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Two component fluidization. LeClair, Brian Peter 1964-10-04

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TWO COMPONENT FLUIDIZATION hy B r i a n P. Le C l a i r B.A.Sc, U n i v e r s i t y of B r i t i s h Columbia, I962 A THESIS SUBMITTED IN PARTIAL TULFILMENT 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 to the r e q u i r e d standard Members of the Department of Chemical Engineering THE UNIVERSITY OF BRITISH COLUMBIA January, 196k I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the r equirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y - a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t per 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 of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s , , I t i s understood that , copying, or p u b l i  c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d without my w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y of B r i t i s h Columbia,. Vancouver 8, Canada. Date (jOu.. /£> j /?* . > v i i Abs t r a c t Studies were made of the d i s t r i b u t i o n of components, when two m a t e r i a l s are f l u i d i z e d i n a l i q u i d . The hypothesis t e s t e d was that the d i s t r i b u t i o n of m a t e r i a l i s a f u n c t i o n o f the bulk d e n s i t y d i f f e r e n c e of •,the component beds. The component bed having the gr e a t e s t bulk d e n s i t y w i l l occupy the bottom of the t o t a l bed. I t i s p o s s i b l e f o r the bulk d e n s i t y of one m a t e r i a l to be grea t e r than the other at low v e l o c i t i e s , and l e s s than the other at high v e l o c i t i e s . At some intermediate c o n d i t i o n the bulk d e n s i t y d i f f e r e n c e between the two beds must be zero. This s i t u a t i o n , c a l l e d the i n v e r s i o n p o i n t , produces homogeneous mixing of the two components. Mixtures of two m a t e r i a l s f o r which an i n v e r s i o n was p r e d i c t e d by the st a t e d hypothesis were t e s t e d . In the intermediate and t u r b u l e n t flow regions i n v e r s i o n s d i d not occur because macroscopic mixing destroyed the bulk d e n s i t y gradients b e i n g e s t a b l i s h e d . However, i n the laminar flow region, where mixing was n e g l i g i b l e , i n v e r s i o n s d i d occur. The q u a l i t y o f the i n v e r s i o n was a f f e c t e d as f o l l o w s . For a sharp c l e a r i n v e r s i o n of the two m a t e r i a l s at the p r e d i c t e d v e l o c i t y , the diameter r a t i o of the two groups of p a r t i c l e s must be much greater than one and the den s i t y r a t i o ( c o r r e c t e d f o r buoyancy) o f the two groups of p a r t i c l e s must be much l e s s than one. Also of importance i s the absolute d e n s i t y ( c o r r e c t e d f o r buoyancy) of the p a r t i c l e s . P a r t i c l e s i z e d i s t r i b u t i o n a l s o appeared to s t r o n g l y a f f e c t the q u a l i t y of the i n v e r s i o n . These d i s t r i b u t i o n s set up ba l k d e n s i t y gradients w i t h i n the s i n g l e component beds. This appeared to cause mixing of the two components and i n some cases even formation of the two i n v e r t e d beds before the p r e d i c t e d i n v e r s i o n v e l o c i t y was reached. v i i i The p r e d i c t i o n of the bed expansion of mixtures was a l s o studied. A c o r r e l a t i o n was developed on the assumption t h a t each component of the mixture c o u l d be t r e a t e d separately. The o v e r a l l expansion thus would be the sum of the expansions of the i n d i v i d u a l components. There was very good agreement between values p r e d i c t e d by t h i s method and experimental data. The method p r e d i c t e d expansion w e l l f o r a l l degrees of mixing o f the two components, but d i d not p r e d i c t w e l l when one of tiie components was near i t s minimum p o r o s i t y f o r f ' l u i d i z a t i o n . The e m p i r i c a l equations of Richardson and Zaki (k) f o r s i n g l e component l i q u i d f l u i d i z a t i o n expansions were checked. The values of the index " n " Obtained from experimental data agreed w i t h i n + 5$ of those c a l c u l a t e d u s i n g the c o r r e l a t i o n s . The equation developed by Richardson and Zaki f o r determining the f r e e s e t t l i n g v e l o c i t y of a s i n g l e p a r t i c l e from e x t r a p o l a t e d expansion data gave r e s u l t s which were w i t h i n + 15$ of those obtained using the standard drag c o e f f i c i e n t - R e y n o l d s number p l o t f o r an i s o l a t e d sphere. v i Acknowledgement I am indebted t o Dr. Norman E p s t e i n , under whose guidance t h i s study was made, f o r h i s encouragement and a s s i s t a n c e during the course of t h i s p r o j e c t . The assistance^ of Mr. R. Muelchen and the Workshop s t a f f i s appreciated f o r t h e i r p r o f i c i e n c y at b u i l d i n g the equipment to the s p e c i f i c a t i o n s r e quired. I a l s o wish to thank the N a t i o n a l Research C o u n c i l of Canada f o r f i n a n c i a l a s s i s t a n e e r r e c e i v e d , and the Department of Chemical Engineering at U.B.C. f o r a d d i t i o n a l support. i Table of Contents * Page Acknowledgement vi A b s t r a c t " vii Nomenclature ix I n t r o d u c t i o n 1 Theory 4 (A) Free S e t t l i n g V e l o c i t y of a P a r t i c l e 4 (B) Bed Expansion C o r r e l a t i o n s 6 (c) F r i c t i o n a l Pressure Drop i n a F l u i d i z e d Bed . . . . 9 (D) S t r a t i f i c a t i o n 10 ( E ) T h e o r e t i c a l D e r i v a t i o n f o r I n v e r s i o n 12 (F) Mixed Bed Height P r e d i c t i o n s l6 Apparatus 19 (A) General 19 (B) Test Sect i o n . . 23 Experimental Procedures 29 (A) General Operating Procedure 29 (B) Flow Meters 29 (C) Measurement of V i s c o s i t y and Density of Test F l u i d . 34 (D) Measurement of P a r t i c l e Density 35 (E) S i z i n g of P a r t i c l e s 35 R e s u l t s 37 (A) Experiments w i t h a Single Species 37 1. Bed Expansion ' 37 2 . D i f f e r e n t i a l Pressure' Measurements 46 (B) Experiments w i t h two Species 50 1. I n v e r s i o n of Mixtures 50 2 . P r e d i c t i o n o f Bed Expansion f o r Mixtures . . . 75 i i Page Conclusions 83 Literature Cited 89 Appendix I - Bearet', s Plots for Prediction of Inversion?! Porosities . 1-1 Appendix II - Sample Calculations and Error Analysis . . . . 2-1 Appendix III - Materials Used . 3-1 Appendix IV - Original Data 4-1 Appendix V - Measurement of Longitudinal Particle Concentration (Proposed Method) 5©! i i i Tables Page 1. O r i f i c e Meter S i z e s . . ' 21 2. Accuracy of Flow Meter C o r r e l a t i o n s 31 3. Least Squares Equations f o r Meters 31 k. Summary of F l u i d i z a t i o n R e s ults f o r P a r t i c l e s i n Water . . . 38 5. Summary of F l u i d i z a t i o n R e s ults f o r P a r t i c l e s i n G l y c o l . . . 39 6. Comparison of Results w i t h Richardson and Zaki C o r r e l a t i o n s - - 'kO Water 7. Comparison of Re s u l t s w i t h Richardson and Zak i C o r r e l a t i o n s - 41 G l y c o l • 8 . I n v e r s i o n Results f o r N i c k e l and B a l l o t i n i 5§ 9/ I n v e r s i o n Results f o r Alundum and B a l l o t i n i "57 10. I n v e r s i o n R e s u l t s f o r .Lead and S t e e l 62 11. I n v e r s i o n Results f o r N i c k e l - G l a s s and B a l l o t i n i 12. Q u a l i t y - o f - I n v e r s i o n P r e d i c t i o n s ' 71 i v L i s t of I l l u s t r a t i o n s Figure Page 1. F r i c t i o n a l Pressure Drop Across a F l u i d i z e d Bed 11 2 . P r e d i c t i o n of F l u i d i z e d Bed Invers ion . 15 3- Schematic Diagram of Apparatus 2 0 4 . Schematic Diagram of a S e c t i o n a l View of the Column . . . . 25 5- Diagram of Entry Sec t ion To and E x i t Sect ion from Column . 26 6 . Diagram of D i f f e r e n t i a l Pressure Measurement System . . . . 28 7. Flow-Meter C a l i b r a t i o n Curves f o r Water . . . . 32 8 . Flow-Meter C a l i b r a t i o n Curves f o r Polyethylene G l y c o l . . . 33 9> P l o t of Alundum and Cataphote Bed Expansion 43 1 0 . V i s u a l Observations of F l u i d i z a t i o n of Spheres 1+5 1 1 . F r i c t i o n a l Pressure Drop P r o f i l e s i n a B a l l o t i n i Bed . . . 48 F l u i d i z e d by Polyethylene G l y c o l 1 2 . F r i c t i o n a l Pressure Drop P r o f i l e s i n an Alundum Bed- F l u i d i z e d by Polyethylene G l y c o l 1+9 1 3 . P l o t of N i c k e l and B a l l o t i n i Bed Expansions 53 14. D i f f e r e n t i a l Pressure P r o f i l e s i n N i c k e l - B a l l o t i n i Bed . . 54 15- P l o t of Bulk Densi ty D i f f e r e n c e and V e l o c i t y f o r the N i c k e l - B a l l o t i n i Bed 55 1 6 . Schematic Diagram of how Inversion Proceeded 56 1 7 . P l o t of Alundum and B a l l o t i n i Bed Expansions i n 58 Polyethylene G l y c o l 1 8 . D i f f e r e n t i a l Pressure P r o f i l e s i n A l u n d u m - B a l l o t i n i Bed . . 59 1 9 . P l o t of Bulk Densi ty D i f f e r e n c e and V e l o c i t y f o r the A l u n d u m - B a l l o t i n i Bed 6 0 2 0 . Schematic Diagram of How Invers ion Proceeded 6 l 2 1 . P l o t of Lead and S t e e l Bed Expansions . . 6 3 2 2 . D i f f e r e n t i a l Pressure P r o f i l e s i n Lead-Steel Bed 64 2 3 . P l o t of Bulk Densi ty D i f f e r e n c e and V e l o c i t y f o r the Lead-Steel Bed 6 5 Figure • Page 24. Plot of Nickel-Glass and B a l l o t i n i Bed Expansions i n Polyethylene G l y c o l 67 2 5 . P l o t of Bulk Density Difference and V e l o c i t y f o r the N i c k e l - G l a s s - B a l l o t i n i Bed 6 8 26. E f f e c t of P a r t i c l e Size D i s t r i b u t i o n on the Point of Inversion 7* 2 7 . P l o t of Alundum-Crystalon Run No.l 77 28. Plot of Alundum-Crystalon Run No.2 7 8 2 9 . Plot of Alundum and B a l l o t i n i Bed Expansions i n Water . 79 ;>30. Plot of Nickel-Glass and B a l l o t i n i Bed Expansions i n Water ' • • 80 3 1 . Plot of Ni c k e l and Alundum Bed Expansions . . . . . . . 8 1 3 2 . P l o t o f Nickel-Glass and B a l l o t i n i Bed Expansions with D i f f e r e n t Volumes of Each Component 8 2 3 3 . P a r t i c l e Size D i s t r i b u t i o n . . . • 8 7 - 3 4 . Beare Plot f o r the Stokes' Law Region 1-3 3 5 . Beare P l o t f o r the Newtons' Law Region . . 1-4 3 6 . Plot of P Ratio P r o f i l e s at Various Average P o r o s i t i e s 5 - 2 IX Nomenclature 2 A - c r o s s - s e c t i o n a l area of column, f t . b* - index i n Lewis and Bowenaan equation, dimensionless . C - modif ied o r i f i c e meter c o e f f i c i e n t , -t^L / P , where LL P V P , - P 2 ^ i s i n c e n t i p o i s e s and.the res t engineering u n i t s . LL / p C" - modif ied o r i f i c e meter c o e f f i c i e n t , - — - / - , a l l P V P, "P 2 engineering u n i t s . D - column diameter, f t . d - average p a r t i c l e diameter, f t . , mm. Fp. - g r a v i t a t i o n a l f o r c e , l b - f o r c e . Fp - drag f o r c e , l b - f o r c e , g - a c c e l e r a t i o n of g r a v i t y , f t . / s e c 2 g c - Newton's law conversion f a c t o r , ( f t . ) ( l b . ) / ( l b - f o r c e ) ( s e c . 2 ) k - v a r i a b l e constant , dimensionless . k ' - constant i n Lewis and Bowerman equat ion, dimensionless . l/m k" - constant c o n t a i n i n g l i q u i d p r o p e r t i e s and k, ^ , vm-l)/2 2-m P M dimensional . ; ' ' L - v e r t i c a l distance i n a f l u i d i z e d bed, f t . ; v e r t i c a l distance between a base p o s i t i o n i n the bed and an e levated p o s i t i o n , f t . M - weight of s o l i d p a r t i c l e s i n a f l u i d i z e d bed, l b s . in - s t a t e - o f - f l o w - i n d e x , dimensionless . n - Richardson and Zaki index, dimensionless . p - f l u i d pressure , l b - f o r c e / f t . App. - f r i c t i o n a l pressure l o s s i n a f l u i d i z e d bed, l b - f o r c e / f t . 2 P - P r a t i o , ( A p / L ) / ( A p / L )^ A. , -> dimensionless . p i p t h e o r e t i c a l Q - volumetric flow r a t e , f t . ^ / s e e . R - p a r t i c l e Reynolds number, ^^P , d imensionless . r - p a r t i c l e dianeterrratio, d ( / d ^ , dimensionless. t - time of e f f l u x f o r f l u i d i n viscometer tube, sec. V - v e l o c i t y of f l u i d , f t . / s e c . V 0 - free s e t t l i n g v e l o c i t y of a p a r t i c l e , f t . / s e c Vj - s u p e r f i c i a l l i q u i d v e l o c i t y when Richardson and Zaki p l o t i s extrapolated to € = 1 . 0 , f t . / s e c . Vp - v e l o c i t y of p a r t i c l e i n a f l u i d i z e d bed, f t / s e c . V s - s u p e r f i c i a l l i q u i d v e l o c i t y , f t . / s e c . VS|jp - s l i p v e l o c i t y "between p a r t i c l e and f l u i d , f t . / s e c . V - volume of a f l u i d i z e d bed f r a c t i o n , f t . 3 - . Vf- - t o t a l volume of f l u i d i z e d bed, l b s . Wm - weight of s o l i d s mixture i n f l u i d i z e d bed, l b s . W - weight of a s p e c i f i c f r a c t i o n of solids, i n f l u i d i z e d bed, l b s . V - density corrected f o r buoyancy r a t i o , ( psy —p )/( p$2.~p)> dimensionless. € - p o r o s i t y of f l u i d i z e d bed, dimensionless. € m f - minimum por o s i t y f o r f l u i d i z a t i o n , dimensionless. €m - average p o r o s i t y of mixture, dimensionless. fJt.,fJLf - v i s c o s i t y of f l u i d , l b . / ( f t . )(sec. ) . p.g v . . . . v i s c o s i t y of i'luidized suspension, l b . / ( f t . ) ( s e c ) . p,Pl - density of f l u i d l b . / f t . 3 . Pg - density of f l u i d i z e d suspension, l b . / f t . . p^ - bulk density of f l u i d i z e d bed, l b . / f t . ^ . p - density of s o l i d p a r t i c l e s , gm./cm.^ , l b s . / f t . 3 . * s <j) - weight f r a c t i o n of a s o l i d component of a mixture, subscripts 1, 2, A, B - s p e c i f i c f l u i d i z e d beds of p a r t i c l e s j 1 and 2 also denote upstream, and downstream taps, r e s p e c t i v e l y , on flowmeters, i - any i n d i v i d u a l f l u i d i z e d bed f r a c t i o n . f r e e s e t t l i n g c o n d i t i o n s . f r i c t i o n a l ; a l s o denotes g r a v i t a t i o n a l u n i t s o f f o r c e t e s t s e c t i o n based on empty tube. INTRODUCTION 1. F l u i d i z a t i o n i s a process w i d e l y used i n i n d u s t r y , but the theory and techniques f o r design of l i q u i d f l u i d i z a t i o n equipment and processes are not f u l l y understood at the present time. Thus a sound program based on t h e o r e t i c a l development and experimentation must be c a r r i e d out to develop r e l i a b l e design c r i t e r i a . The present work was formulated to study l i q u i d f l u i d i z a t i o n of two component mixtures of s o l i d s , f o r example, a mixture of l e a d and s t e e l f l u i d i z e d by water. The two m a t e r i a l s would have s p e c i f i e d diameter and d e n s i t y r a t i o s such t h a t i n v e r s i o n of the m a t e r i a l s w i l l occur at some o v e r a l l p o r o s i t y above the minimum f l u i d i z a t i o n p o r o s i t y . Consider a f l u i d i z e d bed composed of m a t e r i a l A and m a t e r i a l B such th a t PsA *PsB A N ^ C'B > * F o r p a r t i c u l a r r a t i o s of PSA^PSB i n c o n j u n c t i o n w i t h s p e c i f i e d r a t i o s of dr^/d^ , the- f l u i d i z e d bed w i l l respond i n the f o l l o w i n g v/ay to changes i n s u p e r f i c i a l l i q u i d v e l o c i t y . At low flow rates' the f l u i d i z e d bed w i l l be made up of two l a y e r s , one above the other, such t h a t a l l the heavy small p a r t i c l e s w i l l form a f l u i d i z e d assemblage at the bottom of the column q u i t e d i s t i n c t from the l i g h t l a r g e ones which have formed an assemblage above the small heavy p a r t i c l e s . S i m i l a r l y at high v e l o c i t i e s the f l u i d i z e d bed w i l l again be composed of two d i s t i n c t s t r a t a , but now the l a r g e l i g h t p a r t i c l e s w i l l be at the bottom and the heavy small p a r t i c l e s w i l l be at the top of the bed. At some intermediate v e l o c i t y between the two extremes i n v e r s i o n occurs. Trie i n v e r s i o n mode has been de f i n e d as the p o i n t of changeover, or the p o i n t of homogeneous f l u i d i z a t i o n of the two species of p a r t i c l e s . I n v e r s i o n of the sor t described above can occur because of the nature of p a r t i c u l a t e f l u i d i z a t i o n . Wilhelm and Kwauk ( l ) have described p a r t i c u l a t e f l u i d i z a t i o n , u s u a l l y but not always synonymous w i t h l i q u i d f l u i d i z a t i o n , a s " c h a r a c t e r i z e d by the separation of i n d i v i d u a l p a r t i c l e s much i n the manner of a gas. A mean f r e e path can be observed, and the length of the path i s found to increase w i t h v e l o c i t y . " Thus l i q u i d f l u i d i z a t i o n i s observed to be an ordered expansion of the p a r t i c l e s i n the bed, without r a p i d l a r g e s c a l e c i r c u l a t i o n and mixing of p a r t i c l e s . Because of t h i s , the p o s i t i o n of the p a r t i c l e s i n a f l u i d i z e d bed w i l l be governed almost e x c l u s i v e l y by drag and g r a v i t a t i o n a l f o r c e s , on which the i n v e r s i o n phenomenon i s based. Q u a l i t a t i v e observations of i n v e r s i o n s have been described by two e a r l i e r workers, namely, Hancock ( 2 ) and J o t t r a n d ( 3 ) . Hancock ( 2 ) i n 1936 discussed and d e s c r i b e d i n v e r s i o n s of the type described above. The observations made were: ( 1 ) At s i m i l a r v e l o c i t i e s i n a column of f l u i d i z e d mixed sands, the "bulk d e n s i t y , yDg , developed by the bed increases from the top downwards, whereas w i t h a uniform sand the bulk d e n s i t y i s uniform down the bed. ( 2 ) I f one uniform sand has a p a r t i c u l a r bulk d e n s i t y at a p a r t i c u l a r l i q u i d v e l o c i t y , then i t i s p o s s i b l e f o r another uniform sand of a d i f f e r e n t s o l i d d e n s i t y to develop the same b u l k d e n s i t y at the s p e c i f i e d l i q u i d v e l o c i t y i f the s i z e of i t s p a r t i c l e s i s s u i t a b l y r e l a t e d t o the p a r t i c l e s i z e of the former p a r t i c l e s . ( 3 ) When two uniform sands develop the same bulk d e n s i t i e s at a p a r t i c u l a r l i q u i d v e l o c i t y , the t o t a l mixture behaves as one uniform bed. J o t t r a n d ( 3 ) has observed a s i m i l a r phenomenon but, as w i t h Hancock, no q u a n t i t a t i v e measurements were recorded. In J o t t r a n d ' s work a s p e c i a l case i n v o l v i n g one component f l u i d i z e d and the other u n f l u i d i z e d i s reported. The c o n c l u s i o n drawn by J o t t r a n d was", however, equivalent to 3- . t h a t drawn by Hancock, namely t h a t , the primary f a c t o r governing c l a s s i f i c a t i o n i n f l u i d i z e d beds i s the average bulk, d e n s i t y developed by each of the components of the mixture f l u i d i z e d seperately. In order to c o r r e l a t e data obtained on two component f l u i d i z a t i o n , the l i t e r a t u r e was searched to determine the best method f o r measuring p a r t i c l e concentrations at v a r i o u s l o c a t i o n s i n the bed. Most l i q u i d f l u i d i z a t i o n data have been c o r r e l a t e d by bed expansion ( € vs. V s ) and d i f f e r e n t i a l pressure gradient ( App/L v s ; V s ) through the bed. A n a l y s i s showed th a t the bulk d e n s i t y d i f f e r e n c e between two s e c t i o n s of a bed was e'quivalent or at l e a s t p r o p o r t i o n a l to the d i f f e r e n c e i n d i f f e r e n t i a l f r i c t i o n a l pressure gradient between the s e c t i o n s . Therefore measurements of f r i c t i o n a l pressure l o s s p r o f i l e s c o u l d be used to determine bulk d e n s i t y p r o f i l e s and hence l o n g i t u d i n a l p a r t i c l e d i s t r i b u t i o n s , i n a f l u i d i z e d bed. k. THEORY A. Free S e t t l i n g V e l o c i t y of a P a r t i c l e I f a p a r t i c l e i s f a l l i n g under the i n f l u e n c e of g r a v i t y i n a f l u i d medium, the p a r t i c l e w i l l a c c e l e r a t e to a constant t e r m i n a l v e l o c i t y , VQ . T i l l s v e l o c i t y i s dependent on the diameter, shape and d e n s i t y of the p a r t i c l e and the p r o p e r t i e s of the- f l u i d through which i t i s f a l l i n g . The constant t e r m i n a l v e l o c i t y w i l l be achieved when the buoyancy-corrected g r a v i t a t i o n a l a c c e l e r a t i n g f o r c e , Fg, i s counterbalanced by the r e s i s t i n g upward drag f o r c e , F^. For spheres, 6 and F 0= _l_CD/> 7Td 2 V 2 2 8 On equating F g and F Q of equations 1 and 2, the drag c o e f f i c i e n t , C Q , i s then given by . 4 d g c ( p s - f ) 3 ° D = i 3V02/> The p a r t i c l e drag data can be represented i n terras of a p l o t s i m i l a r to the f r i c t i o n f a c t o r - Reynolds number p l o t f o r p r e s e n t i n g p i p e l i n e pressure drop data. The drag c o e f f i c i e n t i s p l o t t e d against the Reynolds number based on a c h a r a c t e r i s t i c p a r t i c l e dimension and on the r e l a t i v e v e l o c i t y between the p a r t i c l e and the f l u i d medium. The drag c o e f f i c i e n t - Reynolds number curve has been d i v i d e d i n t o three regions, the Stokes" Law or laminar range, the intermediate r e g i o n , and the Newton or t u r b u l e n t region. In each region the curve has been approximated by a s t r a i g h t l i n e . For the i n d i v i d u a l ranges Crj iaay be approximated as f o l l o w s . Stokes* Region Re0< 0-3 C D = 24/Re 4 V 0 - D 18/x Intermediate Region 03 < Re0< 500 CD= l8-6Re"0'6 ,H4_ 0-714 «\0-7l4 0 u 0-428 Q 0 289 Newton Region 500 < Re0< 500,000 CD= 0-44 8 3g c d( /3 s - /3 ) l ° - 5 • : 9 G e n e r a l i z i n g , i t can be s t a t e d t h a t the drag f o r c e F Q i s given by the f o l l o w i n g equation: F D =kV 0 r n d m / i 2' m/o m H io At low values of Reynolds number, where f l u i d r e s i s t a n c e i s independent of d e n s i t y , m equals 1 .0 , but t h i s index increases to 2 . 0 at high values of the Reynolds number, where f l u i d r e s i s t a n c e i s independent of v i s c o s i t y . Equating equations 1 and 10, v/e ob t a i n a g e n e r a l i z e d equation f o r the f r e e s e t t l i n g or t e r m i n a l v e l o c i t y of f a l l of a p a r t i c l e : 6. . / » , / m £-1 k ( / V / » <* 11 1 The constant, k, i n the equation v a r i e s from ^-pin the Stokes' region to B. Bed Expansion C o r r e l a t i o n s Numerous equations have been developed f o r c o r r e l a t i n g bed expansion data, but there does not seem to be much agreement among workers as to which c o r r e l a t i o n i s best. At the present time, the most comprehensive and e a s i e s t c o r r e l a t i o n s to apply are the simple power f u n c t i o n s r e l a t i n g p o r o s i t y and s u p e r f i c i a l l i q u i d v e l o c i t y . Various s t u d i e s reported i n the l i t e r a t u r e on the v e l o c i t y - voidage r e l a t i o n s h i p i n m u l t i p a r t i c l e systems are analysed i n the f o l l o w i n g s e c t i o n s . Happel (6) developed an equation f o r expansion r e l a t i o n s h i p s , by using the Navier-Stokes' equations without the i n e r t i a l terms t o describe the motion of m u l t i p a r t i c l e systems. The model of a f l u i d i z e d or sedimenting bed was th a t of a number of c e l l s , each c o n s i s t i n g of a s p h e r i c a l p a r t i c l e at the center enclosed by a s p h e r i c a l envelope of f l u i d . The volume of f l u i d w i t h i n the envelope was such t h a t the p o r o s i t y of a c e l l was equal to the o v e r a l l p o r o s i t y of the bed, and the envelope i t s e l f was assumed to behave l i k e a f r e e surface. That i s , to obey the c o n d i t i o n of zero shear s t r e s s a t the f l u i d - f l u i d boundary. Disturbances caused by p a r t i c l e s were confined to the c e l l i n which they were associated. The r e l a t i o n s h i p developed on these p o s t u l a t e s i s given by in. t h e Newton re g i o n , f o r a s p h e r i c a l p a r t i c l e . V 3 - 4-5(l-€),/s +4-5(l-€)8 / s - 3(l-€)2 7. This equation provides good agreement with experiment at very high and very low voidage, and at low Reynolds numbers, but i s poor outside of these regions. Hawksley (7) developed an equation based on the following proposals: ( l ) What i s important i s not the f l u i d density or v i s c o s i t y but the suspension density and v i s c o s i t y . (2) The r e l a t i v e v e l o c i t y between f l u i d and p a r t i c l e s i s V s / € . Thus the f l u i d i z e d bed density and v i s c o s i t y are given by the following equations: H-€ = H-fe*P £H(I-€)/(0-64+€)] 13 Substitution of equations 13 and 14 into the Stokes' Law equation gives V s = r r — ~ 15 18/xexp [4 l ( l -€) / (0-64 + €)j so that V 0 " exp [41 ( l -€) / (0-64 + € ) j The agreement of t h i s equation with experimental data i s again good at low Reynolds numbers but not at high Reynolds numbers. Richardson and Zaki ( 4 ) have developed an equation based on the dynamic equilibrium of i n d i v i d u a l p a r t i c l e s as a function of the f l u i d i z e d bed and apparatus properties. The equation i s based on a-dimensional analysis development to determine the v a r i a b l e s which are important and how they are grouped, and a comprehensive group of experiments to determine the powers on the various f u n c t i o n a l groups. Dimensional analysis a n t i c i p a t e d the following groupings: •8. Vs f [ < i ^ P d 1 — = T ' » — t € 17 V0 L /J. D J The expansion equation developed was the f o l l o w i n g : Vs n — = € 18 Vi where Vj i s the v e l o c i t y obtained by e x t r a p o l a t i n g the l o g - l o g p l o t of s u p e r f i c i a l l i q u i d v e l o c i t y versus p o r o s i t y to a p o r o s i t y o f one. The power n i s a f u n c t i o n of both the flow regime and the apparatus: n = 4 G 5 + I95(d/D) Re0< 0-2 19 n= [ 4 4 5 + I8(d/D)] Re 0" 0 ' ' O2<Re 0< 2 0 0 20 n = 4-4 5 ReJ* 200<Re 0 < 5 0 0 2 1 n = 2-39 Re. > 5 0 0 2 ? o c-c- A l s o , i t has been shown by Richardson and Zaki;- 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 holds: »og V0 ' = log Vj + d/D 23 The c o r r e l a t i o n s of Richardson and Zaki have been subjected to rigor o u s t e s t s by comparing them w i t h extensive l i q u i d f l u i d i z a t i o n data from numerous l i t e r a t u r e sources. E x c e l l e n t agreement has been obtained, according to Leva ( 5 ) . These c o r r e l a t i o n s are the most r e l i a b l e method of p r e d i c t i n g expansion of l i q u i d f l u i d i z e d beds and are v a l i d v i r t u a l l y up to € = 1.0 . 9- Lev/is and Bowerman (8) developed an equation of the form •7 = V 0(k'€ b ' ) 2k where k' and b' are s p e c i f i c constants. This equation i s intended to take i n t o account the e f f e c t s that p a r t i c l e s may exert on each other. As these e f f e c t s should decrease as i n t e r p a r t i c l e spaces i n c r e a s e , the occurrence of bed voidage i n the r e l a t i o n s h i p shown above appears to be reasonable. In the absence of w a l l e f f e c t , when according to equation 23 V 0 = Vj , equation 2k i s o b v i o u s l y equivalent to equation 18 w i t h b' equal to n-1. C F r i c t i o n a l Pressure Drop i n a F l u i d i z e d Bed The f r i c t i o n a l pressure drop r e l a t i o n s h i p i n a f l u i d i z e d bed i s developed from the s u p p o s i t i o n t h a t the p a r t i c l e s i n a f l u i d i z e d bed are e n t i r e l y supported by the f l u i d . That i s , the weight gradient of the s o l i d bed i s equal to the f r i c t i o n a l pressure gradient through the bed caused by mass flow: Mg Ap - — [p%-p) 25 A£ sg c or Ape g L g c These equations were experimentally corrobbratedfor numerous s o l i d s f l u i d i z e d i n l i q u i d s by Wilhelm and Kwauk ( l ) . Most of Wilhelm and Kwauk's data agree w i t h the t h e o r e t i c a l equation w i t h i n 57°' The r e s u l t s of Richardson and Z a k i (k) tend t o i n d i c a t e t h a t the above equation holds f o r beds composed of p a r t i c l e s which have a r e l a t i v e l y low d e n s i t y and i n which the p a r t i c l e to column diameter r a t i o i s s m a l l . 10. For beds-composed of l a r g e p a r t i c l e s or very heavy p a r t i c l e s , channeling, b r i d g i n g and other aggregative e f f e c t s occur and equation 26 does not agree too w e l l w i t h experiment. Figure 1 shows a graph r e l a t i n g the f r i c t i o n a l pressure drop across a p a r t i c u l a t e l y f l u i d i z e d bed w i t h v e l o c i t y through the bed. A l s o shown i s a diagram of the pressure drop per u n i t length through a f l u i d i z e d bed. D. S t r a t i f i c a t i o n and C l a s s i f i c a t i o n Ah important problem which had not been worked on e x t e n s i v e l y i n the past i s s t r a t i f i c a t i o n and c l a s s i f i c a t i o n i n p a r t i c u l a t e l y f l u i d i z e d beds composed e i t h e r of one m a t e r i a l or of a number of m a t e r i a l s . Work i n the f i e l d of s t r a t i f i c a t i o n by s i z e i s b e i n g c a r r i e d on at the present time i n t h i s department and should provide some u s e f u l i n f o r m a t i o n . Richardson and Z'aki (k) showed t h a t i f a f l u i d i z e d bed i s composed of p a r t i c l e s of two d i s t i n c t s i z e ranges, then the small p a r t i c l e s w i l l form a bed on top of the bed of l a r g e p a r t i c l e s , and there w i l l be a d i s t i n c t i n t e r f a c e between the two beds. In a f l u i d i z e d bed composed of a continuous range of p a r t i c l e s i z e s the s o l i d s w i l l tend to arrange themselves so t h a t the greatest' amount of f i n e s w i l l be i n the upper p a r t of the bed. Verschoor (9) observed that s t r a t i f i c a t i o n of p a r t i c l e s w i l l • occur even f o r very narrow s i z e ranges (100 to 120 mesh). Andrieu (lO) s y s t e m a t i c a l l y s t u d i e d s t r a t i f i c a t i o n by s i z e i n w a t e r - f l u i d i z e d beds and found t h a t the p o r o s i t y o f the f l u i d i z e d bed increased from the bottom to the top of the f l u i d i z e d bed, 'a c o n c l u s i o n which he deduced from the observed decrease i n the. pressure gradient and hence the apparent or bulk d e n s i t y of the f l u i d i z e d bed. This f i n d i n g i s c o n s i s t e n t w i t h Hancock's (2) f i r s t o b s e r v a t i o n , p r e v i o u s l y discussed. 11 log (Ap F) fixed bed* - fluidized bed minimum velocity for fluidization (V m f ) log (V s ) Figure l a . T y p i c a l F l u i d i z a t i o n curve r e l a t i n g f r i c t i o n a l pressure l o s s across f l u i d i z e d "bed to s u p e r f i c i a l l i q u i d v e l o c i t y . fixed bed — tronsport fluidized bed log (Ap F ) L * = * m f log(V s ) Figure l b . T y p i c a l f l u i d i z a t i o n curve r e l a t i n g f r i c t i o n a l pressure l o s s per u n i t height across a bed of p a r t i c l e s to s u p e r f i c i a l l i q u i d v e l o c i t y . 1 2 . E. T h e o r e t i c a l D e r i v a t i o n f o r I n v e r s i o n The d r i v i n g f o r c e f o r segregation or s t r a t i f i c a t i o n o f two groups of p a r t i c l e s i n a p a r t i c u l a t e l y f l u i d i z e d bed' i s assumed to be the d i f f e r e n c e i n bulk d e n s i t y of the beds formed by each group of p a r t i c l e s when they are i n d i v i d u a l l y subjected to the given s u p e r f i c i a l l i q u i d v e l o c i t y . The bulk d e n s i t y of a f l u i d i z e d bed i s given by The d i f f e r e n c e i n bulk d e n s i t y between two beds composed of p a r t i c l e s 1 Many bed expansion f u n c t i o n s e x i s t , but the simplest equation and th a t which represents e m p i r i c a l data best over the whole range encountered i s th a t of Richardson and Zaki (k), which i s PQ = ( i - « ) / > s + € P 27 and 2 , r e s p e c t i v e l y , i s th e r e f o r e 28 29 or from equation 2 3 , 30 The f r e e s e t t l i n g v e l o c i t y i s given by equation 1 1 , which i s v0 - k M (/>,-/» d l/m (3-m)/m Combining equations 30 and 3 1 , = 10 - d / D , II *IP,-P) d l/m (3-m)/m n 13- As p a r t i c l e s 1 and 2 are subjected to the same s u p e r f i c i a l l i q u i d v e l o c i t y , i t f o l l o w s t h a t dj J _ 3 -m, dig I 3 - m 2 k'|lO {ps}-p) 'd, €,' = k'ilO (Psz-P) d 2 2 € 2 2 33 I f the assumption i s made th a t both groups of p a r t i c l e s f l u i d i z e d w i t h i n the same flow regime, t h a t i s , i n a given region of ReQ (e.g. the Stokes' region or the Newton r e g i o n ) , then k^" = k 2", = m 2 and n^ _ = n 2 • These c o n d i t i o n s can be approximately produced experimentally. Also i f i t can be assumed th a t the p a r t i c l e s are small r e l a t i v e t o the column diameter, then 1 0 ^ 2 " ^ l V D n i s equal to 1.0 approximately. S i m p l i f y i n g equation 33 a c c o r d i n g l y , / J / m n , . l 3 - m ) / m n . «2 = €|(/) U) 3* w here / = (psl -p)/{psZ -p) < I , and r = d, / d 2 > I S u b s t i t u t i n g equation 34 back i n t o 28.we have R I (3-rri)/mn / > B . - / > B 2-(A | - / » [ ( I - ^> - M ' - ^mn-l)/mn>] 3 5 I n s p e c t i o n of equation 35 w i l l r e v e a l the f o l l o w i n g i n f o r m a t i o n : (1) suppose that i - _ ( 3 - m ) / m n ' y * e ' ( ' ~ / - n - I V m . > 3 6 The bulk d e n s i t y of bed 1 w i l l then be l e s s than the bulk d e n s i t y of bed 2, and the l a t t e r w i l l occupy the bottom s e c t i o n of the column w i t h bed 1 above i t . 'This i s c l a s s i f i c a t i o n by density. (2) suppose t h a t . ( 3 - m ) / m n 1-1 > « I < I - ^ , M N . 1 ) / M N ) 37 14. The hulk d e n s i t y of bed 2 w i l l be l e s s then the b u lk d e n s i t y of bed 1, and thus bed 2 w i l l occupy the top of the column w i t h bed 1 i n the bottom s e c t i o n . ( 3 ) suppose t h a t . (3-m)/mn ' - y = £ | ( | - £ » . - • ) / . » 1 3 8 The bulk d e n s i t y of bed 1 equals the bulk d e n s i t y of bed 2 and according to Hancock ( 2 ) there should be p e r f e c t mixing of the two sets of p a r t i c l e s , ! , producing one homogeneously f l u i d i z e d bed. I f t h i s c o n d i t i o n holds a t a p a r t i c u l a r value of €| , then f o r values of € | l e s s then t h i s value, s i t u a t i o n 1 w i l l occur and bed 2 w i l l be at the bottom and bed 1 at the .top. S i m i l a r l y f o r values of €| g r e a t e r than t h i s p a r t i c u l a r €| ,' s i t u a t i o n 2 w i l l occur. These s i t u a t i o n s are represented diagramatieally/c by f i g u r e 2 . For s i t u a t i o n 3 f o occur, the bulk d e n s i t y d i f f e r e n c e must be equal to zero, and t h e r e f o r e by equation 3 5 , 1 -x y l /mn r(3-m)/mn _ y € , = 39 The corresponding value of € 2 f ° r t h i s p a r t i c u l a r value of i s given by equation 3 4 , or by applying the c o n d i t i o n of zero bulk d e n s i t y d i f f e r e n c e to equation 2 8 , which then s i m p l i f i e s to Since the v o i d f r a c t i o n i n a p a r t i c u l a t e l y f l u i d i z e d bed can vary only from € m f t o 1, a r e v e r s a l from s o r t i n g t o s i z i n g w i l l occur i n such a 15- BED I EQUATIONS BED 2 EQUATIONS CASE 2 A CASE__3_ PERFECT MIXING CASE I ' ~7[ ~A A A N \ -A \ • f t r f t . > 0 \ \ \ \ LOG(POROSITY) Figure 2 . P r e d i c t i o n of F l u i d i z e d Bed I n v e r s i o n 1 6 . bed during i t s expansion only i f r and y are such that € m f < €, < € 2 < I where €| and € 2 a r e calculated from equations 39 and 3 * (or ko) respectively. Beare ( l l ) has produced a plot for the laminar or Stokes1 region (m=l, n=U.65) relating inversion conditions with particular values of r and y . This' plot i s given in Appendix I. A similar plot also appears for the Newton region (m=2, n=2«39) which can be compared to the laminar plot. F. Mixed Bed Height Predictions Numerous workers have correlated l i q u i d fluidized bed expansion equations for uniform particles, but very l i t t l e work has been done on correlating expansion data for fluidized beds composed of mixed sizes or beds composed of more than one solid material. Lewis and Bouerman (8) studied fluidized beds of non-uniform sized particles and found that the performance of the system could be accurately predicted from equations for the constant diameter spheres. This can be done by using the equations to calculate the performance for each narrow particle size fraction, then summing the contributions for a l l fractions to give the overall bed expansion. If a fluidized bed is composed, of a number of different materials and i t can berassumed that the fluidized bed i s separated into distinct layers of different materials, then the contributions for each section can be similarly summed to give the overall average porosity of the mixture as a function of velocity. Suppose a fluidized bed i s composed of W| poiiinds of particles of density p^^ , vv 2 pc^unds of particles of density p^ > 8 1 1 ( 1 so on. T&en the volume of each section in the fluidized bed i s given by the following equation, i n which the s u b s c r i p t i r e f e r s t o any i n d i v i d u a l s e c t i o n i : VI = T-L- x ' Ui ' I - € i Psi The t o t a l volumes of the bed i s the sum of the volume of the d i f f e r e n t Ejections. 1 * i r s i The average p o r o s i t y of the mixture i s the r a t i o of volume of l i q u i d i n the bed to the t o t a l volume of the f l u i d i z e d bed. €m= ' - g i Psi ^ Psi k 3 i x — Ps y _ i i _ x * L L X Psi _ | Wj < T ! — . X _ J . kk ~ € \ Psi The above equation should h o l d f o r a f l u i d i z e d bed which i s separated i n t o l a y e r s , but not n e c e s s a r i l y when the m a t e r i a l s are mixed together. I t i s here p o s t u l a t e d t h a t equation (kk) a l s o a p p l i e s t o mixed beds. Thus the average p o r o s i t y and the height of a f l u i d i z e d bed of mixed species can be p r e d i c t e d from a knowledge of the p o r o s i t y - v e l o c i t y r e l a t i o n s h i p s of the i n d i v i d u a l components. Hoffman, Lapidus and E l g i n (12) have stud i e d t h i s aspect of f l u i d i z a t i o n and have proposed an equation f o r the o v e r a l l bed expansion of a bed of mixed s i z e s . T h e i r work i s concerned w i t h p a r t i c l e s of the same m a t e r i a l but d i f f e r e n t s i z e s , during the expansion of which the p a r t i c l e s are completely segregated by s i z e and do not mix. The equation they propose i s equivalent to 1 8 . 45 where X: = W; / W, m = weight f r a c t i o n of s i z e i i n the s o l i d mixture. •This equation i s equ i v a l e n t to equation 43 or 44 f o r constant d e n s i t y s o l i d s , but E l g i n et a l make the statement t h a t i t does not hol d f o r f l u i d i z e d beds when the l a y e r s mix. The b a s i c assumption u n d e r l y i n g E l g i n ' s work i s t h a t a unique r e l a t i o n s h i p e x i s t s between the s l i p v e l o c i t y and the h o l d up f o r any p a r t i c u l a t e system. The s l i p v e l o c i t y i s the r e l a t i v e v e l o c i t y between the p a r t i c l e s and the f l u i d and i s given by • For a b a t c h - f l u i d i z e d bed, Vp = 0 and the s l i p v e l o c i t y i s eq u i v a l e n t to the average i n t e r s t i t i a l v e l o c i t y i n the bed. 19- APPARATUS A. General The equipment was designed so that a wide range of flows could be pumped through the test section. A schematic diagram of the apparatus i s displayed in figure 3- The equipment i s an open system composed of two loops. The primary loop consists of the storage tank, pump and heat exchanger which maintains the f l u i d at room temperature. The secondary cir c u i t consists of the flow- and temperature-measuring section and the test column. (a) Pump The test f l u i d i s circulated by a Paramount close-coupled type U 1-3-2 pump driven by a 3 h.p. motor operating at 3450 rpm. The pump was provided with a John Crane mechanical seal to prevent air being sucked into the pump. The capacity of the pump is 50 U.S. gallons per minute against a total head of seventy feet of water and was supplied by Pumps and Power Limited, of Vancouver, B.C. (b) Piping The piping i s 2-inch I.D., type L, Noranada copper seamless pipe, and the fit t i n g s used throughout were a l l copper or brass. A l l shut-off valves except the flow control valves are 2-inch brass gate valves. The two large control valves are globe valves and the small control valves are needle valves. (c) Heat exchanger The heat exchanger which removes heat generated by the pump is a seven-tube baffled, counter-current type. The cooling medium was on the shell side and the test f l u i d was in the tubes. In runs with low viscosity fluids the temperature of the effluent l i q u i d was controlled by adjusting the cooling water throughput. With high viscosity fluids, 2 0 . A - t e s t section - 2"l .D. X 5' long B-calming section - 152" long C-expansion exit section D-equalizing entry section E - thermometer F - capillary flow meter G | f G 2 , G 3 - o r i f i c e meters i i i i H X H B l I I I I • i > k>4 1 ' [ heat exchanger pump Figure 3- Schematic Diagram of Apparatus. 2 1 . where the c o n t r o l l i n g resistance was on the tube side, the temperature was c o n t r o l l e d by adjusting the flow through the primary c i r c u i t . Thermometer E i n fi g u r e 3 w a-s used to measure the e f f l u x temperature to the t e s t section, (d) Flow Meters The liquid-metering section consists of three sharp-edged o r i f i c e meter runs and a c a p i l l a r y flow meter. A calming length upstream of at l e a s t 50 diameters and downstream of at l e a s t 10 diameters was allowed on o r i f i c e meter runs, and a l l o r i f i c e meters were f i t t e d with corner taps. The c a p i l l a r y flow meter consists of a 0 . 2 5-inch dianeter, s t a i n l e s s s t e e l tube 4 ' 7 " long with a calming length upstream, and downstream of 100 pipe diameters and 50 pipe diameters r e s p e c t i v e l y . The pressure drop across the flow meters was measured by means of one of two manometers, a 6 0-inch a i r - f i l l e d inverted U-tube manometer f o r r e l a t i v e l y small pressure drops, and a 3 0-inch m e r c u r y - f i l l e d U-tube Merian manometer f o r higher pressure drops. The tap leads from the meters are connected to a manifold system, so that the pressure drop across any meter may be measured by one or both manometers. Vents were provided at a l l high points.to allow complete removal of a i r from the l i n e s and mercury traps were f i t t e d to the mercury manometer. Pertinent d e t a i l s as to sizes of o r i f i c e s are given i n table I. Table I O r i f i c e Meter Sizes Meter Run O r i f i c e Diameter inches Run Diameter inches 1 2 O .85 0.40 2 . 0 1 . 0 3 0 . 2 0 0 . 5 22. (e) Test F l u i d s The t e s t f l u i d used f o r laminar flow runs was an aqueous s o l u t i o n of polyethylene g l y c o l E-QOOO, supplied by Dow Chemical Company, of Midland, Michigan. For the intermediate region runs, water was used as the t e s t l i q u i d . These l i q u i d s were used because they meet the following require ments: they are ( l ) Newtonian, (2) non-corrosive, (3) stable and r e s i s t a n t to b a c t e r i a l attack, (1+) possess high v i s c o s i t y at high g l y c o l concentrations, are ( 5 ) transparent, and ( 6 ) are not t o x i c . The Newtonian properties of the polyethylene g l y c o l solutions were checked by comparing the Stormer Viscosimeter (Ch.E.2002) curves f o r these solutions with those obtained f o r g l y c e r o l solutions. No non-Newtonian behaviour could be detected a f t e r the g l y c o l solutions were v i o l e n t l y s t i r r e d f o r a long time. To increase corrosion resistance, sodium dichromate and sodium hydroxide were added. These chemicals e f f e c t i v e l y stopped any corrosion but caused the g l y c o l solution to turn a dark orange-brown c o l o r . The s o l u t i o n used was 40yo by weight of polyethylene g l y c o l i n water, which had a v i s c o s i t y of about 0 . 0 9 0 l b . / f t . s e c and a density of 67 .k l b . / f t . 3 a t 70°F. B. Test Section The test section consisted of one of two test columns, an ordinary 2-inch I.D. and 5-foot long industrial Pyrex glass tube and a column constructed of perspex containing pressure taps at numerous positions up the column. The perspex column was also 2-inch I.D. and 5 feet long. A detailed schematic diagram of a pressure tap appeared in figure k. Each pressure tap was connected into one of two headers in such a way that f r i c t i o n a l pressure drop measurements could be made across alternate taps or from the bottom tap to any other tap. , The headers were connected to a 100-cm. long 8-mm. glass U-tube containing carbon tetrachloride. A diagram of the differential pressure measuring system appears in figure 6. The column attachment flanges were constructed so that the column could be aligned vertically, and so that the calming section and column joint could be properly aligned. It was found that the quality of fluidization was affected markedly by these two factors. Non-alignment of column and calming section caused large eddies and channeling in the fluidized bed. Large scale circulation up one wall of the column and down the other resulted from not having the column vertical. The support for the fluidized bed was a 16 mesh stainless steel screen on top of which was a 2-inch deep fixed bed of lead spheres. The diameter of the spheres used in a particular run was determined by the size and density of the material being fluidized in the .column during the run. If the lead spheres were too large, they caused channeling in the fluidized bed and i f they were too small they fluidized and disrupted the bed being studied. The equalizing entry section consisted of a 152-inch long section of straight copper pipe and a concentric 2k. annulus d i s t r i b u t o r to the s t r a i g h t pipe. A diagram of t h i s d i s t r i b u t o r i s shown i n f i g u r e '5. The expansion e x i t s e c t i o n i s a simple overflow • from the 2-inch diameter pipe i n t o a l a r g e r chamber. A diagram of t h i s s e c t i o n i s a l s o shown i n f i g u r e 5- • 25- scale l"= 2" Figure k. Schematic Diagram of a S e c t i o n a l Viev of the Column, ( g l a s s backing flange omitted) 2 6 . Figure 5- Diagram of Entry Section to and E x i t Section from Column. 27- Key to Figure 4 1. p l a s t i c " 0 " - r i n g . 2 . p l u g w i t h l / l b " hole d r i l l e d through i t . 3- 150 T y l e r mesh screen c o v e r i n g pressure tap i n l e t . 4 . 2-inch I.D. entry s e c t i o n to column. 5- 3 / 8 " I m p e r i a l compression nut. 6 . l / 4 " pipe to 3 / 8 " compression' Imperial connector. 7- 2-inch I.'.D. p^xspex column. . 1 1 . 8 . packed bed of l e a d spheres. 9- 16 mesh s t a i n l e s s s t e e l support screen. 1 0 . rubber gasket. 11 . brass adapter flange f o r support screen. 1 2 . brass flange. 1 3 . l / V ' inch I.D. copper tubing. lk. rubber gasket. Key to Figure 5 1.. brass connector f l a n g e . 2 . 2-inch I.D. column extension. 3 . 2-inch I.D. r e t u r n l i n e to storage tank. k. 4-inch I.D. expansion s e c t i o n . 5>& 6 . alignment apparatus f o r sampler used by B.Pruden ( 1 5 ) - 7- 2 - i n c h I.D. l i n e from f l u i d metering s e c t i o n . 8 . 2-inch I.D. calming s e c t i o n below column. 9 . 6 - i n c h I.D. expansion s e c t i o n . MANOMETER HEADERS spring pinch clamps 3 COLUMN AND PRESSURE TAPS TAPS 4' APART TJ TAPS 2' APART TAPS r APART F i g u r e 6. Diagram of D i f f e r e n t i a l Pressure Measurement System. 29- EXPERIMENTAL PROCEDURES A. Operating Procedure For each mixture of s o l i d s t e s t e d the procedure was as f o l l o w s . Each component was run se p a r a t e l y to determine the s i n g l e component p r o p e r t i e s ; then the two components were mixed together and run t o determine how the mixture f l u i d i z e d . During each of the three runs f o r each p a r t i c u l a r mixture, expansion data and f r i c t i o n a l pressure l o s s data were obtained. V i s u a l observations of the bed were a l s o recorded. 1. Expansion data. At the v a r i o u s flow r a t e s a f t e r e q u i l i b r i u m was obtained, the bed he i g h t , room temperature, f l u i d temperature and manometer readings were recorded. When the t e s t f l u i d was polyethylene g l y c o l the bed took about 5 minutes to come to e q u i l i b r i u m a f t e r the flow r a t e was changed. Water f l u i d i z e d beds r e q u i r e d a much s h o r t e r time t o come t o e q u i l i b r i u m . 2. F r i c t i o n a l pressure drop data. At v a r i o u s l i q u i d flow r a t e s and bed h e i g h t s , f r i c t i o n a l - p r e s s u r e drop p r o f i l e s were determined by measuring the di f f e r e n c e ' i n pressure between v a r i o u s pressure taps and a base pressure tap. Manometers were b l e d before any readings were taken, to ensure t h a t no a i r was i n the l i n e s . When the t e s t f l u i d was polyethylene g l y c o l , the manometer took about 15 minutes t o come to e q u i l i b r i u m . The sample c a l c u l a t i o n s presented i n Appendix I I f o r a p a r t i c u l a r mixture w i l l give a good i n d i c a t i o n of how data were taken and how the r e s u l t s were obtained. B. O r i f i c e Meter C a l i b r a t i o n s The method used f o r c a l i b r a t i o n of the o r i f i c e s and the c a p i l l a r y flow meter was as f o l l o w s . At steady s t a t e c o n d i t i o n s , when constant temperature and manometer readings p r e v a i l e d , the time to c o l l e c t f i f t y 3 0 . pounds of f l u i d was measured. The c a p i l l a r y flow meter was c a l i b r a t e d only f o r high v i s c o s i t y polyethylene g l y c o l solutions; whereas the ^-and 1-inch o r i f i c e meters were c a l i b r a t e d f o r b o t h polyethylene g l y c o l solutions andWKater. The data f o r the o r i f i c e meters has been p l o t t e d as C'/Rej against Rej , where Re-j-is the f l u i d Reynolds i number i n the t e s t section and C' fl Re T P V p , - p 2 47. Least squares l i n e s of the data were calcu l a t e d . Maximum and mean deviations of the data from the l e a s t squares l i n e s are given i n Table 2. The c a l i b r a t i o n p l o t s appear i n Figures 7 and 8. The l e a s t squares equations f o r the o r i f i c e s meters are given i n Table 3- The c a p i l l a r y flow meter was c a l i b r a t e d i n the laminar flow range. According to theory, f o r flow i n the laminar region, the f r i c t i o n f a c t o r times the Reynolds number should be a constant and equal to 1 6 . The average of t h i s product as determined from a l l c a l i b r a t i o n runs was a c t u a l l y 15-395> The main source of the discrepancy can be understood by reference to the equation f o r determining the product; p. - p P r 7rD 4 I f . R e T = —I—2 g U 8. I±Q L 8 L m C J Equation 48 shows that a s l i g h t e r r o r i n the measurement of the c a p i l l a r y diameter w i l l be g r e a t l y 1 magnified i n the f-Re-f- product.. , The maximum and mean deviations f o r the c a p i l l a r y flow meter are r e s p e c t i v e l y + 3 ' 5 $ and + 1.24$. The c a l i b r a t i o n equation developed f o r the meter by weighting the 80 data points equally i s Vc = I-468 XlO" 6 P t P g 49. Table 2 Accuracy of Flow Meter C o r r e l a t i o n s meter mean d e v i a t i o n maximum d e v i a t i o n 111 2 > g l y c o l + 2-3$ + ivf, 1", g l y c o l + 2-9$ + 9% lit 2 > water + 2.0$ + 9$ 1", water + 2-9$ - 13$ Table 3 Least Squares Equations f o r Meters Polyethylene g l y c o l s o l u t i o n -!-" meter ' log-5*- = -O.93631og( ReT ) -1.174 1" meter l o g = -0.95231og( ReT ) -0-5574 ReT Water c" meter l o g p"gy= -1.064iog( Ref)i+jl.399 1" meter l o g £L =-1.0l8 log(Re-r) + 1-848 ReT 1 32. 10° 2 3 4 5 6 7 8 9 IO1 2 3 4 5 6 7 8 9 |Q 2 2 TEST SECTION RE F i g u r e 7« Flow-Meter C a l i b r a t i o n Curve f o r Water. i r I I I 1—i—I—i—i—i—i—r— V ORIFICE I ORIFICE o POLYETHYLENE GLYCOL i I i I—I—I I I i I i I i L J l _ L 5 6 7 8 9 | 0 3 2 3 4 5 6 7 8 9 | 0 4 TEST SECTION RE Figure 8 . Flow-Meter C a l i b r a t i o n Curves, i'or Polyethylene G l y c o l . 3h. C. Measurement o f V i s c o s i t y and Density of Test L i q u i d . The kinematic v i s c o s i t y and f l u i d d e n s i t y of the t e s t l i q u i d were measured i n a constant temperature o i l bath w i t h a p r e c i s i o n s c i e n t i f i c temperature c o n t r o l l e r capable of c o n t r o l l i n g w i t h i n + 0.1°F. Samples of the t e s t l i q u i d were taken a t the end of each run, and during the run f o r some of the longer runs. D u p l i c a t e measurements at three temperatures, 70, 75 and 80°F., were made of the samples. These temperatures were chosen because they bracketed the temperature of the f l u i d i n the t e s t column f o r almost a l l the runs. I The d e n s i t y of the f l u i d s was measured using the departmental set of standard hydrometers (Ch.E 1566). These hydrometers are standardized at 60°F., whereas the present experiments were conducted i n ' t h e range of 6o-80°F. The p o s s i b l e e r r o r due t o the temperature e f f e c t was checked using a Westphal balance and- d i s t i l l e d water was employed as an absolute standard. The hydrometers used were found t o give the true d e n s i t y w i t h i n + 0.2$. A Cannon-Fenske v i s c o s i m e t e r (R933> Size 300) tube was e s p e c i a l l y c a l i b r a t e d f o r measurement of the high v i s c o s i t y polyethylene g l y c o l s o l u t i o n s . The tube was c a l i b r a t e d by comparing the discharge time f o r a tube (C-8) p r e v i o u s l y c a l i b r a t e d by De V e r t e u l l (13) w i t h the time taken i n the t e s t v i s c o s i m e t e r . A p r e c i s i o n of + 0.1$ was obtained. The procedure used f o r f i l l i n g , c l e a n i n g and measuring times o f e f f l u x from tubes i s given i n the ASTM manual, DU1+5-53T (lU). For t h i s tube, R933, w i t h i n the recommended range of kinematic v i s c o s i t i e s (50-200 c e n t i s t o k e s ) , .the v i s c o s i t y i n c e n t i s t o k e s i s given by u= 0-2546 t 50 where t = e f f l u x time i n seconds. The c o r r e c t i o n f o r k i n e t i c energy i s 35- n e g l i g i b l e provided the e f f l u x time i s greater than 200 seconds, and was neglected i n t h i s case as the e f f l u x times were of the order of 400 seconds. D. Measurement of P a r t i c l e Density. P a r t i c l e density was measured using a number of 25-ml. s p e c i f i c g r a v i t y b o t t l e s . Two random samples were taken from the bulk of the material and the p a r t i c l e density was measured by the following method. Measurements were obtained by f i r s t weighing the s p e c i f i c g r a v i t y b o t t l e empty, next f i l l i n g i t two-thirds f u l l of p a r t i c l e s and weighing, then f i l l i n g i t completely and weighing and f i n a l l y removing the p a r t i c l e s and weighing the b o t t l e f u l l of water. From these weighings and the temperature i n the laboratory,- the volume and the weight of p a r t i c l e s could be determined, and thus the density of the p a r t i c l e s . E. S i z i n g of P a r t i c l e s . Two methods were used to measure the average diameter of the p a r t i c l e s . For s p h e r i c a l p a r t i c l e s greater than 2 mm., the micrometic method was. used. A f t e r screening the p a r t i c l e s through a seri e s of sieves developed by B. Pruden (15), a random sample of 100 beads were measured using a micrometer. The diameter used f o r the beads was the average of 100 measurements. For beads of 2 mm. or greater the maximum deviation of the measured diameters from the average was about + 5-0$>. For smaller beads and p a r t i c l e s , the arithmatic average of two adjacent screen sizes was used. The procedure was as follows. About 500 grams of p a r t i c l e s were screened between adjacent T y l e r sieves of the 4th root ser i e s i n a Ro-tap machine f o r 10-minute i n t e r v a l s . A f t e r the f i r s t screening, p a r t i c l e s which remained between the two s p e c i f i e d sieves were 36. c o l l e c t e d and screened again. The second, t h i r d and f o u r t h screenings were c a r r i e d out on such p a r t i c l e s only. Each screening was about 10 minutes long, a f t e r which the sieves were r e g u l a r l y cleaned. I t was found t h a t by about the f o u r t h screening a n e g l i g i b l e amount of m a t e r i a l was passing through the smaller sieve. 37- EXPERIMENTAL RESULTS A. Experiments w i t h a S i n g l e Species 1. Bed Expansion Measurements To be able t o p r e d i c t i n v e r s i o n and bed expansions of mixtures of two or more species of p a r t i c l e s u s i n g s i n g l e component equations and data, numerous runs were made w i t h s i n g l e component f l u i d i z e d beds. For each experiment on f l u i d i z a t i o n of a p a r t i c u l a r species, curves were p l o t t e d of l o g V s against l o g € . T y p i c a l curves are shown i n f i g u r e s 13, 17, 21 , 27, 28, 30, and the slopes and i n t e r c e p t s obtained are given i n t a b l e s k and 5- The data were c o r r e l a t e d i n t h i s form because of i t s s i m p l i c i t y and because Richardson and Zak i (h) have shown t h a t i t works q u i t e w e l l over the complete range of f l u i d i z a t i o n . The r e s u l t s obtained f o r the slopes have been compared w i t h values p r e d i c t e d by u s i n g the e m p i r i c a l equations o f Richardson and Zak i i n t a b l e s 6 and J. The agreement i s good i n almost every case. Tables 6 and 7 a l s o compare f r e e s e t t l i n g v e l o c i t y , V0 , as computed from the experimental i n t e r c e p t s and equation 23 , w i t h N^ j as c a l c u l a t e d from the standard drag c o e f f i c i e n t - R e y n o l d s number c o r r e l a t i o n s f o r f r e e s e t t l i n g of spheres. Discrepancies between the r e s p e c t i v e v a l u e s , which range as high as 30$ but average l e s s than IU70, c o u l d be due t o the n o n - s p h e r i c i t y and non-uniformity of the p a r t i c l e s . T r i a l runs were made w i t h a mixture of alundum and g l a s s micro-bead (cataphote) p a r t i c l e s to determine the e f f e c t on a f l u i d i z e d bed of having another f l u i d i z e d bed above o r below the p a r t i c u l a r bed being studied. When the f l u i d i z e d micro-bead bed was above the alundum bed the expansion curve f o r the alundum deviated s l i g h t l y from the curve obtained when there was not bed above. As can be seen i n f i g u r e 9 , the alundum bed i s Table 4 Summary of F l u i d i z a t i o n Results f o r P a r t i c l e s i n Water Wo. P a r t i d>-mm. cles rs > cm.J Material Re 0 > f t / sec log(Vj ) n Figure 1 1.08 2.91 B a l l o t i n i 198 0.590 -0.250 2.56 0.021 29 2 O.767 3-95 Alundum 129 0.543 ' -0.280 2.87 0.015 • .27 3 0.645 3-95 Alundum 97.8 O.516 -0.310 2-95 0.013 28 4 0.912 3-95 Alundum 171 0.606 -0.235 2.76 0.018 31 5 I.83 2.92 B a l l o t i n i 511 0-904 -0.080 2.31 O.O36 29 6 1.08 3.17 Crystalon 195 0.582 -0.256 2-77 0,021 27 7 0.542 4.50 N i c k e l - Glass 89-3 0.532 ' -O.285 3-02 0.011 30 Table 5 Summary of F l u i d i z a t i o n R e s ults f o r P a r t i c l e s i n Polyethylene G l y c o l No. Part d,mm i c l e s ^ s cm 3 M a t e r i a l Re 0 f t / s e c . log(Vj ) a • Figure 8 0.456 8.90 N i c k e l O.025 0.0236' - 1 . 6 3 5 4-75 0 . 0 0 9 1 3 9 0.645 3-95 Alundum 0 . 0 3 1 ' 0.0205 - 1 . 7 0 0 5.36 0 . 0 1 3 1 7 1 0 2 . 28 2.73 B a l l o t i n i O.507 0.0959 -I.O63 4 . 5 9 0 . 0 4 5 1 3 1 1 1.08 2 . 9 1 B a l l o t i n i 0.077 O.O3O9 - 1 . 5 3 0 ' 5 . 1 3 0 . 0 2 1 1 7 1 2 3 - 1 5 7 . 8 3 S t e e l 5.97 O.77O -O.185 4 . 1 3 0 . 0 6 2 2 1 1 3 2 . 0 5 1 1 - 3 3 Lead 2.04 0.404 - 0 . 4 3 3 4 . 1 9 0.040 2 1 14 0. 542 4 . 5 0 N i c k e l - 0.0168 O.OI63• - 1 . 8 0 0 4.84 0 . 0 1 1 24 Glass 40. Table 6 Comparison of Results with Richardson-Zaki and Free S e t t l i n g Correlations. Water No.- Re0 vo f t / s e c . n Experiment Co r r e l a t i o n Expt. Correl'n Expt. Correl'n 1 1 9 8 . 0 ' 2 1 0 . 0 0 . 5 9 0 0 . 6 2 6 2 . 5 6 2 - 5 3 2 1 2 9 - 1 144 0 . 5 4 3 0 . 6 0 6 2 . 8 7 2 . 8 3 3 9 7 - 8 . 102 0 . 5 1 6 0 . 5 3 8 2 - 9 5 2 - 9 7 4 171 198 0 . 6 0 6 0 . 7 0 1 2 . 7 6 2 . 8 0 5 511 537 0 . 9 0 4 0 . 9 5 1 2 . 3 1 2 . 3 8 6 195 218 O.582 0 . 6 5 1 2 . 7 7 2 . 7 2 7 8 9 - 3 • 82 0 . 5 3 2 0 . 4 8 7 • 3 - 0 2 2 . 9 8 41. Table 7 Comparison of Re s u l t s w i t h Richardson-Zaki and Free S e t t l i n g C o r r e l a t i o n s . Polyethylene G l y c o l . Re- V f t / s e c . n No. Experiment C o r r e l a t i o n Experiment C o r r e l a t i o n Experiment C o r r e l a t i o n 8 0 . 0 2 5 0 . 0 2 2 0.0236 0 . 0 2 0 7 4 . 7 5 4.83 9. ' . 0 . 0 3 1 0 . 0 2 3 0 . 0 2 0 5 0 . 0 1 5 3 5 . 3 6 4 . 9 0 10 0 . 5 0 7 0 - 5 7 5 O .0959 O.IO87 4 . 5 9 5 . 2 0 11 0 . 0 7 7 0 . 0 6 8 0 . 0 3 0 9 0 . 0 2 7 4 5 . 1 3 5 . 0 7 12 5 - 9 7 4 . 9 0 O.77O 0 . 6 3 3 4 . 1 3 4 . 7 2 13 2.04 2 - 3 9 0.404 0 . 4 7 4 4 . 1 9 4 . 7 4 14 0 . 0 1 6 8 O.OI36 O.O163 0 . 0 1 3 2 4.84 4.86 4 2 . compressed s l i g h t l y by the presence of the micro-beads (cataphote), but t h i s e f f e c t disappears as the bed i s expanded. Because the d e v i a t i o n was very small i t i s assumed t h a t having one f l u i d i z e d bed on top of another doesn't i n f l u e n c e the f l u i d i z a t i o n of the lower bed. The expansion curve f o r the cataphote bed was not i n f l u e n c e d at a l l by having the alundum bed f l u i d i z e d below i t . Thus s i n g l e component data can be used t o determine o v e r a l l bed expansions f o r mixtures, provided the beds do not mix. R e s u l t s p e r t a i n i n g to expansion curves f o r two components which do mix at c e r t a i n p o r o s i t i e s w i l l be given i n a l a t e r s e c t i o n . The expansions of s e v e r a l of the water f l u i d i z e d beds d i s p l a y an i n t e r e s t i n g behaviour. The expansion curve i s composed of two s e c t i o n s of d i f f e r e n t ' slopes, and the expansion seems to proceed d i f f e r e n t l y i n the two r e g i o n s , as seen i n f i g u r e s 27, 28 and 30- The bed expands at a g r e a t e r r a t e w i t h respect to v e l o c i t y above p o r o s i t i e s of about 55$ than i t does at p o r o s i t i e s below 5 5 $ ' This behaviour seems to depend on the d/D r a t i o , the v e l o c i t y of the f l u i d , and the p o r o s i t y of the bed. The phenomenum was not observed when p a r t i c l e s were f l u i d i z e d i n polyethylene g l y c o l s o l u t i o n s or when very l a r g e p a r t i c l e s were f l u i d i z e d i n water. Diagrams based on v i s u a l observations of how beds appeared to f l u i d i z e and the p a r t i c l e flow p a t t e r n s are given i n f i g u r e 1 0 . At p o r o s i t i e s of about 55$ b u b b l i n g and v o i d wave formations begin to appear i n the f l u i d i z e d bed. The v o i d waves grow as the bed expands. These are undoubtedly a cause f o r the change i n slope of the expansion curve. Observations s i m i l a r t o the above were a l s o noted by Cairns and P r a u s n i t z ( l 6 ) i n t h e i r study of macroscopic mixing i n f l u i d i z a t i o n . C a i r n s and P r a u s n i t z ( 1 7 ) a l s o measured the l i n e v e l o c i t y p r o f i l e s i n water f l u i d i z e d beds i n a 2-inch column using a t r a c e r technique. They found t h a t the v e l o c i t y p r o f i l e s begin t o change t h e i r shape from a 43- -0-5 -0-6 -0-8 - 0 -9 Ui o e 0 € 0 ALUNDUM (cataphote) CATAPHOTE (alundum) ALUNDUM CATAPHOTE MIXTURE -0-3 -0-25 -0-2 -015 LOG(POROSITY) -01 Figure 9- P l o t of Alundum and Cataphote Bed Expansionj I n d i v i d u a l l y and w i t h Cataphote above Alundum. r a d i a l l y f l a t p r o f i l e and develop humps at 3 "to 3 ' 5 p a r t i c l e diameters from the w a l l , at p o r o s i t i e s of about 55$- The height of the humps r e l a t i v e t o the average v e l o c i t y depends on the p a r t i c l e d e n s i t y . There appears to be a l i m i t to which a f l u i d i z e d bed can be' expanded before i t becomes hydrodynamically unstable. On expansion of a bed slowly from a f i x e d to..a .dense and then a more d i l u t e f l u i d i z e d bed, the bed expanded u n i f o r m l y u n t i l a p o r o s i t y of 8 5 $ . The bed was s t a b l e , and disturbances which moved through i t a f f e c t e d the q u a l i t y o f f l u i d i z a t i o n but d i d not-cause any sustained o s c i l l a t i o n s . I f a bed was expanded above 8 5 $ p o r o s i t y , any disturbance beginning i n the bed became a m p l i f i e d as i t moved through the bed and set up continuous v o i d waves and o s c i l l a t i o n s , which remained u n t i l the p o r o s i t y of the bed was decreased. A f t e r decreasing the p o r o s i t y , the o s c i l l a t i o n s slowly disappeared and the bed returned to a homogeneous f l u i d i z e d s t a t e . According to Jackson ( l 8 ) , f l u i d i z e d beds w i l l remain s t a b l e and w i l l not be af f e c t e d - b y d i s c o n t i n u i t i e s unless the bed i s expanded above a c e r t a i n l i m i t . Disturbances i n a f l u i d i z e d bed grow as they move up through the bed, but i f a bed i s . n o t deep enough, the disturbance w i l l have moved out of the bed before i t has become l a r g e enough to d i s r u p t i t . S l i s and Willemse ( 1 9 ) have a l s o observed these disturbances and have developed a theory to account f o r t h e i r v e l o c i t y of propagation. The f l u i d i z a t i o n of p a r t i c l e s i n the polyethylene g l y c o l s o l u t i o n s was much more uniform i n appearance than w i t h water. I t was not u n t i l the bed wascexpanded to about 7 5 $ p o r o s i t y t h a t notable c i r c u l a t i o n . o f the p a r t i c l e s occurred. There was some tendency f o r p a r t i c l e movement down the w a l l s o f the tube and up the c e n t r e , but i t was not very pronounced. The p a r t i c l e s , however, - were c o n t i n u a l l y coming together 11 • # » • f € = 0-85 • • « • »•»• i €=0 -70 € = 0-55 ballotini spheres in water € = 0-43 € = 0-85 ' » « » » > . . . € = 0-65 nickel spheres € = 0-50 in water t € = 0-45 Figure 10. V i s u a l Observation of F l u i d i z a t i o n of Spheres. i n s m a l l groups, then f a l l i n g through the "bed as a group, d i s p e r s i n g , and r i s i n g again. This e f f e c t was p a r t i c u l a r l y n o t i c e a b l e w i t h n i c k e l spheres where 5 or 6 p a r t i c l e s would f a l l as a v e r t i c a l chain. For l a r g e p a r t i c l e such as the l e a d and s t e e l b a l l s , there i s evidence of mass movement of groups of p a r t i c l e s , but i n these runs the p a r t i c l e Reynolds/ number was g r e a t e r than 2 . 0 . P a r t i c l e flow c o n s i s t e d of a "random eddying motion and there were f a i r l y l a r g e v a r i a t i o n s i n the l o c a l s o l i d s c oncentrations throughout the bed. However, disturbances s i m i l a r t o those observed i n deep, w a t e r - f l u i d i z e d beds were not present i n beds f l u i d i z e d by the polyethylene' g l y c o l s o l u t i o n s . Such beds c o u l d be expanded out the top of the column without l a r g e s c a l e voids forming a.s they d i d i n water- f l u i d i z e d beds. Beds f l u i d i z e d i n polyethylene g l y c o l segregated by s i z e t o a much gr e a t e r extent than they d i d i n water, and at high p o r o s i t i e s s e v e r a l beds dis p e r s e d to the p o i n t t h a t no i n t e r f a c e between bed and f l u i d c o u l d be observed. 2 . D i f f e r e n t i a l Pressure Measurements. D i f f e r e n t i a l pressure measurements were made on beds f l u i d i z e d w i t h polyethylene g l y c o l s o l u t i o n . F i g u r e s 11 and 12 are examples of these r e s u l t s . The r e s u l t s obtained are w i t h i n 5$ of the t h e o r e t i c a l values f o r a l l p o r o s i t i e s below 8 5 $ . At p o r o s i t i e s greater than 8 5 $ the p a r t i c l e s were s u f f i c i e n t l y segregated by s i z e t h a t the p o r o s i t y c a l c u l a t e d from bed height was not r e p r e s e n t a t i v e of the bulk of the bed, and thus experimental r e s u l t s were s i g n i f i c a n t l y g r e a t e r than the t h e o r e t i c a l p r e d i c t e d values. Further a n a l y s i s of the r e s u l t s shows th a t f o r low p o r o s i t i e s the experimental values of p o r o s i t y are somewhat l e s s than the t h e o r e t i c a l v a l u e s , w h i l e at hig h p o r o s i t i e s the experimental r e s u l t s are l a r g e r than 47- the t h e o r e t i c a l ones. This c o n d i t i o n has been e x p l a i n e d by Adler and Happel (20) as being caused by the nature of the entrance s e c t i o n . They have s t u d i e d the e f f e c t of calming•section packing and loose-packed bed hei g h t to diameter r a t i o on d i f f e r e n t i a l pressure drop across a f l u i d i z e d bed. The r e s u l t s obtained i n d i c a t e three trends. ( l ) With no packing i n the calming s e c t i o n , the r a t i o of experimental d i f f e r e n t i a l pressure gr a d i e n t to t h e o r e t i c a l pressure gradient c a l c u l a t e d from equation 26, known as the P r a t i o , i s a f u n c t i o n of the looser-packed bed height to diameter r a t i o and the p o r o s i t y o f the f l u i d i z e d bed. (2) For packed calming s e c t i o n s , where the packing i s above the support as i n our case, the P r a t i o i s only a f u n c t i o n of the p o r o s i t y of the f l u i d i z e d bed. Also of importance i s the f a c t t h a t the P r a t i o v a r i e s from about O.9O at p o r o s i t i e s of 60$ t o about 1.10 at p o r o s i t i e s of 90$>. (3) When the packing was below the support screen the P r a t i o s were always l e s s than 1.0. This can be r e a d i l y confirmed by observing Wilhelm and Kwauks' r e s u l t s ( l ) . When measuring the f r i c t i o n a l pressure l o s s through the f l u i d i z e d bed by the method used i n t h i s work, the pressure l o s s due t o w a l l f r i c t i o n i s a l s o measured. The r e s u l t obtained can be t r e a t e d as the sum of the pressure l o s s due to the f l u i d i z e d bed plu..- the pressure l o s s due to the w a l l . C a l c u l a t i o n s were made to determine the maximum e r r o r t h a t the w a l l pressure l o s s c o u l d cause. The highest f r e e s e t t l i n g p a r t i c l e v e l o c i t i e s i n water and i n polyethylene g l y c o l were used i n the c a l c u l a t i o n . The maximum pressure l o s s per f o o t of column i n the polyethylene g l y c o l f l u i d i z e d bed was computed to be 0.039 l b - f o r c e /. f t ? — f t , and i n the water f l u i d i z e d bed 0.002 l b . f o r c e /. ft?_ f t . The measured f r i c t i o n a l pressure l o s s e s i n the f l u i d i z e d bed were never l e s s than 5 l b - f o r c e / f t ? — f t , and thus the e r r o r due to w a l l f r i c t i o n was never greater than I70. 4 8 . S Y M B O L P O R O S I T Y O € e © 588 695 758 811 868 926 THEORETICAL CURVE -\ BASED ON (p 0 -p) F = L( ps- p){\-€)q/qc I 0 2 4 6 8 10 12 14 16 18 20 22 L, INCHES Figure 11. F r i c t i o n a l Pressure Drop P r o f i l e s i n a B a l l o t i n i Bed F l u i d i z e d by Polyethylene G l y c o l . 1.9. B E D H E I G H T , I N C H E S 12. F r i c t i o n a l Pressure Drop P r o f i l e s i n an Alundum Bed F l u i d i z e d by Polyethylene G l y c o l . 50. B. Experiments w i t h two species. 1. I n v e r s i o n of Mixtures. Mixtures of two groups of p a r t i c l e s , f o r which s i n g l e component data had already been measured, were f l u i d i z e d • u s i n g polyethylene g l y c o l s o l u t i o n s and water. Many d i f f e r e n t mixtures were t e s t e d when the f l u i d i z i n g medium was water, but no v i s i b l e i n v e r s i o n s were obtained. Most mixtures expanded i n the f o l l o w i n g manner. At low v e l o c i t i e s the bed was separated i n t o two d i s t i n c t s e c t i o n s and as the f l u i d v e l o c i t y was increased the two components mixed together. The mixing increased as the f l u i d v e l o c i t y i n c reased u n t i l a homogeneous mixed bed was obtained. On f u r t h e r increase i n f l u i d v e l o c i t y no separation of the bed i n t o two s e c t i o n s was observed. This was not unexpected as most p r a c t i c a l i n v e r s i o n s are p r e d i c t e d to occur at a p o r o s i t y of about 85$, and i n water f l u i d i z a t i o n the f l u i d i z e d bed i s very unstable at these p o r o s i t i e s . I t appears t h a t macroscopic mixing i n the w a t e r - f l u i d i z e d beds masked the i n v e r s i o n s , and t h a t the d r i v i n g f o r c e f o r segregation due to bulk d e n s i t y d i f f e r e n c e was not great enough to overcome the f o r c e s producing mixing a f f e c t s and i n s t a b i l i t i e s i n the f l u i d i z e d bed. Bi n a r y mixtures of p a r t i c l e s were a l s o f l u i d i z e d i n polyethylene g l y c o l s o l u t i o n s , and very d e t a i l e d r e s u l t s were obtained f o r fo u r mixtures. The r e s u l t s obtained appear i n Tables 8 - 11, and are f o l l o w e d by a general a n a l y s i s of two component f l u i d i z a t i o n . The i n t e r p r e t a t i o n of data was as f o l l o w s . Expansion data were p l o t t e d as l o g a r i t h m (mean p o r o s i t y ) against l o g a r i t h m ( s u p e r f i c i a l l i q u i d v e l o c i t y ) . The experimental p o i n t s obtained are given and the expansion curve p r e d i c t e d by equation (kk), using s i n g l e component data, i s drawn as a b o l d l i n e . The agreement between experimental and p r e d i c t e d expansions i s very good, as can be seen i n Figur e s 1 3 , 1 7 , '21 and 2k. The f r i c t i o n a l pressure drop data were p l o t t e d as d i f f e r e n c e i n pressure from a base p o s i t i o n t o a higher plane versus height L, which i s the distance between the base p o s i t i o n and the higher plane. The parameter i s s u p e r f i c i a l l i q u i d v e l o c i t y . These data are d i s p l a y e d i n Figur e s lk, 18 and 2 2 . The d i f f e r e n t i a l pressure g r a d i e n t s f o r the i n d i v i d u a l components were obtained by measuring the slopes of the s t r a i g h t l i n e s i n the l a t t e r p l o t s . The d i f f e r e n c e i n bulk d e n s i t y of the two beds i s n u m e r i c a l l y equal to the d i f f e r e n c e i n d i f f e r e n t i a l .-pressure gradient f o r the beds. Development i s given below. ( A P F / L ) , = (!-€,)(/>„-/»g/g c 26 (A^/L), - ( A | > / L ) 2 = (I-«,)( />„ -/>)0/gc-(l-^)(/te-/>>Q/Qc 51 The b u l k d e n s i t y d i f f e r e n c e has already been shown to be given by PB|-/°B2=^|-€|HPsl -P) ~ <l-€2)(Ps2 ~P) 2 8 Thus PB\ ~PB2 = [(Ap F /L)|- (Ap F /L) 2 ]g c /g 52 The measured d i f f e r e n t i a l pressure d i f f e r e n c e s , which are thus e q u i v a l e n t t o the b u l k d e n s i t y d i f f e r e n c e s , are p l o t t e d a g a i n s t the s u p e r f i c i a l l i q u i d v e l o c i t i e s i n Figures 1 5 , 1 9 , 23 and 2 5 - The b o l d l i n e i s the curve obtained by using s i n g l e component expansion data and t h e o r e t i c a l d i f f e r e n t i a l pressures t o determine the i n v e r s i o n p o i n t , as f o l l o w s . At a p a r t i c u l a r s u p e r f i c i a l l i q u i d v e l o c i t y €^ and ^£ w e r e read from the s i n g l e component expansion curves, and these values were used i n equation 51 t o c a l c u l a t e the d i f f e r e n c e i n d i f f e r e n t i a l f r i c t i o n a l pressure gradient between the two components. Table 8 Inversion Results f o r Nic k e l and B a l l o t i n i Mixture Properties of Mixture Components d,mm. Ps Material Wt. of Sample O.I+56 8 .9O N i c k e l I+59.O gm. 2 . 2 8 2 - 7 3 B a l l o t i n i 400.0 gm. r Buoyancy r a t i o Size r a t i o Predicted inversion p o r o s i t y ( € m) by equation ( 3 9 ) Predicted inversion p o r o s i t y ( € m ) using single component data. Experimental inversion p o r o s i t y Flow regime 0 . 2 1 2 . 5 . 0 1 0 . 8 1 7 0 . 8 4 2 O .783 Stoke s 53- €> - NICKEL (d=0-456mm.) ©-BALLOTINI (d=2-28mm.) 0 -MIXTURE : 459gm. NICKEL AND 400gm. BALLOTINI - - P R E D I C T E D CURVE FOR MIXTURE -0 -3 -0-2 -0-1 0 LOG(POROSITY) Figure 13. P l o t of N i c k e l and B a l l o t i n i Bed Expansions. -0-8 - -1-0 - -1-2 -BED HEIGHT, INCHES Figure l U . D i f f e r e n t i a l Pressure P r o f i l e s i n . N i c k e l - B a l l o t i n i Bed. 55- 50 r 1 1 1 1 1 40 30 20 10 0 -10 ro H - 2 0 L L ^ -30 C/) GO _i - 4 0 C J - 5 0 CQ I - 6 0 m o. - 7 0 — - 8 0 - 9 0 -100 1 - 0 / © 2 PREDICTED CURVE" / BASED ON SINGLE _ / COMPONENT DATA / 0 EXPERIMENTAL " -110 -120 ' 1 1 1 1 1 ,-0 0 004 0 008 0 012 0 016 0 020 V s , FT. /SEC. 1 5 . P l o t of Bulk Density D i f f e r e n c e and V e l o c i t y f o r the N i c k e l - B a l l o t i n i Bed. ••••v.* •vvv (2) NICKEL O O o BALLOTINI • o « o # • «~ -o o 'o o • • • » o 0 o o o. (3) •oo o 0 . o » • o * ° 0 # O S •o • # • o * 0 o • o °-! (4) o o o • o • o o o o o o o o ° o t o o o • o o o o (5) INVERSION OF NICKEL AND BALLOTINI MIXTURE CA Figure l6. Schematic Diagram of how Inve r s i o n Proceeded. Table 9 Inversion Results f o r Alundum and B a l l o t i n i Mixture Properties , d,mm 0.645 1 . 0 8 of Ps 3 - 9 5 2 . 9 1 Mixture • Material Alundum B a l l o t i n i Components Wt. of sample 4470 gm. 3200 gm. Buoyancy r a t i o r 0 . 6 4 0 size r a t i o r 1 . 6 7 predicted, inversion p o r o s i t y (€ m) by equation ( 3 9 ) 0 . 8 0 5 • •predicted inversion p o r o s i t y using single component data. O .806 experimental p o r o s i t y ( € m inversion • ) O .763 flow regime Intermediate 58. € ALUNDUM (d=0-645 mm.) © BALLOTINI (d=l079mm.) 9 MIXTURE: 447gm.ALUNDUM / - 0 - 2 -0-1 0 LOG(POROSITY) Figure 17. P l o t of Alundum and B a l l o t i n i Bed Expansions i n Polyethylene G l y c o l . 5 0 4 5 4 0 35 3 0 oo m 2 5 - 2 0 15 10 0 0 S Y M B O L I 2 3 4 € 3 VELOCITY O F FLUID - F T . / S E C . • 0 0 0 9 6 •00316 • 0 0 5 8 9 •0119 8 10 12 14 16 18 2 0 BED HEIGHT 2 2 2 4 26 INCHES 28 3 0 3 2 3 4 3 6 38 4 0 4 2 Figure 1 8 . D i f f e r e n t i a l Pressure P r o f i l e s i n A l u n d u m - B a l l o t i n i Bed. 60. 0 0 0 0 4 0 0 0 8 0012 0016 0 0 2 0 V s , FT . /SEC. Figure . 19- P l o t of Bulk Densi ty D i f f e r e n c e and V e l o c i t y f o r A l u n d o m - B a l l o t i n i Bed. OOCiSC • •• • • (i) (2) • • ALUNDUM o BALLOTINI INVERSION OF ALUNDUM AND BALLOTINI MIXTURE Table 10 I n v e r s i o n R e s u l t s f o r Lead and S t e e l Mixture P r o p e r t i e s of Mixture Components d,mm Ps M a t e r i a l Wt. of sample 3-15 7 . 8 3 S t e e l 8 0 0 . 0 gm. 2 . 0 5 1 1 - 3 3 Lead 9 0 0 . 0 gm. buoyancy r a t i o s i z e r a t i o p r e d i c t e d i n v e r s i o n p o r o s i t y by equation ( 3 9 ) p r e d i c t e d i n v e r s i o n p o r o s i t y using s i n g l e component data experimental i n v e r s i o n p o r o s i t y (€„} flow rdgime O .659 1 . 5 3 6 0 . 8 0 3 0 . 6 8 8 0 . 7 2 1 Intermediate 0 T -0-2 © LEAD © STEEL ® MIXTURE 0-4 0-6 •0-8 -10 -1-2 • S / -1-4 -1-6 0-25 - 0 - 2 - 0 1 5 -01 - 0 0 5 LOG(POROSITY) Figure 21. Plot of Lead and Steel Bed Expansions. 0 SYMBOL I 2 3 4 € Q © VELOCITY OF FLUID - FT. /SEC. •054 •097 • 182 •237 1 6 8 10 12 14 BED HEIGHT, INCHES 16 18 2 0 22. D i f f e r e n t i a l Pressure P r o f i l e s i n Lead-Steel Bed. 65- CO OQ - J 4 5 4 0 3 5 3 0 25 2 0 15 10 5 CM m 0 I - - 5 CD -10 -15 •20 -25 - 3 0 - 3 5 - 4 0 • — i i i I I — : — 3 ® / ® 2 ~ ® I — — / PREDICTED CURVE B A S E D ON SINGLE — / COMPONENT DATA — e EXPERIMENTAL — i 1 1 1 1 0 0 4 0 0 8 012 016 0 -20 V s , F T . / S E C . 0 2 4 Figure 23- P l o t of Bulk Density D i f f e r e n c e and V e l o c i t y f o r the Lead-Steel Bed. Table 11 I n v e r s i o n R e s u l t s f o r N i c k e l - G l a s s and B a l l o t i n i Mixture. P r o p e r t i e s d,mm 0 . 5 4 2 1 . 0 8 of Ps 4 . 50 2 . 9 1 Mixture Components M a t e r i a l Wt. of sample N i c k e l - Glass 296.O gin. B a l l o t i n i 2 9 0 . 0 gm. buoyancy r a t i o X 0 - 5 3 7 s i z e r a t i o r 1 . 9 9 p r e d i c t e d i n v e r s i o n p o r o s i t y by equation ( 3 9 ) 0.804 p r e d i c t e d i n v e r s i o n . p o r o s i t y u s i n g s i n g l e component data 0.841 experimental i n v e r s i o n p o r o s i t y O.8O7 flow regime Stokes 67- LOG(POROSITY) Figure 2U- Plot of Nidkel'-Glass and Bal|otini- Bed-'-Expansio'ris iii Polyethylene-"-Gl-ycoi.- - c-6 8 . - 5 0 1 1 1 1 • I 1 0 0 0 0 4 0 0 0 8 0012 0016 0 0 2 0 V s , FT./SEC. Figure 25- P l o t of Bulk Density D i f f e r e n c e and V e l o c i t y f o r N i c k e l - G l a s s - B a l l o t i n i Bed. 69- The s u p e r f i c i a l l i q u i d v e l o c i t y at which homogeneous f l u i d i z a t i o n occurred f o r the f o u r mixtures was c l o s e to t h a t p r e d i c t e d by equation (39) .and t h a t p r e d i c t e d from s i n g l e component data. V i s u a l observations showed a gradual t r a n s i t i o n from heavy component predominantly at the bottom to the heavy component predominantly at the top of the bed, as the v e l o c i t y of the f l u i d was increased. An instantaneous f l i p - o v e r of the component beds as described i n the theory d i d not occur. The way i n which the i n v e r s i o n s proceeded i s ' i n t e r e s t i n g . As the s u p e r f i c i a l l i q u i d v e l o c i t y was i n c r e a s e d , mixing of the two components began at the i n t e r f a c e between the two beds, producing a r e g i o n of mixed bed. F u r t h e r increase i n v e l o c i t y caused the mixed bed r e g i o n to expand both upwards and downwards, u n t i l i t engulfed the whole f l u i d i z e d bed. F i n a l l y , as the v e l o c i t y was increased f u r t h e r , the heavy small p a r t i c l e s began to move out of the mixed bed and form a bed above the mixed bed. The mixed bed was slowly depleted of heavy small p a r t i c l e s as the v e l o c i t y was increased u n t i l the number of small p a r t i c l e s l e f t i n the mixed bed was very s m a l l . F i g u r e s give a shcematic r e p r e s e n t a t i o n of the i n v e r s i o n of two mixtures. The v e l o c i t y i n t e r v a l over which the i n t e r f a c e between beds was i n d i s t i n g u i s h a b l e occurred between b u l k d e n s i t y d i f f e r e n c e s of approximately • -15 and +k l b s m / f t 3. In t h i s r e gion of small bulk d e n s i t y d i f f e r e n c e s between the two components, the f a c t o r s causing mixing, such as v e l o c i t y d i s t r i b u t i o n and p a r t i c l e s i z e d i s t r i b u t i o n , have- a g r e a t e r e f f e c t than the small bulk d e n s i t y g r a d i e n t s , and the beds remain mixed and do not segregate. * In order to have an almost instantaneous i n v e r s i o n , the'region of small b u l k d e n s i t y d i f f e r e n c e must correspond to a small change i n s u p e r f i c i a l l i q u i d v e l o c i t y . For a sharp c l e a r i n v e r s i o n the r a t e of change of b u l k d e n s i t y w i t h respect t o v e l o c i t y must be l a r g e . Considering 7 0 . equation 2 8 , the p o r o s i t y i s the only v a r i a b l e on the r i g h t hand side which i s a f u n c t i o n of v e l o c i t y . Therefore the gradient o f bulk d e n s i t y d i f f e r e n c e w i t h respect to p o r o s i t y must be d i r e c t l y r e l a t e d to the gradi e n t o f bulk d e n s i t y d i f f e r e n c e w i t h respect to v e l o c i t y . Thus PB\ -PBZ- IP: '•I -P) [ < l - I r ,(3-m)/mn y * ~ € l^ ' ~ ^(mn-ll/mn * 28 D i f f e r e n t i a t i n g w i t h respect to €| , we have dlPm -Psi (3 - m ) / m n = ( ^ s l ~ ^ ' [ y ( m n - l ) / m n - ' ] 53 To have an i n v e r s i o n w i t h y < | , i t i s necessary t h a t | < r and thus r ( 3 - m ) / m n ^ ( m n - | ) / m n > ' R e f e r r i n g to equation 5 3 ; f t i s apparent t h e r e f o r e t h a t f o r a l a r g e gradient of bulk d e n s i t y d i f f e r e n c e w i t h respect to p o r o s i t y , r must be l a r g e , ( p s j —p) must be l a r g e and y must be small. A n a l y s i s of the data shows th a t these f a c t o r s do indeed have the p r e d i c t e d e f f e c t on the q u a l i t y of i n v e r s i o n . A comparison of mixtures appears i n t a b l e 1 2 . 71- Table 12 Q u a l i t y - o f - I n v e r s i o n P r e d i c t i o n s Mixture N i c k e l - B a l l o t i n i N i c k e l - G l a s s B a l l o t i n i Alundum B a l l o t i n i P%\ - P 1.84 gm/cc 1.84 gm/cc 1.84 gm/cc r 5 . 0 1 1 . 9 9 1 . 6 7 r 0 .212 O .537 0.640 ^PB\~PB^^€\ 10.6 gm/cc 2 . 2 1 gm/cc 1.44 gm/cc Comments: . very good • c l e a r - c u t i n v e r s i o n f a i r i n v e r s i o n mixed bed over most of f l u i d i z a t i o n r e g i on - poor i n v e r s i o n . 7 2 . P a r t i c l e s i z e d i s t r i b u t i o n s a f f e c t e d the preciseness of the i n v e r s i o n s and caused them to occur over a range of v e l o c i t i e s . I f a f l u i d i z e d bed i s composed of m a t e r i a l of a range of s i z e s , there w i l l be a p o r o s i t y g r a d i e n t through 'the f l u i d i z e d bed which w i l l gause a b u l k d e n s i t y g r a d i e n t . This has been shown to be so by Andrieu ( 1 0 ) and numerous other workers (h, 8 , 9 ) - Andrieu has a l s o shown that the p o r o s i t y g r a d a t i o n and thus the bulk d e n s i t y gradation increase as the o v e r a l l average p o r o s i t y i s increased. Both components i n the mixture have p a r t i c l e s i z e d i s t r i b u t i o n s and thus both have bulk d e n s i t y d i s t r i b u t i o n s . Three cases a r i s e , ( l ) The b u l k d e n s i t y d i s t r i b u t i o n s of both beds i s equal. . ( 2 ) The bulk d e n s i t y d i s t r i b u t i o n of the small heavy p a r t i c l e s ' i s greater than t h a t of the l a r g e l i g h t p a r t i c l e s . (3.) The bulk d e n s i t y d i s t r i b u t i o n of the heavy small p a r t i c l e s i s l e s s than the b u l k d e n s i t y d i s t r i b u t i o n of the l a r g e p a r t i c l e s . Case ( 2 ) i s the most l i k e l y f o r two reasons. As small p a r t i c l e s cannot be s i z e d as w e l l as l a r g e p a r t i c l e s , the b u l k d e n s i t y d i s t r i b u t i o n w i l l be g r e a t e r f o r the small p a r t i c l e bed. A l s o , the small heavy p a r t i c l e s w i l l be at a higher p o r o s i t y at i n v e r s i o n than the l a r g e l i g h t p a r t i c l e s , so that the b u l k d e n s i t y d i s t r i b u t i o n w i l l again be g r e a t e r f o r the small heavy p a r t i c l e s than f o r the l a r g e p a r t i c l e s . . Case ( 3 ) i s very u n l i k e l y . As the d e n s i t y r a t i o and s i z e r a t i o of the p a r t i c l e s approach u n i t y , the p r o b a b i l i t y of case ( l ) i n c r e a s e s . As case ( 2 ) i s the m o s t . l i k e l y , the way i n which i t a f f e c t s the f l u i d i z e d mixture w i l l be discussed. The beds w i l l begin t o mix when the b u l k d e n s i t y at the bottom of the top bed i s equal to the bulk d e n s i t y at the top of the bottom bed. See f i g u r e 2 6 a . As the bulk d e n s i t y v a r i a t i o n i n the small p a r t i c l e bed i s g r e a t e r than i n the l a r g e p a r t i c l e bed, the small p a r t i c l e s w i l l begin to form a s i n g l e component bed above the mixed bed before the average bulk d e n s i t y d i f f e r e n c e s between the beds i s zero. 73- This i s i l l u s t r a t e d i n f i g u r e 2 6 b , and accounts f o r the f a c t that the observed i n v e r s i o n p o i n t always f e l l to the l e f t of the t h e o r e t i c a l c ross-over p o i n t i n F i g u r e s 1 5 , 1 9 , 23 and 25• The components w i l l f i n a l l y separate completely i n t o two beds when we have th a t s i t u a t i o n which i s shown i n f i g u r e 2 6 c This was r e a d i l y n o t i c e a b l e w i t h the n i c k e l - b a l l o t i n i mixture, where the p a r t i c l e s i z e d i s t r i b u t i o n of the n i c k e l p a r t i c l e s was much l a r g e r than t h a t of the b a l l o t i n i p a r t i c l e s . A f t e r the i n v e r s i o n p o i n t was reached and an apparent homogeneous f l u i d i z e d bed appeared, as the s u p e r f i c i a l l i q u i d v e l o c i t y was increased a n i c k e l bed began t o form on top of the mixed bed. The n i c k e l bed became l a r g e r but a mixed bed region remained u n t i l a much gr e a t e r v e l o c i t y than the i n v e r s i o n v e l o c i t y was reached. The case ( l ) s i t u a t i o n would be s i m i l a r t o t h a t of the alondum- b a l l o t i n i mixture. Here, a f t e r the i n v e r s i o n p o i n t was reached, a b a l l o t i n i bed began to form at the bottom of the mixed bed and an alundum bed at the top. As the s u p e r f i c i a l l i q u i d v e l o c i t y was increased, the reg i o n of mixed bed decreased u n t i l i t disappeared at the centre of the bed. This i s shown i n f i g u r e 2 6 d . 74. M- measured average bulk density difference .bottom TOM BED 26 a. "beds beginning to mix. shaded section — mixed bed region bottom BOTTOM B E D bottom T O P BED 2 6 b . i n i t i a l bottom bed beginning to form bed at top of mixed bed. 2 6 c . i n i t i a l bottom bed nov on top - 2 6 d . a l u n d u m - b a l l o t i n i mixture complete segregation. s i t u a t i o n 1. F i g u r e . 2 6 . E f f e c t of P a r t i c l e Si'£e D i s t r i b u t i o n s on the P o i n t of Inver s i o n . 75- 22 P r e d i c t i o n , of Bed Expansion f o r Mixtures. Equation kk; developed i n an e a r l i e r s e c t i o n t o p r e d i c t bed expansions f o r mixtures of d i f f e r e n t m a t e r i a l s , was t e s t e d f o r numerous mixtures i n f l u i d i z i n g media of water and polyethylene g l y c o l s o l u t i o n s . The equation p r e d i c t s the expansion of the mixed beds very w e l l . In the i n v e r s i o n . r u n s made w i t h polyethylene g l y c o l s o l u t i o n s , the experimental data cover the complete range of mixing of the two components, and equation kk s t i l l p r e d i c t s the expansion t o a high degree of accuracy. Comparisons of experimental and p r e d i c t e d expansions i n polyethylene g l y c o l s o l u t i o n s are given i n f i g u r e s 1 3 ; 1 7 ; 21 and 2k. In each case, the p r e d i c t e d expansion i s represented by the dark b o l d l i n e and the experimental data by the c i r c u l a r p o i n t s . Many runs of d i f i ' e r e n t m a t e r i a l s were made i n w a t e r - f l u i d i z e d beds to t e s t equation kk thoroughly. Mixtures f o r which the . X r a t i o was l a r g e and the r r a t i o s m a l l , represented by f i g u r e s 2 7 ; 28 and 2 9 ; and s i m i l a r l y mixtures w i t h s m a l l y r a t i o s and l a r g e r r a t i o s , represented by f i g u r e s 30 and 3 1 ; were t e s t e d to determine the e f f e c t o f these f a c t o r s on how w e l l the equation p r e d i c t e d the a c t u a l expansion. I t was found t h a t f o r l a r g e r r a t i o s , the equation d i d not p r e d i c t the expansion w e l l at low p o r o s i t i e s . In the r e g i o n where one of the components i s near the minimum p o r o s i t y of f l u i d i z a t i o n , the p r e d i c t e d curve d e v i a t e d from the experimental data. The l a t t e r f e l l much c l o s e r to the expansion l i n e f o r t h a t component which i s near the minimum f l u i d i z a t i o n v e l o c i t y than d i d the p r e d i c t e d r e s u l t s . This can be seen i n Figure 31 A s e r i e s of runs was made w i t h v a r i o u s r a t i o s of n i c k e l - g l a s s and b a l l o t i n i t o t e s t equation kk when there was l a r g e d i f f e r e n c e s i n the volume of each component present. The equation p r e d i c t e d the r e s u l t s f a i r l y w e l l f o r a l l r a t i o s . R e s u l t s are given i n f i g u r e 3 2 . 76. I t i s i n t e r e s t i n g t h a t an equation which i s based on the assumption th a t the two m a t e r i a l s are completely segregated i n t o two beds p r e d i c t s the expansion even when the two components are p a r t i a l l y or completely mixed. This seems t o i n d i c a t e t h a t the b u i l d i n g b l o c k theory of Happel (6), t h a t a f l u i d i z e d bed i s made up of c e l l s , each of which i s a s s o c i a t e d w i t h a p a r t i c l e , and t h a t the s i z e of the c e l l s i s dependent only on the p a r t i c l e and the s l i p v e l o c i t y of the f l u i d , i s sound. - Thus the c e l l s w i l l be the same s i z e whether they are i n the mixture or i n a completely segregated bed. 77- -0-35 -0-3 -0-25 -0-2 -015 -01 LOG(POROSITY) Figure 27- P l o t o f Alundum-Crystalon Run No.l. 78. LOG(POROSITY) Figure 28 . P l o t of Alundum-Crystalon Run No.2. Figure 2 9 - P l o t of Alundum and B a l l o t i n i Bed Expansions i n Water. 8 0 . -0-35 -0-3 -0-25 -0-2 -015 -01 LOG(POROSITY) Figure 3 0 . P l o t of N i c k e l - G l a s s and B a l l o t i n i Bed Expansions i n Water. 81. LOG (POROSITY) Figure 31 . P l o t of N i c k e l and Alundum Bed Exp i i i r ~ MIXTURE: BALLOTINI (B) -1-3 1 — 1 1 1 I I I I I I I I I -0-46 -0-42 -0-38 -0-34 -0-3 -0-26 -0-22 -018 -014 -01 -0 06 LOG( POROSITY) Figure 32. P l o t of N i c k e l - G l a s s and B a l l o t i n i Bed Expansions w i t h D i f f e r e n t 00 Volumes of Each Component. r° 83- CONCLUSIONS 1. The s u p e r f i c i a l l i q u i d v e l o c i t y which produces homogeneous f l u i d i z a t i o n of two species does so at a mean p o r o s i t y f o r the f l u i d i z e d mixture which i s very c l o s e t o tha t p r e d i c t e d by equation 39 and tha t p r e d i c t e d by s i n g l e component data. Equation 39 i s based on the f o l l o w i n g four assumptions: n l ~ n2> m l = m2> ^12= ^2> and (^1 " c^X^n i s small. These c o n d i t i o n s are s a t i s f i e d approximately; each i s i n e r r o r by a small amount. Thus equation 39 can be expected t o give only an approximate value f o r the i n v e r s i o n p o r o s i t y , and corresponding v e l o c i t y . The s i n g l e component data a l s o cannot p r e d i c t i n v e r s i o n v e l o c i t i e s p r e c i s e l y , because the p o r o s i t y - v e l o c i t y r e l a t i o n s h i p s obtained f o r the s i n g l e component beds are average values over the whole bed. P o i n t c o n d i t i o n s i n the f l u i d i z e d bed describe the s i t u a t i o n b e t t e r than average v a l u e s , e s p e c i a l l y when the p a r t i c l e s are not p e r f e c t l y uniform i n s i z e . Homogeneous mixing i n the f l u i d i z e d mixture i s a f u n c t i o n of the r e l a t i v e bulk d e n s i t y d i s t r i b u t i o n i n the s i n g l e component beds. 2 . The experimental mixture p o r o s i t y at homogeneous f l u i d i z a t i o n i s l e s s than t h a t p r e d i c t e d by s i n g l e component data. This was analyzed and i t was found t h a t the only cause c o u l d be p a r t i c l e s i z e d i s t r i b u t i o n i n the two s i n g l e component beds. A l s o , the b u l k d e n s i t y gradation i n the small p a r t i c l e bed must be greater than t h a t i n the l a r g e p a r t i c l e bed. This would cause the p o i n t of homogeneous f l u i d i z a t i o n t o be reached before that p r e d i c t e d from s i n g l e component data. The two c o n d i t i o n s which. Cause the bulk d e n s i t y gradation to be gr e a t e r i n the small p a r t i c l e bed are : ( 1 ) the l a r g e p a r t i c l e s can be s i z e d b e t t e r than the small p a r t i c l e s ; ( 2 ) the s m a l l p a r t i c l e s are at a higher average p o r o s i t y , thus the e f f e c t of p a r t i c l e s i z e d i s t r i b u t i o n on the b u l k d e h s i t y w i l l be much grea t e r 8k. •than f o r the l a r g e p a r t i c l e s , which are at a much lower p o r o s i t y . 3. For a c l e a r - c u t i n v e r s i o n i n the f l u i d i z e d bed the region of low bulk d e n s i t y d i f f e r e n c e s , where mixing f o r c e s are predominant, must be t r a v e r s e d by a small change i n v e l o c i t y . This i s accomplished by having a l a r g e value of r and a correspondingly small value of y . k. In c o n t r a s t to beds f l u i d i z e d by polyethylene g l y c o l s o l u t i o n s , i n v e r s i o n s i n w a t e r - f l u i d i z e d beds were not obtained because the extreme turbulence, p a r t i c l e c i r c u l a t i o n , and p o r o s i t y d i s t r i b u t i o n s d i s r u p t e d the bed too much. Bulk d e n s i t y g r a d i e n t s d i d not get a chance to develop, as mixing f o r c e s were,.;much more predominant. The p o r o s i t y o f the small p a r t i c l e beds r e q u i r e d to produce homogeneous f l u i d i z a t i o n was u s u a l l y greater than 8 5 $ . At p o r o s i t i e s i n t h i s range, w a t e r - f l u i d i z e d beds are hydrodynamically unstable. 5. The p r e d i c t i o n of mixed bed expansion based on s i n g l e component data u s i n g equation kk i s very good. The equation p r e d i c t s the expansion 6'ver the .measured range ofrflMdization:;.forhmixt\ar«'s^^ •ratios-" • as great as 10:1. I t a l s o p r e d i c t s the expansion very w e l l f o r a wide < range of y and r r a t i o s . The p r e d i c t e d values begin to deviate from the experimental values when one of the two components of the mixture i s c l o s e to i t s minimum p o r o s i t y f o r f l u i d i z a t i o n . Even though the equation i s based on the assumption of no mixing of the component beds, i t p r e d i c t s the expansion of the f o u r mixtures which passed through a l l stages of mixing as they were f l u i d i z e d . T his seems to i n d i c a t e that the holdup i n a f l u i d i z e d bed i s only a f u n c t i o n of the i n d i v i d u a l p a r t i c l e s and the s u p e r f i c i a l l i q u i d v e l o c i t y , and u n a f f e c t e d by p a r t i c l e i n t e r a c t i o n s . 6. The Richardson and Zaki method of p l o t t i n g data f o r s i n g l e components appears to be e x c e l l e n t , as most data f e l l on a s t r a i g h t l i n e having a ' slope very n e a r l y equal to t h a t p r e d i c t e d by the Richardson and Zaki equations. 85- The data began to t a i l o f f at very h i g h p o r o s i t i e s , but t h i s i s probably caused by s i z e s t r a t i f i c a t i o n i n the f l u i d i z e d bed. 7» Equation 2 3 , developed by Richardson and Z a k i f o r c a l c u l a t i n g the f r e e s e t t l i n g v e l o c i t y o f the p a r t i c l e s from the expansion l i n e s v e l o c i t y i n t e r c e p t at a p o r o s i t y of 1 0 0 $ , g i v e s answers which are o f t e n 1 0 - 2 0 $ d i f f e r e n t from those c a l c u l a t e d using the drag c o e f f i c i e n t - R e y n o l d s ' number p l o t f o r spheres. This c o u l d be caused by a number of f a c t o r s , two of which may be the n o n - s p h e r i c i t y and non-uniformity of the p a r t i c l e s . On the other hand, there i s a l s o the p o s s i b i l i t y t h a t equation 23 does not adequately c o r r e c t f o r the w a l l e f f e c t . Richardson and Z a k i have assumed t h a t the w a l l e f f e c t i s only a f u n c t i o n of the p a r t i c l e to column diameter r a t i o ; and have ignored other p o s s i b l e v a r i a b l e s such as f l u i d regime. 8. The f r i c t i o n a l pressure drop equation based on a simple f o r c e balance, p o p u l a r i z e d by Wilhelm and Kwauk, p r e d i c t s the experimental r e s u l t s w e l l , except at very high p o r o s i t i e s where there i s a l a r g e amount of segregation by s i z e of the p a r t i c l e s . The average e r r o r i s approximately 5$- The e r r o r due to assuming the w a l l pressure l o s s was n e g l i g i b l e was found t o be l e s s than 1 $ . A l s o i t 1-has been shown t h a t measurement of pressure l o s s p r o f i l e s i s an e x c e l l e n t method f o r determining l o n g i t u d i n a l bulk d e n s i t y and p o r o s i t y d i s t r i b u t i o n s i n f l u i d i z e d beds. 86. Recommendations f o r Further Work 1. Determination of the e f f e c t of p a r t i c l e s i z e d i s t r i b u t i o n on the i n v e r s i o n p o i n t i s important. This may be accomplished by the f o l l o w i n g procedure: (a) F l u i d ! z e ammixture of two m a t e r i a l s of known p r o p e r t i e s and o b t a i n expansion and d i f f e r e n t i a l pressure data f o r the mixture. (b) At a v e l o c i t y j u s t l e s s than the i n v e r s i o n v e l o c i t y , remove se p a r a t e l y the upper and lower p o r t i o n s of the bed. Measure the average p a r t i c l e diameter of the small heavy p a r t i c l e s which were'in the top bed. Dp the same f o r the l a r g e p a r t i c l e s which were i n the small p a r t i c l e bed. (c) With the small p a r t i c l e s which were i n the l a r g e p a r t i c l e bed and the l a r g e p a r t i c l e s which were i n the small p a r t i c l e bed removed,. f l u i d i z e the remaining mixture. . Expansion and d i f f e r e n t i a l pressure data should be obtained. (d) At a v e l o c i t y j u s t g r e a t e r than the i n v e r s i o n v e l o c i t y , remove se p a r a t e l y the upper and lower beds of the mixture. Measure the average p a r t i c l e diameter of the l a r g e p a r t i c l e s which remained i n the top bed and of the small p a r t i c l e s which remained i n the bottom bed. I f the p a r t i c l e s i z e , d i s t r i b u t i o n was approximately Gaussian and i f p a r t i c l e s i z e d i s t r i b u t i o n i s important) the f o l l o w i n g r e s u l t s should be obtained. Figure 33 i s a diagram of the p a r t i c l e s i z e d i s t r i b u t i o n i n the small heavy p a r t i c l e bed and the large- l i g h t p a r t i c l e bed. The average diameter o f the small p a r t i c l e s measured i n ' p a r t (b) should be i n the shaded region A. The average diameter o f the s m a l l particles measured i n p a r t (d) should be i n the shaded r e g i o n B. S i m i l a r l y f o r the l a r g e p a r t i c l e bed, the average diameter of the p a r t i c l e s removed i n pafct (b) should be i n the shaded region D, and the average diameter of the p a r t i c l e s 87- d - d - small heavy particle size large light particle size distribution. distribution. Figure 33' Particle Size Distributions removed in part (d) should be in the shaded region C. If the above conditions are consistent with the experimental results for average particle diameters,, then particle size distribution i s a very important factor affecting inversions. The above procedure may be carried out a number of times u n t i l the' inversion occurs over a very narrow velocity range. 2. Most mixtures subjected to inversion runs in the present research were approximately '}0~50 mixtures by volume. Numerous experiments should be run where the i n i t i a l amount of each component added i s different from 50$ by volume. If the results are similar to those obtained in the present report, i t can be concluded that the relative proportions of each material has noteffect on the mixing and segregation in the fluidized mixture. If the inversions obtained are clear-cut, then runs made with very small amounts of one material added to another 8 8 . can be used to measure rates of mixing. The time for the small amount of material to mix homogeneously in the component of large volume could be measured. This would be a measure of the random mixing of particles, because the driving force due to bulk density difference would then be negligible. 3- Experiments may be made to determine the experimental limits of density and size difference which can be tolerated in seeking an inversion. h. Motion pictures of. inversions may also be taken.to record visually how an inversion takes place. 8 9 . L i t e r a t u r e C i t e d 1. Wilhelm, R.H., and Kwauk, M., Chem.Eng.Progr., 4 4 , 2 0 1 (1948). 2 . Hancock, R.T., The Mining Magazine, 55_, 9 0 ( 1 9 3 6 ) . 3 . J o t t r a n d , R.J., Chem.Eng. S c i . , 3 , 12 ( 1 9 5 4 ) . 4 . Richardson, J.F., and Z a k i , W.N., Trans.Inst.Chem.Engrs. (London), 3 1 , 35 ( 1 9 5 4 ) . 5. Leva, M., F l u i d i z a t i o n , McGraw-Hill Book Co. Inc., New York, 1959- 6 . Happel, J . , A.I.Ch.E. J o u r n a l , 4 , 197 ( 1 9 5 8 ) . 7 . Hawksley, P.G.W., Paper No.7 i n "Some Aspects of F l u i d Flow", London, Edward A r n o l d and Co., 1 9 5 1 . 8 . Lewis, E.W., and Bowerman, E.W., Chem.Eng.Progr., 48, 603 ( 1 9 5 2 ) . 9 . Verschoor, H., Appl.Sci.Research, A2, 1 5 5 ( 1 9 5 0 ) . 10-. Andrieu, R., Ph.D. t h e s i s , U n i v e r s i t y of Nancy, France, 1 9 5 6 . 11. Beare, J.W., B.A.Sc. t h e s i s , U n i v e r s i t y o f B r i t i s h Columbia, I958. 1 2 . Hoffman, R.F., Lapidus, L., and E l g i n , J.C., A.I.Ch.E. J o u r n a l , 6 , 321 ( i 9 6 0 ) . - 1 3 . De V e r t e u i l , G.F., B.A.Sc. t h e s i s , U n i v e r s i t y o f B r i t i s h Columbia, 1 9 5 8 . 1 4 . A.S.T.M. Standards on Petroleum Products and L u b r i c a n t s , B a l t i m o r e , 1 9 5 8 , page 2 0 1 . 1 5 . Pruden, B.B., M.A.Sc. t h e s i s , U n i v e r s i t y of B r i t i s h Columbia, 1 9 6 4 . 1 6 . C a i r n s , E.J., and P r a u s n i t z , J.M., A.I.Ch.E. J o u r n a l , 6 , 554 ( i 9 6 0 ) , 1 7 . C a i r n s , E.J., and P r a u s n i t z , J.M., Ind. Eng. Chem., 5 1 , l 4 4 l , . ( l 9 5 9 ) . 1 8 . Jackson, R.A., Trans.Instn. of Chem.Engrs. (London), 4 l , 1 3 ( 1 9 6 3 ) . 1 9 . S l i s , P.L., Willemse, T.W., Kramers, H., Appl.Sci.Res.Sec. A, 8 , 209 ( 1 9 5 9 ) - 2 0 . A d l e r , I.L., and Happel, J . , Chem.Eng.Symposium S e r i e s , No.38, 5 8 , 9 8 ( 1 9 6 2 ) . • APPENDIX I - BEARE'S PLOTS FOR PREDICTION OF INVERSION POROSITIES. 1-2 Belov/ i s presented Beare. 1 s p l o t f o r the laminar or Stokes' f l o w region. I t r e l a t e s i n v e r s i o n c o n d i t i o n s w i t h p a r t i c u l a r values of f and G . The p l o t i s based on the s i m p l i f y i n g assumptions t h a t 02 =ri|= 4 .65 i n the Richardson-Zaki equations, and t h a t the Stokes' law equation f o r f r e e s e t t l i n g holds. Thus V s = V 0 |€ n' = V o 2 € n 2 and d f ^ S l - / 0 ^ . . 6 8 4 ^ 2 - ^ 9 , 4-66 ( A ) ii7^ 1 ieTi €2 <A> The b u l k d e n s i t y d i f f e r e n c e at i n v e r s i o n equals zero. Therefore PB\ ~PBZ = Ps i ( ' - € i ) + P€\ - Psz^~€z) - P€z = 0 or (I- €,)(Al - P ) = (l-*2>(A>s2-/» whence _ PsZ ~P l" €2 " 3^1 ~P Define Then 1 /°$2 ~P d l / Ps\ ~P d2 and from equation A above, 4-65 i • .2 ••ft] r 2 * a - 2 (c) Manipulating equations B and C, a — I € l ~ a3-65/4-63 r 2/4-68 _. | and c 2 = € , / a + ( a - i ) / a Using the two equations given above, a chart was developed by Beare to give the porosities of the two beds at inversion for any particular combination of r and Cl . The chart,appears in figure 33- A similar chart was also developed by the present author for the Newton region. The assumptions used are: ( l ) 01 = rig = 2-39 and (2) Newton's law for free settling holds. The inversion porosities are then € = 5LzJ 1 gS-78/4-78 1/4-78 _ j and € 2 = €,/a + ( a - i ) / a These equations were used to develop the chart, which works on the same principle as Beare's chart and appears in figure 34. 1-3 POROSITY BED I Figure ^k. Beare P l o t f o r Stokes' Lav/ Region. APPENDIX I I SAMPLE CALCULATION AND ERROR ANALYSIS 2 - 2 Reference L i t e r a t u r e Data: Density of Mercury. Perry, J.H., e d i t o r , Chemical Engineers.' Handbook, Th i r d E d i t i o n , McGraw-Hill Book Co.Inc., New York, 1 9 5 0 , p . 1 7 6 . Density of Carbon Tetrachloride. Riddick, J.A. and Toops, J r . , E.E., Organic Solvents, Volume 7 , Second E d i t i o n , Interscience Publishers, Inc., New York, 1 9 5 5 , P-194. Drag C o e f f i c i e n t - Reynolds' number data. Zenz, A.F., and Othmer, D.F., F l u i d i z a t i o n and F l u i d - P a r t i c l e Systems, Reinhold Publishing Corporation, New York, i 9 6 0 , p.203- Density of Water. .Chemical Engineers' Handbook, p.175 , complete reference above. V i s c o s i t y of Water. Chemical Engineers' Handbook, p - 3 7 4 , complete reference above. A. Porosity of Bed. H = 2 0 . 0 + 0.5 cm. ; p ' = 4 . 0 0 + 0.05 gm./cc. 2 W = 400.0 + 1 . 0 gm. ; A = 2 0 . 2 6 + 0 . 1 8 cm . € = 1 - 400 . 0 / ( 2 0 . 0 x 2 0 . 2 6 x 4 . 0 0 ) = 0 . 7 2 4 1 - € = W//os H A 1 0.05 0.5 0 . 1 8 400 4~00 2 0 . 0 2 0 . 2 6 maximum erro r i n ( l - € ) = ( 0 . 0 4 8 7 ) ( 0 . 2 7 6 ) = maximum erro r i n € maximum percent error i n € = ( 0 - 0 4 8 7 ) ( 0 . 2 7 6 ) x 1 0 0 $ 0 . 7 2 4 = + 1 . 8 6 $ B. C a l c u l a t i o n of Pressure Loss i n a F l u i d i z e d Bed. ^ £ - F = 0 . 3 9 4 - j * - ( p M - p F )g/g c . l b f o r c e / f t . 3 X = 1 0 . 0 + 0 . 2 cm. ; PM = 1 0 0 . 0 + 0 . 3 l b s . / f t . 3 p = 67.O + 0 . 6 l b s . / f t . ; L = 3 - 0 + 0 . 3 1 inches. ( p M - p f ) = ( 1 0 0 . 0 - 67.O) + 0 . 9 l b s . / f t . 3 maximum percent e r r o r i n A p p / L = = 1 + + ° - ° 3 1 3 ) 1 0 0 $ = 5 . 7 7 $ » 1 0 . 0 3 3 . 0 3 . 0 ' C. V e l o c i t y of F l u i d . V = f(Re) D = 2 . 0 + 0 . 3 1 inches p = 6 6 . 6 + 0 . 6 l b s . / f t . ' 2-4 fj.= 0 . 0 9 0 + 0 . 0 0 2 l b s . / f t . sec. Re - taken from c o r r e l a t i o n c h a r t , maximum error' i n V = 2 . 8 $ + ( = 7 . 4 8 $ f o r which the mean e r r o r i s + 2 . 8 $ ° - ° 3 i 3 • + 0 ^ 0 , 0 0 2 ) 1 0 0 # . 2 . 0 * OTQTCF * 0 . 0 9 0 ^ 3 - 1 APPENDIX I I I - MATERIALS USED M a t e r i a l P a r t i c l e Density Average Appendix IV Shape gm./cc. Diameter Run No. mm. Alundum §ranular, 3 - 9 5 0.645 3 jagged 0.645 2*. 0 . 7 6 7 2 0 . 9 1 2 4 1-52 11 B a l l o t i n i g l a s s 2.91- 1 . 0 8 1 spheres 1 . 0 8 2 * I . 8 3 5 2 . 7 3 2 . 2 8 1* Cataphote g l a s s 2 . 4 7 0 . 7 6 7 9 micro-beads C C r y s t a l o n g r a n u l a r . 3 - 5 0 1 . 0 8 6 Lead shot, I I . 3 0 2 . 0 5 3 * s p h e r i c a l N i c k e l s p h e r i c a l 8 . 9 1 0 . 4 5 6 1* 0 . 3 8 4 10 N i c k e l - n i c k e l coated 4 . 5 0 0 . 5 4 2 Glass g l a s s spheres S t e e l b a l l bearings 7 . 8 0 • 3-15 3 * * polyethylene g l y c o l s o l u t i o n run numbers APPENDIX IV - ORIGINAL DATA APPENDIX IV - INDEX Run No. D e s c r i p t i o n Page P o l y e t h y l e n e - g l y c o l 1 B a l l o t i n i - N i c k e l Mixture 4-4 2 B a l l o t i n i - A l u n d u m Mixture 4 - 9 3 Lead-Steel Mixture 4-13 4 B a l l o t i n i - N i c k e l - G l a s s Mixture 4 - l 6 Water 1 B a l l o t i n i ( l . 0 8 mm.) 4-17 2 Alundum (O .767 mm.) 4 - l 8 3 Alundum (0.645 mm.) 4-19 4 Alundum ( 0 . 9 1 2 mm.) 4-19 5 B a l l o t i n i ( 1 . 8 3 m m . ) 4 - l 8 6 C r y s t a l o n ( l . 0 8 mm.) , 4-20 7 B a l l o t i n i - N i c k e l - G l a s s Mixture ( l ) 4 - 2 1 8 B a l l o t i n i - N i c k e l - G l a s s Mixture ( 2 ) 4 - 2 5 9 Alundum-Cataphote Mixture 4-26 10 Alundum-Nickel Mixture 4-28 11 Alundum-Crystalon Mixture ( l ) 4-29. 12 ' B a l l o t i n i - A l u n d u m Mixture 4-30 13 Alundum-Crystalon Mixture ( 2 ) 4-20 A l l o r i g i n a l data f o r the expansion runs and the f r i c t i o n a l p f e s runs are i n c l u d e d i n t h i s s e c t i o n . Explanations o f t a b l e headings are as f o l l o w s : 4-3. Ave. Diameter - the average diameter of the p a r t i c l e s based on the a r i t h m e t i c average of the screen s i z e s . From Run - r e f e r s to the p a r t i c u l a r run i n which the s i n g l e component data f o r the m a t e r i a l appears. Across Taps - the f r i c t i o n a j . pressure g r a d i e n t reading was measured across the f o l l o w i n g two pressure taps. Run 1 (Polyethylene G l y c o l ) - a run i n which the f l u i d i z i n g medium i s the polyethylene g l y c o l s o l u t i o n ; s i m i l a r l y f o r water runs (water). Meter (Mercury), e t c . - r e f e r s t o the p a r t i c u l a r flow meter and manometer f l u i d used to make th a t p a r t i c u l a r reading. 4-4. Run 1 (Polyethylene Glycol) Material: Glass B a l l o t i n i Ave. Diameter: 2.28mm. Wt. of Sample: 1+00 gms. Density: 2*73 gm./cm3. Manometer Reading Temperature Temperature Bed . arm 1 in. inarm 2 in. column °F Room O f •height cm. 9 - 1 5 * 6 . 9 5 7 0 . 8 7 0 . 1 2 3 . 6 14 .00 * 1 0 - 7 5 7 1 . 0 7 1 - 0 29.8 0 . 6 0 4 . 6 0 72.5 7 3 - 4 3 8 . 3 3 - 9 0 4 • 30 7 1 . 0 7 1 . 6 5 4 . 6 5.5O 7 . 0 0 7 1 . 0 7 1 . 4 9 6 . 6 4 - 5 5 * 3 . 1 5 6 9 . 5 6 9 . 6 1 7 . 5 2 . 2 0 * 1 . 0 0 7 0 . 2 70.8 14.1 6 . 6 0 * 4 . 8 0 70.4 7 0 . 9 2 0 . 2 1 5 . 1 0 * 1 1 . 6 5 7 0 . 6 7 1 . 0 3 1 . 8 4 . 1 5 2 . 2 5 70.7 7 1 . 0 4 5 . 3 6 . 1 0 4 . 0 0 7 1 . 0 7 0 . 9 71.8 - Meter (Mercury) - |" Meter (Air) Run 1 (Polyethylene Glycol) Material: Nickel Wt. of Sample: 447 gms. Ave. Diameter: O.456 mm. Density: 8.92 gm./cm^ . Manometer Reading arm 1 in. arm 2 in. Temperature column °F Temperature Room °F Bed height 0 . 9 0 0 . 2 5 7 4 . 0 7 3 - 2 5 . 4 1 . 1 0 0 . 3 5 7 3 - 9 7 3 - 4 5 - 7 1 . 6 0 0 . 7 0 7 4 . 0 7 3 . 8 6 - 7 2 . 0 5 1 . 1 0 7 4 . 0 7 3 - 6 7 - 4 2 . 6 0 1 . 6 0 7 4 . 0 7 3 - 9 8 . 5 3-40 2 . 3 0 7 3 - 9 7 3 - 6 1 0 . 1 3 - 7 5 2 . 6 0 7 3 - 9 7 3 - 7 1 1 . 0 4.40 3 . 1 0 7 3 - 8 - 7 3 . 8 1 2 . 3 4 . 8 5 3 . 5 0 7 3 - 8 7 3 - 7 1 3 . 7 5 . 6 5 4 . 1 0 7 3 . 8 7 3 - 8 1 6 . 0 6 . 1 5 4 . 5 0 7 3 - 8 7 3 - 4 1 7 . 8 6 . 5 0 4 . 8 5 7 3 . 8 7 3 . 4 1 9 . 5 7 . 2 5 5 . 4 5 7 3 . 8 7 3 - 6 2 3 . 0 Meter (Mercury) 4-5 Run 1 (Polyethylene' Glycol) Material: Glass B a l l o t i n i Wt. of Sample: 400.0 gm. From Run Ave. Diameter: 2.28 mm. Density: 2.73 gm./cc. Manometer Reading Temp Temp Bed Across arm 1 arm 2 Column Room Height Taps . cm cm °F O p cm 59-0 61.4 70.8 70.1 23.5 1-2 56.8 63.7 70.8 71. i 1-4 54.3 66.2 71.0 71.0 1-6 52.0 68.6 71.0 71.0 1-8 59-2 61.2' 71.0 71.0 29.8 1-2 57.3 63.O 71.0 71.0 1-4 55.5 . 65.O 72.0 72.5 1-6 53-7 66.9 72.0 72.5 1-8 51.9 68.8 72.0 73-2 1-10 52.6 68.5 • • 72-5 73.4 • 38.3 1-12 53-6 67.1 73.O 73.8 1-10 55.O . 65.6 72.4 . 73-3 1-8 56.4 64.2 •• 72.4 73-3 1-6 50.7 55-6 71.2 71.2 1-4 52.3 53-9 71.0 71.5 1-2 52.6 53-7 71.0 71.6 5426' 1-2 51.7 54.5 71.0 71.8 1-4 • 50.5 55-7 71.0 71.6 1-6 47.4 57.8 71.0 71-4 1-10 . 47.3 59-0 71.0 71.5 1-12 45.4 61.0 71.2 71.5 1-16 43.5 63.O 71.0 71.4 . 1-20 42.3 64.3 71.0 71.4 96.6 1-36 44.1 62.4 71.0 71-1 1-28 46.5 59-9 71-5 71-2 1-20 49.8 56.4 71.2 71.4 1-10 51.4 54.6 69-5 69-6 17-5 1-2- 48.5 57.5 69-6 69.8 1-4 48.5 57-5 70.0 70.4 2-5 51.5 54.7 70.O 70.7 4-5 Run 1 (Polyethylene, G l y c o l ) - M a t e r i a l s : Glass B a l l o t i n i N i c k e l ';'';Wt J* of 'Samples ' 1+00. O^ gmV' ' 1+59-0 gm. From Run. 1 ' 1 . Manometer Reading Temperature Temperature Bed . . arm 1 i n . arm 2 i n . column °F Room °F Heights cm. N i g l a s s 0.1+0 •1-55 71.8 72.0 8.1+ * 21-5 1.10 2-35 71.7 72.6 10.6 . 25.O 1.80 3.10 71.6 72.6 12 .2 2 8 . 0 2.65 1+.10 71.8 72.8 1I+.5 31-5 3-35 ' 4.95 71.5 72.8 16.0 34.1 1+.50 6.35 71.6 • 72.9 - : 37-2 5.60 7.1+5 70.5 70.6 - ' 1+0.2 6.30 8.55 • 70..3 '71.6 39-6 t+8.0 6.70 9.05 71.8 73.5 37-5 59-0 7.30 9.90 72.5 71+.0 3 6 . 0 7 0 . 0 1+.50 6.50 71.0 73-1 - 36.3 8 .20 5.85 71.0 73-2 39-6 1+0.5 •5-" Meter (Mercury) * - Subtract 2.80 from a l l v a l v e s i n column. Run 1 V i s c o s i t y and- Density Temperature V i s c o s i t y 1 6 / f t . s e c . Temperature O p Density gm./cc. 70.0 75-0 80.0 O.O96 0.087 O.O79 75-0 78.1+ 63.8 66.55 66.52 66.73 4-7 Run 1 (Polyethylene Glycol) Materials: Glass Ballot i n i Nickel Wt. of sample: 400.0 gm. 459-0 gm. From Run 1 1 Bed Manometer Reading Temp. Temp. Across Height arm 1 arm 2 Column Room Taps cm. cm. cm. op op 18.7 46.1 60.0 • 71.8 72.0 2-3 39^7 66.6 • 71-9 72.4 2-5 34.2 72.0 71.6 72.5 2-7 25-2 28.1 7 7 . 8 - 71.6 72.6 2-11 3 1 - 8 74.3 . 71-5 72v.4 2-9 35-0 71.1 71.6 72.5 2-7 •39.1 6 7 .2 71.6 ' 72.5 2-5 48.3 58.3 71.6 72.6 2-3 31.3 49.9 56.6 71-5 72.8 2-3 42 .9 63.4 71.7 72.8 2-5 37-3 69.0 71.7 72.9 2-7 34.3 71 .8 71.8 73-0 2-9 31.3 74 .8 71.8 73-0 2-11 37-4 27.8 77-6 70 .5 70.6 2-14 32.8 72.9 70.6 • 71-1 2-11 36.6 69-3 • 70 .3 71.4 2-9 41.0 6 5.I . 70.4 71.6 2 - 7 45.7 60.6 70.2 71.4 2-5 5O.9 56.6 70.5 71-5 2-3 56 .2 30.4 75-7 71.8 73.5 2-14 26 .5 79-6 72.0 73-4 2-18 24.6 81 .5 72.0 73-4 2-22 35.7 70 .8 72.0 73.4 2-11 , 39-1 67 .4 72.0 73-5 2-9 42.8 63.7 71-9 73-3 2-7 47.0 5 9 - 5 72.0 73-8 2-5 51.1 55-6 72.0 73-9 2-3 33.5 26 .7 79-2 71.0 73-1 2-14 31.4 74.6 71.0 73-0 2-11 34.8 71.3 • 71.0 73-0 2-9 38.8 67.5 71.0 73-1 2-7 44.3 62.1 71.0 72.8 2-5 50.2 56.4 71-0 " 73-2 . 2-3 Run 1 (Polyethylene Glycol) Materials: Glass Ba l l o t i n i Nickel Wt. of Sample: 400.0 gm. 4 5 9 .0 gm. From Run 1 1 4 - 8 Bed Manometer Reading Temp. Temp. Acros; Height arm 1 arm 1 Column Room Taps cm. . cm. cm. Ojp Op 3 7 - 7 . 5 0 . 8 5 5 . 8 7 1 - 0 • 7 3 , 2 2 - 3 4 5 . 9 6 0 . 6 7 1 - 0 7 3 - 4 2 - 5 6 5 . 0 7 1 . 0 7 3 - 4 2 - 7 3 7 - 1 6 9 . 1 7 1 . 0 7 3 - 4 2 - 9 6 7 . 2 5 1 . 4 ' 5 5 - 2 7 2 - 5 74.O 2 - 3 4 7 . 5 5 9 - 0 7 2 . 0 7 3 - 6 2 - 5 4 3 . 9 6 2 . 5 7 1 . 8 7 3 . 6 2 - 7 40.6 6 5 . 7 7 1 - 5 7 3 - 4 2 - 9 3 7 - 4 6 8 . 8 7 1 - 5 7 3 - 3 2-11 3 2 . 8 7 3 - 2 7 1 . 4 7 3 - 2 2-14 3 0 . 1 7 5 - 9 , 7 1 . 4 7 3 . 3 2-18 2 7 . 9 7 8 . 1 7 1 . 3 7 3 - 4 2 - 2 2 2 6 . 2 7 9 - 7 •71.3 7 3 - 4 2 - 2 6 2 5 . 1 8 0 . 8 7 1 . 3 7 3 - 2 2 - 3 2 Run 2 (Polyethylene G l y c o l ) M a t e r i a l : Glass B a l l o t i n i Ave. Diameter Wt. of Sample 320 gm. Density 1.08 2.91 ram. gm./cm^. Manometer Reading • Temperature Temperature arm 1 i n . arm 2 i n . Column °F Room °C Bed Height era. 2.60 2.25 75-6 24.0. 9.6 5.5O 5.30 76.0 24.0 10.8 8.O5 5.50 74.5. 24.0 40.6 7-00 4.65 74.7 24.2 32.8 5.80 3-70 74.7 24.3 26.7 4.65 2-75 75-0 24.3 22.4 3-35 1.60 75-0 24.5 18.1 2.47 0.80 75-2 24.6 15.1 12.40 * 13.50 75.6 . 24.6 13-3 9-15 6.40 74.9 24-7 49.4 10.25 7.30 74.8 24.9 66.5 11.05 7.90 74.8 24.8 82.8 9-65 6.80 74.6 24.6 58.6 7.40 5.00 75.O 24.6 35-8 6-35 4.10 75.0 25.0 29.4 5.20 3.15 75-3 25.O.. 24.1 * i " it Meter ( A i r ) in Meter (Mercury) Run 2 (Polyethylene G l y c o l ) M a t e r i a l : Alundum Ave. Diameter: 0.645 mm. Wt. of Sample: 440 gm. Density: 3.95 gm./crn^. Manometer Reading . Temperature Temperature Bed arm 1 i n . Arm 2 i n . Column °F Room °F Height cm. 4.40 2-75 71-3 71.2 31.1 4.75 3-00 71.1 71.0 33-5 5-10 3-20 71.3 - 71.4 36.6 5.5O 3.60 71-3 <I 70.9 40.6 . 6.05 4.10 71.3 • 71.2 47.0 6.5O 4.45 71.4 71.5 53.5 3.85 2.25 71.3 71.2 28.5 3-25 I.70 71.3 71.0 24.4 2.60 1.10 71-3 71.2 20.6 1-95 0.50 71.3 71-3 17-1 1-35 0.00- 71.3 71.4 13.8 Meter (Mercury) 4-10 Run 2 (Polyethylene Glycol) Material: Alundum Wt. of Sample: 440.gm. Ave. Diameter Density 0.645 mm- 3.95 gm./cc. Manometer Reading Temp. Temp. Bed Across arm 1 arm 2 Column Room Height Taps in. in. . o F °F cm. 52.3 55-2 71.1 71.1 32.6 1-2 49.7 . 57-7 71.0 70.9 1-4 47.4 59-9 71.0 71.0 1-6 45.1 62.2 71.0 ' 71.2 1-8 42.8 6&.5 71.2 71.2 1-10 39-3 67.9 71-3 71.4 1-13 40.9 66.3 71.4 70.9 21.1 1-8 -44.5 62.9 71-5 71.2 1-6 48.1 59-4 71-5 71.2 1-4 51-7 55-6 71.2 70.2 1-2 52.5 54.9 71-5 70.6 42.0 1-2 50.5 56.9 71.7 70.8 1-4 48.6 58.8 . 71.6 . 71.0 1-6 46.7 60.6 71.6 71.1 1-8 44.8 62.4 71.6 70.9 1-10 42.0 65.2 71.7 71.2 1-13 38.8 68.2 71-7 71-5 1-17 4-11 Run 2 (Polyethylene Glycol) Materials: v Glass Ba l l o t i n i Alundum Wt. of Sample: \ 320.0 gm. 447-0 gm. From Run - 2 2 Manometer Reading ' Temperature Temperature Bed arm 1 arm 2 Column °F Room °C •Height cm. 7-20 * 7-40 73-5 22.0 25-5 7.00 * 6.90 74.0 22.2 24.8 6 .5O * 7.50 73-1 22.0 25.4 . 8.30 * 9-30 73-5 22.4 27.4 9.9O * IO.85 73-7 22.6 28.9 11.70 * 12.70 73-8 22 ..3 30.5 13-45 * 14.50 73-8 22.3 31-9 2.20 0.50 73-7 - 22-3 33-6 2.50 0.80 73-7 22.4 36.4 3.05 1.25 73-5 22.4 40.7 3-35 . 1-55 73-6 22.5 44.1 3.85 2.00 73-9 . 22.6 48.2 4.30 2.40 73-4 22.4 53-4 4.95 2.90 73-4 22.4 61.1 5.50 3-40 73-2 22.2 69.7 6.10 3.90 73-0 22.1 80.7 6.70 4-35 ' 73-1 22.6 92.8 7-25 4.80 73-0 22.5 108.6 7-75 5-25 73-1 22-7 125.4 * Meter (Air) in Meter (Mercury) Run 2 Viscosity and Density • Temperature Viscosity Temperature Density op lb./ft.sec. °F gm./cc. 70.0 O.O79 70.0 66.67 75-0 O.O87 75-0 66.61 80.0 O.096 80.0 66.55 4-12 Run 2 (Polyethylene Glycol) Materials: Glass Ballot i n i Alundum Wt. of Samples 315-0 gm. 440.0 gm. From Run ' 2 2 Manometer Reading Temp. Temp • Bed Across arm 1 arm 2 Column • Room Height Taps cm. cm. °F o F cm. 31.6 43.9 72.3 72.5 34.0 1-4 27-9 47.6 71-9 72.2 1-6 24.4 51.1 71.7 72.4 1-8 21.1 54.4 71.7 72.0 1-10 16.0 59.4 71-7 72.0 1-13 16.1 59.2 71-2 71.8 45-9 .1.17 21.4 54.1 71.2 71-8 1^ 13 25.5 50.1 71.2 71.2 1-10 28.3 47.4 71.5 . 72.2 1-8 30.9 44.8 71.5 ' 71.3 1-6 33-6 42.1. 7 L 5 71.1 • 1-4 36.5 39-5 71-5 71.6 1-2 35-1 40.6 73-8 72.8 24.5 1^ 2 29.4 46.1 73-8 72.9 1-4 24.2 51.3 73.9 73.9 1-6 19.8 55-6 73-9 74.0 1-8 15.4 59.9 73-9 74.2 1-10 32.6 43.7 74.3 74.3 1-3 27.1 49.5 74.9 74.9 1-5 22.5 54.2 74.8 75.0 1-7 13.4 53.3 74.8 . 74.8 1-9 37.1 38.6 73-5 72.8 100.0 1-2 35.7 40.1 73-5 • 73.2 1-4 '34.2 41.5 73-2 72.9 1-6 32.9 42.6 73.0 72.8 1-8 31.6 43.9 . 73-2 73.2 . 1-10 29.8 45.8 73-3 . 73.6 1-13 27.1 48.4 73-2- 73.0 1-17 24.6 50.7 73-2 72.5. 1-21 22.1 53-2 73-2 72.6 1-25 18.8 56.6 73-0 72.5 1-31 14.9 60.3 73-2 72.9 1-39 13-1 62.1 73-1 73-0 1-43 4-13 Run 3 (Polyethylene Glycol) M a t e r i a l : Lead Wt. of Sample: 900.0 gm. Ave. Diameter Density 2.05 mm. 11.33gm./cc, Manometer arm 1 i n . Reading arm 2 i n . Temperature Column °F Temperature Room °F Bed Height cm. 2.20 * 3.50 73-9 73-4 8.5 4.30 * . 5-20 73.8 73-4 9-7 7.20 * 7.80 73-9 73-4 10.9 0.40 1.50 74.0 73-6 12.3 1.00 2.10 74.0 73.4 14.3 1.70 2.80 74.0 73-4 16.3 2.45 3.70 73-9 73.4 18.5 3.05 4.40 73-9 73.4 20.4 4.15 5-80 74.0 73-4 24.2 4.95 " 6.75 74.0 73-4 27.1 5.80 7-8ai 74.1 73-6 31.1 6.70 ' 9.85 74.0 73-6 35-3 Meter ( A i r ) Meter (Mercury) Run 3 (Polyethylene Glycol) M a t e r i a l : Steel Wt. of Sample: 800 gm. Ave. Diameter Density 3.15mm. 7.83gm./cc. Manometer Redding Temperature Temperature - Bed armtjl^linTrj. e arm'.. 21. i n . Column °F Room °F Height cm. 1.30 * 2.80 74.0 73-2 10.1 4.90 * 5.80 73-9 73-2 11.6 1-55 O.55 73-9 73-2 ' 13-0 2.50 1.40 73-9 73-2 14.7 3-35 2.20 73-9 73-4 15.8 4.15 2.85 73-9 • 73-5 16.9 5.30 3-80 73-9 73.5 I8.3 .6.60 4.90 74.1 73.4 20.0 8.15 6.10 74.2 . 73.3 22.1 9-95 7.60 74.2 73-3 24.6 11.10 8.60 74.1 73-4 26.1 In Meter ( A i r ) Meter (Mercury) 4-14 Run 3 (Polyethylene Glycol) M a t e r i a l : Lead Steel Wt. of Sample: QOO.O gm. 800.0 gm. From Run 3 3 Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 . i n . Column °F Room °F Height cm. 14.30 ** 11.10 72.6 74.4 18.6 2.45 * 3-70 73-7 72.6 20.2 5.6O * 6.30 74.0 72.8 2211 9.70 * 9.90 74.3 73-0 24.4 , 13.50 * 13-20 74.3 73.0 26.4 2.05 . 1.00 73-8 72.8 28.1 2.50 1.40 73-6 73.0 30.1 3-00 11.80 73.5 72.8 32.1 3.50 2.25 73-6 '73-0 34.1 4.30 2.95 74.0 73-0 37-4 .5-55 4.00 74.0 73.2 42.1 6.45 4.70 74.O 73-4 45.6 6.95 55U5 74.0 71.2 47-3 7-85 5.90 74.0 71.0 51.6 '8.65 6.50 73.8 71.2 56.1 9.15 6.90 73-5 70.8 59-6 ' 9.80 7.40 73-2 70.8 63.8 10.30 7.80 73-3 71.0 67.4 10.70 8.15 73-3 71.0 . 71-6 11.20 3.55 73-3 71.0 75-1 * I " Meter ( A i r ) ^" Meter (Mercury) * * t " Meter (Mercury) Run 3 V i s c o s i t y and Density Temperature F V i s c o s i t y l b . / f t . s e c . Temperature °F Density l b . / f t . i 70.0 75-0 80.0 0.081 0.088 O.O99 70.0 75.0 80.0 66.64 66.60 66.49 4 - 1 5 Run 3 (Polyethylene G l y c o l ) M a t e r i a l : Lead S t e e l Wt. of Sample: 9 0 0 . 0 gm. . 8 0 0 . 0 gm. From Run 3 3 Manometer Reading Temperature Temperature • Bed Across arm 1 arm 2 Column . Room Height Taps cm. cm. °F °F cm. 4 2 . 5 6 6 . 8 7 3 - 0 7 1 . 2 2 8 . 8 2 - 4 4 8 . 9 6 0 . 7 7 3 - 0 7 1 . 4 2 - 3 4 8 . 7 6 1 . 0 7 3 - 0 7 1 . 4 3 - 4 4 8 . 5 6 0 . 8 7 3 - 0 7 1 . 4 4 - 5 4 8 . 5 61.O 7 3 - 0 7 0 . 9 5-6 48 .8 6 0 . 4 7 3 - 0 71 .'0 6 - 7 48.6 6 0 . 8 7 3 - 0 7 1 . 2 7 - 8 48 .8 6 0 . 2 7 3 - 3 7 1 . 0 8 - 9 48 .8 6 0 . 6 7 3 - 3 7 1 . 2 9 - 1 0 5 0 . 4 . 5 8 . 6 7 5 . 0 7 3 - 7 4 4 . 6 2 - 3 5 0 . 4 5 8 . 8 7 4 . 7 7 3 - 5 3-4 5 0 . 3 5 8 . 7 7 5 - 0 7 4 . 3 4 - 5 5 0 . 4 5 8 . 7 7 3 - 9 7 2 . 9 5-6 5 0 . 5 5 8 . 4 7 3 . 8 7 2 . 5 6 - 7 5 0 . 4 5 8 . 7 7 4 . 0 7 3 - 2 7 - 8 5 0 . 5 5 8 . 4 7 4 . 1 7 3 - 4 8 - 9 5 0 . 5 5 3 . 6 7 3 - 9 7 2 . 3 .9-10 5 0 . 4 5 8 . 4 7 4 . 0 7 2 . 8 10-11 5 0 . 4 5 8 . 7 7 4 . 0 7 3 - 0 11-12 46.6 6 2 . 4 7 4 . 3 7 2 . 7 12-14 4 6 . 7 6 2 . 4 7 4 . 3 7 2 . 6 14-16 49.O 5 9 - 3 7 3 - 3 7 1 . 4 6 0 . 1 2 2 - 2 0 4 9 . 2 6 0 . 0 ' 7 3 - 5 7 1 . 6 2 0-l ' 8 4 8 . 7 6 0 . 3 7 3 . 6 7 1 . 8 1 8 - 1 6 48 .8 6 0 . 5 7 3 - 5 7 2 . 0 16-14 48.4 6 0 . 5 7 3 - 8 7 2 . 0 14-12 45.O 64 .5 7 3 - 8 7 2 . 2 1 2 - 9 4 4 . 8 64 .4 7 3 . 8 7 2 . 3 9 - 6 4 4 . 6 64 .8 7 3 - 5 7 2 . 0 6 - 3 5 1 . 1 5 7 - 9 7 3 - 5 •' 7 1 . 9 3 - 2 46 .9 6 1 . 3 7 3 - 5 7 1 . 7 2 2 - 7 2 - 3 4 7.I 6 2 . 2 7 3 . 7 7 1 . 7 3-4 46 .8 6 2 . 1 7 3 . 8 7 1 . 8 4 - 5 46 .9 6 2 . 5 7 4 . 0 7 1 . 8 5-6 4 7 . 2 6 1 . 8 7 4 . 0 7 2 . 0 6 - 7 4 9 . 2 6 0 . 1 7 4 . 1 7 2 . 1 7 - 8 4 - i 6 Run 4 (Polyethylene Glycol) M a t e r i a l : N i c k e l Glass Ave.Diameter 0.542 mm. W.t..^  of aSample: 296.0 gm. Density 4 . 50 gm/cc. Manometer Reading Temperature Temperature Bed' arm 1 i n . arm 2 i n . Column °F Room °F Height cm. 0 . 3 0 0 . 5 0 7 5 - 0 7 3 - 4 7 . 2 0 . 6 0 0 . 8 0 7 5 - 0 7 3 - 6 8 . 4 1 . 0 0 1 . 15 7 5 - 1 7 4 . 0 0 .8 1-35 1 . 4 5 7 4 . 9 7 3 - 6 1 0 . 8 1 . 9 5 1-95 7 4 . 8 7 3 - 6 1 2 . 7 2 . 3 5 2 - 3 5 7 4 . 9 . 7 3 . 8 14 .6 2 - 9 5 2 . 8 5 7 4 . 8 7 3 . 6 1 7 - 3 3-40 3 - 2 0 7 4 . 9 7 3 - 6 2 0 . 1 3 . 8 0 3 . 5 0 • 7 4 . 9 7 3 - 8 2 3 . 3 4. 30- 4 . 0 0 7 4 . 9 7 3 - 6 2 8 . 3 Meter (Mercury) Run 4 (Polyethylene Glycol) M a t e r i a l : Glass B a l l o t i n i N i c k e l Glass Wt. of Sample: 2 9 0 . 0 gm. 2 9 6 . 0 gm. From Run 1 4 Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column °F Room °F Height cm. 0 . 3 5 0 . 5 0 7 6 . 7 7 4 . 8 1 6 . 8 0 . 7 0 O .85 7 6 . 8 7 4 . 8 1 9 - 9 1 . 2 0 1 . 3 0 7 6 . 4 7 4 . 4 2 2 . 9 1 . 6 5 1 . 7 0 7 5 - 8 7 4 . 1 2 5 - 7 2 . 1 0 2 . 1 0 7 5 - 6 7 4 . 3 2 8 . 5 2 . 6 0 2 - 5 5 7 5 - 3 7 4 . 2 3 2 . 0 3-15 3 - 0 0 7 5 - 4 7 4 . 4 3 6 . 3 3 - 6 5 3-40 7 5 - 4 7 4 . 2 4 1 . 5 4 . 2 0 3 . 8 5 7 5 - 5 7 4 . 3 4 8 . 3 4 . 6 5 4 . 2 0 7 5 - 6 7 4 . 4 5 6 . 3 Meter (Mercury) * Homogeneous Mixing Point 4 - 1 7 Run 1 (Water) M a t e r i a l : Glass B a l l o t i n i Ave.Diameter 1 . 0 8 mm. Wt. of Sample: 400.0 gm. Density 2 - 9 1 gm./cc. Manometer Reading Temperature Temperature Bed arm 1 ' i n . arm 2 i n . Column OF Room• oc Height cm. 3.40 I . 3 0 7 8 . 9 24.3 1 5 . 8 0 2 . 6 5 O.65 7 8 . 8 24.3 14 .60 2 . 0 5 0 . 0 5 7 8 . 8 24.3 13-40 1 . 4 5 c: 0 . 4 5 7 8 . 7 24.3 1 1 . 9 0 4 . 15 2 . 0 0 7 3 . 7 24.3 1 7 - 0 0 4 . 8 0 2 . 6 0 . 7 8 . 7 24.2 1 7 . 0 0 5 - 3 5 3 .05 7 8 . 7 24.2 I 8 . 7 5.90. 3-45 7 8 . 7 24 .2 19.4 6 . 5 0 4 . 0 0 7 8 . 7 24 .2 20.3 7 . 1 0 4 . 5 0 7 8 . 7 7 8 . 7 24.2 2 1 . 0 7 . 8 5 5-10 24.2 2 2 . 1 8.5O 5-65 7 8 . 7 78.7 24 .0 2 2 . 9 9 . O 5 6 . 1 0 24 .0 2 3 . 6 1 0 . 1 5 7 . 0 0 7 8 . 7 24 .0 2 5 . 2 11.40 8 . 0 0 7 8 . 7 24 .0 2 6 . 8 1 2 . 6 5 9 . 0 0 7 8 . 7 24 .0 2 8 . 6 1 3 . 8 5 9 - 9 5 7 8 . 7 24 .0 30.3 1 5 . 1 0 1 0 . 9 5 7 8 . 7 24 .0 3 2 . 1 •g-" Meter (Mercury) 4 -18 Run 2 (Water) M a t e r i a l : Alundum Ave. Diameter O.767 mm. Wt. of Sample: 5 0 0 . 0 gm. Density: 3 . 9 5 gm/cc Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n Column °F Room ' °C Height cm. 0 . 2 5 0 . 5 5 6 9 . 5 2 2 . 5 1 2 . 0 0 . 5 5 O.85 6 9 - 5 22..5 1 3 - 0 0 . 9 5 1 . 2 0 6 9 . 5 2 2 - 5 1 4 . 0 1-35 1-55 6 9 - 5 2 2 . 5 14.3 1 . 9 0 2 . 0 5 6 9 . 5 ' 2 2 . 5 1 5 - 9 2 - 3 5 2.40 ' 6 9 . 5 • 2 2 . 6 1 6 . 7 2 . 9 5 2 . 9 5 6 9 . 2 2 2 . 6 1 7 - 8 3 . 4 5 3 - 3 5 . 6 9 . 2 2 2 . 6 1 8 . 6 4 . 0 5 3 - 3 5 6 9 - 1 2 2 . 6 1 9 - 5 4 .60 4 .30 6 9.I ' 2 2 . 6 2 0 . 5 5 . 2 0 4 .80 69.O 2 2 . 6 21.4 5 - 9 5 5.40 69.O 2 2 . 6 2 2 . 6 6 . 7 0 6 . 0 0 69.O 2 2 . 6 • 2 3 . 8 7 - 2 0 6 . 4 5 69.O 2 2 . 6 2 4 . 7 7 - 9 5 7 . 0 0 6 9 - 0 2 2 . 6 2 5 . 9 Meter (Mercury) Run 5 (Water) I . 8 3 mm. M a t e r i a l : ' Glass B a l l o t i n i Ave. Diameter Wt. of Sample: 4 0 0 . 0 gm. Density 2 . 9 1 gm/cc. Manometer Reading Temperature Temperature Bed arm 1 i n . arm2. i n Column °F Room oc Height cm. O.85 1 . 0 5 7 0 . 2 2 3 . 0 1 1 . 0 1 . 9 5 2 . 0 0 7 0 . 2 2 3 - 0 1 2 . 0 3 . 4 0 3 - 3 0 7 0 . 1 • 2 3 - 0 1 3 - 3 4 .60 4 .25 7 0 . 1 2 3 . 0 14.1 5.9O 5 . 3 0 7 0 . 1 2 3 - 0 1 5 . 0 • 6 . 9 O 6 . 1 0 7 0 . 1 2 3 . 0 1 5 . 6 8 . 1 0 7 . 0 0 7 0 . 1 2 3 - 0 lb-. 2 9 . 4 5 8 . 0 0 7 0 . 1 2 3 . 0 l b . 9 1 0 . 6 0 9 . 0 5 7 0 . 1 2 3 . 0 17-6 1 1 . 8 0 1 0 . 0 0 7 0 . 1 • 2 3 . 0 1 8 . 2 1 3 - 1 0 1 1 . 0 0 7 0 . 1 2 3 - 0 1 8 . 7 •|" Meter (Mercury) 4-19 Run 3 (Water) M a t e r i a l : Alundum Ave. Diameter 1 0 . 6 4 5 mm. Wt. of Sample: 5 0 0 . 0 gm. . . Density 3 . 9 5 gm/cc. Manometer Reading Temperature Temperature •Bed arm 1 i n . arm 2 i n . Column °F Room .°C Height 0 . 2 5 0 . 5 0 7 0 . 0 ' 2 3 . 2 1 2 . 6 O.65 0 . 9 5 7 0 . 0 - 2 3 - 2 1 4 . 0 1 . 1 0 1 . 3 0 7 0 . 0 2 3 . 2 1 5 - 3 1 . 5 0 1 . 7 0 7 0 . 0 23-'2 1 6 . 2 1-95 2 . 0 5 7 0 . 0 2 3 . 2 1 7 - 3 2 . 3 5 2.40 7 0 . 0 2 3 . 0 1 8 . 1 2 . 8 0 2 . 8 0 7 0 . 0 7 3 - 0 1 9 . 0 3 . 4 5 3 - 3 5 7 0 . 0 2 3 . 0 2 0 . 3 ' 4 . 1 0 3 . 9 0 7 0 . 0 2 3 . 0 2 1 - 5 4 . 8 0 4 . 4 5 7 0 . 0 2 3 . 0 2 2 . 7 5 . 5 0 5 . 0 5 7 0 . 0 • 2 3 . 0 24 . 3 6 . 1 5 5-55 7 0 . 0 2 3 . 0 2 5 . 6 6 . 50 6 . 0 0 7 1 - 1 2 3 . 0 2 6 . 3 7 . 4 5 6 . 6 0 7 1 . 1 2 3 . 0 2 8 . 4 8 . 1 0 7 . 1 0 7 1 . 1 2 3 . 0 2 9 . 6 •§" Meter (Mercury) Run 4 (Wa ter) M a t e r i a l : Alundum Ave. Diameter 0 . 9 1 2 mm. Wt. of "Sample: 5 0 0 . 0 gm. Density 3 . 9 5 gm/cc. Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n Column °F Room °C Height cm. 0 . 3 0 0 . 5 0 7 4 . 2 2 2 . 6 1 1 . 4 0 . 8 0 1 . 0 0 7 4 . 2 2 2 . 6 1 2 . 8 1 . 2 0 1-35 7 4 . 2 2 2 . 6 1 3 . 7 1-95 2 . 0 0 7 4 . 2 2 2 . 6 1 4 . 9 2 . 5 5 2 . 50 7 4 . 3 2 2 . 6 1 5 . 8 3 . 2 0 3 . 1 0 7 4 . 2 2 2 . 6 1 6 . 7 3 - 8 0 3 . 6 0 7 4 . 2 2 2 . 6 1 7 - 5 4 . 4 5 4 . 1 0 7 4 . 2 2 2 . 6 1 8 . 3 5 . 1 5 4 . 7 0 7 4 . 3 2 2 . 6 1 9 . 2 5 . 8 0 5 - 2 0 7 4 . 3 2 2 . 6 2 0 . 0 6 . 7 0 5-95 7 4 . 3 2 2 . 6 2 1 . 1 7 - 7 0 6 - 7 5 7 4 . 3 2 2 . 6 2 2 . 4 Meter (Mercury) 4 - 2 0 Run 6 (Water) M a t e r i a l : C r y s t a l o n Ave. Di amete r • 1 . 0 8 mm. Wt. of Sample: 3 5 0 . 0 gm. Density Manometer Reading Temperature Temperature B£d arm 1 i n . ant 1 2 i n . Column °F Room °C Height cm. 1 0 . 8 0 * 1 0 . 6 0 7 0 . 0 1 9 . 6 11-3 3 - 1 0 * 3 - 2 0 7 0 . 0 1 9 . 6 9 - 8 0 . 2 0 2 . 8 5 7 0 . 0 1 9 - 7 12 . 5 0 - 7 5 3 - 3 0 7 0 . 0 1 9 - 7 1 3 . 3 1-55 4 . 0 0 7 0 . 0 1 9 . 7 1 4 . 4 2 . 5 0 4 - 7 5 7 0 . 0 1 9 . 4 1 5 . 5 3 . 3 5 5 . 4 5 7 0 . 0 1 9 . 6 1 6 . 5 4 . 3 0 6 . 2 0 7 0 . 0 1 9 - 9 1 7 . 6 5 . 5 0 7 . 2 0 7 0 . 1 1 9 . 8 1 9 . 2 7 . 2 0 3 . 6 0 7 0 . 1 1 9 . 6 2 1 . 2 8 . 8 0 9 . 8 0 7 0 . 1 1 9 . 7 2 3 . 2 1 0 . 3 0 1 1 . 0 0 7 0 . 2 1 9 . 8 2 5 . 2 1 1 . 7 0 1 2 . 1 5 7 0 . 3 1 9 . 9 2 7 . 1 * Meter ( A i r ) 3" Meter (Mercury) Run 13 M a t e r i a l r Alundum Wt. of Sample: 3 5 0 . 0 From Run 3 C r y s t a l o n gm. 3 5 0 . 0 gm. Run 6 Manometer Reading Temperature Temperature Bed ana 1 i n . arm 2 i n . Column °F Room °C Height cm. 14 .00 * 1 3 - 6 0 7 0 . 4 1 1 9 - 8 2 1 . 7 0 . 0 5 2 . 7 0 7 0 . 5 2 0 . 0 2 2 . 9 0.40 3 - 0 0 7 0 . 6 2 0 . 0 2 3 - 7 1 . 0 0 3 - 5 5 7 0 . 7 2 0 . 0 2 5 . 6 1.30 4 . 2 0 7 0 . 6 2 0 . 0 2 7 . 7 2 . 8 0 5 . 0 0 7 0 - 7 1 9 - 9 3 0 . 1 3 - 8 0 5 . 8 0 7 0 . 7 2 0 . 0 3 2 . 6 5 - 4 5 7 - 1 0 7 0 . 8 2 0 . 0 3 6 . 7 7 . 2 0 8 . 5 0 7 0 . 3 2 0 . 0 . 41 .3 9-.40 1 0 . 2 5 7 1 . 4 2 0 . 0 4 7 . 3 1 0 . 6 0 1 1 . 2 5 7 0 . 9 2 0 . 0 5 1 . 7 1 1 - 9 5 1 2 . 3 0 7 1 . 0 1 9 . 9 5 6 . 0 1 3 . 6 0 1 3 - 7 5 7 0 . 8 2 0 . 0 63.O * \" Meter ( A i r ) Meter (Mercury) 4-21 Run 7 (Water) M a t e r i a l : Glass B a l l o t i n i Ave. Diameter ' 1 . 0 8 mm. Wt. of Sample: 3 2 0 . S gin. Density 2 . 9 1 Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column °F Room °C Height cm. 4 . 6 0 * 3 - 2 0 7 1 . 8 2 2 . 9 9 - 1 0 .70 * 6 . 6 0 7 1 . 8 2 2 . 9 9 . 9 14.S0 * 1 1 . 5 0 7 1 - 9 2 3 - 0 1 0 . 6 0 . 1 5 ' 2 . 8 0 7 1 . 9 2 2 - 9 1 1 . 4 0 . 9 0 3-40 7 2 . 1 2 2 . 8 1 2 . 3 1 , 8 0 4 . 2 0 7 2 . 3 2 2 . 9 1 3 - 4 2 . 6 0 4 . 8 5 7 2 . 3 2 2 . 9 14.2 3 . 5 0 5-55 7 2 . 4 2 2 . 9 1 5 - 2 4.40 6 . 3 0 7 2 . 3 2 2 . 9 1 6 . 0 5 . 4 5 7 . 2 0 7 2 . 3 2 3 . 0 1 7 . 1 6 . 4 5 ' 7 . 9 0 7 2 . 4 • 2 3 - 0 1 8 . 1 7 . 5 0 8 . 8 0 7 2 . 5 2 3 . 0 1 9 . 2 8.40 9 . 5 0 7 2 . 5 2 3 . 0 2 0 . 1 * I " Meter ( A i r ) Meter (Mercury) Run 7 (Water) M a t e r i a l : N i c k e l - G l a s s Ave. Diameter 0 . 5 4 2 mm. Wt. of Sample: 3 3 4 . 0 gm. Density 4 - 5 0 gm/cc. Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column °F Room °C Height 3 . 1 0 * 3.40 6 7 . 2 1 9 . 6 7 . 0 7 - 1 0 * 7 - 3 0 6 7 . 7 1 9 . 5 7 - 6 1 2 . 7 0 * 1 2 . 8 0 6 7 - 3 1 9 . 5 8 . 4 0 . 2 0 2 . 8 5 6 7 . 4 1 9 . 6 9 - 1 0 . 9 0 3 . 4 5 6 7 . 6 1 9 . 6 1 0 . 0 2 . 0 0 4 . 3 5 6 7 . 8 1 9 . 8 11-3 3 - 1 0 5 - 2 5 6 8 . 1 2 0 . 0 1 2 . 3 4 . 5 0 ' 6.40 6 8 . 3 2 0 . 0 1 3 . 8 6.5O 8 , 0 0 6 8 . 3 1 9 . 7 1 5 . 0 2 . 1 0 4.5O 6 8 . 4 1 9 . 6 1 1 . 4 0 . 5 0 3-10 6 8 . 5 1 9 . 6 9 . 6 0 . 1 0 2 . 5 5 . 6 8 . 6 1 9 - 5 ' 8 . 7 . * ^" Meter ( A i r ) \" Meter (Mercury) 4 - 2 2 Run 7 (Water) Mixture Glass Wt. of Sampler From Run B a l l o t i n i N i c k e l Glass 3 2 0 . 0 gm. 4 9 - 5 gm. 7 7 Manometer Reading Temperature Temperature Bed m l i n . arm 2 i n . Column °F Room °C Height cm. 3 - 1 0 * 4 . 9 0 7 0 . 6 2 2 . 0 1 0 . 1 4 . 3 0 * 6 . 3 0 7 0 . 5 1 0 . 5 8 . 8 0 * 1 0 . 3 0 7 0 . 3 1 1 . 3 0 . 0 5 2 . 5 0 7O.3 1 2 . 2 0 . S 0 3-Q5 7 0 . 2 1 3 . 1 1 . 15 3 - 6 o 7 0 . 2 1 4 . 1 1 . 9 0 4 . 2 0 • 7 0 . 2 1 5 . 0 2 . 7 0 4-95 7 0 . 2 1 6 . 1 3 - 9 0 5 . 9 0 7 0 . 3 1 7 . 4 5 . 4 5 7-15 " 7 0 . 2 1 9 . 2 7 . 0 0 8 . 4 0 7 0 . 2 2 1 . 1 9 . 2 0 1 0 . 0 5 7 0 . 2 2 3 - 5 1 0 . 1 0 1 0 . 8 0 7 0 . 2 2 4 . 7 1 2 . 5 0 1 2 . 8 0 7 0 . 2 2 7 . 5 * •5" Meter ( A i r ) |" Meter (Mercury) Run 7 (Water ) Mixture Wt. of Sample: From Run Glass B a l l o t i n i 3 2 0 . 0 gm. 7 N i c k e l - G l a s s 99.O gm. 7 Manometer Reading Temperature Temperature Bed arm 1. i n . arm 2 i n . Column °F Room °C Height cm. 2 . 7 0 * 4 . 9 0 7 0 . 4 2 2 . 0 1 1 . 1 1 1 . 2 0 * 1 3 . 0 0 7O .5 2 2 . 0 1 3 - 0 0 . 2 0 2 . 8 0 7 0 . 5 2 2 . 0 1 4 . 1 1 . 0 0 ' 3 - 5 0 7 0 . 3 . 2 2 . 0 1 5 . 4 2 . 1 5 4 . 4 5 7O .3 2 2 . 0 1 7 . 0 3 . 2 0 5 .3O 7O .3 • 2 2 . 0 1 8 . 4 4 . 4 0 6 . 2 5 7 0 . 3 2 2 . 1 2 0 . 0 5 . 5 0 7 . 2 0 7 0 . 3 2 2 . 2 . 2 1 - 4 6 . 8 0 8 . 2 0 7 0 . 3 2 2 . 2 2 3 . 2 7 . 9 0 9 - 1 0 7O .3 2 2 . 1 2 4 . 6 9 . 4 5 1 0.40 7 0 . 3 • 2 2 . 2 2 6 . 7 1 1 . 2 0 1 1.30 7 0 . 3 2 2 . 2 2 9 - 3 * \" Meter ( A i r ) •g-" Meter (Mercury) 4 - 2 3 Run 7 (Water) M a t e r i a l : Glas s B a l l o t i n i N i c k e l Glass Wt. of Sample: 3 2 0 . 0 gm. I65.O gm. From Run 7 7 Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 ' i n . Column °F Room °C Height cm. 3 . 7 O * 6.3O 7 0 . 8 2 2 . 4 1 2 . 6 7 . 6 0 * 1 0 . 1 0 7 0 . 9 2 2 . 3 1 3 - 6 1 1 . 3 0 * 1 3 . 6 0 . 7 0 . 8 2 2 . 3 14.3 0 . 1 5 2 . 7 5 7 0 . 7 2 2 . 3 1 5 . 5 1 . 0 0 3 . 5 0 7 0 . 7 2 2 . 3 1 7 - 0 2 . 0 0 4 . 3 0 7 0 . 6 • 2 2 . 4 1 8 . 6 3 - 2 0 5 . 3 0 7 0 . 6 2 2 . 3 2 0 . 4 4 .60 6.40 7 0 . 7 2 2 . 3 2 2 . 4 6 . 1 5 7 . 7 0 • 7 0 . 7 2 2 . 3 24-7 7 . 1 5 • 8.5O • 7 0 - 7 2 2 . 4 2 6 . 3 8 . 8 0 9 . 7 0 7 0 . 6 2 2 . 5 2 8 . 5 1 0 . 3 0 1 1 . 0 0 7 0 . 6 2 2 . 5 3 1 - 0 ; * Meter ( A i r ) •5-" Meter (Mercury) Run 7 (Wate r) M a t e r i a l : Glass B a l l o t i n i Ndckel Glass Wt. of Sample 3 2 0 . 0 gm. 2 4 7 - 5 gm. From Run 7 7 Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column °F Room °F Height cm. 3-10 * 6 . 0 0 7 1 . 0 2 2 . 6 1 4 . 3 8.40 * 1 1 . 5 0 7 1 . 0 2 2 . 7 1 5 . 9 0 . 0 0 2 . 6 0 7 1 . 0 2 2 . 6 17^4 O.65 3 - 2 0 7 1 . 0 2 2 . 5 1 8 . 8 1 . 3 0 3 - 7 5 7 0 . 9 2 2 . 5 2 0 . 2 2 . 1 0 4 . 4 5 7 0 . 9 2 2 . 6 2 1 . 6 3 - 1 0 5 . 2 0 7 1 . 0 2 2 . 7 2 3 - 3 4 . 3 0 ' 6 . 2 0 7 1 . 0 2 2 . 7 2 5 . 3 5 . 0 0 6 - 7 5 7 1 . 0 2 2 . 8 2 6 . 5 • 5 . 8 5 7.40 7 1 . 0 2 2 . 8 2£.l 7 . 1 0 8.5O 7 1 . 0 2 2 . 9 3 0 . 3 * Meter ( A i r ) •5-" Meter (Mercury) 4-24 Run 7 (Water) M a t e r i a l : Glass B a l l o t i n i N i c k e l Glass Wt. of Sample: 194.0 gm. 300.0 gm. . From Ron 7 7 Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column' • ° F Room °C Height cm. 2.80 * 3-60 . . 69.7 23.0 11.6 6.70 * 7-30 70.O 23-0 12.7 13-30 * 13.50 69.8' 23.0 14.2 o.4o 3-00 69-7 23.0 15-6 1.25 3-75 69-7 23.0 17-1 2.05 4.40 69.5 23-0 18.4 3-05 5.20 69.6 23.1 20.0 4.20 6.15 69.6 23-0 21.8 5.05 6.80 69-5 23.0 23.1 6.20 7-70 69.6 23.0 24.9 7.75 8.90 69.5 23.0 27-3 * £ " Meter ( A i r ) •jj-" Meter (Mercury) Run 7 (Water) M a t e r i a l : Wt. of Sample: From Run Glass B a l l o t i n i 38.8 gm. 7 N i c k e l - G l a s s 300.0 gm. 7 Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column ° F Room °C Height 6.40 * 6.70 70.0 22.9 8.0 8.70 * 8.. 90 70.0 23..0 8.4 14.20 * 14.20 69-8 23.0 •9-1 0.45 3.00 6§.7 23.0 10.0 1.30 3-70 69-7 23.0 11.0 2.50 4-75 69.6 23.0 12.4 3-90 5.80 69.5 23.0 13-8 4.90 6.65 69.4 23.O 14.9 5.60 7.20 69.4 23.0 15577 * Meter ( A i r ) Meter (Mercury) 4-25 Run 7 (Water) Ma t e r i a l : Glas s B a l l o t i n i N i ckel Glass Wt. of Sample: 300.0 gm. 19.4 gm. From Run 7 7 Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column °F Room °C Height cm. 4 . 7 0 * ' 4 . 7 0 6 8 . 9 22.2 7.1 8 . 0 0 * 7 . 8 0 6 8 . 8 22.2 7-6 11 . 9 0 * 11 . 6 0 6 8 . 8 22.2 8.1» 0 . 0 5 .2.65 6 8 . 7 22.3 8 . 7 0.55 3-10 6 8 . 7 22.2 • 9-4 1-45 . 3 - 9 0 6 8 . 6 22.2 10.4 2-35 4 . 6 0 6 8 . 6 22.3 11.4 3-50 5-55 6 8 . 7 - 22.3 12.5 4 . 5 0 6 . 3 5 6 8 . 7 22.4 13-6- 5.35 7-00 6 8 . 7 22.4 14.3 * Meter ( A i r ) •q:" Meter (Mercury) Run 8 (Water) Ma t e r i a l : Wt. of Sample: From Run Glass B a l l o t i n i 3 2 0 . 8 gm. 7 Nickel Glass 33^.0 gm. 7 Manometer arm 1 i n . Reading arm 2 i n . 3 . 2 0 * 7 . 9 O * 1 2 . 2 0 * 0 . 0 0 . 5 0 1-25 . 2 . 2 0 3 . 2 0 4.40 5.40 6 - 3 5 7 . 4 5 8 . 8 0 9 . 9 O t 1 i t Meter 3 - 4 0 7 . 8 0 1 2 . 2 0 2 . 7 0 3 - 1 0 3 - 7 5 4 . 5 5 5 .3O 6 . 3 O 7 . 1 0 7 . 8 5 8 - 7 5 9 . 8 0 1 0 . 7 0 (Water ) Temperature Column °F Temperature Room °C 6 9 . 8 6 9 . O 6 Q . 2 6 9 . 4 6 9 . 5 6 9 . 5 6 9 . 6 6 9 . 5 2 0 . 0 6 9 - 7 6 9 . 9 7 0 . 0 6 9 . 8 6 9 . 9 7 0 . 0 Bed Height 1 5 . 9 1 7 . 6 I 8 . 9 2 0 . 1 2 1 - 3 2 3 . 1 2 5 . 1 2 7 - 0 2 9 . 5 3 1 - 4 3 3 - 3 3 5 - 7 3 8 . 3 4 1 . 3 Meter (Mercury) 4-26 Run 9 (Water) M a t e r i a l : Alundum , Ave. Diameter 0 . 9 1 2 mm. Wt. of Sample: ' 4 0 0 . 0 gm. Density 3 -95 gm/cc. Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column °F Room °C Height cm. -0.15 O.55 73-0 23.O 8.5 -0.70 2.05 73-0 23.O 9-9 -0.45 2-35 72.7 23.O 10.4 0 2.80 72.6 23.O 11.1 0.35 3-05 72.5 23-0 11.5 1.25 3-80 72.5 23.0 12.6 1.90 4.40 72.5 23.O 13.5 2.95 5.20 72.7 23.0 1 4 . 4 3-80 5.90 72.7 23-0 15^3 4.70 6.70 72.7 23.0 16.2 0.65 7 .40 72.6 22.6 17.1 6.70 . 8.20 72.6 23.0 18.1 7.80 9.O5 72.7 23.0 19.2 8.90 10.05 72.6 22.9 20.5 * Above run without cataphote bed on top Below - 300.0 gm. of cataphote on - top -0.50 2.25 67.6 20.0 10.2 -0.15 2-55 67.6 20.0 10.7 0.25 2.95 67.8 20.2 H - 3 0.75 3-40 • 67.9 20.2 12.0 1.25 3-85 68.0 20.2 12.6 2.05 4.45 68.1 20.3 13.4 2.85 5-15 68.8 20.3 14 .2 3-6o 5.70 68.9 20.3 15.0 U.25 6.25 69.0 20.3 15.6 5.15 6.90 69.I 20.3 16.5 5-95 7.60 69.2 20.3 17.4 6.70 8.20 69.2 20.3 18.2 7-30 8.70 69.8 20.3 18.8 7.80 9.10 69.9 20.3 19-4 5-" Meter (Mercury) 4-27 Run 9 (Water) M a t e r i a l : Cataphote Ave. Diameter O.767 mm. Wt. of Sample: 300.0 gm. Density 2.47 gm/cc. Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column °F Room 0 C Height -0.50 2.25 67.6 20.2 15.0 -0.15 2-55 67.6 20.2' 16.3 0.25 2.95 67.8 20.2 17.8 0.75 .3-40 67-9 20.3 19.4 11.25 3.85 68.0 20.3 21.1 2.05 4.45 68.1 20.3 23.7 2.85 5-15 63.8 20.3 26.3 3-6o 5.70 68.9 20.3 28.9 4.25 6.25 69.O 20.3 31.5 5-15 6.90 69-1 20.3 35-2 5-95 7.60 69-2 20.3 39.1 6.70 8.20 69-2 ." , 20.3 43-3 7-30 8.70 • '69.8 20.3 46.7 7.80 9.10 69.9 20.3 49.9 Meter (Mercury) 4 - 2 8 Run 10 (Water) M a t e r i a l : Nickel .' Ave. Diameter 0 - 3 8 4 mm. Wt. of Sample: 8 0 0 . 0 gm. Density 8 . 9 2 gm/cc. Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column °F Room °C Height cm. 6.,60 * 3 - 1 0 ' 7 2 . 2 . 2 2 . 5 ' 8 . 0 1 0 . 6 0 * 6 . 9 0 7 2 . 3 . 2 2 . 5 8 . 6 14 . 6 0 * 1 0 . 6 0 7 2 . 4 2 2 . 5 9 . 1 0 . 0 2 . 6 0 ' 7 2 . 5 2 2 . 6 9 . 5 0.40 3 . 0 0 7 2 . 4 2 2 . 7 , 1 0 . 0 1 . 9 0 4 . 2 0 7 2 . 7 2 2 . 7 1 1 . 2 4 . 1 0 * 0 . 7 0 7 2 . 6 2 2 . 8 7 . 6 2 . 4 0 * 1 . 0 0 7 2 . 5 2 2 . 6 7 . 1 * ^" Meter ( A i r ) Meter (Mercury) Run 10 (Water) M a t e r i a l : Alundum Nickel Wt. of Sample: 400.0 gm. 800.0 gm. From Run 10 10 Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column °F Room °C Height 1 . 5 0 * . 3- 30 7 1 . 2 2 2 . 8 1 5 . 5 4 . 5 0 * 6 . 1 0 7 1 . 6 2 3 . 0 1 5 - 9 7 . 0 0 * 8 . 5 0 7 1 - 7 2 3 . 0 1 6 . 2 1 1 . 0 0 * 1 2 . 5 0 7 1 . 7 2 3 . 0 1 7 . 0 0 . 0 5 2 . 6 7 1 - 7 2 3 . 3 1 7 - 7 0 . 3 0 2 . 9 0 7 2 . 0 23.4 I 8 . 5 0 . 5 0 3 - 1 0 7 2 . 1 2 3 . 4 1 9 - 0 0 . 9 5 3.40 7 2 . 3 2 3 . 2 1 9 - 7 1 . 4 5 3.9O 7 2 . 3 2 3 . 3 2 0 . 5 2 . 0 0 4 - 3 5 7 2 . 3 2 3 - 3 2 1 . 4 2 . 50 4 . 7 0 7 2 . 3 2 2 . 8 2 2 . 0 3 - 3 0 5.40 7 2 . 5 2 3 . 0 2 3 . 0 4 . 3 0 6 . 2 0 7 2 . 6 2 3 . 3 • 24 . 1 5 . 4 0 7 . 0 0 7 2 . 7 - 2 3 . 2 2 5 . 2 6 . 3 5 .7 .35 ' 8 . 5 5 7 2 . 7 2 3 . 1 2 6 . 3 7 . 2 5 7 2 . 6 2 3 . 0 2 7 . 2 8 . 2 0 9 . 3 5 7 2 . 8 2 3 . 0 2 8 . 3 9 . 0 0 1 0 . 0 0 7 2 . 7 2 3 - 0 2 9 . 2 * -g-" Meter ( A i r ) -2" Meter (Mercury) 4-29 R ' 10 (Water) M a t e r i a l : Alundum Ave. Diameter 1-52 mm. Wt. of Sample: 500 gm. Density 3.95 gm/cc. Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column °F Room °C Height -0.30 2.30 23.4 65.O 10.9 0.15 2-75 23.4 6S.2 11-3 O.85 3.40 23.7 65.5 12.0 1-35 3.35 23.5 65.7 12.4 3-20 5-20 23.4 65.7 13-5 4.95 6.75 23.5 65.8 14.4 7-30 . 8.60 23-5 66.0 15-7 9.00 10.00 23.5 66.3 I6.5 10.80 11.40 23-5 66.5 17.3 8.10 9.20 23.6 66.5 15.8 5-30 7.00 23.6 66.5 14.4 4.10 6.00 23.6 66.5 . 13-7 2.8S 5.05 23.4 66.6 13.O 1.10 4.05 23.4 . 67.0 12-3 6.50 8.00 23-3 67.2 15.1' 5 " Meter (Mercury) 4 - 3 0 Run 11 (Water) M a t e r i a l : Alundum C r y s t a l o n Wt. oi' Sample: 350.0 gm. 350.0 gm. From Run 2 Run 6 Manometer Reading Temperature Temperature Bed arm 1 i n . arm 2 i n . Column , °F Column °C Height cm. 1.30 * 8.80 71.6 22.0 18.6 4.00 * 11-30 71-6 22.0 • 19-5 0.35 2.30 71-5 22.0 21.0 -0.10 2.60 71-7 22.0 21.9 0.30 2.90 71.8 22.0 23-0 1.10 3-60 72.3 22.1 25.I 2.00 4-35 72.5 22.1 27-1 3-00 5-15 .72.5 22.2 29-5 3.90 5.90 72.6 22.0 31-5 5; 10 6.90 72.6 22.0 34.2 6.60 8.00 72.7 23-7 37-3 7.40 8.80 71-9 23.7 39-8 8.35 9.90 71-9 23-5 43.O 10.20 11.00 71-9 23.4 46.7 11.30 11.80 72.0 23.1 49.3 • 1" Meter ( A i r ) •§•" Meter (Mercury ) 4-31 Run 12 (Water) M a t e r i a l : ; Glass B a l l o t i n i Alundum Wt. of Sample: 320.8 gm. i+50.0 gm. From Run 1 Run 3 Manometer Reading 'Temperature Temperature Bed arm 1 i n . arm 2 i n . Column °F Room °C Height cm. -0.90 1.80 67-8 20.3 20.5 -0.55 2.15 68.2 20.5 22.4 -0.25 2.45' 68.3 20.2 23-7 0.20 2.90 68.3 20.2 25-3 0-55 3-20 68.6 20.2 26.4 1.00 3.60 68.9 20.2 27-9 1.60 4.05 69-0 20.2 29-4 2.15 4.5O 69.2 20.2 30.9 2.80 5.05 69.5 20.2 32.7 3-60 5-75 69.8 20.3 34.8 4.70 6.60 70.0 20.3 37-5 5.60 7.30 70.0 20.3 39-8 6.40 8.00 70.0 20.3 42.0 7.20 8.55 70.0 20.4 43-9 7.80 9.10 70.2 20.5 45-9 8.90 10.00 70.2 20.5 48.7 9.65 10.50 70.3 20.6 51.0 10.30 11.00 72.0 20.8 48.0 11.40 12.00 72.3 21.0 49-5 10.80 11.40 71-9 21.0 49.O 10.30 11.00 71-9 21.0 47.O 9.00 10.00 71.9 21.0 47-7 7-75 9.00 72.2 20.7 45.0 6-35 7.95 72.0 21.0 41.2 5.20 6.95 71.9 21.0 38.2 4.00 6.00 71-9 21.0 35-0 2.70 5.00 71-9 21.0 31-8 1.50 4.00 72.1 21.0 28.7 0.25 2.95 72.0 21.0 28.7 -o.?o 2.00 72.O 21.0 21.3 |" Meter (Mercury) APPENDIX V - MEASUREMENT OF LONGITUDINAL PARTICLE CONCENTRATION (PROPOSED METHOD) An informat ive method of measuring l o n g i t u d i n a l p a r t i c l e concentrat ion g r a d i e n t s , and hence segregation by s i z e , i s a p l o t of P r a t i o vs . v e r t i c a l p o s i t i o n i n the column, using average p o r o s i t y of the bed as a parameter. Such a p l o t i s s'hovn i n Figure 36 f o r the f l u i d i z a t i o n of 2 . 2 8 mm. g lass b a l l o t i n i by the polyethylene g l y c o l s o l u t i o n . The curves obtained give a measure of the f r a c t i o n s o l i d s at a ' p a r t i c u l a r p o s i t i o n r e l a t i v e to the average f r a c t i o n s o l i d s i n the bed, as can be seen by a n a l y z i n g the f o l l o w i n g equations 'W-'. - p - (A) ( A p / L ) , h t o r y (l-«)m(/>s-/» or ( | - € ) , = ( l - € ) m - P (B) 5-2 0-95h- 0-90 Figure 3 6 . P l o t of P. Ratio P r o f i l e s at Various Average P o r o s i t i e s . 

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