E-06 MULTIPLE CORRELATION COEFFICIENT = 0.74743 R SQUARED «= 0 . 55865 VARIANCE RATIO =i 18.354 WITH 2 AND THE OEPENOENT VARIABLE  IS  INDEPENDENT VARIABLE X1CUB CONSTANT TERM =, 0.112462E 00 STANOARO ERROR OF ESTIMATE = 0.889928E-03 RESICUAL VARIANCE = 0.791972E-06 MULTIPLE CORRELATION COEFFICIENT = 0.74770 R SQUARED = 0.55906 VARIANCE RATIO 38.036 WITH 1 AND REGRESSION ANALYSIS, V  THE DEPENDENT VARIABLE  STANDARD DEVI A TION  0. 167328E 02 0.907656E 02  0.135402E 02 0.194341E 03  29  IS  VAR I ANCE RA T t 0 I ,527 0 >?18  DEGREES OF FREEOOM  Y REGRESSION COEFFICIENT 0.443410E 00 0.597398E 02  X1SCR XI FOR  REGRESSION ANALYSIS.  REGRESSION COEFFICIENT  29  STANDARD DEVI AT ION  VAR! ANCE RATIO  0.393214E 00  I ,2 72 0,5 36  0.816352E  02  DEGREES OF FREEOOM  Y REGRESSION COEFFICIENT  STANDARO DEVI AT ION  VARIANCE RATIO  0.104601E 02  0.169605E 01  38,0 36  30 Y  DEGREES OF FREEDOM  M - 6  INDEPENDENT VARIABLE XISQR  REGRESSION COEFFICIENT  STANDARD DEVIATION  VARIANCE RATIO  - 0 . 7 1 7 5 9 3 E OO  0.118386E OO  36.741  > CONSTANT TERM =i 0 . 112655E OO STANDARD ERKCR OF ESTIMATE = 0.898518E-03 RESIDUAL VARIANCE = 0.807334E-06 MULTIPLE CORRELATION COEFFICIENT = 0.74196 R SCUARED = 0.55C5O VARIANCE RATIO =i 36.741 WITH 1 AND REGRESSION ANALYSIS,  THE DEPENDENT VARIA8LE  IS  DEGREES OF FREEDOM  Y  INDEPENDENT VARIABLE X1F0R  30  REGRESSION COEFFICIENT  STANDARD DEVIATION  VARIANCE RATIO  - 0 . 147456E 03  0.248825E 02  35.119  CONSTANT TERM =; 0 . U 2 3 6 3 E 00 STANDARD ERROR OF E6TIMATE = 0.909645E-03 RESIDUAL VARIANCE = 0.827454E-06 MULTIPLE CORRELATION COEFFICIENT = 0.73437 R SCUARED = G.53930 VARIANCE RATIO =i 35.119 WITH 1 AND  30  DEGREES OF FREEDOM  

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