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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, JR. B. S „ s U n i v e r s i t y of Santo Tomas, I 9 6 3 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of CHEMICAL ENGINEERING We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA February, 1 9 7 0 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment o f Chemical E n g i n e e r i n g 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 V a n c o u v e r 8, Canada Date F e b r u a r y 24. 1970 i i ABSTRACT High-speed movie photography of drop coalescence i n a l i q u i d - l i q u i d e x t r a c t i o n column has been used to study the mechanism of coalescence t a k i n g p l a c e between drop p a i r s undergoing mass t r a n s f e r 0 The d i r e c t i o n o f d i f f u s i o n s t u d i e d was mainly from the d i s p e r s e d t o the continuous phase. The d e n s i t y o f the d i s p e r s e d phase was l e s s than t h a t o f the continuous phase o The e x t r a c t i o n system c o n s i s t e d of a g l a s s spray column o f square c r o s s - s e c t i o n and a s s o c i a t e d apparatus. 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 o p t i -c a l system and a high-speed movie camera» The i n v e s t i g a t i o n was c a r r i e d out i n two ways: l o V i s u a l i z a t i o n o f the d i f f u s i o n p r o c e s s , by the use o f the s c h l i e r e n techniques, to study the motion o f v a r i o u s m a t e r i a l s o c c u r r i n g a t and near the drop c o n t a c t area° 2o Measurement of changes i n drop shape with timeo i i i TABLE OF CONTENTS Page INTR ODUCT I ON © O O © © 0 9 © © G O © « O © O O © » © © © © © © © © © © O © © © © O © O © O O Q O © X THE OR Y UNDER STUDY © © © © © © © o © © © © o e © e © o © o © © e o e « © o o © e © © © © e o *7 Jj'ffiSlilM. XNAH|Y INVESTI GAT I ON 0 o e e © o © © © o © o © © e © « o © e © e * « o © o © e © 1 3 A • SCOp© © © © 9 © © o © e © © o © © o © Q © © o © o © © © © © © o © s e © © © © o © © o © 1 3 B • P T O C Q C L I U 1 © • © © © © © © © © • • © © © © © • © © © © © © © © © © • © © © © © © © e © 1 3 MA IN INVESTIGATION © © © o o © o © © e « © o © © © o c o G S G c © e o © © « © « o © o © e © 2 0 A. 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.. 2 0 PART X SCHXiIEREN STUDIES © © © © © © © © o © © © o © o o © © © o o © o o © © © o © © 2 ^ A © SCOP© © © e © & © e © o © © © o 9 © « e © © o © 9 © © 9 © © o © © 0 © © o © © a © o & © 2 3 B. Some Photographic C o n s i d e r a t i o n s . 2 5 EXPERIMENTAI* PROCEDURE © © © © © © © © • © © • © © © © © © © • © © © © © © • © © © © © o 2 9 A. MIBK-Acetic Acid-Water System.................. 3 2 B* MIBK™Wstsi* Systsm © © © © © © © © © © © © © © © o © © © © © © © © © © © © © 3 ^ C. T o l u e n e - A c e t i c Acid-Water System .............. 40 RESULTS © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © a 3 DISCUSSION © © o o © © © e © © © o o © © e © 9 © © e © © o © © © © o © © © © e o © 9 © © e © © o © © 3 ^ A. E f f e c t of K n i f e Edge O r i e n t a t i o n on SChXi©I*©Tl IlH£L££© o e © © © © o © e © © o « © © « © o © © © © © o © © © © © © o 3 ^ B. Drop R o t a t i o n and Solute D i f f u s i o n i n the Continuous Ph&s© © © © © © © © © o © © © © © © © © © © © © © © © © © © © © © 6 0 C. Suspension of Drops a t Ends of Nozzles ........ 6 2 D. Forces I n f l u e n c i n g I n t e r f a c i a l A c t i v i t y ....... 6 4 E. Minimum A t t a i n a b l e Depth of F i e l d 6 6 CONCLUSIONS AND RECOMMENDATIONS 6 ? •PART I I DROP SHAPE STUDIES O © © © © © © © © © © © © © © © © © © © © © © © © © © © 6 9 A * SCOP© e e © © o © © o o © o o © © © © © © © © o © © © o © © © o © © © o © e © © © e © o ^ 0 i v TABLE OF CONTENTS ( c o n f d o ) Page B. Some Photographic C o n s i d e r a t i o n s © © © . © © . o © . © . © . ? 0 Co P r e l i m i n a r y C o n s i d e r a t i o n s ••••••••«••••©©••••• 7 2 EXPERIMENTAL PROCEDURE ©©©©©©0©©©©©©©©©©©©©©©©©©©©©©©©©© 9 0 A. MIBK-Methanol-Water System «©©©©©©©©. ©.©«©©©©©© 9 0 B. Measurement of Pseudo-radius •© .©•© 9 5 Co S t a t i s t i c a l T e s t s ©©©©©©©©©©©©o©©©©©©©©©©©©©©©© 1 0 0 RESULTS © © o o © © e © 0 0 © © o © o © © © © © © © © 0 © O O O Q © © 0 © d © © © © © © Q © 0 0 © 0 © © 1 0 5 A © Experimental Huns o e e o « © © o © © « « o © © © © © © © © © © o o o © © o 1 0 5 B. Pseudo-radius Measurement •••«••«• •••••••* 1 1 2 C© S t a t i s t i c s © © © © e © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © l l 6 DISCUSSION © © © © © © © a © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © ® © © 1 3 7 A. A p p l i c a b l e Photographic Problems «©©© >.. * 1 3 7 B© I n t e r p r e t a t i o n of Data © o © © © © © © © © © © © © © © © © © © © © © © 1^ 1*8 Co P r e c i s i o n of" Drop A n a l y s i s •©•©••••••••©•••©••• I 6 3 CONCLUSIONS AND RECOMMENDATIONS ©...©.. 1 6 9 III ITSR A TURB CI TB D © © © © © © © © © © © © © © a © © © © © © © © © © © © © © © © © © © © © © © © 1 7 ^ APPENDICES A. Determination of 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 the Di s p e r s e d Phase ••©•••©••••••••••••••••• A—1 B. Determination of Methyl A l c o h o l C o n c e n t r a t i o n i n the Di s p e r s e d Pha S © a « « » » 0 © a o e © © e © » © © © e © © © s e 13 " " l C. C a l i b r a t i o n of the Timing L i g h t Generator C - l D. Room Temperature F l u c t u a t i o n s © © » . © o « . « . © © © © © < > « D-l E. Test f o r S i g n i f i c a n c e of L i n e a r R e g r e s s i o n .... E - l F. P r o p e r t i e s of Various Substances Used F - l V TABLE OF CONTENTS (cont ' d o ) Page G. Derivation of Equation for the Locus of Points Generated by a Moving Drop with Respect to a Stationary Movie Camera G-l H. Sample Calculation Showing the Relationship between Linhof and Hycam Exposure Settings e e « H-l I a Calculation of Film Frame Span i n Runs 18 and 19 f o r Negligible Drop Growth E f f e c t 0 0 0 . 0 I - l Jo Heat E f f e c t s Accompanying the Mixing of G l a c i a l Acetic Acid into Water at Room TGHipGrSL t \H*© ©©©©©©•©©©©•©©©©©©©©©•©•©©©©•©•©•o J**"l IC© Ps©ud.o~i*o,ciixzs Efettst ©©o©©©©©©©©©©©©©©©©©©©©©©©© Lo Input and Sample Output of the Library Program, "UBC LQF", f o r Run 19 L - l M. Input and Sample Output of the Multiple Regression Program f o r Run 19 Written by Kozak and Smith (^5) • • • • o * * * o * s o * « o * o o * * * o * * o M—1 v i LIST OF TABLES Table Page I. Experimental Data f o r P a r t I ( S c h l i e r e n StlXCLle S ) © . © • © « . • « © « . . © » 9 . © o . . © . © o a © e o © « o © . . . . . © o 3 3 I I . B a l l Bearing Experimental Data ©.©.......©...©..D 8 5 I I I . R e f r a c t i v e Index-Concentration Data of Methyl A l c o h o l a t 2 5 ° C (Ref. 42) 8 9 IV. 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 R.© pI*OCL\ lCfc (R©f*« ^ 3 ) © © © © © © © © © © © • © © • © © e o e o o © © e o 9 3 V. Experimental Data f o r P a r t I I (Drop Shape StUdi© s) © © © © © © o © © o o o o o © © © © © a © © © © © © o © © o © © © © © © © © © © 9 ^ VI. Drop Holding and C o a l e s c i n g Times © . . © . . . © . . o . © © . 1 0 9 V i l a . A n a l y s i s of Variance Table of L e f t Drop i n Run 18 © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © a © © XI*p V l l b . A n a l y s i s of Variance Table of Ri g h t Drop i n Run X8 © © © © © © © © © © © © © © © © © © © © © © © © © © o © © © © © © © © © © © © XX8 V i l l a . A n a l y s i s of Variance Table of L e f t Drop i n Run X9 ©©©©©©©©©©•©•©©©©©©©©©©©©•©©©©©©©©©©©©© XX9 V H I b . A n a l y s i s of Variance Table of Ri g h t Drop i n Run X9 ©©©©©©*«©©©©©©©©©©©©©©©©©©©©©©*©©©©©©©© X20 i X a . A n a l y s i s of Variance Table of L e f t Drop i n Run 19 (Ext©nd©d) © © © © © © © © a © © © © © © © © © © © © © © © © © © © X2X IXb. A n a l y s i s of Variance Table of R i g h t Drop i n Run 1 9 (Extended) © © a . . © © © © © . © © . © . © © © © © © © © . © © © 1 2 2 X. A General Form of Anova Table .•..•..•«•••••••••• 1 2 3 XI. Drop D i v i d i n g L i n e s whose X-Y R e l a t i o n s h i p s Coi*i*©spond t o Z s r o SXop© © a © © © © © © © © © © © © © © * © © © © © © © X23 X I I . P r e d i c t i v e Equations and R 2 Values Obtained by the M u l t i p l e R e g r e s s i o n Program .............. 1 3 0 A—1« T i t r a t i o n Data ©©•©©«*.©.©..©..©©©.•.•©©•••«©©©.© A—2 B—1 o R e f r a c t i v e Index Data a t 2 0 ° C ................... B—3 C—1. Timing L i g h t C a l i b r a t i o n ........................ C—2 v i i LIST OF TABLES(cont'd.) Table Page D-l. Temperature Fluctuations i n Two Ch. E. Rooms .... D - 3 E - l . Various Properties of Different Substances at 2 0 ^ C where Applicable . . . . * o o » o . . o . . . . . . . . • • « • F—2 J - l . Heats of Solution of Acetic Acid-Water System Q.'fc 18©3^C (Rsf • tyTL ) o©«0«e©o®oo«©»«ooo®©o««o©©«»© J""2 K - l . Pseudo-radius Data of Left Drop i n Run 18 ....... K - 2 K - 2 . Pseudo-radius Data of Right Drop i n Run 18 ...... K - 3 K - 3 . Pseudo-radius Data of Left Drop i n Run 19 ....... K - 4 K-J+e Pseudo-radius Data of Right Drop i n Run 19 ...... K-5 v i i i LIST OF FIGURES Figure Page l o Ternary composition diagram with surface tension as parameter (19) . . © . . a © . . . . . . . . . 8 2 a o Transfer of material from the dispersed phase to the continuous phase for a system of the type corresponding to Figure 1 ( 1 9 ) 9 2 b . Transfer of material from the continuous phase to the dispersed phase f o r a system of the type corresponding to Figure 1 ( 1 9 ) . . . . . 1 2 3 » Schematic flow diagram of the extraction S y S t S f f i © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © f t 1 3 4- . Schlieren arrangement used i n the experiments .. 1 7 5 . Photographic views of the apparatus. (Corresponds to Figure 4©) 18 6© Extraction system O . O O O O O O » . O . O . O . . Q « . « « O » O . O O O O 2 1 7 * Extraction column o o e . « o o 9 « o 9 o o o . o o . o . o » « o . o o . « . 2 1 8. The region of illu m i n a t i o n i n a conventional schlieren system (3 9 ) • • • • • • • • • • • • • • • • • • » • • • • » • • 2 7 9 - 1 3 ° Schlieren photographs of various drop pairs .... ^8 1^4—17o Schlieren photographs of various drop pairs «... 5 2 18. Light bundle - knife edge arrangement i n th© Tosplsi* msttoocL (2 2) ©©©©©©©©©©©©©©©©©©©©©a©© 3 3 1 9 » Image formation, f o r a p a r t i c u l a r case, i n a schlieren system (Toepler method) ......... 5 8 2 0 . Basic photographic arrangement used f o r drop shs.p© stucli©s ©©©©©©©©©©©©©a©©©©©©©©©©©©©©© 7 ^ 2 1 . Conventional photograph of drop p a i r i n run 1 5 » o 7 9 2 2 . Simplified path of l i g h t ray passing between d l * O p S • •©©©•©oe©e©«oo9«©©«e©©eo©©d©e©e©e©G©o 7 ^ 2 3 ° E f f e c t of i r r a d i a t i o n and halation on UHIDSICIC© cL Jf i l n i (^ f*3 ) © © • « © • © © • • © • © © © © © © © • © « • • © © © © © 7 8 i x LIST OF FIGURES (cont'd.) Figure Page 24. Eff 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 contact with each other 7 9 2 5 » V-block mount f o r steel bearing experiments .... 81 2 6 . Photographic arrangement f o r steel bearing experiments and drop shape studies ............. 8 3 2 7 • Blocking of a l i g h t ray due to b a l l misalignment ....««.©» . . . . . . . o . . . ........««»»•.. 84 28. 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*© © © • © • • © • • © © • © • © © © © © © • © © © © © • • • © • • © © © 8^1" 29o CuS-coated b a l l bearings at a distance of separation of 0 . 0 0 1 5 i n . . . . . . . . . . . . . . . . . . . . . . . . . 8 7 3 0 . Locations of various d i v i d i n g l i n e s and reference points f o r drops being measured 9 8 3 1 . Impression of horizontal "band" for p l o t of r e s i d u a l vs. time ( 4 4 ) . . . . . . . . . . . . . . . . . . . . . . 1 0 2 3 2 . P a r t i a l view of coalescing MIBK drops 1 0 7 3 3 • Photograph from run 18 showing blurred grainy images at central area of the picture .......... 114 3 4 . Photograph from run 1 9 showing blurred grainy images at the l e f t and r i g h t side of the piCtUI*© • © © • • • © • © • © © © © © • © © © © © • © © • © • © © © © © • © © • © © © © 1 1 ^ 3 5 » Residual vs. observation no. (and frame no.) with no unexplained v a r i a t i o n . (Corresponds tO F i £ £ U 3 T © 3 1 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 12(7 3 6 . Residual vs. observation no. (and frame no.) with unexplained v & r i & t i o n © • • © • • © • © o * © © © © © © * © « 128 3 7 • Equations f i t t e d and behaviour observed over 0 - 1 5 0 f i l m frames i n run 18 1 3 1 3 8 . 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 1 3 2 3 9 . Equations fitted, and behaviour observed over 0 - 2 0 2 f i l m frames i n run 1 9 (extended) ... 1 3 3 X LIST OP FIGURES (cont'do) Figure Page 40. P l o t of 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 d i v i d i n g l i n e s of the l e f t drop i n run 19 ..................... 1 3 4 41. P l o t of 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 d i v i d i n g l i n e s of the r i g h t drop i n run 1 9 • • 1 3 5 42. Sketch f o r the d e r i v a t i o n of Eq. ( 1 0 ) . . . . . . . . . . 1 3 9 4 3 . Locus of P(Xfl, Yd) f o r two s p h e r i c a l r a d i i ..... 140 4 4 . Sketch showing the image of a p o i n t l o c a t e d i n water when viewed from a i r 145 4 5 . I s o s o l u t e l i n e s between two drops a t an 46. Equations f i t t e d over 0 - 2 0 2 f i l m frames and behaviour observed over 0 ^ - 1 0 0 f i l m frames, i n run 1 9 ..................oooao....... 1 5 2 4 7 * Change i n drop shape i n run 1 9 as the time of coalescence approaches, averaged f o r the two drops. ( T o t a l m a g n i f i c a t i o n of Y ©C[U«3,lS • ) ooa*oeoe««o*o*«oooo*«oaea»eeee«e«9» 3.60 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 ( 2 0°C) B - 4 J - l . Sketch 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) ooooeeoaeoaaoaeaaoaaeeaataaeeee <X~6 x i ACKNOWLEDGEMENTS The author wishes t o express h i s s i n c e r e a p p r e c i a t i o n to Dr. S t u a r t D. Cavers, under whose guidance t h i s study was undertaken, f o r h i s c o n t i n u a l encouragement, v a l u a b l e a s s i s -tance, and h e l p f u l c r i t i c i s m s extended throughout the course of t h i s p r o j e c t . He acknowledges w i t h s p e c i a l g r a t i t u d e the help o f Dr. James S. F o r s y t h , whose a d v i c e , comments, and suggestions are i n every p a r t of t h i s t h e s i s , p a r t i c u l a r l y i n i t s second p o r t i o n . There are many oth e r people who a s s i s t e d i n v a r i o u s ways and i t i s i m p o s s i b l e t o c i t e every one of them. The author wishes to acknowledge h i s debt t o a l l . He a l s o wishes to thank j o i n t l y Dr. Cavers and the N a t i o n a l Research C o u n c i l of Canada, f o r p r o v i d i n g f i n a n c i a l a s s i s t a n c e , and The U n i v e r s i t y of B r i t i s h Columbia, f o r a d d i t i o n a l s u p p o r t . 1 INTRODUCTION "On C e r t a i n Curious Motions Observable a t the Surfaces of Wine and other A l c o h o l i c L i q u o r s " , was the t i t l e a p t l y chosen by James Thomson f o r h i s f a s c i n a t i n g account (1) i n 1855 of surface movements.. This was probably the f i r s t c o r r e c t e x p l a n a t i o n of the phenomena r e l a t e d to surface t e n -s i o n e f f e c t s . H i s f i n d i n g s were never n o t i c e d u n t i l van der Mensbrugghe p u b l i s h e d i n 1869 a review of a l l e a r l i e r expe-riments on s u r f a c e movements and e s t a b l i s h e d t h a t the r e p o r -ted phenomena were a l l caused by l o c a l d i f f e r e n c e s of i n t e r -f a c i a l t e n s i o n . When I t a l i a n p h y s i c i s t C a r l o Marangoni d i s -puted p r i o r i t y of van der Mensbrugghe' s fi n d i n g , ' the r e s u l t -i n g p u b l i c i t y was probably the reason why Marangoni l a t e r took c r e d i t f o r Thomson's e a r l i e r f i n d i n g s which have come to be c a l l e d the Marangoni e f f e c t s (2). Quoting S t e r n l l n g and S c r i v e n (2), the Marangoni e f f e c t s are "...two d i s t i n c t although r e l a t e d surface e f f e c t s . The f i r s t of these i s movement i n a f l u i d i n t e r f a c e . The motion l s caused by l o c a l v a r i a t i o n s of i n t e r f a c i a l t e n s i o n t h a t are caused i n t u r n by d i f f e r e n c e s i n composition or temperature. The second i s the conjugate of the f i r s t : i t i s the departure from e q u i l i b r i u m t e n s i o n t h a t i s produced by e x t e n s i o n or c o n t r a c t i o n of an i n t e r f a c e , that i s , by d i l a t i o n a l deformation". 2 During the l a s t 15 y e a r s , a number of t e r n a r y sys-tems have been found 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 one of the components. T h i s i n t e r f a c i a l t u r b u l e n c e , as many workers agree, i s due to l o c a l v a r i a t i o n s of i n t e r f a c i a l t e n s i o n , that i s , one of the Marangoni e f f e c t s . The e x i s t e n c e of t h i s phenomenon q u i c k l y c o n t r a d i c t e d the t r a -d i t i o n a l t w o - f i l m model of Whitman ( 3 ) t h a t assumed s o l u t e t r a n s f e r i n r e g i o n s c l o s e to the i n t e r f a c e to take p l a c e by pure m o l e c u l a r d i f f u s i o n . Indeed, i t was found t h a t with some t e r n a r y systems, mass t r a n s f e r was accompanied by e r u p t i o n s and spasms i n the i n t e r f a c e , w h ile the surrounding r e g i o n s were a g i t a t e d spontaneously. Although the two-film theory p i c t u r e d a serene p r o c e s s d u r i n g mass t r a n s f e r i n l i q u i d -l i q u i d e x t r a c t i o n , as i t turned out, there were e x c e p t i o n s to the theory, as t y p i f i e d by the c o n f u s i n g and d i s o r d e r l y s t a t e of some u n e q u i l i b r a t e d l i q u i d phases of systems under-going mass t r a n s f e r . Ward and Brooks ( 4 ) were the f i r s t to n o t i c e t h i s spontaneous and l o c a l i z e d i n t e r f a c i a l t u r b u l e n c e , Sigwart and Nassenstein ( 5 , 6 , 7 ) r e p o r t e d s i m i l a r f i n d i n g s on pendent drops, p a r t i c u l a r l y f o r the system carbon t e t r a -c h l o r i d e - a c e t i c acid-water, and obtained e x c e l l e n t s c h l i e r e n photographs of the phenomena. Although there were d i s o r g a n i z e d movements as p o i n t e d out i n the above-mentioned experimental o b s e r v a t i o n s , some appearance of ordered flows, i . e . , organized i n t e r f a c i a l a c t -i v i t y , c o u l d be achieved f o r short p e r i o d s of time under con-t r o l l e d c o n d i t i o n s as r e p o r t e d by Sigwart and Nassenstein ( 6 ) . 3 They d i r e c t e d a j e t of s a t u r a t e d sodium c h l o r i d e i n water s o l u t i o n towards a f l a t i n t e r f a c e of the system water-carbon t e t r a c h l o r i d e from the water side* By c o n t a c t i n g i s o b u t a n o l and water phases, Berg and. Baldwin (8) l i k e w i s e produced e i t h e r d i s o r g a n i z e d or o rganized f l o w s ; the r e s u l t they ob-t a i n e d depended on the d i r e c t i o n of n i t r i c a c i d t r a n s f e r . I t was not, however, u n t i l the i m a g i n a t i v e work of S t e r n l i n g and S c r i v e n (9) that there was any c o n s i d e r a b l e t h e o r e t i c a l treatment of i n t e r f a c i a l t u r b u l e n c e . They formulated a math-e m a t i c a l model to show, through hydrodynamic i n s t a b i l i t y ana-l y s i s , how some systems may e i t h e r experience i n t e r f a c i a l t u rbulence or organized i n t e r f a c i a l a c t i v i t y . T h i s concept was v e r i f i e d p a r t i a l l y by O r e l l and Westwater (10) who r e -p o r t e d t h a t , i n the case of the system g l y c o l - a c e t i c a c i d -e t h y l a c e t a t e , the S t e r n l i n g and S c r i v e n c r i t e r i a were v a l i d , but were i n t u r n i n s u f f i c i e n t t o p r e d i c t completely the beha-v i o u r of the the r e l a t e d system e t h y l a c e t a t e - a c e t i c a c i d -water, w i t h a c i d t r a n s f e r i n t o water. Apart from the e f f e c t of surface a c t i v e contaminants, i n t e r f a c i a l movement d u r i n g the mass t r a n s f e r p r o c e s s a f f e c t s the ease of c o a l e s c e n c e . In a t y p i c a l e x t r a c t i o n column, the search f o r maximum e f f i -c i e n c y has always r e s u l t e d i n s t r i v i n g f o r l a r g e r i n t e r f a c i a l a reas a v a i l a b l e f o r mass t r a n s f e r . I t i s , t h e r e f o r e , neces-sary to e f f e c t i v e l y d i s p e r s e one phase i n the other a t the o u t s e t so as to achieve t h i s , and then to a v o i d coalescence of drops a f t e r f o r m a t i o n since coalescence would r e s u l t i n b i g g e r drops and l e s s s u r f a c e a r e a . 4 Johnson and B l i s s (11) as e a r l y as 1946 p o i n t e d out t h a t i n a spray extraction column, mass t r a n s f e r was h i g h e r when the s o l u t e i n a t e r n a r y system was t r a n s f e r r e d from the continuous phase to the drops© Smith (12) and Groothuis and Zuiderweg ( 1 3 ) probably s u p p l i e d the answer© As to why t h i s was so, they reasoned t h a t due to l o c a l v a r i a t i o n s of i n t e r -f a c i a l t e n s i o n , a d i f f u s i n g s o l u t e can e i t h e r i n h i b i t or a s s i s t the coalescence of drops, depending upon the d i r e c t i o n of transfer© Mahajan (14) was, perhaps, the f i r s t to r e p o r t that i n the coalescence of drops a t a plane i n t e r f a c e , the drops on r e a c h i n g the phase boundary do not c o a l e s c e i n s t a n t a n e o u s l y but r e s t a t the i n t e r f a c e f o r some time© Cockbain and McRoberts ( 1 5 ) measured the r e s t - t i m e s o f such c o a l e s c i n g drops a t a plane l i q u i d - l i q u i d interface© Prom r e s u l t s of other workers, there i s evidence on disagreement of r e s t - t i m e measurements f o r i d e n t i c a l drops© A s i g n i f i c a n t s c a t t e r was found whose r e s t - t i m e magnitude may depend on many f a c t o r s l i k e temperature, contamination, i n t e r f a c i a l t e n s i o n , drop s i z e , geometric shape of the i n t e r f a c e , and the system v i s -c o s i t i e s and d e n s i t i e s . J e f f r e y s and Lawson (16), among o t h e r s , proposed t h a t i n t e r f a c i a l t u r b u l e n c e brought about a c c e l e r a t e d drainage and, t h e r e f o r e , short r e s t - t i m e f o r benzene drops i n an aqueous continuous Phase with acetone as the t r a n s f e r r i n g solute© G i l l e s p i e and R i d e a l (17) gave a th e o r y f o r r e s t - t i m e u s i n g T a y l o r ' s treatment of the approach of p a r a l l e l f l a t d i s c s 5 separated by fluid© T h i s theory accounted w e l l f o r t h e i r experimental results© However© E l t o n and P i c k n e t t (18) were unable t o c o n f i r m t h i s conclusion,, and proposed an a l t e r n a -t i v e s e m i - t h e o r e t i c a l e x p r e s s i o n Although i t i s now known that the g e n e r a l c o a l e s -cence p r o c e s s takes p l a c e i n two stages, namely: drainage of the continuous f i l m which separates the elements© f o l l o w e d by f i l m r u p t u r e and coalescence© the u n d e r l y i n g mechanism to e x p l a i n t h i s phenomenon i s s t i l l not f u l l y understood© Much of the c o n s i d e r a b l e r e s e a r c h i n t h i s f i e l d has been concen-t r a t e d on the coalescence of drops a t a plane i n t e r f a c e and not between p a i r s of drops. Although the same g e n e r a l se-quence of events mentioned above a p p l i e s a l s o to the l a t t e r case© the d e t a i l e d study of the coalescence of drop p a i r s has been neglected© perhaps because of the experimental d i f f i c u l -t i e s i n v o l v e d i n keeping a p a i r of moving drops together© The p r e s e n t study was i n s t i t u t e d t o provide some of the m i s s i n g i n f o r m a t i o n . A t t e n t i o n was g i v e n to the h y p o t h e t i c a l mechanism f o r coalescence i n a t e r n a r y system undergoing mass t r a n s f e r which was proposed by Smith ( 1 2 ) and Independently by Groothuis and Zuiderweg ( 13 ) ° The l a t t e r i n v e s t i g a t e d coalescence by c a u s i n g drops to form from two c a p i l l a r y tubes whose ends were f a c i n g each other. In t h i s manner, the drops were f o r c e d together a t w i l l so c l o s e n e s s of approach c o u l d be e a s i l y controlled© Smith, Caswell, Larson, and Cavers ( 1 9 ) p r o v i d e d 6 experimental i n f o r m a t i o n as to the ease or d i f f i c u l t y of coalescence of f r e e l i q u i d drops i n a column. In b r i e f , both groups of workers suggested t h a t , i n many i n s t a n c e s , coalescence was due to the e f f e c t of a s o l u t e on the i n t e r -f a c i a l t e n s i o n between the two l i q u i d phases. The r e s u l t i n g imbalances of surface t e n s i o n , they e x p l a i n e d , produced movements a t and near the drop i n t e r f a c e . I t i s then the purpose of t h i s work to c a r r y out I n v e s t i g a t i o n s i n o r d e r to p r o v i d e evidence, i f any, to support the theory. A n o z z l e arrangement s i m i l a r to t h a t used by Groothuis and Zuiderweg ( 13 ) was set up. In the hope of o b t a i n i n g v i s u a l r e c o r d s of the coalescence phenomena, high-speed photography u t i l i z i n g o p t i c a l methods such as s c h l i e r e n and o r d i n a r y p i c t o r i a l techniques were used. 7 THEORY UNDER STUDY The h y p o t h e t i c a l coalescence mechanism perhaps i s best e x p l a i n e d by q u o t i n g Smith e t a l (19): "The mechanism proposed t o e x p l a i n the ease or d i f f i c u l t y of coalescence observed i n many experimental cases depends on the e f f e c t of a s o l u t e on the i n t e r f a c i a l t e n s i o n of two l i q u i d s o Murphy. L a s t o v i c a , and F a l l i s (20) have measured i n t e r f a c i a l t e n s i o n i n such t e r n a r y systems. They found, f o r example, that the a d d i t i o n of acetone to the two-phase mixture: water, t o l u e n e , lowered the i n t e r f a c i a l t e n s i o n . The s o r t of behaviour o r d i n a r i l y encountered i s shown i n F i g . 1 where the 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 t e n s i o n s a, b, c, d, and e where the i n t e r f a c i a l t e n s i o n decreases from a t o e." "On 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 the coalescence of drops i s then the f o l l o w i n g . Consider two drops as shown i n F i g . 2. These c o n s i s t o f s o l v e n t A of F i g . 1 and approach one another as i n F i g . 2a d u r i n g t h e i r motion through s o l v e n t B of F i g . 1. Assume t h a t the drops are s a t u -r a t e d with component B, th a t the continuous phase i s saturated, w i t h component A, and th a t s o l u t e C of F i g . 1 i s t r a n s f e r r i n g out of the drops and i n t o the continuous phase. The s o l v e n t B between the drops r e c e i v e s s o l u t e from both drops. F u r t h e r -more, any mixing p r o c e s s g e n e r a l throughout the continuous F i g u r e 1. Ternary composition diagram with s u r f a c e t e n s i o n as parameter ( 1 9 ) . 9 DIRECTION OF INTERFAGAL MOVEMENT DIRECTION OF DROP MOVEMENT DIRECTION OF CIRCULATION IN DROP ZONE OF HIGH SOLUTE - CONCENTRATION F i g u r e 2 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 corre s p o n d i n g to F i g u r e 1 ( 1 9 ) „ 10 phase w i l l be somewhat i n h i b i t e d as f a r as the r e g i o n between the drops i s concerned because of t h i s r e g i o n being p r o t e c t e d somewhat by the drops themselves; "The r e s u l t i s t h a t the s o l u t e c o n c e n t r a t i o n b e t -ween the drops w i l l tend t o r i s e more q u i c k l y than i t w i l l i n the remaining r e g i o n s around the drops. Within each of the drops the s o l u t e c o n c e n t r a t i o n s should decrease s l i g h t l y l e s s i n the r e g i o n f a c i n g the ot h e r drop (e.g., a t G i n F i g . 2a) than i n r e g i o n s more remote from the zone of c l o s e approach (e.g., l o c a t i o n s H i n F i g . 2a). T h i s r e s u l t would be expected because of the reduced d r i v i n g f o r c e f o r m a t e r i a l t r a n s f e r f o l l o w i n g the s o l u t e b u i l d u p between the drop s . " "Thus, i n F i g . 2a s o l u t e c o n c e n t r a t i o n s on both si d e s of the i n t e r f a c e are h i g h e r near G than :they are near H. F i g . 1 then i m p l i e s lower i n t e r f a c i a l t e n s i o n s near G than near H. The unbalanced i n t e r f a c i a l t e n s i o n around each drop w i l l r e s u l t i n s t r e t c h i n g of the i n t e r f a c e i n the zone of drop approach, and the s h r i n k i n g of the i n t e r f a c e s around the remainder of the drops. Streaming of continuous phase f l u i d out of the zone of drop approach w i l l be promoted and, a l s o , a c i r c u l a t o r y movement of drop f l u i d , both r e s u l t i n g from the drag a s s o c i a t e d w i t h the movement of the i n t e r f a c e . The c i r c u l a t i o n w i t h i n the drop w i l l b r i n g f r e s h s o l u t e to the drop i n t e r f a c e t o continue the p r o c e s s . When the l a s t , l a y e r of B between the drops breaks down the drops c o a l e s c e . F i g . 2a i l l u s t r a t e s t h i s b e h a v i o u r . " 11 "On the other hand, when the system i s the same, but the s o l u t e i s being t r a n s f e r r e d from the continuous to the d i s p e r s e d phase, when two drops approach as shown i n Pigo 2b, both draw s o l u t e from the l a y e r of continuous phase bet*= ween them, and, with mixing i n h i b i t e d between the drops, a lower s o l u t e c o n c e n t r a t i o n soon r e s u l t s there than t h a t a p p l i -c a b l e on the s i d e s of the drops remote from the zone of drop approacho In t h i s case, i n t e r f a c i a l t e n s i o n i s comparatively h i g h i n the 'contact' zone and spreading of the i n t e r f a c e takes p l a c e towards t h i s zone. F r i c t i o n a l drag p u l l s more water between the drops and these are f o r c e d a p a r t as i l l u s -t r a t e d i n F i g . 2b. I t should be noted t h a t ' d i r e c t i o n of t r a n s f e r ' f o r the s o l u t e as i t a p p l i e s i n c o n n e c t i o n with t h i s h y p o t h e s i s r e f e r s to ' d i s p e r s e d to continuous phase or v i c e v e r s a ' , and not to 'water phase to o r g a n i c phase or v i c e v e r s a ' , s i n c e whether component A i s water and component B an organic s o l v e n t , or component B water and component A an o r g a n i c s o l v e n t , i s immaterial t o the argument." DIRECTION OF DROP MOVEMENT MOVEMENT CONCENTRATION F i g u r e 2 b , T r a n s f e r of m a t e r i a l from the continuous phase to the d i s p e r s e d phase f o r a system of the type corresponding to F i g u r e 1 (19 )« 13 PRELIMINARY INVESTIGATION A. Scope The 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 meant to r e p r o -duce the behaviour r e p o r t e d by Smith e t a l (19) f o r the system MIBK-* a c e t i c a c i d - w a t e r . * * (They r e p o r t e d , f o r MIBK drops d i s p e r s e d i n water with a c e t i c a c i d t r a n s f e r from MIBK to water, t h a t a t s o l u t e c o n c e n t r a t i o n of 8$w (0.068 l b . moles cu. f t . s o l n . ) , coalescence o c c u r r e d w i t h i n the column, and t h a t coalescence a t the i n t e r f a c e was r a p i d . ) F a m i l i a r i z a t i o n w i t h the s c h l i e r e n equipment and the s t i l l and motion p i c t u r e cameras, and with t h e i r o p e r a t i o n occurred a t t h i s stage. B. Procedure P r e p a r a t i o n of the d i s p e r s e d phase was done by adding a measured amount of s o l u t e , a c e t i c - a c i d , to the o r -g a n i c s o l v e n t , MIBK, to make a d e s i r e d s o l u t e c o n c e n t r a t i o n , i n t h i s case, about 8$w (0.068 l b . moles/cu. f t . s o l n . ) . D i s -t i l l e d water was then added to the mixture, which was shaken, and allowed to stand f o r s e v e r a l minutes. The procedure was * Methyl i s o b u t y l ketone. ** When the c o n s t i t u e n t s of a t e r n a r y system are g i v e n i n the present t h e s i s , the second substance mentioned i s the s o l u t e which i s t r a n s f e r r e d between phases c o n s i s t i n g mainly of the other two substances. 14 repeated u n t i l a t h i n l a y e r of water remained v i s i b l e 0 Thus s a t u r a t i o n of the MIBK phase with water was insuredo Hence, 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 org a n i c s o l v e n t , MIBK, was l e s s than the c a l c u l a t e d amount because some t r a n s f e r of so l u t e t o the t h i n l a y e r of water was not accounted f o r . The continuous phase was prepared by shaking and s a t u r a t i n g the d i s t i l l e d water with MlBKo S i m i l a r procedure was used as above, to i n s u r e s a t u r a t i o n of the water phase wi t h MIBK. F i g . 3 i s a schematic flow diagram f o r the whole system. The l i g h t e r d i s p e r s e d phase flowed through a g l a s s n o z z l e , a t the bottom of the square g l a s s column. Both n o z z l e and column used were those designed by Selby (21). Continuous phase flow e n t e r e d a t the top of the column and was counter-c u r r e n t t o the d i s p e r s e d phase. Two-gallon p o l y e t h y l e n e j a r s served as f e e d and di s c h a r g e tanks. P o l y e t h y l e n e t u b i n g and Saran f i t t i n g s were used f o r p i p i n g and Teflon-packed needle v a l v e s were p r o v i d e d to c o n t r o l the flow of each phase. The r u n was begun by p a r t i a l l y f i l l i n g the g l a s s column wi t h the continuous phase to about 3/k of the column's volume and m a i n t a i n i n g t h a t l e v e l by s u i t a b l e adjustment of the e l e v a t i o n of a weir ( b u i l t by Selby (21)) i n the dis c h a r g e l i n e ( F i g . 3)« Flow of the d i s p e r s e d phase was then s t a r t e d by a d j u s t i n g the needle v a l v e s t h a t c o n t r o l the flow to the n o z z l e . A l l work was c a r r i e d out a t room temperature 0 15 FEED (ORGANIC SOLV-) GLASS COLUMN FEED (WATER) VENT 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 s c h l i e r e n system shown i n F i g - k ( a l s o F i g . 5 with Hycam camera i n pl a c e of screen, S) and d e s c r i b e d f u r t h e r under t o p i c "A" of "DISCUSSION", was put i n t o proper a d j u s t -ment and focussed as f o l l o w s : The p a r a b o l i c m i r r o r , Ml, was t i l t e d so t h a t i t s o f f s e t a n g l e , (9i» was as small as p h y s i c -a l l y p o s s i b l e and, i n any event, l e s s than 10° (22) to reduce a b e r r a t i o n s o The l i g h t source, L, was then l o c a t e d a t the f o c u s of Ml so t h a t c o l l i m a t e d l i g h t r a y s were r e f l e c t e d from it© The p a r a l l e l i s m of these r a y s can be checked by h o l d i n g a f l a t p iece of paper i n the l i g h t path and p e r p e n d i -c u l a r t o l i n e 00'. T h i s paper was p l a c e d i n two p o s i t i o n s — near Ml and near M2» Obviously, the l i g h t c i r c l e s a t both p o i n t s should be equal i n diameter i f the l i g h t r a y s are P a r a l l e l . The t e s t s e c t i o n , T (the g l a s s column), was p o s i -t i o n e d so t h a t i t s w a l l s f a c i n g the l i g h t beam were perpen-d i c u l a r to i t . To c a n c e l coma, m i r r o r M2 was t i l t e d i n the opposite d i r e c t i o n t o Ml so t h a t Q2 was equal t o 0 ^ ° r ^ a e f o c u s of m i r r o r M2 can be determined approximately by h o l d i n g a p i e c e of paper i n the l i g h t beam and n o t i n g the paper's po-s i t i o n f o r minimum s i z e of the l i g h t bundle. The r e c t i l i n e a r k n i f e edge was l o c a t e d i n the h o r i z o n t a l p o s i t i o n a t t h i s p o i n t (K, i n F i g . 4) so that the i l l u m i n a t i o n on the viewing screen changed u n i f o r m l y as the k n i f e edge was moved a c r o s s the l i g h t beam. The k n i f e edge was a d j u s t e d so t h a t the image of the . source was approximately cut i n h a l f as i n the Toepler method (22). T h i s gave equal s e n s i t i v i t y f o r both upward and downward l i g h t r ay d e f l e c t i o n s caused by r e f r a c t i v e index g r a d i e n t s i n the t e s t s e c t i o n . In f o c u s s i n g , 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 F i g u r e 4 K L o c a t i o n of k n i f e edge. L L i g h t source <, Ml» M 2 S c h l i e r e n m i r r o r s . S Viewing s c r e e n * 0 T Test s e c t i o n . f F o c a l l e n g t h of s c h l i e r e n m i r r o r s , M]_ and M2° p D i s t a n c e of t e s t s e c t i o n to m i r r o r , M2. q D i s t a n c e of v i e w i n g s c r e e n to m i r r o r , M2. 01' O2 O f f s e t a n g l e s . * These p i e c e s of equipment comprise the A e r o l a b S c h l i e r e n System, i n c l u d i n g the k n i f e edge assembly ( l o c a t e d a t K) which i s not shown here. L i s a PEK h i g h - p r e s s u r e mercury a r c lamp with a 0.012x0.012 i n . s o u r c e . Mi and M2 are 6 - i n . p a r a b o l i c f i r s t - s u r f a c e m i r r o r s having 4 8 - i n . f o c a l l e n g t h each. S i s a s c r e e n c o n s t r u c t e d of sandblasted p l a s t i c . The k n i f e edge assembly c o n s i s t s of an 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 which c o u l d be used to r e f l e c t the image to a convenient l o c a t i o n f o r S i f d e s i r e d . F i g u r e 5. Photographic views of the apparatus. (Corresponds to F i g u r e 4} 19 be rioted t h a t the dimensions of "p" and "q", as i n the above f i g u r e , may be changed as l o n g as the l e n s equation i s s a t i s -f i e d : 1/p + 1/q = 1/f (1) where p = d i s t a n c e of t e s t s e c t i o n to m i r r o r , M2, mm. q = d i s t a n c e of viewing screen;, to m i r r o r , M2, mm© f = f o c a l l e n g t h of s c h l i e r e n m i r r o r s 0 Ml and M20 mm. The s c h l i e r e n image was focussed on the v i e w i n g screen, S. For photographs, the L i n h o f or Hycam camera, to be d e s c r i b e d l a t e r , each w i t h l e n s removed, was used i n p l a c e of the screen. As soon as the spray column had reached a steady s t a t e with uniform d r o p l e t s and a constant i n t e r f a c e l e v e l , photographs of drop coalescence were taken. Films used were P o l a r o i d Type 55 P/N, Kodak Plus-X Pan, T r l - X Pan, and I l f o r d FP3 f o r the L i n h o f camera, and Kodak T r i - X R e v e r s a l f o r the Hycam camera. Proper f i l m exposure depends on many f a c t o r s such as k n i f e edge s e t t i n g , m a g n i f i c a t i o n , s h u t t e r speed, and i s a f u n c t i o n of the p a r t i c u l a r photographic c o n d i t i o n s i n -v o l v e d . N e v e r t h e l e s s , the o v e r a l l c o n t r a s t and q u a l i t y of the s c h l i e r e n image as recorded on the f i l m were found to be s a t i s -f a c t o r y f o r the f i r s t attempted combinations of s e t t i n g s . Fur-thermore, that coalescence 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 by Smith e t a l (19) was v e r i f i e d , and, with these promising r e s u l t s , i t was decided to continue the i n v e s t i g a t i o n with a more r i g i d column frame and with the e n t i r e e x t r a c t i o n system m o d i f i e d by improving the p i p i n g and p r o v i d i n g l e a k - p r o o f c o n t a i n e r s . 20 MAIN INVESTIGATION A. Attempted M o d i f i c a t i o n s to E x i s t i n g Apparatus I t was necessary to design a more r i g i d and s t a b l e frame to support the e x t r a c t i o n column, securely.. T h i s i s shown i n Figo 6. The column remained the same, but p r o v i s i o n s were made i n the frame so t h a t the p o s i t i o n of the column was a d j u s t a b l e i n the v e r t i c a l d i r e c t i o n ( F i g . 7)» The g l a s s spray n o z z l e s were bent t o make both ends face each other, 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 , as desired. ( F i g . 7)» The p i p i n g system consisted, of n y l o n t u b i n g and. f i t t i n g s except f o r p o r t i o n s l e a d i n g t o the di s c h a r g e tanks which were p o l y -ethylene t u b i n g with Saran f i t t i n g s . The n y l o n t u b i n g being used was found to be q u i t e r i g i d so t h a t i t was necessary to s t r a i g h t e n p o r t i o n s of i t by i n s e r t i n g through i t s u i t a b l e l e n g t h s of g l a s s t u b i n g and then immersing the combination i n a hot water bath u n t i l the new shape was retained, by the n y l o n . For supply tanks, QVF pipe s e c t i o n s were used. These were p r o v i d e d a t both ends with f l a n g e s and b o l t s . P olyethy-l e n e j a r s w i t h t i g h t - f i t t i n g l i d s were r e t a i n e d to serve as r e c e i v e r tanks. I t was found convenient to r e p l a c e the over-f l o w weir by a c o n t r o l v a l u e . To ins u r e a g a i n s t any contami-n a t i n g agents t h a t may a l t e r the surface p r o p e r t i e s of the l i q u i d s b e i n g s t u d i e d , a p p r o p r i a t e p r e c a u t i o n s were taken so t h a t only p o l y e t h y l e n e , Saran, n y l o n , s t a i n l e s s s t e e l (Type 316), T e f l o n , Tygon, and. g l a s s were allowed to come i n con-22 t a c t with the a p p r o p r i a t e l i q u i d s - The schematic flow d i a -gram of the system remained the same as i n F i g . 3 except f o r the m o d i f i c a t i o n s noted above to the spray n o z z l e s and to the means of I n t e r f a c e c o n t r o l . Up t o t h i s p o i n t i n the in v e s t i g a t i o n s , d i s p e r s e d phase flowed by g r a v i t y a t a constant r a t e r e g u l a t e d by two needle v a l v e s , one l o c a t e d near each n o z z l e ( F i g . 6 ) . Thus, i n t a k i n g a photograph, s c h l i e r e . * were ev e r - p r e s e n t near the n o z z l e t i p s due to mass t r a n s f e r l e f t i n the wake of drops t h a t were p r e v i o u s l y r e l e a s e d . The movement of these s c h l i e r e i n the continuous phase medium was observed t o be v e r y much slower than the movement of the s o l u t e t r a n s f e r -r i n g from the oncoming drops which l i k e w i s e formed s c h l i e r e n p a t t e r n s , so t h a t one can be d i s t i n g u i s h e d from the other. In f a c t , the extent of the movement of s c h l i e r e t h a t were due to the mass t r a n s f e r l e f t i n the wake of p r e v i o u s l y de-tached drops can be c o n s i d e r e d n e g l i g i b l e . An i n j e c t o r system c o n s i s t i n g of a hypodermic s y r i n g e a t t a c h e d to the i n l e t end of the d i s p e r s e d phase l i n e was then set up. By means of the s y r i n g e ' s plunger, i t was hoped t h a t drop growth c o u l d be c o n t r o l l e d a t w i l l by means of the plunger of the s y r i n g e . However, d i f f i c u l t i e s arose i n producing p a i r s of drops of ro u g h l y equal v o l u m e t r i c r a t e of growth. Somehow, there was unequal f r i c t i o n l o s s i n * O p t i c a l inhomogeneities i n an otherwise o p t i c a l l y homoge-neous medium, used here instead of the commonly accepted form "schlieren". 23 the l i n e s l e a d i n g to each g l a s s n o z z l e , p o s s i b l y due to d e f e c t i v e needle v a l v e s t h a t were used to r e g u l a t e d i s p e r s e d phase flow. A f t e r f u t i l e attempts to c o r r e c t t h i s , the whole set-up was d i s c a r d e d i n favour of the o l d arrangement. 24 PART I SCHLIEREN STUDIES 25 PART I SCHLIEREN STUDIES A. Scope High-speed photography coupled with the s c h l i e r e n o p t i c a l system was u t i l i z e d to f i n d out i f there were any movements a t or near the drop i n t e r f a c e t o c o n t r i b u t e t o the understanding of the coalescence mechanism. Fundamental s t u d i e s of the s i m p l e s t p o s s i b l e arrangement, a v o i d i n g a l a r g e number of parameters, was made. The column was opera-ted with a stagnant continuous phase, thereby r e d u c i n g the d i s t u r b a n c e made by unnecessary f l u i d flow w i t h i n the e x t r a c -t i o n column. The systems MIBK-acetic acid-water and t o l u e n e -a c e t i c acid-water were used i n the experiments. B. Some Photographic C o n s i d e r a t i o n s In t e c h n i c a l photography, as i n any other f i e l d s of p i c t u r e t a k i n g , among the photographer's c h i e f concerns are the l i g h t i n g techniques used to i l l u m i n a t e the s u b j e c t to be photographed. The problem of o b t a i n i n g enough l i g h t becomes more important when the exposure times i n v o l v e d are one thousandth of a second or l e s s , as i n high-speed photo** graphy. The same b a s i c r u l e s of l i g h t i n g used i n o r d i n a r y commercial photography may be f o l l o w e d i n high-speed work except t h a t the i n t e n s i t y of l i g h t r e q u i r e d i s u s u a l l y very much g r e a t e r than i n most o t h e r areas of a p p l i c a t i o n . As a r e s u l t of t h i s , the s c i e n t i f i c high-speed movie photographer 26 i s often faced with the problem of requiring high i n t e n s i t y continuous l i g h t i n g . Like the commercial photographer, the s c i e n t i f i c worker i s interested also i n the control of l i g h t and shadow to obtain high image qua l i t y and, therefore, an accurate photographic record of the subject i n question. In many instances, 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 aesthetic values i n order to use the most d i r e c t methods possible i n obtaining maximum information out of a picture just as food may be served without, so to speak, the "trimmings". The 4 x 5 i n . Linhof Super Technika V camera, Ch. E. 23450 and the 16mm x 400 f t . Hycam high-speed camera (Model K20S4E), Ch. E. 2355. with lenses removed were subs-t i t u t e d f o r the viewing screen i n the schlieren runs., Proper exposure was found by t r i a l at the start due to the unusual type of o p t i c a l system employed (Fig. 8). Lenses, instead of mirrors, are shown i n t h i s figure for convenience. With no lens aperture involved i n the schlieren arrangement, i t i s possible to determine an equivalent value to t h i s aperture present i n the mirror system which can be used and taken as lens aperture f o r use with the L e i t z Micro-s i x - L l i g h t meter (Ch. E. 2267). To obtain t h i s value equi-valent to that of a lens aperture, the knife edge setting and IMAGE FILM PLANE PLANE F i g u r e 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 (39)» 27a Key to F i g u r e 8 L-|_o L<2 S c h l i e r e n l e n s e s . P A p o i n t on the image p l a n e . P 8 A p o i n t on the f i l m plane corr e s p o n d i n g to P. a Divergence a n g l e . f ] _ 9 f£ F o c a l lengths of s c h l i e r e n l e n s e s , L]_ and L 2 , r e s p e c t i v e l y , h Height of l i g h t s o urce. 28 m a g n i f i c a t i o n of the s c h l i e r e n system must "be c o n s i d e r e d since these two f a c t o r s a c t the same way as a diaphragm a c t s i n a camera to p a r t l y c o n t r o l the l i g h t f a l l i n g on the f i l m 0 F i r s t d e t e r m i n a t i o n of an e q u i v a l e n t f/no. was done by t r i a l o Once a p r o p e r l y exposed f i l m was obtained, a l e n s a p e r t u r e value was read from the meter. T h i s value was based, on the known a p p r o p r i a t e d a t a : f i l m USASI No. (formerly c a l l e d ASA No.), camera s h u t t e r speed, and l i g h t meter r e a d i n g . For example© i n r u n 1 , f o r a l i g h t meter r e a d i n g of 1 5 . 8 and f o r a f i l m of USASI No. of 200 ( d a y l i g h t ) , the proper exposure was o b t a i n e d a t a camera speed, of 600 pps ( p i c t u r e s per sec. some-times r e p l a c e d fps,frames per s e c ) . The camera speed of 600 pps corresponded to a s h u t t e r speed of 1 /1500 sec. obtained by m u l t i p l y i n g 600 pps by 2 .5» the s h u t t e r d u r a t i o n - p e r i o d r a t i o , the product b e i n g the r e c i p r o c a l of the s h u t t e r speed ( 2 3 ) ° A l l o w i n g f o r the wide l a t i t u d e of b l a c k and white f i l m s 9 t h i s gave roughly an f/no. of 2 . 0 a c c o r d i n g to the L e i t z meter. The above procedure was found to provide r e l i a b l e r e s u i t s . A l l movie f i l m s were processed by Trans-Canada F i l m s , L t d . , except where noted otherwise. 29 EXPERIMENTAL PROCEDURE Upon c a l i p e r examination of the g l a s s column, i t •was found t h a t i t s w a l l s were not e x a c t l y p a r a l l e l and, when used i n s c h l i e r e n experiments, showed s t r i a t i o n s t r a v e l l i n g a l o n g the e n t i r e l e n g t h of the column„ Of s e v e r a l other columns a v a i l a b l e , only the ones showing the l e a s t imper-f e c t i o n s of t h i s s o r t were r e t a i n e d f o r use i n the presen t experimentso I t was f e l t t h a t these d e f e c t s would, i n no way, hamper the c o r r e c t i n t e r p r e t a t i o n of the present work since q u a l i t a t i v e and not q u a n t i t a t i v e a n a l y s i s i s involved., As was observed i n the ensuing experiments, the s t r i a t i o n s appeared only when the k n i f e edge was set v e r t i c a l l y and there were on l y a few of these t h a t were e v i d e n t i n the p i c t u r e s o b tained since only a small area was occupied by the c o a l e s -c i n g dropso The experiments c o n s i s t e d of running the spray column under c e r t a i n e x t r a c t i o n c o n d i t i o n s and photographing drop coalescence to study the mechanism« As soon as the. necessary m o d i f i c a t i o n s were com-p l e t e d , a l l equipment i n c o n t a c t with the fluid.s was tho-roughly washed out with MIBK. The 1/4-in. S.S. needle v a l v e s were soaked i n concentrated n i t r i c acid, o v e r n i g h t and then r i n s e d i n running water b e f o r e being soaked a g a i n i n MIBK to remove organic and i n o r g a n i c i m p u r i t i e s . E x t r a care was taken 30 to i n s u r e that no contamination, e s p e c i a l l y of a s u r f a c e -a c t i v e nature, was present i n the system. The d i s p e r s e d and continuous phase feeds were prepared by methods s i m i l a r t o those d e s c r i b e d i n the s e c t i o n , " P r e l i m i n a r y I n v e s t i g a t i o n " . Measurement of l i q u i d s was done by graduate. Each l i q u i d phase was then poured i n t o i t s r e s p e c t i v e f e e d tank. The run was s t a r t e d by f i l l i n g the g l a s s column with the con-t i n u o u s l i q u i d which then was l e f t s tanding f o r a few minutes to c l e a r the l i q u i d of t i n y a i r bubbles trapped w i t h i n . Sometimes i t was necessary to shake those t h a t were c l i n g i n g a l o n g the w a l l s of the c o n t a i n e r by swiping them o f f w i t h a s t i r r i n g rod. As soon as t h i s was done, l i q u i d drop flow was s t a r t e d and recorded on f i l m a t the proper moment. No e f f o r t was made to measure e x a c t l y the d i s p e r s e d phase flow r a t e s i n c e t h i s was not b e l i e v e d to be important. However, a q u a n t i t y c a l l e d "CD" was used to i n d i c a t e the time taken from the moment a p r e v i o u s l y c o a l e s c e d drop was r e l e a s e d from the n o z z l e s t o the onset of coalescence of a new drop p a i r . CD i s dependent, among other t h i n g s , upon the d i s t a n c e between the two n o z z l e t i p s . To determine the c o n c e n t r a t i o n of a c e t i c acid, p r e -sent i n the feed, samples were t i t r a t e d , with c a r b o n a t e - f r e e 0.1 N sodium hydroxide s o l u t i o n , whose s t r e n g t h was checked from time t o time a g a i n s t a standard s o l u t i o n of potassium a c i d p h t h a l a t e (24). The t i t r a t i n g procedures are mentioned elsewhere (24) and w i l l not be repeated here. By an u n f o r -3 1 tunate o v e r s i g h t , measurements of a c e t i c a c i d c o n c e n t r a t i o n f o r the e a r l i e r runs, from run 1 to run 7 , were not d e t e r -mined by t i t r a t i o n , but were simply approximated by graduate on p r e p a r a t i o n of the mixture n e g l e c t i n g the a d d i t i o n of appro-p r i a t e l i q u i d s to i n s u r e mutual s a t u r a t i o n . Determination of the exact s o l u t e c o n c e n t r a t i o n s may a c t u a l l y be s u p e r f l u o u s i n any case, because mass t r a n s f e r i s a l r e a d y t a k i n g place as the drops emerge from the n o z z l e s and before a c t u a l obser-v a t i o n of coalescence i s made. Hence a t the time p i c t u r e s were taken, s o l u t e c o n c e n t r a t i o n was always l e s s than what was r e p o r t e d as a r e s u l t of t i t r a t i o n . . . A l l runs r e p o r t e d i n t h i s t h e s i s s t a r t e d with no s o l u t e i n the phase i n t o which mass t r a n s f e r was t a k i n g p l a c e . The s o l u t e c o n c e n t r a t i o n i n t h a t phase has not been r e p o r t e d due to the d i f f i c u l t y of d e t e r m i n i n g the true value of t h i s c o n c e n t r a t i o n a t the time a t which photographs were taken. T h i s d i f f i c u l t y arose because the drop p a i r s t u d i e d was not n e c e s s a r i l y the very f i r s t p a i r formed when a run was s t a r t e d and, t h e r e f o r e , the s o l u t e c o n c e n t r a t i o n In the phase r e c e i v i n g s o l u t e was p a r t l y due to mass t r a n s f e r because of the presence of p r e c e d i n g drop p a i r s . I t was convenient to modify, whenever necessary, the method of ch a r g i n g the e x t r a c t i o n column with the d i s -p e r sed or continuous phase or both i n order to e l i m i n a t e the n e c e s s i t y of h a n d l i n g heavy and bulky c o n t a i n e r s , such 3 2 as the QVF f e e d tanks, whenever t h e i r c o ntents have t o be emptied, cleaned, and/or f l u s h e d , to accomodate d i f f e r e n t l i q u i d mixtures.. The e x t r a c t i o n column and i t s n o z z l e assembly were thoroughly washed i n tap water, r i n s e d i n d i s t i l l e d water, and then a i r - d r i e d whenever the f e e d com-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 phase was changed i n the experiments© The o r i g i n a l t u b i n g which c a r r i e d each phase to the e x t r a c t i o n s i t e was r e p l a c e d with new m a t e r i a l of the same k i n d . Afterwards, the d i s p e r s e d and continuous phase l i n e s were thoroughly f l u s h e d with whatever l i q u i d mixture was b e i n g used f o r each r e s p e c t i v e l i n e . A l l experiments were made a t room temperature© Temperature d e v i a t i o n s i n the room were found t o v a r y w i t h i n reasonable l i m i t s under s c h l i e r e n c o n d i t i o n s (Appendix D). Operating data f o r a l l the runs can be found i n Table I. A© MIBK-Acetic Acid-Water System 1 ) Nozzle T i p s Oriented H o r i z o n t a l l y T h i s arrangement of the g l a s s n o z z l e s was s i m i l a r t o t h a t of Groothuis and Zuiderweg ( 1 3 ) i n t h e i r i n v e s t i g a -t i o n of the coalescence mechanism as mentioned earlier© For a l l the runs i n t h i s s e c t i o n except as otherwise s t a t e d , the k n i f e edge was a r b i t r a r i l y set to cut the l i g h t r a y s h o r i z o n -Tabla I. Experimental Eteta for Part I (Schlieren Studies) Run No. Solute Cont. Phase Dis-persed Phase Direc-tion of Transfer Solute Concentration. i n 3 x lb.moles ou.ft.soln. Nozzle Orientation Light Source Current Rdg., amp. Knife Edge Setting Film (USASI No., daylight) Leltz Light Me ter Rdg. Camera Camera Frame Speed, PPS Timing Ught Freq. , plp/seo. Film Magnifi-cation 1 Acetic Aold Mater MIBK _ _»* D -*C 68 Horizontal 4. 00 - 4 . 2 5 Horizontal Trl-X Rev. ( 2 0 0 ) 15.8 Hyoam 600 1 0 0 . 7 9 8 2 II II II it 68 II 4.80 - 5 . 00 11 1 6 . 2 5 11 1 2 0 0 1 0 0 0 . 7 9 8 3 it II II ti 68 n 4 . 7 5 - 5 . 0 0 4X Pan. Neg . ( 5 0 0 ) 16.2 11 2 5 0 0 1 0 0 0 . 7 9 0 4 II II II II 68 II 5 . 3 0 - 6.00 Trl-X Rev. ( 2 0 0 ) 17 . 7 11 2 0 0 0 1 0 O O . 7 8 8 5 _ 9) » II 5 . 3 0 - 5 . 5 0 11 1 6 . 7 t> 2 0 0 0 1 0 0 O . 7 8 6 6 Acetlo Acid I. * •t C -<*»D 52 . 6 2 n 5.00 - 5 . 5 0 1 6 . 5 M 2 0 0 0 1 0 0 O . 7 8 6 7 II II * II ti 5 2 . 6 2 i> 5 . 2 0 - 5 . 5 0 V e r t i c a l 11 I 6 . 5 It 2 0 0 0 1 0 0 0 . 7 8 6 8 19 II 56.45 Vortloal 5 . 2 0 - 5 . 5 0 Horizontal II 16.7 II 2 0 0 0 1 0 0 O .78O 9 II j) ti 54.82 - 5 . 2 0 - 5 . 5 0 V e r t i c a l •1 1 6 . 7 II 2 0 0 0 1 0 0 O . 7 6 6 10 » I  II 9.43 - 5 . 7 5 - 6 . 5 0 11 It 17 . 5 II 2 0 0 0 1 0 0 0.780 11 » II II n 9.43 5 . 5 0 - 6 . 5 0 Horizontal II 1 7 . 5 It 2 0 0 0 1 0 0 O .78O 1 2 „ II Ttilusne Bl 6.28 - 5 . 5 0 - 6 . 5 0 11 tl 17 . 5 II 2 0 0 0 1 0 0 0 . 7 6 5 1 3 n It it II 6 . 2 0 " 4.00 11 Trl-X Jfen» (320) 16.0 Linhof 2 5 0 0 . 7 6 5 14 II M t  II 51.96 4.00 11 16.0 it 1 2 5 0 - 0 . 7 6 5 'Unsaturated Phase (Rooohlnl's mixture). **"D" stands f o r dispersed phase and "C" for continuous phase (see Table V a l s o ) . ""These are shutter speed values. In seoonds. 3 ^ t a l l y so t h a t only d e n s i t y g r a d i e n t s i n the v e r t i c a l d i r e c -t i o n were observed ( 2 2 ) . The d i s p e r s e d phase was about 8%m ( 0 . 0 6 8 l b . moles/cu. f t . s o l n . ) a c e t i c a c i d i n MIBK and a c i d t r a n s f e r was from the d i s p e r s e d to the continuous water phase i n s e c t i o n (a) below. T r a n s f e r was reversed, i n s e c t i o n (b) and the continuous phase composition was s i m i l a r to that of R o c c h i n i d e s c r i b e d under (b) to f o l l o w . The Hycam movie camera with the l e n s removed was used, throughout. a) Solute T r a n s f e r r i n g from Drops Run 1 was taken a t 6 0 0 pps with Kodak T r i - X Rever-s a l f i l m (USASI No. 2 0 0 , d a y l i g h t ) . For run 2 , the s h u t t e r speed was i n c r e a s e d t o 1 2 0 0 pps to slow down the motion a t the i n s t a n t of c o a l e s c e n c e . To compensate f o r the somewhat too low exposure t h a t the f i l m received, due t o a h i g h e r s h u t t e r speed and hence s h o r t e r exposure, the i n t e n s i t y of the l i g h t source was corresponding l y i n c r e a s e d from a l i g h t meter r e a d i n g of 1 5 . 8 to 1 6 . 2 5 by a d j u s t i n g the v a r i a b l e r e s i s t o r on the c o n t r o l panel from 4 . 2 5 amps, t o about 5 ° ° amps. T h i s procedure of i n c r e a s i n g the amperage above the i d e a l c u r r e n t range of 4 . 0 - 4 . 5 ( 2 5 ) s hould not be p r a c t i s e d n ormally as t h i s shortens the l i f e of the mercury lamp ( 2 5 ) » However, i f used f o r a s h o r t du-r a t i o n , t h i s may not matter much. 35 Run 3 was made a t 2500 pps to observe coalescence a t a s t i l l h i g h e r camera frame speed. Underexposure n a t u r a l l y would occur a t t h i s frame speed u n l e s s the l i g h t source am-perage c o u l d be i n c r e a s e d to a much higher value s t i l l . In-stead of s a c r i f i c i n g lamp l i f e , use of f a s t e r f i l m s was con-s i d e r e d . An I l f o r d HPS Negative (USASI No. 800 , d a y l i g h t ) was probably as s u i t a b l e as Kodak brands but t h i s make was not immediately a v a i l a b l e a t the time of i n q u i r y . Another Kodak f i l m was used, t h i s time the kX Panchromatic Negative with an USASI No. of 500 ( d a y l i g h t ) . L i g h t source amperage was a g a i n h e l d to about 5 » 0 . For run 4 , camera speed was h e l d down to 2000 pps while u s i n g Kodak T r i - X R e v e r s a l f i l m . V e l o c i t y of d i s p e r s e d phase flow was reduced so that CD was i n c r e a s e d from 1 . 7 s e c , as i n a l l the p r e v i o u s runs, to 3»3 sec..- By d e c r e a s i n g the drop v e l o c i t y a t the n o z z l e and by m a i n t a i n i n g the same d i s -tance of s e p a r a t i o n between n o z z l e t i p s as run 3» the r e a l time i n t e r v a l from drop approach to the onset of coalescence was i n c r e a s e d . b) Solute T r a n s f e r r i n g to Drops In runs 6 and 7» s o l u t e was t r a n s f e r r e d i n the r e -v e r s e d i r e c t i o n , i . e . , from the continuous t o the d i s p e r s e d phase. The continuous phase was not s a t u r a t e d with main com-36 ponent of the d i s p e r s e d phase, and was prepared to have the composition of R o c c h i n i ' s mixture to a v o i d s e p a r a t i o n of phases ( 2 6 ) : 1.29/&* MIBK 9J.6k%w Water 5»07^w A c e t i c a c i d . The use of t h i s mixture was found (26) to prevent m i s t i n g of the continuous water phase upon t r a n s f e r of a c e t i c a c i d from that phase. T h i s m i s t i n g phenomenon was a t t r i b u t e d by R o c c h i n i to the i n f l u e n c e of a s o l u t e and/or temperature on the mutual 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 s o l v e n t s . Without the use of the above mixture, upon e x t r a c t i o n of the a c e t i c a c i d from the MIBK-saturated. water phase, a small amount of ketone w i l l come out of s o l u t i o n . For runs 6 and 7 , a l l l i n e s l e a d i n g t o the e x t r a c -t i o n column were detached and that l i n e c a r r y i n g the d i s -persed phase was s e a l e d f o r the time b e i n g . The QVF tank c o n t a i n i n g the continuous phase was d r a i n e d and the l i n e connected from i t was then j o i n e d t o the nozzle assembly so th a t the d i s p e r s e d phase flow was now s u p p l i e d by that QVF tank which p r e v i o u s l y c o n t a i n e d MIBK-saturated water used as continuous phase. The d i s p e r s e d phase i n runs 6 and 7 s i m i -l a r l y c o n s i s t e d of MIBK and water, except that the l i q u i d b e i n g s a t u r a t e d and the main component of d i s p e r s e d phase was now MIBK and, t h e r e f o r e , no contamination by a t h i r d l i q u i d was p o s s i b l e with the above arrangement. Continuous phase 37 c h a r g i n g of the column was batchwise and was done by f i l l i n g t h i s column, through one of the openings i n the top of i t , w i t h R o c c h i n i • s mixture contained i n a b o t t l e . The column was then t i g h t l y closed, by a nylon f i t t i n g t o prevent any unnecessary vapour leakage. Runs 6 and 7 were a g a i n shot a t 2000 pps; l i g h t meter r e a d i n g s were a l l l6»5 corresponding t o an amperage of about 5°2 as read, from the l i g h t source c o n t r o l p a n e l . Both runs were i d e n t i c a l except t h a t i n run 6, the k n i f e edge was set h o r i z o n t a l l y while i n run 7» t h i s was changed to a v e r t i c a l p o s i t i o n so t h a t i n run 7 d e n s i t y g r a d i e n t s i n the h o r i z o n t a l d i r e c t i o n were observed. T h i s change was made i n order to observe the e f f e c t of 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 of d e n s i t y g r a d i e n t s between the drops. 2) Nozzle T i p s Oriented V e r t i c a l l y The g l a s s n o z z l e s were bent so that the two t i p s were f a c i n g each other v e r t i c a l l y i n order to study c o a l e s -cence when the drops were one on top of the other and buoy-ancy f o r c e s were a c t i n g on the drops i n a d i f f e r e n t manner compared to when the t i p s were o r i e n t e d h o r i z o n t a l l y . Only one d i r e c t i o n of s o l u t e t r a n s f e r was i n v e s t i -gated: from the MIBK drops t o the continuous water phase. The l i q u i d phase p i p i n g system was r e f i t t e d t o i t s o r i g i n a l p o s i -3 8 t i o n as i n runs 1 , 2 , 3 » and 4 when the s o l u t e t r a n s f e r a l s o was from drops to the continuous phase. Both h o r i z o n t a l (runs 8 and 1 1 ) and v e r t i c a l (runs 9 and 1 0 ) o r i e n t a t i o n s of the k n i f e edge were used. Runs 8 and 9 were r e p l i c a t e s w i t h about 0 . 0 5 l b . moles/cu. f t . s o l n . a c e t i c a c i d i n the d i s p e r s e d MIBK phase. S i m i l a r l y , runs 1 0 and 1 1 were r e p l i -c a t e s , w i t h about 0 . 0 0 9 l b . moles/cu. f t . s o l n . a c e t i c a c i d . The 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 runs 1 0 and 1 1 was reduced from t h a t used i n runs 8 and 9 t o decrease I n t e r f a c i a l t u r -bulence ( 9 ) o T h i s was due to the r e l a t i v e l y high s o l u t e con-c e n t r a t i o n , and hence, a high d r i v i n g f o r c e present w i t h i n the system. The Hycam camera w i t h the l e n s removed was used throughout. Other r e l e v a n t data can be found i n Table I. B. MIBK-Water System* In run 5 ° a b i n a r y system was used, without a c e t i c a c i d b e i n g present, with a continuous phase of pure water and a d i s p e r s e d phase of w a t e r - s a t u r a t e d MIBK. T h i s was done i n order t o determine the e f f e c t of MIBK t r a n s f e r i n runs 6 and 7 ° In each of these two runs, R o c c h i n i ' s mixture was used and mass t r a n s f e r o c c u r r e d i n two d i r e c t i o n s a t once -a c e t i c a c i d was t r a n s f e r r e d from the continuous phase to the * Run 5 » i n v o l v i n g the MIBK-water system, was performed b e f o r e runs 6 and 7 ° 39 drops and, simultaneously, MIBK from the drops to the c o n t i -nuous water phase. T h i s l a s t t r a n s f e r was due to mutual un-s a t u r a t i o n of the phases. Since run 5 had a pure water con-t i n u o u s phase, and si n c e i n R o c c h i n i ' s continuous mixture, there was some MIBK, the mass t r a n s f e r r a t e i n run 5 was ex-pected, t o be high e r than those of runs 6 and. 7 because of the l a r g e r MIBK c o n c e n t r a t i o n d r i v i n g f o r c e i n run 5° Usual procedures were undertaken to insure t h a t no a c e t i c a c i d was prese n t . Run 5 was s t a r t e d but then t i n y " c a p s u l e s " of im-m i s c i b l e l i q u i d were observed t o be t r a v e l l i n g up through one of the two g l a s s n o z z l e s . when these reached the t i p of the n o z z l e , no drops were formed. However, o p t i c a l d i s t u r b a n c e s or s c h l i e r e , which could, e i t h e r be due to d e n s i t y or concen-t r a t i o n d i f f e r e n c e s or both, were observed. These s c h l i e r e were l a t e r found to be caused by water from the continuous phase that somehow seeped through the g l a s s t u b i n g - n y l o n t u -b i n g j o i n t . T h i s problem was c o r r e c t e d by r e p l a c i n g the worn n y l o n tubing i n the a f f e c t e d g l a s s - n y l o n j o i n t . Run 5 was repeated with the t i g h t c o n n e c t i o n s . I t was f i l m e d a t 2000 pps wit h l i g h t meter r e a d i n g of 16.7 c o r -responding t o a l i g h t source amperage of about 5°5° The k n i f e edge was set h o r i z o n t a l l y . 40 C. Toluene - A c e t i c A c i d - Water System At t h i s stage, i t was decid e d to r e p l a c e the MIBK with a s o l v e n t of hi g h e r surface t e n s i o n and d e n s i t y . Toluene was used s i n c e i t has 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 was r e a d i l y a v a i l a b l e 0 The sur f a c e t e n s i o n and the d e n s i t y of these two s o l v e n t s are compared i n Appendix Fo I t was decided to take p i c t u r e s w i t h the n o z z l e t i p s o r i e n t e d v e r t i c a l l y only» The reason f o r t h i s was be-cause i n the MIBK runs, the ones wi t h the v e r t i c a l l y - o r i e n t e d n o z z l e t i p s were among the best exposed p i c t u r e s i n the whole s e r i e s of ru n s . By f o l l o w i n g s i m i l a r exposure s e t t i n g s f o r to l u e n e , i t was f e l t a c l o s e comparison c o u l d p o s s i b l y be achieved© Batchwise procedures were used. These were s i m i l a r to the corresponding procedures f o r the MIBK-acetic acid-water r u n s . The QVF feed tank which s u p p l i e d the d i s p e r s e d phase was not used i n order t o prevent contamination since washing out a heavy tank as the above i s cumbersome. T h i s tank was r e p l a c e d by a 250 ml° l e v e l l i n g g l a s s bulb t h a t was covered a t the top by a cork wrapped i n aluminium f o i l and h e l d by clamps a t t a c h e d t o one of the p o s t s of the e x t r a c t i o n column frame. The needle v a l v e s that c o n t r o l l e d drop flow were r e -p l a c e d by screw-type p i n c h clamps t h a t worked s u r p r i s i n g l y w e l l when used with the f l e x i b l e Tygon t u b i n g . A l l l i n e s 41 that had been i n contact with MIBK were removed and replaced with nylon tubing except f o r the dispersed phase l i n e which was made up of Tygon, some polyethylene tubing, and nylon f i t t i n g s . Part of the discharge l i n e which was immediately connected to the bottom of the square glass column was also replaced with fresh tubingo This ensured against any MIBK, which might have been l e f t over from previous runs, finding i t s way back to the glass column and contaminating i t s pre-sent contents. Drop flow once more was made continuous. The flow was gravity-produced, and was regulated by turning the screws i n the pinch clamps which c o n s t r i c t l i q u i d flow through the f l e x i b l e Tygon l i n e . A l l runs involving toluene were made with the knife edge cutting off l i g h t rays h o r i -z o ntally. In run 12, the dispersed toluene phase contained acetic a c i d (6.28 x 10 l b . moles/ cu. f t . soln.), and both phases were mutually saturated with the main component of the other. Camera speed was 2000 pps and the l i g h t meter reading was 1?.5 corresponding to a l i g h t source amperage of about 6»5o Drop coalescence was narrowly missed and the run was not repeated. Pictures of runs 13 and 14 were taken with the Linhof camera (lens removed). The dispersed toluene phase contained 6.2 x 10"" ^  l b . moles/cu. f t . soln. and 51.96 x 10"" 3 l b . moles/cu. f t . soln. of a c e t i c acid i n runs 13 and 14, respectively. Other extraction conditions were i d e n t i c a l to those of run 12. The camera shutter speed was set at 1/250 4 2 seco with the "aperture" opening a t i t s widest (corresponding to f / 4 o 5 when l e n s i s attached)« L i g h t v a l u e s were the same f o r both runs with a l i g h t meter r e a d i n g of I 6 0 O and a l i g h t source amperage of 4 o 0 o The continuous phase was t o l u e n e - s a t u r a t e d watero A l l other data are to be found i n Table L ^3 RESULTS S t i l l and movie photography are extremely important t o o l s i n r e c o r d i n g drop phenomena, p a r t i c u l a r l y high-speed occurrences such as the coalescence of drops» Human e r r o r i n h e r e n t i n o b s e r v a t i o n i s o f t e n reduced when a photographic r e c o r d i s taken of the phenomena.. However, t h i s must be approached w i t h c o n s i d e r a b l e caution© For example, a movie taken a t c o n s i d e r a b l e speed and viewed i n slow motion on a s c r e e n can confuse the viewer accustomed to movements seen i n r e a l time© As was p o i n t e d out e a r l i e r , the purpose of the p r e s e n t work was to p r o v i d e i n f o r m a t i o n on the mechanism of drop coalescence by d e t e r m i n i n g w i t h the use of s c h l i e r e n o p t i c s what v i s u a l changes occur when drops c o a l e s c e under the i n f l u e n c e of mass transfer© I t was hoped that the r e -s u l t i n g s b h l i e r e caused by the d e n s i t y g r a d i e n t s c o u l d supply the neccesary information© Except i n run 1, only one drop coalescence per run was attempted© At h i g h e r camera speeds the a c t u a l coalescence occupied o n l y a f r a c t i o n of the t o t a l time i n v o l v e d from the s t a r t of drop growth t o coalescence© In runs 3 and 6, drop coalescence was not r e c o r d e d on f i l m (and a l s o where noted otherwise) due to poor camera-process s y n c h r o n i z a t i o n which had to be performed manually.. (The comments presented i n t h i s s e c t i o n with regard 44 to movement of m a t e r i a l s were drawn from v i e w i n g the movie f i l m , and not from the p r i n t s shown i n t h i s t h e s i s o ) I n t e r f a c i a l t urbulence (8) i n both drops c h a r a c t e -r i z e d by v i o l e n t movements was e v i d e n t i n the f i l m of run 1 and the presence of e d d i e s prevented the o b s e r v a t i o n of a sharp i n t e r f a c e o About f o u r coalescenceswere noted and as the p i c t u r e was viewed i n slow motion on the screen, i t was e v i d e n t that the camera must be operated a t a f a s t e r r a t e to f u r t h e r slow down the movements w i t h i n the p i c t u r e f o r c l o s e r a n a l y s i s of drop motion. In run 2 , the p i c t u r e appeared to be s l i g h t l y out of f o c u s . I n t e r f a c i a l turbulence was much more pronounced i n the drop a t the r i g h t hand sid e of the p i c t u r e (from here-on t o be c a l l e d , "the r i g h t d r o p " ) . I t was n o t i c e d a l s o t h a t : a d i f f u s i o n a l l a y e r ( 3 0 ) was present which surrounded both drops as a dark border to the upper hal v e s of the drops and i n a l i g h t e r shade on the lower h a l v e s ( F i g . 9)<> T h i s l a y e r was not n e c e s s a r i l y q u i e s c e n t . T h i s d i f f e r e n c e was b e l i e v e d to be a s s o c i a t e d with the k n i f e edge o r i e n t a t i o n and t h i s e f f e c t w i l l be d i s c u s s e d l a t e r under the heading, " E f f e c t of K n i f e Edge O r i e n t a t i o n on S c h l i e r e n Image". The drop a t the l e f t hand s i d e of the p i c t u r e (from hereon to be c a l l e d , "the l e f t d r o p " ) , f o r some r e a -son, e x h i b i t e d a s m a l l e r amount of i n t e r f a c i a l t u r b u l e n c e . 45 Probably, t h i s behaviour r e p r e s e n t e d a r e d u c t i o n i n s o l u t e c o n c e n t r a t i o n d r i v i n g f o r c e owing to e i t h e r incomplete mix-i n g or t o a slower r a t e of drop f o r m a t i o n . A c c o r d i n g to the former r e a s o n i n g , the mixture present i n the l e f t drop was l e a n e r i n the a c i d than what i t would normally be when com-p l e t e mixing d u r i n g the d i s p e r s e d phase p r e p a r a t i o n was a t -t a i n e d . Thus, a lower d r i v i n g f o r c e would r e s u l t . For the l a t t e r , a decay i n i n t e r f a c i a l a c t i v i t y o ccurred due t o the r e d u c t i o n of the s o l u t e c o n c e n t r a t i o n d i f f e r e n c e a c r o s s the i n t e r f a c e d i v i d i n g the d i s p e r s e d phase from the continuous phase g i v i n g r i s e t o s m a l l e r i n t e r f a c i a l t e n s i o n changes. I t was i n t e r e s t i n g to note the - movement of the s c h l i e r e i n the continuous phase j u s t o u t s i d e the p e r i p h e r y of the l e f t drop. T h e s e s c h l i e r e appeared to move around the drop s l i g h t l y and i n a counterclockwise d i r e c t i o n . The behaviour was ob-served t o be i n t e r m i t t e n t . The use of Kodak 4 x Panchromatic Negative (USASI No. 5°°» d a y l i g h t ) i n run 3 to compensate f o r a h i g h e r camera speed, r e s u l t e d i n moderate overexposure and reduced c o n t r a s t . However, s c h l i e r e movement i n t h i s run was more c l e a r l y shown than In run 2 . The s c h l i e r e were seen to be moving i n t e r m i t -t e n t l y i n the counterclockwise d i r e c t i o n around the l e f t drop while i n the r i g h t drop, the corresponding s c h l i e r e e x h i b i t e d c l o c k w i s e motion. 46 Run 4 showed d i f f u s i o n a l l a y e r s i n both drops s i m i -l a r to those r e p o r t e d i n d e s c r i b i n g the r e s u l t s i n run 2 ( i t should be noted that such l a y e r s occurred a l s o i n runs 1 and 3, although t o a l e s s e r e x t e n t ) . The d i r e c t i o n of s c h l i e r e movement was observed t o be v a r i e d . A d i f f u s i o n a l l a y e r was a g a i n observed f o r run 5 w i t h complete absence of any n o t i c e a b l e i n t e r f a c i a l t u r b u -l e n c e . A l s o , s c h l i e r e i n the form of a s i n g l e h o r n - l i k e p r o j e c t i o n appeared on the top of each drop. Coalescence was observed i n the b i n a r y system. In the use of R o c c h i n i ' s mixture i n run 6 where s o l u t e was t r a n s f e r r e d from the continuous t o the d i s p e r s e d phase, the l i q u i d i n the v i c i n i t y of the i n t e r f a c e was d i s -t u r b e d due t o i n t e r f a c i a l t u r b u l e n c e . However, movement of s c h l i e r e , although s l i g h t l y p r e s e n t , took p l a c e i n v a r i o u s d i r e c t i o n s . There were no e r u p t i o n s around the drops but simply d i s t u r b a n c e s of v e r y low i n t e n s i t y t h a t were almost s i m i l a r to a d i f f u s i o n a l l a y e r i n appearance. P i g . 10 i l l u s t r a t e s t h i s . In run 7» same e x t r a c t i o n c o n d i t i o n s were used as i n run 6 except t h a t the k n i f e edge was set v e r t i c a l l y . While i n run 6 the v e r t i c a l components of the d e n s i t y g r a -d i e n t s were v i s u a l i z e d , i n run 7 i t was the h o r i z o n t a l com-ponents (Fig'.. 11). Note the d i f f e r i n g r e g i o n s of decreased. 47 and i n c r e a s e d i l l u m i n a t i o n s i n F i g s . 1 0 and 1 1 when run 6 i s compared with run 7 » Again, the s c h l i e r e were not observed to f a v o u r moving i n any p a r t i c u l a r d i r e c t i o n . . The n o z z l e s were now p o s i t i o n e d v e r t i c a l l y i n run 8 so t h a t the drops were making bottom to top c o n t a c t . F i g . 1 2 shows the. l a t e r stages of drop growth. Under these con-d i t i o n s , the upper or pendent drop was observed to be d i s -t o r t e d i n shape with accompanying clockwise movement of the s c h l i e r e around the drop. S c h l i e r e were observed a l s o around the lower drop. T h e i r motion was i n t e r m i t t e n t , and i n v a r i o u s d i r e c t i o n s once a g a i n . However, pendulum-like motion or os-c i l l a t i o n was observed i n the lower drop. For the lower drop, d i f f u s i o n was not uniform a l l around the drop boundary and appeared l e s s near the n o z z l e t i p . The d i f f u s e d s o l u t e ap-peared suspended i n the continuous f l u i d and was d i s t r i b u t e d i n a unique p a t t e r n ( F i g . 1 2 ) with l i t t l e or no mixing t a k i n g p l a c e w i t h the continuous phase, f o r the d u r a t i o n of the f i l m . The photographic c o n d i t i o n s of run 9 were s i m i l a r t o run 8 , the only d i f f e r e n c e b e i n g t h a t a v e r t i c a l k n i f e edge s e t t i n g was used and t h a t the drops appeared to be s l i g h t l y out of focus ( F i g . 1 3 ) . The s c h l i e r e due to the d i f f u s i n g a c e t i c a c i d appeared to be moving downward a t the r i g h t p o r t i o n of the p i c t u r e . Whether t h i s was s e t t l i n g or simply movements owing to 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 c r e -a t e d by the p r e v i o u s drops d e t a c h i n g and r i s i n g up the column Figures 9 - 1 3 . Schlieren photographs of various drop pairs . 49 and/or movements generated by the drop interface was not cer-ta i n , because of the b r i e f time involved i n taking 100 f t o of f i l m , which comprises the run, approximately 3 secso In addi-tio n , because of the l i m i t e d camera viewing area, the entire solute flow pattern was d i f f i c u l t to distinguisho No notice-able amount of motion by the schliere or drop o s c i l l a t i o n was observed f o r either of the two drops i n the pictureo Inter-f a c i a l turbulence was absent i n the left-hand part of the l o -wer drop located near the nozzle t i p . The absence of t h i s turbulence i s shown i n Fig. 1 3 ° Runs 10 and 11 were carried out at low concentra-tion of solute i n the dispersed phase (9«43 x 10** ^  lbo moles/ cuo f t o s o l n 0 ) 0 Under these conditions, 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 higher concentrations. O s c i l l a t i o n was v i r t u a l l y absent from the pictures obtained (Figs. 14 and 1 5 ) ° The i n -terface was almost turbulent-free and the l o c a t i o n of the d i f -f usional layer, which depends upon the knife edge orientation, 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 than i n previous runs. Direction of movement of the schliere was i n various d i r e c t i o n s . Due to the higher i n t e r f a c i a l tension value of toluene compared to MIBK (Appendix F), with toluene compri-sing the main component of the dispersed phase i n run 12 instead of MIBK, the drops were observed to be bigger i n 50 s i z e . A f t e r one coalescence, the r e s u l t i n g l a r g e drop s t i l l remained a t t a c h e d to the upper nozzle<> Another drop from the lower n o z z l e was made to coalesce w i t h t h i s b i g g e r pendent drop and. t h i s was taken as run 12. (In both runs 11 and 1 2 , the k n i f e edge was set h o r i z o n t a l l y o ) The l i g h t patterns were s i m i l a r i n the two runs as would be expected. Both drops appeared to f l a t t e n a t the zone of c l o s e approach d u r i n g the r e s t - t i m e stage, the lower drop b e i n g f l a t t e r than the upper, perhaps due mainly to the weight of the h e a v i e r and b i g g e r pendent drop b e a r i n g down on i t . Laminar d i f f u s i o n ( 30 ) was observed, i n the form of a q u i e s c e n t d i f f u s i o n a l l a y e r s u r -rounding a smooth i n t e r f a c e and there were no drop o s c i l l a -t i o n s or evidence of l a r g e s c a l e s c h l i e r e n p a t t e r n s present near the drops a t the s o l u t e c o n c e n t r a t i o n l e v e l of run 12 which was s i m i l a r to t h a t runs 10 and 1 1 . Again, the s c h l i e r e movement was i n v a r i o u s d i r e c t i o n s . Run 13 was a r e p e t i t i o n of run 1 2 . Photographs were taken by means of the L i n h o f camera. In run 1 3 , stronger s u r f a c e a c t i v i t y i n the form of sma l l e r u p t i o n s was e v i d e n t i n the lower p a r t s of both drops p a r t i c u l a r l y the pendent drop ( F i g . 1 6 ) . As mentioned e a r l i e r , G o l t z ( 30 ) suggested t h a t stronger a c t i v i t y would be encountered i n the i n t e r f a c e bounding t h a t p a r t of the drop out of which the s o l u t e tended to flow by d e n s i t y c u r r e n t s ( i . e . , the lower p a r t s of both d r o p s ) . Run 13 showed, r e s u l t s which seem- to be i n accord with t h i s e x p e c t a t i o n . The photographs showed a b i g g e r view-51 i n g a r e a than those f o r run 12„ and. i n run 1JS the s o l u t e coming from the lower drop c o u l d be seen to appear f l o w i n g downward along the lower n o z z l e ' s lengtho The s o l u t e c o n c e n t r a t i o n was i n c r e a s e d from appro-x i m a t e l y 6 x 10~3 i D o moles/cu. f t . s o l n . i n run 13 to appro-x i m a t e l y 52 x 1 0 " 3 l b . moles/cu. f t . s o l n . i n run 14. The i n t e r f a c i a l a c t i v i t y i n c r e a s e d a c c o r d i n g l y ( F i g . 1 7 ) . A l l mass t r a n s f e r runs taken together were attempts to p r e s e n t a g e n e r a l v i s u a l study of two drops c o a l e s c i n g under mass t r a n s f e r c o n d i t i o n s . However, although a l a r g e number of f i l m s were examined, no behaviour was found a t or near the i n t e r f a c e i n the zone of drop approach to confirm the h y p o t h e s i s proposed by Groothuis and Zulderweg (13 ) and a l s o by Smith ( 1 2 ) . On the other hand, i t may be that the movement of the s c h l i e r e observed i n some of the runs i n d i -cated drop r o t a t i o n of the s o r t d e s c r i b e d by G o l t z ( 3 0 ) . The behaviour observed i n run 8 was e s p e c i a l l y suggestive of drop r o t a t i o n . The n y l o n t u b i n g used i n most of the l i n e s were found to be s t i f f i n i t i a l l y and i t was necessary a t times to immerse p o r t i o n s of t h i s i n hot water i n order to s t r a i g h t e n them. The n y l o n f i t t i n g s were a l s o found to become b r i t t l e a f t e r a p e r i o d of time. Influence of ambient temperature changes was assumed n e g l i g i b l e c o n s i d e r i n g t h a t maximum room F i g u r e s 14 - 1?. Schlieren photographs of various drop pairs . 53 temperature f l u c t u a t i o n s d u r i n g each run were very small f o r the s h o r t p e r i o d of time i n v o l v e d i n each filming., Influence of ambient a i r d e n s i t y changes was l i k e w i s e n e g l e c t e d since the d e n s i t y g r a d i e n t was r e l a t i v e l y smallo The depth of f i e l d of the s c h l i e r e n systems was c o n f i n e d w i t h i n the square c o l -umn o 5^ DISCUSSION A° E f f e c t of K n i f e Edge O r i e n t a t i o n on S c h l i e r e n Image Runs 6 to 11 show the e f f e c t of k n i f e o r i e n t a t i o n . , In runs 6, 8, and 11, a h o r i z o n t a l k n i f e edge p o s i t i o n was used, i n runs 7» 9» and 10, a v e r t i c a l one. The d i f f e r e n t l i g h t p a t t e r n s observed i n each p a i r of runs(7 and 6, 9 and 8, and 10 and 11) were due to the d i f f e r e n t p o s i t i o n s of the k n i f e edge. Fi g u r e 8 of the paper by Sawistowskl and G o l t z (31) p r o v i d e s a f u r t h e r example of the e f f e c t of k n i f e edge p o s i t i o n . I f i n the t e s t s e c t i o n there i s a r e f r a c t i v e index g r a d i e n t normal to the path of the l i g h t r a y s , the r a y s w i l l be d e f l e c t e d because the speed of l i g h t v a r i e s w i t h changes i n the r e f r a c t i v e index of a medium where the l i g h t t r a v e l s . This d e f l e c t i o n of the l i g h t r a y s may be observed by one of a number of s c h l i e r e n techniques, the one used being c a l l e d the T o e p l e r method (22). In t h i s method, the displacement of the image of the source co r r e s p o n d i n g to the d e f l e c t i o n of the l i g h t p a s s i n g through a p a r t i c u l a r p o i n t i n the s c h l i e r e n f i e l d r e s u l t s i n a change of i l l u m i n a t i o n of the image of t h i s p o i n t on the viewing scree«. Consider F i g . 18. T h i s i s a c r o s s - s e c t i o n a l view of the bundle of l i g h t r a y s p a s s i n g through the f o c a l plane of the second s c h l i e r e n m i r r o r , M2 ( F i g . 4 ) . The image of the l i g h t source i s square and 5 5 NOTE: b = h INITIAL IMAGE OF SOURCE F i g u r e 18. L i g h t bundle - k n i f e edge arrangement i n the T o e p l e r method (22). 56 an opaque k n i f e edge i s placed, a t the f o c a l plane of M2. The edge i s a d j u s t e d so that f o r no d i s t u r b a n c e s i n the t e s t sec-t i o n , p a r t of the l i g h t from the image of the source i s cut o f f so t h a t i l l u m i n a t i o n on the screen i s reduced u n i f o r m l y . When an o p t i c a l d i s t u r b a n c e i s i n t r o d u c e d , p a r t of the image of the source may be d i s p l a c e d to a p o s i t i o n shown i n F<igo 18o I l l u m i n a t i o n of the cor r e s p o n d i n g p a r t of the image on the screen w i l l decrease or i n c r e a s e a c c o r d i n g t o whether the d e f l e c t i o n i s towards or away from the k n i f e edge. D i s -placement of the image of the source p a r a l l e l t o the k n i f e edge produces no e f f e c t a t the screen, and t h i s edge must, t h e r e f o r e , be set p e r p e n d i c u l a r t o the d i r e c t i o n i n which the r e f r a c t i v e index or d e n s i t y g r a d i e n t s are to be observed, i n order to o b t a i n the s c h l i e r e n e f f e c t . Regions t h a t are evenly i l l u m i n a t e d i n a s c h l i e r e n photograph correspond t o zero d e n s i t y g r a d i e n t . From the 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= t o t a l angular l i g h t d e f l e c t i o n s i n the X and ^ d i r e c t i o n s r e s p e c t i v e l y . L - width of t e s t s e c t i o n . Tfo = r e f r a c t i v e index of a i r surrounding t e s t s e c t i o n . 5 7 7jt _ r e f r a c t i v e index of i n t e r e s t i n t e s t s e c t i o n . i t i s seen t h a t l i g h t d e f l e c t i o n s are i n the d i r e c t i o n of the r e f r a c t i v e index g r a d i e n t , i . e . , toward the r e g i o n of h i g h e r d e n s i t y . For the experimental runs i n v o l v i n g the system MIBK-acetic acid-water, the r e f r a c t i v e index of a c e t i c a c i d i s g r e a t e r than t h a t of water (Appendix F) so t h a t the d i r e c t i o n of the r e f r a c t i v e index g r a d i e n t i s opposite to the d i r e c t i o n of mass t r a n s f e r . Taking run 6 as an example, a h o r i z o n t a l k n i f e edge s e t t i n g was employed, to observe the v e r t i c a l component of t h i s g r a d i e n t . The d e f l e c t i o n of l i g h t i s toward the p o s i t i v e d i r e c t i o n s of these components (equations ( 2 ) and ( 3 ) ) o so t h a t the l i g h t r a y s p a s s i n g o u t s i d e each drop but c l o s e to i t s upper r e g i o n are d e f l e c t e d downwards while those p a s s i n g c l o s e to i t s lower r e g i o n are d e f l e c t e d upwards ( F i g . 19). For i l l u s t r a t i o n purposes, l e n s e s 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 and the arrow head and t a i l r e p r e s e n t the upper and lower boundaries of the drop, r e s p e c t i v e l y . On the other hand, the d i r e c t i o n of the d e n s i t y g r a d i e n t i s almost or completely p a r a l l e l to the k n i f e edge s e t t i n g a t some p o r t i o n of the drop boundary p a r t i c u l a r l y a t the zone of drop approach so t h a t the path of the l i g h t r a y s here remains u n d i s t u r b e d . By p o s i t i o n i n g the k n i f e edge to cut o f f the v e r t i c a l components of the l i g h t r a y s which are d e f l e c t e d downwards ( F i g . 19)» an image of v a r i o u s l i g h t tones are produced. Some d e n s i t y g r a d i e n t s , which are not D E F L E C T E D LIGHT RAYS F i g u r e 1 9 . Image formation, 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 (To e p l e r method)„ 59 expected to be v i s u a l i z e d due to the p o s i t i o n of the k n i f e edge, may sometimes appear due to the i n a b i l i t y of the second s c h l i e r e n m i r r o r , M2, to c o l l e c t a l l of the l i g h t r a y s r e f r a c t e d , i n the t e s t s e c t i o n (22). Thus, t h i s m i r r o r can a c t as a c i r c u l a r stop given the proper c o n d i t i o n s , a n d , thus, can a f f e c t the i l l u m i n a t i o n i n the f i n a l image. From the f o r e g o i n g c o n s i d e r a t i o n s , the k n i f e edge can be o r i e n t e d so as to p r o v i d e i n f o r m a t i o n about the d e n s i t y g r a d i e n t i n any d i r e c t i o n . When d e n s i t y g r a d i e n t s have been s t u d i e d i n one d i r e c t i o n and i t i s d e s i r e d t o study them i n the other, the k n i f e edge i s simply r o t a t e d and another p i c t u r e taken. The time l a g between s u c c e s s i v e p i c t u r e s owing to the time r e q u i r e d to make such an adjustment i s not s i g n i f i c a n t when the phenomenon i n v o l v e d I s , f o r example, s t e a d y - s t a t e flow, or i s r e p r o d u c i b l e . Otherwise, c o m p l i c a t i o n s may a r i s e and p i c t u r e s with two d i f f e r e n t k n i f e edge o r i e n t a t i o n s should be taken s i m u l t a n e o u s l y f o r compari-son. From the r e s u l t s obtained, i t seems safe to say t h a t knowledge of the d e f l e c t i o n i n one d i r e c t i o n s u f f i c e s t o give the c o n d i t i o n s p r e v a i l i n g i n the t e s t s e c t i o n of the present experimental study. For a device t h a t forms two separate images of the t e s t s e c t i o n simultaneously, one image i n d i c a t i n g v e r t i c a l d e n s i t y g r a d i e n t s and. the other, h o r i z o n t a l d e n s i t y g r a d i e n t s , the reader i s r e f e r r e d to r e f e r e n c e 32. F u r t h e r -more, s e v e r a l forms of stop have been used by d i f f e r e n t workers (33, 34) to render l i g h t d e f l e c t i o n s v i s i b l e . 6 0 B. Drop R o t a t i o n and Solute D i f f u s i o n i n the Continuous Phase G o l t z ( 3 0 ) observed r o t a t i o n of an u p r i g h t drop and thought t h i s motion was i n i t i a t e d by i m p e r f e c t i o n s i n the n o z z l e . Bakker, van Buytenen, and Beek ( 3 5 ) on the other hand, contended that drop r o t a t i o n was due to l o c a l i z e d l o w e r i n g of i n t e r f a c i a l t e n s i o n which causes the i n t e r f a c e t o move from the a f f e c t e d area towards the u n d i s t u r b e d r e g i o n s . According t o them, suppose the s o l u t e lowers the i n t e r f a c i a l t e n s i o n and i f i n a pendent drop, the incoming d i s p e r s e d phase impinges on the i n t e r f a c e a t an area A, then the i n t e r f a c i a l t e n s i o n a t A becomes lower than a t some other a r e a i n the i n t e r f a c e l i k e B s i n c e the incoming l i q u i d i s r i c h e r i n s o l u t e than the l i q u i d i n the drop. T h i s causes the i n t e r f a c e to move from A t o B and as the l i q u i d w i t h i n the drop i s e n t r a i n e d , the incoming l i q u i d i s c o n t i n u o u s l y f o r c e d i n the d i r e c t i o n of A. The drop s t a r t s r o t a t i n g and maintains a c i r c u l a t i o n i n one d i r e c t i o n . They found out, however, t h a t a t very h i g h r a t e s of drop growth the momentum of the incoming l i q u i d i s so g r e a t t h a t the r o t a t i o n i s d i s t u r b e d and an i r r e g u l a r movement r e s u l t s . Garner, Nut t, and Mohtadi ( 3 6 ) observed t h a t r o t a t i o n depended on: 1. r a t e of drop f o r m a t i o n . 6 1 2. c o n c e n t r a t i o n of s o l u t e . 3» nature of the l i q u i d s . They s t u d i e d pendent drops of nit 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 chloroform c o n t a i n i n g , as s o l u t e s , acetone, e t h y l a l c o h o l , methyl a l c o h o l , and i s o p r o p y l a l c o -h o l . The continuous phase was water. The c o n c e n t r a t i o n of s o l u t e v a r i e d between 2 and 30 per cent. They found out t h a t the a d d i t i o n of a s u r f a c e - a c t i v e agent suppressed r o t a t i o n and the d i r e c t i o n of r o t a t i o n depended on the p o s i t i o n of the zone of c o n c e n t r a t i o n g r a d i e n t w i t h i n the drop. The d i r e c t i o n of r o t a t i o n and accompanying drop d i s t o r t i o n i n run 8 appeared t o agree with t h e i r f i n d i n g s . A l l the above-mentioned workers gave no i n d i c a t i o n as t o whether t h e i r e x p l a n a t i o n s f o r drop r o t a t i o n a p ply to drops of any n o z z l e o r i e n t a t i o n . No attempt was made to check the v a l i d i t y of t h e i r r e a s o n i n g s , but, i f one accepts Bakker e t a l ' s e x p l a n a t i o n , then drop r o t a t i o n can be ex-pected t o continue i n the same d i r e c t i o n as l o n g as the a f -f e c t e d a r e a , which has a lower i n t e r f a c i a l t e n s i o n , remains i n the same p o s i t i o n i n the drop. For two drops approaching each other and t r a n s f e r r i n g s o l u t e t o the surrounding medium, r o t a t i o n may be d i s t u r b e d due to the s h i f t of t h i s a f f e c t e d a r e a towards the r e g i o n of drop approach p r o v i d e d the i n t e r -f a c i a l t e n s i o n i s lower i n the l a t t e r r e g i o n . The I n t e r m i t t e n t n ature of the movements of the s c h l i e r e around the drops as observed i n some of the runs 6 2 (and presumably t r i g g e r e d by drop r o t a t i o n ) may imply that the i n t e r f a c e a f f e c t e d by lower i n t e r f a c i a l t e n s i o n d i d not remain i n the same p o s i t i o n i n the drop a t a l l times. The occurrence of drop r o t a t i o n may have a d i s t u r b i n g , i f not c o n t r o l l i n g , e f f e c t on i n t e r f a c i a l movement and t h e r e f o r e the s o r t of i n t e r f a c i a l s t r e t c h i n g and s h r i n k i n g contemplated i n the theory of Smith ( 1 2 ) and Groothuis and Zuiderweg ( 1 3 ) might be g r o s s l y a f f e c t e d . In runs 1 3 and 14 w i t h v e r t i c a l n o z z l e o r i e n t a t i o n , the p i c t u r e s showed the d i f f u s i n g s o l u t e moving downwards and t r a v e l l i n g a l o n g s i d e the n o z z l e ' s l e n g t h . Due to the l a r g e p i c t u r e a r e a t h a t was obtained w i t h the use of the L i n h o f s t i l l camera, the p a t t e r n of s o l u t e movements was c l e a r l y shown whereas i n the c i n e f i l m s t h i s was not so owing t o a l i m i t e d viewing f i e l d o f f e r e d by the o p t i c s of the Hycam camera. I t was i n t e r e s t i n g to note the s o l u t e behaviour i n these two r u n s . The downward p a t t e r n of flow of s o l u t e was b e l i e v e d due to the absence of a p p r e c i a b l e mixing f o r c e s which prevented the s o l u t e from d i s p e r s i n g e f f i c i e n t l y i n the continuous phase thereby c r e a t i n g l o c a l i z e d high s o l u t e c o n c e n t r a t i on. C. Suspension of Drops a t Ends of No z z l e s . Coalescence of l i q u i d drop p a i r s as encountered i n i n d u s t r y , i n v o l v e s drops i n f r e e t r a v e l . In t h i s s i t u a t i o n , 6 3 drops can come i n t o c o n t a c t a t any con c e i v a b l e angle while t r a v e l l i n g a l o n g the column.. Since drop c o n t a c t i n f r e e t r a -v e l i s d i f f i c u l t t o c o n t r o l and to d u p l i c a t e i n experiments, the suspension of drops a t the ends of n o z z l e s perhaps i s a reasonable way of st u d y i n g coalescence under the circumstances i n v o l v e d . H o r i z o n t a l and v e r t i c a l n o z z l e o r i e n t a t i o n s were used t o simulate s i d e - t o - s i d e and top-to-bottom c o n t a c t s r e s -p e c t i v e l y . In t h i s work, the f o r c e s a c t i n g upon l i q u i d drops i n f r e e t r a v e l were not e n t i r e l y duplicated, i n the experimen-t a l procedure (suspension of drops a t the ends of n o z z l e s ) . F r i c t i o n a l drag, f o r example, a c t s on r i s i n g or f a l l i n g drops and t h i s f o r c e i s absent i n the present work. Drag may induce movement i n the i n t e r f a c e and r e s u l t a n t drop i n t e r n a l c i r c u l a t i o n . For drops suspended a t the ends of n o z z l e s , i n t e r f a c i a l movement may occur a l s o , but i n t h i s case due to l o c a l l y a l t e r e d i n t e r f a c i a l t e n s i o n or other causes d i f f e r e n t from drag. Furthermore, drop o s c i l l a t i o n may occur d u r i n g f r e e t r a v e l , but i s induced i n a d i f f e r e n t way from what i t i s f o r pendent drops, where the o s c i l l a t i o n s may a r i s e , not from drag, but r a t h e r (once a g a i n ) from imba-l a n c e s i n i n t e r f a c i a l t e n s i o n ( 3 5 , 3 6 ) . This d i f f e r i n g f u n -damental nature of o s c i l l a t i o n and drop surface movement i n the two cases (suspended and f r e e drops) may r e s u l t i n o s c i l -l a t i o n and surface movement having d i f f e r i n g importances with r e s p e c t t o coalescence i n the two c a s e s . 64 D. Forces I n f l u e n c i n g I n t e r f a c i a l A c t i v i t y In the i n v e s t i g a t i o n of t e r n a r y l i q u i d systems, changes i n r e f r a c t i v e index can be caused by changes i n con- . c e n t r a t i o n or i n temperature which, i n t u r n , are v i s u a l i z e d by schlieren© No h e a t - r e l e a s i n g chemical r e a c t i o n i s i n -vol v e d i n the prese n t work and i n t e r f a c i a l a c t i v i t y i s i n i -t i a t e d simply by f o r c e s of heat and/or mass transfer© (Heat f o r c e s a r e , of course, those due to heat of s o l u t i o n . ) To i n t e r p r e t the s c h l i e r e n r e s u l t i t i s necessary to determine which of these two processes i s o p e r a t i v e i n the t e r n a r y s y s -tem under c o n s i d e r a t i o n s i n c e heat and mass t r a n s f e r are i n -d i s t i n g u i s h a b l e from each other under s c h l i e r e n . I t i s d i f -f i c u l t t o separate the heat e f f e c t from the mass t r a n s f e r e f f e c t 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 cannot be d i -vorced from mass t r a n s f e r because one causes the other u n l e s s , of course, the t e r n a r y system t h a t was used c o n s i s t e d of i d e a l s o l u t i o n s only. (The system used was not i d e a l . ) In p r a c -t i c e , i n t e r f a c i a l t e n s i o n c o u l d , t h e r e f o r e , be a f f e c t e d by both temperature and composition f o r any mass t r a n s f e r p r o -cess and, consequently, i n t e r f a c i a l a c t i v i t y may be promoted, dampened, or a r r e s t e d , depending on the manner i n which the two e f f e c t s are put to g e t h e r . In the present work, i t was found t h a t the i n t e r f a c e of the t e r n a r y system was l e s s d i s t u r b e d when the d i r e c t i o n of a c e t i c a c i d t r a n s f e r was from the aqueous to the d i s p e r s e d 65 MIBK phase than when s o l u t e t r a n s f e r was r e v e r s e d . This d i f f e r e n c e i n i n t e r f a c i a l a c t i v i t y was ev i d e n t lnyspite of the f a c t t h a t f o r both d i r e c t i o n s of t r a n s f e r , the heat e f f e c t s are of the same magnitude. In a d d i t i o n , the heat e f f e c t s accompanying the mixing of a c e t i c a c i d w i t h water were c a l c u l a t e d (Appendix J ) and found to produce a maximum temperature i n c r e a s e of about 0.14°C f o r t r a n s f e r of a c e t i c a c i d t o a continuous water phase from an MIBK drop where the c o n c e n t r a t i o n was 56.45 x 10~^ l b . moles/cu. f t . s o l n . T h i s temperature e f f e c t i s small compared with t h a t of v a r i o u s other t e r n a r y systems which do not e x h i b i t i n t e r f a c i a l a c t i v i t y and, b e s i d e s , the s c h l i e r e n system p r e s e n t l y used i s not b e l i e v e d t o be s e n s i t i v e enough t o d e t e c t the r e f r a c t i v e index g r a d i e n t r e s u l t i n g from such a temperature r i s e . Prom t h i s c o n s i d e r a t i o n s , i t i s concluded t h a t heat of mixing alone does not cause i n t e r f a c i a l a c t i v i t y and i s not b e l i e v e d to be the c o n t r o l l i n g f a c t o r i n the phenomena, a t the s o l u t e c o n c e n t r a t i o n l e v e l s used. Comparison of heat e f f e c t s accompanying the mixing of the two s o l v e n t s , MIBK and water, and those f o r a c e t i c a c i d i n water/MIBK would probably r e s u l t i n s i m i l a r c o n c l u s i o n s t o those mentioned above but, as of t h i s w r i t i n g , no s u f f i c i e n t data were found i n the l i t e r a t u r e to make any heat e f f e c t comparisons f o r these l a t t e r systems. 66 Eo Minimum Attainable Depth of F i e l d The depth of f i e l d of the conventional schlieren system being used, which has fi x e d f o c a l length mirrors, i s a function of the size of the l i g h t source (39)» As shown i n F i g . 8, the l i g h t rays passing through the test section 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 angle, a, i s related to the source height, h, and f o c a l length, f, by the equation a = h (4) f One can see that only when the angle, a, i s inc. creased i s i t possible to increase the angle at P 1 and there-by reduce the depth of f i e l d . Since the divergence angle, a, i s constant along the length bounded by L1L2, the present setup i s characterized by a single value of the depth of f i e l d . This was measured to be approximately 2-in. There-fore, a considerable region of disturbances on e i t h e r side of the object plane and t h e o r e t i c a l l y encompassing the entire column width w i l l appear i n sharp focus at 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 in the column where the various density gradients occur. These over-laps could account for the over-abundance of schliere seen i n the films and confusion, due to superimposition of images, as to whether the desired region to be v i s u a l i z e d i s being ob~ served at a l l . Depth of f i e l d can be reduced considerably by the use of multiple knife edges (40). 67 CONCLUSIONS AND RECOMMENDATIONS Schliere movements near the drop interface were observed i n some runs. These movements were those of the continuous phase f l u i d highly concentrated with respect to acetic a c i d solute* For run 8, th i s behaviour was believed to be c h a r a c t e r i s t i c of drop rotation.. In the rest of the affected runs, i t was d i f f i c u l t to pinpoint what caused such movements, l e t alone determine whether these movements were triggered by motion i n the interface i t s e l f , or were purely due to mixing or other processes attributable to d i f f u s i o n . However, the i n t e r f a c i a l disturbance predicted by Smith (12) and Groothuis and Zuiderweg (13) i n the form of i n t e r f a c i a l stretching and shrinking (Marangoni e f f e c t ) , and accompanying streaming of the continuous phase, were not observed i n any of the runs examined. It i s suggested that using a d i f f e r e n t ternary sys-tem that would produce stronger i n t e r f a c i a l movements, and also t h e i r conjugate, more pronounced sweeping of the adja-cent continuous phase, might provide the necessary answer. However, a search f o r such a system was not made i n this work. In addition, i t i s suggested that the schlieren depth of f i e l d be reduced (40) for better i n t e r p r e t a t i o n of the coalescence mechanism.* However, the equipment needed i s extensive (40) and w i l l require considerable time and e f f o r t to assemble. It i s f e l t that study should be focussed. also on a more imme-68 d i a t e problem of understanding how drop shape changes w i t h time p r i o r t o c o a l e s c e n c e . In such work, o r d i n a r y p i c t o r i a l photography would be used. Measurements of drop dimensions would show any drop d i s t o r t i o n r e s u l t i n g from l o c a l l o w e r i n g of i n t e r f a c i a l t e n s i o n . The second p a r t of t h i s t h e s i s des-c r i b e s work a l o n g the l i n e s of t h i s l a s t p r o p o s a l . 6 9 PART I I DROP SHAPE STUDIES 7 0 PART I I DROP SHAPE STUDIES A. Scope Work was i n i t i a t e d to study the g e n e r a l shape p a t t e r n of the drops as they c o a l e s c e d under the i n f l u e n c e of mass t r a n s f e r o High-speed, photography u t i l i z i n g o r d i n a r y p i c t o -r i a l techniques were used, e x t r a c t i o n procedures and prepa-r a t i o n "being s i m i l a r to those i n the pr e v i o u s s c h l i e r e n work . B. Some Photographic C o n s i d e r a t i o n s L i q u i d drops w i t h i n a l i q u i d medium are compara-t i v e l y weak i n p i c t u r e c o n t r a s t due to small d i f f e r e n c e s i n r e f r a c t i v e indices.. The use of dyes a p p a r e n t l y p r o v i d e s a simple s o l u t i o n t o the problem of producing h i g h 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 such dyes are not surface a c t i v e . A reasonable a l t e r n a t i v e to dyes i s the proper use of l i g h t i n g e f f e c t s t o achieve an a c c e p t -a b l e p i c t u r e c o n t r a s t . K i n t n e r , Horton, Graumann, and Amberkar (41) presented v a r i o u s photographic techniques i n bubble and drop i n v e s t i g a t i o n t h a t were found t o be v e r y u s e f u l . 7 1 A d i f f u s e r was used f o r most of the runs, to p r o -vide uniform i l l u m i n a t i o n . T h i s c o n s i s t e d of e i t h e r a s i n g l e sheet of t r a c i n g paper or a ground g l a s s , whichever was more s u i t a b l e f o r the p a r t i c u l a r problem. To minimize d i s t o r t i o n of the image caused by shadows and r e f l e c t i o n s o c c u r r i n g i n the t e s t s e c t i o n , the camera l e n s should be p r o p e r l y a l i g n e d with the l i g h t source. 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 time, to o b t a i n the bes t r e s u l t s f o r a s p e c i f i c ap-l i c a t i o n . Because c o n v e n t i o n a l photographic methods were employed, the use of an exposure meter t o o b t a i n the c o r r e c t exposure was well-adapted f o r most s i t u a t i o n s u s i n g d i f f u s e d l i g h t f o r b a c k l i g h t i n g . On the other hand, when a naked l i g h t source was used (as one done on o c c a s i o n ) , the uneven l i g h t d i s t r i b u t i o n present gave i n c o r r e c t exposure r e a d i n g s , and i t was found convenient t o determine proper exposure by t r i a l and e r r o r . In some cases, the f i l m speed was too slow f o r the poor l i g h t i n g c o n d i t i o n s a v a i l a b l e , but, f o r t u n a t e l y , good exposure was s t i l l o b t a ined f o r b l a c k and white f i l m s due t o t h e i r wide l a t i t u d e s of exposure. Except f o r those of run 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 the f i l m s were done i n the department's dark room u s i n g mostly I l f o r d chemicals, p a r t i c u l a r l y the I D - 1 1 and I D - 2 0 d e v e l o p e r s , I F - 1 3 and I F - 1 5 h a r d e n e r - f i x e r s , and Kodak p r i n t -i n g papers. Standard p h o t o f i n i s h i n g procedures were f o l l o w e d 72 and need not be mentioned h e r e . Determination of development times i n f i l m p r o c e s s i n g was done by c u t t i n g s t r i p s of the f i l m m a t e r i a l and. t r e a t i n g them f o r d i f f e r e n t immersion times i n the d e v e l o p i n g s o l u t i o n u n t i l the a p p r o p r i a t e f i l m d e n s i t y was o b t a i n e d . C. P r e l i m i n a r y C o n s i d e r a t i o n s There are o p t i c a l and photographic problems i n v o l v e d i n the proper i n t e r p r e t a t i o n o f n o n - s c h l i e r e n images. These 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 t o the e f f e c t s of r e f r a c t i o n , , r e f l e c t i o n , and t r a n s m i s s i o n of l i g h t , and f i l m i r r a d i a t i o n . 1) MIBK-Acetic Acid-Water System The t e s t s e c t i o n was the u s u a l 40 mm. x 40 mm. square g l a s s e x t r a c t i o n column used p r e v i o u s l y i n a l l the s c h l i e r e n runs. In the a c t u a l experimental work, t h i s run (run 15) was done before run 12, which was p r e v i o u s l y des-c r i b e d and which i n v o l v e d the use of toluene as a main com-ponent of the d i s p e r s e d phase. Hence there was no contami-n a t i o n problem of the s o r t which c o u l d have a r i s e n from s w i t c h i n g from one chemical t o another, a procedure which would have been necessary had run 15 f o l l o w e d run 12. The g l a s s n o z z l e s were oriented, h o r i z o n t a l l y i n run 15 and the d i f f u s e r was a s i n g l e sheet of t r a c i n g paper. The l i g h t source was the u s u a l PEK hig h - p r e s s u r e mercury a r c lamp used 73 i n the p r e v i o u s s c h l i e r e n runs. A cardboard box was c o n s t r u c t e d t o c o n t a i n the d i f f u s e r and s h i e l d the t e s t s e c t i o n from a l l extraneous l i g h t except t h a t which f a l l s d i r e c t l y upon the f i e l d of i n t e r e s t and comes from the a r c lamp. E i g . 20 shows the experimental photographic set-up. Run 15 was the only experiment made with the MIBK-Acetic Acid-Water system. The run was photographed a t 5000 pps w i t h T r i - X f i l m . T r a n s f e r of a c e t i c acid, was from the MIBK drops to water, where the a c i d c o n c e n t r a t i o n i n a drop was 53.52 x 10""^  l b . moles/cu. f t . s o l n . The widest e f f e c t i v e a p e r t u r e t h a t can be achieved by the 75 Dim. Cosmicar l e n s (attached t o the Hycam camera) was only about f/3-5 although i t was r a t e d up to f / l . 9 . A Hycam r e p r e s e n t a t i v e confirmed t h i s and e x p l a i n e d t h a t the l i m i t a t i o n was due to the i n h e r e n t o p t i c a l c h a r a c t e r i s t i c s of the Hycam camera. The Pentax 1°/21° spotmeter, Ch. E. 2359, read a l i g h t - l e v e l number of 16.0 when d i r e c t e d towards an a p p r o p r i a t e spot i n the o b j e c t . At f/3.5 and with a 45 mm. e x t e n s i o n tube added to the l e n s b a r r e l , the camera speed corresponded to a value of about 2600 pps. T h i s value does not a l l o w f o r an allowance t h a t must be g i v e n t o account f o r a slower f i l m speed due to a d i f f e r e n t c o l o u r temperature of l i g h t a t which the f i l m i s b e i n g used. However:*-, i t was d e c i d e d to run the camera a t 5000 pps hoping t h a t the wide l a t i t u d e of the b l a c k and white f i l m would take care of one stop i n underexposure. CD was 5 seconds. The procedure to a r r i v e a t the camera speed value of 2600 pps i s d e s c r i b e d f u l l y under the heading, "Procedure, D i f f u s e d L i g h t " . 74 -o- MERCURY ARC LAMP DIFFUSER SQUARE GLASS COLUMN DROPS HOLLOW SQUARE CYLINDRICAL BOX (BLACKENED INTERIOR) MOVIE CAMERA F i g u r e 20. B a s i c photographic arrangement used f o r drop shape s t u d i e s . 75 I t was suspected t h a t the dark b l o t c h l o c a t e d between the two drops a t the zone of drop approach ( F i g . 2 1 ) was not a l i q u i d b r i d g e or "waist" j o i n i n g the two drops but p u r e l y an o p t i c a l e f f e c t brought on by l i g h t r e f r a c t i o n , r e f l e c t i o n , and t r a n s m i s s i o n . As the two MIBK drops approach each other with a c e t i c a c i d t r a n s f e r r i n g from these drops t o the continuous phase ( F i g . 2 1 ) , the r e f r a c t i v e index of the r e s u l t i n g a c i d - r i c h l i q u i d o u t s i d e the drops a t the zone of drop approach i s d i f f e r e n t from that of the pure continuous water phase owing t o a d i f f e r e n c e i n the r e f r a c t i v e I n d i c e s between a c e t i c a c i d and water. Thus, l i g h t r a y s are r e f r a c t e d i n t h a t r e g i o n . A s i n g l e l i g h t r a y e n t e r i n g the h i g h concen-t r a t i o n zone ( F i g . 2 2 ) i s s c a t t e r e d by a s e r i e s of r e f r a c t i o n , r e f l e c t i o n , and t r a n s m i s s i o n steps before i t can re a c h i t s d e s t i n a t i o n which i s , f o r t h i s case, the f i l m i n s i d e the camera. I t i s h i g h l y probable from the s i m p l i f i e d sketch of F i g . 2 2 , t h a t the i n t e n s i t y of such l i g h t r a y s i s d i m i -n i s h e d or even i s reduced t o zero before r e a c h i n g the camera f i l m s i n c e only a p o r t i o n of the o r i g i n a l l i g h t may a c t u a l l y a r r i v e , the r e s t being s c a t t e r e d elsewhere. F i l m i r r a d i a t i o n occurs s i n c e l i g h t f a l l i n g on a f i l m emulsion ( F i g . 2 3 ) i s n a t u r a l l y s c a t t e r e d w i t h i n i t and i n t u r n i s p a r t l y absorbed by the s i l v e r h a l i d e g r a i n s and p a r t l y passed on through the emulsion. The l i g h t absorbed by the s i l v e r h a l i d e g r a i n s accounts f o r the e f f e c t c a l l e d i r r a d i a t i o n . I t s conjugate, h a l a t i o n , occurs when the l i g h t 76 77D(MIBK) > 77 D(ACETIC ACID) > ^ ( W A T E R ) FROM LIGHT SOURCE MIBK-sat'd WATER PHASE F i g u r e 22, S i m p l i f i e d path of l i g h t ray p a s s i n g between two drops o 77 which passed on through the emulsion reaches the f i l m base (Figo 2 3 ) and may pass through the base or be r e f l e c t e d back to the emulsion t o produce a secondary image e f f e c t o T h i s e f f e c t i s c a l l e d h a l a t i o n 0 However, most modern f i l m s such as the Kodak T r i - X , come with a backing made of a l i g h t -a b s o r b i n g m a t e r i a l so t h a t h a l a t i o n i s p r a c t i c a l l y n i l . , I r r a d i a t i o n , on the other hand, can s t i l l be encountered, f o r example, i n the case of a c o n t r a s t y s u b j e c t such as a s i l h o u e t t e of c o a l e s c i n g dropso Such a s i l h o u e t t e i s ob-t a i n e d when p a r a l l e l l i g h t r a y s are used f o r i l l u m i n a t i o n o I r r a d i a t i o n can produce an impression of a "waist" between the two drops, p r o v i d e d the f i l m i s overexposed and i t s emulsion i s r a t h e r t h i c k and grainy.. This impression i s best i l l u s t r a t e d , i n F i g . 24a taken u s i n g s o l i d spheres (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 o t h e r i n air© Uncoated spheres a l s o showed the same r e s u l t as i n F igo 24bo D e t a i l s on experiments d e a l i n g with spheres are given below, 2) S t e e l Bearing Experiments In order to determine whether r e f r a c t i o n produces a darkening e f f e c t between the drops, an experiment was un-dertaken wherein two spheres were h e l d a t convenient d i s t a n c e s from each other with a i r between. By t h i s procedure, d e n s i t y g r a d i e n t s concentrated i n the c r i t i c a l zone between the spheres are e l i m i n a t e d and the adverse e f f e c t s of r e f r a c t i o n RAYS OF LIGHT FROM SMALL BRIGHT OBJECT F i g u r e 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 unbacked f i l m (43). 79 Figure 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 contact with each other. 80 can be i g n o r e d . To decrease r e f l e c t i o n , a l i g h t - a b s o r b i n g substance was used to coat the spheres. L i g h t t r a n s m i s s i o n , of course, was absent. The spheres were s t e e l b a l l b e a r i n g s , 5 / 3 2 - i n . i n diameter and a c c u r a t e to w i t h i n 0 . 0 0 1 - i n . These had appro-x i m a t e l y the c u r v a t u r e of the p a r t s of the drops s t u d i e d i n run 1 5 » These b e a r i n g s were mounted on a p a i r of Perspex V-blocks h e l d t o g e t h e r a t both ends by rubber bands ( F i g . 2 5 ) ° The b l o c k s were covered with paper blackened by f e l t pen i n k to produce a n o n - r e f l e c t i n g s u r f a c e . The b l o c k s were de-signed w i t h s l o t s to enable a f e e l e r gauge to be s l i p p e d between the b a l l s t o measure t h e i r d i s t a n c e of s e p a r a t i o n . A c o a t i n g of cuprous s u l f i d e was a p p l i e d to the s t e e l b a l l b e a r i n g s . The c l e a n e d b a l l s were f i r s t dipped i n copper s u l -f a t e s o l u t i o n . They were then removed and p l a c e d i n a t e s t tube where hydrogen s u l f i d e was passed over them. Since i r o n i s above copper i n the a c t i v i t y s e r i e s , i r o n (coming from the s t e e l b a l l b e a r i n g ) reduced Cu from the s u l f a t e s o l u t i o n to the f r e e metal which d e p o s i t e d on the surface of the b a l l s . R e a c t i o n with hydrogen s u l f i d e produced b l a c k cuprous s u l f i d e . The c o a t i n g of t h i s s u l f i d e was examined under a microscope and found to be reasonably even. P i c t u r e s were taken f o r two d i f f e r e n t l i g h t i n g con-d i t i o n s . P a r a l l e l l i g h t r a y s were used and, a l s o , d i f f u s e d l i g h t i n g , the l a t t e r f o r most of the work and the former only F i g u r e 2 5 . V-block mount f o r s t e e l b e a r i n g experiments. 82 f o r purposes of comparison. The photographic set-up f o r both l i g h t i n g c o n d i t i o n s i s shown i n F igo 2 6 . P i c t u r e s of s t e e l b a l l s a t d i s t a n c e s of s e p a r a t i o n of 0, 0 . 0 0 1 5 , 0.002, and 0o0025 i n s . were taken, both cuprous s u l f i d e coated and bare. A 75 mm. e x t e n s i o n tube was a t t a c h e d to the Cosmicar l e n s of the Hycam camera i n s t e a d of the 45 mm. tube, t o o b t a i n the same m a g n i f i c a t i o n as most of the runs being s t u d i e d which were f i l m e d u s i n g a 75 mm. tube attachment a l s o . Alignment of the system was done by making the o p t i c a l a x i s of the system pass p e r p e n d i c u l a r to the common a x i s of the b a l l s midway between the two spheres. I t i s obvious t h a t any misalignment, e s p e c i a l l y a t small b a l l s e p a r a t i o n s , c o u l d r e s u l t t o l i g h t b l o c k i n g ( F i g . 27)° Fur-thermore, these requirements apply e s p e c i a l l y when the l i g h t r a y s are c o l l i m a t e d , since any i n c l i n a t i o n from the normal angle would cut o f f a p o r t i o n of the l i g h t bundle that should have passed through. Some guesswork and experimentation were i n v o l v e d i n d e t e r m i n i n g the c o r r e c t exposure. At f i r s t a few p i c t u r e s were made with T r i - X R e v e r s a l but were found to be overex-posed. (Table I I ) . Samples of these p i c t u r e s show how the e f f e c t of i r r a d i a t i o n , due to overexposure, can produce a f a l s e p i c t u r e of a "waist" between the s t e e l b a l l s ( F i g s . 24a and 24b). The l i g h t e d areas i n both f i g u r e s i n c r e a s e d to cover p a r t of the b a l l s i l h o u e t t e and l e f t the impression of a "waist" a t t h a t spot where the b a l l s 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 F i g u r e 26. Photographic arrangement for. s t e e l b e a r i n g experiments and drop shape s t u d i e s . 84 COMMON AXIS Figure 27. Blocking of a l i g h t ray due to b a l l misalignment. PROPERLY EXPOSED BALL OUTLINE OVEREXPOSED BALL OUTLINE Figure 28. 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 overexposure. Table II. Ba l l Bearing Ezparlmantal Data Steal Dlatanoa Lighting Bearing Separation, Condition Dia.,In. Coating In. Leltz Light Film Light Source (USASI No.. Meter Current daylight) Rdg. Bdg.,amp. P.ln. Camera Camera Timing Ext. Frame Light Tube Speed, Freq., Length, pps plp/seo. mm. Lens Film Aper-Eiposure ture 5_ 32 CuO CuS None 0, 0.0015, 0.002, 0.003, 0.006 0, 0.0015, 0.002, 0.0025 0, 0.0015, 0.002. 0.003 0, 0.0015, 0.002, 0.0025 Trl-X Rev. (200) Fine-Grain Dupl. Pos. Trl-X Bev. (200) Fine-Grain Dupl. Pos. 16.7 17.3 16.8 17.3 4.0 5.0 4.0 5.0 48 48 48 48 Hyoam Hyoam Hyoam Hyoam 10 25 10 25 10 10 75 75 75 75 overex-posed f/16 oorreot r/3-5 overex-posed oorreot f/11 f/3.5 32 CUS 0, 0.0015 Fine-Grain Dupl. Pos. 18.5 3.7 52 Hyoam 75 None 0, 0.0015 Fine-Grain Dupl. Pos. 18.5 3.7 52 Hycam 75 oorreot f/3.5 correct f/3.5 Refer to Plg.Zft. **Thls ooatlng was'first used prior to switching to the better CuS coating. 86 A f i l m of slower emulsion speed, was then t r i e d . This was the Kodak Fine G r a i n 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 d u p l i c a t i n g f i l m which has f i n e g r a i n and very h i g h r e s o l u t i o n . I t s emulsion speed was not g i v e n but i t i s b e l i e v e d to be around USASI 5 0 or l e s s ( d a y l i g h t ) . The main reason f o r employing t h i s f i l m was t h a t i t has the a b i l i t y to r e c o r d f i n e d e t a i l , which was e s s e n t i a l i n p i c t u r e s of s t e e l b a l l s separated by a mere 0 . 0 0 1 5 i n . P i c t u r e s obtained with t h i s f i l m were found to be very s a t i s f a c t o r y . Photographic data are shown i n Table I I . The r e s u l t s o b t a i n e d show no a p p r e c i a b l e evidence of a "waist" or dark b l o t c h between the two s t e e l b a l l s f o r any of the d i s t a n c e s of s e p a r a t i o n s t u d i e d r e g a r d l e s s of the p e r s p e c t i v e obtained. Some of the r e s u l t s are g i v e n i n F i g s . 2 9 a and 2 9 b . T h e r e f o r e , t h i s "waist" or dark b l o t c h observed i n run 1 5 c o u l d l a r g e l y be due to the presence of a r e f r a c t i v e index g r a d i e n t and by s e l e c t i n g a s u i t a b l e s o l u t e to e l i m i n a t e t h i s g r a d i e n t , image d i s t o r t i o n due to t h i s o p t i c a l e f f e c t would a l s o be e l i m i n a t e d or, a t l e a s t , reduced to a p o i n t t h a t i t s e f f e c t would be n e g l i g i b l e . 3) S e l e c t i o n of a S u i t a b l e Solute From the f o r e g o i n g r e s u l t s , i t was d e s i r a b l e t o f i n d a s o l u t e such t h a t , upon i t s t r a n s f e r from the d i s p e r s e d MIBK t o the continuous water phases a t the c o n c e n t r a t i o n s p r e v i o u s l y used, the r e f r a c t i v e index g r a d i e n t obtained i n (a) . D i f f u s e d l i g h t ( b ) . P a r a l l e l l i g h t F i g u r e 2 9 . 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 . 88 the a r e a of drop approach would be s m a l l enough to be n e g l e c t e d . To s a t i s f y the above c r i t e r i o n , a s o l u t e would be needed with a r e f r a c t i v e index i d e n t i c a l or n e a r l y so, to t h a t of MIBK-sat'd water which served as the continuous phase. Methyl a l c o h o l was found to come c l o s e t o t h i s requirement. Furthermore, i t had the added advantages of b e i n g r e a d i l y a v a i l a b l e . The 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 r e l a t i o n s h i p , f o r methyl 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 Table I I I , o b t a i n e d from r e f e r e n c e 42. I t i s obvious from these data t h a t i f one p l o t s %w c o n c e n t r a t i o n of methanol vs. 7 ^ of methanol/water s o l u t i o n with methanol c o n c e n t r a t i o n as a b s c i s s a , the r e s u l t i n g curve w i l l have a very small slope over the c o n c e n t r a t i o n range of 0.0 to 2l.?$w. The r e f r a c t i v e index g r a d i e n t w i t h i n t h i s range, i s , t h e r e f o r e , p r a c t i c a l l y n e g l i g i b l e , n e g l e c t i n g the t h i r d component e f f e c t of the MIBK used to s a t u r a t e the continuous water phase i n the a c t u a l work. Furthermore, the r e f r a c t i v e index of methyl a l c o h o l a t 2 5 ° C i s 1.33232. That of MIBK-saturated water a t 2 5 ° C (the continuous phase) 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 i n d i c e s are much c l o s e r t o gether than i s the r e f r a c t i v e index of a c e t i c a c i d a t the same temperature (1.3715)• 8 9 Table I I I . R e f r a c t i v e Index - C o n c e n t r a t i o n Data of Methyl A l c o h o l a t 2 5 ° C (Bef. 4 2 ) r Methanol 7? 2 5 ° % O o O 1 . 3 3 2 3 2 2 1 o 7 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 Methanol = 5 3 ^ 9 0 EXPERIMENTAL PROCEDURE A. MIBK-Methanol-Water System The e x t r a c t i o n procedures were i d e n t i c a l t o those of the p r e v i o u s runs u s i n g a c e t i c a c i d as the solute<> Due • to the d i f f i c u l t y of p r e v e n t i n g contamination when a new s o l u t e i s used, the d i s p e r s e d phase l i n e was r e p l a c e d w i t h new n y l o n t u b i n g . As i n the toluene runs, a l e v e l l i n g b u l b 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 experiments i n v o l v i n g a c e t i c acido The d i s p e r s e d phase p i p i n g system was s u f f i c i e n t l y vapour t i g h t . Part of the d i s c h a r g e l i n e was r e p l a c e d with new t u b i n g of the same m a t e r i a l i n order t o prevent any p o s s i b l e contamination of the contents of the square g l a s s column 0 The l i g h t i n g arrangement u t i l i z e d mo-v i n g the s c h l i e r e n m i r r o r away from or towards the l i g h t source i n order to produce converging, p a r a l l e l , or d i v e r g i n g l i g h t r a y s whichever were needed. T h i s set-up was the same as t h a t used i n the s t e e l b e a r i n g experiments i n F i g . 2 6 and was s i m i l a r l y a l i g n e d . 1 ) C o l l i m a t e d L i g h t Run 1 6 was performed u s i n g p a r a l l e l l i g h t r a y s with no d i f f u s e r . Methyl a l c o h o l was t r a n s f e r r e d from the d i s p e r s e d MIBK phase where the a c i d c o n c e n t r a t i o n was 0 . 0 0 3 9 l b . moles/ cu. f t . s o l n . t o the continuous water phase, both phases, of 9 1 course, b e i n g mutually s a t u r a t e d with the main component of the o t h e r. A f i l m was taken by the Hycam camera a t $000 pps with 7 5 mm. e x t e n s i o n tube a t t a c h e d t o the Cosmicar l e n s set a t an a p e r t u r e opening of f / 3 . 5 « Due t o the l i g h t r e d u c t i o n r e s u l t i n g from the use of the 7 5 nmi» e x t e n s i o n tube, i t was decided t o t r y a f i l m s l i g h t l y f a s t e r than T r i - X R e v e r s a l but slower than 4X Panchromatic Negative. This was the Kodak Double-X Panchromatic Negative with a USASI No. of 2 5 0 (day-l i g h t ) . An LLN ( l i g h t - l e v e l number) r e a d i n g of 1 6 . 8 was obtained by the L e i t z exposure meter when i t was p l a c e d a c r o s s the p a r a l l e l beam of l i g h t with the l i g h t source ammeter r e a d i n g f l u c t u a t i n g between 3 « 6 and 4 . 0 amps. 2 ) D i f f u s e d L i g h t Ground g l a s s was chosen over t r a c i n g paper as the d i f f u s e r because the t r a c i n g paper was found t o cut down the l i g h t i n t e n s i t y by 1 LLN more than the ground g l a s s on the Pentax spotmeter s c a l e . Use of the ground g l a s s d i f f u s e r r e s u l t e d i n a decrease of 5 LLN as read on the Pentax s c a l e , c u t t i n g down exposure by about 5 s t o p s . To make up f o r t h i s l o s s , a f a s t f i l m , Kodak 4X Panchromatic Negative (USASI No. 5 0 0 , d a y l i g h t ) , was used. At f i r s t , s e v e r a l attempts t o o b t a i n an a c c e p t a b l e exposure f a i l e d when u s i n g t r i a l and e r r o r . Exposure t e s t s were then made by the L i n h o f s t i l l camera and when the c o r r e c t exposure was obtained, a p p r o p r i a t e c o n v e r s i o n s (Appendix H) were made to t r a n s l a t e the L i n h o f camera 92 s e t t i n g s to e q u i v a l e n t Hycam v a l u e s i n order to a r r i v e a t the same c o r r e c t exposure. In run 17 the e x t r a c t i o n c o n d i t i o n s were s i m i l a r to those of run 16. However, since d i f f u s e d l i g h t was u t i -l i z e d here, r e d u c t i o n of i l l u m i n a t i o n o c c u r r e d . In order to compensate f o r t h i s decrease, the s c h l i e r e n m i r r o r - l i g h t source d i s t a n c e was a l t e r e d to make the l i g h t converge afrom a 6 i n . diameter c r o s s - s e c t i o n to a s m a l l e r a r e a having a s l i g h t l y e l l i p t i c a l shape having major and minor axes of 1/2 i n . and 7/16 i n . r e s p e c t i v e l y . The e l l i p t i c a l form was due to i n h e r e n t o b l i q u e a b e r r a t i o n . The Pentax spotmeter r e a d 12.82 and the mercury a r c source, 3,6 amps. The l e n s aper-ture was a t f/3'5 and a l l these r e a d i n g s corresponded to a camera frame speed of about 300 pps when a 150 mm. e x t e n s i o n tube was being used. T h i s tube cut down the exposure by approximately 3 stops. To a r r i v e a t the above c o n c l u s i o n , c o n s i d e r Table IV, reproduced from r e f e r e n c e 43. To use t h i s t a b l e , i t i s convenient to "... f i r s t f i n d e i t h e r the b e l l o w s e x t e n s i o n expressed i n f o c a l l e n g t h s (column 2), or the s c a l e of r e p r o -d u c t i o n (column 3)° The l a t t e r can f r e q u e n t l y be e s t i m a t e d with s u f f i c i e n t accuracy by v i s u a l comparison of the l e n g t h s of image and o r i g i n a l . Exposure times can then be found by u s i n g the a p p r o p r i a t e f a c t o r from columns 4, 5» °r 6". Use of 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. Exposure Factors for Different Scales of Reproduction (Ref. 43) (4) (3) Marked (1) (2) Linear Scale f-number Object Bellows of must be Distance Extension Reproduction Multiplied by (5 ) or Exposure Indicated f o r Object at must be Mul t i p l i e d by* (6) or Exposure Indicated for Same-size Reproduction must be Mul-t i p l i e d by (u) (v) (m = v/f - 1) (1 + m) (1 + m) 2 ((1 + m) 2/4) CO f 0 x 1 x 1 X 1/4 l - l / 8 f 1/8 x 1-1/8 x 1-1/4 X 5/16 l - l / 4 f 1/4 x 1-1/4 x 1-1/2 X 3/8 l-l/2f 1/2 x 1-1/2 x 2-1/4 X 1/2 l-3/4f 3/4 x 1-3A x 3 X 3/4 2f 2f 1 (Same-size) x 2 x 4 X 1 2-l/2f 1-1/2 x 2-1/2 x 6 X 1-1/2 3f 2 x 3 x 9 X 2-1/4 4f 3 x 4 x 16 X 4 5f 4 x 5 x 25 X 6 exposure factors i n columns 5 and 6 are p r a c t i c a l approximations. 94 l e n s f o c u s s e d a t i n f i n i t y (column 5) or a t an o b j e c t two f o c a l l e n g t h s away ^column 6). Since no r e l i a b l e method has yet been e s t a b l i s h e d to q u i c k l y determine the c o r r e c t exposure by the use of a l i g h t m e t e r i n t h i s work, column 4 was found t o be the most p r a c t i c a l to use. For the c u r r e n t problem, the use of a 150 nim° e x t e n s i o n tube with the 75 l e n s i s e q u i -v a l e n t to a t o t a l b ellows e x t e n s i o n of 225 mm. or Jf i n t a b l e IV, " f " b e i n g the f o c a l l e n g t h of the l e n s . On the same row i n which 3f appears i n column 2, column 4 shows t h a t the marked f-number must be m u l t i p l i e d by a f a c t o r of 3° I f one now goes back to the Pentax spotmeter s c a l e s and s e t s the f o l l o w i n g combination of 12.82 f o r l i g h t r e a d i n g , 500 f o r f i l m speed, and 3°5 f o r f/no, one f i n d s t h a t these v a l u e s correspond t o a frame speed of about 900 pps. With the ex-t e n s i o n tube taken i n t o c o n s i d e r a t i o n , the a c t u a l f/no« should be m u l t i p l i e d by 3 g i v i n g f/10.5 and a new c o r r e c t e d v a l u e of about 100 p p s , f o r frame speed. T h i s exposure s e t -t i n g i s e q u i v a l e n t t o f/3°5 and about 300 pps by law of r e -c i p r o c i t y . The frame speed of 300 pps obtained above i s too slow f o r the purpose but i t was decided, anyway, to take a chance and f i l m the r u n a t 4500 pps. T h i s procedure was ex-p e c t e d to produce an underexposure corresponding to 4 stops l e s s than the c o r r e c t f/no. s e t t i n g . A number of t e s t s t r i p s were developed i n ID-11 and, s u r p r i s i n g l y , an a c c e p t a b l e image on the n e g a t i v e was obtained a t a development time of 8 min. 95 40 sec. Appropriate pictures were printed on I l f o r d No. 5 bromide paper. It should be noted here that the nozzle t i p s disappeared from the camera f i e l d of view due to a high magnification obtained with the use of the 150 mm. extension tube. The disappearance of the nozzle t i p s and, hence, of the known nozzle diameter resulted i n the absence of a convenient l i n e a r scale f o r use as reference i n this run. In run 18, only 75 mm. length of extension tube was used and the camera speed was increased to 5000 pps. Methyl alcohol concentration i n the dispersed phase was 0.0020 l b . moles/cu. f t . soln. Run 19 was again similar to run 18 except that the methanol concentration i n each drop i s higher (0.088 l b . moles/cu. f t . soln.) was used. Tri-X Reversal f i l m was used here since 4X Panchromatic Negative f i l m was not available and i n order to compensate somewhat for the slower f i l m speed, the l i g h t source amperage was increased to 5»5 amps. Additional data on a l l the runs are shown i n Table V. B. Measurement of Pseudo-Radius To determine the shape pattern of a drop as i t coalesces with another, the changes i n shape of the drop must be measured. Table V. Experimental Data f o r Part I I (Drop Shape S t u d i e s ) Run No. 1 5 1 6 1 7 18 1 9 Solute A c e t i c A c i d Methanol Methanol Methanol Methanol Conto Phase Water Water Water Water Water Dispersed Phase MIBK MIBK MIBK MIBK MIBK D i r e c t i o n of T r a n s f e r D—>C D—> C D —> C D — » C D—>C Solute cone., 1 0 3 x l b o m o l e / c u o f t . s o l n . 5 3 - 5 2 3 o 9 0 4 . 2 1 1 . 9 5 8 7 . 7 8 Nozzle O r i e n t a t i o n H o r i z o n t a l H o r i z o n t a l H o r i z o n t a l H o r i z o n t a l H o r i z o n t a l L i g h t Source Current Reading, amp. 5 . 5 - 6 . 0 4 - 3.6 3 . 6 3o6 5 ° 5 F i l m (USASI No., d a y l i g h t ) T r i - X Rever-s a l ( 2 0 0 ) Double-X ( 2 5 0 ) 4X Panchro-matic ( 5 0 0 ) 4X Panchro-matic ( 5 0 0 ) T r i - X Rever-s a l ( 2 0 0 ) L i g h t Meter Reading 1 6 . 5 ( L e i t z ) 1 6 . 8 ( L e i t z ) 1 2 . 8 2 (Pentax) 1 2 . 8 2 (Pentax) 1 3 0 9 (Pentax) D i f f u s e r S i n g l e Sheet of T r a c i n g Paper None Ground Glass Ground Glass Ground Glass S i z e of L i g h t Image on D i f f u s e r * Major A x i s , i n . 3_ ( c i r c l e ) 4 1 2 1 2 1 2 Minor A x i s , i n . 3_ ( c i r c l e ) h h h Camera Hycam Hycam Hycam Hycam Hycam Camera Frame Speed,pps 5 0 0 0 5 0 0 0 4 5 0 0 5 0 0 0 5 0 0 0 Lens Aperture f / 3 . 5 f / 3 ° 5 f / 3 . 5 f / 3 . 5 f / 3 . 5 E x t e n s i o n Tube Length, mm. 4 5 7 5 1 5 0 7 5 - 7 5 Timing L i g h t Frequency, pip/sec0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 F i l m M a g n i f i c a t i o n 0 . 9 3 1 . 3 3 2 . 3 3 1 . 3 3 1 . 3 3 L i g h t i n g C o n d i t i o n D i f f u s e d P a r a l l e l D i f f u s e d D i f f u s e d D i f f u s e d * D i f f u s e r i s p o s i t i o n e d as shown i n F i g . 2 0 . 97 P r e l i m i n a r y work was c a r r i e d out on runs 15. 18, and 19. P i c t u r e s were chosen from the e n t i r e l e n g t h of f i l m i n a g i v e n run so t h a t a f i x e d number of frames i n t e r v e n e d between each p i c t u r e or frame s t u d i e d . For t r a c i n g purposes, the p i c t u r e s on the 16 mm. movie s t r i p were p r o j e c t e d by means of the f i l m e n l a r g e r a v a i l a b l e i n the department's darkroom onto a sheet of paper a t approximately 24X m a g n i f i -c a t i o n . The image then was t r a c e d by hand. F i x e d r e f e r e n c e p o i n t s l o c a t e d i n s i d e each drop were chosen ( p o i n t s P* and P" i n F i g . JO). These p o i n t s were f i x e d c o n s i s t e n t l y a t the same l o c a t i o n f o r every t r a c i n g a c c o r d i n g to the set p o s i t i o n of the n o z z l e t i p s from which these two r e f e r e n c e p o i n t s were l o c a t e d . The two c o r n e r s of each n o z z l e t i p shown i n each t r a c i n g were used i n determining the l o c a t i o n of P» and P" ( F i g . 3 0 ) . Each drop was then d i v i d e d i n t o s e c t o r s . The r a d i a l l i n e s bounding the s e c t o r s were measured from p o i n t s P' to P" to the drop p e r i p h e r y f o r each t r a c i n g . The d i s t a n c e s obtained f o r each l i n e were p l o t t e d a g a i n s t time. These d i s t a n c e s were c a l l e d , "pseudo-r a d i i " . The r e f e r e n c e p o i n t s P* and P" and the r a d i a l l i n e s o r i g i n a t i n g from them were a c t u a l l y drawn on a master sheet which was superimposed on each t r a c i n g t o be measured. To l o c a t e these two p o i n t s the f o l l o w i n g procedure was f o l l o w e d . A master sheet made of paper with p o l a r c o o r d i n a t e l i n e s was prepared f o r each of the l e f t and the r i g h t drops. Consider 9 8 L E G E N D 1 - 7 0 ° 6 - 170° 2 - I00 Q 7 - 185. 3 - ! 3 0 o 8 ~ I95 Q 4 - I45 0 9 - 2 2 0 o 5 - 155 10 - 250 1 1 - 2 8 0 F i g u r e 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 being measured„ 99 the master sheet to be prepared f o r the r i g h t drop ( F i g o 30)o P o i n t P" f i r s t was chosen on a sample t r a c i n g a t about the c e n t r a l area i n the r i g h t drop. P o i n t X a l s o was l o c a t e d on t h i s t r a c i n g , a t the p o i n t of c o n t a c t of the two drops. These two points,, P" and X, then were t r a n s f e r r e d to the p o l a r coor-d i n a t e paper or master sheet i n such a way t h a t P" was a t the o r i g i n and X was along the 170°-line on the c o o r d i n a t e paper© P o i n t s A, B, C, and D (comprising a l l f o u r corners of the two n o z z l e t i p s ) then were marked on the master sheet as a d d i t i o n a l r e f e r e n c e s as mentioned earlier» The master sheet f o r the l e f t drop contained s i m i l a r r e f e r e n c e p o i n t s . P o i n t P' was not l o c a t e d a r b i t r a r i l y as was P" but depended on the p o s i t i o n of P". The l o c a t i o n of P' on the drop, u s i n g the same sample t r a c i n g , was determined as f o l l o w s . The f i r s t master sheet was set i n p o s i t i o n on the t r a c i n g . Point P' was marked on the o r i g i n of the second c o o r d i n a t e sheet and t h i s paper was superimposed on the f i r s t so that the 10°-line of the second sheet passed through p o i n t X. T h i s sheet was now a d j u s t e d , m a i n t a i n i n g p o i n t X on the 10°-llne, u n t i l l i n e 0°, o r i g i n a t i n g n o from p o i n t P', and l i n e 180 , o r i g i n a t i n g from p o i n t P" of the f i r s t master sheet, overlapped and formed one s i n g l e l i n e o P o i n t s A, B, C, and D then were marked on the second sheet© There were e l e v e n r a d i a l or d i v i d i n g l i n e s drawn f o r the r i g h t drop, s t a r t i n g from an angle of 7 0 ° and ending a t the 280°-line© Symmetry r e q u i r e d that the l e f t drop a l s o have the same number of r a d i a l l i n e s and that each of these l i n e s be named a c c o r d i n g to each corresponding m i r r o r image ( F i g o 30)© 100 In reporting the f i n a l data on runs 18 and 19, the tracings were replaced by photographic p r i n t s which are accu-rate reproductions of the negative imageso Likewise, the polar coordinate paper, used as master sheet:., was found to be too thick to c l e a r l y see through i t so that i t was replaced by tracing paper, trans f e r r i n g a l l the appropriate points and l i n e s o The drops measured were those of runs 18 and 19= Co S t a t i s t i c a l Tests The observed dependence of one variable upon another, i n t h i s case the pseudo-radius(Y) upon time (X), was i n i t i a l l y considered 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 of such l i n e was obtained by the method of l e a s t squares. Calcu-l a t i o n was done on an IBM 7044 elec t r o n i c d i g i t a l computer using the l i b r a r y subroutine, "UBC LQP", for least squares f i t (Appendix L)» The l i n e a r model was then tested for significance of regression© This was done by a t-test of the n u l l hypo-thesis 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 was c a r r i e d out to examine the confidence i n t e r v a l (at the proba-b i l i t y l e v e l used) i n order to see i f the value of or slope l i e s i n the Interval that includes zero. I f so, then the n u l l hypothesis, H 0 :j9/= 0, could not be rejected and i t suffices to say that the r e s u l t could be accepted but only on the basis 1 0 1 of the observed d a t a 0 I t may w e l l happen t h a t i n another s e t of data evidence i s found which i s c o n t r a r y to the n u l l hypo-t h e s i s and so r e j e c t i t 0 The adequacy of the l i n e a r model was determined by checking out f o r any evidence of u n e x p l a i n e d v a r i a t i o n i n the observed data where the n u l l h y p o thesis was e i t h e r r e j e c t e d or not r e j e c t e d , i . e . , where the s l o p e s of the r e g r e s s i o n l i n e s were e i t h e r non-zero o r z e r o , T h i s was done by an examination of the r e s i d u a l s . The r e s i d u a l , as o r d i n a t e , was p l o t t e d a g a i n s t time and any d e v i a t i o n from the impression of a h o r i z o n t a l "band" of r e s i d u a l s ( F i g . 3 1 ) was a n a l y z e d a c c o r d i n g t o the g r a p h i c a l time sequence p l o t method ( 4 4 ) . Where the l i n e a r model was found to be inadequate, a m u l t i p l e r e g r e s s i o n program was used to s e l e c t the "best" r e g r e s s i o n e quation among the d i f f e r e n t p o l y n o m i a l models t h a t were used. T h i s program was w r i t t e n by Kozak and Smith ( 4 5 ) of the U.B.C. F a c u l t y of F o r e s t r y i n F o r t r a n l V language f o r an IBM 7 0 4 4 Data P r o c e s s i n g System. T h i s p a r t i c u l a r program uses the backward e l i m i n a t i o n technique wherein a r e g r e s s i o n e quation of a predetermined form as shown below (where m i s s e t a t a v a l u e of 4 ) i s computed and the X v a r i a b l e i s e l i m i n a t e d one exponent a t a time. m 1 0 2 TIME F i g u r e 3 1 o Impression of h o r i z o n t a l "band" f o r p l o t of r e s i d u a l v s . time ( 4 4 ) . 103 T h i s i s done by c a l c u l a t i n g the v a r i a n c e r a t i o n of the c o n t r i -b u t i o n of each independent v a r i a b l e (X , where i = 1, 2,..0,m) in c l u d e d i n the e q u a t i o n . where Fj, = v a r i a n c e r a t i o f o r the i H L power of the independent v a r i a b l e , b i = r e g r e s s i o n c o e f f i c i e n t f o r the i — power of the independent v a r i a b l e . Sb^ = standard d e v i a t i o n of the r e g r e s s i o n c o e f f i c i e n t c o r r e s p o n d i n g to the i ~ power of the independent v a r i a b l e . The v a r i a b l e with the s m a l l e s t v a r i a n c e r a t i o i s e l i m i n a t e d f i r s t . The whole process i s repeated minus one v a r i a b l e t h a t was d e l e t e d each time. T h i s process c o n t i n u e s u n t i l a l l the v a r i a b l e s are e l i m i n a t e d from the t o t a l model. Then the p r o -gram s e l e c t s the three independent v a r i a b l e s (powers of X) which have the h i g h e s t simple c o r r e l a t i o n c o e f f i c i e n t with the dependent v a r i a b l e , Y, and c a l c u l a t e s equations f o r a l l the p o s s i b l e combination of the three independent v a r i a b l e s t h a t comprise t h i s s e t . T h i s program was u s e f u l f o r comparing the adequacy of v a r i o u s polynomial models with t h a t of a l i n e a r one. Of course, the improvement i n the present model must be one where-by adding a new term to the model would produce some r e a l sig= 104 n i f i c a n c e and not simply due to the f a c t t h a t the number of parameters i n the model i s g e t t i n g c l o s e to s a t u r a t i o n p o i n t (the number of o b s e r v a t i o n s ) . Probably the b e s t method of s e l e c t i n g the "best" r e g r e s s i o n e q u a t i o n i s to t r y every p o s s i b l e combination of a l l the v a r i a b l e s chosen (X*„ where 1 = 1, 2, .... m) and then s e l e c t from a l l the equations thus o b t a i n e d . T h i s method i s b e l i e v e d to be very time-consuming even with the use of e l e c t r o n i c computers so t h a t i t i s hoped the method used i n the p r e s e n t work co u l d prove u s e f u l i n r e t a i n i n g a l l the important and s i g n i f i c a n t v a r i a b l e s (powers of X) i n the e q u a t i o n a t a l l stages of a n a l y s i s . T h i s b e l i e f i s shared by Kozak based on the l a r g e number of t r i a l runs used i n the method (46). However, p e r s o n a l judgement and experience are s t i l l e s s e n t i a l i n e v a l u a t i n g the data s i n c e no unique s t a t i s t i c a l procedure i s a v a i l a b l e f o r doing t h i s . 105 RESULTS A o Experimental Runs In a l l the runs where o r d i n a r y photographs were taken without the use of s c h l i e r e n o p t i c s , adequate l i g h t i n t e n s i t y remained a problem except i n run 16 where no d i f -f u s e r was used. C o n t r i b u t i n g f a c t o r s were high camera speeds of 4500 to 5000 pps (2=5 times more pps than f o r the s c h l i e r e n r u n s ) , and the use of a d i f f u s e r . As a r e s u l t of these p r o -blems, the f i l m s obtained mostly were underexposed i n s p i t e of the f a s t e r f i l m emulsions used. To compensate f o r the r e -s u l t i n g l o s s i n c o n t r a s t , the p i c t u r e s were p r i n t e d on hard paper (Kodak P-5 or I l f o r d B5-1P)» S e v e r a l runs were, never-t h e l e s s , r e j e c t e d due to gr o s s underexposure. The use of p a r a l l e l l i g h t i n run 16 r e s u l t e d i n a predominantly dark image of the drop s i l h o u e t t e d a g a i n s t a l i g h t e r background. The use of methyl a l c o h o l f o r s o l u t e reduced t o a l a r g e extent the dark b l o t c h t h a t was f i r s t no-t i c e d i n t h i s r e s e a r c h i n the photographs of run 15<> With methyl a l c o h o l used as s o l u t e , the i n t e r f a c i a l boundaries were w e l l d e f i n e d a t the zone of drop approach. L i k e run 15, run 16 was p r o p e r l y exposed. The stages of coalescence were observed as f o l l o w s : As the two opposing drops met, the s u c c e s s i o n of events t h a t 106 f o l l o w e d showed t h a t the drops d i d not coalesce i n s t a n t a n e o u s -l y but appeared t o r e s t a t the i n t e r f a c e f o r some time. When they c o a l e s c e d , a l i q u i d " b r i d g e " or "neck" of c y l i n d r i c a l shape was i n s t a n t a n e o u s l y formed to u n i t e the two drops (P igo 32)o T h i s " b r i d g e " or "neck" r a p i d l y grew i n s i z e , drawing l i q u i d from both drops u n t i l only one b i g g e r drop remained. The d e p l e t i o n of f l u i d from both drops accounted f o r t h e i r c o l l a p s e and i n c r e a s e d both the diameter and l e n g t h of the "br i d g e " . Before the onset of coalescence, the dark b l o t c h i n run 1 5 ( F i g . 2 1 ) , a c c o r d i n g t o the r e s u l t s of the p r e v i o u s s t e e l b a l l experiments was not b e l i e v e d to be the begi n n i n g of coalescence with the appearance of a l i q u i d " b r i d g e " or "neck" between two opposing drops but simply an o p t i c a l phe-nomenon a s s o c i a t e d with the presence of r e f r a c t i v e index g r a -d i e n t s . For p r a c t i c a l purposes, t o t a l e l i m i n a t i o n of t h i s dark b l o t c h was not obtained a f t e r u s i n g methyl a l c o h o l a l -though i t appeared from the photographs of funs 1 6 , 1 7 , 1 8 , and 19 mentioned i n t h i s s e c t i o n that the appearance of a dark b l o t c h was d i m i n i s h e d . The time between the f i r s t ap-pearance of a dark b l o t c h i n the space which separates the drops and the s t a r t of coalescence was measured,,and c a l l e d " h o l d i n g time". This time i s almost s i m i l a r to " r e s t time" i n l i t e r a t u r e ( 4 7 ) „ which i s d e f i n e d to be the time which e l a p s e s between the a r r i v a l and the s t a r t of coalescence of a drop with i t s common phase. The two d e f i n i t i o n s d i f f e r be-cause the appearance of a dark b l o t c h between the two drops does not n e c e s s a r i l y mean the a r r i v a l or meeting of two i n -107 Figure 3 2 . P a r t i a l view of coalescing MIBK drops. 108 terfaceso "Coalescence time" was taken to be the time bet~ ween the onset of coalescence characterized, by the i n i t i a l formation of the l i q u i d "bridge" and. the eventual formation of one larger 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 alcohol concentration of 0 o0039 l b o moles/cuo f t o s o l n o i n the dispersed phase. This concentration i s lower than that of run 15° The holding time was found, through frame-by-frame analysis of the cine f i l m , to be roughly 40 times larger than i n run 15 (Table VI) which u t i l i z e d the d i f -fusedlighting arrangement and, of course, a d i f f e r e n t solute. Other relevant data on runs 15-19 i n c l u s i v e , are found i n Table V. In run 17, magnification, which i s taken to be the r a t i o of f i l m image size to object size, was measured to be approximately equal to 2:\due to the use of a 150 mm. exten-sion tube. The two nozzle t i p s were out of view as seen i n the cine f i l m because of this magnification. Holding time was found to be about 8 times l e s s than that i n run 16 (Table VI). Diffused l i g h t was used i n this run whereas i n run 16, p a r a l l e l l i g h t was used. A very s l i g h t darkening at the zone of drop approach was noticed as the two drops met each other. The nozzle t i p s again were seen in runs 18 and 19 where only the 75 nmi. extension tube was used. 109 Table VI. Drop Holding and Coalescence Times Run N o . H o l d i n g Time, sec. Coalescence Time, sec. 1 5 O0OO39 0.014-9 1 6 O . I 6 7 0 . 0 1 4 2 1 7 0 . 0 2 1 0 . 0 1 3 2 18 O . I 3 6 5 0 . 0 1 1 4 1 9 0 . 0 2 5 6 0 . 0 1 3 8 110 The holding times obtained, for a l l the runs con-taining methanol show that there was no consistency with res-pect to holding times among them (Table VI), p a r t i c u l a r l y between runs 1 7 and 18 where the extraction conditions were about the same but whose holding times d i f f e r by 55G%° Runs 1 7 and 19 gave close values although t h e i r solute concentra-tions were not the same (Table VI). Likewise, runs 16 and 18 gave close values of holding time with about the same solute concentration 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 that the v a r i a t i o n i n holding times obtained must be treated with caution since t h i s process i s s t a t i s t i c a l i n nature and the number of observations, f o r one thing, are too small to make any conclusions. Nevertheless, the r e s u l t s obtained may suggest that there are other factors aside from solute concentration, l i g h t i n g arrangement, and magnification which could influence and/or control holding times. Brown and Hanson (48) mentioned a number of workers who reported a s i g n i f i c a n t spread of rest times for i d e n t i c a l drops i n the same system but as yet, they cannot agree on what causes th i s considerable scatter. They believed rest time magnitude may depend on any or a l l of the following: tem-perature, drop siz e , the geometric shape of the interface, the degree of purity of the components, the i r v i s c o s i t i e s and de n s i t i e s , the i n t e r f a c i a l tension, and the occurrences of shock. Since, by d e f i n i t i o n , r e s t time can influence holding I l l t i m e s presumably any s c a t t e r i n r e s t time r e s u l t s can be r e -f l e c t e d i n the f i n d i n g s shown i n Table VI. Coalescence time f o r a l l runs i n t h i s s e c t i o n of the t h e s i s i s shown i n Table VI. Close v a l u e s of coalescence time f o r runs 15-19 i n c l u s i v e , were obtained. No f u r t h e r a t -tempt was made to study the s i g n i f i c a n c e of these data s i n c e any study i s outside the scope of t h i s p r o j e c t . During the formation of the l i q u i d " b r i d g e " , t h a t r e g i o n which connected i t with the drop appeared t o cave i n (as shown a t P, Q, R, and S i n F i g . 32). This phenomenon was s i m i l a r t o t h a t i n photographs shown by K i n t n e r (49) of two n - b u t y l benzoate drops c o a l e s c i n g i n water. An i n t e r e s t i n g s i d e l i g h t of run 19 was t h a t the r i g h t drop i n F i g . 34, c o n s i s t i n g of w a t e r - s a t u r a t e d MIBK with a methanol c o n c e n t r a t i o n of 0.088 l b . moles/cu. f t . s o l n . , was fogged by extremely f i n e d r o p l e t s of water. R o c c h i n l (26), working w i t h s i m i l a r s o l v e n t s , water and MIBK, a t t r i b u t e d t h i s m i s t i n g phenomenon to the i n f l u e n c e of a s o l u t e and/or tempe-r a t u r e on the mutual 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 s o l v e n t s , i n t h i s case, water and MIBK. From F i g . 34*- i t i s seen t h a t f o g g i n g was not uniform but appeared i n patches which, are darker than the r e s t of the drop c o n t e n t s . The for m a t i o n of emulsion i n the r i g h t drop showed t h a t , a t the time the f u n was f i l m e d , s e p a r a t i o n of phases had o c c u r r e d i n the r i g h t 112 drop. Upon vie w i n g the movie f i l m , i t was observed through-out the event p r i o r to coalescence t h a t the l i q u i d m a t e r i a l i n s i d e the drop appeared to be c i r c u l a t i n g i n the c l o c k w i s e d i r e c t i o n , , T h i s c i r c u l a t i o n was made v i s i b l e by the dark emulsion patches p r e s e n t . I t i s reasonable to expect t h i s behaviour to Induce i n t e r f a c i a l movement a l s o . The l e f t drop a l s o might be c i r c u l a t i n g . However, such c i r c u l a t i o n c o u l d not be observed i n the l e f t drop because of the absence of e m u l s i f i c a t i o n . B. Pseudo-Radius Measurement The v a r i o u s p s e u d o - r a d i i of the drops i n run- 18 and run 19 were measured i n t h i s study f o r comparison purposes, both runs being s i m i l a r except f o r the d i f f e r e n t l e v e l of s o l u t e c o n c e n t r a t i o n used f o r each. T h e r e f o r e , i t c o u l d be determined whether s o l u t e c o n c e n t r a t i o n has any e f f e c t on drop shape as a p a i r of drop c o a l e s c e s . I t was found t h a t unnecessary s c a t t e r r e s u l t e d as pseudo-radius was p l o t t e d a g a i n s t time when hand t r a c i n g was employed. This e r r o r was e a s i l y a t t r i b u t e d t o i n a c c u r a c i e s i n t r a c i n g and c o r r e c t e d by u s i n g photographic p r i n t s i n s t e a d . For convenience, the m e t r i c s c a l e was used i n measu-r i n g the p s e u d o - r a d i i . Minimum l e n g t h d i s c e r n i b l e i n the photographs ( t o t a l m a g n i f i c a t i o n = 24x) was 0 . 0 5 cm. (A t o t a l m a g n i f i c a t i o n «= 24x was adopted, f o r i l l u s t r a t i o n purposes, i n 113 F i g s . 33 and 34 Therefore, i n a sphere, a change i n drop volume corresponding t o a l i t t l e l e s s than 0.05 cm. change i n r a d i u s would pass undetected under the present measurement procedure. Measurements of drop p s e u d o - r a d i i i n s u c c e s s i v e f i l m frames had to "be r e s t r i c t e d t o a span of frames over which the pseudo-radius change i s l e s s than 0.05 cm. i n the photographs to e l i m i n a t e any e f f e c t due to drop growth. Assuming a p p r o p r i a t e l y - s i z e d spheres were s u b s t i t u t e d f o r the drop, i t was estimated (Appendix I) t h a t a span of about 1390 and 800 frames ( p r i o r t o the onset of coalescence) f o r runs 18 and 19 r e s p e c t i v e l y , were r e q u i r e d to i n c r e a s e the r a d i u s u n i f o r m l y by 0.05 cm. i n the photographs. In p r a c t i c e , drop pseudo-radius changes vary over the e n t i r e i n t e r f a c e due to buoyancy and, to some extent, t o i n e r t i a and o p t i c a l d i s t o r t i o n . These e f f e c t s may i n t e r f e r e a l s o , i n a d d i t i o n to drop growth or volume change, i n the e f f o r t to determine any pseudo-radius changes t h a t may a r i s e due s o l e l y t o i n t e r f a c i a l t e n s i o n imbalance accompanying mass t r a n s f e r . An i n e r t i a l ' - e f f e e t was c o n s i d e r e d because as the d i s p e r s e d phase flows i n t o the drop, t h a t surface of the drop on which t h i s m a t e r i a l impinged tended t o bulge t e m p o r a r i l y due to i t s v e l o c i t y . N o n - p a r a l l e l i s m of the w a l l s of the square g l a s s column and i m p e r f e c t i o n s i n the g l a s s i t s e l f (e.g., s t r i a t l o n s ) may c o n t r i b u t e 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 magnitude of t h i s e f f e c t was c o n s i d e r e d to be minimal. Mostly because of the e f f e c t of buoyancy and a l s o to the i n h e r e n t i n -accur a c y of the above frame span estimate owing to the assump-114 F i g u r e 3 4 . Photograph from run 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 s i d e of the p i c t u r e . 115 t i o n of a sphere, the a c t u a l frame spans t h a t were s t u d i e d and c o n s i d e r e d to be drop growth-free f o r runs 18 and 19 were t r e a t e d with c a u t i o n . Conservative f i g u r e s of 151 and 101 frames { p r i o r to the onset of coalescence) f o r runs 18 and 19 r e s p e c t i v e l y , were t h e r e f o r e adopted f o r a n a l y s i s . Each of these f i l m spans corresponded to a uniform i n c r e a s e i n the s p h e r i c a l r a d i u s of 0.004 cm. i n the photographs. I t i s assumed, of course, that w i t h i n these f i l m frame spans i n t e r -f a c i a l t e n s i o n - i n d u c e d shape changes, i f any, would be s i g -n i f i c a n t l y e v i d e n t . The frame span b e i n g c o n s i d e r e d was d i v i d e d i n t o twenty-six p a r t s each c o n t a i n i n g an equal number of frames. At the end of each s u c c e s s i v e f i l m i n t e r v a l the pseudo-radius was measured a l o n g each d i v i d i n g l i n e i n runs 18 and 19° Ta-b l e s K - l , K-2, K-3, and K-4 i n Appendix K show the d i s t r i b u -t i o n of f i l m frames over the span c o n s i d e r e d . Note that i n Table K-3 and K-4 of run 19, s i x a d d i t i o n a l frames were taken i n t o account, s t a r t i n g from frame No. 101 and. ending on frame No. 202. When these a d d i t i o n a l frames are i n c o r p o r a t e d i n the d i s c u s s i o n of run 19, t h i s run w i l l be c a l l e d , "run 19 (extended)". For any g i v e n frame, only one measurement was taken f o r each pseudo-radius t h a t was c o n s i d e r e d . A l a r g e number of p r i n t e d photographs of runs 18 and 19 showed s l i g h t l y blurred, spots i n c e r t a i n areas of the p i c t u r e ( F i g s . 33 and 34). At f i r s t , i t was thought that t h i s was due to the presence of a h i g h r e f r a c t i v e index g r a -1 1 6 d i e n t m a t e r i a l i n these l o c a t i o n s (see "DISCUSSION") . How-ever , upon c l o s e r examination, i t was d i s c o v e r e d t h a t the e n l a r g e r c a r r i e r f o r the f i l m n e g a t i v e i n the p r i n t i n g p r o -cess was not h o l d i n g the n e g a t i v e f l a t so t h a t the n e g a t i v e s u r f a c e was not l y i n g i n one p l a n e . T h i s problem c o u l d be due to two p o s s i b l e reasons: 1 . The n e g a t i v e c a r r i e r , which was meant f o r use with 3 5 mm. f i l m s , was too l a r g e t o h o l d the 1 6 mm. n e g a t i v e e n t i r e l y f l a t . 2. The n e g a t i v e c a r r i e r was so designed t h a t the n e g a t i v e was h e l d i n t h i s c a r r i e r between two open frames so t h a t there was a tendency f o r the negative or p a r t s of i t to "jump" from one plane to another under the i n f l u e n c e of heat. When t h i s happened between f o c u s s i n g and exposing, the p r i n t or p a r t s of i t went out of f o c u s . By stopping down the e n l a r g e r l e n s to i n c r e a s e depth of f i e l d , b l u r r i n g c o u l d be minimized. C. S t a t i s t i c s The a n a l y s i s of v a r i a n c e (ANOVA) t a b l e s f o r runs 18 and 1 9 I n t e r p r e t e d by the l i n e a r model are shown i n Tables V i l a , V l l b , V i l l a , V H I b , IXa and IXb. To f a c i l i t a t e understanding of the terms shown i n 117 Table V i l a . A n a l y s i s of Variance Table of L e f t Drop i n Run 18 Degrees Sum of Mean D i v i d i n g of Square s Square C a l c u l a t e d Line Source Freedom x l O - 6 x 10~° t-va l u e T o t a l ( c o r r e cted) 25 37.434 70° R e g r e s s i o n (b^) 1 8.3613 8.3613 -2.6272 Re s i d u a l 24 29.073 1.2114 T o t a l ( c o r r e c t e d ) 25 10.463 100° Reg r e s s i o n ( b i ) 1 2.6546 2.6546 -2.8564 Re s i d u a l 24 7.8086 0.32536 T o t a l ( c o r r e c t e d ) 25 8.0248 130° R e g r e s s i o n ( b i ) 1 0.84307 0.84307 -I.6785 R e s i d u a l 24 7.1818 0.29924 T o t a l ( c o r r e c t e d ) 25 17.153 145° Regression (b]_) 1 1.3949 1.3949 -1.4576 R e s i d u a l 24 15.758 O.65658 T o t a l (corrected.) 25 27.095 155° R e g r e s s i o n ( b i ) 1 0.13465 0.13465 0.3462 Re s i d u a l 24 26.960 1.12333 T o t a l ( c o r r e c t e d ) 25 5.0506 185° Regr e s s i o n ( b i ) 1 0.00246- 0.00246- 0.1082 Re s i d u a l 24 5.0481 0.21034 T o t a l ( c o r r e c t e d ) 25 12.474 195° Regr e s s i o n ( b i ) 1 1.2633 1.2633 1.6445 R e s i d u a l 24 11.210 0.46708 T o t a l ( c o r r e c t e d ) 25 9.1354 220° Regression ( b i ) 1 1.4381 1.4381 2.1176 R e s i d u a l 24 7.6973 0.3207 . 2509 T o t a l ( c o r r e c t e d ) 25 13.398 R e g r e s s i o n ( b i ) 1 3.4659 3.4659 2.8939 R e s i d u a l 24 9.9326 0.41386 T o t a l ( c o r r e c t e d ) 25 28.230 280° Regr e s s i o n ( b i ) 1 1.0468 1.0468 0.9614 Re s i d u a l 24 27.183 1.1326 1 1 8 Table V l l b o A n a l y s i s of Variance Table of Right Drop i n Run 1 8 Degrees Sum of Mean D i v i d i n g of Square s Square C a l c u l a l Line Source Freedom x 1 0 - 6 x 1 0 - 6 t - v a l i T o t a l ( c o r r e c t e d ) 25 1 4 o 9 5 1 70° R e g r e s s i o n ( b l ) 1 O0I7856 O .I7856 -0.539 Re s i d u a l 2 4 I 4 c 7 7 2 0 . 6 1 5 5 T o t a l ( c o r r e c t e d ) 25 1 9 . 9 2 5 1 0 0 ° R e g r e s s i o n ( b l ) 1 809664 8.9664 - 4 . 4 3 1 R e s i d u a l 2 4 10.959 0.4566 T o t a l ( c o r r e c t e d ) 25 1 0 . 4 0 0 130° Regression ( b l ) 1 2o7669 2.7669 -2.950 R e s i d u a l 2 4 7»633 0 . 3 1 8 0 T o t a l ( c o r r e c t e d ) 25 21.972 1450 R e g r e s s i o n ( b l ) 1 1 1 . 4 3 7 11.437 - 5 . 1 0 4 Re s i d u a l 2 4 10.535 O.43896 T o t a l ( c o r r e c t e d ) 25 28.636 155° R e g r e s s i o n ( b l ) 1 6.3362 6.3362 - 2 . 6 1 1 R e s i d u a l 2 4 22.300 0 . 9 2 9 1 7 T o t a l ( c o r r e c t e d ) 25 1 3 » 8 0 9 1 8 5 ° R e g r e s s i o n ( b l ) 1 0 . 6 9 3 5 1 0 . 6 9 3 5 1 -1.126 R e s i d u a l 2 4 13 . 1 1 6 0 . 5 4 6 5 T o t a l ( c o r r e c t e d ) 25 1 0 . 4 2 8 195° Regression ( b l ) 1 0 . 1 8 5 3 7 0 . 1 8 5 3 7 - 0 . 6 5 9 Re s i d u a l 2 4 1 0 . 2 4 3 0 . 4 2 6 7 9 T o t a l ( c o r r e c t e d ) 25 21.973 2 2 0 ° R e g r e s s i o n ( b l ) 1 0.02053: 0.02053; - O 0 I 5 O R e s i d u a l 2 4 21.952 0 . 9 1 4 7 T o t a l ( c o r r e c t e d ) 25 3 9 . 4 9 4 250° R e g r e s s i o n ( b l ) 1 1 . 2 4 7 7 1 . 2 4 7 7 O0885 R e s i d u a l 2 4 3 8 . 2 4 6 1.5936 T o t a l ( c o r r e c t e d ) 2 5 1 8 . 8 2 0 2 8 0 ° R e g r e s s i o n ( b l ) 1 0 . 8 4 5 5 3 . 0 . 8 4 5 5 3 1 . 0 6 2 R e s i d u a l 2 4 17.974 0 . 7 4 8 9 1 1 9 ["able V l l l a o A n a l y s i s of Variance Table of L e f t Drop i n Run Degrees Sum of Mean Dividi n g of Square s Square C a l c u l a Line Source Freedom x 1 0 - 6 x 10~6 t - v a l ' T o t a l ( c o r r e c t e d ) 25 2 2 . 9 3 7 7 0 ° R e g r e s s i o n ( b i ) 1 0 , 2 8 6 0 1 0 , 2 8 6 0 1 - O . 5 5 O R e s i d u a l 24 2 2 o 6 5 1 0 . 9 4 3 7 9 T o t a l ( c o r r e c t e d ) 25 31=931 1 0 0 ° R e g r e s s i o n ( b i ) 1 13*350 13 . 3 5 0 - 4 . 1 5 3 Re s i d u a l 24 1 8 , 5 8 0 0 . 7 7 4 1 7 T o t a l ( c o r r e c t e d ) 25 3 6 . 0 5 3 130O Regression ( b i ) 1 23.506 23 . 5 0 6 - 6 . 7 0 5 R e s i d u a l 24 1 2 . 5 4 7 0 . 5 2 2 7 9 T o t a l ( c o r r e c t e d ) 25 4 30 5 4 6 145° R e g r e s s i o n ( b l ) 1 I 8 0 O 7 2 1 8 . 0 7 2 - 4 . 1 2 6 R e s i d u a l 24 2 5 . 4 7 4 1 . 0 6 1 4 T o t a l ( c o r r e c t e d ) 25 29.558 155° R e g r e s s i o n ( b i ) 1 130444 13 . 4 4 4 - 4 . 4 7 5 Re s i d u a l 24 1 6 O 1 1 4 0 . 6 7 1 4 T o t a l ( c o r r e c t e d ) 1 2 8 o 7 1 3 1 1 7 0 ° R e g r e s s i o n (b]_) 1 5 . 3 2 6 3 5 . 3 2 6 3 - 4 . 1 5 9 Re s i d u a l 1 1 3.3868 O . 3 0 7 8 9 T o t a l ( c o r r e c t e d ) 25 7 . 1 8 1 6 1 8 5 ° R e g r e s s i o n ( b i ) 1 0 o 6 l 7 3 2 0 . 6 1 7 3 2 - 1 . 5 0 2 R e s i d u a l 24 6 , 5 6 4 3 0 . 2 7 3 5 T o t a l ( c o r r e c t e d ) 25 15 . 8 7 3 1 9 5 ° Regression ( b i ) 1 1 , 2 8 6 7 1 . 2 8 6 7 - 1 . 4 5 5 Re s i d u a l 24 1 4 O 5 8 6 0 . 6 0 7 7 5 T o t a l ( c o r r e c t e d ) 25 2 8 , 7 2 6 2 2 0 ° R e g r e s s i o n (b]_) 1 1 0 , 1 4 5 1 0 . 1 4 5 3 . 6 2 0 R e s i d u a l 24 1 8 , 5 8 0 0 . 7 7 4 1 7 T o t a l ( c o r r e c t e d ) 25 1 4 , 9 6 3 2 5 0 ° R e g r e s s i o n (b]_) 1 6 , 0 1 0 1 6 . 0 1 0 1 4 . 0 1 4 R e s i d u a l 24 8 o 9 5 3 3 0 . 3 7 3 0 5 120 Table V l l l b o A n a l y s i s of Variance Table of R i g h t Drop i n Run 1 9 Degrees Sum of Mean D i v i d i n g of Squares Square C a l c u l a t e d Line Source Freedom x 10-6 x 1 0 - 6 t-value T o t a l ( c o r r e c t e d ) 2 5 9 = 1 9 6 7 1 0 0 ° R e g r e s s i o n (bi) 1 0 o 1 2 4 4 7 0 . 1 2 4 4 7 0 . 5 7 4 R e s i d u a l 2 4 9 . 0 7 2 2 O . 3 7 8 O I T o t a l ( c o r r e c t e d ) 25 I 6 . I 6 5 130° R e g r e s s i o n (bl) 1 1 . 6 7 8 8 I 0 6 7 8 8 - 1 . 6 6 8 R e s i d u a l 2 4 1 4 . 4 8 6 0 . 6 0 3 5 8 T o t a l ( c o r r e c t e d ) 2 5 1 5 . 8 8 5 1 4 5 ° R e g r e s s i o n (bl) 1 4 . 8 7 9 1 4 . 8 7 9 1 - 3 . 2 6 2 R e s i d u a l 2 4 1 1 . 0 0 6 O . 4 5 8 5 8 T o t a l ( c orre cted) 25 1 6 . 6 4 1 155° R e g r e s s i o n (b^ ) 1 3 . 8 7 1 9 3 . 8 7 1 9 - 2 . 6 9 8 R e s i d u a l 2 4 1 2 . 7 6 9 0 . 5 3 2 0 4 T o t a l ( c o r r e c t e d ) 1 2 6 . 2 2 5 9 1 7 0 ° R e g r e s s i o n (b]_) 1 0 . 2 3 8 6 4 0 . 2 3 8 6 4 - 0 . 6 6 2 R e s i d u a l 1 1 5 . 9 8 7 3 0 . 5 4 4 3 T o t a l ( c o r r e c t e d ) 2 5 2 . 6 1 9 9 1 8 5 ° R e g r e s s i o n (bl) 1 0 . 1 3 4 7 7 0 . 1 3 4 7 7 - 1 . 1 4 1 R e s i d u a l 2 4 2 . 4 8 5 1 0.1035 T o t a l ( c o r r e c t e d ) 25 9 . 1 8 0 4 1 9 5 ° Regre s s i on (bi) 1 0.23032 0.23032 O . 7 8 6 R e s i d u a l 2 4 8.9501 0 . 3 7 2 9 T o t a l ( c o r r e c t e d ) 2 5 5 . 0 1 1 9 250° R e g r e s s i o n (b^ ) 1 0 . 4 1 6 0 1 0 . 4 1 6 0 1 1 . 4 7 4 R e s i d u a l 2 4 4 . 5 9 5 9 0 . 1 9 1 5 T o t a l ( c o r r e c t e d ) 25 2 . 6 2 5 1 2 8 0 ° R e g r e s s i o n (bx) 1 0 . 2 3 8 5 2 0 . 2 3 8 5 2 1 . 5 ^ 9 R e s i d u a l 2 4 2 . 3 8 6 6 0 . 0 9 9 4 1 2 1 Table IXa. A n a l y s i s of Variance Table of L e f t Drop i n Run 1 9 (Extended) D i v i d i n g L i n e Source Degrees of Freedom Sum of Square s x 1 0 " ° Mean Square x 10-6 C a l c u l a t e d t-value T o t a l (corre cte d) 3 1 7 0 ° R e g r e s s i o n ( b i ) 1 R e s i d u a l 3 0 T o t a l ( c o r r e c t e d ) 3 1 100° R e g r e s s i o n ( b l ) 1 R e s i d u a l 3 0 T o t a l ( c o r r e c t e d ) 3 1 1 3 0 ° R e g r e s s i o n ( b l ) 1 R e s i d u a l 3 0 T o t a l ( c o r r e c t e d ) 3 1 145° R e g r e s s i o n ( b i ) 1 R e s i d u a l 3 0 T o t a l ( c o r r e c t e d ) 3 1 1 5 5 ° R e g r e s s i o n ( b l ) 1 R e s i d u a l 3 0 T o t a l ( c o r r e c t e d ) 18 1 7 0 ° Regression ( b l ) 1 R e s i d u a l 17 T o t a l ( c o r r e c t e d ) 3 1 185° R e g r e s s i o n ( b i ) 1 R e s i d u a l 3 0 T o t a l ( c o r r e c t e d ) 3 1 195° R e g r e s s i o n ( b l ) 1 R e s i d u a l 3 0 T o t a l ( c o r r e c t e d ) 3 1 220° R e g r e s s i o n ( b l ) 1 R e s i d u a l 3 0 T o t a l ( c o r r e c t e d ) 3 1 250O R e g r e s s i o n ( b i ) 1 R e s i d u a l 3 0 T o t a l ( c o r r e c t e d ) 3 1 280° R e g r e s s i o n ( b l ) 1 R e s i d u a l 3 0 5 3 o 8 9 2 2 4 . 1 3 3 2 9 . 7 5 9 82.084 60.884 2 1 o 2 0 0 9 0 o l l 5 7 4 . 4 7 4 15=641 8 7 o 4 6 0 5 4 . 9 5 1 3 2 . 5 0 9 4 1 . 7 9 8 1 7 . 6 0 6 2 4 . 1 9 2 2 4 . 1 3 3 0 . 9 9 1 9 7 60.884 O . 7 0 6 7 7 4 . 4 7 4 0 . 5 2 1 3 7 5 4 . 9 5 1 1 . 0 8 3 6 1 7 . 6 0 6 0 . 8 0 6 4 1 6 . 4 6 7 5 . 3 6 2 3 5 . 3 6 2 3 1 1 . 1 0 5 0 . 6 5 3 2 9 . 4 7 6 1 0 . 0 0 0 1 2 0 . 0 0 0 1 2 9 . 4 7 5 9 O . 3 1 5 8 6 2 5 . 6 1 6 0.29873 25=317 52.542 32.324 20.218 47.766 3 4 . 2 8 6 13.480 0.29873 0.8439 3 2 . 3 2 4 0 . 6 7 3 9 3 4 . 2 8 6 0 . 4 4 9 3 16.819 7.5895 7.5895 9 . 2 2 9 5 O . 3 0 7 6 5 - 4 . 9 3 2 - 9 . 2 8 2 - 1 1 . 9 5 2 - 7 . 1 2 1 - 4 . 6 7 2 - 2 . 8 6 5 0 . 0 2 0 0 . 5 9 5 6 . 9 2 6 8 . 7 3 5 4 . 9 6 7 1 2 2 Table I X b o A n a l y s i s of Variance Table of Ri g h t Drop i n Run 1 9 (Extended) Degrees Sum of Mean D i v i d i n g of Squares Square C a l c u l a t e d Line Source Freedom x 1 0 - 6 x 1 0 ~ 6 t-value T o t a l ( c o r r e c t e d ) 3 1 9 o 5 4 8 3 100O R e g r e s s i o n ( b l ) 1 0 . 4 0 6 6 7 0 .40667 L 1 5 5 R e s i d u a l 3 0 9 c 1 4 1 7 0 . 3 0 4 7 T o t a l ( c o r r e c t e d ) 31 I60I67 1300 R e g r e s s i o n ( b i ) 1 0 . 4 1 8 2 7 0 . 4 1 8 2 7 - 0 . 8 9 3 R e s i d u a l 3 0 15 . 7 4 8 0 . 5 2 4 9 T o t a l ( c o r r e c t e d ) 31 2 6 . 9 7 8 1 4 5 ° R e g r e s s i o n ( b i ) 1 1 4 . 5 4 2 1 4 . 5 4 2 - 5 . 9 2 3 R e s i d u a l 3 0 1 2 . 4 3 5 0 . 4 1 4 5 T o t a l ( c o r r e c t e d ) 31 4 1 . 8 1 8 155° R e g r e s s i o n ( b l ) 1 2 7 c 2 9 5 2 7 . 2 9 5 - 7 . 5 0 9 R e s i d u a l 3 0 1 4 . 5 2 3 0 . 4 8 4 1 T o t a l ( c o r r e c t e d ) 1 8 1 8 . 1 4 7 1 7 0 ° R e g r e s s i o n (b^) 1 1 0 . 6 0 3 1 0 . 6 0 3 - 4 . 8 8 8 R e s i d u a l 1 7 7 . 5 4 4 0 .44376 T o t a l ( c o r r e c t e d ) 3 1 4 1 . 0 1 1 1 8 5 ° R e g r e s s i o n ( b j ) 1 2 9 o 8 5 4 2 9 . 8 5 4 - 8 . 9 6 0 R e s i d u a l 3 0 1 1 . 1 5 7 0 . 3 7 1 9 T o t a l ( c o r r e c t e d ) 3 1 4 2 . 7 9 6 1 9 5 ° R e g r e s s i o n ( b l ) 1 2 2 . 0 4 3 2 2 . 0 4 3 - 5 . 6 4 5 R e s i d u a l 3 0 2 0 . 7 5 3 0 . 6 9 1 7 7 T o t a l ( c o r r e c t e d ) 3 1 3 0 . 8 8 6 2 2 0 ° R e g r e s s i o n ( b l ) 1 1 8 . 8 9 9 1 8 . 8 9 9 - 6 . 8 7 8 R e s i d u a l 3 0 1 1 . 9 8 6 0 . 3 9 9 5 2500 T o t a l ( c o r r e c t e d ) 3 1 1 5 o 8 6 l R e g r e s s i o n (b^) 1 5 o 3 1 3 5 » 3 1 3 - 3 . 8 8 7 R e s i d u a l 3 0 1 0 . 5 4 8 O . 3 5 1 6 T o t a l ( c o r r e c t e d ) 3 1 7 0 3 8 6 1 2 8 0 ° R e g r e s s i o n ( b l ) 1 0 . 5 4 4 7 2 0 . 5 4 4 7 2 - 1 . 5 4 6 R e s i d u a l 3 0 6 . 8 4 1 4 0 . 2 2 8 0 5 ) 1 2 3 these t a b l e s , some e x p l a n a t i o n s are i n order.. I t i s commonly understood t h a t Sum of squares _ Sum of squares + Sum of squares about the mean about r e g r e s s i o n due to r e g r e s s i o n In e q u a t i o n form t h i s can be expressed as f o l l o w s : £(Yi - Y ) 2 = £(Yi - Y i ) 2 + £(Yi - Y ) 2 , i = i , 2 , 00 0 ,n (?) where Y i = i ~ o b s e r v a t i o n of the dependent v a r i a b l e s the pseudo-radius ° Y = mean of Y. A Y i =• p r e d i c t e d value of Y f o r a given X ( t i m e ) . Corresponding t o E q 0 ( 7 ) , the s p l i t of the degrees of f r e e -dom ( 4 4 ) i s ( n - 1 ) = ( n - 2 ) + 1 ( 8 ) where n = no» of se t s of o b s e r v a t i o n s ( X i , Y]_), (Xg, ^2^° O O O O 9 ( X^l 9 l£tl ) o Using Eqso ( 7 ) and ( 8 ) and employing a l t e r n a t i v e computa-t i o n a l forms f o r the e x p r e s s i o n s of E q , ( 7 ) an. ANOVA t a b l e i s 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 of ANOVA Table, Degrees of Sum of Mean About mean ( t o t a l , c o r r e c t e d f o r mean) n - 1 „ 2 ( E Y i ) 2 n R e g r e s s i o n 1 b l « (£xi)(£Yi)" L x i Y i -n MS R About r e g r e s s i o n ( r e s i d u a l ) n - 2 by s u b t r a c t i o n S 2 124 where b i = estimate of slope parameter of the model, j8j . X]_ = i t h o b s e r v a t i o n of the independent v a r i a b l e , time. S = mean square 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 " ) . M SJJ = mean square due to r e g r e s s i o n . The "Mean Square" column i s obtained by d i v i d i n g each "SS" or Sum of Squares e n t r y by i t s corresponding degrees of f r e e -dom. Note t h a t the e n t r i e s i n t h i s t a b l e under the .'^Source" column are worded d i f f e r e n t l y i n the ANOVA Tables V i l a - IXb, i n c l u s i v e . However, the d i f f e r e n c e i s onl y due t o c o n t r a c t i o n , f o r b r e v i t y i n the l a t t e r . A d d i t i o n a l r e l a t e d equations used are shown i n Appendix E. Comparisons made of the c a l c u l a t e d a b s o l u t e t - v a l u e s w i t h the a p p r o p r i a t e t ( n - 2 , 1-iOO from a t - t a b l e (44) having (n-2) degrees of freedom and (1-iOO percentage p o i n t s of a t - d i s t r i b u t i o n showed which drop d i v i d i n g l i n e s have slo p e s where the n u l l h y p o t h e s i s , Ho:^9/ = 0, c o u l d not be r e j e c t e d . The t e s t was a two-sided t e s t conducted a t the 100(1 -Ot)% confidence l e v e l . The l e v e l of s i g n i f i c a n c e , OC , used was 0.01 to o b t a i n r e s u l t s t h a t were 99% s i g n i f i c a n t . The v a r i o u s d i v i d i n g l i n e s c o r r e s p o n d i n g to |t| l e s s than t ( 2 4 , 0.995) = 2.797» i . e . , c o r r e s p o n d i n g t o no dependency r e l a t i o n s h i p between v a r i a b l e s X and Y (zero s l o p e ) , are shown i n Table XI. In other words, f o r these l i n e s , the n u l l h y p o t h e s i s could not be r e j e c t e d . Table XI. Drop Dividing Lines whose X-Y Relationships Correspond to Zero Slope Confidence Run No. Level 99$ 99*9$ Drop Left 130°,145°,155°.185°,195°.280°,220°,70° L.H.S.* plus 100°8250° Right 70°,185o,195O.220O,250o,280o,155° L.H.S.* plus 130° Left 70°,185°,195°.280 o** L.H.S.* plus 220 Right 70°**,100°,130°,170°,185°,195° 220°,250°,280°,155° L.H.S.* plus 145 Left 185°,195 .170 Right 70°,100°,130°,280° *Left hand side entry under confidence l e v e l of 99^ » **Dividing l i n e s along which no pseudo-radius changes were ac t u a l l y measured. 126 There were a few other d i v i d i n g l i n e s where the n u l l h y p o t h e s i s was not s t r o n g l y rejected, a t the 99$ c o n f i -dence l e v e l and f o r t h i s l i n e s , the slope of the l i n e a r model was t e s t e d to be zero a t the 99»9$ confidence l e v e l (Table X I ) . One i s f a c e d with the d e c i s i o n of whether to r e j e c t or not to r e j e c t the n u l l h y p o t h e s i s f o r these d i v i d i n g l i n e s a t the 99$ confidence l e v e l . I t i s f e l t t h a t f u r t h e r i n v e s t i g a -t i o n s of these l i n e s are warranted s i n c e there i s no s t r o n g evidence t h a t the n u l l h y p o t h e s i s c o u l d be r e j e c t e d . In t h i s t h e s i s , the slope of these l i n e s were non e t h e l e s s c o n s i d e r e d , f o r a l l p r a c t i c a l purposes, t o assume a value of zero s i m i l a r t o t h a t a s s i g n e d to the r e s t of the l i n e s l i s t e d i n Table XI. T h i s d e c i s i o n was i n f l u e n c e d by J.M. Wetz (44) who suggested t h a t i n order t h a t an equation should be regarded as s a t i s -f a c t o r y p r e d i c t o r , the observed t - v a l u e should exceed not merely the s e l e c t e d percentage p o i n t of the t - d i s t r i b u t i o n , but about two times the s e l e c t e d percentage p o i n t o T h i s suggestion serves o n l y i n the present work as a c u r r e n t expe-d i e n t f o r assessment of those l i n e a r equations where the t e s t t h a t the n u l l h y p o t h e s i s , H Q : f y = 0, was not s t r o n g l y r e j e c -t e d a t the 99% confidence l e v e l and i s not meant to be the r u l e f o r a l l remaining l i n e a r equations embodied i n t h i s t h e s i So F i g s . 35 and 36 show t y p i c a l p l o t s of r e s i d u a l v s . o b s e r v a t i o n number (time) showing the absence and presence of unexplained v a r i a t i o n i n the l i n e a r model, r e s p e c t i v e l y . > 0 - 2 faO + CO a H as -p o o oo ooo ooooo o o — OOOOO o o --0-I < ZD Q UJ -0-2 -0-3 OO ooooo o 26 L 24 22 20 18 - 16 14 12 10 OBSERVATION NO- (X) i i i i i i i i _ 8 150 138 126 114 102 90 78 66 FRAME NO- PRECEDING 54 42 30 18 COALESCENCE F i g u r e 35. 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 Fi g u r e 3 1 . ) 821 1 2 9 The pseudo-radius data i n Appendix K show t h a t l i n e 1 7 0 ° r e s u l t s do not appear i n run 18 s i n c e no measurement cou l d be taken due to the appearance of a dark b l o t c h . In run 19» measurement of the l i n e a t 1 7 0 ° was incomplete f o r the same reason. The use of o b s e r v a t i o n numbers i n s t e a d of time v a l u e s as the a b s c i s s a i n p l o t s of pseudo-radius (Y) v s . time (X) was adopted, f o r the sake of convenience. The c o n v e r s i o n i s shown, f o r example, i n Appendix K. P r e d i c t i v e e q uations obtained by the 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 r e l a -t i o n s h i p s were found to have non-zero slope are shown i n Table X I I . These equations would, of course, not apply t o value s of 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 c o e f f i c i e n t of d e t e r m i n a t i o n , R , shown i n t h i s t a b l e i s d e f i n e d : R 2 _ SS due to r e g r e s s i o n /Q \ T o t a l SS, c o r r e c t e d f o r mean This term measures the p r o p o r t i o n of t o t a l v a r i a t i o n about — 2 the mean, Y, e x p l a i n e d by the r e g r e s s i o n ? R i s e x p l a i n e d more f u l l y i n a l a t e r t o p i c under "DISCUSSION". F i g s . 3 7 . 3 8 , and 39 show the v a r i o u s l o c a t i o n s of the r e g i o n s i n the drop where pseudo-radius changes were observed. F i g s . 40 and 41 show the f i t t e d p l o t s of pseudo-r a d i u s v s . o b s e r v a t i o n number f o r run 1 9 . The reason f o r not showing the p l o t s f o r run 18 are e x p l a i n e d under the heading, "DISCUSSION, I n t e r p r e t a t i o n of Data". Table Xllo P r e d i c t i v e Equations and R Values Obtained by the M u l t i p l e R e g r e s s i o n Program Run No. Drop D i v i d i n g Line P r e d i c t i v e Equation R 2 18 R i g h t 1 0 0 ° 145° ii II 0.13136 0.13426 + 0 . 15825X + 2.97346X2 0 . 2 9 1 4 7 X - 55°5509X 2 + 2 7 2 7 . 5 4 x 3 - 41525» OX2* 0 . 5 4 8 1 0 . 6 3 0 0 7 0 ° Y = 0 . 1 1 2 4 6 - 10.4601x3 0.5591 1 0 0 ° Y = 0.12735 - 3*10448x 2 + 310 4036x3 0 . 7 7 4 7 130° Y = 0 .12930 - 3 .73441X 2 + 3907336x3 0 . 8 4 8 8 L e f t 145° Y = 0 .12346 - 3 .77947X 2 + 4 2 . 7 1 7 9 x 3 0.7027 155° Y = 0 .12108 - 0 . 0 7 6 8 6 X + 1 3 3 . 0 1 5 X ^ 0.5997 2 2 0 ° Y = 0.09895 + 0 . 0 5 3 1 5 X 0 .6157 250° Y = 0.10486 + 2 . 2 0 1 1 7 X 2 - 2 1 . 5 7 2 6 x 3 0 . 7 4 4 2 19 (Ext-ended ) 2 8 0 ° Y = 0.12656 - 0 . 0 9 2 7 3 X + 6.68294X2- 155.609X3 + : L 2 0 8 . 3 0 X 1 * 0.7049 145° Y = 0 .12638 - 3 .78106X 2 + 105.629X3 - 8 4 2 . 3 8 0 X ^ 0 . 5 7 4 6 155° Y = 0 . 12486 - 0 . 04884X 006543 170° Y = 0.11890 - 0 . 04578X 0o5844 Ri g h t 1 8 5 ° Y = 0 .11473 + 2 . 3 3 9 5 0 X 2 - 115o786x 3 + 1035°81X^ 0.9082 195° Y = 0.11310 - O . II538X + 1 0 . 5 6 5 4 X 2 • - 293o319x3 + 2225o63X^ 0 . 7 8 4 1 2 2 0 ° Y = 0 . 1 1 0 1 4 - 0.09673X + 7 .72334X 2 • - 192.583x3 + 1306.01X^ 0.9323 250° Y = 0.11660 - 0 . 0 7 0 1 9 X + 6 .68546X 2 • - 176.423x3 + 1279o71X^ 0.6575 131 Figure 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. L E G E N D 1 - 70° 6 - 170° 2 - 100. 7 - 185° 3 - I30 0 8 - 195° 4 - ! 4 5 0 9 - 2 2 0 o 5 - 155 10 - 250 II - 280° F i g u r e 3 8 . 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 . 1 3 3 L E G E N D t - 70° 6 - 170° 2 - 100 o 7 - I85 Q 3 - ! 3 0 o 8 - I95 Q 4 - I45 Q 9 - 2 2 0 o 5 - 155 10 - 250 1 1 - 2 8 0 F i g u r e 3 9 ° Equations f i t t e d and behaviour observed over 0 - 2 0 2 f i l m frames i n run 1 9 ( e x t e n d e d ) „ 13 5h 130 X (VI cn < a UJ < n - 12 Oh e> < < i-o 11-51-CM CO Q < tr i o O 10 5h UJ CO a . IOOF o - — DIVIDING LINE 7 0 ° e • — I I I I 100° 6 — n I I 130° 9 — I I I I 145° — I I I I 155° — I I I I 170° • — I I I I 185° n — I I I I 195° — I I I I 2 2 0 ° - o — n u 2 5 0 ° € — I I It 2 8 0 ° ADDITIONAL SCALE J 0 0 0 0 6 sec. NOTE : LINES 170? 185* AND 195° NOT SHOWN COMPLETELY. THESE ARE PARALLEL TO THE ABSCISSA AT THE VALUES INDICATED. LEFT DROP 6 6 6 © 6 © © © © © 6 © t> o o o o o o o o o o o o o o o oo- o o o o o o o 32 31 202 185 30 29 28 27 26 22 OBSERVATION NO- ( X ) 18 168 151 134 Tl7 100 8* 68 52 F R A M E NO PRECEDING COALESCENCE 36 20 Figure 40. Pseudo-radius vs. observation no. (and frame no.) f o r various d i v i d i n g of the l e f t drop i n run 19. s 4 CD H O ct tr CD ct P-4 o CD p< o i » P-ci CO <1 CO H" O CO 13 t—1 ct . o 3 O P. >-b 4 SB B CD o o 4 4 CO P. (XJ. CD CO PSEUDO-RADIUS (Y) I02 x f t (TOTAL MAGNIFICATION EQUALS 24 x) o 6 o IN) GO T| CD _ 03 m S2| z O OJ ' * n 3D m o m o — o z o CD GO o * O > m o> co o m z o rn Co ro o OJ ro OJ oi o co m >0D z ™ ro ro ro GO 9 cn e 6 © n • 3 c - o o - © 9 I I I i i i I i i I s s s ; a I < i\> 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 n n i n d n i tt ) : tt 5 tt ro 6 6 OJ cn -O O X H O ZD O TJ > GO CO O CO CO > o o "0 r m H m r -< O H m z m co > I . ° o _i m co m m o o Ol o < > f-c m co -o 0 5 > ro 30 00 > o I- ° — r~~ z z m o o r~ H o > H w m o p * 9 o l o CO (ft a a > O o o z > CO o > r m 1 3 6 A c c o r d i n g to Table XI, f o r the l e f t drop of run 18, the X-Y r e l a t i o n s h i p s a l l showed zero slopes f o r a l l d i v i d i n g l i n e s considered o As w e l l , f o r the r i g h t drop a l l but two of the X-Y r e l a t i o n s h i p s were found t o have zero s l o p e s . Data f o r both d i v i d i n g l i n e s were f i t t e d t o polynomial equations, as mentioned e a r l i e r . In run 19 (extended) (Table X I ) , f o r the d i v i d i n g l i n e s measured i n the l e f t drop, s i m i l a r equa-t i o n s were f i t t e d , to seven of them. However, f o r the l i n e 2 2 0 ° , a l i n e a r equation was found t o f i t reasonably w e l l . In the r i g h t drop, two out of seven equations f i t t e d were l i n e a r . These were the c o r r e l a t i o n s f o r the l e n g t h s of the l i n e s a t 1 5 5 ° and 1 ? 0 ° . No attempt was made to f i t the data of run 1 9 s i n c e the p r e d i c t i v e equations obtained f o r run 1 9 (extended) n a t u r a l l y a p p l y , except t h a t they are l i m i t e d to a range of X v a l u e s from 2 6 to 1 o b s e r v a t i o n numbers o n l y . Input and sample output data of the m u l t i p l e r e -g r e s s i o n program ( 4 5 ) from which the above p r e d i c t i v e equa-t i o n s were obtained are shown i n Appendix M. 1 3 7 DISCUSSION A. A p p l i c a b l e Photographic Problems 1 ) E f f e c t of P e r s p e c t i v e The e f f e c t of p e r s p e c t i v e on photographic images used i n drop study i s well-known. The measurement of drop s i z e s , f o r example, i s a f f e c t e d by t h i s phenomenon i n t h a t i f measurements were made from a p i c t u r e taken by a camera s i t u a t e d r e l a t i v e l y c l o s e t o the drop, the true dimension and shape of the drop w i l l not be o b t a i n e d . T h e o r e t i c a l l y , the camera must be p l a c e d a t an i n f i n i t e d i s t a n c e to view the t r u e o u t l i n e of the drop but- f o r p r a c t i c a l purposes, a camera equipped with a t e l e p h o t o l e n s w i l l be s u f f i c i e n t . In the present study, the use of such a l e n s (of 3 0 0 mm. f o c a l l e n g t h l e n s ) was found to produce a much lower m a g n i f i c a t i o n (Attachment of an e x t e n s i o n tube t o t e l e p h o t o l e n s was not p r a c t i c a l . ) than what was obtained by u s i n g an arrangement of 7 5 mm. l e n s p l u s 7 5 mm. e x t e n s i o n tube. P r i n t enlargement of the image obtained by the use of the former l e n s c o u l d only produce a much g r a i n i e r p i c t u r e than t h a t obtained with the 7 5 mm. l e n s p l u s e x t e n s i o n tube. Since a g r a i n y p i c t u r e i s hard to take measurements on, the l a t t e r set-up was adopted f o r the work d e s c r i b e d here. 1 3 8 R e s o r t i n g t o the l e n s - e x t e n s i o n tube system of photography i n t r o d u c e s a p e r s p e c t i v e e f f e c t which can be e x p l a i n e d thus: I f one assumes the drop to be a sphere of a r a d i u s r i n f r e e space ( F i g . 42 - exaggerated f o r c l a r i t y ) whose common a x i s with an opposing drop i s a l o n g the Y^-axls, and t h a t both drops approach each other, then, i f a l e n s i s focus s e d a t p o s i t i o n L(XJ J, 0) and al o n g the X^-axis, which i s the l i n e b i s e c t i n g the d i s t a n c e - s e p a r a t i n g the two drops, then the drop h o r i z o n or o u t l i n e , i n two-dimensions, i s viewed a t the t a n g e n t i a l p o i n t P(X^, " % ) . S i m i l a r l y , a corresponding p o i n t on the other drop i s a l s o seen but t h i s i s not shown because the second, drop and the p o s i t i o n of the second t a n g e n t i a l p o i n t are symmetrical. As the drop moves toward coalescence with the other drop, S-»0 and P-»S. Therefore, the drop o u t l i n e i s never viewed a t a s i n g l e f i x e d plane, by the l e n s a t LtX^, 0), with r e s p e c t t o time, but a t an i n f i n i t e number of planes as, i n two-dimensions, a t P(X d, Y d) and a l o n g the a r c P S;., The l o c u s of P(X^, Y d ) , as generated from i t s t a n g e n t i a l l o c a t i o n t o i t s f i n a l p o s i t i o n (at the o r i g i n ) , i s shown i n F i g . 4-3 f o r two s p h e r i c a l diameters, 0.108 and O . I 5 6 i n . The former diameter s i z e i s the one used i n c a l c u l a t i n g the maximum number of s u c c e s s i v e f i l m frames i n runs 18 and 19 (Appendix I ) . The l a t t e r l s the diameter of b a l l b e a r i n g s d e s c r i b e d i n t h i s t h e s i s under the heading, "STEEL BEARING EXPERIMENTS". The equation of the l o c u s of P ( X d , Y d) was c a l c u l a t e d and found to be: 139 Figure 42. Sketch f o r the derivation of Eq o(10). 140 141 where Y d = d i s t a n c e a t any time of p o i n t P from the o p t i c a l a x i s ( X ^ - a x i s ) , i n . X d = d i s t a n c e a t any time of p o i n t P from the common a x i s of the two spheres ( Y ^ - a x i s ) , in» X^ = o b j e c t conjugate, equals 5»09 i n . r = r a d i u s of sphere, i n . Appendix G shows how Eq. (10) was obtained. In P i g . 43, as X^->0.108/2 i n . and as X^ -^ 0.156/2 i n . f o r curves whose equ a t i o n s c o n t a i n e d r = 0.108/2 = 0.054 i n . and r = 0.156/2 = O . O 7 8 i n . r e s p e c t i v e l y , Y i n c r e a s e s I n d e f i n i t e l y ; the l i n e s X^ = 0.054, X^ = O . O 7 8 a r e , t h e r e f o r e , asymptotes. The only i n t e r s e c t i o n w i t h the a x i s i s a t (0,0) since the drops, which are r e p r e s e n t e d here as spheres, c o a l e s c e a t t h i s p o i n t . These f i n d i n g s are e a s i l y deduced from Eq. (10). Sinc e , i n run 18, i t was d i f f i c u l t t o d i s t i n g u i s h the d i s t a n c e between drops due to the dark b l o t c h that appeared i n the space between them, the maximum drop s e p a r a t i o n was taken from run 19 as about 0.004 i n . ( i n f i l m frame no. 202). The r e f o r e , Y d i s a p p r o x i -mately 0.002 i n . The a p p l i c a b l e span of Y d v a l u e s was then from 0.002 to 0 since when Y d = 0 the two drops, which are re p r e s e n t e d here as spheres, f i n a l l y meet and c o a l e s c e . The area i n F i g . 43 covered by t h i s span and i t s co r r e s p o n d i n g X^ v a l u e s are seen t o be e x c e e d i n g l y s m a l l . The consequence of a steep p e r s p e c t i v e f o r the pre s e n t s i t u a t i o n , brought about by a c l o s e o b j e c t - t o - l e n s 142 d i s t a n c e , which w i l l "be i n v e s t i g a t e d a r e : image b l u r r i n g , apparent i n c r e a s e i n pseudo-radius, and f a u l t y assessment of d i s t a n c e o f drop s e p a r a t i o n . The presence of image b l u r can be d e t e c t e d by knowing by how much Xa changes as Y d goes from 0 , 0 0 2 i n , t o 0 , I f the change of X^ i s l a r g e r than the depth of f i e l d then image b l u r would be expected. T h i s change i n was c a l c u l a t e d from Eq. ( 1 0 ) t o be 0.000018 i n . f o r spheres of r = 0 . 0 5 4 i n . , and 0 . 0 0 0 0 3 i n . f o r spheres of r = O . O 7 8 i n . The depth of f i e l d i s o b v i o u s l y g r e a t e r than e i t h e r of the above quoted changes of X^ and, t h e r e f o r e , the a r c P S a t i t s maximum l e n g t h (when P ( X £ , Y d) i s a t the t a n g e n t i a l p o i n t ) , i s w i t h i n the r e g i o n of sharp f o c u s . The Increase i n each pseudo-radius a f f e c t e d by the movement of P, from the t a n g e n t i a l p o i n t towards S, as the two drops approach each other i s equal t o (r - CK). For both r 8 s ( 0 . 0 5 4 i n . and O . O 7 8 i n . ) , the va l u e of (r - CK) obtained was found t o be l e s s than 0 . 0 0 1 i n . Compared t o a minimum d i s c e r n -i b l e l e n g t h of 0 . 0 5 cm. ( 0 . 0 1 9 7 i n . ) i n the measurement of the p s e u d o - r a d i i i n the photographs, the above value 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 measuring methods. The d i s t a n c e of drop s e p a r a t i o n as viewed through the camera l e n s a t L(Xj_,, 0 ) i s not the true d i s t a n c e since the d i s t a n c e of P ( X £ , Y d) from i t s corresponding p o i n t (by symmetry) i n the opposing drop i s d i f f e r e n t from the true d i s t a n c e , 1 . e., 2Y d ¥ 2S0 ( F i g . 42), except, of course, when both drops 143 touch each other (when P(X-|. Y d ) i s a t S)» However, t h i s d i f -f e r ence i s n e g l i g i b l e because a r c P S a t i t s maximum l e n g t h , or a r c p ( X d , Y d ) S , i s s t i l l p r a c t i c a l l y zero f o r both g i v e n r a d i i when deduced from e a r l i e r considerations.. Besides, the nature of the study i s such t h a t o n l y changes i n s i z e a re im-p o r t a n t and not the s i z e i t s e l f <> A study of the e f f e c t of p e r s p e c t i v e on the e n t i r e drop o u t l i n e can be c a r r i e d out a l o n g the same l i n e s as des-c r i b e d above but i t i s f e l t t h a t these c a l c u l a t i o n s show the e f f e c t of p e r s p e c t i v e t o be so i n s i g n i f i c a n t ( F i g . 42) t h a t i t can be concluded t h a t s i m i l a r f i n d i n g s w i l l be obtained f o r a l l the remaining p o r t i o n s of the drop D Furthermore, i t seems h i g h l y probable t h a t t h i s c o n c l u s i o n w i l l be v a l i d even though the a c t u a l drops are not p e r f e c t l y spherical» 2) E f f e c t of R e f r a c t i o n In d i s c u s s i n g the e f f e c t of p e r s p e c t i v e , i t was a s -sumed t h a t no d e n s i t y g r a d i e n t was pre sent« I f t h i s g r a d i e n t was to be co n s i d e r e d , as i n the pr e s e n t work, the e f f e c t of r e f r a c t i o n on the p o s i t i o n and shapes of the o b j e c t must be consideredo When a ray of l i g h t t r a v e l l i n g i n ( i o e - . b e i n g t r a n s -m i t t e d by) one medium passes i n t o another having d i f f e r e n t op-t i c a l p r o p e r t i e s i t s d i r e c t i o n i s changed (except when the l i g h t r a y e n t e r s n o r m a l l y ) , I.e., the r a y i s bent. F i g . 44 144 shows how an observer i n an a i r medium a t E views p o i n t 0 i n some o p t i c a l l y dense medium, say, water. The observer a c t u a l -l y sees an apparent p o i n t I i n s t e a d of the r e a l image a t 0o T h e r e f o r e , p o i n t 0 w i l l a c t u a l l y appear c l o s e r to the s u r f a c e a t a d i s t a n c e i than i t a c t u a l l y i s a t d i s t a n c e o, by a r e -f r a c t i v e index f a c t o r of -*= p r o v i d e d the i n c i d e n t r a y s are par-ty a x i a l , which means that they can make only a small angle with the normal (5'0). I f the observer i s l o c a t e d a l o n g the a x i s p a s s i n g through p o i n t s I and 0, i . e . , the o b j e c t i s viewed from a d i r e c t i o n normal to the s u r f a c e , p o i n t 0 w i l l a c t u a l l y appear c l o s e r t o the s u r f a c e a t a d i s t a n c e 1 than i t a c t u a l l y i s a t d i s t a n c e o and the apparent depth of p o i n t 0 with r e s p e c t to the s u r f a c e w i l l be equal to d i s t a n c e o over (51)« In the p r e s e n t work, three r e f r a c t i n g media must be c o n s i d e r e d . These are the continuous phase (MIBK-saturated water with the 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 methanol), the e x t r a c t i o n column ( g l a s s ) , and the surroundings ( a i r ) . The l i g h t r a y s encounter these three media i n the order named as the r a y s pass from the o b j e c t (the e x t r a c t i o n column) to the camera l e n s . A l i g h t r a y w i l l s t i l l behave as i n F i g . 44 except t h a t i t w i l l be bent each time t h a t i t e n t e r s a medium having a d i f f e r e n t r e f r a c t i v e index. To complicate the matter, the r e g i o n wherein the s o l u t e d i f f u s e s i s made up of a d e n s i t y g r a d i e n t f i e l d , as i n the exaggerated sketch of F i g . 459 so t h a t a l i g h t r a y w i l l be bent c o n t i n u o u s l y as i t passes through the c o n c e n t r a t i o n or d e n s i t y g r a d i e n t f i e l d . ( I t should be borne i n mind t h a t F i g . 45 r e p r e s e n t s a map of the d e n s i t y 1 4 5 F i g u r e 4 4 . Sketch showing the image of a p o i n t l o c a t e d i n water when viewed from a i r . 146 F i g u r e 4 5 » I s o s o l u t e l i n e s between two drops a t an i n s t a n t i n time. 147 g r a d i e n t a t an i n s t a n t i n time. However, the c o n c e n t r a t i o n s i n the present experiments change with time and, t h e r e f o r e , the degree of r e f r a c t i o n of the l i g h t r a y s b e i n g observed are a l s o changed w i t h time.) The v i s u a l e f f e c t over a f i n i t e time i n t e r v a l can be obtained by s i m p l i f y i n g the s i t u a t i o n and r e -f e r r i n g t o Figo 44 0 I f one t h i n k s of the a i r medium i n t h i s f i g u r e as r e p r e s e n t i n g both the a i r and the g l a s s i n each of which the d e n s i t y g r a d i e n t i s zero and of the water medium as the r e g i o n of s o l u t e d i f f u s i o n , and i f one imagines a camera l e n s a t E, then a p o i n t 0 on the drop surface w i l l a c t u a l l y be viewed a t I, and i w i l l v a r y since 7^ v a r i e s with time© I f , a t any time, the extent of change i n i exceeds the depth of f i e l d , p o i n t I w i l l appear b l u r r e d . As p o i n t I c o n s t a n t l y changes i n p o s i t i o n with time, measurements of the pseudo-r a d i u s could be a f f e c t e d s i n c e the e n t i r e drop image i s con-t i n u o u s l y d i s t o r t e d . The e x t e n t of t h i s d i s t o r t i o n i s not c a l c u l a b l e i n t h i s work s i n c e the d e n s i t y g r a d i e n t map of the e n t i r e system must f i r s t be obtained as a f u n c t i o n of time and such measurements are o u t s i d e the scope of t h i s p r o j e c t . One can only assume d i s t o r t i o n and image b l u r e r r o r s to be n e g l i g i b l e due to the presence of a small r e f r a c t i v e index g r a d i e n t f i e l d i n the neighbourhood of the drops obtained by the use of the methanol s o l u t e . A l s o , the p r e s e n t measuring procedures f o r pseudo-radius are not s e n s i t i v e enough to de-t e c t changes l e s s than 0 . 0 5 cm. ( i n the photographs) of which the above e f f e c t s are expected to c o n t r i b u t e . 148 B. Interpretation of Data Over the i n t e r v a l 3 2 S X S 2 6 i n Figs. 40 and 41, any dependency r e l a t i o n s h i p that may show must be treated with caution since there are only six f i l m frames sampled for curve f i t t i n g over a population of 1 0 2 f i l m frames, whereas over the in t e r v a l 2 6 > X > 1 , which i s equivalent to a population of only 1 0 0 frames, there are twenty-six frames sampled. The smaller sample size i n the former population w i l l , therefore, provide a regression equation l e s s useful f o r predictive purposes than w i l l be obtained from the l a t t e r sample. Data over the Interval 3 2 S X > 2 6 (corresponding to 1 0 2 f i l m frames) was included i n order to supply additional information on run 19 within the drop growth-free zone of 800 frames. Unfortunately, t h i s decision was made a f t e r performing pseudo-radius measurements on run 18 and no further action was taken for t h i s run to match the additional treatment performed on run 1 9 « In thi s section, run 1 9 w i l l be discussed i n two parts: One, for data over i n t e r v a l 2 6 ^ X 2 1 and the other, f o r data over the in t e r v a l 3 2 > X > 1 . Then run 18 i s compared with run 19 over the f i r s t of these i n t e r v a l s . However, in f i t t i n g curves for run 1 9 , the regression equations were obtained from data over the in t e r v a l 3 2 S X S 1 since these same equations n a t u r a l l y apply to the in t e r v a l 2 6 > X ^ 1 except that the value of the equations may be somewhat r e s t r i c t e d within the i n t e r v a l mentioned as already noted. Further remarks concerning t h i s subject w i l l be made l a t e r . 149 Analyzing the upper region 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 (Fig. 40) one can see that, over the i n t e r v a l 2 6 >X > 1 , corresponding to a time i n -terval of from 0 o 0 3 4 sec. to the onset of coalescence, the curve of l i n e 7 0 ° f l a t t e n s out as X tends to 1 . However, the curves of l i n e s 1 0 0 ° and I 3 0 0 slope upwards, but also f l a t t e n out over the l a s t f i v e observation nos. before the onset of coalescence. In other words, between 0 . 0 3 4 sec. and 0 . 0 0 5 4 sec. p r i o r to the start of coalescence the drop interface appears to reach upwards at that segment or region (described by points of inte r s e c t i o n and their v i c i n i t i e s ) where the d i -viding l i n e s 1 0 0 ° and 1 3 0 ° intersect the interface. Within the l a s t few s p l i t seconds (corresponding to about the l a s t f i v e observation nos.) the interface concerned seems to stop i t s motion. Likewise, from X = 2 6 , 0 . 0 3 4 sec. (from Appendix K) to the onset of coalescence, the region of interface crossed by l i n e 7 0 ° appears to 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 lengths of di v i d i n g l i n e s belonging to the upper region of the r i g h t drop i n run 19 (Fig. 41). In the lower region (covered by di v i d i n g l i n e s 2 2 0 ° , 2 5 0 ° , and 280°) of the l e f t drop i n run 1 9 (Fig. 40) over the i n t e r v a l 2 6 > X > 1 , l i n e 2 2 0 ° i s represented by a l i n e a r r e l a t i o n s h i p having a negative slope. The curve of l i n e 2 5 0 ° i s likewise shown to slope downwards and then f l a t t e n out 1 5 0 g r a d u a l l y towards X = 1 while the curve of l i n e 280° i s gene-r a l l y taken t o have zero slope,, i m p l y i n g no dependency r e l a -t i o n s h i p . In the lower r e g i o n of the r i g h t drop i n run 1 9 ( F i g . 41) over the i n t e r v a l 2 6 > X > 1 , the curves of l i n e s 220° and 2 5 0 ° can be c o n s i d e r e d to have no observed depen-dency of Y upon Xo Although both curves appear wavy, the "no 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 c o n s i d e r i n g the r e l a t i v e l a c k of any a p p r e c i a b l e Y changes and ob s e r v i n g t h a t the maximum range of movement of the wavy curve i n the l a t e r a l d i r e c t i o n , i 0 e o , twice t h e i r amplitudes, i s l e s s than the measurement e r r o r or the minimum d i s c e r n i b l e change i n Y which can be measured ( 0 , 0 5 cm. or approximately 0,0016 f t . i n F i g . 41), so t h a t the equations f o r both curves of l i n e s 220° and 2 5 0 ° are " f i t t e d t o the e r r o r s " only, (The same c o n c l u s i o n a p p l i e s a l s o t o the a n a l y s i s of the curve of l i n e 280° i n the l e f t drop,) Line 280° of the r i g h t drop shows no s i g n i f i c a n t changes i n the measurement of i t s l e n g t h . I t must be p o i n t e d out t h a t , whereas c e r t a i n seg-ments of curves 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 e x h i b i t a change i n Y, or pseudo-radius, l e s s than O 0 O 5 cm0 or appro-x i m a t e l y O0OOI6 f t . i n F i g s , 40 and 41, the measurement e r r o r or the minimum d i s c e r n i b l e change i n Y, such segments of curv e s , e 0 g , , t h a t f o r l i n e 145° over the I n t e r v a l 2 6 > X > 1 i n F i g , 41, show a d e f i n i t e o v e r a l l t r e n d towards a h i g h e r Y v a l u e . On the other hand, the o v e r a l l t r e n d of the curves 151 f o r l i n e s 220° and. 250° mentioned i n the pr e c e d i n g paragraph i s towards a f i x e d Y val u e , and i n these cases the d i s p l a c e -ment from t h i s value by the curves over the s p e c i f i e d range of X i s r e l a t i v e l y s m a l l . T h e r e f o r e , l i n e 145° i n t h i s example can reasonably be c o n s i d e r e d t o i n d i c a t e a dependency r e l a t i o n s h i p of Y upon X. The behaviour of the lower r e g i o n s of the drops can be i n t e r p r e t e d p h y s i c a l l y i n a way s i m i l a r to t h a t g i v e n f i v e paragraphs back f o r the upper r e g i o n s . (The lower drop r e g i o n i n c l u d e s l i n e s a t 220°, 250°, and 280° as shown i n P i g . 46, f o r example.) The same goes f o r the r e g i o n s of the drops d e s c r i b e d as the "zone of drop approach", as mentioned i n the succeeding d i s c u s s i o n s . For run 19, the behaviour of the i n t e r f a c i a l r e g i o n i n the zone of drop approach i n the l e f t drop, i s d e s c r i b e d by l i n e s 145°, 155°, 170°, 185°, and 195° i n F i g . 40. The curves f o r l i n e s 145° and 155° i n d i c a t e an upward t r e n d over the i n t e r v a l 26>X>5. At X«=5, the curve of l i n e 145° f l a t -tens out, whereas t h a t of l i n e 155° cont i n u e s upward. 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 170°, 185°, and 195°. For the above-mentioned r e g i o n of the r i g h t drop i n run 19 ( F i g . 41) over the i n t e r v a l 26>XSl, the curve of l i n e 195° can a g a i n be i n t e r p r e t e d s i m i l a r l y t o those of l i n e s 220° and 250° of the r i g h t drop ( a l s o shown i n F i g . 41). 1 5 2 L E G E N D 1 - 70° 6 - 170° 2 - I00„ 7 - 185° 3 - l 3 0 o 8 - 195° 4 - 145. 9 - 2 2 0 o 5 - 155 10 - 250 II - 2 8 0 F i g u r e 46„ Equations f i t t e d over 0 - 2 0 2 f i l m frames and behaviour observed over 0 - 1 0 0 f i l m frames, i n run 1 9 o 153 Thus, there seems t o be no dependency of Y on X f o r l i n e 195° f o r the X range s p e c i f i e d above. L i n e s 155° and 170° are l i -near h aving p o s i t i v e s l o p e s . The curve of l i n e 145° e x h i b i t s an upward trend a t the same time showing a n o t i c e a b l e i n c l i n a -t i o n t o l e v e l o f f as the curve moves toward X = 1. The curve of l i n e 185° i s taken to have zero s l o p e . The marks i n F i g . 46 show the v a r i o u s l o c a t i o n s on the i n t e r f a c e e x h i b i t i n g pseudo-radius changes over the i n -t e r v a l 26>X>1 except f o r l i n e 170° of the r i g h t drop whose a p p l i c a b l e i n t e r v a l i s 26 2 r X > l 4 . I t should be noted t h a t the r e s u l t s shown i n t h i s f i g u r e are d i f f e r e n t from those of F i g . 38 f o r the same run and over the same i n t e r v a l . T h i s d i f f e -rence i s due to the f a c t t h a t F i g . 46 r e l a t e s t o the 26>X>1 segments of curves f i t t e d over a wider time p e r i o d ( c o r r e s -ponding to the i n t e r v a l 3 2 > X 2 l ) than f o r F i g . 38 ( c o r r e s -ponding t o the i n t e r v a l 2 6 > X S l ) . As a r e s u l t , the presence of a l o n g e r term t r e n d was e s t a b l i s h e d than c o u l d be shown i f only twenty-six o b s e r v a t i o n nos. were c o n s i d e r e d f o r curve f i t -t i n g . Observations must be taken over a s u f f i c i e n t range of va l u e s of the independent v a r i a b l e , X, so th a t an e m p i r i c a l curve i s obtained with a shape a t any p o i n t which i s r e l i a b l e f o r p r e d i c t i v e purposes. Such a curve w i l l not be obtained i f an attempt i s made to f i t d a t a taken over a narrow range of X val u e s ( F i g . 38) e s p e c i a l l y i f the data show c o n s i d e r a b l e v a -r i a n c e or repeated v a l u e s i n " c l u s t e r s " (as was the case i n t h i s work). 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 from here on i n -stead of F i g . 38 f o r s t u d i e s p e r t a i n i n g t o the i n t e r v a l 262rX5L 154 A n a l y s i s of the i n t e r f a c i a l r e g i o n s d e s c r i b e d by l i n e s 70°, 1 0 0 ° , 130°, 145°, and 155° i n the l e f t drop and l i n e s 145°, 155°, 170°, I 8 5 0 , 195°, 2 2 0 ° , and 250° i n the r i g h t drop, both of run 19, suggests t h a t over the span 32SX>26, the t r e n d of the segments of the curves concerned i s t o pr o g r e s s towards a h i g h e r value of Y as X-»26. In other words, the i n t e r f a c e s of both drops appear t o bulge a t 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 j u s t men-tioned,, However, changes i n l i n e s 2 2 0 ° , 250°, and 280° i n the l e f t drop of run 19 over the same span seem t o show j u s t the opposite e f f e c t , i . e . , the i n t e r f a c i a l r e g i o n d e s c r i b e d by these l i n e s appear t o recede. For some of the curves the magnitude of the observed t r e n d i s r e l a t i v e l y small so th a t f u r t h e r i n v e s t i g a t i o n i s n e c e s s a r y . For run 1 9 . the response curves that were obtained a t v a r i o u s t e s t l o c a t i o n s on the i n t e r f a c e (through which the d i v i d i n g l i n e s pass) show t h a t over the i n t e r v a l 26>X£;1, the pseudo-radius appears to i n c r e a s e a t some l o c a t i o n s i n the upper r e g i o n . o f both drops ( F i g . 46). With r e s p e c t to the lower p a r t s of the drops, o n l y the l e f t drop experienced any changes, and these took the form of a pseudo-radius de-crease a t two t e s t l o c a t i o n s . One c o u l d surmise from the pre c e d i n g d e s c r i p t i o n t hat the upper and lower r e g i o n s of the l e f t drop e x h i b i t e d movements s i m i l a r t o those a s s o c i a t e d w i t h buoyancy. (See a l s o e a r l i e r d i s c u s s i o n r e g a r d i n g the i n t e r v a l 3 2 S X S 2 6 f o r s i m i l a r behaviour of the upper and lower r e g i o n s of the l e f t drop.) A c c o r d i n g l y , l i n e s 1 0 0 ° and 130° are 155 l e n g t h e n i n g whereas those of l i n e s 220° and 250° are decreas-i n g , c orresponding to the drop moving upwards under the i n -f l u e n c e of buoyancyo On the other hand, one c o u l d expect w i t h c o n s i d e r a b l e j u s t i f i c a t i o n t h a t the combination of i n -c r e a s e s and decreases i n pseudo-radius i s not i n d i c a t i v e of buoyancy but, i n s t e a d , of drop d i s t o r t i o n , . Increase i n the dimensions of some p a r t s of a drop must n a t u r a l l y be o f f s e t by decreases i n other p a r t s , assuming no drop growth. (The absence of any changes i n the upper and lower r e g i o n s of the r i g h t drop over the i n t e r v a l 26 >X>1 could, be due to the use of fewer measuring p o i n t s i n these r e g i o n s compared with the zone of drop approach, thereby o v e r l o o k i n g those r e g i o n s t h a t may e x h i b i t pseudo-radius changes.) Now, however, t h a t i f one c o n s i d e r s a l l the d i v i -d i n g l i n e s of the r i g h t drop i n P i g . 41 (whether over i n t e r -v a l s 26>X>1, 32>X>26, or 32>X>1), no evidence of pseudo-r a d i u s decrease i s present, and, i n f a c t , the l e n g t h s of a l l p s e u d o - r a d i i are e i t h e r i n c r e a s i n g or remaining c o n s t a n t . The i n c r e a s e i n drop s i z e cannot be due to drop growth, e s p e c i a l -l y s i n c e f o r 32^XS1, a mere 202 f i l m frames have been used out of a p o s s i b l e span of 800 drop-growth f r e e frames. In f a c t , the r a t e of change of pseudo-radius i n F i g . 41 i s about an order of magnitude g r e a t e r than the average v o l u m e t r i c growth r a t e . The t o t a l absence of any decreases i n pseudo-r a d i i may be accounted f o r by three f a c t o r s , a c t i n g alone or i n combination: 156 1. drop r e g i o n s e x h i b i t i n g decreases i n pseudo-r a d i u s were not considered, i n the measurements, 2 . drop volume i n c r e a s e d due to p o s s i b l e " s p r i n g " i n the system, and 3° drop was o s c i l l a t i n g . Item 2 and/or 3 c o u l d e x p l a i n the very r a p i d growth r a t e . By ,'!spring" i n the system i s meant, not that the flow r a t e was suddenly i n c r e a s e d , but, r a t h e r , t h a t , as the r e s u l t of a decreased pressure i n the d i s p e r s e d phase volume, changes w i t h i n the system e n c l o s i n g the d i s p e r s e d phase r e -s u l t e d i n l i q u i d being "squeezed out" i n t o the drops. The d i s p e r s e d phase pressure i n s i d e the l i n e s l e a d i n g to the g l a s s n o z z l e would f a l l as the drop r a d i i i n c r e a s e d , the r e l a t i o n - * s h i p being, f o r a s p h e r i c a l drop, (11) r where A p = pressure d i f f e r e n c e between the drop (Pg) and the continuous phase ( P j ) , given byAP = P^ - P^, dyne/cm. 2 d - i n t e r f a c i a l t e n s i o n , dyne/cm. r = drop r a d i u s , cm. S i m i l a r l y , r e d u c t i o n i n i n t e r f a c i a l t e n s i o n a l o n g the drop p e r i p h e r y would a l s o r e s u l t i n a l o w e r i n g of the pressure w i t h i n the l i n e . Then, f o r example, i f an a i r bubble was trapped i n the l i n e , t h i s would expand as the pressure der creased or, i f the t u b i n g was r e l a t i v e l y f l e x i b l e , the r e -d u c t i o n i n pressure would a l l o w the t u b i n g w a l l s to c o n t r a c t 157 on the l i q u i d c o n t e n t s . E i t h e r mechanism would r e s u l t i n the "squeezing out" of l i q u i d toward the n o z z l e t i p s and, t h e r e f o r e , i n t o the drops. ( I t should be noted t h a t i n the p r e s e n t work, n y l o n t u b i n g was used. T h i s i s more f l e x i b l e than g l a s s or metal t u b i n g , c e r t a i n l y , but much l e s s so than, f o r example, rubber.) I f the drop were o s c i l l a t i n g ( f a c t o r 3 above), the drop c o u l d move i n a manner such t h a t the i n c r e a s e i n pseudo-r a d i u s as viewed i n e l e v a t i o n was balanced by a c o r r e s p o n d i n g decrease i n pseudo-radius as viewed i n p l a n . The p i c t u r e s o b t a i n e d i n t h i s work were e l e v a t i o n views, and, t h e r e f o r e , no i n f o r m a t i o n on behaviour i n p l a n i s a v a i l a b l e . However, no o s c i l l a t i o n s were apparent when the movie f i l m of run 19 was viewed a t a p r o j e c t i o n r a t e of 16 pps. (The number of frames observed before coalescence was about 900 ; i t w i l l be r e c a l l e d t h a t only the f i n a l 202 of these were measured. ) The f i l m s f o r run 15 (where the s o l u t e i s a c e t i c a c i d ) and f o r run 18 were p r o j e c t e d s i m i l a r l y . (A t o t a l of 2000 and 1500 frames r e s p e c t i v e l y were viewed i n these runs.) I t must be borne i n mind t h a t the f i g u r e s of 1500 and 900 frames p r i o r t o coalescence mentioned here are not n e c e s s a r i l y p r o p o r t i o n a l t o time p r i o r t o coalescence s i n c e these frames were exposed w h i l e the camera was b u i l d i n g up to i t s set speed (5000 pps). No o s c i l l a t i o n p a t t e r n s were observed a l s o . T h e r e f o r e , with a f a i r degree of c e r t a i n t y , the i n c r e a s e i n drop s i z e noted i n F i g . kl c o u l d not be due to o s c i l l a t i o n . 158 The Smith (12) and Groothuis and Zuiderweg (13) hypothesis predicts that, f o r solute t r a n s f e r r i n g out of the drops, the lowering of the i n t e r f a c i a l tension at the zone of drop approach would r e s u l t i n the stretching of the i n t e r -face at t h i s zone. In addition, i t i s believed that f o r the present work, as water i s swept out from between the drops during the process of coalescing (solute transfer out of the drops), and i n the absence of drop growth, these drops may reach out toward one another to f i l l the void. (The drops cannot move f r e e l y , being attached to the glass tubes. ) Also, with low i n t e r f a c i a l tension at the zone of drop ap-proach, the drops may bulge toward one another because of weak surface forces. ( I n t e r f a c i a l tension tends to hold drop contents i n . If i n t e r f a c i a l tension i s weakened l o c a l -l y , the drop should bulge at that point. For the same ex-t r a c t i o n condition (transfer out of the drops) t h i s l a s t mechanism may operate even i n the Smith (12) case where the drops were free to move about i n the continuous medium.) The incidence of pseudo-radius changes i s l e s s among the regions examined i n the ri g h t drop than i n the l e f t drop (Figs. 38, 39. and 46). This behaviour may have a d i r e c t bearing on the t o t a l lack of pseudo-radius decreases i n the ri g h t drop of run 19 (extended) (Fig. 41). 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 to behave simi-l a r l y at any given instant (although i t should be borne i n mind that there was apparent emuls i f i c a t i o n i n the r i g h t drop i n run 19). Thus, the sets of pseudo-radius data f o r the l e f t 159 and the r i g h t drops are e s s e n t i a l l y d u p l i c a t e s . T h e r e f o r e , by a v e r a g i n g them, i t i s p o s s i b l e t o minimize the " s t r a y " e f f e c t s t h a t can a r i s e i f only the measurements made on one of the drops i s c o n s i d e r e d . (Such " s t r a y " e f f e c t s can, f o r example, be due to the d i f f i c u l t y of determining small pseudo-r a d i u s d i f f e r e n c e s . ) The average increment i n pseudo-radius, A Y , then 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 w i t h o b s e r v a t i o n number s e r v i n g as the parameter ( F i g . 47). ( D i v i d i n g l i n e 170° was not co n s i d e r e d due to incomplete d a t a . ) In d e t a i l , A Y ' v a l u e s were determined from F i g . 40 ( l e f t drop) f o r each d i v i d i n g l i n e by s u b t r a c t i n g the pseudo-r a d i u s a t o b s e r v a t i o n no. 32 from the pseudo-radius a t a chosen observation, number (see F i g . 47). Corresponding v a l u e s of A Y ' were ob t a i n e d from the r i g h t drop by use of F i g . 41. Then the value obtained f o r each drop a t the same d i v i d i n g l i n e and the same o b s e r v a t i o n number are added together and d i v i d e d by 2. The r e s u l t i s an average v a l u e , A Y i n F i g . 47. For example, i n d i v i d i n g l i n e 145° i n the l e f t drop ( F i g . 40), the pseudo-radius a t o b s e r v a t i o n nos. 32 and 1 are 0.1200 f t . and 0.1235 f t . r e s p e c t i v e l y . S u b t r a c t i n g 0.1200 f t . from 0.1235 f t . g i v e s O . O O 3 5 f t . S i m i l a r l y , i n d i v i d i n g l i n e 145° i n the r i g h t drop ( F i g . 41), the cor r e s p o n d i n g values are 0.1233 f t . and 0.1264 f t . , g i v i n g 0.0031 f t . as the d i f f e r e n c e . Adding O . O O 3 5 f t . and 0.0031 f t . t o g e t h e r and d i v i d i n g the sum by 2 equals O .OO33 f t . ( A Y ) . T h i s value of A Y i s then marked down on F i g . 47 along the a b s c i s s a a t d i v i d i n g l i n e 145°, f o r the o b s e r v a t i o n no. 1. (Note t h a t the numerical 60 80 100 120 140 160 180 200 220 DROP DIVIDING LINE , deg. 240 260 280 Figure 47 <> Change i n drop shape i n run 19 as the time of coalescence approaches, averaged for the two drops,, (Total magnification of / \ Y equals 24x.) 161 v a l u e s quoted here a l l are 24 times the a c t u a l s i z e s of the p h y s i c a l system since they i n c l u d e the m a g n i f i c a t i o n f a c t o r p r e s e n t i n F i g s . 40, 41, and 47.) Thus F i g . 47 i n d i c a t e s the average change i n shape of both drops as they approach each other and proceed toward coalescence, s t a r t i n g from 202 frames b e f o r e the onset of coalescence a t an o r d i n a t e of z e r o . T h i s graph i n d i c a t e s t h a t the drops p r o g r e s s i v e l y reach out toward one another i n the r e g i o n d e s c r i b e d by l i n e s 145° and 155°» r e a c h i n g a h i g h p o i n t a t l i n e 145° as the o b s e r v a t i o n no. 1 i s reached. T h i s behaviour i s found to be c o n s i s t e n t , a t l e a s t , with the Smith (12) and Groothuis and Zuiderweg (13) h y p o t h e s i s s i n c e the bulge may w e l l be due to a l o w e r i n g of i n t e r f a c i a l t e n s i o n i n the zone of drop approach. One i n t e r e s t i n g p o i n t i n the a n a l y s i s of run 19 i s the mutual p a r a l l e l i s m of most curves whose d i v i d i n g l i n e s are a d j a c e n t to each o t h e r . Thus, l i n e s 100°, 130°, and 145° i n the l e f t drop ( F i g . 40) are approximately p a r a l l e l and so are l i n e s 185° and 195° ( F i g . 41), l i n e s 220° and 250° ( F i g . 41), e t c . Given t h a t l i n e s 185° and 195°» f o r example, l i e side by si d e i n such f i g u r e s as 38, 39« and 46, then i t i s reasonable to assume that l i n e s i n the v i c i n i t y of these two l i n e s e x h i b i t s i m i l a r c h a r a c t e r i s t i c s . For t h i s reason, the behaviour of those two p o i n t s i n the drop i n t e r f a c e where l i n e s 185° and 195° Pass can be extended to i n c l u d e the e n t i r e i n -t e r f a c i a l segment bounded by these two l i n e s p l u s a reason* a b l e p o r t i o n on each si d e o u t s i d e the boundaries of the seg-ment. G e n e r a l l y speaking, one can reasonably speak of a " r e -162 g i o n " or "segment" i n s t e a d of " p o i n t s " where c e r t a i n drop pseudo-radius changes might occur so l o n g as the v a r i o u s i n -t e r f a c i a l " p o i n t s " e x h i b i t i n g such behaviour have one common movemento A l l the curves of P i g s . 40 and 41, except f o r those f o r l i n e s 155° and 220° i n the l e f t drop and f o r l i n e 155° i n the r i g h t drop, appear to approach zero slope a t l e a s t w i t h i n the l a s t few s p l i t seconds before the s t a r t of coalescence., ( w i t h i n approximately the l a s t 5 o b s e r v a t i o n n o s . ) . In other words, the drops e x h i b i t no s i g n i f i c a n t changes i n t h e i r pseudo-radius over much of t h e i r I n t e r f a c e s near the p o i n t of c o a l e s c e n c e . The reason f o r t h i s behaviour may be q u i t e s i g -n i f i c a n t ; however, the reasons f o r i t are not understood. In run 18, o n l y l i n e s 100° and 145° i n the r i g h t drop, out of a p o s s i b l e of twenty measured l i n e s i n both drops, show s i g n i f i c a n t changes i n pseudo-radius over the i n t e r v a l 2 6 S X S 1 ( F i g . 37) • A l s o , the f a c t t h a t d i f f e r e n t behaviour i s encountered when the range of X i s extended as i n run 19 ( F i g . 46 as compared to F i g . 38) c a s t s some doubt on the r e s u l t s f o r run 18 ( P i g . 37) f o r which only the l i m i t e d range of X was c o n s i d e r e d . T h i s unfortunate behaviour was not a n t i c i p a t e d i n the e a r l i e r p a r t of the work so t h a t no measure-ments were taken beyond X = 26 i n run 18. T h e r e f o r e , because of a l l these d i f f i c u l t i e s , n e i t h e r w i l l any attempt be made to e l a b o r a t e on the r e s u l t s o b tained f o r run 18, nor w i l l any comparison, of run 18 and run 19 be made wit h r e s p e c t to the 163 e f f e c t of s o l u t e c o n c e n t r a t i o n on pseudo-radius. Likewise, the p l o t s of the f i t t e d curves f o r l i n e s 100° and 14-5° f o r the r i g h t drop of run 18 are not shown. C o P r e c i s i o n of Drop A n a l y s i s The experimental e r r o r s i n v o l v e d i n t h i s work are obtained mainly from pseudo-radius measuring methods. In most cases, the main data r e v e a l e d only three d i s t i n c t v a l u e s of Y obtained over the i n t e r v a l 32 2 X S 1 . Each of these three v a -l u e s i s d i f f e r e n t from the next one by 0 . 0 5 cm. (about 0.0016 f t . ) ? the minimum d i s c e r n i b l e d i f f e r e n c e i n l e n g t h that c o u l d be measured by present methods. (Of course, the value, 0 . 0 5 cm., was obtained, a t a p r i n t m a g n i f i c a t i o n of approximately 24X). Thus, the e r r o r i n measuring a d i v i d i n g l i n e i s taken t o be i o . 0 5 cm. T h i s e r r o r arose because the o u t l i n e of the drops was not sharp enough to enable more accurate measurements to be made. The g r a i n y image p r i n t e d was a r e s u l t of p i c t u r e e n l a r g i n g . C u t t i n g down on the m a g n i f i c a t i o n would not produce a b e t t e r r e s u l t s i n c e the s i z e of the p r i n t e d image would be reduced, with the r e s u l t t h a t i t would become harder to measure s i z e changes i n i t . Another source of e r r o r r e s u l t s from the process of superimposing the master sheet over every p r i n t t h a t i s b e i n g measured. The r e f e r e n c e p o i n t s P' and P" (e.g., i n F i g . 39 )s which are drawn on the master sheet, must always l i e on the corresponding spots i n every p r i n t s i n c e the l e n g t h s of the d i v i d i n g l i n e s are measured from these p o i n t s . 164 B l u r r e d spots e x i s t i n c e r t a i n areas of the p r i n t s of runs 18 and 19» as mentioned e a r l i e r . (These were due to the n o n - f l a t n e s s of the n e g a t i v e d u r i n g the p h o t o e n l a r g i n g p r o c e s s . ) The b l u r r e d spots c o n t r i b u t e to l o s s of sharpness of image over the a f f e c t e d r e g i o n s . When these r e g i o n s over-l a p the drop o u t l i n e , measurements are n a t u r a l l y a f f e c t e d . As mentioned e a r l i e r , the m u l t i p l e c o e f f i c i e n t of 2 d e t e r m i n a t i o n , R , measures the " p r o p o r t i o n of t o t a l v a r i a t i o n about the mean Y e x p l a i n e d by the r e g r e s s i o n " . From Eq. (9), 2 v a l u e s of R c l o s e to u n i t y are t h e r e f o r e d e s i r a b l e s i n c e a value of, say, 0.9 means t h a t the r e g r e s s i o n e q u a t i o n obtained e x p l a i n s 90$ of the t o t a l v a r i a t i o n , when expressed as a p er-centage. However, there i s a e s p e c i a l danger i n t h i s meaning 2 s i n c e R can be made u n i t y simply by employing a c e r t a i n number of p r o p e r l y s e l e c t e d c o e f f i c i e n t s ' i n the model since a model can then be chosen which f i t s the data e x a c t l y . For example, i f we have an o b s e r v a t i o n of Y a t f o u r d i f f e r e n t v a l u e s of X, a t h i r d - o r d e r polynomial model such as Eq (5) where m = 3 Passes e x a c t l y through a l l f o u r p o i n t s . In Table XII which shows the d i f f e r e n t p r e d i c t i v e equations f o r v a r i o u s d i v i d i n g l i n e s i n runs 18 and 19, the value of R f o r each l i n e i s a l s o i n c l u d e d . The v a l u e s range from a low of 0.5481 to a h i g h of 0.9323° The e q u a t i o n f o r which an R 2 value of 0.5481 was de-r i v e d , f o r example, shows t h a t i t i s b a s i c a l l y a l e s s u s e f u l p r e d i c t o r as compared to t h a t e q u a t i o n having R^ equal to 0.9323° g i v e n t h a t the number of parameters i n each model i s not c l o s e to the s a t u r a t i o n p o i n t ( i . e . , the number of obser-165 v a t i o n s ) . A more complex model, other than the one used, c o u l d provide an adequate a l t e r n a t i v e to o b t a i n a h i g h e r 2 value of R , assuming, of course, t h a t the m u l t i p l e r e g r e s -s i o n program had p r o v i d e d the "best" e q u a t i o n from the a v a i l -a b l e modelo As w e l l , a s t a t i s t i c a l t e s t f o r " l a c k of f i t " to determine i f the p o s t u l a t e d model i s i n c o r r e c t , or s u f f e r s 2 from l a c k of f i t , c o u l d be made to a s s e s s R , p r o v i d e d repeat measurements of the dependent v a r i a b l e , Y, i . e . , two or more measurements, are a v a i l a b l e a t the same value of the indepen-dent v a r i a b l e , X, to o b t a i n an estimate of the v a r i a n c e , (f ( 4 4 ) . By "repeat measurements", when mentioned anywhere i n t h i s t h e s i s , i s meant a genuine repeated run and not j u s t r e p e t i t i o n s of the measurement of Y a t the same value of X. However, the r e q u i r e d data are not a v a i l a b l e i n t h i s work. A c r i t e r i o n f o r s e l e c t i n g the proper p r e d i c t i v e e q u a t i o n having the "best s e t " of X terms among an a r r a y of d i f f e r e n t equations presented i n the computer p r i n t o u t s of the m u l t i p l e r e g r e s s i o n program i n v o l v e s the c o n s i d e r a t i o n of the v a l u e s of R and the r e s i d u a l v a r i a n c e g i v e n by the pro-gram. This program, i n c i d e n t a l l y , i s p r i m a r i l y designed to handle as many as 70 v a r i a b l e s ( i n c l u d i n g transformed and c a l -c u l a t e d v a r i a b l e s ) any of which can be s e l e c t e d as the depen^ dent v a r i a b l e . In the p r e s e n t problem a f o u r t h - o r d e r polyno-m i a l w i t h one independent v a r i a b l e was chosen to provide the h i g h e s t - o r d e r e d polynomial handled. The v a r i o u s polynomial e q u a t i o n s t h a t were c a l c u l a t e d by the program were obtained by the method of l e a s t squares. I t i s the same method as that 166 used by the l i b r a r y s u b r outine, "UBC LQF", which was p r e v i o u s -l y a p p l i e d on the l i n e a r model. As p o i n t e d out e a r l i e r , t h i s p a r t i c u l a r program has the advantage of p r o v i d i n g the user an adequate s e l e c t i o n of v a r i o u s models or equations computed from good p o s s i b l e combinations of X terms. From these equa-t i o n s , the r e l a t i v e v a l u e s of E r and of r e s i d u a l v a r i a n c e are s t u d i e d , and an equation i s f i n a l l y s e l e c t e d to be c o n s i d e r e d as having the most important terms i n c l u d e d . For each r e g r e s s i o n a n a l y s i s (Appendix M), the f o l -l o w i n g i n f o r m a t i o n i s p r o v i d e d : 1. the code name of the v a r i a b l e s i n the subset f o r r e g r e s s i o n a n a l y s i s , 2. r e g r e s s i o n c o e f f i c i e n t s , 3 . standard d e v i a t i o n s of the r e g r e s s i o n c o e f f i -c i e n t s , 4. a v a r i a n c e r a t i o ("F" value) f o r each X term i n the e q u a t i o n , 5. i n t e r c e p t (constant term), 6. standard e r r o r of estimate, 7. r e s i d u a l v a r i a n c e , 8 . m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t (R), 9» m u l t i p l e c o e f f i c i e n t of d e t e r m i n a t i o n (R ), and 10. a v a r i a n c e r a t i o ("F" v a l u e ) f o r the m u l t i p l e r e g r e s s i o n , with the a p p r o p r i a t e degrees of freedom. 167 Some of these terms are I n t e r r e l a t e d . The standard e r r o r of estimate (item 6) i s the square r o o t of the r e s i d u a l v a r i a n c e (item 7-), while the r e l a t i o n of item 8 to item 9 i s obvious. A c r i t e r i o n f o r s e l e c t i o n of the "best" r e g r e s s i o n equation among the l o t was e a r l i e r mentioned to be based on item 6 or 7 and item 9« As.:.well, the v a r i a n c e r a t i o (item 1 0 ) c o u l d be taken i n t o c o n s i d e r a t i o n . However, i n te'sting the g e n e r a l h y p o t h e s i s t h a t a l l p a r t i a l r e g r e s s i o n c o e f f i c i e n t s are equal to zero, one can use e i t h e r of "F" (variance r a t i o ) or R 2 ( m u l t i p l e c o e f f i c i e n t of d e t e r m i n a t i o n ) ( 5 2 ) . Because of the e x t r a i n f o r m a t i o n about the p r o p o r t i o n of sum of squares accounted f o r by the e q u a t i o n gained by the use of R 2, t h i s term i s p r e f e r r e d i n s t e a d of "F" 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 . As p o i n t e d out e a r l i e r , g i v e n that the number of s e t s of o b s e r v a t i o n s , n, i s much g r e a t e r than the number of potential (n - 1) powers of the X v a r i a b l e i n the polynomial model under c o n s i d e r a t i o n (Eq. ( 5 ) ) . the a d d i t i o n of a new power of X w i l l p always i n c r e a s e R u n t i l the number of parameters i n the model equals n and the polynomial passes through a l l data p o i n t s , p R can, t h e r e f o r e , be made u n i t y without 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 use of a polynomial model up to the f o u r t h power of X (Eq. ( 5 ) , where m = 4 ) was c o n s i d e r e d to be s u f f i c i e n t t o c l o s e l y approximate the e x i s t i n g r e l a t i o n s h i p p r o v i d e d the model i s adequate and the program has p r o p e r l y s e l e c t e d the " b e s t " r e g r e s s i o n e q u a t i o n . Other-wise, an a l t e r n a t i v e model may have t o be used. 168 The procedure f o l l o w e d i n a r r i v i n g a t a d e c i s i o n as to what p a r t i c u l a r form of the polynomial model i s most a p p r o p r i a t e i s to f i n d t h a t arrangement whose a n a l y s i s p r o v i d e s the best combination of the X terms having a high R (R 0 . 5 ) a t the lowest p o s s i b l e value of the r e s i d u a l v a riances S ( a l s o c a l l e d the sample v a r i a n c e ) . 1 6 9 CONCLUSIONS AND RECOMMENDATIONS In the present work, drop pseudo-radius changes were measured as a means of attempting to throw l i g h t on the coalescence mechanism of drop p a i r s i n a spray column. Just b e f o r e the onset of coalescence, the drops were found to un-dergo shape changes. The v a r i a t i o n s observed i n the pseudo-r a d i o s oover t h a t p o r t i o n of the i n t e r f a c e i n the upper p a r t of the zone of drop approach i n d i c a t e t hat the drops tend to reach out toward one another perhaps as a r e s u l t of l o c a l l y lowered i n t e r f a c i a l f o r c e s . The behaviour was c o n s i s t e n t with the hypothesis of Smith ( 1 2 ) and of Groothuis and Zuiderweg ( 1 3 ) . The time i n t e r v a l c o n s i d e r e d i n t h i s work was mea-sured backward from the i n s t a n t when the two drops began to c o a l e s c e . T h i s i n t e r v a l was covered by o b s e r v a t i o n nos. 2 6 to 1 , e q u i v a l e n t to a t o t a l time of about 0 . 0 3 4 sec. Over t h i s i n t e r v a l , the magnitude of i n t e r f a c i a l movements charac-t e r i z e d by an i n c r e a s e of pseudo-radius i n v a r i o u s l o c a t i o n s on the i n t e r f a c e was g e n e r a l l y g r e a t e r i n the l e f t drop. Drop pseudo-radius measurements were a l s o c a r r i e d out i n run 1 9 over the X i n t e r v a l 3 2 t o 2 6 . T h i s was an a u x i l i a r y study and not a complete i n v e s t i g a t i o n over t h i s i n t e r v a l . For t h i s reason, the data were l e s s l i k e l y to y i e l d c o n c l u s i v e r e -s u l t s than were those obtained over the o t h e r i n t e r v a l . None-t h e l e s s , the a u x i l i a r y data i n d i c a t e d the presence of drop shape v a r i a t i o n s . 170 A d d i t i o n a l work must f i r s t be done i n the area i n which i n v e s t i g a t i o n was c o n c e n t r a t e d b e f o r e the r e s u l t s c o u l d be taken to be f i r m l y c o n c l u s i v e 0 For example, the f o r c e s i n f l u e n c i n g the observed drop shape v a r i a t i o n s are not yet f u l l y understood. A l s o , i n view of the small changes observed i n some of the v a r i o u s p s e u d o - r a d i i measured, and the need to a p p l y s t a t i s t i c a l t e s t s to see how the curves t r e n d , * 6 r e p l i -c a t e s , say, are needed f o r each experiment. Then c o n s i s t e n c y c o u l d be t e s t e d between curves, f o r example, those f o r the 145° l i n e of a drop i n the 6 r e p l i c a t e experiments. In a d d i -t i o n , the f o l l o w i n g suggestions w i t h i n the framework of the c u r r e n t r e s e a r c h are o f f e r e d : 1. Determination of the e f f e c t s of drop growth and buoyancy upon drop shape, without the i n f l u e n c e of mass t r a n s f e r , over an i n t e r v a l t h a t s u f f i -c i e n t l y covers the e n t i r e response time of the h y p o t h e t i c a l coalescence mechanism advanced by Smith (12) and Groothuis and Zuiderweg (13). Such a study would, once and f o r a l l , provide the r i g h t amount of c o r r e c t i o n due to a l l i n c i -d e n t a l f o r c e s a f f e c t i n g drop shape other than those e x e r t e d by mass t r a n s f e r o Of course, an e x c e l l e n t p r o p o s i t i o n would be to use a system f o r which the d e n s i t i e s of the two phases were equal, and constant with time ( i . e . , when mass * See e a r l i e r comments under Topic C, DISCUSSION on need f o r t e s t i n g " l a c k of f i t " f o r any assumed model t h a t may have a low v a l u e . 1 7 1 t r a n s f e r was o c c u r r i n g ) , so as to e l i m i n a t e the f o r c e s due to buoyancy. However, such a system would be hard to f i n d . 2 . A study of drop shape behaviour c a r r i e d on over a time i n t e r v a l l o n g e r than t h a t used i n the present r e s e a r c h so as to determine the form of any long-term i n t e r f a c i a l move-ments which might have been missed over the short-time i n t e r v a l used i n the present study. T h i s p r o p o s a l can be a p p l i e d to the remaining unmeasured p o r t i o n s of the f i l m s concerned. I t may be n e c e s s a r y a l s o to de-v i s e a method of determining the exact frame span t h a t i s drop growth-free more a c c u r a t e l y than i s p o s s i b l e by the s u b s t i t u t i o n of a sphere f o r a drop i n making the c a l c u l a t i o n . 3. I t would be i n t e r e s t i n g to determine how the drop shape i s d i s t o r t e d o p t i c a l l y ( i f a t a l l ) as a consequence of the e x i s t e n c e of a r e f r a c -t i v e index g r a d i e n t i n the continuous phase i n the p r e s e n t work. T h i s proposed study c o u l d be c a r r i e d out perhaps by the use of s o l i d spheres i n p l a c e of drops so t h a t the shape remains c o n s t a n t . The spheres should p o s s i b l y be porous so as to permit the r e l e a s e of s o l u t e m a t e r i a l which c o u l d e n t e r each sphere through a bored passage. A l s o , measurements c o u l d be made of any c o n t r i b u t i o n to o p t i c a l d i s t o r t i o n by the square g l a s s column as a r e s u l t of non-p a r a l l e l i s m of w a l l s and/or g l a s s i m p e r f e c t i o n s (e.g., s t r i a t i o n s ) . 4 . Reduction i n the r e a d i n g and measuring e r r o r s , as o u t l i n e d e a r l i e r i n the d i s c u s s i o n . 5 » The search f o r a t e r n a r y system t h a t would f u r t h e r i n c r e a s e the i n t e r f a c i a l t e n s i o n Imbalance t h a t , a c c o r d i n g to the theory proposed by Smith ( 1 2 ) and Groothuis and Zuiderweg ( 1 3 ) , t r i g g e r s i n t e r f a c i a l motion. The use of t h i s system would h o p e f u l l y r e s u l t i n i n t e r f a c i a l movements r e l a t i v e l y g r e a t e r i n magnitude than those a t t a i n e d i n the present work. Then any important behaviour t h a t may have passed undetected so f a r might be r e v e a l e d . Such a t e r n a r y system must have p h y s i c a l p r o p e r t i e s s u i t e d to the p a r t i c u l a r requirements of the r e s e a r c h work, as, indeed, the MIBK-methanol-water system d i d , a t l e a s t i n some r e s p e c t s . 6. The study of the changes i n the pseudo-radius a t other c r o s s - s e c t i o n s of the drop t o determine the e n t i r e drop shape c h a r a c t e r i s t i c s . T h i s suggestion c o u l d imply f u r t h e r complete experiments. However, f u r t h e r simple steps 1 7 3 c o u l d be taken with use of the f i l m s obtained i n the present study. These c o u l d be used to p r o v i d e f u r t h e r pseudo-radius measurements a l o n g other d i v i d i n g l i n e s than those measured so f a r . 7 . Replacement of the n y l o n t u b i n g t h a t served as the d i s p e r s e d phase l i n e with a more r i g i d m a t e r i a l (e.g., s t a i n l e s s s t e e l ) t o prevent the p o s s i b i l i t y of " 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 with the opposite d i r e c t i o n of s o l u t e t r a n s f e r , i . e . , from the continuous to the d i s p e r s e d phase t o see whether or not the behaviour would be c o n s i s t e n t w i t h the h y p o t h e s i s r e f e r r e d t o e a r l i e r ( 1 2 , 1 3 ) . 9« A device f o r producing metered drops of equal s i z e s s i m u l t a n e o u s l y would r e s u l t i n the g e n e r a l improvement of the experiments. 174 LITERATURE CITED 1. Thomson, J., P h i l , Mag., 10,' Ser. 4 , 3 3 0 (1855). 2. Sternling, CV. and Scriven, L.E., Nature, 187. 186 (I960). 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 ( 1 9 5 2 ) . 5» Sigwart, K. and Nassenstein, H., Naturwissenschaften, 42, 458 (1955). 6. Sigwart, K. and Nassenstein, H., Ver Deut. Ing. Zeit., 28, 453 ( 1 9 5 6 ) . 7. Nassenstein, H. and Kraus, W., Chem. Ing. Tech., 28, 220 ( 1 9 5 6 ) . 8. 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November. 1965. 260 R o c c h i n l , R.J., M.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, 1961. 27° Stecher, P.G. (Ed.), The Merck Index, p. 671, 1117. 6, 8th E d i t i o n , Merck and Co., Inc., N.J., 1968. 28. Cheronis and E n t r i k i n , Chem. and Eng. News, 22, 2 0 08 (1955). 29o B r i t i s h Pharmacopoeia, pp. 41-42, The Pharmaceutical Press, London, 1948. 30. G o l t z , G.E., J . Imp. C o l l . Chem. Eng. S o c , 12, 40 (1958/9). 31. Sawistowski, H. and G o l t z , G.E., Trans. I n s t . Chem. Engrs. (London), 41, 174 (1963). 32. Barry, F.W. and Edelman, G.M., J . A e r o n a u t i c a l S c i . , 15. 364 (1948). 33* Holder, D.W., Thomson, J.S., and Macphail, D.C., Modern  Developments i n F l u i d Dynamics - High Speed Flow. Chapter XI, Oxford U n i v e r s i t y P r e s s , Oxford, 1953• 34. T a y l o r , H.G. and Waldrum, J.M., J . Sc. Inst.,10,378(1933). 35. Bakker, C.A.P., van Buytenen, P.M., and Beek, W.J., Cheiru, Eng. 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Weber, R.L., White, M.W., and Manning, K.V., College  P h y s i c s , p. 6 4 5 , 6 4 4 , 2nd E d i t i o n , McGraw-Hill Book Co., New York, 1952. 5 2 . Kozak, A., Research Notes. F a c u l t y of F o r e s t r y , The U n i v e r s i t y of B r i t i s h Columbia, No. 57, A p r i l 1966. 177 53- Timmermans, J o , Physico-chemical Constants of Pure Organic  Compounds, p. 273. V o l I I , E l s e v i e r Publ. Co., Inc., Amsterdam, 195°» I b i d . . p. 152, Vol I. 55» Pe r r y , J.H. (Ed.), Chemical E n g i n e e r s ' Handbook, p. 3 6 3 , 3rd E d i t i o n , McGraw-Hill Book Co., New York, 1950. 5 6 . Brinsmade, D.S. and B l i s s , H., Trans. Am. I n s t . Chem. Engrs., 22., 679 (1943). A - l APPENDIX A Determination of 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 the D i s p e r s e d Phase The t i t r a t i n g procedures used f o r d e t e r m i n i n g the c o n c e n t r a t i o n of a c e t i c a c i d present i n the d i s p e r s e d phase composed of w a t e r - s a t u r a t e d MIBK were those of S w i f t (24). These procedures c o n s i s t of t i t r a t i n g each sample with c a r -bonate-free O o l N sodium hydroxide s o l u t i o n and u s i n g phe-n o l p h t h a l e i n i n d i c a t o r . The o p e r a t i n g methods are common and need not be mentioned here. The n o r m a l i t y of the prepared carbonate-free sodium hydroxide s o l u t i o n was determined by s t a n d a r d i z i n g the hydro-xide s o l u t i o n a g a i n s t potassium h y d r o p h t h a l a t e . The n o r m a l i t y was c a l c u l a t e d to be 0.097 N. A s u i t a b l e amount of SDAG-1K mixture was added to each ketone-dominated sample to p r o v i d e a homogeneous, s i n g l e phase as the sample was t i t r a t e d . The end p o i n t c o u l d then be determined e a s i l y (or much more e a s i l y than would have been true i f two phases had been p r e s e n t ) . (SDAG-1K mixture i s made i n d u s t r i a l l y by mixing 100 g a l l o n s of dehydrated e t h y l a l c o h o l w i t h 5 g a l l o n s of dehydrated methyl a l c o h o l . ) T i t r a t i o n data are shown i n Table A - l . A - 2 Table A - l . T i t r a t i o n Data Run No, Volume of Volume of Sample, SDAG-1K ml. added, ml, Volume of NaOH used, ml. For Sample For Blank 8 9 10 11 12 13 14 15 5 5 15 15 15 15 5 5 25 25 25 25 50 50 75 25 46 .78 45.40 23.46 23-46 15o73 1 5 . 5 0 4 3 . 0 0 4 4 . 1 7 46.63 45 .30 23.60 23.60 15.80 15.60 43.20 44.40 0 . 1 0 0 . 0 9 0.17 0.17 0 . 2 0 0 . 2 0 0 . 2 0 0 . 1 0 0 . 0 9 0 . 0 9 0.16 0.16 0 . 2 0 0 . 2 0 0 . 2 0 0 . 1 0 B - 1 APPENDIX B Determination of 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 Methanol c o n c e n t r a t i o n i n the 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 r e f r a c t i v e index to composition. A c a l i b r a t i o n p l o t ( F i g . B - l ) was c o n s t r u c t e d by determining the r e f r a c t i v e index, through the use of the Abbe r e f r a c t o m e t e r , C h o E o 2 4 4 7 . of each w a t e r - s a t u r a t e d MIBK sample o f known me-t h y l a l c o h o l c o n c e n t r a t i o n . (The Abbe r e f r a c t o m e t e r was p r e -v i o u s l y a d j u s t e d a c c o r d i n g to the i n s t r u c t i o n s s u p p l i e d w i t h the instrument.) The methanol composition of each unknown sample i s then determined d i r e c t l y from the smooth l i n e drawn through the p o i n t s i n t h i s p l o t . The s t r a i g h t l i n e was f i t t e d by the method of l e a s t squares. The method to o b t a i n the e x a c t c o n c e n t r a t i o n of each sample to be used i n the c a l i b r a t i o n p l o t was as f o l l o w s . A known amount of MIBK was p i p e t t e d i n t o a thoroughly cleaned and d r i e d f l a s k and i n t o i t was mixed an e q u a l l y known volume of methanol. D i s t i l l e d water was then added i n t o the homoge-neous mixture from a b u r e t t e , drop by drop, while s w i r l i n g the mixture c o n s t a n t l y u n t i l a new phase appeared. When i t was c l e a r t h a t the s e p a r a t i o n of phases would p e r s i s t , f u r t h e r methanol was added c a r e f u l l y by b u r e t t e u n t i l the water phase j u s t d isappeared. Care was taken to be sure t h a t no excess B - 2 methanol was used. Water-saturation of the MIBK-methanol mixture was assumed to be reached at this point. Knowing the exact volume of each component that was added, the concentratkn was calculated and expressed i n wt.$. The density of each constituent i n the mixture at room temperature (20°C) was obtained from l i t e r a t u r e (27, 53. 55)« Discrepancies i n density readings between actual room temperature and 20°C may be avoided by obtaining d i r e c t l y the mass of each constituent by the use of the a n a l y t i c a l balance. The errors involved i n the present procedure, however, are assumed to be r e l a t i v e l y i n s i g n i f i c a n t as f a r as present requirements are concerned. The r e f r a c t i v e index of each solution was read i n t r i p l i c a t e . The prisms of the refractometer were cleaned thoroughly with benzene and petroleum ether between readings. Table B-l shows the r e f r a c t i v e index data for runs 16, 1 7 . 18, and 1 9 and f o r preparing F i g . B-l at 20°C. Since the methanol w i l l tend to d i s t r i b u t e i t s e l f should a two-phase mixture of water and MIBK r e s u l t , care was taken to ensure that no separation of phases occurred i n the monophase samples. The entire operation of mixing the solution and measuring i t s r e f r a c t i v e index i n preparing Fig. B-l was performed at the same si t e to avoid the p o s s i b i l i t y of sudden room temperature changes, i f any. During the period that the samples for runs 16, 17. 18, and 19 were transported B - 3 from the e x t r a c t i o n a r e a i n room 218 to room 328A where the r e f r a c t o m e t e r was s i t u a t e d , there were no phase changes ob-served d u r i n g the e n t i r e r e l o c a t i o n processo Measurement of d i f f e r e n c e s i n ambient temperature between the above-mentioned rooms and temperature 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 both rooms (Appendix D-l) i n d i c a t e no apparent 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 c o u l d r e s u l t . Table B - l . R e f r a c t i v e Index Data a t 20°C Weight Run F r a c t i o n R e f r a c t i v e Index, No. Me thanol 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 ~ 1-3920 x UJ Q - 1-3910 UJ > £ 1-3900 < or u_ £ 1-3890 1-3880 2 3 4 5 6 C O N C E N T R A T I O N , wt % F i g u r e 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). C - 1 APPENDIX C C a l i b r a t i o n of the Timing L i g h t Generator The t i m i n g l i g h t generator, Ch. E. 2 3 5 6 , was used t o mark r e g u l a r b l i p s of l i g h t a t p r e s c r i b e d f r e q u e n c i e s a l o n g the outer s t r i p of the movie f i l m i n order to determine the exact camera speed c o r r e s p o n d i n g to any g i v e n segment of the f i l m s t r i p . The generator was c a l i b r a t e d a g a i n s t the Darcy/ TSI D i g i t a l Frequency Meter (Model £ 6 0 ) , Ch. E. 2 5 7 3 . u s i n g a photo pi c k u p , Ch. E. 2 5 2 3 . to r e l a y the l i g h t b l i p s . Data were taken every 10 sec. i n t e r v a l t h a t the t i m i n g generator was o p e r a t i n g . C a l i b r a t i o n data are shown i n Table C - l . From these data, 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 -t i o n s i n v o l v i n g the use of camera speed v a l u e s . For example, in Appendix I, the generator frequency was set a t 100 p i p s / s e c . while the observed frequency was found to have an average r e a d i n g of 117 (Table C - l ) . T h e r e f o r e , the camera speed o b t a i n e d should be m u l t i p l i e d by a c a l i b r a t i o n f a c t o r of 117 100 to o b t a i n the c o r r e c t frame speed. C - 2 Table C - lo Timing Light Calibration Rated Frequency, ^ \ p i p / s e c O b s e r v a - ^ \ tion Number 1 2 3 4 5 6 7 8 9 1 0 11 12 1 3 14 1 5 1 0 1 0 0 1 0 0 0 Observed. Frequency,, pip/sec 808 1 1 6 1040 8 o 9 1 1 7 1 0 3 9 8 c 8 1 1 7 1 0 3 9 9 o 0 118 1 0 3 9 9 - 1 1 1 7 1 0 3 9 808 1 1 6 1 0 3 9 8 o 5 1 1 7 1 0 3 8 8 . 7 117 1 0 3 9 8 . 6 1 1 7 1 0 3 8 8 o 5 116 1 0 3 9 8 . 5 118 1 0 3 9 8 . 6 1 1 7 1 0 3 8 8 . 8 116 1 0 3 9 9 . 0 116 1 0 3 9 8 . 7 1 1 7 1 0 3 8 D - 1 APPENDIX D Room Temperature Fluctuations Measurements of temperature f l u c t u a t i o n were taken for two enclosed rooms i n the Chemical Engineering building on several occasions. The purpose of these tests 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 locations where experimental work was being undertaken,, and also to measure the temperature difference between these two locations at i d e n t i c a l times. Temperature measurements were made i n room 218 on March 2, 6, and 8, 1967. The thermometer was located beside the square column and inside the path of the collimated l i g h t rays with the schlieren system arranged as i n F i g . 4. The thermometer was located between the column and the schlieren mirror, Ml. 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 taking temperature readings simultaneously i n room 328A where the Abbe r e f r a c t o -meter was situated. This thermometer reads 0.06°F higher than the one used i n room 218. The data shown i n Table D-l for the thermometer used i n room 328A are corrected values. This thermometer was placed above the laboratory bench on D - 2 which the r e f r a c t o m e t e r s a t . The thermometer was above the working a r e a to the r i g h t of the instrument (with the operator f a c i n g i t ) . No a b s o l u t e c a l i b r a t i o n of the thermometers was obt a i n e d . D - 3 Table D - l . Temperature F l u c t u a t i o n s i n Two Ch. E. Rooms Date Time Room 218 Room 328A March 2 , 1967 8 : 2 5 P.m. 6 7 o 7 5 ° F 6 8 . 1 ° F " 8 : 3 0 6 8.42 6 8 = 1 8 : 3 5 6 8 . 4 5 68 . 2 " 8:40 6 8 . 5 1 6 8 . 3 " 8 : 4 5 6 8.64 6 8.48 " 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 8 . 5 .....Maroli., 6^^1967 1 1 : 1 5 a.m. 6 8 . 2 5 6 9.14 1 1 : 2 0 6 8 . 5 6 9 . 4 3 " 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 : 3 5 6 8 . 9 5 6 9 . 8 7 1 1 1 1:40 6 9 . 0 6 9 . 8 6 " 1 1 : 4 5 6 9 . 0 3 7 0 . 2 " 1 1 : 5 0 6 9 . 0 2 7 0.04 " 1 1 : 5 5 6 9 . 0 2 7 0 . 1 5 " 1 2 : 0 0 6 9 . 1 8 7 0 . 0 6 March 8 , 1 9 6 7 2 : 0 5 p.m. 7 O . O 3 7 0 . 9 7 2 : 1 0 7 0 . 0 5 7 0 . 9 7 " 2 : 1 5 7 0 . 0 9 7 1.08 " 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 7 0.82 " 2 : 4 5 6 9 . 5 7 0.81 2 : 5 0 6 9 . 9 5 7 0 . 7 5 E - 1 APPENDIX E Test f o r S i g n i f i c a n c e of L i n e a r Regression I t i s assumed t h a t the reader i s f a m i l i a r w i t h f i t -t i n g a s t r a i g h t l i n e by the e s t i m a t i o n procedure of " l e a s t squares" so t h a t most of the 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 not be mentioned<> We can w r i t e the est i m a t e s of the linear» f i r s t -order model to be Y = b Q + b-L X ( E - l ) A where Y = the p r e d i c t e d value of Y f o r a g i v e n X„ the pseudo-radius. X = observed independent v a r i a b l e , t i m e 0 b Q = estimate of i n t e r c e p t parameter of the model, « b i = estimate of slope parameter of the model s> o E q 0 ( E - l ) i s the p r e d i c t i v e equation.. We can a l s o w r i t e the s o l u t i o n s f o r b Q and b i ( 4 4 ) to be b 0 = Y - b i X (E - 2 ) JT(Xi - X ) ( Y i - Y) b i = — i = 1 , 2,..,n (E-3) £(Xi - X ) 2 E - 2 where X, Y = mean v a l u e s of the X and Y v a r i a b l e s , r e s p e c t i v e l y . X i , Yi= i t h o b s e r v a t i o n of the X and Y v a r i a b l e s , r e s p e c t i v e l y , n = no. of s e t s of o b s e r v a t i o n s (X^. Y^), Eq. ( 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^ and Yj^ are known. We now t a c k l e the q u e s t i o n of what measure of p r e c i s i o n can be a t t a c h e d to the estimate of the r e g r e s s i o n l i n e (Eq. E - l ) . Consider the f o l l o w i n g i d e n t i t y : Y i - Y i = Y i - Y - (Yi - Y) -; (E-4) I f we square both s i d e s and sum from i = 1 t o n, we o b t a i n (Y i - Y ) 2 = (Yi - Y i ) 2 + ( Y i - Y ) 2 (7) We can express Eq. (7) i n words as f o l l o w s : Sum of squares Sum of squares Sum of squares = + about the mean about r e g r e s s i o n due to r e g r e s s i o n The l a s t two pre c e d i n g e x p r e s s i o n s are a l s o mentioned i n an e a r l i e r d i s c u s s i o n . ("Sum of squares" term i s now a b b r e v i a -t e d as "SS".) Using Eqs. (7) and (8) and employing a l t e r n a -t i v e computational forms f o r the e x p r e s s i o n s of Eq. (7) we can w r i t e a more workable r e l a t i o n s h i p a s : SS about the mean ^Y^2 ~ ( ^ Y l ) 2 (E-5) ( c o r r e c t e d f o r mean) " n E - 3 (E-6) j £ X i Y i - i l x i i l l l i i j SS due to regression = b^  We now test the null hypothesis that the slope para-meter of the model, j9 /, is equal to ^ 8j0» whereiS i^s a speci-fied value which, in this case, is zero, against the alterna-tive that JSj,, is different from ^0/o(usually stated "H 0: 9^/ = ^0versus K± :^ 9/ ) by calculating the "t" statistic as follows (44): t = (bT - j8/o)[ p X j - X ) 2 ]* ( 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 2)o The absolute value of t is compared with t(n-2, 1-iOO from a t-table (44) with (n-2) degrees of freedom - the number on which s2 is based, and at a level of significance, OC o of 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. p - 1 APPENDIX P P r o p e r t i e s of V a r i o u s Substances Used Sodium hydroxide and g l a c i a l a c e t i c a c i d were r e -agent grade (A.C.S. s p e c i f i c a t i o n ) and were obtained from N i c h o l s Chemical Co., L t d . , M o n t r e a l . The MIBK was t e c h n i c a l grade s u p p l i e d by Canadian Chemical Co., Edmonton. Methyl a l c o h o l ( a b s o l u t e ) and toluene, were reagent grade f u r n i s h e d by Fisher • S c i e n t i f i c Co., Vancouver. Table F - l l i s t s some p r o p e r t i e s of g l a c i a l a c e t i c a c i d , methyl a l c o h o l , MIBK, to l u e n e , and water t h a t are of i n t e r e s t . The r e f r a c t i v e index v a l u e s r e p o r t e d i n t h i s t a b l e are f o r l i g h t - i h a v i n g the wavelength of the D l i n e of sodium o (5892o6 A ) . R e f r a c t i v e i n d i c e s can be g i v e n as e i t h e r abso-l u t e or r e l a t i v e v a l u e s : a b s o l u t e , when the index of r e f r a c -t i o n of a medium i s i t s index r e f e r r e d t o a vacuum, and r e l a -t i v e , when i t s index i s compared, t o t h a t of dry a i r a t s t a n -dard c o n d i t i o n s . Since the a b s o l u t e index f o r dry a i r l s 1.0002918 f o r the sodium D l i n e and so near to u n i t y , i t f o l -lows t h a t , f o r a sol i d , or a l i q u i d , the ab s o l u t e index, and the index r e l a t i v e t o a i r , d i f f e r only s l i g h t l y and i t i s not necessary to d i s t i n g u i s h between them f o r present purposes. The square column i s made of b s o r o s i l i c a t e g l a s s . No r e f r a c t i v e index v a l u e c o u l d be found i n the l i t e r a t u r e F - 2 Table F - l o V a r i o u s P r o p e r t i e s of D i f f e r e n t Substances a t 20°C where A p p l i c a b l e . Substance Property- Value Ref c G l a c i a l A c e t i c A c i d Methyl A l c o h o l MIBK Toluene Water Crown Glass Dry A i r d e n s i t y , gmo/cc. r e f r a c t i v e index,7? f t molecular weight P d e n s i t y , gm<»/cco r e f r a c t i v e index,7f~ molecular weight ™ d e n s i t y , gm . /cco r e f r a c t i v e index,7^0 surface t e n s i o n , dynes/cm. d e n s i t y , gm./cc. surface t e n s i o n , dynes/cm 0 d e n s i t y , gm./cc. r e f r a c t i v e index,7jp surface t e n s i o n , dynes/cm. r e f r a c t i v e index r e f r a c t i v e index, (standard c o n d i t i o n s ) 1.049 1 O 3 7 1 8 6 O 0 O 5 0.7924 1=3292 3 2 0 04 0.8007 1.396 23.9 0.8669 28.52 0.99998 1.333 72o8 1 . 5 1 7 1.000292 27 27 5 3 5 4 27. 5 5 5 1 5 1 f o r t h i s m a t e r i a l , and crown g l a s s i s shown i n s t e a d i n Table F - l . G - 1 APPENDIX 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 Consider F i g o k2° Assuming the drop to be a sphere of r a d i u s , r , having i t s c e n t r e , C, on the a x i s of o r d i n a t e , Y d, and moving a l o n g i t s a x i s towards Y d = 0 , the l o c u s of the t a n g e n t i a l p o i n t , P(X d, Y d ) , with r e s p e c t to p o i n t L ( X L , 0 ) can be found by the r e l a t i o n Since CK = V r 2 •- Xd , i n s e r t i n g t h i s r e l a t i o n i n t o Eq. (H-lA) y i e l d s C L 2 = P L 2 + CP; (H-l) S u b s t i t u t i n g a p p r o p r i a t e terms we f i n d ( Y d + C K ) 2 + ( X L ) 2 = Y d 2 + (Xd - X L ) 2 + r 2 (H-lA) [(Y d + r2 - X d 2 ) 2 + (X L ) 2 ] [Y d2 + (Xd - X L ) 2 ] + r 2 Y d l £ 2 ^ X ? Xd 2 - Xd X L Yd Xn - X L) ( 1 0 ) Vr 2 - Xd 2 H - 1 APPENDIX 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 Suppose a c o r r e c t l y exposed negative was obtained by the L i n h o f s t i l l camera w i t h the c o a l e s c i n g drops as sub-j e c t and y i e l d e d the f o l l o w i n g exposure time, ti*9 and r e l a -t i v e a p e r t u r e , N L : t L = 1/125 sec, N L = 11 or f/11 The f i l m used was b l a c k and white and has a speed of USASI 125« The o b j e c t - t o - l e n s d i s t a n c e , U*L, was 10,5 i n . and the l e n s - t o -image d i s t a n c e , V L , was 11.625 i n . The f o c a l l e n g t h of the L i n h o f l e n s was 135 nmi° (5°32 i n . ) . We now d e s i r e to change to the Hycam high-speed mo-v i e camera (lens f o c a l l e n g t h , f j j = 75 mm. or 2.95 i n . ) , to o b t a i n an e q u a l l y exposed n e g a t i v e while d o u b l i n g the f i l m speed to USASI 250 and changing the o b j e c t - t o - l e n s d i s t a n c e , UJJ, to 5«7 i n . The i l l u m i n a t i o n i s assumed to be constant and equal f o r both L i n h o f and Hycam shots. However, from the l e n s e q u a t i o n (43). 1 + 1 = 1 (H-l) u v f * S u b s c r i p t "L" stands f o r L i n h o f while "H" i s f o r Hycam, H - 2 we choose f i r s t to f i n d a new L i n h o f exposure time s e t t i n g to correspond 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 h o l d i n g the r e l a t i v e a p e r t u r e , N^, constant. We now take U L(= Ug) = 5«7 i n . and the value of f ^ remains the same. S u b s t i t u t i n g these v a l u e s to Eq. ( H - l ) , we o b t a i n V L = 80.00 i n . Given the e x p r e s s i o n (43) m a g n i f i c a t i o n , m = v - 1 (H-2) f and s u b s t i t u t i n g , Mr = 80.00 i n . - 1 = 14.00 5.32 i n . A value of i s a l s o determined f o r the o r i g i n a l L i n h o f exposure s e t t i n g s . This i s found t o be M L ( o l d ) = 11.625 i n . - 1 = 1.19 « 1 5.32 i n . From r e f e r e n c e 43 (see Table IV' a l s o ) , the exposure time r e q u i r e d f o r the new set of L i n h o f s e t t i n g s i s g i v e n by the e q u a t i o n t'(new) = t ( o l d ) x (1 + M(new) ) 2 (H-3) pr o v i d e d the m a g n i f i c a t i o n , ML, i n the o r i g i n a l s e t t i n g (M L(01d)) was equal t o u n i t y . We can t h e r e f o r e a p p l y Eq. (H-3) t o y i e l d 2 t(new) = 1 sec. x (1 + 14.00) = _1 s e c . ~ 1 sec. 125 4 2.22 2 H - 3 Since the Hycam camera uses a f i l m whose speed i s twice as f a s t (USASI 250), we must reduce the exposure time, t(new), by h a l f . Therefore, the new L i n h o f exposure s e t t i n g i s f/11 a t 1/4 sec. In other words, i f we move the Linhof camera from U L = 10.5 i n . to U-^  = 5»7 i n . we co u l d expect the exposure time a l t e r e d from 1/125 sec. to 1/4 s e c , h o l d i n g the r e l a t i v e aperture c o n s t a n t . For 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 determine the e q u i v a l e n t Hycam exposure s e t t i n g t o o b t a i n an i d e n t i c a l l y exposed n e g a t i v e . From Eq. ( H - l ) , 1__ + _1_ = 5.7 i n . Vg v H = V H i s giv e n by: 1 2.95 i n . 6.12 i n . I f we choose to set the r e l a t i v e a p e r t u r e of the Hycam l e n s t o f/3»5» i»e., a t i t s widest l e n s opening, the cor r e s p o n d i n g exposure time s e t t i n g i s c a l c u l a t e d by f i r s t d e t e r m i n i n g the l i g h t - p a s s i n g power r a t i o of the Hycam l e n s t o the L i n h o f l e n s , ^H, g i v e n by the r e l a t i o n (43) (H-4) H - 4 S u b s t i t u t i n g a p p r o p r i a t e Hycam and L i n h o f exposure s e t t i n g s a t U H = U L = 5 . 7 i n . , 1 1 x 8 0 i n . LH _ _ . - L L p . 5 x 6 . 1 2 i n 5 ° ? 2 In. = I6?.j = 5 1 9 o O 7 . 2 6 2 . 9 5 i n . Since 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, ( 4 3 ) by *s = H t L L l ( H - 5 ) S u b s t i t u t i n g , t j i = 1 sec. x 1 = 1 sec, 4" 5 1 9 . 0 2 0 7 5 D i v i d i n g the denominator by 2 . 5 » the s h u t t e r d u r a t i o n - p e r i o d r a t i o ( 2 3 ) , and t a k i n g the r e c i p r o c a l of the r e s u l t , converts the exposure time, s e c , to the camera speed, pps. Thus, we o b t a i n = 8 3 0 pps. Co J The e q u i v a l e n t Hycam exposure s e t t i n g I s , t h e r e f o r e , f / 3 . 5 a t 8 3 0 pps. I - l APPENDIX 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 The minimum d i s c e r n i b l e l e n g t h of the pseudo-radius was O 0 O 5 cm. i n the photographs (as i n F i g s . 33 and 34). The no. of s u c c e s s i v e f i l m frames i n runs 18 and 19 was determined which would provide a change i n the pseudo-radius by an amounts 0.05 cm. The drop, as shown i n the same p r i n t s , was assumed to be of s p h e r i c a l shape having a diameter, d, of 55 nim. a t the s t a r t of shape measurements, which i s roughly one-half the d i s t a n c e of s e p a r a t i o n of the two n o z z l e t i p s i n both runs ' ( F i g s . 33 and 34). The volume of the sphere, V s = ^ x 7T x ^  ^ m m J = 87114.00mm3 The new volume, V"sis> a f t e r a r a d i a l i n c r e a s e of 0.05 cm. i s V s i = 4 x7Tx|5^inm + 0.5 mm) 3 \* J = 91952.54mm3 Av = v S i - v s = 91952.54 - 87114.00 = 4838.54mm3 The time taken from the i n s t a n t a c o a l e s c e d drop detaches from both n o z z l e to the onset of coalescence of a new drop p a i r , which was c a l l e d by the term "CD", was measured to be 7*5 sec. 1 - 2 T h i s value i s now used to c a l c u l a t e the d i s p e r s e d phase flow r a t e , F, assuming t h a t the volume of the sphere a t t h i s p o i n t i s s t i l l V s . = 1 1 0 6 C C o s e c o The p e r i o d , t , necessary to produce a r a d i a l i n c r e a s e of O 0 O 5 cm. i s then t = A v F = 0 . 4 sec. S t a r t i n g a t the onset of coalescence and going "back i n time u n t i l t = 0 . 4 s e c , the e q u i v a l e n t frame span was estimated to be about 1 3 9 0 frames f o r run 18 and about 8 0 0 frames f o r run 1 9 which corresponded to an i n c r e a s e i n r a d i u s by 0 . 0 5 cm. The camera speed v a r i e s over these f i l m frame v a l u e s . The c a l c u l a t i o n s i n v o l v e d i n o b t a i n i n g these v a l u e s are l e n g t h y , i n c l u d i n g a summation of about f o r t y terms i n one i n s t a n c e , and w i l l not be shown. S i m i l a r computational procedures are presented below, however, f o r s h o r t e r frame spans. The e l a p s e d times f o r l i 5 0 and 1 0 0 frame spans f o r runs 18 and 1 9 r e s p e c t i v e l y , were determined. V a r i a t i o n s i n camera speed f o r a range of f i l m frames are shown below. 1 - 3 Run 1 8 : Camera speed, pps 3860 3850 3825 3800 Run 19: Camera speed, pps 2560 2550 2500 24?5 2460 Frame no. 0-8 8-85 85 - 123 123 - 150 Frame no o 0 - 3 3 - 29 29 - 54 54 - 78 78 - 100 Frame span, frame 8 77 38 27 150 frames Frame span, frame 3 26 25 24 22 100 frames Average camera speed (Run 18) = J L ( 3 8 6 0 ) + Z 2 J 3 8 5 0 ) + __28(3825) + 27 (3800) 150 150 150 150 = 205.87 + 1 9 7 6 . 3 3 + 9 6 8 . 9 9 + 684.00 = 3835.19 PPS 1 - 4 Average camera speed (Run 1 9 ) = _1_(2560) + 2 6 J 2 5 5 0 ) + 21_(2500) + 24_(24?5) 100 100 100 100 + 22 (2460) 100 = 7608O + 663=00 + 6 2 5 . 0 0 + 594o00 + 5 4 l » 2 0 = 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 = O 0 O 3 9 sec. Elapsed 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 obtain the corresponding change i n r a d i i for both runs, l e t us consider the elapsed time of 0 . 0 3 9 sec. to apply f o r both cases since the difference between the two times i s very small. A timing l i g h t c a l i b r a t i o n factor (Appendix C) of 100 i s m u l t i p l i e d to th i s value. 0 . 0 3 9 s e c , to give an 117 elapsed time (corrected) of 0 . 0 3 4 sec. Volume increase = flow rate x elapsed time (corrected.) , cc 0 , = 1 1 . 6 x O.O34 sec. = 0 . 4 cc. 1 - 5 The new diameter, d 1 0 corresponding to a volume i n c r e a s e of 0o4 cc. i s obtained from the r e l a t i o n (87.114 + 0.4)cc. = 7T d j 3 6 d i 3 = 87.514 x 6 = 1 6 7 . 1 3 9 c c . 3.1416 d^ = 5°508 cm. Radius change = di - 5° 5 cm. 2 = 0.004 cm. J - 1 APPENDIX J Heat E f f e c t s Accompanying the Mi x i n g 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 Temperature A heat of s o l u t i o n produced by the t r a n s f e r of g l a -c i a l a c e t i c a c i d from the d i s p e r s e d MIBK phase to the c o n t i -nuous water phase was determined as fo l l o w s o In Table J - l (4-2) below, heats of s o l u t i o n , Q, i n k i l o j o u l e s e v olved /gm-mole s o l u t e , are given, f o r v a r i o u s a c e t i c a c i d c o n c e n t r a t i o n l e -v e l s , expressed as the number of moles of water, M s, added to one mole of a c e t i c a c i d . For l a c k of any d e f i n i t e statement i n r e f . 42, the a c i d mentioned l s assumed to be g l a c i a l a c e t i c a c i d . From r e f . 5 6 , an MIBK phase c o n t a i n i n g O .OO76 l b . moles of a c e t i c a c i d / c u . f t . s o l n . i s i n e q u i l i b r i u m a t about 1 9 ° C w i t h a water phase c o n t a i n i n g 0 . 0 1 3 9 l b . moles of a c e t i c a c i d / cu. f t . s o l n . L e t us assume t h a t the f o l l o w i n g r e l a t i o n s h i p s h o l d : 1 . The continuous phase i s i n i t i a l l y f r e e o f a c e t i c a c i d and c o n t a i n s water o n l y . 2. The r a t e of a c e t i c a c i d t r a n s f e r i s uniform with r e s p e c t t o time and no f r e s h d i s p e r s e d phase m a t e r i a l flows to each drop d u r i n g the mass t r a n s f e r p r o c e s s . J - 2 3« No mixing o c c u r s i n the continuous phase d u r i n g the e n t i r e p e r i o d of s o l u t e t r a n s f e r so t h a t the d i f f u s e d s o l u t e can be c o n s i d e r e d to be c o n f i n e d w i t h i n the v i c i n i t y of the drops o n l y 0 4 . E q u i l i b r i u m between the two phases i s reached with r e s p e c t t o a c e t i c a c i d concentration<> 5» The opposing drops are separated from each other j u s t enough to prevent any i n t e r m i x i n g of s o l u t e so as to enable the s o l u t e concen-t r a t i o n i n the continuous phase to be the same throughout the a f f e c t e d space (F igo J - l ) ; the a f f e c t e d continuous phase i s a l a y e r which envelopes each drop and has a volume equal to t h a t of the drop which i t surrounds (F igo J - l ) 0 Table J - l o Heats of s o l u t i o n of a c e t i c a cid-water system a t 1 8 O 5 ° C ( 4 2 ) . 139 I0I2 197 l o 5 3 * 207 I0I5 4 1 1 l o 3 7 00 1 . 9 0 * At ! 3 o 6 ° C o J - 3 The maximum temperature r i s e i n the continuous phase can be expected with the use of h i g h e s t 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 the d i s p e r s e d phase because under those c o n d i t i o n s 9 maximum t r a n s f e r of a c e t i c a c i d out of the drops and i n t o the continuous phase can be obt a i n e d . Only a c i d compositions a c c u r a t e l y measured by a n a l y t i c a l methods are considered,, and on t h i s b a s i s run 8 had the h i g h e s t d i s p e r s e d phase a c e t i c a c i d c o n c e n t r a t i o n : 5 6 ° 4 5 x 1 0 " 3 l b o moles ace-t i c a c i d / cu, f t o s o l n D The q u a n t i t y , M s, f o r t h i s run i s c a l c u l a t e d 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 the aqueous phase (from d i s t r i b u t i o n data) = 56.45 x 1 0 ~ 3 l b . moles x 0.0139  cu. f t . s o l n . (0.0139 + 0.0076) = 3 6 . 4 - 9 x 10"" 3 l b . moles/cu. f t . s o l n . Volume of a c e t i c a c i d i n the aqueous phase/cu. f t . s o l n . = 36.49 x I P " 3 l b 0 moles x 60.05 l b . / l b . mole (1.049 x 62 .43) l b . / c u . f t . = 3» 3 5 x 1 0 " 2 cuo f t . Volume of cor r e s p o n d i n g water/cu. f t . s o l n . (assuming a d d i -t i v i t y of volumes hold) = 1.0 - O.O335 = O.9665 cu. f t . Lb. moles of corresponding water/cu. f t . s o l n . = 0.9665 x 62.43 = 3 ° 3 5 18 . 0 2 ii - 4 Moles water added to one mole a c e t i c a c i d , M s (to produce a s o l u t i o n of c o n c e n t r a t i o n equal t o that of the continuous phase under c o n s i d e r a t i o n ) = 3' 3 5 - = 91.73 36.49 x 10~J In Table J - l , we l o o k f o r the value of Q corre s p o n d i n g t o M g = 91.73. We f i n d t h i s value m i s s i n g from the t a b l e but can r e a s o n a b l y be c o n s i d e r e d t o be about 1 k i l o j o u l e s evolved/gm. mole s o l u t e by e x t r a p o l a t i o n . We now assume t h a t the drop oc c u p i e s a volume of 0.02 c c , conforming to assumption 5 which i m p l i e s that both drops have not y e t f u l l y grown, and t h a t the l a y e r of continuous water phase immediately surrounding i t , from assumption 6, has the same volume. Heat evolved i n the continuous phase = (1 x 1000) Joules x 463.6 gms. gm. mole a c i d l b . x (36.49 x 10"3) l b . moles -srO.02 cc.x cu. f t . cu. f t . s o l n . 28317 cc, = 1:.17 x 10"2 j o u l e s Weight of the continuous phase *0.02 28317 cu. f t . x 62.43 l b . x 453.6 gms. cu. f t . l b . = 20.00 x 10~3 gm. J - 5 Temperature r i s e i n the continuous phase/drop = 1.17 x 1 0 ~ 2 j o u l e s  4.184 j o u l e s / c a l x 1 cal/(gm°C) x 20.00 x 10~3 g m . = 0.14 °C LAYERS F i g u r e J - l . Sketch 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 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 metric 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 to the dark blotch appearing between the drops, as mentioned e a r l i e r . Table K - l . Pseudo-radius Data of L e f t Drop i n Run 1 8 Time p r i o r ^ D i v i d i n g F i l m to onset ^ \ L i n e Frame of c o a l e s - Obser-" No. cence.secc v a t i o n Nd> 70° 100° 1 3 0 ° 145° 1 5 5 ° 1 7 0 ° 1 8 5 ° 1 9 5 ° 220O 2 5 0 ° 280° Pseudo-radius, cm. (Measurements on the enlargement; magnification = 2kx) 0 0 1 3 . 8 0 4 . 3 0 £ o 3 5 4 . 2 0 4 . 0 0 3 . 6 0 3 . 4 5 3 . 3 5 3 - 5 5 4 . 3 5 6 0 . 0 0 1 3 2 3 o 7 5 4 . 3 0 4 . 3 5 4 . 1 5 4 . 0 0 3«60 3 . 4 5 3 . 3 5 3 . 5 0 4 . 3 0 1 2 0 . 0 0 2 7 3 3 . 8 0 £c35 4 . 4 0 4 . 2 0 4 . 0 0 3 . 6 0 3 . 4 5 3 » 3 5 3 = 50 4 . 3 0 1 8 0 . 0 0 4 0 4 3 . 8 0 4 . 3 0 4 . 3 5 4 . 2 0 4 . 0 0 3 . 6 0 3 ° 5 0 3 o 3 5 3°55 4 = 3 5 2 4 0 . 0 0 5 3 5 3 . 8 0 4 . 3 5 4 . 3 5 4 . 2 0 4 . 0 0 * 3 . 6 0 3 . 4 5 3 * 3 5 3 - 5 0 4 . 2 5 30 0 . 0 0 6 7 6 3 . 8 0 4 . 3 0 4 . 3 5 4 . 2 0 3 . 9 5 •a 3 . 6 0 3 . 4 5 3 . 3 5 3°55 4 . 3 0 36 0 . 0 0 8 0 7 3 . 8 0 4 . 3 5 4 . 4 0 4 . 2 0 3 . 9 5 •a- 3 . 6 0 3 c 4 5 3°35 3 » 5 5 4 . 3 o tt 4 2 0 . 0 0 9 3 8 3 . 8 0 4 . 3 0 4 . 3 5 4 . 1 5 4 . 0 0 # 3»6o 3 . 4 5 3 . 3 5 3°55 4 . 3 0 , 4 8 0 . 0 1 0 6 9 3 . 7 5 4 . 3 0 4 . 3 5 4 . 1 5 4 . 0 0 3 . 6 0 3 . 5 0 3 . 3 5 3 . 5 5 ^ • 3 5 f\j 5 4 0 . 0 1 2 0 1 0 3 . 8 0 4 . 3 0 ' - 4 . 3 5 4 . 2 0 4 . 0 0 * 3 . 6 0 3 - ^ 5 3 . 3 5 3 = 5 5 4 . 3 0 6 0 0 . 0 1 3 3 1 1 3 . 7 5 4 . 3 0 4 . 3 5 4 . 2 0 4 . 0 0 * 3 . 6 0 3 . ^ 5 3 . 3 5 3 - 5 5 4 . 3 5 6 6 0 . 0 1 4 6 1 2 3 . 7 5 4 . 3 0 4 . 3 5 4 . 2 0 4 . 0 0 * 3 c 5 5 3 . 4 5 3 . 3 5 3 » 5 5 4 . 3 5 7 2 0 . 0 1 6 0 13 3 . 7 5 4 . 3 0 4 . 3 5 4 . 2 0 3 . 9 5 •a- 3 . 6 0 3 - ^ 5 3 . 3 5 3 . 5 5 4 . 3 5 7 8 0 . 0 1 7 3 1 4 3 . 7 5 4 . 3 O 4 . 3 5 4 . 1 5 3 . 9 5 3 . 5 5 3 . 4 5 3 . 3 5 3 = 5 5 4 = 3 5 8 4 0 . 0 1 8 6 15 3 . 8 0 4 . 3 0 4 . 3 5 4 . 2 0 4 . 0 0 3 . 6 0 3 - ^ 5 3 o 3 5 3 - 5 5 4 . 3 5 90 0 . 0 2 0 1 16 3 . 8 0 4 . 3 0 4 . 3 5 4 . 1 5 3 . 9 5 * 3 . 6 0 3 . ^ 5 3 . 3 5 3°55 4 . 3 0 9 6 0 . 0 2 1 4 17 3o70 4 . 3 0 4 . 3 5 4 . 1 5 4 . 0 0 * 3 . 6 0 3 ^ 5 3 . 4 0 3 . 6 0 4 . 3 5 1 0 2 0 . 0 2 2 8 1 8 3 . 8 0 4 . 3 0 4 . 3 0 4 . 1 5 4 . 0 0 3 . 6 0 3 . 4 5 3 - 3 5 3 = 55 4 . 3 0 1 0 8 0 . 0 2 4 1 1 9 3c 70 4.3O 4 . 3 5 4 . 2 0 4 . 0 0 3 . 6 0 3 . 4 5 3 . 4 0 3 . 5 5 4=35 1 1 4 0 . 0 2 5 5 2 0 3»70 4 . 3 0 4 . 3 5 4 . 2 0 4 . 1 0 * 3 . 6 0 3 . 5 0 3 » 3 5 3 . 5 5 4 . 3 0 1 2 0 0 . 0 2 6 8 2 1 3 . 8 0 4 . 3 0 £ . 3 5 4 . 1 5 3 o 9 5 • 3 . 6 0 3 . 4 5 3 . 4 0 3 . 5 5 4=30 1 2 6 0 . 0 2 8 3 2 2 3 . 8 0 4 . 3 0 4 . 3 5 4 . 1 5 3 o 9 5 # 3 o 6 0 3 . 4 5 3 - 3 5 3 - 5 5 4 . 2 5 1 3 2 0 . 0 2 9 7 23 3 c 7 5 4 . 3 O 4 . 3 5 4 . 1 5 4 . 0 0 3 . 6 0 3 . 5 0 3°35 3 . 6 0 4 . 3 5 1 3 8 0 . 0 3 1 0 2 4 3 . 7 5 4 . 3 0 £ c 3 5 4 . 2 0 4 . 0 0 # 3 . 6 0 3 . 4 5 3 » 3 5 3°55 4 . 3 5 1 4 4 0 . 0 3 2 4 25 3 - 7 5 4 . 3 0 £ . 3 5 4 . 2 0 4 . 0 0 3 . 6 0 3.50 3 . 4 0 3 - 5 5 4 . 3 5 150 0 . 0 3 3 7 26 3 . 7 0 4 . 2 5 £ . 3 5 4 . 1 5 4 . 0 0 * 3 . 6 0 3 . 5 0 3 . 3 5 3 * 5 5 4 . 3 5 Table K - 2 . Pseudo-radius Data of Right Drop i n Run 1 8 Time p r i o r F i l m t o onset Frame of c o a l e s -Noo cence.sec. . D i v i d i n g _ . _ , .Line 7 0 ° 100° 130° 145° 1 5 5 ° 170° 185° 195° 2 2 0 c Obser-^ v a t i o n No> Pseudo-radius, cm, (Measurements on the enlargement; magnification = 2kx) 2 5 0 ° 280c 0 6 1 2 18 24 3 0 3 6 42 48 54 6 0 6 6 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 o 0 0 1 3 0 . 0 0 2 7 0 . 0 0 4 0 0 . 0 0 5 3 0 . 0 0 6 7 0 . 0 0 8 0 0 , 0 0 9 3 0 . 0 1 0 6 0 . 0 1 2 0 0 . 0 1 3 3 0 . 0 1 4 6 0 . 0 1 6 0 0 . 0 1 7 3 0 . 0 1 8 6 0 . 0 2 0 1 0 . 0 2 1 4 0 . 0 2 2 8 0 . 0 2 4 1 0 . 0 2 5 5 0 . 0 2 6 8 0 . 0 2 8 3 0 . 0 2 9 7 0 . 0 3 1 0 0 . 0 3 2 4 0 . 0 3 3 7 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 14 1 5 1 6 1 7 18 1 9 2 0 2 1 2 2 2 3 24 2 5 2 6 3 . 4 0 3 . 4 0 3 . 4 0 3 . 4 0 3 . 3 5 3 . 4 0 3 . 4 0 3 . 4 0 3 . 3 5 3 » 3 5 3 . 4 0 3 . 3 5 3 . 4 0 ,40 ,40 ,40 ,40 • 3 5 3 . 3 5 3 . 4 0 3 - 3 5 3 . 4 0 3 . 4 0 3 . 3 5 3 « 4 o 3 . 4 0 4 . 0 0 4 . 0 0 4 . 0 0 4 . 0 0 3 . 9 5 3 . 9 5 4 . 0 0 4 . 0 0 3 . 9 5 3 c 9 5 3 . 9 5 3 . 9 5 3 . 9 5 3 c 9 5 3 . 9 5 3 o 9 5 3 . 9 0 3 o 9 5 3 c 9 5 3 o 9 5 3 . 9 5 3 . 9 5 3 . 9 5 3 . 9 0 3 . 9 5 3 c 9 5 4 . 1 0 4 . 1 5 4 . 1 5 4 . 1 5 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 0 5 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 1 0 4 . 0 5 4 . 1 0 4 . 1 0 4 . 0 5 4 . 0 5 4 . 1 0 4 . 0 5 4 . 0 5 4 . 0 5 4 . 0 5 4 . 0 5 4 . 0 5 4 . 0 5 4 . 0 5 4 . 1 0 4 . 0 5 4 . 0 5 4 . 0 5 4 . 0 0 4 . 0 5 4 . 0 5 4 . 0 5 4 . 0 0 4 . 0 0 4 . 0 0 3 . 9 5 3 . 9 5 4 . 0 0 4 . 0 0 3 . 9 5 4 . 0 0 4 . 0 0 3 - 9 5 4 . 0 0 4 . 0 0 3 . 9 5 4 . 0 0 3 . 9 5 3 c 9 5 4 . 0 0 4 . 0 0 4 . 0 0 3 . 9 5 4 . 0 0 3 . 9 5 •a-3 » 7 0 3 o 7 0 3 » 7 0 3 - 7 0 3 . 7 0 3 . 7 0 3 . 7 0 3 . 6 5 3 . 6 5 3 . 7 0 3 . 6 5 3 * 7 0 3 . 7 0 7 0 6 5 7 0 7 0 7 0 7 0 3 . 6 5 3 c 7 0 3 . 7 0 3 . 7 0 3 . 7 0 3 . 6 5 3 . 6 5 3 . 6 0 3 . 6 0 3 . 6 0 3 . 6 O 3 . 6 0 3 . 6 0 3 . 6 0 3 . 6 5 3 . 6 0 3 . 6 5 3 . 6 0 3 . 6 0 3 . 6 0 3 . 6 0 3 . 6 0 3 . 6 0 3 . 6 0 3 . 6 0 3 . 6 5 3 . 5 5 3 . 6 0 3 . 6 0 3 . 6 0 3 . 6 0 3 . 6 0 3 . 6 0 3 . 5 0 3 . 5 0 3 . 5 0 3 . 5 0 3 . 5 0 3 . 5 5 3 . 5 5 3 . 5 5 3 . 5 5 3 . 5 5 3 . 4 5 3 . 5 0 3 . 5 0 3 - 5 5 3 . 5 5 3 . 5 5 3 . 5 0 3 . 5 5 3 . 5 5 3 . 5 0 3 - 5 5 3 . 5 0 3 - 5 ° 3 . 5 ° 3 . 5 0 3 . 5 ° 3 . 6 5 3 . 6 5 3 . 7 0 3 . 6 5 3 . 6 5 3 . 7 5 3 . 7 5 3 . 7 0 3 . 7 5 3 . 7 5 3 . 7 0 3 . 7 5 3 . 7 0 3 . 7 0 3 . 7 5 3 . 7 0 3 . 7 5 3 . 7 0 3 . 7 0 3 . 6 5 3 . 7 5 3 . 6 5 3 . 7 ° 3 - 7 5 3 . 7 0 3 . 7 ° 4 . 4 0 4 . 3 5 4 . 4 0 4 . 3 5 4 . 3 5 4 . 4 5 4 . 4 5 4 . 4 0 4 . 4 5 4 . 4 0 4 . 4 0 4 . 4 0 4 . 4 0 4 . 4 0 4 . 4 0 4 . 4 0 4 . 4 0 4 . 4 0 4 . 4 0 4 . 4 0 4 . 4 0 4 . 4 0 4 . 4 0 4 . 4 5 4 . 4 0 4 . 4 0 Table K-3. Pseudo-radius Data of Left Drop In Run 19 Time prior .Dividing Film to onset ^ \ L l n e Frame of coales- Obser-No. cence.seo. vatlon NoV 70° 100° 130° 145° 155° 170° 185° 195° 220° 250° 280° Pseudo-radius, cm, (Measurements on the enlargement; magnification = 0 0 1 4 0.0013 2 8 0.0027 3 12 0.0040 4 16 0.0054 5 20 0.0067 6 24 0.0080 7 28 0.0094 8 32 0.0109 9 36 0.0123 10 40 0.0137 11 44 0.0150 12 48 0.0164 13 52 0.0178 14 56 0.0193 15 60 0.0207 16 64 0.0221 17 68 0.0235 18 72 0.0249 19 76 0.0262 20 80 0.0278 21 84 0.0292 22 88 O.O306 23 92 0.0320 24 96 0.0333 25 100 0.0347 26 117 0.0412 27 134 0.0477 28 151 0.0538 29 168 0.0606 30 185 0.06?3 31 202 O 0 O 7 3 6 32 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 3.35 3»35 3*35 3«3Q 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 3.75 3.75 3»75 3.95 3.95 3.95 3.90 3.95 3.95 3.95 3.95 3.95 3.90 3.95 3.90 3.90 3.90 3.90 3.90 3-90 3.90 3.85 3.85 3.85 3.90 3.90 3.90 3.85 3-85 3.85 3.80 3.80 3.80 3.80 3.80 3.75 3.75 3.75 3.80 3.75 3.75 3.75 3-75 3.75 3.75 3.75 3.75 3.75 3.70 3-75 3.75 3.75 3.75 3.65 3.70 3-65 3.70 3.75 3.75 3.65 3-65 3-65 3.65 '3.60 3o65 3.65 3-65 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 3.25 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 . 2 5 . 2 5 . 2 5 .25 >30 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 3.10 3.10 3.15 3.20 2 4 x ) 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 3.20 3.20 3.20 3.20 3.20 3.20 3.20 3. 3< 3< 3. 3. 3< 20 20 20 20 25 20 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 Table K - 4 . Pseudo-radius Data of Right Drop i n Run 1 9 Time p r i o r F i l m to onset Frame of c o a l e s -No. cence.sec. 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 0.0306 0.0320 0.0333 0.0347 0.0412 0.0477 O.O538 0.0606 0.0673 0.0736 D i v i d i n g X i n e Obser-v a t i o n NcV 1 2 3 4 5 6 7 8 9 10 11 12 n 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° 220° 250° 260° Pseudo-radius, cm. (Measurements on the enlargement; magnification = 24x) 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. 3. 3. 3-3. 3-3. 3« 3-3« 3« 3. 3« 25 25 25 25 25 25 25 25 25 25 25 25 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 3-3. 3. 3. 3. 3< 75 75 75 75 75 75 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 3.85 3.85 3.80 3.80 3.85 3.85 3.80 3.80 3.85 3.80 3.05 3.85 3.80 3.80 3-85 3.80 3.80 3.80 3.80 3.80 3.80 3.80 3.75 3.80 3.80 3.80 3.80 3.80 3.80 3.80 3.75 3.80 3.80 3.80 3.75 3.75 3.80 3.80 3.75 3-75 3.80 3.75 3.80 3.80 3.75 3.75 3.80 3.75 3.75 3.75 3.75 3.70 3.70 3.70 3.70 • # 3.60 3.60 3.60 3.60 3.60 3.55 3.60 3.60 3.55 3.55 3.60 3.60 3.6O 3.55 3.55 3.55 3.55 3.55 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 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 3-3-3. 3. 3. 35 35 35 35 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 L Input and Sample Output of the L i b r a r y Program, "UBC LQF", f o r Run 19 The sample output on page L - 4 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. The u n i t s of the X and Y v a r i a b l e s are seconds and f e e t r e s p e c t i v e l y . L - 2 PLEASE RETURN TO THE CHEMICAL ENGINEERING BUILDING JOB NUMBER 16006 CATEGORY F •> JOB START 16HRS 25MIN 46.3SEC S J ' O B 16006 LEOPOLDO CORDERO JR. $P AGE 30 '^FORTRAN i. C LEAST SQUARES FIT FOR RUN 19 . . . ..  ^ 1 DIMENSION X(200 ) ,Y(200) , Y F ( 2 0 0 ) t W ( 2 0 C ) t E l ( 5 0 ) » E ? ( 5 0 ) iP(50 ) .RES(5C 0 l fF(200)»R(200) tYSUM(200) ? 3 READ(5,1) N,MtNI 3 1 F0RMAT13I5) 4 YSUM(1)=0. 5 DO 39 1=1,5 > 6 39 P ( I ) = 0 . 0 7 2 FORMAT!13F6.2) 10 READ(5,2) (F( I ) ,R(I) ,I = 1,N) 11 DO 18 1=1iN 12 I F ( F ( I ) . L T . 3 . 0 ) GO TO 20 13 I F ( F ( I).GT.3 .0.AND.F(I ).LT.29.0) GO TO 21 14 I F ( F ( I )..GT.29.0.AND.F( I ).IT.54.0) GO TO 2 2 "- 15 I F ( F ( I ) ..GT. 54.0. AND. F ( I ) .LT.78.0) GO TO 23 16 I F ( F ( I ) . G T . 7 8.0.AND.F( I).LT.101.) GO TO 30 17 I F ( F ( I ) . E Q . 1 1 7 . ) GO TO 31 20 I F ( F ( I ) ..EQ. 134. ) GO TO 32 21 I F ( F ( I ) . E Q . 1 5 1 . ) GO TO 32 22 I F ( F ( D..EQ.168. ) GO TO 34 23 I F ( F ( I ) . E Q . 1 8 5 . ) GO TO 35 « 24 I F I F I I ) . E Q . 2 0 2 . ) GO TO 36 25 20 X(I )=F ( I)/(2560.*1.17) 26 GO TO 17 27 21 X( I)=F{ I)/(2550.*1. 17) 30 GO TO 17 31 22 X ( I ) = F ( I ) / ( 2 5 0 0 . * 1 . 17 ) 32 GO TO 17 33 23 X( I)=F( I)/(2475.*1. 17 ) 34 GO TO 17 35 30 X ( I ) = F { I ) / ( 2 4 6 0 . * l . 1 7 ) 36 GO TO 17 s 37 31 X ( I)=F( I)/(2430.*1.17) 40 GO TO 17 41 32 X ( I ) = F ( I ) / ( 2 4 0 0 . * 1 . 17) . t 42 GO TO 17 t- 43 34 X( I)=F( I)/(2370.*1 . 17) 44 GO TO 17 p- 45 35 X( I)=F( I)/(2350.*1. 17) 46 GO TO 17 47 36 X( I)=F( I)/(2345.*1.17) 50 17 Y d )=R( I ) /30.48 51 18 YSUM(1)=YSUM(1)+Y ( I ) 52 YBAR=YSUM(1)/FLOAT(N) 53 EXTERNAL AUX 54 CALL LQF(X,Y,YF,W,E1,E2,P,0.,N,M, NI» NO,EP,AUX ) 55 IF(ND.EO.O) GO TO 3 56 WRITE(6,40) USER'S NAME- LEOPOLDO CORDERO USE V9M011 OFF L - 3 57 40 F(.)RMAT(66II ESTIMATES OF ROOT MEAN SQUARE STATISTICAL CR •<0R I \l THE 1 PARAME TER S) 60 WRITE(6, 5) ( E l ( I ) , 1 = 1 »M ) 61 WRITE(6,4) 62 4 F0RMAT(60H ESTIMATES OF ROOT MEAM SQUARE TOTAL ERROR IN THE PARAME ITERS) 63 WRITE(6,5) ( E 2 ( I ) ,1 = 1, M) 64 5 FORMAT(1X,OG15.5) 65 WRITE(6,6) 66 6 FORMAT(88H VALUES OF X VALUES OF Y FITTED VALUES OF Y RESI 1DUALS Y BAR Y-YBAR) 67 DO 7 I=1,N 70 D I FF = Y{ I)-YBAR 71 R E S ( I ) = Y ( I ) - Y F ( I ) 72 7 WRITE(6,5) X ( I ) , Y ( I ) , YF( I ) ,RES(I) tYBAR,DIFF 73 WRITE(6,8 ) 74 8 FORMAT(1H1) 75 GO TO 3 76 END SIBFTC THS5B 77 FUNCTION AUX(P,.D,X,L) j 100 DIMENSION P ( 5 0 ) , D ( 5 0 ) ! 10:1 D(1 ) = 1. 102 AUX=P(1) 103 DO 10 J=2,5 104 o ( j ) = n ( J - I ) * x , 105 10 AUX = AUX,+ P ( J )*D( J) 106 RETURN 107 END GENTRY L - 4 EXECUTION INTERMEDIATE ESTIMATES OF PARAMETERS 0.00000E-38 0.00000E-38 FINAL ESTIMATES OF PARAMETERS NO 0 0.11310 -0.45928E-01 ESTIMATES OF ROOT MEAN SQUARE STATISTICAL ERROR IN THE PARAMETERS 0.29124 9.3490 ESTIMATES OF ROOT MEAN SQUARE TOTAL ERROR IN THE PARAMETERS 0.28971E-03 0.92999E-02 VALUES OF X VALUES OF Y FITTED VALUES OF Y RESIDUALS 0.00000E-38 0.11319 0. 11310 0.93316E-04 0.13407E-02 0.11319 0. 11303 0.15489E-03 0.26814E-02 0.10991 0.11297 -0 .30644E-02 0.4O221E-O2 0.11155 0.11291 -0.13624E-02 0.53628E-02 0.11319 0.11285 0 .33962E-03 0.67035E-02 0.11319 0.11279 0 .40119E-03 0.80442E-02 0.11319 0.11273 0.46277E-03 0.93850E-02 0.11155 0.11266 -0.11161E-02 0.10940E-01 0.11319 0.11259 0 .59577E-03 0.12308E-01 0.11319 0.11253 0 .65858E-03 0.13675E-01 0.11319 0.11247 0.72139E-03 0.15043E-01 0.11155 0.11240 -3 .85622E-03 0.16410E-01 0.11155 0.11234 -0 .79342E-03 0.17778E-01 0.11155 0.11228 -0.73061F-03 0.19339E-01 0.11319 0.1122 1 0 .98150E-03 0.20720E-01 0.11319 0.11214 0 . 10449E-02 0.22101E-01 0.11155 0. 11208 -0 .53204E-03 0.23483E-01 0.11155 0.11202 -0 .46860E-03 0.24864E-01 0.11319 0.11195 0 .12353E-02 0.26245E-01 0.11319 0.11189 0 . 12987E-02 0.27795E-01 0. 11319 0.11 182 0. 13699E-02 0.29185E-01 0.11155 0.11176 -0.20671E-03 0.30575E-01 0.11155 0.11169 -0.14288E-03 0.31964E-01 0.11319 0.11163 0 . 15614E-02 0.33354E-01 0.11155 0.11156 -3.15221E-04 0.34744E-01 0.11155 0.11150 0.48608E-04 0.41152E-01 0.11155 0.11121 0.34293E-03 0.47721E-01 0.11155 0.11090 3.64461E-03 0.53775E-01 0.10991 0.11063 -0.71776E-03 0.60586E-01 0.10991 0.11031 -0.40493E-03 0.67285E-01 0.10991 0.11001 -0.97276E-04 0.73625E-01 0.10827 0. 1097 1 -3.14465E-02 M - 1 Appendix M Input and Sample Output of the Multiple Regression Program for Run 19 Written by Kozak and Smith (45) The 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. (The predictive equation chosen i s i n Table XII and i s shown graphically i n F i g . 40.) Under the heading, "Independent Variable", the terms X(I), X1SQR, XICUB, and XIFOR -correspond to X, X 2, X 3, and. X^ respectively i n the polynomial model. The unit used f o r length (e.g., Y) i s feet, and f o r time (e.g., X), seconds. M - 2 L E O P O L D O C O R D E R O J R . F O R T R A N S O U R C E L I S T I S N S O U R C E S T A T E M E N T 0 S I B F T C D A T A C MULTIPLE REGRESSION PROGRAM (CODED BY A. KOZAK) FOR RUN 19 1 * 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) 2 D I M E N S I O N X ( 7 0 ) , A V I 7 0 ) , P R O D ( 7 0 , 7 0 ) , X M I N ( 7 0 ) , X M A X ( 7 0 ) 3 * DO 5 K = 1 , N K 0 W 4 R E A D ( 5 , 4 ) ( X ( I ) , I = 1 , N R E A D ) 1 1 t 4 F O R M A T ( 2 F 1 5 . 7 ) c X = V A R I A B L E S + c T R A N S F O R M A T I O N S E N T E R E D H E R E 12 X ( 3 ) = X ( 1 ) * X ( 1 ) 1 3 * X ( 4 ) = X ( 3 ) * X ( I ) 1 4 * X ( 5 ) = X ( 4 ) * X ( 1 ) 15 IF I K . N C I ) GO TO 3 1 c 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 2 0 * DO 2 I = i , N V A R 2 1 * X M I N U )=X( I ) 2 2 * 2 X M A X ( I ) = X{ I ) 2 4 3 DO 1 I = 1 , N V A R 2 5 * I F ( X ( I ) . L T . X M I N ( I ).) X .MINI I ) = X ( I ) 3 0 * I F ( X ( I ) . G T . X M A X ( I ) ) X M A X I I )=.X( I ) 3 3 1 C O N T I N U E t C C A L C U L A T E SUMS ( A V ) AND P R O D U C T S ( P R O D ) 3 5 * DO 5 I = 1 , N V A R 3 6 * AV{ I ) = A V ( I ),+ X( I ) 3 7 DO 6 J = I , N V A R 4 0 * P R O D ( I , . J ) = P R O D ( I , J )+X ( I ) *X { J ) 4 1 6 P R C D ( J , I ).= P K C D ( I »J . ) . 4 3 * 5 C O N T I N U E 4 6 * R E T U R N 4 7 * END I NO M E S S A G E S FOR A B O V E A S S E M B L Y 0 1 H R S 4 6 M I N 2 9 . 9 S E C M - 3 R E G R E S S I O N A N A L Y S I S , THE D E P E N D E N T V A R I A B L E I S Y I N D E P E N D E N T R E G R E S S I O N STANDARD V A R I A N C E V A R I A B L E C G E F F I C IENT D E V I A T I O N R A T I O X I I ) G . 2 2 0 3 2 1 E - 0 1 0 . 1 2 2 9 7 0 E 0 0 0 , 0 3 2 X 1 S C R - 0 . 5 9 2 4 2 5 E OO 0 . 7 4 0 9 2 9 E 0 1 0 . 0 0 6 X I C U B - 0 . 1 4 0 9 0 0 E 0 2 0 . 1 5 9 5 7 4 E 0 3 0 . 0 0 8 X 1 F 0 R 0 . U 6 9 6 9 E 0 3 0 . 1 1 1 1 5 0 E OA 0 . 0 1 1 CONSTANT TERM ^ 0 . 1 1 2 3 4 6 E 0 0 STANDARD ERROR OF E S T I M A T E = 0 . 9 3 1 8 4 1 E - 0 3  K E S I C U A L V A R I A N C E = 0 . 8 6 8 3 2 7 E - 0 6 M U L T I P L E C O R R E L A T I O N C O E F F I C I E N T = 0 . 7 5 1 5 9 R SQUARED = 0 . 5 6 4 8 9 V A R I A N C E R A T I O =i 8 . 7 6 3 WITH 4 ANO 2 7 D E G R E E S OF FREEDOM THE V A R I A B L E TO OE OMITTED I S = X 1 S G R R E G R E S S I O N A N A L Y S I S , THE DEPENDENT V A R I A B L E I S Y I N D E P E N D E N T R E G R E S S ION STANDARD VAR I A NCI": V A R I A B L E C O E F FIt IENT D L V I A I ION RA nn X ( I ) 0 . 1 2 5 4 3 8 E - 0 1 0 . 3 1 6 6 7 0 E - 0 1 0 , 1 5 7 X I C U B - 0 . 2 6 6 3 5 9 E 0 2 0 . 2 8 5 2 8 1 E 0 2 0 , 8 7 2 X 1 F 0 R 0 . 2 0 1 3 7 0 E 0 3 0 . 3 4 1 8 5 4 E 0 3 0 , 3 4 7 CONSTANT TERM =; 0 . 1 1 2 3 7 9 E 0 0 STANDARC ERROR OF E S T I M A T E = 0 . 9 1 5 1 5 8 E - 0 3 R E S I D U A L V A R I A N C E «= 0 . 8 3 7 5 1 4 E - 0 6 M U L T I P L E C O R R E L A T ICN C O E F F I C I E N T = 0 . 7 5 1 5 2 R SQUARED = C . 5 6 4 7 9 V A R I A N C E R A T I O =; 1 2 . 1 1 2 WITH 3 AND 2 8 D E G R E E S OF FREEDOM THE V A R I A B L E TO BE OMITTED I S = XI I ) R E G R E S S I O N A N 4 L Y S I S , THE D E P E N D E N T V A R I A B L E I S Y I N D E P E N D E N T R E G R E S S I O N STANDARD VAR ! ANCE V A R I A B L E C O E F F I C I E N T DEVI AT ION R A T I O X I C U B - 0 . 1 6 7 3 2 8 E 0 2 0 . 1 3 5 4 0 2 E 0 2 1 . 5 2 7 X 1 F 0 R 0 . 9 0 7 6 5 6 E 0 2 0 . 1 9 4 3 4 1 E 0 3 0 . 2 1 8 CONSTANT TERM =, 0 . 1 1 2 5 1 6 E 0 0 STANDARD ERROR: OF E S T I M A T E = 0 . 9 0 1 7 5 7 E - 0 3 R E S I D U A L V A R I A N C E = 0 . 8 1 3 1 6 5 E - C 6 M U L T I P L E C O R R E L A T I O N C O E F F I C I E N T = 0 . 7 4 9 9 0 R SQUARED >= C . 5 6 2 3 5 M - 4 VARIANCE RATIO = 18.631 WITH 2 AND 29 DEGREES OF FREEDOM THE VARIABLE TO BE OMITTED IS = X1FCR REGRESSION ANALYSIS, THE DEPENDENT VARIABLE IS Y INDEPENDENT REGRESSION STANDARD VARIANCE VARIABLE COEFFICIENT DEVIATION RAT3U XICUB -0. 104601E 02 0.169605E 01 33,036 CONSTANT TERM =; 0.112462E 00 STANDARD ERROR OF ESTIMATE = 0.B89928E-03 RESIDUAL VARIANCE * 0.791972E-06 MULTIPLE CORRELATION COEFFICIENT = 0.74770  R SQUARED <= 0. 55906 VARIANCE RATIO =. 38.036 WITH I AND 30 DEGREES OF FREEDOM THE VARIABLE RETAINED IS = XICUB THE VARIABLES SELECTED FOR ALL COMBINATIONS ARE = XICUB XISQR X1F0R REGRESSION ANALYSIS, THE DEPENDENT VARIABLE IS INDEPENDENT VARIABLE XICUB XISQR X1F0R REGRESSION COEF.FIC IENT -G.400221E 02 0.688595E 00 0. 2 8 6 1 U E 03 STANDARD DEVIATION 0.660099E 02 0.190892E 01 0.576366E 03 VAR I A N C E R A T I O 0,363 0,130 0.246 CONSTANT TERM =. 0. 112433E 00 STANDARD ERROR OF ESTIMATE = 0.915593E-03 RESIDUAL VARIANCE = 0.8383UE-06 MULTIPLE CORRELATION COEFFICIENT = 0.75125 R SQUARED = 0.56437 VARIANCE RATIO =i 12.092 WITH AND 28 DEGREES OF FREEDOM REGRESSION ANALYSIS, THE DEPENDENT VARIABLE IS INDEPENDENT VARIABLE REGRESSION COEFFICIENT STANDARD OEVIATION VARIANCE RAT 5 0 XICUB X1SCR -0.759214E 01 -G.201739E 00 0.932951E 01 0.644984E 00 0,662 0,098 CONSTANT TERM =, 0. 1 12520E 00 STANDARD ERROR OF ESTIMATE = C.903619E-03 RESIOUAL VARIANCE * 0.816527E-06 MULTIPLE CORRELATION COEFFICIENT = 0.74869 M - 5 c R SCUARED = C56C54 VARIANCE RATIO =. 10.495 WITH 2 AND REGRESSION ANALYSIS. THE DEPENDENT VARIABLE IS 29 OEGREES Y OF FREEDOM ? INOEPENDENT VARIABLE REGRESSION COEFFICIENT STANDARD DEVI A TION VAR I ANCE RA T t 0 X1CUQ 0. 167328E 02 0.135402E 02 I ,527 XIFOR 0.907656E 02 0.194341E 03 0 > ? 1 8 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 29 DEGREES OF FREEOOM REGRESSICN ANALYSIS, THE DEPENDENT VARIABLE IS Y INDEPENDENT VARIABLE REGRESSION COEFFICIENT STANDARD DEVI AT ION VAR! ANCE RATIO X1SCR 0.443410E 00 0.393214E 00 I ,2 72 XI FOR 0.597398E 02 0 . 816352E 02 0,5 36 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 29 DEGREES OF FREEOOM REGRESSION ANALYSIS. THE OEPENOENT VARIABLE IS Y INDEPENDENT VARIABLE REGRESSION COEFFICIENT STANDARO DEVI AT ION VARIANCE RATIO X1CUB 0.104601E 02 0.169605E 01 38,0 36 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 30 DEGREES OF FREEDOM V REGRESSION ANALYSIS, THE DEPENDENT VARIABLE IS Y M - 6 INDEPENDENT REGRESSION STANDARD VARIANCE VARIABLE COEFFICIENT DEVIATION RATIO XISQR -0 .717593E 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 30 DEGREES OF FREEDOM REGRESSION ANALYSIS, THE DEPENDENT VARIA8LE IS Y INDEPENDENT REGRESSION STANDARD VARIANCE VARIABLE COEFFICIENT DEVIATION RATIO X1F0R - 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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