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UBC Theses and Dissertations

Hindered settling Chong, Yu Sen 1968

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HINDERED  SETTLING  by YU SEN CHONG B.Sc.,  Nanyang U n i v e r s i t y ,  A THESIS SUBMITTED IN  PARTIAL  1966  FULFILMENT  OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D in  the  SCIENCE  Department of  CHEMICAL ENGINEERING  We a c c e p t  this  the r e q u i r e d  Members o f  thesis  as  conforming to  standard  the  Department  of  Chemical  Engineering THE UNIVERSITY OF BRITISH COLUMBIA December,  1968  In p r e s e n t i n g t h i s t h e s i s  i n p a r t i a l f u l f i l m e n t o f the requirements f o r  an advanced degree a t the U n i v e r s i t y . o f  B r i t i s h C o l u m b i a , 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 p e r m i s s i o n f o r e x t e n s i v e c o p y i n g of t h i s  thesis  f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department or by h i s r e p r e s e n t a t i v e s .  It  i s understood t h a t c o p y i n g o r 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 w i t h o u t my written permission.  Department of C h e m i c a l  Engineering  The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date  December  2 7 , 1968  ii  ABSTRACT N a t u r a l and commercially a v a i l a b l e  p a r t i c l e s of  uniform shape and s i z e were used t o study the e f f e c t of p a r t i c l e shape'on h i n d e r e d s e t t l i n g i n c r e e p i n g flow 0 . 1 ) , where f l u i d flow behaviour i s independent  c  of p a r t i c l e , '  Reynolds number and the e f f e c t of shape i s most P a r t i c l e s of d i f f e r e n t  (Re <  prominent.  shapes used were s p h e r i c a l  glass  beads, c u b i c s a l t (NaCl) c r y s t a l s and ABS p l a s t i c p e l l e t s , f l a k y sugar c r y s t a l s and angular m i n e r a l ( s i l i c a t e ) c r y s t a l s . They were c a r e f u l l y s i z e d by s i e v i n g and l i q u i d e l u t r i a t i o n to a v o i d other e f f e c t s  l i k e size segregation.  Constant  settl-  ing data were processed i n the form of ui/ r a t h e r than u t o e l i m i n a t e the e f f e c t of temperature v a r i a t i o n  on v i s c o s i t y .  The e f f e c t of the w a l l on h i n d e r e d s e t t l i n g r a t e was found t o be s m a l l i n most c a s e s .  -The method proposed by  Beranek and Klumpar f o r c o r r e l a t i n g different  shaped  p a r t i c l e s was found t o be o n l y moderately  successful i n correlating ferent  f l u i d i z a t i o n data on  the present s e t t l i n g data f o r d i f -  shapes. R e s u l t s were p l o t t e d  index n of the e q u a t i o n l e a s t squares.  uz//(ui/)  It varied  the smooth spheres t o 5.4 or a n g u l a r p a r t i c l e s .  as loguv ext  versus l o g € , and the  = €  n  by  from an average v a l u e of 4.8 f o r f o r the cubes t o 5.8 f o r the f l a k y  In c o n t r a s t t o the corresponding term  proposed by Richardson and Z a k i , the term a b l y lower than uv f o r f r e e tropic particles.  was c a l c u l a t e d  (uv)  e x t  was measur-  s e t t l i n g of the s p h e r i c a l l y  More s i g n i f i c a n t l y , the index n was  isograph-  iii  ically  found to d i s p l a y a d e f i n i t e  f i x e d bed p o r o s i t y , ed,  which  a n d may t h e r e f o r e  meter  is  shape d e p e n d e n t and e a s i l y  t u r n out  f o r t a k i n g account of  t r e n d w i t h t h e random l o o s e  t o be a s i m p l e and u s e f u l  shape  variation.  measurpara-  iv  ACKNOWLEDGEMENTS I  am g r e a t l y  David A . Ratkowsky, for  their  course of writing  this  is I  for  invaluable  financial  Fellowship, additional  assistance  the  and  s t u d y was  and e n c o u r a g e m e n t d u r i n g  The h e l p o f  Dr.  Epstein  i n the  made, the final  appreciated.  to thank the assistance  University  received  of  i n the  British  Columbia  form of a  and the N a t i o n a l R e s e a r c h C o u n c i l o f  Graduate  Canada  for  support.  The c o o p e r a t i o n o f of  D r s . Norman E p s t e i n  u n d e r whose g u i d a n c e t h i s  project.  deeply wish  indebted to  M r . M u e l c h e n and t h e o t h e r  C h e m i c a l E n g i n e e r i n g Workshop  apparatus,  and t h e a s s i s t a n c e  the use of  the  of Mr.  in fabricating M u s i l of  photomicrograph f a c i l i t i e s ,  are  staff  the  Metallurgy also  in  appreciated.  V  TABLE OF CONTENTS Page INTRODUCTION  1  LITERATURE SURVEY  2  1.  Single P a r t i c l e  2  2.  Multiparticle  4  3.  The Work of Beranek and Klumpar  GENERAL THEORETICAL CONSIDERATIONS  12 16  1.  Free Settling  16  2.  Hindered Settling  20  3.  Wall Effect  24  EXPERIMENTAL  26  1.  Variables Studied  26  2.  Materials  26  A.  P a r t i c l e Selection  26  B.  Discussion on Segregation  27  C.  Separation of P a r t i c l e s  28  D.  Liquid E l u t r i a t i o n  30  E.  Description of the P a r t i c l e s  32  F.  Test Liquids  37  3.  Apparatus  37  4.  Experimental Procedures  40  A.  P a r t i c l e Size Measurement  40  B.  General Procedure  41  C.  Experimental Technique and Settling Data Selection ,  43  D.  Data Processing  RESULTS AND DISCUSSION  • 46 48  vi  Page 1.  General  48  2.  Index n for Hindered S e t t l i n g  50  3.  Comparison with Single P a r t i c l e Results  4.  Settled Bed Porosity  74  5.  Beranek-Klumpar Plot  81  6.  n - €  81  7.  Observations  b  Plot  .. 71  87  CONCLUSIONS  90  RECOMMENDATIONS  92  NOMENCLATURE  94  LITERATURE CITED  97  APPENDICES I. II. III. IV. V. VI. VII. VIII. IX. X. XI. XII. XIII.  THEORY OF SEDIMENTATION DESCRIPTION AND TESTING OF LIQUID ELUTRIATION APPARATUS NEWTONIAN BEHAVIOUR OF POLYETHYLENE GLYCOL SOLUTION MEASUREMENT OF DENSITY AND VISCOSITY CALIBRATION OF VISCOMETERS JUSTIFICATION OF USING uu ORIGINAL DATA ON HINDERED SETTLING CALCULATED RESULTS FOR HINDERED SETTLING DATA AND RESULTS FOR FREE SETTLING MICROSCOPIC MEASUREMENT OF PARTICLE SIZE DATA ON SETTLED BED POROSITY SAMPLE PLOT OF EXPERIMENTAL BED HEIGHT vs. SETTLING ..TIME. SAMPLE CALCULATIONS AND ERRORS  vii  LIST OF TABLES Table  Page  1.  E q u i v a l e n t Diameters  21  2.  Shape F a c t o r s  21  3.  Properties of Particles  4.  Dimensions of S e t t l i n g Columns  5.  Summary of R e s u l t s f o r S p h e r i c a l Glass Beads .... 51  6.  Summary of R e s u l t s f o r Cubic P a r t i c l e s  7.  Summary of R e s u l t s f o r Sugar C r y s t a l s and  .  33 38  51  Mineral Crystals  66  8.  Comparison of uv f o r Glass Beads  72  9.  Comparison of uv f o r Cubic P a r t i c l e s  73  10.  Comparison of Diameters of Glass Beads  75  11.  Comparison of Cube Lengths of Cubic P a r t i c l e s  III-l. V-l.  ... 76  C a l c u l a t e d V i s c o s i t y of PEG from D i f f e r e n t S i z e Viscometers ..III-l Summary of Viscometer C a l i b r a t i o n V-2  viii LIST OF FIGURES Figure 1.  Page Modified Plot of C and Suspension  D  - Re for Single P a r t i c l e 10  2.  Beranek-Klumpar Plot based on Richardson-Zaki Empirical Equations  13  3.  Comparison of S e t t l i n g Rates of Different Size Distributions of P a r t i c l e s  29  4.  Schematic Apparatus  31  5.  Photographic Pictures of P a r t i c l e s  34  6.  Assembly Drawing of S e t t l i n g Apparatus  39  7.  I l l u s t r a t i o n of Suspension C i r c u l a t i o n  44  8.  Logui/-loge Plot of Glass Beads i n 40% PEG  52  a.  Dv = 0.114 cm, Dy/D = 0.045  52  b.  D = 0.114 cm, D /D  t  = .0.030  52  c.  D = 0.114 cm, D /D  t  = 0.022  53  8g.  Drawing of Liquid E l u t r i a t i o n  t  v  v  v  v  Loguzz-loge Plot of Glass Beads i n 45% PEG  53  d.  D  v  = 0.114 cm, D /D  = 0.045  53  e.  D  v  = 0.114 cm, D /D = 0.030  54  f.  D = 0.114 cm, D /D v  v  v  t  t  v  = 0.022  t  54  Logui/-loge Plot of Glass Beads i n 35.4% PEG D  = 0.0097  55  Wall Effect on Glass Bead S e t t l i n g  56  10.  Results of n Plotted against D /D  57  11.  Logui/-loge Plot of Salt Crystals i n O i l  9.  v  = 0.0492 cm, D /D v  fc  v  t  59  a.  D  v  = 0.0341 cm, L\/D  t  = 0.0134  59  b.  D  v  = 0.0341 cm, D /D  t  = 0.0090  59  c.  D  v  = 0.0341 cm, D /D  t  = 0.0067  60  d.  D  v  = 0.0341 cm, D /D  t  = 0.0044  60  v  v  v  ix  Figure  Page e.  D  f.  D  g.  D  v  v  v  =  0.0391 cm, D / D  =  0.0103  61  =  0.0391 cm, D / D  =  0.0077  61  =  0.0282 cm, l V t = 0.0056  62  v  t  v  t  D  Loguz/-log€ Plot of ABS Pellets i n O i l h.  D  =  0.288 cm,  D /D  i.  Dy- =  0.288 cm,  D /D  v  v  v  t  f c  63  =  0.0374  63  =  0.0285  63  12.  Wall E f f e c t on Salt P a r t i c l e S e t t l i n g  64  13.  Loguz/-log€ Plot of Sugar Crystals i n O i l  67  14.  ?il5a-.  a.  D  b.  D  c.  D  v  v  v  =  0.1346 cm, D / D  =  0.1346 cm, D / D  =  0.1133 cm, D / D  v  t  v  v  t  =  0.0356  67  =  0.0265  67  =  0.0223  68  t  Loguz/-log€ Plot of Mineral Crystals i n O i l a.  D  b.  D  c.  D  d.  D  v  v  v  v  =  0.0508 cm, D / D  =  0.0508 cm, D / D  =  0.0426 cm, D / D  =  0.0426 cm, D / D  v  v  =  0.0134  69  =  0.0100  69  =  0.0113  70  =  0.0084  70  f c  v  v  t  t  69  t  Settled Bed Porosity of Glass Beads  77  15b.  Settled Bed Porosity of Cubic P a r t i c l e s  78  15c.  Settled Bed Porosity of Mineral and Sugar Crystals  79  16a.  Beranek-Klumpar Plot using  (u-ui )/u  16b.  Beranek-Klumpar Plot using  u/u  •••  ••• S3  16c.  Beranek-Klumpar Plot using  (u-u^J/ua,  84  16d.  Beranek-Klumpar Plot using  u/u«,  85  n  e x t  e x t  ........ 82  17.  n vs. €  18.  Comparison of the Present Results for Spheres to Models i n the Literature  b  Plot  86 89  X  Figure  Page  I-l.  Sedimentation Flux P l o t ,  Single  Concave  1-3  1-2.  Sedimentation Flux P l o t ,  Double Concave  1-3  II-3.  D e t a i l e d Drawing of  Screen Gate  II-3  .1  INTRODUCTION Single  spherical particle  of spheres i n a quiescent  settling or free  infinite  f l u i d within the creeping  f l o w r e g i m e was s t u d i e d t h e o r e t i c a l l y b y S t o k e s w e l l known S t o k e s ' mental data  (2).  settling  (1), and t h e  l a w h a s been v e r i f i e d b y v a r i o u s e x p e r i Hindered  settling,  i n contrast t o free  s e t t l i n g o f i s o l a t e d p a r t i c l e s , d e s c r i b e s a swarm o f p a r t i cles settling tions.  s i m u l t a n e o u s l y , a s i n most p r a c t i c a l  I t i s different  from f r e e s e t t l i n g because o f t h e  i n t e r f e r e n c e on t h e f l u i d  stream surrounding  p a r t i c l e by t h e p r e s e n c e o f n e i g h b o u r i n g An and  a given  particles.  e a r l y i n v e s t i g a t i o n of sedimentation  Clevenger  ( 3 ) showed t h a t ' s e d i m e n t a t i o n  with a constant  sedimenta-  made b y Coe  u s u a l l y began  r a t e , a n d t h a t p a r t i c l e s were  continuously  d e p o s i t i n g on t h e b o t t o m o f t h e c o n t a i n e r t o f o r m a b e d o f sediment. contant  The s e t t l i n g r a t e i n t h i s p e r i o d i s c a l l e d t h e  initial  view, hindered  settling rate. settling  From a h y d r o d y n a m i c p o i n t o f  o f a monosize system i s s i m i l a r t o  p a r t i c u l a t e f l u i d i z a t i o n when t h e r e a r e n o b o u n d a r i e s p a r t i c l e bed.  In fact  mentary t o each o t h e r . chemical  studies i n these  two a r e a s  e n g i n e e r i n g and other  f i e l d s , a c o n s i d e r a b l e amount  Most w o r k i n t h e l i t e r a t u r e  simple  a r e comple-  Because o f t h e i r wide a p p l i c a t i o n i n  o f s t u d y h a s b e e n made o f s u c h f l u i d - p a r t i c l e  particle  t othe  systems.  deals with s p h e r i c a l  s y s t e m s , p r e s u m a b l y b e c a u s e a s p h e r e h a s t h e most  c o n f i g u r a t i o n , o f w h i c h t h e s i z e and shape a r e e a s i l y  defined.  I n v e s t i g a t i o n s on n o n s p h e r i c a l p a r t i c l e s a r e m o s t l y  restricted t o free  settling.  2  LITERATURE SURVEY 1.  Single P a r t i c l e The e a r l i e s t s t u d y on r e s i s t a n c e of a s i n g l e  spherical  body moving r e l a t i v e t o f l u i d was made by Stokes ( 1 ) , whose a n a l y t i c a l r e s u l t i s a p p l i c a b l e w i t h i n the creeping or v i s cous f l o w r e g i o n , where f l u i d i n e r t i a i s n e g l i g i b l e compared to viscous shear.  L a t e r , s t u d y was extended t o somewhat  h i g h e r Reynolds numbers by Proudman and Pearson ( 4 ) , Whitehead ( 5 ) , Oseen (6) and Jenson ( 7 ) . An a n a l y t i c a l  solution  o f c r e e p i n g f l o w p a s t an e l l i p s o i d has been developed by Oberbeck  (8) and Gans ( 9 ) , who proved t h a t a body p o s s e s s i n g  t h r e e p e r p e n d i c u l a r p l a n e s o f symmetry has no tendency t o assume any p a r t i c u l a r o r i e n t a t i o n as i t s e t t l e s .  Subsequent-  l y , t h e o r e t i c a l s t u d y on f r e e s e t t l i n g o f a s i n g l e p a r t i c l e was extended t o s e t t l i n g a t h i g h e r Reynolds numbers, t o cases where t h e f l u i d i s bounded by s o l i d w a l l s and a bottom, t o i r r e g u l a r shaped body s e t t l i n g , and t o improved m a t h e m a t i c a l techniques of a n a l y s i s .  The s t u d i e s a r e w e l l d e s c r i b e d by  Happel and Brenner ( 1 0 ) . An e x p e r i m e n t a l s t u d y on s i n g l e n o n - s p h e r i c a l p a r t i c l e s o f w e l l - d e f i n e d shape was made by P e r n o l e t ( 1 1 ) , who i n v e s t i g a t e d cubes, d i s c and p r i s m s o v e r a narrow range o f Reynolds number.  P e t t y j o h n and C h r i s t i a n s e n (12) s p e c i f i c a l l y  s t u d i e d i s o m e t r i c p a r t i c l e s over a l a r g e range o f Reynolds number, and were a b l e t o c o r r e l a t e t h e S t o k e s ' law shape f a c t o r s o f f i v e i s o m e t r i c b o d i e s i n c r e e p i n g f l o w r e g i o n , as w e l l as drag c o e f f i c i e n t s a t h i g h e r Reynolds number r e g i o n , with sphericity.  S i m i l a r work was done by Chowdhury (13) and  3  a similar conclusion was obtained.  Heiss and Coull  (14)  studied the e f f e c t of orientation and shape on the s e t t l i n g v e l o c i t y of non-isometric p a r t i c l e s i n the viscous region, and reached the conclusion that sphericity alone was not s u f f i c i e n t to take account of both shape and orientation e f f e c t s on the free s e t t l i n g of non-isometric orthotropic bodies.  Correlation of sphericity to Stokes' law shape fac-  tor was possible by including as additional parameters the diameter of a sphere of equal volume and the diameter of a c i r c l e of equal projected area to the body i n question. Recently Blumberg and Mohr (15) have extended  the study of  c y l i n d r i c a l p a r t i c l e s in viscous flow to orientations i n t e r mediate between horizontal and v e r t i c a l .  Other experimental  studies on orthotropic bodies were those of McNown and Malaika (16), who  investigated discs, cylinders, a prismatic body and  a conical body s e t t l i n g p a r a l l e l to the p a r t i c l e axis, and determined  the l i m i t of the viscous flow region for the various  shapes; and Jayaweera (17), who  studied the free s e t t l i n g of  cylinders and cones over a p a r t i c l e Reynolds number range of 0.01  to 1000.  At high p a r t i c l e Reynolds number, free s e t t l i n g  of single p a r t i c l e s was  found to depend on the density r a t i o  of s o l i d to l i q u i d , as well as on shape, by both Christiansen (18) and Isaacs (19). Becker (20) has attempted  to correlate shape and  Reynolds number with drag c o e f f i c i e n t , for various l i t e r a t u r e data.  A review by Torobin and Gauvin  (21) covered extensive  references on the e f f e c t of p a r t i c l e shape and roughness.  So  f a r , even for single p a r t i c l e s e t t l i n g , the choice of a s u i t -  4 able shape factor which i s applicable to a l l the experimental data has been found to be extremely d i f f i c u l t because of the complicating effects of orientation, and of rotation of nonisometric orthotropic bodies.  The problem i s further compli-  cated by the d i f f e r e n t character of flow at d i f f e r e n t Reynolds numbers, by the dependence of free roientation on Reynolds number, and by the vast i r r e g u l a r i t y and d i v e r s i t y of p a r t i c l e shapes to be considered. 2.  Mult ipar t i d e Empirical and a n a l y t i c a l approaches to the dynamics of  hindered s e t t l i n g have often followed two methods: i.  treating the dynamics of a single p a r t i c l e and trying  to extend the r e s u l t to a multiple p a r t i c l e system by appropriate modification  of the boundary conditions, which usually  turned out to be some function of the concentration of p a r t i cles i n the f l u i d ( 22, 23, 24, 25, 26). ii.  modifying the continuum mechanics of a single phase  f l u i d by treating the suspension as a l i q u i d , the properties of which are altered by the presence of p a r t i c l e s (10, 27, 28, 29, 30). Some empirical equations also resulted from adopting the law of flow through packed beds with certain  modifications  (31, 32, 33). The problem of the motion of a swarm of s o l i d  spherical  p a r t i c l e s through f l u i d has been treated t h e o r e t i c a l l y by various investigators by the approach of method i i . cosity of d i l u t e suspension was derived  The v i s -  by Einstein (34), and  5  was  later  their  a d o p t e d by Vand and H a w s k l e y  equation  e q u a t i o n was valid  over  cles.  for  sedimentation  B a s e d on t h e  inertia,  and Bandukwala  c o n c e n t r a t i o n range  a n d on D a r c y ' s  equation  for  fluid  (36) a l s o a r r i v e d  centrated  s u s p e n s i o n s w h i c h was v e r i f i e d  Verschoor  (37).  fluid  for  spherical  By m o d i f i c a t i o n o f t h e  flowing past  a single  assumed a n d s t u d i e d e i t h e r  flow  at  surface  model o f H a p p e l  and t h e n u m e r i c a l  experimentally  and H a m i e l e c  m o d i f i c a t i o n of of  Stokes  a suspension of  1  fine,  study law  by R o b i n s o n  closely  ion factor  for the  to account  p s e u d o - s i n g l e phase cles.  Loeffler  of  a n d be s i m i l a r  to  By  porosity rated  comparison to dependent  i n t o the  free  settling  to  f i n d the  settling  of  the  parti-  settling  law a s p o r o s i t y  approaches a  l o o s e l y packed s p h e r i c a l  the Kozeny e q u a t i o n t h e y  correction  correct-  presence of the  rates  Steinour  f l o w t h r o u g h a p a c k e d bed a t  0.48,the v a l u e a s s i g n e d t o  cles.  1  LeClair  (38) s u g g e s t e d a  (33) c o n s i d e r e d t h a t  c o n d i t i o n should agree with Stokes unity  settling,  change i n t h e p r o p e r t i e s  s u s p e n s i o n due t o t h e  and Ruth  (26), the  sized p a r t i c l e s .  a p p r o a c h , was a b l e  been  Kuwabara ( 2 3 ) .  p r e d i c t i n g the  (30), using a s i m i l a r  on  namely  h i g h e r R e y n o l d s number by  for  by  models have  or n u m e r i c a l l y ,  ( 2 4 ) f o l l o w i n g t h e model o f  An e x p e r i m e n t a l  con-  boundary c o n d i t i o n s  (22) f o r v i s c o u s r e g i o n  s o l u t i o n at  fluid  through  t h e h e x a g o n a l c o n f i g u r a t i o n o f R i c h a r d s o n and Z a k i free  be  parti-  a solution for  sphere, various  analytically  Their  (28) t o  equation of m o t i o n , n e g l e c t i n g the  packed b e d s , Brinkman  a  developing  i n the v i s c o u s r e g i o n .  c o n f i r m e d by H a n r a t t y  a certain  ( 3 5 , 27) i n  porosity parti-  obtained a  f u n c t i o n w h i c h c o u l d be i n c o r p o equation, Richardson  (31) and  6  Harris for  (32), r e s p e c t i v e l y ,  fluid  flow  calculated  Oliver  (39) a l s o  e x p r e s s i o n by m o d i f y i n g t h e body and i n s e r t i n g  viscosity  change  due t o  the  empirical  earlier  a correction  expressions  were a l s o  function  surrounding  factor  different  obtained a  stream  spherical  stated  friction  t h r o u g h an expanded bed a t  concentrations.  Other  the  semi-empirical for  a  factor  single for  the  particles.  b a s e d on t h e  found i n p a r t i c u l a t e  approaches  fluidization  (40, 41, 4 2 ) . An o v e r a l l and p a r t i c u l a t e wide r a n g e and Z a k i  experimental  f l u i d i z a t i o n of  of Reynolds  was  The r e s u l t s  carried  of  correlated.  out  dynamics,  both pairs  of  velocity,  u,  the  Richardson Reynolds  Q  with extrapolation mately  the  free  t o any  of  a  Richardson  spherical  plotted  straight  line  similarly  the  was  of unity  velocity,  hydrosettling  coordinates.  f o u n d by  free  settling  the g i v e n u n i f o r m - s i z e giving  particles, approxi-  Uoo :  The e x p o n e n t n depended on w a l l e f f e c t ,  n = 4.65 + 19.5-S-  of  p o r o s i t y , € on l o g - l o g  to a porosity  settling  by  over  sophisticated  (43) t o depend on t h e  number, R e ,  particles  were c o m p a r a b l e and  investigators  the r e s u l t i n g  and Z a k i  settling  by G a s p a r y a n and I k a r y a n ( 2 5 ) .  Without r e s o r t i n g  The s l o p e o f  spherical  hindered s e t t l i n g  both s t u d i e s  against  of hindered  number was u n d e r t a k e n  ( 4 3 ) , and l a t e r  particles  study  in addition  to  Re :  R e < 0.2 (2a) Q  Q  7  n = (4.35 + 1 7 . 5 - ^ ) R e o n = (4.45 + L S - ^ R e o n = 4.45 R e o  0.2 < R e  0 , 0 3  0 , 1  0 , 1  n = 2.39  Q  < 1  (2b)  1  <  Re  Q  < 200  (2c)  200  <  Re  0  < 500  (2d)  500  <  Re  c  (2e)  T h i s method of c o r r e l a t i o n had p r e v i o u s l y attempted by Hancock (44).  been  The c o r r e l a t i o n , though simple,  was found t o be g e n e r a l l y v a l i d  i n i d e a l hindered  settling  without f l o c c u l a t i o n and p a r t i c u l a t e f l u i d i z a t i o n .  Fluidi-  z a t i o n data o f Wilhelm and Kwauk (42) and o f Lewis e t a l (40) were a l s o found t o be w e l l c o r r e l a t e d i n t h i s way. Most o f the p r e v i o u s i n v e s t i g a t i o n s have been done on s p h e r i c a l p a r t i c l e s , and o c c a s i o n a l l y on i r r e g u l a r p a r t i c l e s , but without p a r t i c l e shape as a s p e c i f i e d v a r i a b l e of study. The  e f f e c t o f p a r t i c l e shape i n p a r t i c u l a t e  z a t i o n a t h i g h Reynolds number has been s t u d i e d son and Z a k i  (43) f o r n o n - s p h e r i c a l  fluidi-  by R i c h a r d -  p a r t i c l e s of r e g u l a r  g e o m e t r i c a l shape, namely cubes, p l a t e s , c y l i n d e r s and hexagonal p r i s m s .  I t was found t h a t i n the h i g h Reynolds  number range, the p a r t i c u l a t e f l u i d i z a t i o n expansion data of these p a r t i c l e s d i d not d i f f e r v e r y much from the c o r r e s ponding r e s u l t s f o r s p h e r i c a l p a r t i c l e s . e x p o n e n t i a l form the power n could  When c o r r e l a t e d i n  be r e l a t e d t o the  Heywood v o l u m e t r i c shape f a c t o r : 3 K  v  - 6 D  3 c  (3)  8  Irregular large  Reynolds  Ikaryan fluid to  number r a n g e was  hindered s e t t l i n g  to  the  surface  o f an  hindered s e t t l i n g  irregular  particles  equation  for  thus have t o particle  Reynolds  shape c o r r e c t i o n  factors  purposes.  like  shape i s However,  r e g i o n o f R i c h a r d s o n and M e i k l e mina p o w d e r ,  of  Jottrand  G a s p a r y a n and I k a r y a n crushed b a r i t e ,  to  factors.  particles,  for  any  were  and  specific  in  the  particles  for  a n d a s h i g h as  not  assumed in  the  different  particles  crushed when  from t h a t  around 6 . 5 for  for  and o f basalt,  of  the  spherical  Thus v a l u e s  crushed  alumina powder, for  alu-  correlated  form,show v a l u e s  number r a n g e .  1 0 . 5 for  sand,  for  viscous  ( 3 1 ) on s e d i m e n t a t i o n o f  t o 4 . 6 5 f o u n d by R i c h a r d s o n and Z a k i Mueller  low  problems,  usually  experimental data  irregular  sand,  at  Gasparyan are  ( 4 6 ) on f l u i d i z a t i o n o f  same R e y n o l d s  were o b t a i n e d  those of  therefore  exponential  exponent n s i g n i f i c a n t l y particles  in practical  ( 4 5 ) on s e d i m e n t a t i o n o f  and o t h e r  the R i c h a r d s o n - Z a k i  Reynolds  extend  coefficient"  s e d i m e n t a t i o n of n o n - s p h e r i c a l p a r t i c l e s  number, which o f t e n p r e v a i l s  predictive  5.6  to  so as  correction  irregular  be d e t e r m i n e d e x p e r i m e n t a l l y  known, and a s p h e r i c a l  in  immobile  spherical particles  and " v o l u m e  systems of  and  particle,  by means o f a p p r o p r i a t e  different  of  a  shape. In  the  layer  t h e y were a b l e for  The s o - c a l l e d " f o r m c o e f f i c i e n t " different  that a  irregular  f o r m a smooth p s e u d o - p a r t i c l e ,  their  over  s t u d i e d by G a s p a r y a n  Using the h y p o t h e s i s  ( 4 5 ) .  clings  shape p a r t i c l e  of  basalt compared  spheres.  a n d Schramm ( 4 7 ) s u g g e s t e d t h a t  in  the  low  number r e g i o n , e x p a n s i o n o f a f l u i d i z e d bed o f n o n -  9  s p h e r i c a l p a r t i c l e s which possess a maximum l e n g t h dimens i o n l e s s than 1.5 times the maximum width could be p r e d i c t e d from the same graph which a p p l i e s t o s p h e r i c a l p a r t i c l e s ; and that o n l y a t Reynolds numbers beyond the c r e e p i n g flow r e g i o n was a d i f f e r e n t graph f o r i r r e g u l a r particles required.  The graph presented by these authors  can a l s o be found i n the textbook by Zenz and Othmer ( 4 8 ) , who i n d i c a t e that the graph was prepared by drawing  smooth  curves through the e x p e r i m e n t a l data of a number of i n vestigators. 2  The graph i s a l o g - l o g p l o t of  (Re/Cn) ^ 1  1/3  a g a i n s t (ReCo) '  w i t h bed p o r o s i t y as parameter.  Thus the  v a r i a b l e s v e l o c i t y and diameter each appear o n l y on the r e s p e c t i v e c o o r d i n a t e axes, thereby e l i m i n a t i n g the u s u a l t r i a l and e r r o r procedure when e i t h e r of these v a r i a b l e s i s the unknown. For convenience, F i g u r e 1 was prepared based on the accepted 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 s i n g l e sphere s e t t l i n g  ( 4 9 ) , and on Richardson and Z a k i ' s e m p i r i c a l  equations f o r h i n d e r e d s e t t l i n g , assuming  no w a l l  effect.  The graph appears t o be i n f a i r agreement w i t h that of M u e l l e r and Schramm.  The v a r i a b l e , diameter, on the a b s c i s s a , when  a p p l i e d t o a n o n s p h e r i c a l p a r t i c l e , was taken by M u e l l e r and Schramm to be the diameter of a sphere having the same v o l ume as the g i v e n p a r t i c l e .  I t i s noted that i n the c r e e p i n g  flow r e g i o n ( R e < a p p r o x . 0.2) the l i n e s f o r each p o r o s i t y c  are s t r a i g h t and p a r a l l e l to each o t h e r , and have a slope o f 2.  T h i s r e s u l t a r i s e s from S t o k e s  the form  1  law, which can be put i n  Figure  1.  M o d i f i e d P l o t of C and S u s p e n s i o n  D  - Re  for Single  Particle  ^ 1 / 3  The  «  c Re ) /3 2  (  vertical  D  2  0  s p a c i n g between t h e s e  ent  porosity is.proportional  and  2, a n d i s c o n s t a n t  n = 4.65.  In t h e l i g h t  nonspherical particles the graph crushed  (  lines  o f t h e few e x p e r i m e n t a l  d a t a on  i n c r e e p i n g flow mentioned  creeping flow, the p r e d i c t i o n  is  interesting  Zaki's r e s u l t s  on a r t i f i c i a l  i n which  Mueller quired  forirregular  crystals  i s poor.  It  Richardson particles  i n the h i g h Reynolds  flow, while  a n d Schramm s u g g e s t e d  creeping  particles  on t h e o t h e r  number  hand  t h a t a separate graph  was r e -  o n l y i n t h e r e g i o n beyond  flow. It  has  i n creeping  nonspherical  f o r ex-  between t h e i n d e x n f o r n o n -  and t h a t f o r spheres  range than  graph  t h a t , on t h e one h a n d ,  showed a s m a l l e r d i f f e r e n c e spheres  of this  earlier,  powder a n d  o f t h e p r e s e n t work on c u b i c s a l t  in  and  1  i n t h e c r e e p i n g f l o w r e g i o n , where  Even f o r n o n s p h e r i c a l p a r t i c l e s  t o note  )  of d i f f e r -  t h e maximum l e n g t h i s e q u a l t o t h e maximum w i d t h , ample t h e d a t a  a  t o the index n of equation  o b v i o u s l y does n o t a p p l y t o a l u m i n a  basalt.  4  c a n be c o n c l u d e d  been done on t h e e f f e c t  between h i n d e r e d  settling  t h a t no e x t e n s i v e  investigation  o f shape on t h e r e l a t i o n s h i p  r a t e and c o n c e n t r a t i o n , except  possibly  i n t h e h i g h R e y n o l d s number r a n g e .  particle  shape e f f e c t ,  particularly  A study  i n the creeping  of the flow  12  r e g i o n s , s h o u l d t h e r e f o r e be u s e f u l and 3.  significant.  The Work of Beranek and Klumpar In t h e i r paper t i t l e d  "A New  Theory of F l u i d i z a t i o n " ,  Beranek and Klumpar ( 5 0 ) , i n c o r r e l a t i n g expansion data of f l u i d i z e d beds, suggested  t h a t a p l o t of ( l - € ) / ( l - 6 5 )  a g a i n s t e i t h e r u/u^ or ( u - u ) / u i n  0 O  was  superior to other  methods of c o r r e l a t i o n which d i d not f i t t h e i r  experimental  d a t a . Here e i s the p o r o s i t y of the expanded bed, e  b  i s the [  f i x e d bed p o r o s i t y c o r r e s p o n d i n g t o a random l o o s e packed bed o b t a i n e d by l e t t i n g the p a r t i c l e s i n s u s p e n s i o n  settle  f r e e l y u n t i l they had reached a c o n s t a n t h e i g h t , and u i i s the i n c i p i e n t f l u i d i z a t i o n v e l o c i t y . (1-65)  was  denoted  The  term  n  (1-e)/  as " c h a r a c t e r i z i n g the g e o m e t r i c  similar-  i t y " . Without u s i n g any c o n v e n t i o n a l shape f a c t o r , they were a b l e t o p l o t b o t h s p h e r i c a l p a r t i c l e d a t a and gular p a r t i c l e s data, obtained at d i f f e r e n t free Reynolds  numbers, on the same c u r v e .  irre-  settling  However, p l o t t i n g of  d a t a a t d i f f e r e n t f r e e s e t t l i n g Reynolds numbers on a s i n g l e curve i s i n p r i n c i p l e wrong, s i n c e i t i s w e l l known t h a t dependence of u/uo, on p o r o s i t y f o r p a r t i c l e s of f i x e d shape (e.g.  s p h e r i c a l ) v a r i e s w i t h f r e e s e t t l i n g Reynolds  number.  T h i s p o i n t becomes more o b v i o u s by r e f e r e n c e t o F i g u r e 2 , where the R i c h a r d s o n - Z a k i e m p i r i c a l e q u a t i o n s f o r s p h e r i c a l p a r t i c l e s a r e p l o t t e d i n the manner of Beranek, assumming € 5 e q u a l t o 0.435. That Beranek and Klumpar were a p p a r e n t l y a b l e t o c o r r e l a t e t h e i r d a t a on a s i n g l e c u r v e may  be a t t r i b u t e d t o  13  F i g u r e 2 .  B e r a n e k - K l u m p a r Z a k i E m p i r i c a l  P l o t b a s e d o n R i c h a r d s o n E q u a t i o n s  14  the  relatively  number  similar  values  of Re  shape v a r i a t i o n  bed p o r o s i t y h a s sphericity  of  p o r o s i t y has than cal  settling  Reynolds  could r e a l l y  Q  of  it  the  fall  must be €  b  particles.  on t h e  data  at  same  curve  ^l7hich a c c o u n t s Random l o o s e  i n d e e d been r e p o r t e d t o be r e l a t e d  particles the  shape  of  without  which  is  for  fixed to  the  s u c h a f i x e d bed  b e i n g much e a s i e r  factors,  "shape measurement" of p a r t i c l e s ,  The u s e o f  (51).  advantage  conventional  tion  free  s p h e r i c a l and n o n s p h e r i c a l p a r t i c l e  s u g g e s t e d by B e r a n e k ,  the  of  covered. If  as  narrow range  to  and o f g i v i n g a referring  to  the  measure  statistiorienta-"  assumed random i n a r a n d o m l y  packed bed. As t h e concentration Beranek to  effect  dependence of  and K l u m p a r ,  the v a l i d i t y  and Klumpar,  in  fact  of t h e i r  K w a u k ( 4 2 ) , whose  plotted in  variation  of  index, n,  h i g h e r Reynolds the  fluid  flow  comparison of  data of  Wllhelm  mentioned s t u d i e s  behaviour effects  form,  In is  due t o  the  give in  Beranek  and  (31, 45,  46)  fluidization  more  creeping  sensitive flow than  creeping flow r e g i o n ,  independent of Reynolds  of v a r i o u s  at where  number,  shape may be s i m p l i f i e d .  Therefore a study of hindered s e t t l i n g  as  f o r random l o o s e  and p a r t i c u l a t e  w i t h shape  numbers.  i g n o r e d by  i n c l u d e d some d a t a  f i x e d bed p o r o s i t y was n o t  exponential  the  Furthermore  result,  and a l s o the  The p r e v i o u s l y  on  no c o n c l u s i o n can be drawn  correlation.  show t h a t h i n d e r e d s e t t l i n g data,  number l e v e l  bed e x p a n s i o n was  in presenting their  on p o r o u s p a r t i c l e s ,  packing.  of Reynolds  shape  15  p a r t i c l e s i n the creeping described  i n this  flow r e g i o n , which w i l l  work, s h o u l d  c l a r i f y the v a l i d i t y  o t h e r w i s e o f t h e above s t a t e d s u g g e s t i o n Klumpar.  be or  by B e r a n e k and  16  GENERAL THEORETICAL 1.  Free  CONSIDERATIONS  Settling Consider  a single,  uniform  s i z e , L s e t t l i n g with a constant and  constant  v i s c o s i t y fj..  d e n s i t y p a r t i c l e of  terminal velocity  u^  o r i e n t a t i o n i n an i n f i n i t e f l u i d medium of When the motion i s i n the c r e e p i n g  r e g i o n , the t o t a l drag  f o r c e on the p a r t i c l e , which con-  s i s t s of both v i s c o u s shear f o r c e s and pressure p r o p o r t i o n a l t o L, u ^  flow  forces, i s  and LA, and i s independent of the  f l u i d density p : F = KLtt The  (5)  U o o  c r i t e r i o n of flow behaviour i s the p a r t i c l e  Reynolds number, which i s the r a t i o o f f l u i d  i n e r t i a to  v i s c o u s f o r c e s and i s d e f i n e d as  R e  o  <6)  =  At low R e , f l u i d Q  inertia i s relatively  compared t o v i s c o u s shear, and equation Re  G  \.within c e r t a i n l i m i t s .  unimportant  5 a p p l i e s a t any  The flow i s c a l l e d  creeping  flow or v i s c o u s flow and i s c h a r a c t e r i z e d by the absence o f wakes and of boundary l a y e r s e p a r a t i o n of f l u i d behind the particle.  Beyond the c r e e p i n g flow r e g i o n the f l u i d  inertia  can no longer be n e g l e c t e d , and the r e s i s t a n c e f o r c e on the particle  cannot be expressed  by equation  5.  A sphere i s the simplest shaped p a r t i c l e , the s i z e of which can be d e s c r i b e d by a s i n g l e dimension, diameter D,  17  irrespective  of i t s o r i e n t a t i o n .  E q u a t i o n 5, w r i t t e n  for a  s p h e r e , becomes F =  STTD^U^  (5a)  w h i c h c a n be p r o v e d a n a l y t i c a l l y f r o m t h e e q u a t i o n o f t i o n and has been v e r i f i e d e x p e r i m e n t a l l y .  The  mo-  Reynolds  number t h e n becomes  Reo = ^  (6a)  I n g e n e r a l , f o r a l l p a r t i c l e shapes and numbers, the d r a g f o r c e  Reynolds  i s e x p r e s s e d as  2 F  For  = C j / p  1  ^  a s p h e r e , w h e r e Ap  c l e normal t o the f l o w C  C  D  (7)  i s the p r o j e c t e d area of the p a r t i axis.  D = tr = f(Re )  ° °-  Re Re  c  c  By e q u a t i n g t h e d r a g f o r c e p a r t i c l e to the g r a v i t a t i o n a l force on i t , t h e t e r m i n a l calculated  »-  > 0.2 e x e r t e d on a  <  2  (4b) spherical  l e s s the buoyancy  force  s e t t l i n g v e l o c i t y o f t h e p a r t i c l e can  as  -  which i s a f a m i l i a r s p e c i a l  <*> form of Stokes' law  to p a r t i c l e motion i n a g r a v i t a t i o n a l  field.  (4)  applicable  be  18  The more r e g u l a r p a r t i c l e s of i n t e r e s t w i t h shapes other than s p h e r i c a l  may  be c l a s s i f i e d i n t o s p h e r i c a l l y  t r o p i c p a r t i c l e s , which have t h r e e equal mutually c u l a r axes of symmetry, and o r t h o t r o p i c  iso-  perpendi-  p a r t i c l e s , which  possess t h r e e mutually p e r p e n d i c u l a r planes of symmetry and which s p h e r i c a l l y  i s o t r o p i c p a r t i c l e s / are a p a r t i c u l a r  case.  N o n s p h e r i c a l p a r t i c l e s e t t l i n g i s more complicated than of spheres because of the u n l i m i t e d number of which are p o s s i b l e  The problem i s f u r t h e r  that  orientations  and the v a r i a t i o n of t r a n s n a t i o n a l  ance w i t h o r i e n t a t i o n .  of  resist-  complicated  by  r o t a t i o n of p a r t i c l e s at h i g h e r Reynolds numbers, or by shape assymmetry even at low  Reo.  W i t h i n the c r e e p i n g flow r e g i o n , a s p h e r i c a l l y tropic particle settles in i t s i n i t i a l orientation d i r e c t i o n of the g r a v i t i o n a l  force.  ance i s the same i n any o r i e n t a t i o n a sphere of equal volume (12).  iso-  and i n the  The t r a n s l a t i o n a l r e s i s t and  i s l a r g e r than that  The drag f o r c e  on  e x e r t e d on a  s t e a d i l y s e t t l i n g p a r t i c l e i n c r e e p i n g flow i s then given by  F  = KS; V-«>  <>  U  5 B  Thus  where Dv i s the diameter c a l l e d the Stokes* function  of a sphere of equal volume and  law shape f a c t o r , which was  of s p h e r i c i t y An o r t h o t r o p i c  Kgj-is  found to be a  (12). p a r t i c l e , i f s e t t l i n g i n the c r e e p i n g  19 flow r e g i o n , w i l l preserve i t s i n i t i a l o r i e n t a t i o n , but w i l l not  necessarily f a l l  i n the d i r e c t i o n of theg r a v i t a t i o n a l  f o r c e e x c e p t when i t s a x i s i s p a r a l l e l force  (14).  to theg r a v i t a t i o n a l  The t r a n s l a t i o n a l r e s i s t a n c e d e p e n d s o n t h e  o r i e n t a t i o n f o r a s p e c i f i e d shape p a r t i c l e . law  s h a p e f a c t o r c a n be d e r i v e d  A s i m i l a r Stokes'  f o r some a r t i f i c i a l  t r o p i c p a r t i c l e s (14), b u t s i n c e c o r r e l a t i o n o f t h i s  orthofactor to  s p h e r i c i t y alone i s i n s u f f i c i e n t , such parameters as r a t i o o f axis  l e n g t h s , and d i a m e t e r s d e f i n e d  i n various  w a y s , become  n e c e s s a r y t o account f o r t h e volume and o r i e n t a t i o n o f t h e particle  (14,  15).  P a r t i c l e s w i t h o u t a n y a x i s o f symmetry a n d i r r e g u l a r p a r t i c l e s , when s e t t l i n g  i n creeping  flow, w i l l  r o t a t e and thus  rotational .resistance arises i n addition tot r a n s l a t i o n a l resistance. the  fluid  Both r e s i s t a n c e s  exerted  c o n t r i b u t e t o the drag force of  on t h e p a r t i c l e .  Beyond t h e c r e e p i n g  flow region,  s e t t l i n g of a p a r t i -  cle  may i n v o l v e s p i n n i n g , w o b b l i n g a n d o t h e r  and  the particle orientates  fluid  motions,  i n s u c h a way t h a t r e s i s t a n c e t o  f l o w i s a maximum, a t l e a s t f o r many p a r t i c l e s s t u d i e d ( 2 0 ) . A n a l y t i c a l proofs  bodies of r e v o l u t i o n l i k e can  secondary  f o r creeping  flow are available f o r  spheres and s p h e r o i d s .  These  proofs  be i n t u i t i v e l y a p p l i e d t o p a r t i c l e s o f . s y m m e t r i c s h a p e  plane surfaces, experimental To  f o r which a n a l y t i c a l  with  s o l u t i o n s a r e d i f f i c u l t but  verifications are possible. a c c o u n t f o r v a r i a t i o n i n s h a p e , many methods h a v e  been s u g g e s t e d f o r "measuring t h e shape" o f n o n s p h e r i c a l c l e s and t h e i r e q u i v a l e n t  diameters.  The e q u i v a l e n t  parti-  diameter  20  of a nonsphere has u s u a l l y been based on a sphere of equal volume, or equal s u r f a c e area or equal s e t t l i n g v e l o c i t y , of which has i t s own j u s t i f i c a t i o n on hydrodynamical  each  grounds.  Examples a r e g i v e n i n Tables 1 and 2. The  Stokes' law shape f a c t o r , Kgx, has been c o r r e l a t e d  to the other shape f a c t o r s , which can be determined hydrodynamic measurements ( 1 2 ) . s u c c e s s f u l f o r p a r t i c u l a r shapes,  by non-  Use o f shape f a c t o r may be but not g e n e r a l l y s a t i s f a c t o r y  f o r a l l shapes, e s p e c i a l l y when o r i e n t a t i o n e f f e c t s a r e important and other parameters  are required.  The measurement of a shape f a c t o r such as s p h e r i c i t y i s always d i f f i c u l t .  As p r e v i o u s l y mentioned, the f i x e d bed poro-  s i t y o f uniform s i z e and shape p a r t i c l e s has been suggested t o be i n some way r e l a t e d t o s p h e r i c i t y ( 5 1 ) .  F i x e d bed packing,  however, does not g i v e an unique p o r o s i t y f o r a s e t of p a r t i cles.  Spheres,  f o r example, g i v e four c o n s i d e r a b l y d i f f e r e n t  p o r o s i t i e s corresponding t o s p e c i a l geometric arrangements i n the bed (53) of which random packing can be c o n s i d e r e d t o be mixtures i n v a r y i n g p r o p o r t i o n s .  Random loose packing however,  was found t o g i v e r o u g h l y a constant p o r o s i t y . 2.  Hindered  Settling  In a m u l t i p a r t i c l e system, the e f f e c t of the presence of other p a r t i c l e s i n the v i c i n i t y of the p a r t i c l e must be c o n s i d e r e d ; t h i s e f f e c t may be hydrodynamical  or mechanical.  Richardson and Z a k i (43), by means of d i m e n s i o n a l a n a l y s i s and c o n s i d e r i n g the p o s s i b l e e f f e c t o f the w a l l on p a r t i c l e  motion,  a r r i v e d a t the f o l l o w i n g grouping of dimensionless q u a n t i t i e s  21  Table  1  Equivalent Equivalent diameter  Definition:  Diameter o f same  Dv  volume o r d r a g  D  surface  s  Table Shape Shape  factor  of  sphere  force  area  settling  Du  f  Diameters  rate  2  Factors  Variable  compared  Fixed  variable  = A /A  surface  area  volume o r force  drag  0  = C»/C  perimeter of projection  projected  area  K  =7TDV/6D£  volume  K  s  v  ST=  Uco/Uv  settling  rate  volume o r drag f o r c e  22  for spherical LL_  =  0  particles: (fijiau,  IL.e)  (9)  where e i s the p o r o s i t y of the bed.  The e m p i r i c a l equations  were presented i n the form  J = c ext  (la)  n  u  where u  i s the v e l o c i t y o b t a i n e d by e x t r a p o l a t i n g the l o g - l o g  e x t  p l o t of s e t t l i n g r a t e versus p o r o s i t y t o a p o r o s i t y of u n i t y , and was  found to be approximately  the same as the f r e e  settling  v e l o c i t y of a s i n g l e p a r t i c l e i n an i n f i n i t e medium.  Thus,  m u l t i p a r t i c l e s e t t l i n g i s r e l a t e d t o f r e e s e t t l i n g by a c o r r e c t i o n term which i s a f u n c t i o n of p o r o s i t y .  In the c r e e p i n g flow  r e g i o n , R e < 0 . 2 , t h i s f u n c t i o n does not v a r y with R e , and o  Q  equation l a becomes  U u  = .4.65 € ' H  ext  (lb)  O J  when w a l l e f f e c t i s n e g l i g i b l e .  The f u n c t i o n  v a r i e s with  Reynolds number beyond the c r e e p i n g flow r e g i o n . A n a l y t i c a l s o l u t i o n s of c r e e p i n g flow hindered have been proposed models.  settling  (22, 23, 24, 26) based on some i d e a l i z e d  The agreement with experiment  i s not e n t i r e l y  f a c t o r y , the experimental r e s u l t s always showing h i g h e r r a t e s than p r e d i c t e d .  satissettling  Two p a r t i c l e s s e t t l i n g r e p r e s e n t s a  p a r t i c u l a r case of m u l t i p a r t i c l e s e t t l i n g .  Both a n a l y t i c a l and  experimental r e s u l t s , i n good agreement (10) with each o t h e r ,  23  h a v e shown t h a t m u t u a l i n t e r f e r e n c e always reduces the the  settling  result  is  faster  for  on t h e  two s p h e r i c a l  particles,  than the  free  and  settling  c o n t r a d i c t i o n to equation  fractional  therefore  small,  is  i n apparent  p o r o s i t y as is  rate  drag force  of  volume o f  example a t h i g h p o r o s i t y ,  rate.  la,  number o f  particles  In  analysing  spherical particle  should not  dynamical,  that  the  spheres  does n o t a f f e c t  the  drag f o r c e a p p r e c i a b l y  For n o n s p h e r i c a l p a r t i c l e s ,  settling  non-vertical  ween p a r t i c l e s ,  of r o t a t i o n  studies  c l u s i o n s are  of  the  in  creeping flow  is  settling hindered bet-  interference  the  the  is  viscous  contact  possible number o f Even i n  systems, of  it  hydro-  Thus t h e  complicated.  An i n v e s t i g a t i o n in  suitable  shapes.  This  sedimentation period,  for uniform size p a r t i c l e s grounds  (see  Appendix  the  the  con-  effect  therefore  s t u d y was  of reason-  confined  the u n i v e r s a l  can be j u s t i f i e d I).  an  though  free  an i n f i n i t e  spherical multiparticle  available,  theoretical  includes  of  for  t o an e x p e r i m e n t a l s t u d y on u n i f o r m p a r t i c l e s  constant rate  of which  which  may be r a t h e r  shape on h i n d e r e d s e t t l i n g  various  even  c h a n g e d by m e c h a n i c a l  Analysis  not u n i q u e .  ably r e s t r i c t e d  do n o t r o t a t e ,  however,  and o r i e n t a t i o n  nonspherical particles diverse  essentially  i n a d d i t i o n t o pure hydrodynamic  c a u s e d by n e i g h b o u r s . effects  is  m o t i o n and r o t a t i o n .  r a t e may be f u r t h e r  is  hindered s e t t l i n g  effect  It  be a p p l i e d .  the hindrance  may i n v o l v e  considering  equation  a l w a y s assumed t h a t  flow.  This  particles  the general  "infinite"  rotation  consequently  f l u i d u n o c c u p i e d by s o l i d .  s u g g e s t e d t h a t when t h e number o f  and a l s o  particles  of to  existence even  on  24  3.  Wall  Effect The w a l l e f f e c t on a s i n g l e p a r t i c l e a r i s e s from the  backflow of l i q u i d which i s d i s p l a c e d by the s e t t l i n g i n a v e s s e l w i t h a f i n i t e boundary. g i o n , when a sphere  particle  In the c r e e p i n g flow r e -  s e t t l e s a x i a l l y along a tube, the a c t u a l  drag f o r c e on the sphere  (10) i s g i v e n by  F  F'=  (10)  where F i s the drag f o r c e on a sphere s e t t l i n g i n an i n f i n i t e medium g i v e n by equation 5a and k has a numerical v a l u e of 2.104. tion.  The sphere  s e t t l e s without r o t a t i o n i n t h i s center l o c a -  A t any other ( e c c e n t r i c ) p o s i t i o n , however, a torque i s  e x e r t e d on the sphere and i t r o t a t e s i n one d i r e c t i o n or another while s e t t l i n g .  Consquently  k changes i n accordance  r a d i a l l o c a t i o n of the p a r t i c l e . slightly  w i t h the  The v a l u e of k decreases  very  (about 37.) when the l o c a t i o n o f the sphere changes  from  the c y l i n d e r a x i s t o a d i s t a n c e from the a x i s equal t o 0.4 of the c y l i n d e r r a d i u s . crease i n k.  F u r t h e r e c c e n t r i c i t y causes an abrupt i n -  N o n s p h e r i c a l p a r t i c l e s , besides undergoing  t i o n , may a l s o d r i f t ect as f o r spheres  sideways.  rota-  The same c o r r e c t i o n f o r w a l l e f f -  i s a p p l i c a b l e t o n o n s p h e r i c a l p a r t i c l e s i f l\  i s used as the c h a r a c t e r i s t i c diameter  of the p a r t i c l e ( 5 4 ) .  The approximate form f o r equation 10, obtained by performing the d i v i s i o n and n e g l e c t i n g h i g h e r orders of D/D , i s t  F«= F(l+k §-)  (11)  25  The c o r r e s p o n d i n g c o r r e c t i o n f o r  Uo> = u ( l 0  The l a t t e r  was  account  (55).  has  at  low D / D ( < 0 . 1 ) t  At h i g h e r Reynolds  significant.  inertia,  is  (12)  f o u n d t o be v a l i d  becomes l e s s fluid  settling velocity  + k-g^)  creeping flow r e g i o n effect  free  in  the  numbers  The p r o b l e m , t a k i n g  been s t u d i e d by F a x e n and  wall into  others  (10). Wall effect  in multiparticle  solved t h e o r e t i c a l l y . include  the w a l l e f f e c t  index n of  equation  1.  found, with wall e f f e c t  s e t t l i n g has n o t  been  R i c h a r d s o n and Z a k i h a v e a t t e m p t e d for  sedimentation of  The same t r e n d as being important at  and a b s e n t a t h i g h R e y n o l d s n u m b e r s .  for  spheres free  in  to  the  settling  low R e y n o l d s  was  numbers  26  EXPERIMENTAL 1. Variables Studied ' The main object of the experimental work was  to i n -  vestigate the effect of p a r t i c l e shape on hindered s e t t l i n g in creeping flow and Klumpar.  testing the correlation of Beranek and  Other effects such as segregation, which was  found  to have an appreciable effect on s e t t l i n g behaviour, were to be avoided as far as possible.  The  were hindered s e t t l i n g rate, u, and sity^.  Fixed bed porosity, € , D  Klumpar p l o t .  i s  experimental data collected the corresponding bed  poro-  required for the Beranek-  Since estimated free s e t t l i n g rate was  found to  be obviously d i f f e r e n t from the extrapolated va porosity of unity, data on free s e t t l i n g rate, u , 0  ed for spherically  isotropic particles.  the boundary on s e t t l i n g was  The  were c o l l e c t -  possible effect of  studied by performing tests on  the  same systems in columns of d i f f e r e n t s i z e s , the highest value of Dv/Dt being 0.045. 2.  Materials A.  Particle  It was  Selection  desirable to have p a r t i c l e s of uniform shape and  s i z e , a requirement which was The  impossible to f u l f i l l absolutely.  c r i t e r i a used for selecting p a r t i c l e size may  as follows.  On the one hand, the size had  be described  to be large enough  so that such e l e c t r o s t a t i c effects as f l o c c u l a t i o n were n e g l i gible and  individual p a r t i c l e shape could be e a s i l y observed.  On the other hand, a preliminary test showed that with the perimental method adopted, the p a r t i c l e size had  ex-  to be r e l a t i v e -  27  l y small i n order t o get uniform  suspension  of the p a r t i c l e s .  To a s s u r e t h a t s e t t l i n g was i n t h e c r e e p i n g f l o w r e g i m e , an e x t r e m e l y v i s c o u s l i q u i d was r e q u i r e d f o r t h e l a r g e r p a r t i c l e s . A g i t a t i o n of the suspension  t h e n became d i f f i c u l t .  Another  o b j e c t i o n t o t h e use o f l a r g e p a r t i c l e s was t h a t t h e r e l a t i v e l y large w a l l e f f e c t p o s s i b l y present  i n c r e e p i n g f l o w might  overshadow t h e e f f e c t o f p a r t i c l e shape.  The i n i t i a l i d e a was  t o manufacture a l a r g e q u a n t i t y o f a r t i f i c i a l p a r t i c l e s c u t from square and round r o d s .  Because o f t h e l e n g t h y  fabrication  time r e q u i r e d , however, use was i n s t e a d made o f n a t u r a l o r commercially  a v a i l a b l e p a r t i c l e s which conformed t o t h e above  r e q u i s i t e s as f a r as p o s s i b l e and, i n a d d i t i o n , were o f homogeneous d e n s i t y , f r e e r u n n i n g , n o n - h y g r o s c o p i c and i n s o l u b l e i n an a p p r o p r i a t e s e t t l i n g medium and washing B.  D i s c u s s i o n on  liquid.  Segregation  P e r f e c t l y monosize p a r t i c l e s a r e p r a c t i c a l l y to o b t a i n by v a r i o u s methods o f s i z i n g .  impossible  The degree o f s e g r e g a -  t i o n l b y s i z e w i l l be d i f f e r e n t f o r d i f f e r e n t s i z e  distributions,  and w i l l be a t t e n u a t e d a t h i g h e r p a r t i c l e c o n c e n t r a t i o n s . and  Davies (56) r e p o r t e d t h a t s e g r e g a t i o n by s i z e was  Kaye  observable  v i s u a l l y i n t h e s e t t l i n g o f a b i n a r y m i x t u r e o f two s e t s o f p a r t i c l e s h a v i n g a mode mean s i z e d i s t r i b u t i o n r a t i o o f about 1.3,  when t h e p o r o s i t y was h i g h e r than 0.6.  from two c o n s e c u t i v e  Binary  mixtures  f o u r t h r o o t s e r i e s T y l e r Screens have  been observed t o g i v e s i z e s e g r e g a t i o n i n f l u i d i z a t i o n  (57).  In a p r e l i m i n a r y t e s t i t was found t h a t a m i x t u r e o f s i z e d s a l t p a r t i c l e s from two c o n s e c u t i v e  fourth root series  28  screens, minor  the  size  smaller  fraction  in  the  showed t h e  was  top p o r t i o n of  the b e d .  mesh m i n e r a l p a r t i c l e s 107o  fourth root  screen  show t h a t t h e pecially ty  at  effect  of  The e f f e c t s t u d i e d by L o e f f l e r They found t h a t  This result  particle  only  57o.  cylinders  3 5 / 4 2  same  material  smaller  size  in  plotted  in  the  Figure 3 ,  significant,  emphasized the  s i z e d i s t r i b u t i o n was  and R u t h ( 3 3 )  using spherical  series  maximum s i z e d i s t r i b u t i o n o f  of  concentrated  es-  necessi-  particles.  fourth root  r a t e as c a r e f u l l y  final  the  s i z e d i s t r i b u t i o n was  sized of  the next  the  c o m p a r i s o n was  similar  The r e s u l t s ,  high porosity.  of u s i n g c l o s e l y  in  and a 9 0 7 . m i x t u r e o f  series.  Visual  size particles  settling  displayed  However,  A quantitative  mesh p a r t i c l e s ,  4 2 / 4 8  0.87.  difficult.  colored smaller  o b t a i n e d by s i m u l t a n e o u s l y  with  colored,  s e g r e g a t i o n up t o a p o r o s i t y o f  observation during s e t t l i n g sediment  o f w h i c h was  less  carefully  particles.  screen f r a c t i o n s , than  207.,  settled  with a at  ground s p h e r e s which had a d i a m e t e r  Thus f o u r t h r o o t  series  p r o d u c i n g " m o r i o s i z e s p h e r e s " as  far  screens are  the  same  variation  capable  of  as h i n d e r e d s e t t l i n g  is  concerned. C.  Separation  Two methods o f ional  sieving  elutriation. differences sieving,  on T y l e r  of  separating p a r t i c l e s fourth root  Liquid elutriation, i n hydrodynamic d r a g ,  since particles  s e p a r a t e d by  Particles,.  sieving.  of  series which was  different  were u s e d :  s c r e e n s and  separates  conventliquid  particles  introduced in addition shape may n o t  be  well  by to  29  -0.2  -0.15  -0.1  -0.05  0.0  L0G(€) Figure  3.  Comparison of S e t t l i n g Rates of S i z e D i s t r i b u t i o n s of P a r t i c l e s  Different  30  In s i e v i n g , about 400 grams of s o l i d was i n t r o d u c e d on t o the t o p s c r e e n .  A f t e r the f i r s t  t i o n s were c o l l e c t e d and f u r t h e r  s i e v i n g , the p a r t i c l e f r a c -  s c r e e n i n g was performed on these  primary f r a c t i o n s , u s i n g 100 gram samples obtained by combining l i k e f r a c t i o n s from s e v e r a l  primary s c r e e n i n g s .  Subsequent  s i e v i n g was c a r r i e d out f o r 10-minute i n t e r v a l s , u n t i l the change i n weight of each p a r t i c l e f r a c t i o n became n e g l i g i b l e . Blind sieves  were cleaned a f t e r each s i e v i n g .  S i e v i n g was  performed on a Ro-tap shaker. D,  Liquid Elutriation  L i q u i d e l u t r i a t i o n i s fundamentally p a r t i c u l a t e zation at high porosity,  fluidi-  where s e g r e g a t i o n by s i z e i s prominent.  I t was c a r r i e d out i n a g l a s s  column o f 4.6 cm. I.P.,  equipped  w i t h a s u p p o r t i n g screen S, and a screen gate G, as shown i n F i g u r e 4.  L i q u i d was s t o r e d  i n j a r A and was pumped t o the  column F through an e x p l o s i o n - p r o o f c e n t r i f u g a l pump P. The flow r a t e of l i q u i d was c o n t r o l l e d  by a diaphragm v a l v e D. The  l i q u i d , a f t e r p a s s i n g through the column, was r e t u r n e d t o the storage j a r from t h e o v e r f l o w H. water c o o l i n g  c o i l C.  Pump heat was removed by the  The f i n e p a r t i c l e s c a r r i e d over by the  l i q u i d were c o l l e c t e d on screen B.  Detailed  description  of the  e l u t r i a t i o n apparatus and i t s t e s t i n g i s r e p o r t e d i n Appendix II.  The method was capable of s e p a r a t i n g s p h e r i c a l  of d i f f e r e n t s i z e as e f f e c t i v e l y as f o u r t h r o o t  particles  series  Tyler  screens. The sieved  p a r t i c l e s which underwent e l u t r i a t i o n were a l l  as d e s c r i b e d above.  An a p p r o p r i a t e q u a n t i t y of p a r t i c l e s  31  Figure  4„  Schematic Apparatus  Drawing  of L i q u i d  Elutriation  32  t o -make a f l u i d i z e d bed o f p o r o s i t y a b o u t  0.95 i n the  available  /  l e n g t h was  introduced into  on a n d . e l u t r i a t i n g  the  l i q u i d was  column.  C o o l i n g w a t e r was  circulated  through the u n i t ,  f l o w r a t e b e i n g c o n t r o l l e d by a d j u s t i n g t h e The q u a n t i t y r o u g h l y by t r i a l particles. of the  In  a certain  particles  and e r r o r  a trial,  quantity  screen gate  on t h e  the  of  closed,  on top of  particles  the  the  same c o l u m n .  The t o p m o s t p a r t  visual which larger  ual  of  for  the  "smaller"  the  total  into trials  the  than i n the  of  the  same w e i g h t  of  c l o s i n g the  screen  E.  particles  particles  to  the  D e s c r i p t i o n of  beads, cubic  pellets, flaky  the  column.  If  were p e r f o r m e d  trial,  to a larger  u n t i l no  vis-  particles.  were s e p a r a t e d by f l u i d i z i n g final  by  r e c o r d e d bed h e i g h t  the  and  gate. the  Five kinds of p a r t i c l e s glass  those  collected  original particles  previous  the  The r e m a i n -  bed was a g a i n  s e g r e g a t i o n c o u l d be o b s e r v e d i n t h e r e m a i n i n g  Other batches  After  s e g r e g a t i o n by f l u i d i z i n g i n of  of  closing  size portion.  w h i c h was r e c o r d e d , a n d r e m o v i n g a  particles  set  f l u i d i z e d bed  was r e c o r d e d b e f o r e  observed, further  f l u i d i z i n g the  bed h e i g h t ,  quantity  of  c o l o r e d , and r e - i n s e r t e d  s e g r e g a t i o n was involved  batch of a given  s c r e e n g a t e were r e c o v e r e d .  were t e s t e d  screen gate,  determined  c o l u m n was d i s a s s e m b l e d a n d  ing p a r t i c l e s  the  first  its  valve.  t o be removed was  t o t a l height  t o remove t h e  s c r e e n g a t e was particles  of  turned  salt  (NaCl)  b o t h of w h i c h a r e  sugar c r y s t a l s ,  Particles were u s e d . crystals  They w e r e :  and c u b i c ABS  i s o m e t r i c and s p h e r i c a l l y  and i m p e r f e c t  spherical copolymer  isotropic,  octahedron-shaped mineral  33  (silicate) crystals crystals).  (henceforward r e f e r r e d t o as m i n e r a l  T h e i r p r o p e r t i e s are d e s c r i b e d i n T a b l e 3, and  t h e i r shapes are i l l u s t r a t e d i n F i g u r e 5.  Table 3 P r o p e r t i e s of P a r t i c l e s Particle shape  Materials  Spherical  g l a s s beads  Cubic  salt  ABS Flaky  crystals  pellets  sugar  Angular  crystals  mineral crystals  S i z e , By cm  Density g/cm  Run  0.0492  2.959  7  0.114  2.977  1,2  0.0282  2.161  5  0.0341  2.169  3  0.0391  2.163  4  0.288  1.061  6  0.113  1.590  12  0.135  1.590  11  0.0426  2.632  10  0.0508  2.632  9  The g l a s s beads were p r a c t i c a l l y s p h e r i c a l . c r y s t a l s were c u b i c i n shape, w i t h rounded twin c r y s t a l s were p r e s e n t .  No.  J  Most of the s a l t o f f corners.  A  few  The ABS p e l l e t s , which had been  o r i g i n a l l y chopped from p l a s t i c rods and o c c a s i o n a l l y contained pores w i t h i n the p a r t i c l e s , were used without f u r t h e r  treatment.  They were not p e r f e c t cubes, but they were uniform i n shape and size.  The  sugar c r y s t a l s d i d not have any plane of symmetry and  xl2  xl2 G l a s s b e a d s , Run  7-3  S a l t c r y s t a l s , Run 4-  F i g u r e 5.  G l a s s b e a d s , Run  1,2-  ABS  6-  Photographic P i c t u r e s of  p e l l e t s , Run  Particles  35  x5 Sugar c r y s t a l s ,  Run  12-3  Sugar c r y s t a l s ,  Run  11-  x24 Mineral  crystals,  Run  10  x24  x24  Discarded mineral c r y s t a l s from l i q u i d e l u t r i a t i o n , Run 10-  Figure  5.  Photographic  Discarded mineral c r y s t a l s from l i q u i d e l u t r i a t i o n , Run 9-  P i c t u r e s of P a r t i c l e s  (continued)  36 d i f f e r e d m a r k e d l y f r o m s p h e r e s o r g r a n u l e s ; and t h e  mineral  crystals  of  longer  than the  other  imperfect  grown  two a n d a p p e a r e d t o be l e s s u n i f o r m t h a n the  other p a r t i c l e s . the  o c t a h e d r o n h a d one a x i s  The p a r t i c l e s  sugar c r y s t a l s  other  than the g l a s s  had m i c r o s c o p i c a l l y rough s u r f a c e s ,  p r o t u b e r a n c e s were s m a l l compared t o t h e p a r t i c l e and i t  is  mically  therefore  likely  that  the p a r t i c l e s  but  and the  dimensions,  were h y d r o d y n a -  smooth. The b e h a v i o u r  basis  beads  for  w i t h the  of  particles  of  free  settling  i n the  results  literature.  was u s e d a s same shape  different  were u s e d b e c a u s e c u b e s a r e  and because available  spherical particles  c o m p a r i s o n w i t h o t h e r work on ithe behaviour  particles  of  for  shape.  spherically  a  and  Cubic  isotropic,  such p a r t i c l e s  Thus c o m p a r i s o n s w i l l  are be more  significant. The g l a s s ing;  subsequent e l u t r i a t i o n  Sugar  crystals  ation.  and m i n e r a l  The raw p a r t i c l e s  crystals,  besides  shaped m a t e r i a l sieving. cles ing.  beads and s a l t  d i d not crystals  of  which c o u l d not crystals  with rough s u r f a c e s ,  About  separation.  were s i e v e d b e f o r e  elutri-  some b r o k e n brittle  needle-  be c o m p l e t e l y removed by  w h i c h were s t i l l  10-20% o f  siev-  c o n t a i n e d some i r r e g u l a r  T h e s e unwanted p a r t i c l e s  elutriation  show i m p r o v e d  b e i n g c o n t a m i n a t e d by o t h e r  The m i n e r a l  liquid.  were s i z e d by  sugar contained  of  removed by l i q u i d e l u t r i a t i o n . tion  crystals  present a f t e r  siev-  odd shape o r s i z e were  Benzene was u s e d a s an the p a r t i c l e s  from each s e t a f t e r  parti-  sieving.  elutria-  were removed by  37  F.  Test  Liquids  The t e s t preferably storage.  of  show v i s c o s i t y Test  ethylene  l i q u i d s h a d t o be N e w t o n i a n stability  with respect  l i q u i d s u s e d were w a t e r  for  s o l u b l e i n aqueous s o l u t i o n . was t h a t  the  blending.  The o i l  to  to time  of  those p a r t i c l e s of  these  c o u l d be o b t a i n e d by  glycol-water  t e s t e d a n d f o u n d t o behave as N e w t o n i a n the  experimental range.  3.  Apparatus was  Details  carried  are  out  columns w i t h v e r t i c a l  b o t t o m ends o f  the  of  different  directions,  sity  of  fitted  glass  Thus t h e  by m e a s u r i n g t h e  given  final  the p a r t i c l e s . with threaded  bed h e i g h t ,  flanges,  The b o t t o m s u r f a c e s  trapped a i r  Holes of flanges  and e x c e s s  appropriate at  accurate  liquid  flanges. in  calculated and d e n -  c o l u m n were to  threaded  t h e p l u g s were  with-venting  valves  slightso  c o u l d e s c a p e on t i g h t e n i n g .  s i z e were d r i l l e d positions  of  The  practically  w h i c h were a c c e s s i b l e  c o n i c a l and t h e a p e x e s were f i t t e d  that  walls.  knowing t h e w e i g h t the  III.  significantly  c o u l d be  The t o p e e n d s o f  in  flat-  blind  column w a l l s were  bed p o r o s i t y  were  least  long,  cylindrical  of  Newtonain  i n Appendix  columns d i d n o t v a r y and the  final  plexiglass plugs. ly  suitable  l i q u i d s , at  columns were c l o s e d by f l a t  Diameters  straight.  liquids  solutions  i n two-foot  bottomed g l a s s  the  were  s o l u t i o n s , w h i c h were m i s c i b l e m i x t u r e s  The 457o p o l y e t h y l e n e  Settling  grades  which  two N e w t o n i a n h y d r o c a r b o n l i q u i d s , were n a t u r a l l y liquids.  poly-  different  The a d v a n t a g e s  desired viscosity  and  s o l u t i o n s of  g l y c o l , and b l e n d e d s o l u t i o n s o f  automobile crank case o i l  fluids  i n the  for mounting.  t o p and bottom Paper  scales  gra-  38  duated to one m i l l i m e t e r were f i x e d to the column, and  several  movable h a i r l i n e s made from cellophone were p r o v i d e d f o r easy v i s u a l i z a t i o n during timing. F i v e columns of d i f f e r e n t available,  i n t e r n a l diameters were  i n order t o o b t a i n r e s u l t s at d i f f e r e n t p a r t i c l e to  column s i z e r a t i o s .  The mean diameter of each column  was  determined from d i r e c t measurement of diameters i n d i f f e r e n t directions.  The volume of each column was  weight of water which  filled  calculated  the empty column. • The  from the  diameter  and volume of each column i s shown i n Table 4.  Table 4 Dimensions Column No.  of S e t t l i n g Columns Mean i n s i d e diameter, cm  Volume cm3  1  2.54  313  2  3.78  692  3  5.08  1250  4  7.71  2877  5  10.12  4893  The assembly Each column was  of the apparatus i s shown i n F i g u r e 6.  mounted on the s u p p o r t i n g frame, with space  a l l o w a b l e f o r more than one column to be t e s t e d s i m u l t a n e o u s l y , and was  c a r r i e d on an angle i r o n rack a t p i v o t , 6.  The  1 SETTLING  COLUMN  6 PIVOT  2 COLUMN P L U G 3 LIQUID V E N T I N G  7 CLANKING H A N D L E VALVE  4 COLUMN-SUPPORTING F R A M E 5  STOPWATCH  F i g u r e 6.  8 STOPPING C L A M P 9  S U P P O R T I N G HOOK  10 SUPPORTING  BOLTS  Assembly Drawing of S e t t l i n g A p p a r a t u s  40  s u p p o r t i n g frame could be cranked  by handle,  7, and s e t v e r t i c a l  by the stopping clamp, 8, which was r e l e a s e d d u r i n g  cranking.  To assure a v e r t i c a l p o s i t i o n of the column d u r i n g s e t t l i n g , the u n i t was p l a c e d on a h o r i z o n t a l s u r f a c e a d j u s t e d by a l e v e l . Hooks, 9, and b o l t s , 10, were a c c u r a t e l y l o c a t e d d u r i n g  fabrica-  t i o n i n such a p o s i t i o n t h a t any o f the columns was i n a v e r t i c a l p o s i t i o n when mounted on i t .  The p o s i t i o n of the stopping  clamp was a d j u s t a b l e f o r v e r t i c a l alignment 4.  Experimental A.  o f the columns.  Procedures  P a r t i c l e S i z e Measurement  P a r t i c l e s i z e s were measured by three d i f f e r e n t methods. Small samples o f a p p r o p r i a t e s i z e were obtained by means of a sample  splitter. a.  A sample of about 1000 p a r t i c l e s was c o l l e c t e d ,  counted and weighed on an a n a l y t i c a l balance.  From the known  d e n s i t y of the p a r t i c l e s , the average volume o f a s i n g l e p a r t i c l e was c a l c u l a t e d .  The average s i z e of the p a r t i c l e s  c o u l d then be e a s i l y c a l c u l a t e d i f a p a r t i c l e shape was def i n e d i n the f i r s t b.  place.  P a r t i c l e s from a sample were s e t t l e d one a t a time  i n the same l i q u i d as used f o r the hindered  s e t t l i n g runs, a t  the center p o s i t i o n of one of the l a r g e r g l a s s columns.  The  temperature of the l i q u i d was recorded along with the s e t t l i n g rate.  From the...average v a l u e of uz/, a p a r t i c l e s i z e could be  calculated. c.  Samples of g l a s s beads and s a l t c r y s t a l s were  measured dn a microscope equipped with a prism t o p r o j e c t the  41 enlarged picture With a s u i t a b l e  of the p a r t i c l e s onto a ground g l a s s  combination of lenses, the s i z e of the enlarged  particles pictures,  w h i c h were o f t h e o r d e r o f an i n c h ,  be m e a s u r e d by V e r n i e r c a l i p e r s . i n an a r b i t r a r y  screen.  could  The g l a s s b e a d s w e r e m e a s u r e d  but c o n s i s t e n t d i r e c t i o n .  The s a l t  crystals  were measured i n b o t h d i r e c t i o n s  p a r a l l e l t o t h e i r two e d g e s .  The m e a s u r e m e n t s w e r e c a l i b r a t e d  a g a i n s t a gage o f s i z e  the  B.  T h i s measurement General  i s r e p o r t e d i n A p p e n d i x X.  Procedure  E x p e r i m e n t s w e r e s e t up t o f i n d t h e h i n d e r e d  bed  a t v a r i o u s bed p o r o s i t i e s , as w e l l as t h e f i n a l porosity,  shapes. had  mm.,  image o f w h i c h was p r o j e c t e d o n t o t h e s c r e e n a n d m e a s u r e d  similarly.  rate  1  o f homogeneous p a r t i c l e s o f d i f f e r e n t  I t was e s s e n t i a l  that the i n i t i a l p a r t i c l e  settling settled sizes  suspension  uniform concentration corresponding to the o v e r a l l  t h r o u g h o u t t h e c o l u m n , a n d t h a t t h e c o l u m n was position  during s e t t l i n g .  were r e s p e c t i v e l y Westphal balance.  and  voidage  in a vertical  The v i s c o s i t y a n d d e n s i t y o f l i q u i d s  m e a s u r e d by C a n n o n - F e n s k e v i s c o m e t e r s a n d The p a r t i c l e d e n s i t y was d e t e r m i n e d by  conventional s p e c i f i c gravity d e s c r i b e d i n Appendix IV.  bottles.  These measurements a r e  The r o u t i n e p r o c e d u r e s u s e d were a s  follows: a.  Samples were t a k e n from t h e s p e c i f i e d  p a r t i c l e s i n o r d e r t o measure p a r t i c l e b.  size.  D e n s i t y o f t h e p a r t i c l e s was a l s o  q u a n t i t y of p a r t i c l e s required highest desired porosity, quired for specified  set of  measured.  The  f o r a column t o a t t a i n t h e  and t h e subsequent increments r e -  l o w e r p o r o s i t i e s , w e r e w e i g h e d on a  scale  42  having a s e n s i t i v i t y accumulated e r r o r cles  of at  least  i n weight  was  + 0.05 grams.  The p o s s i b l e  c h e c k e d by w e i g h i n g t h e  remaining. c.  Based on t h e measured p h y s i c a l p r o p e r t i e s  s o l i d and the a p p r o x i m a t e d e n s i t y required viscosity  of  the  of  liquid for  the  centration  of  liquid  test  liquid,  of v i s c o s i t y  solution, a,suitable  quantity  cosity  at  at  room t e m p e r a t u r e  intervals  of  room t e m p e r a t u r e d.  test  vs.  of  liquid.  tiny  b u b b l e s t o be r e l e a s e d  air  then f i l l e d with excess v e n t i n g v a l v e when t h e the  system.  liquid  The the  the h i g h e s t  range  porosity  the  particles  from the  for  liquid.  w h i c h was v e n t e d  started  again u n t i l  on  completely  entrained  The c o l u m n was through  p l u g was t i g h t e n e d t o e x c l u d e a i r  A g i t a t i o n was  vis-  experiments.  s t a n d i n g was a l l o w e d  liquid,  test  The s u s p e n s i o n was a g i t a t e d  s u p p o r t i n g frame by c r a n k i n g t o g e t A s h o r t p e r i o d of  con-  t h e maximum c o n c e i v a b l e  required for  wetted.  estimated;  was m e a s u r e d , a s was  t o be e n c o u n t e r e d i n t h e  The p a r t i c l e s  were s o a k e d i n t h e the  1°F. o v e r  the  the  l i q u i d was p r e p a r e d w i t h t h e r e q u i r e d c o n c e n t r a t i o n . l i q u i d density  of  c r e e p i n g f l o w was  and f r o m a p r e - c o m p o s e d e m p i r i c a l c h a r t  of  parti-  particles  the from and  came t o t h e r m a l e q u i l i b r i u m w i t h t h e room t e m p e r a t u r e .  The t e m p e r a t u r e  of  the  l i q u i d was  t h e n measured by t h e  t h e r m o m e t e r w h i c h h a d been u s e d i n t h e v i s c o s i t y e.  The c o l u m n was  cranked c a r e f u l l y  speed and c o n s t a n t  observation u n t i l  out the  believed  c o l u m n was  set v e r t i c a l l y . interface  had f a l l e n  several  measurements,  w i t h an  appropriate  uniform suspension through-  t o h a v e been a t t a i n e d .  T i m i n g began a f t e r  same  the  It  was  then  supernatant-suspension  centimeters.  Two s t o p w a t c h e s ,  one  43 o f w h i c h hung on t h e Height  of  interface  s t r i n g beside  After  the  settling  h a n g i n g w a t c h was still  a certain height, r a t e range  estimated  from a f i r s t  s t o p p e d , w h i l e the  used f o r r e c o r d i n g h e i g h t  particle  c o l u m n , were  trial,  and t i m e .  within the non-  string  was  Observation Those t r i a l s  of which  c i r c u l a t i o n were d i s c a r d e d .  f;  The t i m i n g was u s u a l l y  the r e s u l t  t o be  one on t h e  m o t i o n c i r c u l a t i o n was r e p o r t e d .  had o b v i o u s  started.  and c o r r e s p o n d i n g t i m e were r e c o r d e d  constantly. constant  the  was  satisfactory  c i r c u l a t i o n and c o n s t a n t  by t h e  rate  repeated at criteria  settling.  least  o f no  once  if  obvious  Otherwise  more  trials  were p e r f o r m e d . g. every  The t e m p e r a t u r e  two t r i a l s .  Airrwas  of  the  l i q u i d was measured  e x c l u d e d from the  e a c h o p e n i n g and r e t i g h t e n i n g  of  the p l u g f o r  liquid  after  after  temperature  i  measurement.  F i n a l "bed h e i g h t  s e t t l i n g were r e c o r d e d a f t e r long  and a p p r o x i m a t e d u r a t i o n  the  of  s u s p e n s i o n had s e t t l e d  for  porosities,  of  a  period. For  particles  e x p e r i m e n t s on l o w e r  were added and t h e p r o c e d u r e  increments  from s t e p d .  was  repeated. C.  E x p e r i m e n t a l T e c h n i q u e and Data  After  the  Selection c o l u m n was  cranking motion, c i r c u l a t i o n observed, of  the  cranking.  Settling  set v e r t i c a l of  the  from i t s  s u s p e n s i o n was  rotary often  d i r e c t i o n b e i n g always o p p o s i t e to the  direction  An u n r e p r o d u c i b l y h i g h s e t t l i n g v e l o c i t y  would  44  then r e s u l t .  The c i r c u l a t i o n phenomenon, i l l u s t r a t e d i n  F i g u r e 7 , may be e x p l a i n e d a s f o l l o w s .  F i g u r e 7.  I l l u s t r a t i o n of Circulation  Suspension  B e f o r e t h e column i s s e t v e r t i c a l , i t i s i n an i n clined  position,  the lower  d u r i n g which  particles  s i d e o f t h e column w a l l .  o f f e r e d by t h e w a l l ,  the p a r t i c l e s  start settling  onto  Because o f t h e o b s t r u c t i o n c a n o n l y move by " s l i d i n g  down" a l o n g t h e w a l l t o t h e b o t t o m o f t h e t u b e , t h e l i q u i d d i s p l a c e d b e i n g f o r c e d upward a l o n g t h e upper w a l l and t h e r e b y creating circulation  i n the opposite d i r e c t i o n  to the cranking.  By t h e t i m e t h e c o l u m n h a s b e e n s e t v e r t i c a l , t h i s m o t i o n persists  u n t i l i t s force i s f u l l y Circulation  i n the d i l u t e  still  damped. s u s p e n s i o n was more v i g o r o u s  than t h a t i n the concentrated suspension, but both cases  could  45  result  in a faster  culation  initial  and i n v a l i d a t e d  concentration*  velocity  diluted  tendency  for  with a gentle late,  the  slight  introduced unpredictable  trouble  This  circulation.  action,  c o l u m n was inclination  circulation,  after  t e c h n i q u e was  dency.  For  tribution the  c a u s e d by the  fine  of  swung s l o w l y in  on  which  successful  n o t e d by P e a r c e  to at  of  t o p r o d u c e an  slowly  stage  the  to  opposing  vertical. ten-  t h e m o t i o n and c o n c e n t r a t i o n  dis-  to v i s u a l i z e  by e y e ,  column d u r i n g s e t t l i n g even i f  beginning.  the  some o f  c h e c k e d by a  T h i s phenomenon h a d  In  a diffuse  while tiny  been  column  the  column.  When i t  t o get was  the  rise  downward  important  ex-  large  during  bubbles which  w i t h the  in  liquid, a  interface  air  c r a n k i n g was  form suspension throughout  the  successful  the v i s c o u s  can i n t e r f e r e  The s p e e d o f  did  level.  column.  settling,  also  above method  The v e r t i c a l p o s i t i o n i n g o f  during s e t t l i n g  particles.  circu-  circulation  develop,  (58).  from the  of  set  i n damping t h e  the  bubble always i n t r o d u c e s  early  vertical  opposite d i r e c t i o n  The e x p e r i m e n t a l method a d o p t e d was cluding air  set  watching  were c o l o r e d .  circulation  therefore  i n the  was a g a i n g e n t l y  w h i c h were d i f f i c u l t  particles  avoid  it  speed and  motion  suspension tended to  s u c h a way as  particles,  caused c i r c u l a t i o n  air  the  forces  cranking  The column was  b u t when t h e  Any i n c l i n a t i o n  was  initial  the upper p o r t i o n of  was m i n i m i z e d by c r a n k i n g w i t h a s u i t a b l e  a  cir-  particles. The c i r c u l a t i o n  the  than without  the assumption of u n i f o r m  Circulation  bed and u n d o u b t e d l y a l s o the  settling  too  moving a  unifast,  46  a  centrifugal  a c t i o n was  i n t r o d u c e d and c o n c e n t r a t i o n  suspension at  b o t h ends was o b s e r v e d v i s u a l l y ,  was  the p a r t i c l e s  too slow,  end o r k e e p on c i r c u l a t i n g column.  Acceptance  of  would e i t h e r  if  it  concentrate  at  one  pective any of  sedimentation of  theory  t h e mode o f  initially constant  the  settling  settling  rate,  which  line  tial  s e c t i o n at  constant rate p e r i o d .  such a p l o t  curves  (implying  opposite)  a test  was  intervals was  within  end o f  the  the  were d i s c a r d e d .  D.  or  initial  constant  concave  being r a r e l y  settling  with  ini-  concentrated downward  The s e t t l i n g  rate  duration  rate and  of  time  period.  higher  t h a n 57. and  Processing the  liquid varied  temperature among t h e  f r o m one p o r o s i t y  was n o t tests  controlled,  viscosity  on a g i v e n p o r o s i t y ,  to a n o t h e r .  It  s e l e c t i o n method was  37*.  Data  sides varying  the  from c o r r e s p o n d i n g h e i g h t  standard deviation  Because the  therefore  An example o f  ( i m p l y i n g more bed)  period  specified  Those t e s t s  f o u n d t h a t t h e r e p r o d u c i b i l i t y by t h i s  usually within  of  lower  then c a l c u l a t e d  acceptable,  curve,  experiments,  each t r i a l .  c o n c a v e upward  the  should  the present  for  the  beginning, for  included in Appendix XII.  suspension at the  time p l o t  based  Irres-  flux-concentration  the  In  t i m e was p l o t t e d  is  settling  judgement,  corresponds to  have a s t r a i g h t  height versus  require-  u n i f o r m s u s p e n s i o n s h o u l d h a v e an i n i t i a l  The h e i g h t v e r s u s  the  the  d i s c u s s e d i n A p p e n d i x I.  concentration.  of  of  conformed to the  ment o f u n i f o r m c o n c e n t r a t i o n was by i n d i r e c t on t h e  the  while  about the middle p a r t  data which  of  In  order  that  be-  47  v i s c o s i t y n o t become a n a d d i t i o n a l of  s e t t l i n g rate  a l o n e was t r e a t e d  with porosity, as a v a r i a b l e  shown i n A p p e n d i x V I .  parameter  i n the correlation  t h e p r o d u c t uv i n s t e a d  of u  independent o f temperature, as  For those t e s t s  v a r i a t i o n was n o t e d , t h e a r i t h m e t i c  i n which  temperature  mean o f t h e t e m p e r a t u r e  b e f o r e a n d a f t e r a t e s t was u s e d t o c a l c u l a t e  the v i s c o s i t y .  The v i s c o s i t y a t a n y t e m p e r a t u r e was o b t a i n e d b y l i n e a r i n t e r polation  from a s e r i e s  of temperature-viscosity data which brac-  keted the experimental temperature. on v i s c o s i t y o f t h e t e s t per  °F. b e i n g t y p i c a l .  T e m p e r a t u r e h a d much  l i q u i d s , a change o f about 3 p e r c e n t In the f i n a l  v a l u e o f uv a t one p o r o s i t y  correlation  the average  was u s e d .  Similarly, i n calculating the size of particles several  measurements of f r e e  as a product i n s t e a d  effect  from  s e t t l i n g v e l o c i t y , uv was a v e r a g e d  o f u and v i n d i v i d u a l l y .  48  RESULTS AND DISCUSSION 1.  General Experimental results for uz/ at different  for various runs on d i f f e r e n t shapes and different  porosities particle-to-  column diameter r a t i o s are reported.in Appendix VII.  For each  run, average values of uv at each porosity were plotted as log  uv against log e .  It was found that a straight  l i n e could be  drawn through the data i f one or a few points i n the d i l u t e r e gion were l e f t out i n the c u r v e - f i t t i n g .  The best straight  lines  were drawn through the data by the least squares method, using loge as the independent  variable.  Those data i n the d i l u t e  region which had to be l e f t out i n the straight were obvious from the p l o t .  line f i t t i n g  They invariably turned out to be  more than 67« lower than the values from the accepted best f i t equation.  For the runs l i k e Run 11- and Run 12-, where the data  were i n t r i n s i c a l l y more scattered, data i n the d i l u t e region which deviated s l i g h t l y more from the estimated best f i t values were s t i l l accepted. Results were presented i n the above form because of i t s simplicity. collected  Data on sedimentation and particulate f l u i d i z a t i o n  from the l i t e r a t u r e (29, 30, 33, 42) showed that, by  discarding a few data i n the very d i l u t e and very concentrated regions, straight Reynolds numbers.  line f i t t i n g was acceptable even at higher By correlating  i n t h i s manner, p a r t i c l e shape  and particle-to-column diameter r a t i o were expected to show their effect i n the index n. The processed data are presented i n Appendix VIII. slopes of the f i t t e d straight  The  lines i n the log uv -log€ p l o t s ,  49 and t h e i r respective 95% confidence l i m i t s , were calculated. The possible e f f e c t of the wall was studied by comparing the results obtained for d i f f e r e n t particle-to-column diameter r a tios. The value of ( u i / )  e x t  , obtained by extrapolating the  least squares l i n e s to a porosity of unity, and their respective 95% confidence l i m i t s , were calculated and compared to the experimental free s e t t l i n g results (Appendix IX) for the glass beads, salt c r y s t a l s and ABS p e l l e t s , the shape factors of which were a l l known.  The corresponding Stokes p a r t i c l e sizes were  compared with microscopic size measurements (Appendix X) and results from weighing p a r t i c l e samples. The method suggested by Beranek and Klumpar (50), that of using fixed bed porosity i n order to account for shape v a r i a tion i n c o r r e l a t i n g s e t t l i n g data on p a r t i c l e s of d i f f e r e n t shapes, was tested. According to equation 2a, using D  v  as p a r t i c l e  a linear relationship exists between log u and D /D v  porosity.  t  diameter,  at a fixed  Thus, for the present linear extrapolation of log uv  versus Dv/Dt  t  o  zero D /D , at constant € , should eliminate any  wall effect present.  v  fc  However this method i s not appropriate to  the present data because of the v a r i a t i o n of uv within a t e s t , and because of the limited number of values of D /D v  t  a v a i l a b l e , which  may give rather uncertain extrapolation. The v a r i a t i o n of uv i n the o r i g i n a l data might be due to experimental error, including the d i f f i c u l t y of getting absolutel y uniform suspensions.  From the respective average values of  uv , a wall e f f e c t appears to manifest i t s e l f , but not prominently.  50 The r e s u l t s sented below. used i n the 2.  In  f o r the  all  l o g nv-loge  curve-fitting  Index n f o r H i n d e r e d A.  Spherical  The s e t t l i n g summary o f r e s u l t s shows t h e pective  least  correction  from Appendix V I I I  (equation  effect, al  the lay  plotted  values  of  in Figures is  the  given  8 a - 8 g , and a  in Table  with their  res-  the g l a s s  b e a d s were  all  limits.  2a),  of n f o r  but  s l i g h t l y higher  without  4.65  calculated outside  which  5,  index n,  s u g g e s t e d by R i c h a r d s o n and Z a k i  son-Zaki v a l u e of Run 7-3,  s o l i d p o i n t s were n o t  Beads  data are  squares  than those  pre-  Settling  The m e a s u r e d v a l u e s lower  plots,  are  calculation.  Glass  confidence  95%  f i v e kinds of p a r t i c l e s  the  957o  than the  wall correction.  Richardson-Zaki confidence  (43)  For  with  wall  Richard-  all  but  i n d i c e s , assuming w a l l limits  of the  experiment-  values. In  particles  Figure  9,  average  settling  in  columns o f  for wall effect. except  i n the  appear  reversed.  ratios  are  of n f o r  plotted  R i c h a r d s o n and Z a k i why t h e v a l u e s from those o f criterion  Runs  1-2  (43)  trends  and 1-3,  different  in Figure  o f uv  different  The q u a l i t a t i v e  case of  Values  values  10,  for  the  sizes are  seem t o be  experiments are is  f o r a c c e p t i n g or r e j e c t i n g  o p p o s e d t o t h e methods o f e i t h e r  probably the settling  which  diameter  recommended by  included for comparison.  R i c h a r d s o n and Z a k i  reasonable  particle-to-column line  of  compared  the p o s i t i o n s of  with the  of n i n the p r e s e n t  same s e t  The  reason  different rigorous  data used h e r e ,  s i m p l y t i m i n g an i n i t i a l  as  sett-  51  Table 5 Summary o f R e s u l t s f o r S p h e r i c a l Glass Beads  I>v»  Run No. 1-1  n with 957» Confidence l i m i t s  cm  0.114  Eqt. 2a, n = 4.65 4 19.5 D / D  0.045  4.97 + 0.35  5.53  1-2  0.030  4.83 + 0.11  5.24  1-3  0.022  4.82  0.09  5.08  2-1  0.045  4.68 + 0.32  5.53  2-"2  0.030  4.74 + 0.37  5.24  2-3  0.022  4.67 + 0.16  5.08  0.0097  4.69 + 0.16  4.84  7-3  0.0492  4  Table 6 Summary of R e s u l t s f o r Cubic Particles Salt  n w i t h 957. Confidence l i m i t s  Dv cm  Dv/D  5-3  0.0282  0.0056  5.45 + 0.08  3-lA  0.0341  0.0134  5.54 + 0.12  3-2  0.0090  5.50 + 0.09  3-3  0.0067  5.38  4  0.07  3-4  0.0044  5.24  4  0.06  0.0103  5.55  4  0.07  0.0077  5.49  4  0.05  0.0374  5.44  4  0.13  0.0285  5.45 ± 0.22  Run No.  4-2  0.0391  4-3 ABS  Particles  6-4 6-5  0.288  t  t  1  1  r  i  i  i  R U N 1-2  -0.2  -0.16  -0.12  -0.08  -0.04  0.0  L06(€) a„  D  v  Figure  = 0 1 1 4 cm, D / D t = 0 . 0 4 5 o  8„  v  Logu^-loge Plot  of  Glass  i  1  -0.2  b,  1 -0.16  D  v  Beads i n . 40 % PEG  1  1 -0.12  i  L0G(€)  -0.08  = 0 . 1 1 4 cm, D / D v  i, I  -0.04  t  = 0 030 o  0.0  J  -0.2  -0.16  -0.12  -0.08  -0.04  0.0  -0.2  1  1  -0.16  LOG(€ )  D  v  v  F i g u r e 8c  a  1  I  -0.12  -0.08  I  1  L  -0.04  0.0  LOG(e)  = 0 1 1 4 cm, D /D 0  1  t  = 0.022  Loguz/-logc P l o t of Glass Beads i n 4 0 % PEG  D  v  = 0 1 1 4 cm, D /Dt - 0 0 4 5 0  v  o  F i g u r e 8 d . Logul/-log€ P l o t of G l a s s Beads i n 4 5 % PEG  2.0 h  CD O  I  -0.2  -0.16.  -0.12  -0.08  -0.04  0.0  i  -0.2  I  i  -0.16  LOG(e)  D  v  I  I  -0.12  I  i  -0.08  i  -0.04  i  I  0.0  LOG(e)  = 0.114 cm, D /D v  t  = 0.030  F i g u r e 8e„ Loguz/-log € P l o t of Glass - ' beads i n 45% PEG  D  v  = 0 114 cm, D /D 0  v  t  = 0„022  F i g u r e 8 f . LoguJ/-log€ P l o t of G l a s s . . . :. Beads i n 45% PEG .  !pi  1.5  0.3  1  I  1  -0.2  '  -0.16  I  i  -0.12  i  I  -0.08  i  i  -0.04  I  0.0  L0G(€) D  y  «= 0.0492 cm, D / D = 0.0097  Figure  t  8g„ L o g u i z - l o g e P l o t o f G l a s s Beads i n 3 5 „ 4 % PEG  LL nn  56  L0G(«) -0.2  -0.15  -0.1  -0.05  0.0  i—i—i—i—n—r—i—r~i — i — r  i — i — r  2.0 SYMBOL 1.9  1.8  RUN NO.  Dv/Dt  o  0.045  o  0.030  +  0.022  1-3  X  o +  A A  1.7  X  1.6  3  A  1-5  o LJ  .ft  A 1.4  1.3  1.2  SYMBOL  ©  Dv/Dt  RUN NO.  L  0.045  2-1  A  0.030  2-2  0.022  2-3  .0  0.9  J  L -0.2  L -0.15  I  L  -0.1  -0.05  L O G (e)  F i g u r e 9 . W a l l E f f e c t on G l a s s Bead S e t t l i n g  0.0  [_l 7.0  I  I o a  6.5  I | I  I  I I | I I I I | I I  SPHERICAL, GLASS - CUBIC, SALT  I I | I I  I I | I  I I I  l I  I  | I I I  I | i_  i  1 I  I  BEADS  CRYSTALS S  ABS  A  ANGULAR, MINERAL  a  FLAKY,  -  USED IN CURVE FITTING OF  SUGAR  I I | I  PELLETS  CRYSTALS  CRYSTALS EQT. 13  6.0  4.5 I 0.0  0.005  0.01  0.015  i  I  I  1 M  0.02  I  I  I  1 1 l  0.025  I  1 I 1 I I  0.03  Dv/Dt Figure  10.  R e s u l t s of n P l o t t e d a g a i n s t D /Dt v  I  i i  0.035  i  0.04  I  I  0.045  58 l i n g p e r i o d , or drawing a tangent curve and The  to any i n i t i a l  settling  computing the constant s e t t l i n g r a t e from t h i s  former method was  a p p a r e n t l y used by Richardson  and  tangent. Zaki.  E i t h e r method would have g i v e n a v a r i a t i o n as l a r g e as 107. i n the present  experiments.  B.  Cubic S a l t C r y s t a l s and ABS  Pellets  R e s u l t s f o r c u b i c shape p a r t i c l e s are p l o t t e d i n Figures l l a - l l i  and  summarized i n T a b l e 6, the d e t a i l of which  are i n Appendix V I I I . The  s l o p e s of the best s t r a i g h t l i n e s , g i v e n by the  index n, were c o n s i s t e n t l y h i g h e r than those f o r the g l a s s beads, as shown i n F i g u r e 10. averaged  F i g u r e 12 i s a p l o t of the  data f o r p a r t i c l e s of the same s i z e s e t t l i n g i n columns  of d i f f e r e n t diameters. the w a l l was  In t h i s range of D /D , the e f f e c t of v  t  a g a i n not prominent, p a r t i c u l a r l y a t h i g h p o r o s i t y  where the p o i n t s o v e r l a p p e d .  D i f f e r e n c e s i n v a l u e s of the i n -  dex n mainly arose from the d i f f e r e n c e s i n s e t t l i n g r a t e a t porosity.  No d e f i n i t e t r e n d c o u l d be observed  However, by i g n o r i n g Run runs on the ABS  3-4  given  two  p e l l e t s , and p l o t t i n g n f o r each run a g a i n s t l i n e f i t to the p o i n t s  by  n = 5.33  + 17.3  T h i s form of equation was Z a k i who  graphs.  on the s a l t c r y s t a l s and the  Dy/Dt, as i n F i g u r e 10, the best s t r a i g h t was  i n the  low  obtained  (13) suggested  by Richardson  and  -0.16  -0.2  -0.12  -0.08  -0.04  0.0  L0G(€)  LOG(e) D  y  = 0.0341 cm, D / D  Figure  v  t  = 0 0134 0  lla„ L o g u i / - l o g e P l o t o f S a l t Crystals i n O i l  D  v  = 0.0341 cm, D / D t  Figure  v  llb  0  = 0,009  LoguI/-loge P l o t o f S a l t Crystals i n O i l  * *°  i  RUN  r  "i  1  1  r  3-4  0.4 CD O  -0.2  -0.16  Figure  0.0341 cm,  i _i i  -0.12  -0.08  -0.04  0.0  L0G(€)  LOG(€) Dv =  j  D / D t = 0,0067 v  11c„ LoguZ/-log€ P l o t o f S a l t Crystals i n O i l  D  v  = 0,0341 cm,  Figure  D / D t = 0.0044 v  l i d . Logul/-loge P l o t of S a l t Crystals i n O i l  ON O  I.I  i.l  !  RUN  !  1  1  1  I  1  4-2  /  •  0.8 i i —  1  0.5  i i  0.2  i  0.1  -0.2  i  i  -0.16  i  i  -0.12  i  -0.08  i  -0.04  0.0  L0G(€) D  v  = 0 0 3 9 1 cm, D / D t = 0„0103  Figure  0  v  l i e . LdguV-log € P l o t of S a l t Crystals i n O i l  -0.4 -0.2  -0.16  -0.12  -0.08  -0.04  0.0  L0G(€) D  v  = 0o0282 cm, D / D v  t  = 0 0056 0  F i g u r e llg„ Logu«v-loge P l o t o f S a l t Crystal i n o i l .  T  -0.2  1  1  -0.16  -I  1  -0.12  1  -0.08  I  T  T  -0.04  0.0  L06(€) D  v  L0G(€)  = 0 2 8 8 cm, D / D t = 0.0374 o  1—r  v  F i g u r e l l h , Logul/-log € P l o t Pellets i nO i l  o f ABS  D  v  - 0,288 cm, D / D  Figure  v  t  = 0,0285  H i , LoguI/-log€ P l o t Pellets i nO i l  o f ABS  64  1.1  i  ~i—i—i—r  r  1.0 0.9  SYMBOL  0.8  Dv/Dt  RUN  NO.  e  0.0103  4-2  o  0.0077  4-3  Dv =  0.0391 CM  6  0.7 0.6  „]  0.4  0.3 0.2 SYMBOL  Dv/Dt  RUN NO.  o  0.0134  3-!A  o  0.0090  3-2  A  0.0067  3-3  A  0.0042  3-4  0.1  0.0\ -0.1  Dv =  A  0.0341  -0.2 1  -0.  -0.15  -0.1  1 1  i  1  CM  1  1 ..]_._  -0.05  LOG(<0 Figure  12.  Wall Effect  on S a l t  Particle  Settling  0.0  65  n = 4.65 + 19.5-jj£  f o r spheres. be extended  The l i n e corresponding t o equation 13 c o u l d not t o the ABS p e l l e t s , which  r e g i o n o f n as t h e s a l t D /D . v  t  (2a)  l i e almost  i n t h e same  c r y s t a l s but have h i g h e r v a l u e s o f  The l i n e a r r e l a t i o n s h i p may n o t be a p p l i c a b l e t o those  h i g h e r v a l u e s o f D /D , where n appears t o l e v e l o f f , a t l e a s t v  temporarily.  t  Richardson and Z a k i o b t a i n e d s i m i l a r u n e x p l a i n e d  r e s u l t s f o r spheres a t h i g h e r R e C.  D  and h i g h e r D/D  (0.04).  t  F l a k y Sugar C r y s t a l s and Angular M i n e r a l C r y s t a l s  The r e s u l t s a r e summarized i n Talbe 7 and shown i n F i g u r e s 13a - 14d.  The l e a s t squares v a l u e s o f the index n f o r  the sugar c r y s t a l s and t h e m i n e r a l c r y s t a l s were much h i g h e r than those f o r the g l a s s beads, and somewhat h i g h e r than those f o r the s a l t  c r y s t a l s and the ABS p e l l e t s , i n the same range o f  Dy/Dt ( F i g u r e 10).  T h i s was c o n s i s t e n t , s i n c e f l a k y and angu-  l a r shapes have a lower s p h e r i c i t y than cubes, which  i n turn are  of course lower i n s p h e r i c i t y than spheres. The  s e t t l i n g r a t e of s i m i l a r p a r t i c l e s i n columns o f  d i f f e r e n t diameters  (Runs 9-, 10-, 11- i n Appendix  show any c o n s i s t e n t w a l l The  V I I I ) d i d not  effect.  index n thus appears t o be more s e n s i t i v e t o p a r t i -  c l e shape than t o w a l l e f f e c t , a t l e a s t f o r the present d a t a . Comparison o f shape e f f e c t  i s , n e v e r t h e l e s s , best made a t s i m i -  l a r p a r t i c l e - t o - c o l u m n diameter  ratios.  I t has been r e p o r t e d t h a t n f o r n o n s p h e r i c a l p a r t i c l e s of s p e c i f i e d shape v a r i e d w i t h a b s o l u t e p a r t i c l e However, from the present r e s u l t s f o r d i f f e r e n t  size (59). sets o f s a l t  66  Table 7 Summary o f R e s u l t s f o r Sugar C r y s t a l s and M i n e r a l C r y s t a l s Particles Sugar  Mineral  Run No.  n with 95% Confidence l i m i t s  Dv» cm  Dv/Dt  12-3  0.113  0.0222  5.83 + 0.34  11-2  0.135  0.0356  5.69 + 0.33  11-3  0.135  0.0265  5.66 + 0.45  10-2  0.0426  0.0113  5.89 + 0.19  10-3  0.0426  0.0084  5.76 + 0.08  9-2  0.0508  0.0135  5.69 + 0.07  9-3  0.0508  0.010  5.69 + 0.10  i  i  i  i  i—i  1.9  1 — i — r  i—r RUN 11-3  1.6  CD O  -0.2  -0.16  -0.12  -0.08  -0.04  0.0  LOG(e)  D  v  Figure  -0.12  -0.08  -0.04  0.0  LOG (€ )  = 0 1 3 4 6 cm, D / D o  0.7 I L •0.2 -0.16  v  t  = 0.0356  13a„ L o g u j / - l o g € P l o t o f Sugar Crystals i n O i l  D  v  = 0.1346 cm, D / D  Figure  v  t  = 0.0265  13b„ L o g u i / - l o g € P l o t o f Sugar Crystals i n O i l  Figure  13c  LoguZ/-log*FPlot o f Crystals in O i l  Sugar  ON  co  0.2 I -0.2  I  I  I  -0.16  D  v  I ,1 -0.12 -0.08 L06(€)  = 0„0508 cm, D / D  Figure  v  14a  0  -0.04  t  0.0  = 0„0134  Logul/-loge P l o t o f M i n e r a l Crystals i n O i l  0.2 I -0.2  I  D  v  1 I I 1 ' ' ' ' I -0.16 -0.12 -0.08 -0.04 0.0 L0G(€) = 0.0508 cm, D / D t = 0.010  Figure  v  14b. L o g u i / - l o g € P l o t o f M i n e r a l g> Crystals i n O i l  LOG  D  v  (e)  = 0.0426 cm, D / D  Figure  v  t  = 0.0113  14c. LoguV-loge P l o t of M i n e r a l Crystals i n O i l  71  c r y s t a l s h a v i n g average  s i z e s which d i f f e r e d by a f a c t o r s of  1.5 and s i m i l a r narrow s i z e d i s t r i b u t i o n s  (Appendix X), the  index n f o r the same shape d i d not depend on the p a r t i c l e The d e v i a t i o n of the data a t h i g h p o r o s i t y from the best s t r a i g h t  (e~0.90-0.95)  l i n e cannot be regarded as an  behaviour of i d e a l suspensions.  size.  intrinsic  T h i s can be judged from the  l o g u v - l o g e p l o t s , which show that the s t r a i g h t l i n e s f o r the f i n e r p a r t i c l e suspensions a p p l y t o h i g h e r p o r o s i t i e s than those f o r the c o a r s e r p a r t i c l e suspensions.  Despite the g r e a t e r d i -  f f i c u l t y i n o b t a i n i n g a narrow cut of the f i n e r p a r t i c l e s , the c o a r s e r p a r t i c l e s were s u b j e c t t o a s l i g h t l y g r e a t e r u n c e r t a i n t y i n the l o c a t i o n of the supernatant-suspension i n t e r f a c e , and were a l s o more s u b j e c t to the p o s s i b l e d i s t o r t i n g e f f e c t of c i r c u l a t i o n and the w a l l . 3.  Comparison with S i n g l e P a r t i c l e R e s u l t s In Tables 8 and 9, v a l u e s of uv o b t a i n e d by e x t r a p o l a t -  i n g the loguz/-logc p l o t to a p o r o s i t y of u n i t y are compared to the average v a l u e s of the same product obtained by f r e e ing. 12.  settl-  Both have a l s o been c o r r e c t e d f o r w a l l e f f e c t by equation Values of ( u i / ) t and e x  percent lower than (uv)  Q  (uz/)ext  and  (uv)^  a  r  e  consistently  several  r e s p e c t i v e l y , which i s d i f -  f e r e n t from what Richardson and Z a k i (43)  suggested.  To check the v a l i d i t y of the s m a l l samples used i n the f r e e s e t t l i n g experiments, sphere diameter and cube l e n g t h were c a l c u l a t e d from ( u 2 / )  e x t  and  (uz/)^ by e q u a t i o n 8a:  (8a)  Table 8 Comparison of xxv f o r Glass Beads Run  3 -2 iii/ (0.01 cm sec )  No. < ^)ext u  (ui/)» t ex  1-1  115.4  126.2  1-2  116.5  1-3  (ui/)  (ui/)o>  (uiO'ext  u„i/ (u2/)'ext  0  125.7  1.027  0.998  123.8  1.047  1.017  114.3  119.6  1.083  1.052  2-1  106 .8  116.8  1.092  1.061  2-2  111.2  118.2  1.080  1.048  2-3  110.0  115.2  1.107  1.076  1.142  1.105  7-3  20.85  21.27  129.6  123.7  127.6  125.9  123.9  -  23.8  24.3  23.5  Table 9 Comparison of uv f o r Cubic Particle  Run  uv  No.  ABS  ) (uz/)  UyV  (yjAs (ui/)«  ext  (ui/)'  (u2/) t  < >'ext  5-3  5.30  5.36  6.50  6.57  6.54  1.23  1.22  3-lA  7.68  7.90  8.79  8.91  9.67  1.13  1.22  3-2  7.63  7.77  1.15  1.24  3-3  7.51  7.62  1.17  1.27  3-4  7.33  7.39  1.20  1.31  4-2  10.72  10.9  1.10  1.16  4-3  10.53  10.67  1.12  1.18  6-4  70.2  75.7  1.25  1.25  6-5  76.5  81.1  1.16  1.17  ex  Salt  (0.01 car sec  Particles  uZ/  11.78  87.4  D  11.97  94.3  12.6  94.8  e x t  74  For a cube K and  L  = 0.93  ST  3  =  (12)  D (^) 3  The calculated diameters and cube lengths are recorded i n Tables 10 and 11.  Agreement between diameters and cube lengths  calculated from the free s e t t l i n g experiments and those by both microscopic measurements and sample weighing was  satisfactory,  thus confirming that the small samples used i n the free s e t t l i n g experiments were representative, and that the log uv - loge plots therefore do r e a l l y extrapolate at a porosity of unity to values of uz/ lower than those obtained by free s e t t l i n g . Gasparyan and Ikaryan (25) obtained a similar r e s u l t i n the creeping flow region, and found that the difference between the extrapolated u and the u calculated for free s e t t l i n g  was  greater than 20% at higher Reynolds numbers. The agreement between the calculated average lengths of the s a l t c r y s t a l s and those from both microscopic measurements and sample weighing indicates that the chosen s a l t c r y s t a l s behaved as cubes even though they had rounded-off corners. 4.  Settled Bed Porosity The settled bed porosity was found to approach a const-  ant: value a short time after the observable s e t t l i n g process had subsided.  These values were reproducible, and are plotted against  sediment bed height i n Figures 15a-c for d i f f e r e n t shapes of particles.  Those data at low bed height were rendered less r e -  l i a b l e than the others because of the boundary effect at the  Table 10 Comparison of Diameters of G l a s s Beads Run No.  Sieve openings cm  1-1  0.0991/0.117  1-2  ave. 0.108  Sample weighing Dy 0.114  Sphere diameter, cm. from (ui/)'ext 0.109  0.114  0.110  0.113  1-3  0.109  0.111  2-1  0.106  0.111  2-2  0.108  0.111  2-3  0.107  0.110  0.0463  0.0468  7-3  ave. 0.0456 0.0417/0.0495  0.0492  (uv)  microscope  0  0.114  0.116  0.112  0.0494 0.050  0.492  Table 11 Comparison Particles  Run No.  of Cube Lengths of Cubic  Sieve openings cm  Salt  5-3  0.0208/0.0250  Length of Cube, cm., from  Dv cm 0.0282  Particles  (uz/) t, ex  0.0212  (ui/)«ext 0.0214  (uz/)  0  (ui/)^  0.0234 0.0236  ave. 0.0229  ABS  3-lA  0.0250/0.0295  3-2  ave. 0.0273  0.0341  0.0258  0.0253  0.0256  3-3  0.0252  0.0254  3^4  0.0248  0.0249  0.0302  0.0305  0.0295  0.0302  0.207  0.214  0.216  0.221  0.0295/0.0351  4-3  ave. 0.323  6-4 6-5  0.0229  Sample weighing 0.0234  0.0232 0.0254  4-2  microscope  0.0391  0.288  0.0272 0.0274  0.0273  0.0272  0.0274  0.0316 0.0318  0.0316  0.0316  0.0319 0.230  0.239  0.232  ON  77  1 1 1  I < | i ji ! >1 '1 ' 1 ° o  r  0-44  0-44 0 43  0  L  -  o  °  o  o  o  o  o  o  °  o  o  9  o  ©  Q  o  NO.  g  I-I  o  0  RUN  9  0  „  0  o  0  o ^  £  1-2  1  1-3  0-42 o  VI/ 0-44 >  0-4 3 1 : 0 42  CO O 0 44 CC  o  O  •  O  o  _  Q  Q  ° 8 o o o  0 43 0 42.  o  O  =  O  z  o  0  ~c?  °  1  2- 1  2-2  Q. 0-44 f 0-43 f0-42 0-44 043  8  °  o o  Q  fi>  0  g l  -E 2-3  o  ° ° « o  r  ° o o  « o  O  O  £  ^ 7-3  ' 1 1 1 1 1 1 1 1 1 1 , 1 1 1 11  0  Figure  5  10 15 20 25 30 35 40  HEIGHT OF FIXED BED, mm.  15a.  Settled  Bed P o r o s i t y of G l a s s  Beads  78 0-47 0-46 : 0-45 0-44 0-47 0-46 =_ 0 45 0 44 0-46 045 0-44  1  1 O  11 1  1  ° O O  o  oo  o  11 1.  ,  o  o  1  ' 1  RUN NO.  O o "  0  o  o  o  o  o  o  o  o  0  '~  0  _j  o  3-IA  -  3-2  I  °  ° ° ° °o  046 0-45 [ 0-44 :  °  ° o  o  o  o  o  0  °  CO r O 0-46 0^ 0 45 L  °  °  °  o  °  o  o o  1 j  0  °  o  046 >- 0-45 \ r~2 0-44  o  0  °  O  1  o  0  r  3-4  4-2  ~  ° °  °  0-46 r  3-3  £  o  o  ^~ 0-47  1  1  °  o o 0  o  °  o  o  °  o  o  o  0-45  3  Q  0  i i  4-3  5-3  0  6-4  6-5  —  o  llll. Ill III IIIll  o 0  o  o o  o o  o  l l l l l l l l l l l l l l l l  o  o  o  ,M ,i, ii,  o  048 0-47 0-46 0-45  |UM,MU,,M.|  048 0-47 0-46 0-45  i T r i  0-44  5 10 15 20 25 30 35 40 HEIGHT OF FIXED BED, mm.  F i g u r e 15b,  Settled  Bed P o r o s i t y o f C u b i c  Particles  79  0-50 0-49 'L 0-48  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 RUN NO. ° = ° ° o o o „ -. ° ° o o o j 9-2 0  0-50 : 0-49 : 048  O  o  •o 0-50 ^ 0-49  o  >~  0-48  g  050 L  o  O  ~ O J  :  °  0-50 I 0-49 0-48 L  o  °  °  °  O  j  o o  o  e  O  °  O  o  o  J 10-2  0  °  O  :  o  0  o  o  o  O  O  O  o  10-3  ;  O  O o o ° °  O 0 48 CL 0-50 0-49 0-48  9 -3  o  o  o  11-2  o "  0 u  o  o  ^  o ° °'ft °  r  o  0-50 0-49 L 0-48  1  5  .  1  .  ° °  o  0  1  0  o  = 1 1-3  J 0  ° I  1  .  15c.  O F  F I X E D  12-3  o I  10 15 20 25 30 35  H E I G H T  Figure  o  o ° o  1  ° °  B E D ,  S e t t l e d Bed P o r o s i t y Sugar C r y s t a l s  .  I  ,  40 mm.  of M i n e r a l  and  80  bottom, complicated p o s s i b l y by uneveness of the w a l l s a t the bottom of the columns. F i x e d or s e t t l e d bed p o r o s i t y decreased bed h e i g h t .  The  s l i g h t l y with  probable e x p l a n a t i o n f o r t h i s t r e n d i s t h a t ,  the g r e a t e r the bed h e i g h t , the g r e a t e r the a p p l i e d p r e s s u r e on the lower p o r t i o n of the bed, and hence the g r e a t e r the degree of compaction  off the  I t was ciably different  bed.  found t h a t those p a r t i c l e s with shapes from spheres  appre-  showed a g r e a t e r s e n s i t i v i t y of  to bed h e i g h t than the spheres.  b  Stacked beds of n o n - s p h e r i c a l  bodies or rough bodies have been observed  to form beds of  less  s t a b l e p o r o s i t y w i t h r e s p e c t to pressure then smooth spheres T h i s e f f e c t , however, was  c  (60).  o n l y a minor one f o r the random loose  packed beds of the present  experiments.  The mean v a l u e s of €  D  f o r each run were estimated  by  drawing a h o r i z o n t a l l i n e through the data, i g n o r i n g the p o i n t s a t low bed h e i g h t .  The mean v a l u e s of e  fe  obtained were 0.435  ( v a r i a t i o n 0.432-0.438) f o r the s p h e r i c a l g l a s s beads, 0.455 ( v a r i a t i o n 0.450-0.461) f o r t h e c u b i c s a l t c r y s t a l s , 0.486 (var i a t i o n 0.485-0.487) f o r the m i n e r a l c r y s t a l s and 0.485 f o r the sugar c r y s t a l s .  The ABS  p e l l e t s showed an a p p r e c i a b l e change of  with bed h e i g h t , due presumably t o t h e i r low d e n s i t y which r e q u i r e s a g r e a t e r bed h e i g h t to produce packing  stability.  Comparing with the packed bed p o r o s i t y r e s u l t s of Browne11 e t . a l . (51),  the v a l u e of  o b t a i n e d f o r the g l a s s beads agrees  very  c l o s e l y to t h e i r v a l u e of random loose p o r o s i t y f o r uniform smooth spheres, while €^ of the s a l t c r y s t a l s corresponds dom  to t h e i r r a n -  loose packed bed of p a r t i c l e s having a s p h e r i c i t y of  0.84.  81  The  latter figure  perfect  i s a l i t t l e h i g h e r than the s p h e r i c i t y of a  cube, 0.806, and might be a t t r i b u t e d  t o the rounded-off  c o r n e r s of the s a l t c r y s t a l s which i n c r e a s e d t h e i r 5.  Beranek-Klumpar  sphericity.  Plot  F i g u r e s 16a-16d, r e s p e c t i v e l y ,  a r e t e s t s o f four v a r i a -  t i o n s of the Beranek-Klumpar method, u s i n g the experimental data of the present study. abscissa, plotted,  Where  r a t h e r than u x t  i  s  e  o n l y the data f o r s p h e r i c a l l y  used i n the  i s o t r o p i c p a r t i c l e s are  s i n c e Ug, f o r the other p a r t i c l e s i s a f u n c t i o n of  orientation.  The data f o r ABS p e l l e t s were not i n c l u d e d because  of the l a r g e  bed h e i g h t e f f e c t on ^fo»  The term  was o b t a i n e d  Uixn  from uin = u  t b €  e x  (14)  n  u s i n g the e x p e r i m e n t a l l y determined v a l u e s of n f o r the given run  and of €fc f o r the g i v e n p a r t i c l e s shape.  four v a r i a t i o n s  i s F i g u r e 16a, which does r e s u l t i n some  l a t i o n o f the data f o r d i f f e r e n t dered a p e r f e c t  The best of the  correlation,  corre-  shapes, but can h a r d l y be c o n s i -  the maximum h o r i z o n t a l  spread between  the  p o i n t s averaging about 157o. A d i s t i n c t d i f f e r e n c e  the  curves f o r d i f f e r e n t shapes s t i l l  persists  between  even when the com-  p a r i s o n i s r e s t r i c t e d t o s i m i l a r p a r t i c l e - t o - c o l u m n diameter r a t i o s . 6.  n - €  b  Plot  Ignoring the w a l l e f f e c t , the index n was p l o t t e d the  s e t t l e d bed p o r o s i t y  i n F i g u r e 17.  f o r n to i n c r e a s e w i t h €5.  An obvious trend was found  The l a t t e r i s r e l a t e d  shape i n g e n e r a l and s p h e r i c i t y  against  i n particuler  to p a r t i c l e  (51).  We thus have  82  1.0 —  I l l  1  1  1  1  1  1  1  1  I I I  i  0.8 —  0.6 _  -  -  0.4  —  —  -  -  iCQOO A _  0.3  —  Q77  0.2  —  —  -  V  O  SPHERICAL, GLASS BEADS  V CUBIC, SALT CRYSTALS  0.1 —  0.08  A  ANGULAR, MINERAL CRYSTALS  +  FLAKY,SUGAR  + -H-/AAA  CRYSTALS  —  —  1 1 1 0.08  0.1  ,  I  I  0.2  I  1  1  0.3  0.4  Plot  using  i  1  I I I  0.6  0.8  U-Uin Uext  Figure  16a„  Beranek-Klumpar  (u-u^ )/u n  e x  t  1 1.0  83  1.0  III  1  1  1  1  1  1  l l l l  1  1  0.8  —  0.6  —  0.4  —  l-€  rxoo  0.3  5  fe  —  Wc -Mb  0.2  w  0.1  ~~  -r-ffAAA  0.08  1  I I I  0.08  0.1  i  0.2  1  0.3  1  |  l l l l  i 1  0.4  0.6  U Uext  Figure  16b.  B e r a n e k -Klumpar  Plot using  (Symbol - see F i g u r e 16a  0  u  )  / ext u  0.8  1.0  84  0.08  0.1  0.2  u-u U  Figure  16c.  0.3  0.4  0.6  Plot  using  Cu-u^/u^  i n  oo  Ber anek-Klumpar  (Symbol - see F i g u r e  16a  0  )  0.8  1.0  85  III  1  1  1  '  1  1  1  1  I  1  I  1  —  VWV  occD  0  —  W  OCD  vw l-€  b  _  OCD  —  V  0.3 —  V  —  0.2  0.1  — —  Vr]  0.08 I  l  ,  l  0.1  1  1 . 1 , 1  0.2 U  0.3  0.4  0.6  Uco  Figure  16d  0  Beranek-Klumpar (Symbol  Plot  - see F i g u r e  using 16a.  I  u/u )  I  11 0.8  1.0  86  (The numbers i n t h e g r a p h Run N o s . )  indicate  87  a potentially cle  shapes.  useful Any  method o f  predicting  u n c e r t a i n t y i n the  prediction  method i s p r o b a b l y s m a l l e r t h a n t h e by  the  = €  (up  n by  parti-  this  207o) i n c u r r e d  to  e  x  in  t  (la)  n  ext  Observations For  spherical  s u s p e n s i o n , the  g l a s s beads, the  t h i c k n e s s of  space.  rarely  Relative  of  bed  and  the  the  of a  on  particles  settling  order of a  particles within  then f a l l  Below t h i s calm l a y e r ,  layer  p a r t i c l e s arranged  occurred, except that o c c a s i o n a l l y  upward t h r o u g h the face.  m o t i o n of  top  w h i c h was  p a r t i c l e d i a m e t e r s , c o n s i s t e d of in  error  of  R i c h a r d s o n - Z a k i m e t h o d o f u s i n g Uoo i n s t e a d o f u  u  7.  n for different  few  randomly this  layer  a p a r t i c l e m i g h t move i t s a r r i v a l at travelled  e a c h o t h e r i n a p p a r e n t l y random d i r e c t i o n s .  the  inter-  relative  Clusters  to  of  p a r t i c l e s w e r e m o v i n g downward, w h i l e some n e a r b y c l u s t e r s p a r t i c l e s were r i s i n g . moment and  fall  movement.  By  t h e r e was in  and  "cluster"  i s meant a g r o u p o f  r o t a t e d as  a w h o l e , but  no  d i s t i n c t difference  outside a cluster.  not  i n the  Lateral  motion of  radial direction.  i n t e r p a r t i c l e c o n t a c t between s p h e r i c a l The l i n g beds of  same g e n e r a l t y p e o f  during i t s which  i n the  same  flocculation;  in i n t e r p a r t i c l e distance particles  lower p o r t i o n of a suspension.  systematically  one  particles  agglomorated p a r t i c l e s which occur i n  observed i n the not  might r i s e at  a t a n o t h e r moment, o r m i g h t b r e a k up  moved t o g e t h e r and s e n s e as  A given cluster  of  The  was  motion  occurrence  particles  b e h a v i o u r was  nonspherical particles.  The  with-  was  of  uncertain.  found i n the  O r i e n t a t i o n of  was  the  sett-  individual  88  particles  was a p p a r e n t l y  T h e r e was o b s e r v a b l e A particle  random and c h a n g i n g d u r i n g  interparticle  contact  settling.  between some  particles.  w o u l d change i t s o r i e n t a t i o n when i t was d i v e r t e d by  a neighbour  e i t h e r by d i r e c t  o b s t r u c t i o n o r by h y d r o d y n a m i c i n -  terference. It  i s likely  that t h e n e t motion of the p a r t i c l e s  affected  by p a r t i c l e  settling  bed may n o t be t h e one w h i c h g i v e s  to f l u i d  flow and, i n a d d i t i o n , mechanical c o n t a c t  cles  orientation.  The o v e r a l l  causes f u r t h e r energy d i s s i p a t i o n .  why n o n s p h e r i c a l dered  settling  particles  with  flaky  was  o r i e n t a t i o n of a  the l e a s t  resistance  between  parti-  T h i s m i g h t be one  reason  or angular  shapes have h i n -  r a t e s more a f f e c t e d by c o n c e n t r a t i o n  t h a n do  spheres. Experimental  settling  rates  h e r e and many i n t h e l i t e r a t u r e considerably higher with  spheres  than  those  i n cubic array  predicted  model o f H a p p e l Richardson  than those  f o r a mechanically  t o be  e x t e n d e d bed  (61), and a l s o c o n s i d e r a b l y : h i g h e r by b o t h  (26) (see F i g u r e  motion  reduced drag,  which could,  models.  reported  the " f r e e  surface"  ( 2 2 ) a n d t h e h e x a g o n a l c o n f i g u r a t i o n model o f  and Z a k i  experimental  flow  ( 3 3 , 43, 62) were f o u n d  theoretically  multiparticle  the  i n creeping  i n small  results  18).  On t h e o t h e r  c l u s t e r s was r e p o r t e d  e x p l a i n the f a s t e r  compared  t o those  hand,  (10) t o have  settling  rates of  of the i d e a l i z e d  89  0.5  Figure  0.6  18.  0.7  0.8  0.9  Comparison of the Present R e s u l t s f o r Spheres t o Models i n the L i t e r a t u r e  1.0  90  CONCLUSIONS 1.  Hindered  s e t t l i n g without  and n o n s p h e r i c a l narrowly  f l o c c u l a t i o n of s p h e r i c a l  s i z e d p a r t i c l e s of uniform shape i n  c r e e p i n g flow can be w e l l r e p r e s e n t e d by a simple s t r a i g h t f i t t e d to the data on l o g uv-  l o g e c o o r d i n a t e s , i f a few data i n  the d i l u t e r e g i o n (€~0.90-0.95) are excluded. of t h i s r e g i o n was  The  non-linearity  b e l i e v e d to a r i s e from the u n c e r t a i n t y i n the  low c o n c e n t r a t i o n s .  The  slope n of the f i t t e d  l i n e depends on  p a r t i c l e shape, ranging from an average v a l u e of 4.8 spheres t o 5.4 2.  f o r cubes t o 5.8  The  line  f o r angular  index n f o r spheres was  f o r smooth  crystals.  c l o s e to t h a t found i n  the l i t e r a t u r e (25, 43), but the r e s u l t s f o r d i f f e r e n t to-column diameter r a t i o s  particle-  (D /D < 0.045) d i d not show n e a r l y the v  t  same e f f e c t of the w a l l as t h a t r e p o r t e d by Richardson and Z a k i (43).  On the other hand, f o r c u b i c s a l t c r y s t a l s , n c o u l d be r e -  presented s t a t i s t i c a l l y up t o D v / t D  n = 5.33  + 17.3  lVD  =  0»015 by  t  the w a l l c o r r e c t i o n constant of which i s c l o s e to that of R i c h a r d son and Z a k i . of D /D v  t  However, t h i s constant f a i l s completely a t v a l u e s  above 0.015. 3.  The method recommended by Beranek and Klumpar f o r  c o r r e l a t i n g both s p h e r i c a l and n o n s p h e r i c a l p a r t i c l e data was  o n l y moderately  fluidization  s u c c e s s f u l i n c o r r e l a t i n g the present  s e t t l i n g data f o r d i f f e r e n t shapes.  The  fluidization  data  p l o t t e d by Beranek and Klumpar i n c l u d e d some on porous p a r t i c l e s  91  and  were t h u s p r o b a b l y  m i s l e a d i n g ; and e v e n t h o s e  data  showed  considerable scatter. 4.  The s e t t l i n g r a t e s o b t a i n e d  on l o g - l o g c o o r d i n a t e s lower  by l i n e a r e x t r a p o l a t i o n  t o a p o r o s i t y o f u n i t y w e r e f o u n d t o be  than the corresponding  free s e t t l i n g rates obtained  p e r i m e n t o r c o m p u t e d by s i z e m e a s u r e m e n t . . T h i s ported  by some c a r e f u l e x p e r i m e n t a l 5.  The i n d e x n o b t a i n e d  was c o n s i s t e n t l y h i g h e r particles.  This greater  data  finding  i s sup-  i n the l i t e r a t u r e (33).  for non-isotropic  than that f o r s p h e r i c a l l y  particles  isotropic  c o n c e n t r a t i o n dependence o f t h e non-  i s o t r o p i c p a r t i c l e s e t t l i n g rates could  be c a u s e d by t h e random  o r i e n t a t i o n and consequent g r e a t e r m u t u a l h i n d r a n c e i s o t r o p i c p a r t i c l e s , observed 6.  by e x -  visually.  The i n d e x n showed a d e f i n i t e  s e t t l e d o r random l o o s e f i x e d  o f the non-  increase w i t h the  bed p o r o s i t y o f t h e p a r t i c l e s .  The l a t t e r d e c r e a s e d s l i g h t l y w i t h bed h e i g h t  f o r l o w bed h e i g h t s .  92  RECOMMENDATIONS Prediction It  is  of  i n d e x n by m e a s u r i n g €  s u g g e s t e d t h a t more d a t a a t  shapes,  low D / D v  i n c l u d i n g elongated needle  creeping taining  flow region  to  also desirable  to  study  s h i p t o Uco , w h i c h h a s  value of  the  ^  prediction  of u  a unique value  in  A procedure  s h o u l d be u s e d .  b  particle  be c o l l e c t e d  c o n f i r m the method.  a more c o n s i s t e n t  s h o u l d be u s e f u l .  for various  t  shapes,  b  e  x  t  independent  for  It  and i t s of  the ob-  is  relationorientation  i  only the  for  spherically  free  which  settling  isotropic  velocity  v  of  does h a v e a u n i q u e v a l u e  applied instead  for mixing a fast ing data further  f l u i d i z a t i o n as With l i q u i d careful effect  present settling  i n t h e ui/ f o r m i s work a t  the  entrance  a given  particle,  spheres, c o u l d be  s u s p e n s i o n , and t h e method o f inapplicable  process-  beyond c r e e p i n g  flow,  numbers s h o u l d be done by  using  well controlled.  fluidization  T h i s would  particles  more i n f o r m a t i o n  than  free  settling  better  (63)  on a r t i f i c i a l l y  shapes  understood.  In  shapes would  since  extended to n o n - s p h e r i c a l  the  give  behaviour current  spheres  in  work  c o u l d be  particles.  on h i n d e r e d s e t t l i n g  f o u n d by R i c h a r d s o n and Z a k i  their  addition,  expanded p a c k e d beds o f  The w a l l e f f e c t  involve  screen.  with regular  irregular  method,  column and e x a m i n a t i o n o f  d e s i g n and s u p p o r t i n g  Artificial  profitably  for  volume  b o t h t h e m i x i n g and f l u i d - s o l i d c o n t a c t i n g  temperature  is  an e q u i v a l e n t  bodies,  e x p e r i m e n t a l method c o u l d n o t be u s e d  h i g h Reynolds  design of of  For n o n - i s o t r o p i c  o f Uoo ,  Since the  cles  u  bodies.  did not  of  spherical  agree w i t h the  parti-  present  93  work,  w h i c h was n o t  The w a l l e f f e c t was  on s p h e r e s  effect  u w i t h D/Dt.  for hindered s e t t l i n g  influence  (64),  effect.  More work of  who u s e d € as a is  spheres  o f n o n - s p h e r i c i t y on t h i s  w o u l d be p a r t i c u l a r l y volving  to study w a l l  i n t h e h i g h R e y n o l d s number  s t u d i e d by N e n z i l a n d H r d i n a  and c o r r e l a t e d  the  aimed s p e c i f i c a l l y  useful for  the use of r e l a t i v e l y  further  large  region parameter  r e q u i r e d on w a l l  i n creeping flow effect.  This  work i n t h i s  particles  in  small  and  information field  in-  containers.  94  NOMENCLATURE A  2  s u r f a c e area of sphere of equal volume  cm  Ap  p r o j e c t e d area of p a r t i c l e  cm^  A  s u r f a c e area of p a r t i c l e  cm  C  perimeter of the p a r t i c l e p r o j e c t e d onto a s u r f a c e  cm  C  cm  Cn  circumference of a c i r c l e of area equal t o the p r o j e c t e d area of the p a r t i c l e drag c o e f f i c i e n t  Cv  c a l i b r a t i o n constant of viscometer  c  v o l u m e t r i c c o n c e n t r a t i o n o f suspension, (1-e)  D  diameter of sphere  cm  diameter of a c i r c l e of same area as the p r o j e c t e d area of the p a r t i c l e l y i n g i n i t s most s t a b l e p o s i t i o n  cm  s  2 2 2  ^cs/sec  D  c  D  s  diameter o f sphere of equal s u r f a c e area  cm  D  t  column diameter  cm  D  u  diameter of sphere of equal s e t t l i n g irate  cm  Dy  diameter of sphere of equal volume  cm  F  drag f o r c e on p a r t i c l e s e t t l i n g i n i n f i n i t e medium  ~ g.cm.sec" „2  F'  drag f o r c e  g.cm.sec  f  f u n c t i o n of  g  a c c e l e r a t i o n of g r a v i t y  K,k  p r o p o r t i o n a l i t y constant  KST  Stokes' law shape factor^  I<v  Heywood v o l u m e t r i c shape f a c t o r d e f i n e d as  980 cm.sec"  7TDv/6D^ L  dimension  of l e n g t h  n  Richardson-Zaki  index  "  cm  -95  Re Re  particle free  c  c  t  e  r  u u  e x  ui u  settling  particle  u  t  n  V  o  r  R e y n o l d s number d e f i n e d  Dup> . DyUoo . o r Lutto  s  t  R e y n o l d s number d e f i n e d a s ^  v  duration of constant rate s e t t l i n g  sec  efflux  sec  time of l i q u i d i n viscometer  hindered s e t t l i n g r a t e or s u p e r f i c i a l velocity of liquid i n fluidization  cm s e c " ^  extrapolated free settling rate  cm s e c ~ ^  incipient  cm sec"^"  fluidization velocity  single particle bounded medium  free s e t t l i n g rate i n  cm sec"^"  Uoo  single particle free settling rate i n i n f i n i t e medium  cm sec"^"  u  f r e e s e t t l i n g r a t e of sphere of equal v o l u m e i n i n f i n i t e medium  -cm sec"*"  Q  v  (uz/)  corresponding t o uext  e x t  (ui/)4xt (ui/)  0  (uiOoo U  (  U I /  x  v  ) e x t c o r r e c t e d f o r w a l l b y e q t . 12  corresponding to u  0  x v  c o r r e s p o n d i n g t o u<x> x v upward t r a v e l l i n g r a t e o f c o n c e n t r a t i o n d i s c o n t i n u i t y plane i n hindered s e t t l i n g  (0.01cm s e c " ) (0.01cm s e c ) 3  (0.01cm s e c ) 3 —7 (0.01cm s e c ) cm sec"^" 3  V W  volume upward t r a v e l l i n g r a t e o f a c o n s t a n t c o n c e n t r a t i o n element i n h i n d e r e d settling  cm cm sec"''"  Zi  initial  cm  Greek e e P  suspension  bed h e i g h t  Letters p o r o s i t y o f s u s p e n s i o n o r f l u i d i z e d bed  b  fixed  bed p o r o s i t y  density of l i q u i d  -2  g.cm  96  pp  g.cm  density of p a r t i c l e  0  function of  \p  sphericity  p-  visoosity  of l i q u i d  c p o r (0.01gcm"^"sec~^).  v  kinematic liquid  v i s c o s i t y of  c s o r (0.01cm s e c  defined as A /A s  Abbreviations DIST  distance  Eqt.  equation  HTB  height  o f s e t t l e d bed  PEG  polyethylene  TEMP  temperature  WT.  weight of s o l i d  STD.DEV.  standard  glycol  deviation  2  -1 )  97  LITERATURE  CITED  1.  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Co., (1962-63)  I-l  APPENDIX I A theory of  THEORY OF SEDIMENTATION  of  sedimentation without  the hydrodynamics of  and v e r i f i e d analysis  is  particles  restricted  there  shape and d e n s i t y ,  concentration.  d r i c a l container. is  any  suspension,  =  (66).  The  absence of  d e p e n d e n t o n l y on t h e  wall local  Consider such a suspension i n a  By m a t e r i a l  balance  concentration gradient an e l e m e n t a l plane of  it  cylin-  c a n be shown t h a t  present  constant  p r o p a g a t e upward t h r o u g h t h e bed w i t h  w  al.  (65)  by t h e a s s u m p t i o n o f a n i d e a l s u s p e n s i o n ,  and s e t t l i n g v e l o c i t i e s  particle  consideration  s u g g e s t e d by K y n c h  e x p e r i m e n t a l l y by Shannon e t .  namely, uniform p a r t i c l e effect,  was  detailed  i n the  if  settling  concentration  will  velocity  . *Lisl-  (I-l)  a c where c i s  the  local particle  p l a n e under c o n s i d e r a t i o n . flux. the at  If  d i s c o n t i n u i t y of  concentration at  The t e r m uc i s concentration is  the  elemental  the v o l u m e t r i c present  d i s c o n t i n u i t y p l a n e w i l l move upward t h r o u g h t h e a velocity  A  =  _  where A s i g n i f i e s a f i n i t e discontinuity.  plete  it  settling  (uc)2 - (uc)i C2 - c i  dispersion  change o f  (I-?)  concentration at  W i t h t h e s e r e l a t i o n s h i p s and t h e  between s e t t l i n g I-l,  i n the bed,  of  TJ - - ( u c ) Ac  Figure  solid  is  f l u x , u c , and c o n c e n t r a t i o n , c ,  relationship as  p o s s i b l e to p r e d i c t q u a n t i t a t i v e l y  curve  f o r a suspension of  given  the  shown  in  the  com-  concentration,  1-2  and a t  least  qualitatively,  the  having a c e r t a i n v a r i a t i o n shape o f  the  settling  settling  curve  of  curve  f o r any  dispersion  concentration with height.  f l u x graph has a p r o f o u n d e f f e c t  derived  from i t .  The s e t t l i n g  (62),  f o u n d t o be o f  t h o u g h argument a r o s e a s  curve at h i g h c o n c e n t r a t i o n can s t i l l  be shown t h a t  have a p e r i o d o f  pension of  initial  t o an u l t i m a t e  settling rate between  is  u =  concentration sediment of  u^ w h i l e  c  spite  of  point,  it  uniform suspension should  settling  rate,  with a  concentration.  For a  c i which  settles  concentration  c,^,  t h e upward v e l o c i t y  sus-  discontinuous-  the  of  solid  initial  discontinuity  s h o u l d be  (  cr  =  U  the the  then at  height  f l u x graph i s (66)  concentration  constant  rate  of  of  the  the double concave  and shown i n  Figure  c^ h a p p e n s t o be i n a  settle  corresponds to  - * 2  in  the  s u c h a way initial  }  period  "  3 )  suspension.  that  type  1-2,  as  and i f  the  concentration  r e g i o n where a d i s c o n t i n u o u s s t e p change t o c suspension w i l l  for a  1  ( I  initial  s u g g e s t e d by Shannon  still  the  c  is  is  this  a  1-2  i i~0 -c-  settling  If  initial  initial  the o v e r a l l  All  t  z±  In  shape o f  c^ a n d c^,, a c c o r d i n g t o e q u a t i o n 1-2,  U  where  to the a c t u a l  (67).  the  ideal  f o r m shown i n F i g u r e  an i n i t i a l l y  constant  f l u x corresponding to  ly  the  on  f l u x graph of  m i c r o g l a s s bead s u s p e n s i o n w h i c h was a n u n f l o c c u l a t e d s u s p e n s i o n was  The  m  is  unstable,  the upper  concentration  ci  the  portion  and t h e  lower  1-3  part varies  abruptly  continuously the  curve.  will  f r o m Co, a t  t o C 2 , where  t h e b o t t o m t o C 3 , and  C3 and C2 a r e  The e l e m e n t a l p l a n e o f  inflexion points  constant  p r o p a g a t e upward w i t h v e l o c i t y  thence on  concentration  corresponding to  C2  equation  I-l W = -  a(uc) dc  at  c  (I-la) 2  and t h e downward m o v i n g r a t e o f face  is  ui.  The f i r s t  -cr is  of  ui  p e r i o d of  it  duration  (1-4)  + W  constant r a t e .  hits  inter-  zi  After  natant-suspension interface as  supernatant-suspension  time t will  c r  ,  t h e downward m o v i n g s u p e r -  settle  t h e upward moving e l e m e n t  with a decreasing  planes  of  rate  increasing  concentration.  uc  uc  F i g u r e 1-1. Sedimentation F l u x P l o t , S i n g l e Concave  F i g u r e 1-2. Sedimentation F l u x P l o t , D o u b l e Concave  II-l  APPENDIX I I  DESCRIPTION AND  TESTING  OF LIQUID ELUTRIATION APPARATUS The column c o n s i s t e d of two p a r t s , with a s u p p o r t i n g screen midway i n the lower p a r t , so t h a t a c o n s i d e r a b l e l e n g t h of column a c t e d as an entrance  calming  s e c t i o n (see F i g u r e 4 ) .  The two p a r t s of the column were i n s e r t e d i n t o matching p o l y ethylene blocks w i t h openings equal to the column diameter. connections  between the column and the p o l y e t h y l e n e blocks were  s e a l e d w i t h O-rings umn.  to f a c i l i t a t e easy disassembly  of the c o l -  A gate with a screen a t the center was i n s t a l l e d  gap between the two b l o c k s . ing so t h a t f r e e flow through pushed i n t o the opening the s c r e e n . Figure.II-l.  The  i n the  I t c o u l d be p u l l e d out of the openthe opening  was p e r m i t t e d , or  so t h a t only l i q u i d c o u l d pass  through  D e t a i l s of the screen gate u n i t are shown i n The column was clamped to an i r o n support and s e t  i n v e r t i c a l p o s i t i o n by means of a plummet. The column was t e s t e d with s p h e r i c a l g l a s s beads which had been c l o s e l y s i z e d by s i e v i n g .  Mixtures of g l a s s beads  from two c o n s e c u t i v e f o u r t h r o o t s e r i e s T y l e r screens were p r e pared  i n the p r o p o r t i o n 90% of the l a r g e r s i z e f r a c t i o n and 107.  of the s m a l l e r , the l a t t e r c o l o r e d b l a c k by marking i n k .  The  volume of column a v a i l a b l e f o r a f l u i d i z e d bed was c a l c u l a t e d , and the amount of mixture which would produce a f l u i d i z e d bed of p o r o s i t y 0.95 was obvious  introduced.  V i s u a l s e g r e g a t i o n by s i z e  i n the f l u i d i z a t i o n even a t lower p o r o s i t y .  s e p a r a t i o n was n a t u r a l l y i m p o s s i b l e .  Nevertheless  was  C l e a r cut  the column  II-2  was  able to separate  e f f e c t i v e l y as t e s t was  s p h e r i c a l p a r t i c l e s of d i f f e r e n t  the f o u r t h r o o t s e r i e s T y l e r s c r e e n s .  done by  fluidizing  fourth root s e r i e s screens  c l o s e l y s i z e d g l a s s beads i n t h e c o l u m n and  sizes  A further from  collecting a  p o r t i o n o f t h e p a r t i c l e s a t t h e t o p m o s t p a r t o f t h e bed t i n g the screen gate. c l e s were c o l o r e d as t h i s c a s e no v i s u a l  The  recovered  b e f o r e and  as  by  small shut-  "apparently smaller" p a r t i -  r e - i n s e r t e d i n the column.  s e g r e g a t i o n c o u l d be  observed.  In  II-3  -®-  LOWER PART OF P O L Y E T H Y L E N E BLOCKS  SECTION  I-l  SCREEN  GATE  r  J  *-<  GROVE  "mil  P  ^ I  SECTION  2-2  SCALE -g-  Figure  II-l.  D e t a i l e d Drawing of Screen Gate  III-l  APPENDIX I I I NEWTONIAN BEHAVIOUR OF POLYETHYLENE GLYCOL  SOLUTION  The 45% p o l y e t h y l e n e water s o l u t i o n Newtonian behaviour of d i f f e r e n t  was t e s t e d f o r  i n c a p i l l a r y viscometers  sizes.  (Cannon-Fenske)  Table I I I - l shows that the  calculated  v i s c o s i t y d i d not change w i t h c a p i l l a r y diameter.  This i n -  d i c a t e d that the l i q u i d behaved l i k e a Newtonian f l u i d a t l e a s t below the shear s t r e s s  experienced by the l i q u i d i n the  t e s t , the h i g h e s t of which was i n the l a r g e s t  capillary.  can be shown that the c a p i l l a r y viscometers of d i f f e r e n t calibrated  It sizes  with Newtonian l i q u i d s do not g i v e constant appa-  rent v i s c o s i t y f o r a  Table  III-l  Calculated Viscosity Different  Size  Temperature:  of PEG from  Viscometers 77.05°F  Viscometer  Approx. I.D. of Capillary* cm  E f f l u x Time Sec.  Calculated V i s c o s i t y cs  C 3 ( s i z e 200)  0.102  2383.6  259.8  D91(size 300)  0.126  1130.7  259.9  C965(size 400)  0.188  222.1  260.0  * from A.S.T.M. D445-53T (68)  non-Newtonian  liquid.  The maximum shear s t r e s s  of the t e s t ,  which occured a t the w a l l of the c a p i l l a r y j and the l a r g e s t c a p i l l a r y was estimated by the laminar pipe flow equation f o r  III-2  a Newtonian f l u i d (69).  -TrzlF^-^frwhere T  rz)  (III-la)  R i s the a x i a l d i r e c t i o n shear stress at the wall of  the c a p i l l a r y the radius of which i s R andAP i s the pressure difference over the c a p i l l a r y length L.  In the viscometer, AP  can be taken as Lpg (In fact A P i s larger than Lpg since the driving head in the viscometer i s larger than the c a p i l l a r y length', which causes the main f r i c t i o n to f l u i d flow).  Neglect-  ing the unsteady state flow, equation I I I - l a becomes  T r z | R =  Approximate  -£|£_  (Ill-lb)  shear stress for viscometer C965 was estimated as  T r z | R  =  1„082 x 0,094 x 980  =  4  9  #  8  d y n e s / c m  2  The possible maximum shear stress experienced by the l i q u i d i n glass bead s e t t l i n g was estimated from the equation for a single sphere s e t t l i n g i n an i n f i n i t e medium (69)  T r e i  where T | r9  R  R  = | ^  S  i  n  dII-2)  e  i s the shear stress in the angular d i r e c t i o n at the  sphere surface which i s larger than that beyond the surface,  u  m  i s the free s e t t l i n g v e l o c i t y and R i s the radius of the sphere, Maximum shear stress occurs at 6 = 77/2.  From free s e t t l i n g  data on 0.1135 mm glass beads, taking R = 0.058 cm,  Ill-3  T r  elR  =  2  which i s w i t h i n  0.058  =  3  6  ,  3  d  y  n  e  s  /  c  m  the shear s t r e s s of the t e s t .  Thus 457»  p o l y e t h y l e n e g l y c o l water s o l u t i o n conformed to Newtonian behavior i n the present experimental  condition.  IV-1  APPENDIX IV  MEASUREMENT OF DENSITY AND  A.  VISCOSITY  Measurement of L i q u i d  L i q u i d d e n s i t y was  Density  measured with a Westphal balance  which had been c a l i b r a t e d with d i s t i l l e d water a t room temp e r a t u r e , from which the a p p r o p r i a t e c o r r e c t i o n f a c t o r a p p l i e d to a l l subsequent measurements.  The  was  s e n s i t i v i t y of  the balance depended on the v i s c o s i t y of the l i q u i d and estimated to be b e t t e r than 0.001 B.  was  gram/cu.cm.  Measurement of P a r t i c l e  Density  Conventional s p e c i f i c g r a v i t y b o t t l e s were used measure the d e n s i t y of the p a r t i c l e s .  The-density was  to based  on the known d e n s i t y of water (71), i n which the p a r t i c l e s were immersed. second  For those p a r t i c l e s which were" s o l u b l e i n water, a  immersing medium, benzene, was,.used.  The b o t t l e s which  c o n t a i n e d l i q u i d and p a r t i c l e s were b o i l e d to d r i v e out the a i r bubbles  trapped between the p a r t i c l e s .  a t the same temperature'by s t a n t temperature immediately  A l l weighings  were made  l e t t i n g the b o t t l e s stand i n a con-  bath s l i g h t l y above room temperature,  and  t i g h t e n i n g the cap on removing the b o t t l e from  the  bath i n order to a v o i d l o s i n g l i q u i d by e v a p o r a t i o n . C.  Measurement of L i q u i d  Viscosity  The k i n e m a t i c v i s c o s i t y of v a r i o u s t e s t l i q u i d s determined  was  by Cannon-Fenske v i s c o m e t e r s of a p p r o p r i a t e s i z e ,  e s s e n t i a l l y conforming  to the s p e c i f i c a t i o n s and  d e s c r i b e d i n ASTM manual (68).  procedures  The viscometers were immersed  IV-2  i n a constant temperature bath with temperature c o n t r o l l e d to w i t h i n + 0.05°F.  The e f f l u x time of the t e s t l i q u i d was mea-  sured by a stopwatch graduated i n d i v i s i o n s  of 0.2 seconds.  The stopwatches used were a l l t e s t e d a g a i n s t N.B.S. time n a l s broadcasted on S t a t i o n WWV  sig-  over 12-hour p e r i o d s , and  were found t o be a c c u r a t e to w i t h i n 0.027..  Calibration  of a  s e r i e s o f v i s c o m e t e r s r a n g i n g from s i z e 100 to s i z e 400 i s r e p o r t e d i n Appendix V.  V-1  APPENDIX V The  CALIBRATION OF VISCOMETERS  Cannon-Fenske v i s c o m e t e r s ranging from s i z e 100  s i z e 450 were c a l i b r a t e d liquid  by comparing  the e f f l u x time of a  i n two v i s c o m e t e r s of c o n s e c u t i v e s i z e number i n the  same bath a t 77°F.  Viscometer No.  B78 was  the standard on  which a l l the other l a r g e r v i s c o m e t e r s were based. calibrated  by Cannon L a b o r a t o r i e s .  c a l i b r a t i o n , which was  I t was  T h i s step-up procedure  o r i g i n a l l y suggested  found to be s a t i s f a c t o r y  f o r the r o u t i n e v i s c o m e t e r s .  The  for  s i z e viscometers at l i q u i d  the l a r g e r  than 200  seconds.  v  =  C t v  correction  f o r k i n e t i c energy  Thus v i s c o s i t y was  e f f l u x time h i g h e r  v  i n the viscometer of  The c a l i b r a t i o n constant of the  v i s c o m e t e r of the h i g h e s t s i z e number was  checked  standard o i l s u p p l i e d by Cannon L a b o r a t o r i e s . l e s s than 0.5%.  measuring  Procedures  for f i l l i n g ,  The  by the difference  c l e a n i n g and  e f f l u x time are d e s c r i b e d i n the A.S.T.M. manual ( 6 8 ) .  The for  as  e  c a l i b r a t i o n constant, C .  was  listed  is negligible  calculated  i s the e f f l u x time of the l i q u i d  e  was  The  c a l i b r a t i o n constant of each of the v i s c o m e t e r s used a r e i n T a b l e V-1.  of  i n A.S.T.M.  D445-53T (68) f o r b a s i c c a l i b r a t i o n of master v i s c o m e t e r ,  where t  to  excellent  agreement i n Table V-1  the l a r g e s t viscometer as determined  between C  v  (2.590)  by the standard o i l  (S-600) and t h a t o b t a i n e d by the step-up procedure u s i n g the blended s o l u t i o n s of automobile  crank case o i l s  (2.583) i s a  strong i n d i c a t i o n t h a t the l a t e r o i l s were Newtonian.  Table V-1 Summary of Viscometer C a l i b r a t i o n  Calibrated viscometer  Reference viscometer No."  No.  S i z e No.  B78  100  •&  H69  150  B78  C3  200  H69  ca  200  D91  300  C3  Standard liquid  Efflux time sec  Efflux time ratio  Ave. E f f l u x time ratio  Calibration constant a t 77*F C cs/sec v  -  -  -  0.01246  Oil A Oil B  208.7 324.4  2.581 2.584  2.582  0.03218  Oil C Oil D  334.7 338.7  3.390 3.387  3.388  0.1090  -  -  -  -  0.1086  Oil E Oil F  222.4 336.7  2.109 2.107  2.108  0.2299  -  '••  -'"  J781  '300  D91  PEG s o l *n  619.7  1.081  1.081  0.2485  C965  400  D91  Oil G Oil H  225.5 249.0  5.095 5.096  5.096  1.171  E60  400  D91  Oil H  254.0  4.985  4.985  1.149  V389  450  C965  Oil I PEG sol'n  160.4 337.9  2.205 2.206  2.206  2.583  V389  450  O i l S-600  562.5  -  -  2.590  *  C a l i b r a t e d by Cannon L a b o r a t o r i e s , Penn. State C o l l e g e .  •K*  C a l i b r a t e d by De V e r t e u i l ( 7 0 ) .  •SHHS-  Standard o i l s u p p l i e d by Cannon L a b o r a t o r i e s , k i n e m a t i c v i s c o s i t y = 1457 c s . a t 77  VI-1  APPENDIX V I  J U S T I F I C A T I O N OF  In the v i s c o u s f l o w r e g i o n the a particle  =  f r e e s e t t l i n g r a t e of  <»  L (/V?)g . 18 pv*,. 2  k K  u  general expression for multiparticle  - £ - « « .  and  «•„,  settling  w h e r e u and  (9)  (vi-i)  €  u  w  a r e m e a s u r e d u n d e r t h e same p h y s i c a l c o n d i t i o n s , much e f f e c t on  the v i s c o s i t y  the other p h y s i c a l p r o p e r t i e s i n equation. Uoo^eo  liquid viscosity  a t w h i c h Ua,  but not  Thus  = constant  u of e q u a t i o n VI-1  n  container  0i( )  Temperature change has  the  system i s  j£)  under v i s c o u s f l o w c o n d i t i o n s i n a g i v e n  =  if  uv  i n a given orientation i s  u  The  USING  (VI-2)  i s measured a t a temperature isv  t  which i s d i f f e r e n t  i s m e a s u r e d , u«» c a n  be  f o r which  from the  value  corrected to  i - Pm Mm  which i s then  the f r e e s e t t l i n g v e l o c i t y a t v i s c o s i t y v .  Equation VI-1  then  becomes  on  VI-2  UJL.  = 0.( )  (Vl-la)  €  Thus when temperature i s not c o n s t a n t , u^/u^itc-has the same f u n c t i o n a l r e l a t i o n s h i p as u/uco  p r o v i d e d that the r i g h t hand  s i d e of e q u a t i o n 8b i s independent of temperature. V a r i a t i o n of the r i g h t hand s i d e of equation 8b w i t h temperature was checked by the data from Run 2-, G l a s s beads i n Polyethylene G l y c o l s o l u t i o n .  The p a r t i c l e dimension, L, and, ..  p a r t i c l e d e n s i t y , yo , should not c o n t r i b u t e s i g n i f i c a n t change p  s i n c e s o l i d expansion c o e f f i c i e n t  i s v e r y s m a l l (0.274x10"^ i n  volume, ( 2 ) ) . V a r i a t i o n of l i q u i d d e n s i t y over 8 F a h r e n h e i t deg. of 457. PEG s o l u t i o n was from 1.085 to  g/cm  a t 67.2°F  3  1.0825 g/cm  3  a t 75.2°F  The c o r r e s p o n d i n g v a r i a t i o n of (p -p)/p 3 on/0= 2.977 g/cm as p  was c a l c u l a t e d  based  1.744 a t 67.2°F and  1.750 a t 75.2°F  Percentage change i s 0.357,.  Temperature  e f f e c t on the other  l i q u i d was expected t o be of the same o r d e r .  Actual  tempera-  t u r e v a r i a t i o n i n the experiment was much s m a l l e r than 8 F a h r e n h e i t degrees, as shown i n the o r i g i n a l data i n Appendix V I I .  APPENDIX V I I ORIGINAL DATA ON HINDERED SETTLING The f i r s t number i n Run No. s i g n i f i e s a combination of p a r t i c l e s and l i q u i d .  Except i n Run 8-P and 8-M, where  P and M stand f o r "pure" and "mixture" r e s p e c t i v e l y , the second number r e p r e s e n t s and the s i z e of the column used i n the s e t t l i n g .  The column diameters of 2.54 cm, 3.78 cm,  5.08 cm, 7.71 cm and 10.12 cm a r e denoted r e s p e c t i v e l y  by the  numbers 1 to 5. Nomenclature i n a l l computer p r i n t out i s e x p l a i n e d i n Appendix X I I I .  APPENDIX V I I  INDEX  SETTLING DATA  Run No.  Particles*  Liquid  Column Diameter  Page  S p h e r i c a l shape 1-1  0.114 cm Glass Beads  40% PEG S o l u t i o n  2.54 cm  VII-4  1-2  0.114 cm Glass Beads  40% PEG S o l u t i o n  3.78 cm  VII-5  1-3  0.114 cm Glass Beads  40% PEG S o l u t i o n  5.08 cm  VII-6  2-1  0.114 cm Glass Beads  45% PEG S o l u t i o n  2.54 cm  VII-8  2-2  0.114 cm Glass Beads  45% PEG S o l u t i o n  3.78 cm  VII-9  2-3  0.114 cm Glass Beads  45% PEG S o l u t i o n  5.08 cm  VII-10  7-3  0.0492 cm Glassi Beads  35.4% PEG S o l u t i o n  5.08 cm  VII-11  2.54 cm  VII -12  3.78 cm  VII -13  5.08 cm  VII -14  7.71 cm  VII -15  3.78 cm  VII -16  5.08 cm  VII -17  Cubic shape 3 -IA  0.0341 cm S a l t  Crystals  84.9% SAE  3 -2  0.0341 cm S a l t  Crystals  84.9% SAE  3 -3  0.0341 cm S a l t  Crystals  84.9% SAE  3 -4  0.0341 cm S a l t C r y s t a l s  84.9% SAE  4 -2  0.0391 cm S a l t C r y s t a l s  88.1% SAE  0.0391 cm S a l t C r y s t a l s  88.1% SAE  4 -3  *Dv i s used t o i n d i c a t e p a r t i c l e  size  low + Kerosene low + Kerosene low + Kerosene low 4 Kerosene low Kerosene low + Kerosene  <  APPENDIX VII INDEX (continued) SETTLING DATA Run No. Cubic  Particles*  Liquid  Column Diameter  Page  shape  5- 3  0.0282 cm S a l t C r y s t a l s  88.1% SAE 10W 4 Kerosene  5.08 cm  VII-18  6- 4  0.288 cm ABS P e l l e t s  66% SAE 30 + Kerosene  7.71 cm  VII-19  6-5  0.288 cm ABS P e l l e t s  66% SAE 30 + Kerosene  10.12 cm  VII-20  Segregation t e s t 8-P  35/42 mesh M i n e r a l Crystals  88.1% SAE 10W + Kerosene  3.5 cm  VII-21  8- M  90% 35/42 mesh + 10% 42/48 mesh Mixture of Mineral C r y s t a l s  88.1% SAE 10W + Kerosene  3.5 cm  VII-22  Angular  shape  9- 2  0.0508 cm M i n e r a l C r y s t a l s  95% SAE 10W + Kerosene  3.78 cm  VII-23  9-3  0.0508 cm M i n e r a l C r y s t a l s  95% SAE 10W + Kerosene  5.08 cm  VII-24  10-2  0.0426 cm M i n e r a l C r y s t a l s  88.1% SAE 10W + Kerosene  3.78 cm  VII-25  10-3  0.0426 cm M i n e r a l C r y s t a l s  88.1% SAE 10W + Kerosene  5.08 cm  VII-26  i  APPENDIX INDEX (continued) SETTLING Run No.  Particles*  DATA Liquid  Column  Page  Diameter F l a k y shape 11-2  0.135 cm Sugar C r y s t a l s  667, SAE 30 + SAE 10W  3.78 cm  VII-27  11- 3  0.135 cm Sugar C r y s t a l s  667, SAE 30 + SAE 10W  5.08 cm  VII-28  12- 3  0.113 cm Sugar C r y s t a l s  247, SAE 30 + SAE 10W  5.08 cm  VII-29  VISCOSITY DATA  VII-30  • '  <  M r-l I  VII-4  RUN 1-1 PARTICLES = GLASS BEADS LIQUID= P.E.G. SOLN 40/100 PARTICLE SIZE D = 0.1135 CM, D SIEVE OPENINGS 0.991/1 .168 MM ,  t  v  TEMP °F  DIST CM  SETTLING TIME SEC  74.23 74.23 75.42 74.55 75.00 78. 10 78.10 78. 10 77. 30 75.26 74.20 74.20 74.20 74.20 73.38 73.28 69,30 69.30 69.70 69. 70 69.80 69.80 71.80 71.80 72.90  20.0 20.0 20.0 30.0 30.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 10.0 10.0 10.0 10.0 10.0 10.0 6.0 6.0 6.0  51.8 51.5 49.2 81.8 82.3 45.4 45.9 45.5 45.6 52.0 52.7 52.8 51.4 49.8 65.7 64.4 56.8 52.4 67.5 69.2 91.4 92.4 69.9 65.9 66.5  DENSITY= 2.977 GM/CM DENSITY= 1.071 GM/CM = 2.54 CM, Dv/Ot = 0.0447 NO ELUTRIATION 3  3  U CM/SEC 0.386 0.388 0.407 0.367 0. 365 0.330 0.327 0.330 0.329 0.288 0.285 0.2 84 0.292 0.301 0.228 0.2 33 0. 176 0.191 0. 148 0.145 0.109 0. 108 0.086 0.091 0.090  U*NU 0.01CM /SEC 3  63.0 63.4 64.8 59.5 .58.6 49.9 49.3 49.7 50.4 46.1 . >6.5 46.4 47.6 49.2 37.9 3 8.7 31.8 34.5 26.5 25.9 19.6 19.4 14.7 15.6 15.1  EPS 2  0.90 0.90 0.90 0.88 0. 88 0.85 0.85 0.85 0.85 0.83 0.83 0.83 0.83 0.83 0.80 0.80 0.77 0.77 0.74 0.74 0.70 0.70 0.67 0.67 0.67  VII-5  RUN 1-2 PARTICLES= GLASS BEADS LIQUID= P.E.G.SOLN 40/100 PARTICLE SIZE D = 0.1135 CM, D SIEVE OPENINGS 0.991/1.168 MM, v  TEMP °F  DIST CM  SETTLING TIME SEC  75.03 75.03 75.00 75.00 74.00 74.00 73.40 73.40 74.00 74.63 75.57 75.00 74.83 77.13 77.13 76.60 76.10 73.60 73.60 73.60 73.80 73.88 73.40 73.40 73.40 70. 50 70.50 70.50 70.50 70.12 69.20 70.5 0 71.00 72.10 71.00  30.0 30.0 30.0 30.0 20.0 20.0 20.0 20.0 30.0 30.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 6.0 6^0 6.0 6.0 6.0  72.2 73.0 72.2 72.4 48.2 48.0 52.8 51.5 79.9 78.7 43.6 47.0 46.8 48.8 48.6 48.9 49.4 62.6 60.8 61.7 61.8 73.4 50.8 48.2 48.2 69. I 64.1 65.0 65.7 86.6 64.4 62.0 64.1 75.0 76.8  DENS ITY= 2.977 GM/CM DENS ITY= 1.071 GM/CM = 3.78 CM, Dv/Dt = 0.0300 NO ELUTRIATION 3  3  t  U CM/SEC 0.416 0.411 0.416 0.414 0.415 0.417 0.379 0.388 0.375 0.381 0.344 0.319 0.321 0.307 0.309 0.307 0.304 0.240 0.247 0.2 43 0.243 0.204 0.197 0.207 0.207 0.145 0.156 0.154 0.152 0.115 0.093 0.097 0.094 0.080 0.078  U*NU 0.01CM /SEC  EPS  3  66.8 66.0 66.8 66.6 68.0 68.3 62.8 64.4 61.5 . 61.7 54.7 51.3 51.7 47.3 47.5 47.7 47.7 39.6 40.8 40.2 39.9 33.6 32.7 34.4 34.4 25.5 27.5 27.1. 26.8 20.5 16.9 17.1 16.3 13.6 13.6  0.90 0.90 0.90 0.90 0.90 0.90 0.88 0.88 0.88 0.88 0.85 0.85 0.85 0.83 0.83 0.83 0.83 0.80 0.80 0.80 0.80 0.77 0.77 0.77 0.77 0. 74 0.74 0.74 0.74 0.70" 0.67 0.67 0.67 0.64 0.64  VII-6  RUN 1-3 PARTICLES= GLASS BEADS . LIQU.ID= P.E.G.SOLN 40/100 PARTICLE SIZE D = 0.1135 CM, Of SIEVE OPENINGS 0.991/1.168 MM, v  TEMP °C . 22.15 22.15 22.15 22.15 22.05 22.05 21.95 21.95 22.15 22.15 22.40. 21.65 21.85 22. 10 22.10 22.10 22.80 22.80 22.75 22.75 22.65 21.58 22.00 22.50 22.40 22.40 22.35 22.25 22.25 22.20 22.20 22.20 22.15 22.15 22.20 22.20 21.65 21.80 21.85 21.85 21.85 21.80 21.80 21.90  DIST CM 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 15.0 20.0 15.0 15.0 15.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 9.0 9.0 9.0 9.0 9.0 6^0 6.0 6.0 6.0 6.0 6.0 6.0  DENS ITY= 2.977 GM/CM DENS ITY= 1.071 GM/CM = 5.08 CM, Dv/Dt = 0.0223 NO ELUTRIATION  SETTLING TIME SEC  U CM/SEC  52.4 51.0 53.4 51.6 52.8 51.8 55.8 56.6 56.6 56.8 55.9 66.8 67.4 65.3 65.8 65.4 72.1 69.8 71.5 53.1 72.0 65.4 62.5 66.0 51.4 50.6 51.6 60.6 63.2 63.4 61.0 62.5 58.4 58.8 57.3 56.8 78.9 51.8 51.0 47.4 49.7 61.6 62.0 62.8  0.382 0.392 0.375 0.388 0.379 0.386 0.358 0.353 0.353 0.352 0..358. 0.299 0.297 0.306 0.304 0.306 0.277 0.287 0.280 0.282 0.278 0.229 0.240 0.227 0.233 0.237 0.233 0.198 0.190 0.189 0.197 0. 192 0.154 0.153 . 0.157 0.158 0.114 0.1 16 0.118 0.127 0.121 0.097 0.097 0.096  3  3  U*NU 0.01CM /SEC  EPS  3  .  65.1 66.9 63.9 66.2 64.9 66.1 61.6 60.8 60.3 60.1 .60.5 52.1 51.2 52.4 52.0 52.3 46.2 47.7 46.7 47.1 46.5 40.0 41.2 38.3 39.5 40. 1 39.4 33.7 32.3 32.2 33.5 32.7 26.3 26.1 26.8 27.0 19.9 20.0 20.3 21.9 20.8 16.9 16.7 16.5  0.90 0.90 0.90 0.90 0.90 0.90 0.88 0.88 0.88 0.88 0..88 0.85 0.85 0.85 0.85 0.85 0.83 0.83 0.83 0.83 0.83 0.80 _ 0.80 0.80 0.80 0.80 0.80 0.77 0.77 0.77 0.77 0.77 0.74 0.74 0.74 0.74 0.70 0.70 0.70 0.70 .0.70 0.67 0.67 0.67  VII-7 21.90 21.70 21.70 21.70 21.70  6.0 6.0 6.0 6.0 6.0  62.4 81.0 78.3 77.4 79.6  0.096 0.074 0.077 0.078 0.075  16.6 12.9 13.3 13.5 13.1  0.67 0.64 0.64 0.64 0.64  VII-8  RUN 2-1 PARTICLES= GLASS BEADS DENS ITY = 2.977 GM/CM LIQUID= P.E.G.SOLN 45/100 DENSITY^ 1.082 GM/CM PARTICLE SIZE Dv = 0.1135 CM, D+, = 2.54 CM, D /D| = 0.0447 SIEVE OPENINGS 0.991/1.168 MM, NO ELUTRIATION 3  3  v  TEMP °F 71.00 71.05 71.05 71.10 71.20 71.20 72.20 72.20 72.20 72.20 72.00 72.00 72.00 73.40 73.40 73.40 72.20 74.40 75.30 75.40 72.10 73.20 75.30  DIST CM  SETTLING TIME SEC  U CM/SEC  37.0 37.0 37.0 37.0 37.0 37.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 16.0 16.0 12.0 16.0 38.0 38.0 38.0 16.0 28.0 20.0  186.0 196.0 186.0 191.5 208.0 208.0 126.8 122.8 123.4 122.3 137.5 134.2 135.8 12 7.6 123.7 94.3 128.8 344.5 330.0 332.0 198.1 421.0 354.0  0.1989 0. 1888 0.1989 0.1932 0.1779 0.1779 0.1577 0. 1629 0.1621 0.1635 0. 1455 0.1490 0.1473 0. 1254 0.1293 0.1273 0.1242 0*1103 0.1152 0. 1145 0.0808 0.0665 0.0565  U*NU 0.01CM /SEC  EPS  3  63.4 60. 1 63.3 61.4 56.4 56.4 48.9 50.5 50.2 50.7 45.3 46.4 45.8 37.7 38.9 38.3 38.5 32.4 33.2 32.9 25.1 20.1 16.3  0.90 0.90 0.90 0.90 0.88 0.88 0.85 0.85 0.85 0.85 0.83 0.83 0.83 0.80 0.80 0.80 0.80 0.77 0.77 0.77 0.74 0.70 0.67  VII-9  RUN 2-2 PARTICLES= GLASS BEADS LIQUID* P.E.G.SOLN 45/100 PARTICLE SIZE D = 0.1135 CM, D S I E V E OPENINGS 0.991/1.168 MM, v  DENSITY* 2.977 GM/CM DENSITY* 1.082 GM/CM = 3.78 CM, Dv '/Dt = 0.0300 NO ELUTRIATION 3  t  TEMP °F  DIST CM  SETTLING TIME SEC  U CM/SEC  U*NU 0.01CM /SEC  70.70 71.50 71.40 71.40 71.40 72.87 72.87 72.87 72.87 71.50 72.50 72.50 72.40 72.20 74.50 75.50 72.60 72.60 74. 10 74.60  38.0 38.0 38.0 38.0 38.0 21.0 20.0 20.0 20.0 20.0 16.0 16.0 18.0 16.0 30.0 30.0 22.0 2 2.0 20.0 20.0  196.5 202.5 234.5 227.0 234.5 137.6 134.0 132.6 129.2 164.2 157.2 157.2 2 03 . 4 1 82.6 397.0 370.0 424.0 388.5 480.0 460.0  0. 19 34 0.1877 0.1620 0.1674 0.1620 0.1526 0.1493 0.1508 0.1548 0.1218 0.1018 0.1018 0.0885 0.0876 0.0756 0.0811 0.0519 0.05 66 0.0417 0.04 35  .62.1 59. 1 51.2 5 2.9 51.2 46.5 45.5 46.0 47.2 38.4 31.3 31.3 2 7.3 27. 1 22.2 23. 3 15.9 17.4 12.3 12.7  3  EPS 2  0.895 0.880 0.850 0.850 0.850 0.830 0.830 0.830 . 0.830 0.800 0.770 0.770 0.740 0.740 0.700 0.700 0.670 0.670 0.640 0.640  •VII-10  RUN 2-3 DENSITY* 2.977 GM/CM PARTICLES = GLASS BEADS DENSITY* 1.082 GM/CM SOLN 45/100 LIQUID* P . E . G. PARTICLE SIZE D = 0.1135 CM, Dt = 5. 08 CM, D /Dt = 0.0223 SIEVE OPENINGS 0.991/1.168 MM , NO ELUTRIATION 3  3  v  v  °F  D l ST CM  SETTLING TIME SEC  U CM/SEC  71.80 71.80 72.00 69.90 69.90 70.2 0 70.20 70.10 69. 58 69.58 69.58 69.80 69.80 69.80 69.95 70.00 70. 10 70.10 71.90 71.90 71.90 71.90 72.30 72.30 72.70 72.30 72.70 72.80 72.80 73.00 73.15 73. 15 75.50 75.50 70.60 72.05 72.05 72.15 72.15  20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 10.0 10.0 10.0 10.0 8.0 8.0 8.0 15.1 15.6 20.8 21.0 6.0 20.9 21.3 20.9 20.9 21.2 21.1 20.2 20. 1 21.0  96.4 96.2 96.2 100.8 103.7 108.8 109.5 109 .1 128.3 123.6 129.8 123.0 12 5.6 127.0 141.3 142.0 141.7 13 7.2 75.2 75.8 76.8 74.4 73. 1 74.5 74.0 139.0 149.0 234.0 244.0 68.2 305.5 311.0 278.0 305.0 423.0 398.0 371.0 429.0 481.5  0.2075 0.2079 0.2079 0.1984 0.1929 0.1838 0.1826 0.1833 0.1559 0.1618 0.1541 0.1626 0.1592 0.1575 0.1415 0.1408 0.1411 6.1458 0.13 30 0.1319 0.1302 0.1344 0.1094 0.1074 0.1081 0.1086 0.1047 0.0891 0.0863 0.08 80" 0.0684 0.0686 0.0752 0.0685 0.0500 0.0530 0.0544 0.0469 0.0436  TEMP  U*NU 0 .01CM /SEC 3  64.9 65.0 64.7 64.9 63.1 59.7 59.3 59.7 51.3 53.3 50.8 53.3 52.2 51.6 46.2 45.9 45. 9 47.4 41.5 41.2 40.6 41.9 33.8 33.2 33. 1 33.6 3 2.0 27.2 26.3 26.7 20.7 20.8 21.6 19.7 16.1 16.5 16.9 14.5 13.5  EPS 2  0.90 0.90 0.90 0.90 0.90 0.88 0.88 0.88 0.85 0.85 0.85 0.85 0.85 0.85 0.83 0.83 0.83 0.83 0.80 0.80 0.80 0.80 0.77 0.77 0.77 0.77 0.77 0.74 0.74 0.74 0.70 0.70 0.70 0.70 0.67 0.67 0.67 0.64 0.64  VII-11  RUN 7-3 DENSITY= 2.959 GM/CM PARTICLES = GLASS BEADS DEN SITY= 1.062 GM/CM LIQUID= P.E.G. SOLN 35.4 % PARTICLE SIZE O = 0.0492 CM, D t = 5. 08 CM, D /Dt = 0.0097 SIEVE OPENINGS 0.417/0.495 MM ,. NO ELUTRIATION 3  3  v  v  TEMP °F  DIST CM  SETTLING TIME SEC  U CM/SEC  U*NU 0 . 01CM / SEC  73.20 73.20 73.75 73.75 73.75 71.60 71.60 71.60 71.60 72.70 72.70 72.70 72. 70 73.70 73. 70 74.05 74.90 70.70 70.70 72.25 72.55 72.90 73.65 73.65 73.65 71.60 71.60 73.20 74.20 75.20  9.0 9.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 9.0 9.0 9.0 9.0 10.0 10.0 10.0 10.0 10.0  66.4 66.8 97.2 98.8 99.4 113.4 107.4 107.3 109.0 117.8 119.8 111.6 118.5 132.0 132.2 156.4 152.0 167.6 163.9 176.2 176.2 156.0 194.2 190.0 191.2 268.6 262.0 3 30.0 320.0 381.0  0.1355 0.1347 0.12 35 0.1215 0.1207 0.1058 0.1117 0.1118 0.1101 0.1019 0.1002 0.1075 0.1013 0.0909 0.0908 0.0 76 7 0.0789 0.0716 0.0732 0.0681 0.0681 0.0577 0.0463 0.0474 0.04 71 0.0372 0.0382 0.0303 0.0313 0.0262  14.75 14.67 13.30 13.08 13.00 11 .90 12.57 12.58 12.38 11.20 11.02 11.83 11.14 9.80 9.79 8.22 8.32 8.19 8.38 7.56 7.51 6.32 5.00 5.11 5.08 4. 19 4.29 3.30 3.34 2.75  3  EPS 2  0.95 0.95 0.92 0.92 0.92 0.90 0.90 0.90 0.90 0.88 0.88 0.88 0.88 0.85 0.85 0.82 0.82 0.82 0.82 0.80 0.80 0.77 0.74 0. 74 0.74 0.71 0.71 0.68 0.68 0.65  VII-12  RUN 3-1A PARTICLES= SALT CRYSTALS DENS ITY= 2.169 GM/CM LIQUID= SAE 10W 8 4 . 9 % + KEROSENE, DENS IT Y= 0.858 GM/CM PARTICLE SIZE D = 0.0341 CM, Dt = 2. 54 CM, Dv/Dt = 0.0134 SIEVE OPENINGS 0.250/0.298 MM , NO ELUTRIATION 3  3  v  TEMP °F  DI ST CM  SETTLING TIME SEC  U CM/SEC  71.10 71.10 71.10 71.80 71.80 71.80 71. 95 72.40 72.40 71.80 72.00 72.00 72.00 73.30 71.70 72.50 73.30 73.50 73.40 73.40 73.85 73.85 74.65 70.80 70.80 71.10 70.40 70.20  5.0 5.0 5.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0  29.8 31.0 28.6 65.4 67.1 69.6 65.5 70.2 72.8 84.6 82.3 103.2 95.0 96.0 114.6 116.0 136.4 132.7 163.2 165.7 210.3 210.4 2 05.0 279.0 294.5 270.6 296.6 285.6  0.1678 0. 1613 0.1748 0. 1529 0. 1490 0.1437 0. 1527 0.1425 0.13 74 0.1182 0. 1215 0.0969 0.1053 0.1042 0.0873 0.0862 0.0733 0.07 54 0.0613 0.0604 0.0476 0.04 75 0.0488 0.0358 0.0340 0.0370 0.0270 0.0280  io.b  10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 8.0 8.0  U*NU 0. 01CM /SEC 3  5.395 5. 186 5.622 4.827 4.704 4. 535' 4.800 4.429 4.271 3.731 3.815 3.042 3.305 3. 168 2.762 2.674 2.229 2.281 1.859 1.831 1.427 1.426 1.435 1. 161 1. 100 1. 188 0.883 0.921  EPS 2  0.95 0.95 0.95 0.92 0.92 0.92 0.92 0.90 0.90 0.88 0. 88 0.85 0.85 0.85 0. 83 0.83 0.80 0.80 0.77 0.77 0. 74 0.74 0.74 0.71 0.71 0.71 0.68 0.68  VII-13  RUN 3-2 P A R T I C L E S * SALT CRYSTALS DENSITY* 2.169 GM/CM LIQUID* SAE 10W 8 4 . 9 % + KEROSENE, DENSITY* 0.858 GM/CM PARTICLE SIZE D = 0.0341 CM, Dt = 3.78 CM, D /Dt = 0.0090 SIEVE OPENINGS 0.250/0.298 MM, NO ELUTRIATION 3  v  TEMP °F 71.20 71.20 71.20 71.80 71.80 71.80 71.85 72.40 72.40 72.40 71.90 71.90 72.00 71.80 71.80 71.80 72.90 71.50 72.40 73.45 73.60 73.45 73.45 73.80 73.80 74.30 70.90 70.90 71.20 70.30 70.30 70.30 70.30  v  DIST CM  SETTLING TIME SEC  U CM/SEC  U*NU 0.01CM /SEC  10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 9.9 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 8.0 8.0 8.0 8.0 8.0 6^0 6.0  59.1 60.5 59.5 66.8 67.4 68.7 67.1 71.7 70.7 72.3 84.6 83.0 82.0 96.7 99.8 99.0 95.8 116.0 115.0 136.2 135.3 165.2 167.0 210.7 205.8 205.0 222.8 226.4 215.5 287.6 294.1 273.2 274.8  0.1692 0. 1653 0.1681 0.1497 0.1484 0.1456 0.1490 0. 1395 0.1414 0.1383 0.1182 0.1205 0.1220 0. 1034 0.1002 0.1010 0.1028 0.0862 0.0870 0.0734 0.0739 0.0605 0.0599 0.0475 0.0486 0.0488 0.0359 0.0353 0.0371 0.0278 0.0272 0.0220 0.0218  5.427 5.301 5.390 4.726 4.683 4.595 4.698 4.336 4.398 4.300 3.721 3.793 3.829 3.264 3.163 3.189 3.157 2.743 2.704 2.225 2.231 1.834 1.814 1.426 1.460 1.448 1.161 1.142 1.191 0.912 0.892 0. 720 0.716  3  2  0.95 0.95 0.95 0.92 0.92 0.92 0.92 0.90 0.90 0.90 0.88 0.88 0.88 0.85 0.85 0.85 0.85 0.83 0.83 0.80 0.80 0.77 0.77 0.74 0.74 0.74 0.71 0.71 0.71 0.68 0.68 0.65 0.65  VII-14  RUN 3-3 P A R T I C L E S * SALT CRYSTALS DENSITY* 2.169 GM/CM LIQUID* SAE 10W 8 4 . 9 % + KEROSENE, DENSITY* 0.858 GM/CM PARTICLE SIZE D = 0.0341 CM, Dt = 5.08 CM, Dv/Dt = 0.0067 SIEVE OPENINGS 0.250/0.298 MM, NO ELUTRIATION 3  3  v  TEMP °F 72.70 72.70 72.70 72.70 72.00 72.00 72.00 72.00 72.20 72.20 72.20 71.75 71.75 71.75 71.75 72.30 72.30 72.30 72.30 73.70 73.70 73.70 74.10 74.10 74.70 74.70 74.70 75.10 75.30 75.30 75.30 75.30 73.80 74.20 75.00 75.30 75.30 75.50 75.50  DIST CM 16.0 16.0 12.0 12.0 13.0 13.0 12.0 12.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 12.0 16.0 16.0 16.0 16.0 16.0 14.0 20.0 20.0 20.0 16.0 16.0 16.0 16.0 8.0 8.0 8.0 8.0 8.0 8^0 8.0  SETTLING TIME SEC  _  U CM/SEC  U*NU 0.01CM /SEC  92.1 0.1737 91.1 0.1756 68.8 0.1744 68.8 0.1744 86.3 . 0.1506 87.0 0.1494 79.9 0.1502 79.9 0.1502 117.0 0.1368 120.0 0.1333 116.2 0.1377 132.6 0.1207 133.3 0.1200 134.5 0. 1190 130.2 0.1229 161.2 0.0993 154.5 0.1036 158.5 0.1009 118.0 0.1017 173.0 0.0925 173.7 0.0921 171.2 0.0935 209.5 ^0.0764 213.0 6.0751 182.3 0.0768 314.5 0.0636 322.0 0.0621 322.5 0.0620 322.5 0.0496 312.0 0.0513 311.0 0.0514 307.0 0.0521 204.0 0.0392 200.0 0.0400 200.8 0.0398 245.5 0.0326 239.3 0.0334 309.4 0.0259 320.0 0.0250  5.361 5.420 5.383 5.383 4.730 . 4.692 4.716 4.716 4.273 4.166 4*302 3.814 3.794 3.760 3.884 3.094 3.228 3.146 3.170 2.785 2.774 2.815 2.278 2.240 2.257 1. 869 1.825 1.804 1.436 1.484 1.489 1.508 1.178 1.190 1.162 0.943 0.968 0.745 0.720  3  EPS 2  0.95 0.95 0.95 0.95 0.92 0.92 0.92 0.92 0.90 0.90 0.90 0.88 0.88 0.88 0.88 0.85 0.85 0.85 0.85 0. 83 0.83 0.83 .0,80 0.80 0.80 0.77 0.77 0.77 0.74 0.74 0.74 0.74 0.71 0.71 0.71 0.68 0.68 0.65 0.65  VII-15  RUN 3-4 PARTICLES= SALT CRYSTALS DENSITY* 2.169 GM/CM SAE 10W 8 4 . 9 % + KEROSENE, DENS ITY= 0.858 GM/CM LIQUID= PARTICLE SIZE D = 0.0341 CMIt D = 7.71 CM, D /Dt = 0.0044 SIEVE OPENINGS 0.250/0.298 MM , NO ELUTRIATION 3  3  t  v  TEMP °F  DIST CM  SETTLING TIME SEC  U CM/SEC  70.50 70.50 70.50 70.62 70.62 71.83 71.83 70.05 70.39 70.39 70.53 70.53 71.07 71.07 71.20 71.11 71.11 71.52 71.55 71.05 71.05 71.45 71.20 71.45 71.50 71.80  14.0 8.0 8.0 8.0 8.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 12.0 10.0 10.0 10.0 10.0 10.0 10.0 8.0 8.0 8.0 6.0 6.0  85.8 48.6 49.6 54.5 55.7 75.0 75.0 77.7 85.7 86.7 102.2 103.6 117.3 116.5 140.2 141.0 141.3 173.7 172.2 214.6 213.4 209.6 214.7 259.7 246.8 245.5  0. 1632 0.1646 0.1613 0.1468 0.1436 0.13 33 0.1333 0.12 87 0.1167 0.1153 0.0978 0.0965 0.0853 0.0858 0.0856 0.0709 0.0708 0.05 76 0.0581 0.0466 0.0469 0.0382 0.0373 0.0308 0.0243 0.0244  v  U*NU 0. 0 1 C M / S E C 3  5.318 5. 365 5.256 4.770 . 4.667 4.203 4.203 4.241 3.813 3.769 3. 186 3.143 2.739 2.758 2. 742 2.277 2.272 1.829 1. 844 1.498 1. 507 1.215 1. 193 0.981 0. 773 0.771  EPS 2  0.95 0.95 0.95 0.92 0.92 0.90 0.90 0.90 0. 88 0.88 0.85 0. 85 0.83 0.83 0.83 0.80 0.80 0.77 0.77 0.74 0.74 0.71 0.71 0.68 0.65 0.65  VII-16  RUN 4-2 P A R T I C L E S - SALT CRYSTALS DENSITY* 2 . 1 6 3 G M / C M LIQUID* SAE 10W 8 8 . 1 % + KEROSENE, DENSITY* 0.861 GM/CM PARTICLE SIZE D = 0.0391 CM, Dt = 3.78 CM, Dv/Dt = 0.0103 SIEVE OPENINGS 0.295/0.351 MM, NO ELUTRIATION 3  3  v  TEMP °F 71.20 71.20 71.20 71.20 72.40 72.40 72.40 70.70 70.70 71.40 71.40 71.40 72.46 72.46 72.46 72.46 71.00 71.00 71.00 71.00 72.73 72.73 72.73 69.25 69.25 69.25 70.50 70.50 70.52 72.00 72.00 72.00 72.40 71.25 71.75 71.75 72.00 72.00 72. 15 73.20 73.20  Dl ST CM  SETTLING TIME SEC  U CM/SEC  10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 11.0 10.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 15.0 11.0 11.0 14.0 11.0 11.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 8.0 8.0 . 10.0 8.0 8.0  53.0 52.3 54.5 51.7 55.1 56.0 57.5 59.7 59. 1 65.0 63.2 70.0 71.9 74.5 79.8 78.0 98.8 98.9 94.7 94.7 148.3 108.3 106.1 180.8 141.9 144.1 156.0 157.1 157.0 191.2 193.2 181.3 191.0 244.4 242.3 242.3 236.1 242.1 303.4 295.5 296.6  0.18 87 0. 1912 0.18 35 0.19 34 0. 1815 0. 1786 0.1739 0.1675 0.1692 0.1538 0.1582 0.1571 0.1391 0.1477 0.13 78 0.1410 0.1113 0.1112 0.1162 0.1162 0.1011 0.1016 0.1037 0.0774 0.0775 0.0763 0.0641 0.06 37 0.0637 0.0523 0.0518 0.0552 0.0524 0.0409 0.0413 0.0413 0.0339 0.0330 0.0330 0.0271 0.0270  U*NU 0.01CM /SEC 3  7.30 7.39 7.09 7.48 6.80 6.69 6.52 6.56 6.63 5.92 6.09 6.04 5.20 5.52 5.16 5.28 4.33 4.32 4.51 4.51 3.76 3.77 3.85 3.15 3.15 3. 10 2.52 2.51 2.51 1.98 1.96 2.09 1 .96 1.58 1 .57 1.57 1.28 1.25 1.24 0.99 0*99  EPS 2  0.950 0.950 0.950 0.950 0.920 0.920 0.920 0.920 0.920 0.900 0.900 0.900 0.880 0.880 0.880 0.880 0.850 0.850 0.850 0.850 0.830 0.830 0.830 0.800 0.800 0.800 0.770 0.770 0.770 0.740 0.740 0.740 0.740 0.710 0.710 0.710 . 0.680 0.680 0.680 0.650 0.650  VII-17  RUN 4-3 P A R T I C L E S * SALT CRYSTALS DENSITY* 2.163 GM/CM LIQUID* SAE 10W 8 8 . 1 % + KEROSENE, DENSITY* 0.861 GM/CM PARTICLE SIZE D = 0.0391 CM, Df = 5.08 CM, Dv/Dt = 0.0077 SIEVE OPENINGS 0.295/0.351 MM, NO ELUTRIATION 3  v  TEMP °F 71.15 71.15 71.15 71.15 72.15 72.15 72.15 71.40 71.40 71.40 72.55 72.55 72.55 72.55 70.90 70.90 70.90 72.60 72.60 72.60 69.20 69.20 69.20 70.48 70.48 70.48 72.05 72.05 72.05 72.40 70.95 71.65 71.65 71.65 71.90 71.90 72.03 73.05 73.05  DIST CM 10.0 10.0 10.0 10.0 10.0 10.0 ' 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 11.0 11.0 11.0 15.0 11.0 11.0 14.0 11.0 11.0 10.9 10.9 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 8.0 8.0 8.0 8^0 8.0  SETTLING TIME SEC  U CM/SEC  54.0 53.8 53.4 52.0 56.5 56.4 58.2 66.3 64.7 64.7 72.3 71.2 72.2 72.2 98.0 99.5 95.1 148.8 107.6 106.5 184.3 144.0 145.4 173.3 172.8 156.0 189.5 191.7 180.5 185.7 245.7 236.9 237.7 238.5 234.4 240.0 241.3 299.1 298.0  0.1852 0.1859 0.1873 0.1923 0.1770 0.1773 0.1718 0. 1508 0.1546 0.1546 0.1383 0.1404 0.1385 0. 1385 0.1122 0.1106 0.1157 0.1008 0.1022 0. 1033 0.0760 0.0764 0.0757 0.0629 0.0631 0.0641 0.0528 0.0522 0.0554 0.0539 0.0407 0.0422 0.0421 0.0419 0.0341 0.0333 0.0332 0.0267 0.0268  U*NU 0.01CM /SEC 3  7.17 7.20 7.25 7.45 6.67 6.69 6.48 5.80 5.94 5.94 5.16 5.24 5.17 5.17 4.37 4.31 4.51 3.76 3.81 3.85 3.09 3.11 3.08 2.48 2.48 2.53 1.99 1.97 2.09 2.02 1.58 1.61 1.61 1.60 1.30 1.27 1.25 0.99 0.99  EPS 2  0.950 0.950 0.950 0.950 0.920 0.920 0.920 0.900 0.900 0.900 0.880 0.880 0.880 0.880 0.850 0.850 0.850 0.830 0.830 0.830 0.800 0.800 0.800 0.770 0.770 0.770 0.740 0.740 0.740 0.740 0.710 0.710 0.710 0.710 0.680 0.680 0.680 0.650 0.650  VII-18  RUN 5-3 P A R T I C L E S * SLAT CRYSTALS DENSITY* 2.161 GM/CM LIQUID* SAE 10W 8 8 . 1 % + KEROSENE, DENSITY* 0.861 GM/CM PARTICLE SIZE D = 0.0282 CM, Dt = 5.08 CM, D /Dt = 0.0056 SIEVE OPENINGS 0.208/0.250 MM, NO ELUTRIATION 3  3  v  v  TEMP °F  DIST CM  SETTLING TIME SEC  U CM/SEC  U*NU 0.01CM /SEC  70.65 70.65 70.65 70.70 70.70 71.92 71.92 69.92 70.37 70.37 70.55 70.55 71.20 71.40 71.21 71.21 71.35 71.50 70.90 70.90 71.30 71.10 71.41 71.65 71.99 72.90 72.69  8.0 8.0 8.0 8.0 8.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 8.0 8.0 8.0 8.0 6.0 6.0 7.0  85.4 85.4 84.7 94.5 95.0 123.9 126.6 128.6 140.7 142.6 159.4 160.4 173.2 174i8 199.4 195.4 244.9 247.2 307.4 298.9 297.4 302.7 375.6 464.0 351.2 453.2 518.4  0.0937 0.0937 0.0945 0.0847 0.0842 0.0807 0.0790 0.0778 0.0711 0.0701 0.0627 0.0623 0.0577 0.0572 0.0502 0.0512 0.0408 0.0405 0.0325 0.0335 0.0269 0.0264 0.0213 0.0172 0.0171 0.0132 0.0135  3.681 3.681 3.712 3.322 3.305 3.068 3.002 3.114 2.813 2.776 2.472 2.456 2.237 2.205 1.942 1.982 1.576 1.555 1.270 1. 306 1.039 1.026 0.821 0.660 0.648 0.490 0.503  3  EPS 2  0.950 0.950 0.950 0.920 0.920 0.905 0.905 0.905 0.890 0.890 0.870 0.870 0.850 0.850 0.830 0.830 0.800 0.800 0.770 0.770 0.740 0.740 0.710 0.680 0.680 0.650 0.650  VII-19  RUN 6-4 DENSITY* 1.061 GM/CM PARTICLES = ABS CUBIC PELLETS DENSITY* 0.876 GM/CM LIQUID* SAE 30 6 6 % + KEROSENE PARTICLE SIZE D * 0.2880 CM, Dt = 7.71 CM, D /Dt = 0.0374 NOMINAL LENGTH 1/10 INCH, NO SIEVING 3  3  v  TEMP °F  DIST CM  70.90 70.90 71.15 71.15 71.15 71. 15 70.50 70.50 71.42 71.42 71.42 72.38 72.38 72.38 72.38 71.85 70.05 70.05 70.78 70.78 71.95 72.12 69.67 69.67  10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 11.0 9.0 9.0 9.0 9.0 9.0 6.0 6.0 6.0 9.0  v  SETTLING TIME SEC 43.4 42.4 48.8 49.4 49.4 52.6 62.1 60.2 70.0 71.0 72.2 75.3 78.2 74.4 85.8 88.8 114.0 113.8 140.7 138.0 109.6 112.0 136.0 199.4  U CM/SEC  U*NU 0 .01CM /SEC  0.2304 0.2358 0.2049 0.2024 0.2024 0.1901 0.1610 0.1661 0.1429 0.1408 0.1385 0.1328 0.1279 0.1344 0.1282 0.1014 0.0789 0.0791 0.0640 0.0652 0.0547 0.0536 0.0441 0.0451  48.30 49.44 42.57 42.05 42.05 39.49 34.22 35.30 29.36 28.94 28.46 26.31 25.33 26.62 2 5.39 20.46 17.04 17.07 13*46 13.73 11.01 10.71 9.64 9.86  3  EPS 2  0.95 0.95 0.92 0.92 0.92 0.90 0.88 0.88 0.85 0.85 0 . 85 0.83 0.83 0.83 0.83 0.80 0.77 0.77 0.74 0.74 0.71 0.71 0.68 0.68  VII-20  RUN 6 - 5 D E N S I T Y * 1.061. GM/CM P A R T I C L E S * ABS CUBIC P E L L E T S D E N S I T Y * 0.876 GM/CM LIQUID* SAE 30 66 % + KEROSENE P A R T I C L E S I Z E D = 0 . 2 8 8 0 C M , Of = 1 0 . 1 2 C M , D / D t = 0 . 0 2 8 5 N O M I N A L L E N G T H 1 / 1 0 I N C H , NO S I E V I N G 3  3  v  v  TEMP °F  DIST CM  72.80 72.95 72.95 73.30 73.30 74.30 74.30 74.30 75.60 75.70 76.90 7 7 . 10 7 7 . 10 72.40 72.50 72.50 72.90 73.00 73.00 73. 10 71.10 71.10 7 1 . 10 71.90 72. 15 72. 15 73.40 73.40  12.0 12.0 6.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 9.0 9.0 9.0 9.0 9.0 6.0 6.0 6.0 9.0  SETTLING TIME SEC 45.0 49.0 24.7 48.0 48.0 56.4 54.4 53.8 54.5 55.4 61.8 61.2 62.8 84.2 88.5 84.0 103.2 105.5 101.0 98.2 131.8 129.5 127.2 150.0 100.8 103.2 115.0 185.3  U CM/SEC  U*NU 0.01CM /SEC  EPS  0.2667 0.2449 0.2429 0.2500 0.2500 0.2128 0.2206 6.22 3 0 0.2202 0.2166 0.1942 0.1961 0.1911 0.1425 0.1356 0.1429 0.1163 0.1137 0.1188 0.0916 0.0683 0.0695 0.0708 0.0600 0.0595 0.0581 0.0522 0.0486  52.06 47.56 4 7 . 18 47.95 47.95 39.42 40.87 41.33 39.05 38.28 32.85 32.93 32.09 28.21 26.75 2 8 . 18 22.62 22.05 23.03 17.70 14.21 14.47 14.73 12.09 11.88 11.61 9.97 9.28  0.95 0.95 0.95 0.92 0.90 0.90 0.90 0.90 0.88 0.88 0.85 0.85 0.85 0.83 0.83 0.83 0.80 0.80 0.80 0.77 0.74 0.74 0.74 0.71 0.71 0.71 0.68 0.68  3  VII-21  RUN 8-P PARTICLES* MINERAL CRYSTALS DENSITY* 2.623 GM/CM LIQUID* SAE 10W 8 8 . 1 % + KEROSENE, DENSITY* 0.861 GM/CM PARTICLE SIZE D.= 0.0384 CM, Dt = 3.50 CM, Dv/Dt = 0.0110 FROM SIEVING 35/42 MESH, SEGGREGATION TEST 3  3  v  TEMP °F  DIST CM  SETTLING TIME SEC  U CM/SEC  74.85 74.85 74.85 74.85 72.30 72.30 73.35 73.35 73.00 73.00 73.50 73.50 73.50 73.50 73.50 74.10 74. 10 74.10 74.10  10.0 4.0 4.0 4.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 3.0 3.0 3.0 3.0  37.0 15.5 15.4 15.4 26.8 27.0 37.4 37.4 57.2 54.0 59.0 54.7 57.6 55.4 57.4 45.2 52.0 50.8 50.2  0.2703 0.2581 0.2597 0.2597 0.1866 0.1852 0.1337 0.1337 0.0874 0.0926 0.0847 0.0914 0.0868 0.0903 0.0871 0.0664 0.05 77 0.0591 0.0598  U*NU 0.01CM /SEC 3  9. 54 9.11 9.16 9.16 7.03 6.98 4.90 4.90 3.23 3.42 3.09 3.34 3. 17 3.29 3.18 2.39 2.07 2.12 2.15  2  EPS 0.90 0.90 0.90 0.90 0.85 0.85 0.80 0.80 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.70 0.70 0.70 0.70  VII-22  RUN 8-M DENSITY* 2.623 GM/CM PARTICLES = MINERAL CRYSTALS LIQUID* SAE 10W 8 8 . 1 % + KEROSENE, DENSITY* 0.861 GM/CM PARTICLE SIZE D = 0.0378 CM, Dt = 3. 50 CM, Dv/Dt = 0.0108 SEGGREGATI ON TEST MIXTURE 9 0 % 35/42 MESH + 10 % 42/48 MESH , 3  3  v  TEMP °F  Dl ST CM  SETTLING TIME SEC  U CM/SEC  74.75 74.75 74.75 74.75 72.30 72.30 73.40 73.40 73.40 72.95 72.96 73.40 73.40 73.40 73.40 73.40 74.00 74.00 74.00 74.00  10.0 4.0 4.0 4.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 3.0 3.0 3.0 3.0  42.8 17.8 18.1 18.5 30.0 30.0 41.0 40.7 40.9 60.4 58.4 62.0 57.4 60.1 59.4 60.4 48.2 54.5 53.2 53.3  0.2336 0.2247 0.2210 0.2162 0.1667 0.1667 0.1220 0.1229 0.1222 0.0828 0.0856 0.0806 0.0871 0.0832 0.0842 0.0828 0.0622 0.05 50 0.0564 0.0563  U*NU 0. 01CM /SEC 8.26 7.95 7.82 7.65 6.28 6.28 4.46 4.50 4.47 3.06 3.17 2.95 3. 19 3.04 3.08 3.03 2.24. 1.98 2.03 2.03  EPS 0.90 0.90 0.90 0.90 0.85 0.85 0.80 0.80 0.80 0.75 0.75 0. 75 0.75 0.75 0.75 0.75 0.70 0.70 0.70 0.70  VII-23  RUN 9-2 P A R T I C L E S * MINERAL CRYSTALS DENSITY* 2.632 GM/CM LIQUID* SAE 10W 9 5 % + KEROSENE DENSITY* 0.862 GM/CM PARTICLE SIZE D = 0.0508 CM, Dt = 3.78 CM, Dv/Dt = 0.0134 SIEVE OPENINGS 0.417/0.495 MM, SIEVING + ELUTRIATION 3  v  TEMP °C  DIST CM  SETTLING TIME SEC  U CM/SEC  U*NU 0.01CM /SEC  26.65 26.65 26.65 26.65 27.37 27.37 27.37 27. 55 27.55 27.64 27.64 27.64 27.75 2 5.97 25.97 25.97 26.20 26.55 26.55 26.55 26.63 26.70 26.85 26.85 26.90 26.90 26.90 23.63 23.63 23.80 24.40 24.40 24.50 24.82 25.67 25.67 25.80  6.0 6^0 6.0 6.0 6.0 6.0 6.0 6^0 6.0 12.0 _12.0 12.0 12.0 12.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 12.0 12.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9^0 9.0 6.0 6.0 6.0 6.0  18.0 18.9 19.2 18.1 20.0 19.2 19.6 19.6 19.7 42.2 40.7 41.7 40.0 49.4 62.8 63.8 60.4 72.8 73.3 75.2 83.4 83.0 80.8 80.8 61.0 77.8 76.4 116.6 111.8 111.0 141.4 136.4 137.8 116.0 111.6 109.6 139.9  0.3333 0.3175 0.3125 0.3315 0.3000 0.3125 0.3061 0.3061 0.3046 0.2844 0.2948 0.2878 0.3000 0.2429 0.2389 0.2351 0.2483 0.2060 0.2046 0.1995 0.1799 0.1807 0.1485 0.1485 0.1475 0. 1157 0.1178 0.0772 0.0805 0.0811 0.0636 0.0660 0.0653 0.0517 0.0538 0.0547 0.0429  15.68 14.93 14.70 15.59 13.61 14.18 13.89 13.77 13.70 12.74 13.21 12.89 13.36 11.80 11.60 11.42 11.94 9.74 9.67 9.43 8.47 8.48 6.91 6.91 6.85 5.37 5.47 4.22 4.40 4.40 3.35 3.47 3.42 2.66 2.65 2.70 2.10  3  2  0.95 0.95 0.95 0.95 0.92 0.92 0.92 0.92 0.92 0.90 0.90 0.90 0.90 0.88 0.88 0.88 0.88 0.85 0.85 0. 85 0.83 0.83 _ 0.80 0.80 0.80 0.77 0.77 0.74 0.74 0.74 0.71 0.71 0.71 0.68 .0.68 0.68 0.65  VII-24  RUN 9-3 PARTICLES* MINERAL CRYSTALS DENSITY* 2.632 GM/CM LIQUID* SAE 10W 9 5 % + KEROSENE DENSITY* 0.862 GM/CM PARTICLE SIZE D = 0.0508 CM, Dt = 5.08 CM, D / D f = 0.0100 SIEVE OPENINGS 0.417/0.495 MM, SIEVING + ELUTRIATION 3  3  v  v  TEMP °C 26.50 26.50 26.50 26.50 27.34 27.34 27.34 27.55 27.65 27.65 27.65 27.75 25.90 25.90 25.90 26.10 26.50 26.50 26.50 26.60 26.60 26.65 26.85 26.85 26.90 26.90 26.90 26.90 23.55 23.55 23.70 24.32 24.32 24.45 24.80 25.62 25.62 25.85  DIST CM 6.0 6^0 6.0 6.0 6.0 6.0 6.0 6^0 12.0 12.0 12.0 12.6" 12.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 12.0 12.0 9.0 9^0 9.0 9.0 9.0 9.0 9.0 9^0 9.0 9.0 7.0 6.0 6.0 6.0  SETTLING TIME SEC  U CM/SEC  U*NU 0.01CM /SEC  18.3 18.3 19.0 18.6 19.5 19.0 19.7 19.6 42.3 41.0 41.7 41.4 47.8 63.3 63.3 61.8 73.3 74.1 74.4 83.0 82.7 83.6 81.0 81.8 60.5 76.6 75.7 75.2 113.2 112.2 112.0 139.2 138.5 135.1 134.7 109.5 107.6 142.5  0.3279 0.3279 0.3158 0.3226 0.3077 0.3158 0.3046 0.3061 0.2837 0.2927 0.2878 0.2899 0.2510 0.2370 0.2370 0.2427 0.2046 0.2024 0.2016 0.1807 0.1814 0.1794 0.1481 0.1467 0.1488 0. 1175 0.1189 0.1197 0.0795 0.0802 0.0804 0.0647 0.0650 0.0666 0.0520 0.0548 0.0558 0.0421  15.54 15.54 14.97 15.29 13.98 14.35 13.84 13.77 12.70 13.10 12.88 12.91 12.24 11.55 11.55 11.72 9.70 9.60 9.56 8.52 8.55 8.44 6.89 6.83 6.90 5.45 5.52 5.55 4.37 4.41 4.38 3.41 3.43 3.49 2.68 2.71 2.76 2.06  3  EPS 2  0.95 0.95 0.95 0.95 0.92 0.92 0.92 0.92 0.90 0.90 0.90 0.90 0.88 0.88 0.88 0.88 0.85 0.85 0.85 0.83 0.83 0.83 0.80 0.80 0.80 0.77 0.77 0.77 0.74 0.74 0.74 0.71 0.71 0.71 0.68 0.68 0.68 0.65  VII-25  RUN 10-2 P A R T I C L E S * MINERAL CRYSTALS DENSITY* 2.632 GM/CM LIQUID* SAE 10W 8 8 . 1 % + KEROSENE, DENSITY* 0.858 GM/CM PARTICLE SIZE Dv* 0.0426 CM, Df = 3.78 CM, Dy/Df = 0.0113 SIEVE OPENINGS 0.351/0.417 MM, SIEVING + ELUTRIATION 3  3  TEMP °F 74.75 74.75 75.60 75.60 75.70 75.70 76.30 76.30 76.30 76.10 76.10 75.95 75.95 73.8 5 73.85 73.85 74.80 74.80 74.80 71.90 71.90 71.90 73.65 73.65 74.25 74.40 74.40 73.50 73.50 73.20 73.20  DIST CM 9.0 9^0 9.0 9.0 12.0 12.0 9.0 9^0 9.0 12.0 12.0 12.0 12.0 12.0 12.0 9.0 12.0 12.0 12.0 12.0 9.0 9.0 9.0 9.0 9.0 6.0 6.0 6.0 6.0 6.0 6.0  SETTLING TIME SEC  U CM/SEC  24.5 23.0 29.0 28.4 36.2 38.3 28.6 30.0 29.0 46.0 44.0 58.3 59.2 72.6 76.8 55.6 81.6 77.2 82.2 110.8 81.2 83.6 100.1 98.2 127.6 86.6 86.8 114.2 112.7 143.4 141.0  0.3673 0.3913 0.3103 0.3169 0.3315 0.3133 0.3147 0.3000 0.3103 0.2609 0.2727 0.2058 0.2027 0.1653 0.1562 0.1619 0.1471 0.1554 0.1460 0. 1083 0.1108 0.1077 0.0899 0.0916 0.0705 0.0693 0.0691 0.0525 0.0532 0.0418 0.0426  U*NU 0.01CM /SEC  EPS  3  13.00 0.95 13.84 0.95 10.74 0.92 10.97 0.92 11.45 0.92 10.82 0.92 10.70 0.90 10.20 0.90 10.55 0.90 8.92 0.88 9.32 . . . 0 . 8 8 7.06 0.85 6.96 0.85 5.99 0.82 5.66 0.82 5.86 0.82 5.20 0.80 5.49 0.80 5.16 0.80 4.13 0.77 4.23 0.77 4.10 0.77 3.27 0.74 3.34 0.74 2.53 0.71 2.47 0.71 2.47 0.71 1.92 0.68 1.95 0.68 1.54 0.65 1.57 0.65  VII-26  RUN 10-3 P A R T I C L E S * MINERAL CRYSTALS DENSITY* 2.632 GM/CM LIQUID* SAE 10W 8 8 . 1 % + KEROSENE, DENSITY* 0.858 GM/CM PARTICLE SIZE D = 0.0426 CM, Df = 5.08 CM, D /D| = 0.0084 SIEVE OPENINGS 0.351/0.417 MM, SIEVING + ELUTRIATION 3  3  v  TEMP _°F 74.50 74.50 75.40 75.40 75.40 76.30 76.30 76.30 76.10 76.10 76.00 76.00 76.00 76.00 73.80 73.80 73.80 74.60 74.60 71.80 71.80 71.80 73.60 73.60 74.20 74.20 74.40 73.50 73.50 73.20 73.20 73.20  DIST CM 9.0 9.0 12.0 9.0 9.0 9.0 9.0 11.0 11.0 12.0 14.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 9.0 9.0 9.0 9.0 9.0 6^0 6.0 6.0 6.0 6.0 6.0 6.0  v  SETTLING TIME SEC  U CM/SEC  26.2 25.6 39.5 29.7 29.5 29.6 31.6 36.4 44.3 44.8 66.1 55.6 59.6 56.8 72.0 73.7 74.5 83.3 83.2 114.2 85.1 84.5 99.2 98.0 125.1 85.6 83.0 110.8 112.0 139.0 144.4 142.2  0.3435 0.3516 0.3038 0.3030 0.3051 0.3041 0.2848 0.3022 0.2483 0.2679 0.2118 0.2158 0.2013 0.21 13 0.1667 0.1628 0.1611 0.1441 0.1442 0.1051 0.1058 0.1065 0.0907 0.0918 0.0719 0.0701 0.0723 0.0542 0.0536 0.0432 0.0416 0.0422  U*NU 0.01CM /SEC  EPS  3  12.23 12.52 10.57 10.54 10.61 10.34 9.69 10.28 8.49 9.16 7.26 7.40 6.90 7.24 6.04 5.90 5.84 5.12 5.12 4.02 4.04 4.07 3.31 3.35 2.58 2.52 2.58 1.98 1.96 1.5*9 1.53 1.55  0.95 0.95 0.92 0.92 0.92 0.90 0.90 0.90 0.88 0.88 0.85 0.85 0.85 0.85 0.82 0.82 0.82 0.80 0.80 0.77 0.77 0.77 0.74 0.74 0.71 0.71 0.71 0.68 0.68 0.65 0.65 0.65  VII-27  RUN 11-2 P A R T I C L E S * SUGAR CRYSTALS DENSITY* 1.590 GM/CM LIQUID* SAE 30 6 6 % + SAE 10W DENSITY* 0.876 GM/CM PARTICLE SIZE D = 0.1346 CM, Dt = 3.78 CM, Dv/Dt = 0.0356 SIEVE OPENINGS 0.991/1.168 MM, SIEVING + ELUTRIATION 3  3  v  TEMP °F 71.90 71.90 71.90 72.70 72.70 72.70 73.40 73.40 73.80 73.80 73.80 73.20 73.20 73.20 73.20 73.70 73.70 73.70 71.50 71.50 71.50 73.70 73.70 74.00 73.60 74.20 72.50 72.50 74.20  DIST CM 9.0 9_±0 9.0 9.0 9.0 9.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 9.0 9^0 9.0 9.0 9.0 9.0 6.0 6^0 6.0 6.0 5.8  SETTLING TIME SEC  U CM/SEC  U*NU 0.01CM /SEC  39.4 39.4 41.0 44.6 43.4 43.2 60.8 61.7 64.5 64.0 66.4 77.4 78.8 75.0 75.5 96.3 90.6 91.8 85.0 83.0 81.2 103.1 95.4 96.2 78.0 85.5 112.2 107.4 133.0  0.2284 0.2284 0.2195 0.2018 0.2074 0.2083 0.1974 0.1945 0.1860 0.1875 0.1807 0.1550 0.1523 0. 1600 0.1589 0.1246 0.1325 0.1307 0.1059 0. 1084 0.1108 0.0873 0.0943 0.0936 0.0769 0.0702 0.0535 0.0559 0.0436  43.35 43.35 41.66 37.21 38.24 38.42 35.48 34.96 32.95 33.21 32.01 28.07 27.58 28.97 28.78 22.15 23.55 23.24 20.38 20.87 21.34 15.52 16.77 16.45 13.73 12.25 9.93 10.38 7.62  3  2  0.95 0.95 0.95 0.92 0.92 0.92 0.90 0.90 0.88 0.88 0.88 0.85 0.85 0.85 0.85 0.82 0.82 0.82 0.80 0.80 0.80 0.77 0.77 0.77 0.74 0.74 0.71 0.71 0.68  VII-28  RUN 11-3 P A R T I C L E S * SUGAR CRYSTALS DENSITY* 1.590 GM/CM LIQUID* SAE 30 6 6 % + SAE 10W DENSITY* 0.876 GM/CM PARTICLE SIZE D = 0.1346 CM, Dt = 5.08 CM, Dv/Dt = 0.0265 SIEVE OPENINGS 0.991/1.168 MM, S I E V I N G + ELUTRIATION 3  v  TEMP °F 71.65 71.65 72.70 72.70 72.70 73.40 73.40 73.40 73.85 73.85 73.85 73.20 73.20 73.30 74.05 71.30 71.30 72.00 73.65 73.65 73.90 73.00 73.20 73.20 74.30 73.30 73.30 72.70 73.50  DIST CM 9.0 9^0 9.0 9.0 9.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 9.0 9.0 9.0 9.0 9_^0 9.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0  SETTLING TIME SEC  U CM/SEC  U*NU 0.01CM /SEC  41.0 41.0 44.4 43.0 43.2 60.4 59.4 61.0 65.2 66.0 65.8 75.2 75.3 94.4 92.0 82.8 81.0 81.0 97.0 97.2 97.0 83.4 79.7 80.2 78.3 109.6 108.2 143.0 138.8  0.2195 0.2195 0.2027 0.2093 0.2083 0.1987 0.2020 0. 1967 0.1840 0.1818 0.1824 0.1596 0.1594 0.1271 0.1304 0.1087 0.1111 0.1111 0.0928 0.0926 0.0928 0.0719 0.0753 0.0748 0.0766 0.0547 0.0555 0.0420 0.0432  42.03 42.03 37.38 38.60 38.42 35.71 36.32 35.36 32.54 32.14 32.24 28.90 28.86 22.93 22.89 21.07 21.54 21.01 16.53 16.49 16.37 13.12 13.63 13.55 13.34 9.88 10.00 7.74 7.74  3  2  0.95 0.95 0.92 0.92 0.92 0.90 0.90 0.90 0.88 0.88 0.88 0.85 0.85 0.82 0.82 0.80 0.80 0.80 0.77 0.77 0.77 0.74 0.74 0.74 0.74 0.71 0.71 0.68 0.68  VII-29  RUN 12-3 DENSITY* 1.590 GM/CM PARTICLES = SUGAR CRYSTALS DENSITY* 0.870 GM/CM SAE 30 2 4 % + SAE 10W LIQUID* PARTICLE SIZE D * 0.1133 CM, Dt = 5. 08 CM, Dv/Dt = 0.0223 SIEVE OPENINGS 0. 883/0.991 MM, SIEVING + ELUTRIATION 3  3  v  TEMP op  74.90 74.90 74.90 76.50 76.50 76.50 78.20 78.20 78.20 78.20 78.20 77.25 77.25 77.25 79.40 79.40 79.40 75.20 75.20 76.80 79.45 79.45 79.50 80.10 80.80  DIST CM  SETTLING TIME SEC  U CM/SEC  U*NU 0 .01CM /SEC  9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 12.0 12.0 9.0 12.0 12.0 12.0 12.0 11.9 9.0 9.0 9.0 6.0 6.0 6.0  32.4 31.8 30.4 32.5 33.0 32.4 32.4 31.7 33.0 31.6 33.4 47.5 49.8 36.2 49.4 51.4 52.0 74.6 73.2 59.3 68.2 67.2 59.4 75.0 92.6  0.2778 0.2830 0.2961 0.2769 0.2727 0.2778 0.2778 0.2839 0.2727 0.2848 0.2695 0.2526 0.2410 0.2486 0.2429 0.2335 0.2308 0.1609 0.16 26 0.1518 0.1320 0.1339 0. 1010 0.0800 0.0648  31 .43 32.02 33.50 29.73 29.28 29.82 28.24 28.87 27.73 28.96 27.40 26 .49 25.27 26.07 23.78 22.86 22.59 18.02 18.21 16.14 12.90 13.09 9.86 7.65 6.04  EPS  3  0.95 0.95 0.95 0.92 0.92 0.92 0.90 0.90 0.90 0.90 0.90 0.88 0.88 0.88 0.85 0.85 0. 85 0.82 0.82 0.80 0.77 0.77 0.74 0.71 0.68  VISCOSITY DATA Run 1-1,2 . Temperature °F Viscosity cs  68.00 185.90  69.00 181.90  70.00 178.06  71.03 174.26  71.96 170.98  73.01 167.21  74.01 163.80  75.00 160.79  Temperature °F Viscosity cs  77.02 154.14  77.99 151.23  78.99 148.26  18.80 194.79  20.10 184.86  20.48 182.26  21.16 177.80  22.02 171.50  23.05 165.02  24.16 158.45  25.00 153.39  Temperature °F Viscosity cs  68.02 341.11  69.00 333.74  70.03 326.00  71.02 318.51  72.00 311.31  73.02 303.52  74.45 293.50  75.10 289.47  Temperature °F Viscosity cs  77.13 278.46  68.02 341.11  69.00 333.74  70.03 326.00  71.02 318.51  72.00 311.31  73.02 303.52  75.10 289.47  77.13 278.46  Temperature op Viscosity cs  67.00 35.66  68.00 34.86  69.03 33.86  70.00 33.04  71.00 32.24  72.01 31.39  73.00 30.63  75.02 29.15  Temperature °F Viscosity cs  77.20 27.64  75.97 157.55  Run 1-3 Temperature °C Viscosity cs Run 2-1,2 76.25 283.00  Run 2-3 Temperature °F Viscosity cs Run 3-lA,2,3 76.00 28.43,  VISCOSITY DATA  (continued)  Run 3-4  Temperature ° F Viscosity cs  68.00 34.72  69.01 33.86  70.00 32.99  71.00 32.19  71.95 31.43  73.01 30.62  74.00 29.88  68.00 42.04  69.00 40.94  70.00 39.88  71.00 38.87  72.00 37.85  73.00 36.90  74.00 35.90  68.00 42.17  69.01 41.05  70.00 39.96  71.00 38.94  71.95 37.98  73.01 36.94  74.00 36.02  68.05 231.6  69.20 221.9  69.98 216.3  71.10 208.2  72.00 200.7  73.00 193.9  74.00 186.9  Temperature ° F Viscosity cs  68.05 231.64  69.20 221.86  69.98 216.3  71.10 208.16  72.00 200.66  73.06 193.87  74.00 186.96  Temperature ° F Viscosity cs  76.20 173.43  77.20 167.34  Run 4 - 2 , 3  Temperature ° F Viscosity cs Run  5-3  Temperature ° F Viscosity cs Run  75.00 34.94  6-4  Temperature ° F Viscosity cs Run 6-5  Run 7-3  Temperature ° F Viscosity cs  74.90 181.97  w 70.00 116.07  71.00 113.73  72.00 111.64  73.00 109.27  74.00 107.20  75.00 105.18  76.00 103.06  • t—i £  VISCOSITY DATA (continued) Run  8-P,M  Temperature °F Viscosity cs  72.00 38.01  73.05 36.92  73.98 36.06  74.90 35.24  Temperature °C Viscosity cs  23.00 56.56  23.50 55.06  24.00 53.67  24.50 52.32  25.00 51.04  25.50 49.70  26.00 48.51  Temperature °C Viscosity cs  27.50 45.10  28.00 44.00  71.00 39.04  71.85 38.18  73.00 37.02  74.10 35.98  75.05 35.10  76.10 34.18  77.10 33.32  71.00 195.90  72.00 189.10  73.00 182.40  74.00 175.80  75.00 169.90  75.00 112.80  76.00 109.00  77.00 105.70  78.00 102.30  79.00 99.15  Run 9-2,3 26.50 47.40  Run 10-2,3 Temperature °C Viscosity cs Run 11-2,3 Temperature °F Viscosity cs  70.00 203.00  Run 12-3 Temperature °F Viscosity cs  74.00 116.30  80.00 96.02  81.20 91.90  27.00 46.16  VIII-1  APPENDIX V I I I  CALCULATED RESULTS FOR HINDERED SETTLING  Data not used  in  curve  fitting  of  eqt.  la  VIII-2  •55  Hi  Hi  55 ills  it .!  c  1  Ilil  m  SPSS  ml  ,1  si  is Nil* I ii  :fi= s s c s ••???<?<  r  £55  Mil  1 Hi i m H-.  mi  P 55° Bit  IIIIlSIs:  2-°  ???????  4  'Sn  \  i  ????  =1  J- <N O  !1!  IS  m  H  iii  I!!  is ?P SSSSS f  m is:  r  21111  AM  p 2  sgssss  l i t  i illll  Issssi  I  -  m  sllll  illll  II  .s  -ESS  mm km  illll  O  s  mum  2  ;I§=II§  iff  , 0 0 0 0 c . .  ' s i * " Mi ?S P S 'ha  O > - IM  4  o  a  llfs  s liii=5|E  ????  55 2  j!3'j§  11  m  V I I I-3  VIII-4  is  si 55'  il  S5Ssi;=s=s?  i,  is  S3  I i i  tm  .i.sss:  IIsag  hi  j:l ll  mi?  I OCo  f,  o o o o o o o o o  ???  BP  SIMS  -a  I'  ESS  iii  .illls  s- s 1  IS!  m  °"i i i  55  sssssissl 11 aSssss Id d o  ????  1=5  ????  55°  .22  3OO  iii  •5s  d  L lis  s s!ss==lsl  dd  3SBS  I' ESS  Esse  11 -1 -  - :  Ills  S?3  3  0  •sj O ^ -  00  l =a  nnnmm  So -  m  Ilff  s~i s  -  1  55°'  iSS  I  ????  m  EI  i Hi: i  22i  I!liIi=I Up  IB.si::  ill  ddd  o—  his ±11  is  Isli  Ii;  ^S3i  s=s Is!  iii >oco  ii  il! Ik  ii  fffiiiiiiiii  is  55 S  IssssissSs?  5  Iddc  d s  fe  IK s.' „S . 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X  ••€5  ?????  22  111,  Hi  Ills;  Ilisi 0 0 = 0 0  -a  illll-  ooooc  odo  , 0 0 0 0  §5B¥  OJ O  lis!  w  5  2SSS  Sog  00  5  o  S  £  I  2 s  55  2  I  So'  2  lUV:  il3  0 0 0 0 0 0 , 0 0 0 0 0  ft  Is!  fill  i;  P Ldo  SEES  ^-  m r\j IN (V — ^  hili  —o IS  IX-1  APPENDIX IX  DATA AND RESULTS FOR FREE SETTLING Original  Run No.  Data  Particles  Column  Page  2-Single  0.114 cm Glass Beads  7.71 cm  IX-2  7-Single  0.0492 cm Glass Beads  5.08 cm  IX-4  3-Single  0.0341 cm S a l t  Crystals  5.08 cm  IX-6  4-Single  0.0391 cm S a l t  Crystals  5.08 cm  IX-8  5-Single  0.0282 cm S a l t  Crystals  5.08 cm  IX-10  6-Single  0.288 cm ABS P e l l e t s  7.71 cm  IX-12  Calculated Results Run No.  Page  2-Single  IX-13  1-Single  IX-13  7-Single  IX-14  3-Single  IX-15  4-Single  IX-16  5-Single  IX-17  6-Single  IX-18  VISCOSITY DATA The f i r s t number i n Run No. i n d i c a t e s  IX-19 the same combina-  t i o n of p a r t i c l e s and l i q u i d as used i n the h i n d e r e d s e t t l i n g tests.  IX-2  Run 2- S i n g l e  TEMP DEG. F  .  0.114  DIST CM  70.50 10.0 10.0 70.50 20.0 70.50 20.0 70.60 20.0 70.60 20.0 70.60 70.80 20.0 20.0 . 70.80 20.0 70.80 70.80 20.0 70.80 20.0 20.0 70.80 20.0 70.80 20.0 70.80 20.0 70.10 70.20 20.0 20.0 70.20 70.20 20.0 20.0 70.20 20.0 70.20 20.0 70.20 70.20 20.0 70.20 20.0 20.0 70.20 20.0 70.20 20.0 70.20 70.20 20.0 20.0 70.20 70.20 20.0 20.0 70.20 20.0 70.20 20.0 . 70.20 70.20 20.0 20.0 70.20 70.20 20.0 70.20 20.0 20.0 70.20 70.20 .20.0 20.0 70.20 20.0 70.20 20.0 70.20 20.0 70.20 70.20 20.0 _70..20_.._ .... . 2 0 . 0 70.20 20.0 70.20 20.0 20.0 70.20  cm G l a s s Beads i n 7.71 cm Column  SETTLING TIME SEC  U CM/SEC  16.4 15.6 28.5 27.4 35. 1 35.1 32.4 35.3 32.7 34. 1 35.8 36. 1 33.5 34.2 35.0 27.2 33.9 30.4 33.2 35.7 38.0 34.7 35.0 35.9 32.0 28.4 35.4 31.5 35.6 29.8 33.2 38.0 30.0 27.2 35.0 37.4 28.7 35.0 31.2 36.4 31.0 33.5 30.7 28.2 31.0 27.4 26.9  0.61 0.64 0.70 0.73 0.57 0.57 0.62 0.57 _ 0.61 0.59 0.56 0.55 0.60 0.58 0.57 0.74 0.59 0.66 0.60 0.56 0.53 0.58 0.57 0.56 0.63 0.70 0.56 0.63 0.56 0.67 0.60 0.53 0.67 0.74 0.57 0.53 0.70 0.57 0.64 0.55 0.65 0.60 0.65 ... 0.71 0.65 0.73 0.74  U*NU 0.01CM /SEC 3  123.32 129.65 141.93 147.37 115.04 115.04 124.20 113.99 123.06 118.01 112.40 111.47 120.12 117.66 116.37 149.49 119.94 133.75 122.47 113.89 107.00 117.18 116.17 113.26 127.06 143.17 114.86 129.08 114.21 136.44 122.47 107.00 135.53 149.49 116.17 108.72 141.67 116.17 130.32 111.70 131.16 121.37 132.44 144.18 131.16 148.39 151.15  2  ..  .  . _  _  ...  _._ ... .  70.20 70.20 70.20 70.20 70.20 70.20 70.20 70.20 70.20 70.20 70.20 68.85 68.68 68.65 68.65 68.65 68.80 68.80 68.80 68.80 68.90 69.00 69.00 69.00 69.00 69.00 69.00 69.00 69.00 69.25 69.70 69.25 69.25 69.40 69.40 69.40 69.50 69.50 69.50 69.50 69.50 69.70 69.70 69.70 69.70 69.70 69.70 69.70 69.70 69.70 69.80 69.80 69.90  .  20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 .; 20.0 20.0 20.0 10.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 10.0 20.0 20.0 20.0 20.0 10.0 20.0 20.0 20.0 20.0 20.0 10.0 20.0 20.0 20.0  29.2 36.1 31.3 26.6 38. 1 35.7 35.3 33.6 37.4 33.8 36. 1 17.6 30.0 36.3 36.0 31.6 34.0 29.0 31.9 29.9 33.0 31 .3 29.6 31.8 32.6 34.8 34.8 32.9 35.3 31.7 32.2 34.6 36.2 32.8 35.4 30.6 26.4 34.8 15.4 36.6 33.6 33. 1 28.8 16.8 33.7 34.2 34.0 33.6 30.2 16.8 29.4 28.6 35.9  _..  0.68 0.55 0.64 0.75 0.52 0.56 0.57 0.60 0.53 0.59 0.55 0.57 0.67 0.55 0.56 0.63 0.59 0.69 0.63 0.67 0.61 0.64 0.68 0.63 0.61 0.57 0.57 0.61 0.57 0.63 0.62 0.58 0.55 0.61 0.56 0.65 0.76 0.57 0.65 0.55 0.60 0.60 0.69 0.60 0.59 0.58 0.59 0.60 0.66 0.60 0.68 0.70 0.56  IX-3 139.25 112.63 129.90 152.86 106.72 113.89 115.18 . 121.01 108.72 120.30 112.63 118.96 140.09 , 115.85 116.82 133.09 123.29 144.55 131.41 140.20 126.76 133.35 141.01 131.26 128.04 119.94 119.94 126.87 118.24 130.93 127.58 119.96 114.65 126.11 116.85 135.18 156.33 118.59 133.99 112.76 122.83 124.11 142.65 122.27 121.91 120.12 120.83 122.27 136.03 122.27 139.41 143.31 113.91  IX-4  Run 7-  Single  DI ST CM  TEMP DEG. F  _  69.75 69.75 69.70 69. 70 69. 70 69.70 69.80 69.80 69. 80 69.90 70.00 70.05 70.05 70.10 70.10 70. 10 70.40 70.40 70.40 70.40 70.45 70.50 70. 50 70.50 70.60 70.60. 70. 70 70. 70 70.75 70.75 "70.80 70.80 70.80 70.90 70.90 70.90 70.95 71.00 71.00 71.00 71.00 71.05 71.05 71.10 71. 10 71.15 71.15  0 . 0 4 9 7 cm G l a s s  .  •10.0 _..io.o 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10..0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10,0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0  Beads In 5.08 cm Column  SETTLING TIME SEC 52.4 48.8 44.8 52.8 44.2 45.6 47.8 43.6 50.6 46.4 56.6 50.0 47.2 38.8 46.8 38.0 54.2 43.0 48.2 44.0 42.0 45.6 49.4 47.6 44.8 50. 2 44.0 47. 8 49.0 43. 2 43. 8 40.6 43.6 51.4 55.3 50.4 53.8 45.8 39.8 51.2 52.9 45.8 58. 5 48.2 44.0 51.6 51.8  U CM/SEC 0. 19 0.20 0.22 0.19 0.23 0.22 0. 21 0.23 0.20 0.22 0.18 0.20 0.21 0.26 0.21 0.26 0. 18 0.23 0.21 0.23 0.24 0.22 0.20 0.21 0.22 0.20 0.23 0.21 0.20 0.23 0.23 0.25 0.23 0. 19 0.18 0.20 0. 19 Q.22._ 0.2 5 0.20 0.19 0.22 0. 17 0.21 0.23 0. 19 0. 19  U*NU 0.01CM / S E C 3  21.69 23.29 25.39 21.55 25.74 24.95 23.75 26.04 22.44 24.42 19.98 22.59 23.93 29.08 24. 11 29.69 20.69 26.08 23.27 25.49 26.68 24.55 22.66 23.51 24.93 22.25 25.34 23.32 22.73 25.78 25.40 27.40 25.52 21 .60 20.08 22.03 20.62 24.19 27.84 21.64 20.95 24. 17 18.92 22.94 25.13 21.41 21.33  2  _  71.15 71.50 71.50 71.50 71.50 71.50 71.50 71.40 71.40 71.40 71.40 71.40 71.55 71.55 71.55 71.55 71.60 71.60 71.60 71.60 71.70 71.70 71.70 71.70 71.70 71.70 71.70 71.80 71.80 7 1 . 80 71.80 71.80  10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 1-0.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0  46.6 56.8 51.6 52.9 46.4 43.6 44.0 48.6 44. 4 44.2 42.0 43.6 42.0 43.0 48.0 52.0 44.0 43.6 39. 5 40.4 52.6 53.8 40.8 40.6 45.6 40.2 48.6 54.0 47. 5 51.6 42.2 49.6  0.21 0.18 0. 19 0. 19 0.22 0.2 3 0.23 0.21 0.23 0.23 0.24 0.23 0.24 0.23 0.21 0. 19 0.23 0. 23 0.25 0.25 0.19 0.19 0.25 0.25 0.22 0.25 0.21 0. 19 0.21 0.19 0.24 0.20  IX-5 23.71 19.32 21.27 20.75 23.65 25. 17 24.94 22.62 24.76 24.88 26. 18 25.22 26. 10 25.50 22.84 21.08 24.89 25. 12 27.73 27.11 20.78 20.32 26. 79 26.93 23.97 27.19 22.49 20. 21 22.97 21.15 25.86 22.00  IX-6  Run 3- S i n g l e  TEMP DEG. F 74.50 74.45 74.45 74.50 74.52 74.50 74.50 74.60 74.60 74.65 74.65 . 74.65 74.65 74.80 74.80 74.80 75.20 75.20 75.20 75.20 75.20 75.20 75.20 75.20 75.20 75.20 75.20 75.20 75.20 75.20 75.20 74. 55 74.55 74.5 5 74.55 74.55 74.55 74. 80 74.80 74. 80 74.80 74.80 74. 80 74.80 74.80 74. 80 . 74.80  0.0341 cm S a l t  DIST CM 10.0 10.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 10.0 20.0 20.0 20.0 20.0 20.0 2 0.0 30.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 ' 20.0 ,20.0 40.0 30.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0  C r y s t a l s I n 5.08 cm Col nmn  SETTLING TIME SEC 38.6 31.0 58.0 60.1 57.0 60.2 63.3 56.8 55.6 66.1 54.2 57.1 71.0 31.0 65.4 64. 8 62.5 69. 4 64.5 .62.6 105.0 72.8 69.2 54.4 66.6 54.2 66.0 63. 1 70.9 75.0 55.0 78.0 99.2 78.0 65.4 68.0 69.7 80.0 150.4 95.8 66.3 69.0 64.9 64.9 71.7 65.8 74.6  U CM/SEC 0.26 0.32 0.34 0.33 0.35 0.33 0.32 0.35 0.36 0.30 0.37 0.35 0.28 0.32 0.31 0.31 0.32 0.29 0.31 0.32 0.29 0.27 0.29 0.37 0.30 0.37 0.30 0. 32 0.28 0.27 0.36 0.26 0.20 0.26 0.31 0.29 0.29 0.25 0.27 0.31 0.30 0.29 0.31 0.31 0.28 0.30 0.27  U*NU 0.01CM /SEC 3  7.72 9. 62 10.28 9.91 10.45 9.89 9.41 10.46 10.69 8.98 10.95 10.39 8.36 9.54 9.04 9.13 9.37 8.44 9.08 9.36 8.37 8.04 8.46 10.77 8.79 10.81 8.87 9.28 8.26 7.81 10.65 7-63 6.00 7.63 9.10 8.75 8.54 7.39 7.86 9.26 8.92 8. 57 9.11 9.11 8.25 8.99 7.93  2  _. . ..  74. 80 74.80 74.80 74.80 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 ' 74.60 74.60 74.60 74.60 74.60 74.60 74.6 0 74. 60 74.60 74.60 74.60  20.0 20.0 20.0 20.0 10.0 10.0 10.0 10.0 10.0 20.0 10.0 10.0 20.0 20.0. 10.0 10.0 10.0 10.0 10.0 10.0 10.0 30.0 20.0 10.0  74.2 65.5 85.0 73.2 37.8 36.8 32.2 34.0 31.2 76.2 35.6 46. 8 71.8 63.3 37. 2 36.1 39.2 40.0 38.0 37 . 8 . 35.2 78.2 67.8 34.5  0.27 0.31 0.24 0.27 0.26 0.27 0.31 0.29 0.32 0.26 0.28 0.21 0.28 0.32 0.27 0.28 0. 26 0.25 0.26 0.26 0.28 0.38 0.29 0.29  IX-7 .7.97 9.03 6.96 8.08 7.86 8.07 9.23 .8.74 9.52 7.80 8.35 6.35 8.28 9.39 7.99 8.23 7.58 7.43 7.82 7. 86 8 . 44 11.40 8.76 8.61  IX-8  Run 4 - S i n g l e  TEMP DEG. F  .  73.60 7 3.60 73.75 72.80 72.80 72.80 72.80 73.10_ 76.65 76.65 76.65 76.65 76.65 76.65 76.65 76.65 76.65 71.70 71.70 71.70 . 71.70 71.80 71.90 72.00 72.05 72.10. 72. 20 72.20 7 2.20 72.20 72.20 72.40 72.20 72.40 72.40 72.40 72.50 72.50 . 72.50 72.50 72.50 72.50 72.50 72.50 72. 50 72.50 72. 50  0.0391 cm S a l t  C r y s t a l s In 5.08 cm Column  DIST CM  SETTLING TIME SEC  10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 30.0 10.0 20.0. 10.6 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 20.0 10.0 10.0  28.6 30.1 28.0 28.6 25.6 29.0 25.0 28.7 25.6 . 27. 5 30.0 29.6 29.4 29. 2 24.9 32.0 29.4 107.4 25.6 50.6 27.6 27.2 27.2 27.6 28.0 34.4 35.8 25.9 28.6 34.0 30.8 .54.5 30.3 32.4 25.8 33.8 30.6 32.0 31.4 34.6 28.4 31.8 30.0 30.6 67.2 32 .0 31.4  U CM/SEC 0.35 0. 33 0.36 0.35 0.39 0.34 0.40 0.35 0.39 0.36 0.33 0.34 0.34 0.34 0.40 0.31 0.34 0.28 0.39 0.40 •0.38 0.37 0.37 0.36 0.36 0.29 0.28 0.39 0.35 0.29 0.32 0.18 0.33 0.31 0.39 0.30 -0.33 .0,31 0.32 0.29 0.35 0.31 0.33 0.33 0.30 0.31 0.32  U*NU 0.01CM /SEC 3  12.73 12.09 12.95 12.99 14.51 12.81 14. 86 12.84 13.13 12.22 11.21 11.36 11 . 43 11.51 13.50 10. 51 11.43 10.69 14.94 15.12 14.69 14.03 13.99 13.75 13.54 11.00 10.55 14.58 13.20 11. 10 12.26 6.89 12.46 11.59 14.56 11.11 12.24 11.70 11.93 10.83 13.19 11.78 12.48 12.24 11.15 11.70 11.93  2  72.50 72.50 72. 50 71.50 71.50 71.50 71.50 71.. 50 71.50 71.50 71.50 71.50 7 1 . 50 71.50 71.50 71.50 71.60 71.60 71.60 71.60 71.60 70.60 70.60 70.50 70. 50 70.50 70. 50 70.50 70.50 70.40 70.40 70.40 70.40 70.40 70.40 70.40 70.80 70.80. 71.10 71.20 71.20 71.20  20.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 .10.0 10.0 10.0 10.0 10.0 20.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 . 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0.. 10.0 10.0 10.0 20.0  55.0 34.2 29.6 37. 2 33.4 35.2 32.6 33.0 32.2 32.4 34.9 28.6 31.8 34. 6 27.9 36. 1 35.1 35.6 56.8 33.6 30.0 38.4 46.2 83.6 32.6 37.7 38.9 40. 7 35.6 42. 2 37.5 45.4.. 75. 5 37.4 55.0 33.2 30.0 31.6 32 .4 29.0 29.8 65.2  0.36 0.29 0.34 0.27 0.30 0.28 0.31 0.30 0.31 0.31 0.29 0.35 0.31 0.29 0.36 0.28 0.28 0.28 0.35 0.30 0.33 0.26 0.22 0.12 0.31 0.27 0.26 0.25 • 0.28 0.24 0.27 0.22 0. 13 0.27 0.18 0.30 0.33 0.32 .0.31 0.34 0.34 0.31  TX=9~ 13.62 10.95 12.65 10.34 11.52 10.93 11.80 11.66 11.95 11. 87 11.02 13.45 12.10 11.12 13.79 10.66 10.93 10.78 13.51 11.42 12.79 10.26 8.53 4.72 12.11 10.48 10.15 9.70 11.09 9.38 10.56 8 .72 5.24 10.59 7.20 11.93 13.06 12.40 12.00 13.37 13.01 11.89  IX-10  Run  5-Single  TEMP DEG. F  .  74.40 74.40 74.20 74.50 74.50 74.50 74.50 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.20 74.60 74.60 74.60 74.60 74.60 74.60 74.60 74.90 75. 10 75.10 75.20 75.20 75.20 75.20 75.20 75.20 75.20 75.30  0 . 0 2 8 2 cm S a l t  DIST CM 10.0 20.0 20.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 20.0 10.0 10.0 10.0 10.0 10.0 . 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 20.0 20.0 10.0 20.0 10.0 10.0 10.0 10.0 10.0 20.0 10.0  C r y s t a l s In  SETTLIMG TIME SEC 85.2 148.2 124.0 62.8 56.0 47.8 59.6 _47.5 57.8 56.0 67.2 60.2 68.0 63.4 140.7 48.8 65. 3 62.9 63.4 60.6 55.6 60.9 63.0 67. 6 65.3 62.3 58.8 69 .0 56.4 57.0 48.0 49.6 41.0 44.0 45.4 45 .0 106.2 102.0 45.0 90.6 45.2 47.0 49.4 45.8 57.2 97.2 57.2  5.08 cm Column  U CM/SEC 0.12 0.13 0.16 0.16 0. 18 0.21 0.17 0.21 0.17 0. 18 0.15 0.17 0.15 0, 16 0.14 0.20 0.15 0.16 0. 16 0. 17 0.18 0. 16 0.16 0.15 0.15 0.16. 0.17 0.14 0.18 0.18 0.21 0.20 0.24 0.23 0.22 0.22 0. 19 0.20 0.22 0.22 0.22 0.21 0.20 0.2.2 0.17 0.21 0.17  U*NU 0.01CM /SEC 3  4.18 .4.81 5.78 5.66 6.35 7.44 5.96 7.46 6.13 6.33 5.28 5.89 5.21 5.59 5.04 7.26 5 . 43 5.64 5.59 5.85 6.38 5.82 5.63 5.24 5.43 .5.69 6.03 5.14 6.35 6.22 7.39 7.15 8.65 8.06 7.81 7.88 6.62 6.86. 7.77 7.70 7.72 7.42 7.06 7.62 6.10 7.18 6.08  2  IX-11  ...  „  75.30 75.30 75.30 75.40 75.40 75.40 75.40 75.40 75.40 75.40 75.60 75.60 75.60 75.60 75.60 75.60 75.80 7 5.80 75.80 76.00 76.00 76.00 76.00 76.00 76. 10 76.20 76.20 76. 20 76.20 76.20 76.30 76.30 76. 30 76.30 76.30 76.40 76.40 76.40 76.40 76.40 76.40 76.40 76.40 • 76.40 76.40 76.50 76.50 76.50 76.50 76.50 76.50 76. 50  I 0.0  10.0 10.0 10.0 10.0 10.0 10.0 10.0 2 0.0 10.0 10.0 10.0 10.0 2 0.0 10.0 10.0 10.0 10.0 10.0 10.0 10. 0 10.0 .10.0 10.0 10.0 .10.0 10.0 10.0 10.0 10.0 20.0 30.0 10.0 20.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 20.0 10.0 10.0 10.0 20.0 3 0.0 10.0 10.0 10.0  50.0 54.6 5.5.5 63.3 53.6 53.4 55. 1 46.4 92.9 44.0 57.8 50.8 47.8 106.2 49. 1 57.6 57.4 57. 1 51. 2 51.4 44.6 56.0 56.0 50.4 45.8 44.2 49. 4 46.6 52.2 55.8 112.0 143.6 53. 4 117.0 59.0 54.8 57. 2 51.4 58.4 50.0 53.6 52. 8 57.6 103. 1 44.4 60.4 46.9 91.0 155.3 46. 1 51.2 49.2  0.20 0. 18 0.18 0. 16 0. 19 0.19 0.18 0.22 0.22 0.23 0.17 0.20. 0.21 0. 19 0.20 0. 17 0.17 0.18 0.20 0.19 0.22 0. 18 0.18 0.20 0.22 0.23 0.20 .0.21 0. 19 0.18 0. 18 0.21 0. 19 0.17 0.17 0.18 0.17 0. 19 0. 17 0.20 0.19 0. 19 0.17 0.19 0.23 0.17 0.21 0.22 0. 19 0.22 0.20 0.20  ;  6.96 6.37 6.27 5 .48 6.48 6.50 6.30 7.48 7.47 7.89 5.97 6.80 7.22 6.50 7.03 5.99 5.98 6.02 6.71 6.65 7.66 6. 10 6.10 6.78 7.44 7.69 6.88 7.30 6.51 6.09 6.06 7.09 6.35 5.80 5.75 6. 17 5.91 6.58 5.79 6.77 6.31 6.41 5.87 6.56 7.62 5.59 7.20 7.42 6.52 7.32 6.59 . 6.86  IX-12  Run 6-Single  TEMP DEG. F 70.20 70.20 70.20 70.20 70.20 70. 30 70.30 70.40 70.40 70.40 70.50 70.50 70.55 70.5 5 70.55 70.60 70.60 70.60 70.60 70.65 70.65 70.65 70.90 70.90 70.90 70.90 70.85 70.85 70.85 70.82 70.85 .7.0.85 70.85 70. 85 70.85  0.288 cm ABS P e l l e t s In 7.71 cm Column  DIST CM 16.0 16.0 16.0 1.6.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 . 16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 16.0 .16.0 16.0 16.0 16.0 16.0 16.0 8.0 16.1 16.0 16.0  SETTLING TIME SEC 36.8 40.2 36.2 36.8 38. 2 38.8 36.8 36.9 39. 2 35.6 44. 3 46.0 38.4 43.0 40.0 33.7 36. 7 34.7 36.9 51.0 34. 5 38. 2 39.4 41 .8 37.7 . . 40.0 33.0 39.2 37.4 40.7 39. 5 19.2 45.4 38.8 38. 2  u CM/SEC  ......  0.43 0.40 0.44 0.43 0.42 0.41 0.43 0.43 0.41 0.45 0.36 0.35 0.42 0.37 0.40 0.47 0.44 0.46 0.43 0.31 0.46 0.42 0.41 0.38 0.42 0.40 0.42 0.41 0.43 0.39 0.41 0.42 0.35 0.41 0.42  U*NU 0. 01CM / SEC 3  93.40 8.5.50 94.95 93.40 89.98 88.28 93.08 92.51 87. 08 95.88 76.79 73.95 88.43 78.97 84.89 100.59 92.36 97.69 91 .86 66.35 98.08 88.58 85.13 80.24 88.97 83.86 88.43 85.72 89.84 82.65 85.07 87.50 74.34 86.60 87.96  IX-13  Run 2 - S i n g l e  . _  Calculated  107..00 112..40 113..89 115..04 116..17 118..01 119..94 121..01 122..47 124..11 127.. 58 130,.93 133..09 136..03 141..01 144..18 151 . 15  106. 72 1 1 1 . 70 113. 89 114. 86 116. 17 117. 66 119. 94 120. 83 122. 27 123. 32 127. 06 130. 32 132. 44 135. 53 .140.20 143. 31 149. 49  Results  107. 00 112. 63 113. 91 115. 04 116. 37 118. 24 119. 96 121. 37 122. 47 124. 20 128. 04 131. 16 133. 35 136. 44 141. 67 144. 55 152. 86  10 8.72 112. 63 113. 99 115. 18 116. 82 118. 59 120. 12 121. 91 12 2.83 126. 11 129. 08 131. 16 133. 7 5 139. 25 141. 93 147. 37 15 6.33  108. 72 1 1 2 . 76 114. 21 115. 85 116. 85 118. 96 120. 12 122. 27 1 2 3 . 06 126. 76 129. 65 1 3 1 . 26 133. 99 139. 41 142. 65 148. 39  I l l .47 113 .26 114 .65 116 .17 117 .18 119 .94 120 .30 122 .27 123 .29 126 .87 129 .90 131 .41 135 .18 140 .09 143 . 17 149 .49  125.74 (0.01CM /SEC ) AVERAGE U*NU CORRECTED FOR WALL = 129.64 (0.01CM /SEC ) 11.89 (O.OICMVSEC ) STANDARD DEVIATION = NO. OF MEASUREMENTS= 100 3  2  3  2  ..  1  Run 1 - S i n g l e Results  f r o m Run 2 - S i n g l e  U*NU  corrected  for  = 123.7  (0.01cm /sec )  CORRECTED FOR WALL 1 2 7 . 6  (0.01cm /sec )  3  3  2  2  liquid  density,  Run 7 - S i n g l e  18.92 20.62 .... . .21.15 21.64 22.49 22.94 23.65 24. 17 24.89 25. 17 25.50 26.08 2 7.11 29.69  Calculated  19.32 20.69 .21.27 21.69 2 2.59 22.97 23.71 24.19 24.93 25.22 25. 52 26.10 27.19  AVERAGE U*NU CORRECTED FOR WALL = STANDARD DEVIATION = NO. OF MEASUREMENTS=  Results  19.98 20.75 21.33 22.00 22.62 23.27 23.75 24.42 24.94 25.34 25.74 26. 18 27.40  :  20.08 2 0. 78 2 1.41 22.03 22.66 2 3 . 29 23.93 24.55 2 4.95 25.39 2 5.78 26.68 27.73  23.81 ( 0 . 01CM /SEC*) 24.29 ( 0 . 01CM /SEC*) 2.37 ( 0 . 01CM / S E C ) 79 3  3  J  20.21 20.95 21.55 22.25 22.73 23. 32 23.97 24.76 25.12 25.40 25.86 26. 79 27.84  20. 32 21 .08 21.60 _ 22.44 22.84 23.51 24. 11 24.88 2 5 . 13 25.49 26.04 26.93 29.08  IX-15  Run 3 - S i n g l e  6.00 7.63 7.86 8.04 8.28 8.46 8.76 9. 03 9.13 9.39 9.91 10.69  Calculated  Results  6.35 7.63 7. 86 8.07 8.35 8.54 8. 79 9. 04 9.23 9.41 10.28 10.77  6.96 7.72 7.86 8.08 8.36 8.57 8.87 9.08 9.26 9.52 10. 39 10.81  AVERAGE U*NU CORRECTED FOR WALL = STANDARD DEVIATION = NO. OF MEASUREMENTS*  7.39 7.80 7.93 8.23 8.37 8.61 8.92 9.10 9.28 9.54 10.45 10.95  8.79 (COICM'/SEC ) 8.91 (O.OICMVSEC ) 1.08 (O.OICMVSEC ) 71 2  2  2  7.43 7.81 7.97 8.25 8.44 8.74 8.98 9.11 9.36 . 9.62 10.46 11.40  7.58 7.82 7 .99 8. 26 8.44 8.75 8.99 9.11 9. 37 9.89 10.65  IX-16 Run  .  . . . ..  4-Single 4.72 9.38 L0.51 10.78 11.02 11.21 11.52 11.80 11.95 12.24 12.65 12.99 13.37 13.75 14.58  Calculated Results 5.24 9. 70 10.55 10.83 11.09 11.36 11 .59 11 .87 .12.00 12.24 12.73 13.01 13.45 13.79 1.4.69  AVERAGE U*NU = CORRECTED FOR WALL = STANDARD DEVIATION = NO. OF _MEASUREMENTS=  6.89 10.15 10.56 10.93 11.10 11.42 11.66 11.89 12.09 12.26 12.79 13.06 13.50 13.99 14.86  8.53 10.34 10.66 10.95 11.12 11.43 11.70 11.93 12.11 12.46 12.84 13.19 13.54 14.51 15.12  7.20 10.26 10.59 10.93 11.11 11.43 1 1.70 11.93 12.10 12.40 12.81 13.13 13.51 14.03 14.94  11.78, ( 0. 01CM /SEC ) 11.97 (0.01CM /SEC ) 1.88 ( 0 . 01CM /SEC ) 89 3  2  3  2  3  2  8.72 10.48 10.69 11.00 11.15 11.51 11 .78 11.93 12.22 12.48 12.95 13.20 13.62 14.56  IX-17 Run 5 - S i n g l e A. 18 5.28 5.59 5.78 5.89 6.02 6.10 6.30 6.37 6.51 6.65 6. 86 7.15 7.32 7.46 7.69 7.89  Calculated Results 4.81 5.43 5.63 . 5.79 5.91 6.03 6.10 6.31 6.38 6.52 6.71 6.88 7.18 7.39 7.47 7.70 8.06  AVERAGE U*NU CORRECTED FOR WALL = STANDARD DEVIATION = NO. OF MEASUREMENTS  5.04 5.43 ..5.64 5 .80 5.96 6.06 6.13 6.33 6.41 6.56 6.77 6.96 7.20 7.42 7.48 7.72 8.65  5.14 5.48 5 . 6.6 .. 5.82 5.97 6.08 6.17 6. 35 6.48 6.58 •:. 6.78 7.03 7.22 7.42 7.62 7 . 77  6.50 (0.01CM /SEC ) 6.57 (0.01CM /SEC ). 0.83 (0.01CM /SEC ) 99 3  3  2  2  3  2  5.21 5.59 5.69 5.85 5.98 6.09 6.22 6.35 6.50 6.59 6.80 7.06 7.26 7.44 7.62 7.81  5 .24 5.59 5 . 75 5.87 5.99 6.10 6.27 6.35 6. 50 6.62 6.86 7.09 7.30 7.44 7.66 7.88  IX-18  Run 6 - S i n g l e  66.35 82.65 85.72 88.43 91.86 94.95  Calculated Results  73.95 33. 86 86.60 88.43 92.36 95.88  AVERAGE U*NU CORRECTED FOR WALL = STANDARD DEVIATION = NO. OF MEASUREMENTS*  74.34 84.89 87.08 88.58 92.51 97.69 87.40 94.27 7.29 35  7 6.79 85.07 87.50 88.97 93.08 98.08 (0.01CM /SEC ) (0.01CM /SEC ) (0.01CM /SEC ) 3  2  3  2  3  2  78.97 85.13 87.96 89.84 93.40 100.59  80.24 85 . 50 88.28 89.98 93.40  VISCOSITY DATA Run 2-Single Temperature Viscosity  o cs  68.00 213.20  69.00 208.70  70.00 204.00  71.00 200.50  o cs  69.02 33.94  70.00 33.06  71.00 32.24  72.00 31-46  73.00 30.67  74.00 29.88  75.02 29.15  76.00 29.43  o cs  69.02 a.03  69.98 40.03  71.00 38.98  72.00 37.95  73.10 36.86  74.00 36.03  75.05 35.02  76.00 34.17  77.20 33.15  6 . cs  69,02 41.03  69,98 40.03  71.00 3898  72.00 37.95  73.10 36.86  74.00 36.03  75.05 35.02  76.00 34.17  77.20 33.15  o cs  69.20 221.86  70.00 216.3  71.10 208.16  72.00 200.66  o cs  69.00 115.42  70.00 113.06  71.00 110.80  71.90 108.90  p  Run 3-Single Temperature Viscosity  F  Run 4-Single Temperature Viscosity,  F  Run 5-Single Temperature Viscosity  p  Run 6-Single Temperature Viscosity  F  Run 7-Single Temperature Viscosity  F  X-1  APPENDIX X  MICROSCOPIC MEASUREMENT OF PARTICLE SIZE  The r e s u l t s were c a l c u l a t e d  from the measurement of  p a r t i c l e images of an order of an inch by V e r n i e r c a l i p e r s , and arranged  i n an i n c r e a s i n g  order.  Two dimensions of the  s a l t c r y s t a l s were measured.  INDEX Run No.  Particles  Page  1,2  0.114 cm (Dv) Glass Beads  X-2  7  0.0492 cm Glass Beads  X-3  3  0.0341 cm S a l t C r y s t a l s  X-4  4  0.0391 cm S a l t C r y s t a l s  X-5  5  0.0282 cm S a l t C r y s t a l s  X-6  X-2  Run  1,2  0.1017 0.1045 0.1056 0.1060 0.1066 0.1080 0.1092 0.1100 0.1108 0.1113 0.1119 0.1128 0.1142 0.1168 0.1179 0.1210 0.1228 0.1263  M i c r o s c o p i c Measurement of  .  0.1019 0.1049 0.1058 0.1063 0.1067 0.1081 0.1094 .0.1102 0.1108 0.1114 0.1122 0.1132 0.1145 0.1169 0.1189 0.1213 0.1229 0.1272  AVERAGE LENGTH STANDARD DEVIATION NO. OF MEASUREMENTS  0.1024 0.1050 0.1058 0.1065 0.1067 0.1082 0.1099 0.1102 0.1109 0.1117 0. 1124 0.1138 0.1147 0.1171 0.1195 0.1217 0.1233 0.1285  0 . 1 1 4  0.1031 0.1056. 0.1060 0. 1065 0.1067 0.1082 0.1099 0.1104 0.1112 0.1117 0.1125 0.1140 0.1154 0. 1173 0.1207 0.1217 0.1236  0.1123 CM (diameter) 0.0063 CM 1 0 51  cm G l a s s  Beads  0.1039 0.1056 0.1060 0.1065 0.1070 0.1089 0.1099 0.1106 0.1112 0.1119 0.1125 0.1141 0.1154 0.1173 0.1207 0.1218 0. .1243  0.1044 0.1056 0.1060 0.1066 0.1071 0.1090 0.1100 0.1108 0.1112 0.1119 0.1125 0.1141 0.1164 0.1175 0.1210 0.1223 0.1245  X-3  Run 7 0.0448 0.0454 0.0458 0.0460 0 . 04 63 0.0467 0.0470 0,0.4.74. 0.0476 0.0480 0.0482 0.0485 0.0488 0.0494 0.0498 0.0503 0.0514  Microscope Measurement of 0.0492 cm Glass Beads 0.0450 0.0455 0.0458 0.0461 0 . 0465 0.0467 0.0470 . .0,0475 0.0476 0.0480 0 . 0484 0.0486 0.0488 0.0495 0.0498 0.0503 0.0516  0.0450 0,0456 0.0459 0.0461 0.0465 0.0468 0.0471 0.04 7 5 0.0478 0.0481 0.0484 0.0486 0.0490 0.0496 0.0499 0.0505 0.0517  0.0450 .0.0456 0.0459 0.0462 0.046 5 0.0469 0.0471 0.0475 0.0478 0.0481 0.0484 0.0486 0.0492 0.0497 0.0500 0.0505 0.0520  A V E R A G E , LENGTH = . 0 . 0.479_ CM (diameter) STANDARD D E V I A T I O N = 0 . 0 0 . 1 8 CM N O . OF MEASUREMENTS = 1 0 1  0.0452 0.0457 0.0460 0.0462 0 . 0465 0.0470 0.0472 0.0475 0.0478 0.0481 0.0485 0.0487 0.0493 0.0497 0.0500 0.0509 0.0536  0.0454 0.0458 0.0460 0.0462 0.0465 0.0470 0.0474 0.0476 0.0480 0.0482 0.0485 0.0487 0.0494 0.0497 0.0503 0.0511  X-4  Run 3  Microscope  0.0208 0.0226 0.0239 0.0240 0.0245 0.0246 0.0250 0.0252 0.0256 0.0257 0.0261 0.0265 0.0266 0.0267 0.0269 0.0271 0.0272 0.0274 0.0275 0.0278 0.0279 0.0281 0.0283 0.0285 0.0286 0.0287 0.0288 0.0289 0.0289 0.0291 0.0293 0.0295 0.0302 0.0304 0.0309 0.0314  Measurement  0.0230 0.0269 0.0227 0.0272 0.0255 0.0253 0.0258 0.0274 0.0244 0.0280 0.0258 0.0293 0.0277 0.0248 0.0275 0.0283 0.0272 0.0264 0.0301 0.0278 0.0265 0.0258 0.0291 0.0260 0.0293 0.0302 0.0267 0.0297 0.0280 0.0300 0.0311 0.0297 0.0277 0.0308 0.0304 0.0276  of  0.0217 0.0230 0.0240 0.0240 0.0245 0.0248 0.0252 0.0254 0.0256 0.0261 0.0262 0.0265 0.0266 0.0267 0.0270 0.0271 0.0274 0.0275 0.0276 0.0278 0.0280 0.0282 0.0284 0.0285 0.0286 0.0287 0.02 88 0.0289 0.0290 0.0291  0.0294 0.0296 0.0303 0.0307 0.0310 0.0319  0 . 0 3 4 1 cm S a l t  0.0281 0.0221 0.0253 0.0264 0.0277 0.0230 0.0261 0.0254 0.0246 0.0283 0.0293 0.0236 0.0274 0.0257 0.0242 0.0278 0.0291 0.0235 0.0275 0.0295 0.0274 0.0278 0.0266 0.0293 0.0314 0.0291 0.0286 0.0265 0.0281 0.0304 0.0297 0.0248 0.0271 0.0286 0.0318 0.0300  AVERAGE LENGTH = 0.0273, 0.0275 CM STANDARD DEVIATION = 0.0023, 0.0024 CM NO. OF MEASUREMENTS = 108 PAIRS  Crystals  0.0225 0.0237 0.0240 0.0240 0.0245 0.0250 0.0252 0.0255 0.0257 0.0261 0.0262 0.0266 0.0266 0.0269 0.0271 0.0272 0.0274 0.0275 0.0276 0.0278 0.0280 0.0283 0.0284 0.0285 0.0287 0.0288 0.0288 0.0289 0.0290 0.0292 0.0294 0.0297 0.0304 0.0308 0.0314 0.0326  0.0272 0.0387 0.0237 0.0249 0.0262 0.0260 0.0240 0.0274 0.0280 0.0265 0.0273 0.0250 0.0268 0.0269 0.0252 0.0272 0.0266 0.0313 0.0301 0.0284 0.0265 0.0260 0.0266 0.0289 0.0269 0.0265 0.0305 0.0246 0.0296 0.0312 0.0276 0.0261 0.0316 0.0279 0.0291 0.0269  X-5  Run 4  M i c r o s c o p i c Measurement  0.0233, 0.0278, 0.0288, 0.0293, 0.0298, 0.0300, 0.0301, 0.0303, 0.0304, 0.0307, 0.0309, 0.0309, 0.0309, 0.0313, ' " 0.0315, 0.0315, 0.0318, 0.0319, 0.0321, 0.0322, 0.0325, 0.0327, 0.0330, 0.0330, 0.0334, 0.0336, 0.0337, 0.0345, 0.0352, 0.0427,  0.0233 0.0319 0.0335 0.0302 0.0338 0.0300 0.0312 0.0311 0.0296 0.0300 0.0326 0.0286 0.0311 0.0305 0.0302 0.0301 0.0318 0.0321 0.0349 0.0309 0.0316 0.0344 0.0289 0.0374 0.0316 0.0338 0.0359 0.0349 0.0283 0.0325  of  0.0262, 0.0280, 0.0290, 0.0294, 0.0299, 0.0300, 0.0302, 0.0303, 0.0305, 0.0307, 0.0309, 0.0309, 0.0312, 0.0313, 0.0315, 0.0316, 0.0319, 0.0320, 0.0321, 0.0323, 0.0325, 0.0327, 0.0330, 0.033L, 0.0335, 0.0336, 0.0338, 0.0347, 0.0358,  0 . 0 3 9 1 cm S a l t  0.0335 0.0295 0.0320 0.0312 0.0291 0.0307 0.0310 0.0314 0.0358 0.0344 0.0299 0.0305 0.0312 0.0343 0.0311 0.0341 0.0319 0.0335 0.0318 0.0259 0.0347 0.0323 0.0329 0.0324 0.0343 0.0334 0.0334 0.0360 0.0337  AVERAGE LENGTH = 0.0316, 0.0319 CM STANDARD DEVIATION = 0.0024, 0.0025 CM NO. OF MEASUREMENTS = 88 PAIRS  Crystals  0.0269, 0.0286, 0.0290, 0.0295, 0.0300, 0.0300, 0.0303, 0.0304, 0.0306, 0.0308, 0.0309, 0.0309, 0.0312, 0.0313, 0.0315, 0.0318, 0.0319, 0.0320, 0.0322, 0.0325, 0.0326, 0.0329, 0.0330, 0.0332, 0.0336, 0.0337, 0.0342, 0.0349, 0.0383,  0.0291 0.0370 0.0297 0.0279 0.0286 0.0343 0.0332 0.0296 0.0306 0.0323 0.0306 0.0310 0.0356 0.0315 0.0297 0.0292 0.0336 0.0309 0.0307 0.0300 0.0296" 0.0311 0.0337 0.0341 0.0331 0.0370 0.0355 0.0320 0.0354  Run 5  Microscopic 0.0197, 0.0203, 0.0207, 0.0208, 0.0211, 0.0214, 0.0215, 0.0217, 0.0218, 0.0220, 0.0222, 0.0223, 0.0225, 0.0227, 0.0230, 0.0230, 0.0231, 0.0235, 0.0237, 0.0240, 0.0246, 0.0247, 0.0250, 0.0252, 0.0254, 0.0259,  Measurement o f P a r t i c l e  0.0181 0.0210 0.0218 0.0223 0.0250 0.0212 0.0232 0.0218 0.0221 0.0240 0.0244 0.0250 0.0239 0.0231 0.0264 0.0241 0.0215 0.0227 0.0224 0.0221 0.0220 0.0214 0.0237 0.0254 0.0231 0.0205  Size  0.0198, 0.0205, 0.0207, 0.0209, 0.0212, 0.0215, 0.0216, 0.0217, 0.0219, 0.0221, 0.0223, 0.0224, 0.0225, 0.0227, 0.0230, 0.0230, 0.0232,  0.0198 0.0227 0.0260 0.0216 0.0262 0.0255 0.0200 0.0242 0.0230 0.0224 0.0227 0.0228 0.0265 0.0229 0.0247 0.0213 0.0258  0.0201, 0.0206, 0.0208, 0.0211, 0.0213, 0.0215, 0.0216, 0.0217, 0.0220, 0.0222, 0.0223, 0.0225, 0.0227, 0.0229, 0.0230, 0.0230, 0.0234,  0.0212 0.0189 0.0278 0.0221 0.0234 0.0228 0.0237 0.0221 0.0275 0.0222 0.0217 0.0215 0.0213 0.0235 0.0220 0.0244 0.0223  0 . 0 2 3 5 ,  0 . 0 2 3 9  0 . 0 2 3 5 ,  0 . 0 2 2 6  0.0237, 0.0241, 0.0246, 0.0247, 0.0251, 0.0253, 0.0255, 0.0269,  0.0230 0.0222 0.0247 0.0243 0.0227 0.0226 0.0232 0.0285  AVERAGE LENGTH = 0.0229, 0.0232 CM STANDARD DEVIATION = 0.0017, 0.0020 CM NO. OF MEASUREMENTS = 78 PAIRS  0.0237, 0.0244, 0.0246, 0.0248, 0.0252, 0.0254, 0.0258, 0.0280,  0.0223 0.0241 0.0264  0.0282 0.0234 0.0244  0.0232 0.0224  APPENDIX XI  DATA ON SETTLED BED POROSITY INDEX  Run No.  Page  Particles  1-1  0.114 cm Glass Beads  XI-1  1-2  0.114 cm Glass Beads  XI-1  1-3  0.114 cm G l a s s Beads  XI-2  2-1  0.114 cm Glass Beads  XI-2  2-2  0.114 cm Glass Beads  XI-3  2-3  0.114 cm Glass Beads  XI-3  7-3  0.0492 cm Glass Beads  XI-4  3-lA  0.0341 cm S a l t C r y s t a l s  XI-4  3-2  0.0341 cm S a l t C r y s t a l s  XI-5  3-3  0.0341 cm S a l t  Crystals  XI-5  3-4  0.0341 cm S a l t  Crystals  XI-5  4-2  0.0341 cm S a l t  Crystals  XI-6  4-3  0.0391 cm S a l t  Crystals  XI-6  5-3  0.0282 cm S a l t C r y s t a l s  XI-6  6-4  0.288 cm ABS P e l l e t s  XI-7  6-5  0.288 cm ABS P e l l e t s  XI-7  9-2  0.0508 cm M i n e r a l  Crystals  XI-7  9-3  0.0508 cm M i n e r a l C r y s t a l s  XI-8  10-2  0.0426 cm M i n e r a l C r y s t a l s  XI-8  10-3  0.0426 cm M i n e r a l C r y s t a l s  XI-8  11-2  0.135 cm Sugar C r y s t a l s  XI-9  11-3  0.135 cm Sugar C r y s t a l s  XI-9  12-3  0.113 cm Sugar C r y s t a l s  XI-9  X I - 1  •Kui\  1-1  0 . 1 1 4 CM GLASS  cPi>  SETTLED HEIGHT  0.90 0.68 "0T8~5~ 0.80 0 . 7 7_ TJ774" 0.74  0.74  0.74 0.70 0_»_70__  BED CM  11.10 13.28  Hf&TST  .  . 0..114  '16.53 ' 16.55 1 8 . 80 __ ' " 2 2 -'T 5" 2 5 . 35 2  0 .67 7JT6 4 0.64 0.64  ' **'  OjLfL^L  0.438 . 0.438 0.440 6T4 40. 0.433'  " ~  '"'"  .  ~ 0". 4 37" 0 . 4 37  _^'^  3  ~ 0.4 33 '  ~  ^°l ' l^ •  iL  7J7433 0.4340.433  '• • HR  L  HRS  '" '  0.433 br  1  .  39  JLii. _  39". 3 5 .39.40 '39.35  APPROX. TIME  f3  3 3". 10 ""'""" " 3 6  HRS HRS  °_*j? _  36 .0 o  0.67___  5 10  BEADS  """"  _ _ *JA _  "  HRS  0.442  0  3  10  S E T T L E D BED POROSITY  JLl!* __ _ " " 2 8.-60 ~ " 3 3.05  0._77 CT.74 ' 0.70  HR  0.435 0.435 0.434  CM G L A S b  13.25  0.85 0.'S5 0 ._83 0". 8~0 0.7 7  O.70"  "  11.10  0.88  0_.70  57442 0 . 4 4 0 ." 0 . 4 38  S E T T L E D BED HclGHT CM  0.9 0  ~~ 1  0,. 4 4 2 ___  ""29.00 33.38 3 3_.2 2 36.35 39.64  EPS  '  9  0.67 0.64  APPROX. TIME  0.439 0 . 4 37 0 7436 0.439 - 0.440 0.442 0 . 4 40  1_^°_2. T6T4TJ"  1-2  S E T T L E D BED POROSITY  22.20 _ 25 .60 29.00 28.9 0  0.67  RON  BcADS  2 _  __  HRS _ _  2  4 3 5  ~  H  R  b  HRS H.RS HRS  XI-2  RUN  1-3  SETTLED BED HEIGHT CM  EPS  0.90 0.88 0 .85 0.35 0.83 CT. 8 0 0.80 0 .77 0.74 0.74 0 . 74 0 . 70 0.70 0.67 0 . 6 7 0.67 0.64 0.64 0.64 0.64 !  RON'  0.114 CM GLASo BEADS  2-1  EPS  0.90 0 . 8 8  0.85 0.85 0.63 0.80 0 . 6 0  0.77 0.77 0 .7 7  0.74 0.74 0.70 "0T5T  11.10 13.20 16.50 16.50 18 . 70  0 ..4 4 4  . 439 0 . 439 0.439 0.439 0 . 4 39 0.439 0.437 0 . 4 37 0 . 4 37 0.437 0.438 0.437 0 . 4 36 0 . 442 0.435 0.436 0.434 0.433 0.433 0  22.00  21.97 25.20 28.50 28 . 50 2 8.48 32.90 3 2.35 36.10 3 6.50 36.00 39.38  39.23 39.15 39.15  0.114  CM  SETTLED BED POKOS I.TY  SETTLED BED POROSITY  11.10 13.15 16.45 16.45 18.60 21.80 21.85 2 4.30 25.15 25.05 28.20 28.15  0.442 0.434 0.435 0.435 0.434 0.431 0 .433 0.42 5 0.433 0.431 0.429 0.4280.432 0.42 5  32.75  5 . 5 5  25 1  MINS .5  10 20 1• 5 5  20 0.5 2 40 10 1 10 30 3.5  HRS  MI MS MINS HRS MI NS MINS HR  M I NS MI NS MI NS HR MI N S M I No HRS  1  MI  6  HRS  .5 1.75  N  HRS  GLASS BEADS  SETTLED BED HEIGHT CM  3  APPROX T IME  APPROX • • TIME 2. 5 16 0. 5 1 2  HRS  14 20 36  MI  0.5 2  hi R S H Ro HR HR HRS.  .5  2 11 5.5 . 10  N S  H R S  HR HR  S  "HRS  HRS .HRS  hRo.  XI-3  \ RuiM 2-2  0.114 CM. GLASo BL-ADS SETTLED BED  oETTLED BED  HE I_GHT  POROSI TY  •3d  CM.  13-20  _°A___ ,b  • 0.44  _ _ ___ . OTd 5 16 740" 18.60 _ !. ^ 0.7 7 " ~2"5"V"Z"0 " " °* 28.40 0  ,  0  ,  8  1  6  ,45  3  8  0  2 1  8  _  7 4  U  JL  7 0  "O.tW °«64 0  ,  6  4  RUN 2-3 EPS '  3  _ !>°_  0.4 38 0V4 36 0.437 0.437 "0.437 0.436 0-429  2  3 6.<X0 38.90 38.70  "  0.114 CM GLASS • SETTLED BED HEIGHT CM  u.4 3~5 0.430 0.427  ' APPROA. j j HE  1.75 15 • T5" 11.5 15 2 3.339  ~3 0.5 10.5  HRS MINS HRS""" HRS HRS ~MB— HRS HRS  ~TR~S~" HR HRS  BEADS SETTLED BED POROSIT Y  0.9 0 11.05 _G_. 90 LL?_°J? '0.68 13.25 " G.85 16.45 . 0_._8_5 16.45 _. "0.83 ' i d . o:; '" 0.8 0 2 1.85 0 • 8_0_ 2_1__. 85__ "0 . 77 25 ."20 ' 0.74 2 8.55 • 0.7_4 2 3 . 50__ "0~.70 " " "32 740" ~ 0.6 4 3 9 .40. 0.64 39.20 _ 0.64 39.40  APPROX. TI ME•  0.442 °_*Ji12 1 _ _ DAYS_ 0.441 " 1 HR " 0.438 0 . 4_3 8_ 10 MINS 0.4 i i " " l'. 5 HRb 0.435 50 MINS 0 ._435; ' _ _20 __M I Nb 0"7 437 " " To' " ~ MT'Ni> 0.438 14 MINS 0.4_3 7 18 M_INS 07'4 2"9 i f " ' ~HRS" 0.4 36 16 MINS Q_.h3_U 17_ MlJjS_ 0.436 11 MINS  XI-4  RON  7-3  0.0492  EPS  CM  GL A b o  o ti T T LEO BED HEI6HT CM  SETTLED bED POROSIT Y  APPROX. TlME  0.436 0.4 37 07T4 33 0.4 36  10.5 HRS 24 HRS. 4" "HRo 20 HRS  C92 8 . 75 _ _1 _ _°_'_ ' 0.8 8~ " 13 .05" °.85 16.40 _0.82_ 19.50__ 07 8 ' 2 1 9 . 6 5 0.80 21.80 0  9  l  0  _0_* Z 0774 0.71  A:  RoN  0.71 0_.6_8 "07"6 5""'"  9.1^ 1}_  ~~  5  ""'"' "3 4.7*0" "" 34.50  0.0341  CM S A L T  SETTLED BED. HEIGHT CM  .95  TJ7T4  " *0VO'5 0.434  7  EPS  "790 0.88 0.85 TJ.83 0.3 0 0 .77  3 0  5_!^ „  3  3-lA  . .92  °_*A__  " '2 8.Z0~ 3 1.40  68  07 68"" 0*68  95  2 4.95  7  5 .8.0  '  JiL^-P  JEADS  0.431 0.4 30  1 1  -1  H R S  40" 2.75  0^5  4 9  0.430  50  07"43l 0.428  10  M iTTB" HRS  HR  7iR"7" HRS MINS  4 F R S HRS  CRYSTALS  S E T T L E D oc'u ' POROSITY 0.462  0.465  APPROX. TIME 5.3  MINS  1.7 3 H R S  IT.60 * 0.46 1 HR 13.92 0.464 24 HRS 19_.6_0_ 0 . 5 24_ ' 9 .HRS_ 177 36 ' """0.391 3.5 HRS ' 2 3.03 0.460 2 HRo 26 .46 0 459 2 HRb 7277 93 " 0 . 4 5 9 " " l "" H R S 3 3 . 33. 0.459 10 HRS _ ^ 72 _ _ J O . 4 58 _ 1 . 5 ' -HRS 4 0.05 ' " 674 5 6 12 HRS 3  XI-5 RsN  3-2  0.0341  CM S A L T  SETTLED HEIGHT 0.95 0.92 0.90 ' 0.88 0.85 0 .8 3 •0.30 • 0.77 0.74 0.71 0.68 0.55  RsN  3-3  EPS  0.0341  3-4  CM S A L T  EPs  0.88 0.85 "0 . 8 3 0.80 0.7 7 0.74 0 .7 1 0.68 0.65  BED CM  5 .70 5 . 70 9 . 17 11.40 13.6 3 17.00 19.20 22 . 5.5 2 5.90 29.20 32.60 35.90 39 . 2 8  0-0341 SETTLED HEIGHT  APPRO X . T I ME  S E T T L E D BED. POROSITY  5 .80 9. 32 11.63 ' 13.92 17.36 19 . 60 2 3.03 2 6.45 2 9.86 3 3.28 36.60 39 .90  SETTLED HEIGHT  0.95 0.95 0.92 0.90 0.88 0.85 0.33 0.80 0.77 0.74 0.71 0.68 0.65  RJN  BED CM  CRYSTALS  0 .469 0.4 7 1 0 . 4 70 0.469 0.467 0.465 0.465 0.464 0.463 0.463 0.461 0 . 4 59  50 M I NS 1 . 7 5 . HRs HR 1 HRS 24 HRS' 3.5 9 HRS HRS 2 HRs 2 1 HR 10 HR0 ' HRS 1.5. HRo 12  CRYSTALS S E T T L E D BED POROSITY  APPROX. T I ME  0 . 459 0 . 4 59 0.462 0 . 4 59 0.457 0.456 0.454 0 . 45 3 0.452 0.45 1 0.451 0.450 . 0.450  CM SALTBED CM  13.70 17.00 19.20 22.55 . 25.35 28.90 3 2.40 35.70 3 9.00  10 10 21. 2.5 23 12 2 1.5 33 6 17.5 15  • M'INS HRs MI No HRS HRs ri K s HRS HRS HRS HRS M I MS M I NS h RS  CRYSTALS APPROX.  S E T T L E D BED POROSITY •  T I ME  0.460  0.456 0.454 0.453 0.451 0T4 4 5' 0 .448 0 . 4 47 0.446  3 ?0  ....  13 • 1 0.5 ,  6  HRS HRS  HRS HRS HR HRS HR s HRS  3. 0 11 2". 5 ™""'""HRS"  XI-6 RUN 4- 2 EPS  0.9 5 0.92 U .90 0.88 0.85 0.83 0.80 0.77 0.74 0.71 0.68 0<.6 5 0.65  RoN 4- 3 EP8  0.95 0.92 0V9TJ 0.88 0.85 O.B"3 0.80 0.77 0T7"4 0.71 0.68 0.65  RoN 5- 3 EPS  0.92 0 .89 GT8T" 0.85 0.80 o.7 r 0 .74 0.71 0.66. 0.6 5  0.039 1 CM SALT CRYSTALS SETTLED BED HEIGHT CM 5.75 . 9.15 1 1 .40 13.60 16.95 19 . 20 22.50 25.86 29 .20 32.53 35.78 38.93 39 .20  SETTLED BED POROSITY 0.464 0.461 0.459 0.456 0.455 0.454 0.452 0.452 0.451 0.451 0.449 0.446 0.450  APPROX• • TI ME 10 3 25 16 3 57 17 2.75 9.5 3 4 0.7 0.7  HRS HRS MINS HRS HRS MI No HRS. HRS HRS HRS HRS HR HR  0.0391 CM SALT .CRYSTALS SETTLED BED HEIGHT CM 5.80 9.20  r i ."w 13.65 17.05 19.30 22.60 25 .96' 29.30 32.65 35.95 39". 2 8  SETTLED BED POROSITY 0 .468 0.464 0. 4 5 9 • 0.458 0.457 0.457 0.454 0.453 0.453 0.452 0.451 0.430  APPROX • i I.-iE 10 3 25 16 3 57 17 . 2.73 9.5 3 4 0.7  HRS HRS  MlTTS""  HRS HRS MI NS 1-1R S HRS HRS H Ko HRS HR '  0.0282 CM SALT CRYSTALS SETTLED BED HEIGHT CM 9.30 12.70 14 . 9 7 17.15 22.80 "26.10 29.60 3 2.97 3 6.33 3 9.65  SETTLED BED POROSITY 0.469 0.466 0.464 0.460 0.459 0 .4 56" 0.453 0.457 0.457 0.455  APPROX T I ME  3 20" 18 0.5 3.5 11 2.5 3. 5  HRS TTR 6 HRS HR HRo HRS HRS 1-1 Ro HRo  XIRUN  6- 4  EPS  0.28 8  ABS  P E L L E T S  S E T T L E D  BED-  S E T T L E D  H E I G H T  CM  POROSITY  0.95 0 .92. 0.90 0.85 0.33 0.80 0.77 0.74 0.71 0 .68  R  CM  o N 6 •5 -  0.28 8  EPs  S E T T L E D  BED  SETTLED  HEIGHT  CM  POROSITY  RUN  9--2  t_Ps 0.95 0.92 0.90 0 .90 0.83 0.85 0.85  0.60 0.77 0.74 0.71 0.63 0.66 0.65  CM  ABS  8.30 12.10 19.60 23.00 29.60 33.00 36.00  0.0508  CM  MINERAL  DED  O E I T L E D POROSITY  ' '  HR  1 . 5 2 1.0 11 6.5 16 24  HR HRS HR HRS HRS HRS HRS  T I  l-'i E  3  HRS  9 3  HRS  0.5 8  HR  HRS  3  HRS  HRS  C R Y S T A L S  CM  6.10 9 .70 12.10 12.10 14.45 i s'VYo 2 0.50 24.00 2 7.55 31.15 34.70 3 6.10 33.25 41.66  0.5  APPROX  bED  0.414 0.497 0.4 72 • 0.471 0 .466 0.46 5 0.459  n li' I  li T  T I ME  P E L L E T S  B E I T L E D G  APPROX  '.  0.486 0.501 0 .49 0 0.4 79 0.478 0.470 0.465 0.460 0.456 0.453  6.00 9.90 12.10 17.75 20.10 23.30 26.50 2 9.70 32.90 36. 10  0.92 0 .9 0 0.83 0.80 0.74 0.71 0.63  BED  APPROX  BELV  0.49 5 0.492 0 .49 I 0.491 0.483 '""0.4 89 0.489 0.486 0.465 0.466 0 . 4 6 5. 0.482 0.434 0.4c2  T I  1.5 0.5 1.5 '  10  43 2 43 17 16 43 19 3 13 14  .'  r-i E HRS HR HRS HRS MI NS  HRs M [ Ns M I No H R0 M I NS MI  Ns  HRS MINS  HRs  XI-8 RofM 9-3 EPS  0.0508 CM MINERAL SETTLED BED HEIGHT CM  0.9 5 0 • J>_2__  0.90 0.88 0,65 0.83 0^80 '•'0.7 7'. 0.74 _0_« 1_ C66 0 .68 0.65  A!_°_  2  ''  10-2  EPS  5  2 7.60 31.20 34_. 7 0 3 8 . 20 " 3 8 .20 41.70  EPS  0.77 0.74  1.5 1  HRS HR_  1  HR  CRYSTALS APPROX. Tlrin  . 6.15 9 W_5_ IZVlb 14.30  0.499 0 . 494 1^5 ~~ """7)7 49 5 ~ 15 ' 0.483 20 ll.9b_ 0.435 25 " "18.C0 '" " 0.4 86 " "3 21.45 0.433 1.2 2 3 .90 ___ .°_L JA . Ly ; 27750 "0.484 "" ' 5 3 1.03' 0.484 3.5 34_.60 OjL^? ___A '33. \ G"" '" 0.48 2" ~ 0.5 41.43 0.479 9.5  hiRS MINS MINS MINS HRo HR  4  3  3  MINo" HRS _A HR HRS H  0.0426 CM MINERAL CRYSTALS  6.20 9.7 5  T'ZTH>~  :  5  "07T7  APPROX. TIME  1.5 HRS 4_3_ _ .hi N S_ " "'2 HRS 43 MINS 17 _MLNS_ . "ieT ~ H~RS~ • 43 MINS 19 MI N S_ "" 3 ' ~ HRS 18 MI No 14 HRS  SEIT LE D BED P0KUS1TY  SETTLED BED riblGHT CM  0.95 0.9 2 TJT97J 0.88 0.85 - -- - 0.8 2 0.80 g  0.49 4  0.490 0.469 0.4 90" 0.4 90 0.487 0.486 0.486 0_. 4 8 4 " " 0/483 0.483 0.482  0.0426.CM MINERAL  RoN 1 0 - 3  0  5  SETTLED BED HEIGHT CM  0.95 0 . 92 '""0T90~ 0.68 _0_"_3 _ 0.85"" 0.82 0 . 8_0 0.7 7 0.74 0.71 ""07 6 8" 0.65  0.494 0.494  ~9TT5~  ""12. 10 14 .5 0 18".T5" 20.55  7  RON  SETTLED BED POROSITY  6.10 9.75  "07~"9"2  CRYSTALS  _  14.40 18.05 To . I"5 2 1.65 23 .9 5  S E l T L t D BED POROSITY  '  0.502 0.494 07492 0.436 0 . 4 3 7  07490 0.487 /0.435  2 7 7 6 3 0 . 4 ~ 8 6  27. 70 31.40  "0" '771  3 4 7 3 3 - —  0 .63 0.65  38.45 41.80  '  0.483 0.489 — "07 4 3 7  0.487 0.483  APPROX. TIME 1.5  IT  20 25 3"'" i.2 10 ~20  5 3.5 2 77  0. 59.5  H R ;  °_  M7'N7  MINs MINo_ HRS"""" HRS HRS_ Mlilo  MIN S HRS HRS  HR HRS  XI-9 RON 11--2 EPS  SETTLED BED hEIGriT CM  0.95 0.92 0.90 0.88 0.85 0.82 0.80 0.80 0.77 0 .74 0.71 0.68 RON  0.135 CM SUGAR CRYSTALS  11 -3  6.20 '. 9 . 70 12.10 14.50 18.00 21.65 24.00 23.90 27.45 31.05 34.45 3 7.95  SETTLED BED POROSITY 0.503 0.492 0.49 1 0.490 0.486 0.4 88 0.486 0.434 0.484 0.484 0.431 0.480  SETTLED BED HEIGHT C M  SETTLED BED POROS I I.Y  0.9 5 0.92 0.90 0.88 0.85 ' ' 0.8 2 0 .30 0.80 0.77 0.74 0 . 74 "" 0 ."71 0.68  6.25 9 .80 12.20 14.55 18.05  0.506 0.496 0.494 0.491 0.487 •0 .483 0.486 0.486 0.435 0.483 0.483 0.481 0.482  EPo 0.95 0.92 0.90 0.68 0 .8 5 0.62 0.60 0.77 0.74 0.71 0.68  v  15 1 1 0.5 0.5 0.5 10 0.53.5 40 9 2  MI Nb HR HR HR HR HR HRS HR HRs M I Ns HRS HRs  0.135 CM S UGAR CRYSTALS  EPS  RON 12 -3  APPROX T1 iiE  24.00 24.00 2 7.55 3 1.00 31 .00 34.45 38. 10  APPROX. 1 I ME 15 1 1 0.5 0.5 u.5 lu 0.5 3. 5 40 9 35 4 .  MINS HR HR HR HR HR ""' HRs HR HRs MI NS HRS M1 Ns HRs  0.113 CM S UGAR CRYSTALS SETTLED BED r; EIGHT CM 6.25 9.90 12.20 14.55 18.05 "2 1 . 6 0" 24.00 27.50 31.00 34.35 37_._7_0  SETTLED BED POROSI 1 Y 0.506 0.501 0.494 . 0.491 0.4 87 ' 0.486 0.486 0.464 0.483 0 .4 79 0.476 •  APPROX. 1 I ME 9 1.0 3 1.59 • 20 2.5 12 lu 22 o  HRs HR HRS HR HRs MI NS HRS MI NS M I N -/ MI Ns HRs  APPENDIX X I I  SAMPLE PLOT OF EXPERIMENTAL BED HEIGHT v s .  SETTLING TIME  XIII-1  APPENDIX X I I I  SAMPLE CALCULATIONS AND ERRORS  Sample c a l c u l a t i o n s a r e g i v e n b e l o w ; random c a s e s f o r error 1.  analysis  are included.  (Settling rate)x(Liquid  viscosity)  u = DIST/TIME By  linear  i n t e r p o l a t i o n between s h o r t  „ V  a.  =  1  f  (TEMP-TEMPI )  (TEMP2-TEMP1)  7  temperature  interval,  .  &2' l) v  x  Run 3-lA a t e = 0.92 DIST = 1 0 . 0 ± 0 . 2 cm TIME = 65.4 ± 0 . 2 s e c u = 10.0/65.4 =0.153 cm/sec  Maximum r e l a t i v e  error  4o.O  1  +  in u  65.4  ;  *  TEMP = 71.8 + 0.15 d e g . F where + 0.15 d e g . F i s t h e u n c e r t a i n t y temperature. T E M P ! s 70.1 + 0.03 d e g . F TEMP2 = 72.01 ± 0.03 d e g . F .  V j v2  By  linear  = 32.24 (+ 0 . 2 % ) c s = 31.39 (± 0 . 2 % ) c s  interpolation  i n the estimated  liquid  XIII-2  v = 31.57 cs Maximum r e l a t i v e e r r o r i n estimated v r  +  0  QQ2  _.32.24, ,0.15+0.03  + o.o.ozx ; K L  3 1  5 7  =+0.8%  0  <  7  +  0.03+0.03  +  9  1  #  0  +  0,002+0.002)  +  0  #  8  5  0.671  ; x  3 1 # 5  7j  "  Thus maximum r e l a t i v e e r r o r  i n uz/,  = + (2.4 + 0.8) = + 3.2% b.  Run 3-2 a t e = 0.74 w i t h the l a r g e s t temperature  variation  DIST = 10.0 + 0.2 cm TIME = 205.0 + 0.2 sec u  = 10.0/205.0 = 0.0488 cm/sec  Maximum r e l a t i v e e r r o r i n u  =  ±  (  Toto  +  205?0  )  =  -  2 , 0  °  / o  TEMP = 74,3 + 0.5 deg. F TEMP  1=  73.0 + 0.03 deg. F  TEMP = 75.02 + 0.03 deg. F 2  v  - 30.63 (+ 0.2%) cs  1  V  = 29.15 (+ 0.2%) cs  2  By i n t e r p o l a t i o n  v  = 29.68 cs  Maximum r e l a t i v e e r r o r of estimated v  =  + [ 1 L * 0 u  30,63. 29.68  O Q 2 x UOZx  = + 1.6%  + +  (Q.5+Q.Q3 + Q.Q3+Q.P3 + 0.002+0,002) 0^9 9 5 _ 1.3 * 2.02 1.48 29. 68 v  +  ;  x  XIII-3  i n uv  Maximum r e l a t i v e e r r o r  = + (2.0+1.6)% = + 3.6% Error  i n the l i n e a r i n t e r p o l a t i o n  o f v i s c o s i t y over a small  temperature i n t e r v a l should be comparatively n e g l i g i b l e . , 2.  Porosity Porosities  were s e l e c t e d  to c a l c u l a t e  the r e q u i r e d  amount of p a r t i c l e s t o be weighed WT = V  (l-e)^  s  WT = Z ( i n c r e m e n t a l weight f o r p o r o s i t y change ofA^)  € = 1-WT/Vps a.  Run 3-lA a t e = 0.65 V = 313.0 + 1.0  p  s  cm  3  = 2.169 + 0.005 g/cm  3  WT = 313 x 2.169 x (0.05+0.03x8+0.02x3) = 237.4 g. accuracy WT = 237.4 + 0.3 g Maximum r e l a t i v e e r r o r * + (0.36 - 437.4  + +  1.0 313.0  = + 0.37% b.  in e  Run 3-3 a t € = 0.65  +  0.005) 2.169  ;  x  0^31 0.65  XIII-4  V = 1250 + 1.0 cm  3  WT = 1250 x 2.169 x (0.05 + 0.03 x 8 + 0.02 x 3) = 949.2 + 0.4 g Maximum r e l a t i v e -  error in €  + (0.4 - ^949.2  _1__ 1250  0.0Q5) 2.169  +  ;  0^35 0.65  x  = ± 0.19% 3.  F i x e d bed p o r o s i t y €  . ! . b ~ ' HTBxD ^x0.7854 K  L  t  Run 3-3 a t € = 0.65 WT = 1250x2.169x(0.05+0.03x8+0.02x3) = 949.2+0.4 g = 2.169+0.005  p  B  g/cm  3  HTB = 39.28+0.05 cm D  t  = 5.08+0.01 cm  -  -i b -  1  949.2/2.169 " 39.28x5.08^x0.7854  = 0.450 Maximum r e l a t i v e  =  error i n e  + P,4 - ^949.2 (  +  0.0Q5 2.169  b  0,05 39.28  +  0.01x2s 5.08  ;  x  0^55 0743  = + 0.96% 4.  Effect  of U n c e r t a i n t y of e on u v  Consider equation  l a , t a k i n g n = 5.  i n € could cause an u n c e r t a i n t y  A 0.4% u n c e r t a i n t y  of 2% i n uy. T h e r e f o r e any v a -  XIII-5  riation that  i n uv w h i c h was  c a u s e d by e ,  nonuniformities 5.  in  larger  than  its  own maximum e r r o r  s h o u l d be c o n s i d e r e d t o a r i s e the  suspension dicussed in  from the  the  plus minor  text.  Computation The d a t a on h i n d e r e d s e t t l i n g were p r o c e s s e d by  c o m p u t e r p r o g r a m A on page X I I I - 6 w h i c h terpolation, calculation. mates o f  the  averaging  does the v i s c o s i t y  o f uv a n d p r e l i m i n a r y  P r o g r a m B was u s e d t o do t h e processed data  the  from program A .  least  least  in-  squares  squares  esti-  XIII-6  Program A Variables  of  the  programs  RUN  r u n number  PTC  particle  LIQ  d e s c r i p t i o n of  SCREEN  sieve  T(A)  tA,  0.05  value  TIME  settling  time,  DIST  s e t t l i n g d i s t a n c e , cm  EPS  porosity  U  settling rate,  NU  kinematic v i s c o s i t y ,  UNU  ui/, ( 0 . 0 1  name liquid  opening  sec  cm/sec cs  cm sec" ) 3  2  o  3 UNUA  average  TEMP TEMPS  temperature ° F or ° C r e a d - i n temperature of v i s c o s i t y a s TEMP  NUS  read-in v i s c o s i t y  NUMIN,  uv  t  (0.01  cm s e c  data  )  i n cs a t  data, unit  same  TEMPS  NUMAX, minimum and maximum v a l u e o f NU i n a  run  3 DENP  particle  density  g/cm  DENLIQ DV  l i q u i d density diameter of sphere of the p a r t i c l e  DT  column d i a m e t e r  DRATIO  DV/DT  NTEST  number o f  3  same v o l u m e a s  -g/cm cm cm  tests  3 STNDD  s t a n d a r d d e v i a t i o n of average  LGUNUA  l o g . of average  LGEPS  l o g . of €  uv  uv  ,  (0.01  cm s e c  _2 )  XIII-7  SLUNU  sum o f l o g (uz/)  SLGE  sum o f  SLUNU2  sum o f [ l o g (uz/)j  SLUNE  sum o f l o g ( u v ) x l o g €  SLGE2  sum o f  N  least  LGUNUO  extrapolated  UNUO  (ui/) (0.01  loge 2  (loge) squares estimated Richardson-Zaki  index n  l o g (uz/) t o € = 1  calculated cm /sec?)  e x t  from e x t r a p o l a t e d  l o g (uv)  3  CFDN  957o  confidence i n t e r v a l  of n  CFDLUN  957o  confidence interval  of extrapolated  UNU01-UNU02  957o  confidence l i m i t s (0.01 c m / s e c ) 3  of extrapolated  l o g (uv)  (uz/)„ -, v l  2  DP EXT  sphere diameter  DPEXT1-DPEXT2  sphere diameter c a l c u l a t e d from confidence l i m i t s of (uz/) xt»  calculated  from ( u z / )  e  DPEXCO  sphere diameter c a l c u l a t e d c o r r e c t e d by w a l l , cm  REOMIN, REOMAX  maximum and minimum R e  Q  c  from  e x t  957o m  (uz/) t e x  b a s e d on DPEXT  , cm  FASF  •B  RETURN  16116  TO THE  CHEMICAL  JOG  NUMhER  JOB  START CHONG  80  I ME  i  ORTRAN  PROGRAM A  4 5  6 • 7 10 11 1? 13 14 15 16 17 20 if 21 22 23 24 25 26  27 30 31 3? 33 34 35 36 37 40 41 42 43 44 45 46 47  MG  16116 <4'.  K-HRS  YU-StM  AGE  1 2 3  c  INE  f U  NG  CATEGORY  F  5:  EC  I ,  OS.  XIII-8  KUILOIIMG U S E R ' S  MAMFV  YU-SEM  USER  CHUNG  9 M 011  OFF-  ,  REAL. N U , N , N U $ , L G U N U A , L G E » S , LGuNUO•NUMIN,NUMAX COMMON TEMP , I , N U , TEMP S , ,MUS , UNUA, MUM IN , NUMAX DIMENSION T I M E { 1 0 ) , D I S T ( 1 0 ) , E P S ( 1 5 ) , U ( 1 0 ) , U N U ( 1 5 ) , I T E M P < ? 0 ) , M U < ? 0 ) , T E M P S ( 2 0 ) ,NUS(2''>.) , U N U A ( 2 0 ) , L G I H J A ( 15) , L G E P S ( 1 5 ) D I M E N S I O N P T C ( 3 ) , L I 0 ( 4 ) , S C R E E N ! 12) , R U N ( 2) DI M E N S I O N  T(14)  DATA T ( 2 ) » T ( .3 ) , T ( 4 ) » T ( 5 ) » T ( 6 ) , T ( 7 ) » I < 8 ) » T ( 9 ) , T ( 1 0 ) , I" ( 1 I ) » T ( 1 2 ) , 13) , T( 14 ) / 4 . 3 u 3 , 3 . 1 8 2 , 2 . 7 7 6 , 2 . 5 7.., 2 . 4 4 7 , 2 . 3 6 5 , 2 . 3 06 , 2 . 2 62 , 2 . 2 2 6 , 2 . 7 201,2.179,2.160,2.145/ D I M E N S I O N F ?•' T ( 1 6 ) ,FMOUT 1 ( 1 6 ) , FM0UT2 ( 16 ) , F ^ 0 U T 3 ( 1 6 ) DIMENSION S T N D P t 1 5 ) , N T F S T( 15) 1 C 0 0 0 READ 1 1 4 , P U N , P T C , D E N P , L I O , D F N L I Q , C V » D T , S C R E F N 114 FORMAT ( 2 A 6 » 3 A 6 , F 6 . 3 , 4 A 6 , F I 0 . 4 / 2 F 1 0 . 4 / 1 2 A6 ) WRITE ( 7 , 1 1 4 ) RUN,PTC,PENP,LIO,LENLIQ,DV,OT,SCREEN READ 1 1 1 , (TEMPS(M),NUS(M),tf=1,i2) 111 FORMAT ( 8 F 1 0 . 0 ) READ 1 , F M T , FMOU T I , F M D U T ? , FMOUI3 1 FORMAT ( 1 6 A 5 ) WRIT F ( 7 , 1 1 ) F M 0 U T 2 , F M O O T 3 11 FORMAT ( 1 6 A 5 / ) NUMIN=2C00.0 NUMAX=0.0 DRAT I 0 = DV/DT PRINT 2 , R U N , P T C , O E N P , L I Q , D E N L I G , D V , O T , D R A T I O , S C R t E N 2 FORMAT ( 1 H 1 , / / / / / / , 2 ? X , ? A 6 / 2 3 X , 1 1 HPART I C L E S = , 3 A 6 , 8 X , 3HD E N S I T Y = , 1 F 6 . 3 , 7 H GM/CM / 2 3 X , 1 1 H L I Q U I D = , 4 A 6 , 2 X , 8 H D E N S I T Y = »F6 . 3 , 7 H G>-/L ?M / 2 3 X , 1 7 H P A R T I C L E S I Z E 0 = , F 7 . 4 , 9 H C M , D = , F 6 . 2 , l ? H CM, 0 /0 = 3,F7.4/21X ,12A6 /) P R I N T 21 21 FORMAT ( 26 X , 4HTEMP , 5 X , 4HD I 3 T , 4X , G HS FTTL I M G , G X , 1 H U , 8 X ,4HU * N U , 6 X , 3 H E 1 P 5 / 3 6 X , 2 H C M , 5 X , B H T I M F SEC , 2 X , 6 H C M/S EC » 2 X , 1 1 H O . " 1 CM S/ E L. / ) DO 1 0 0 0 1 1 = 1 , 1 5 DO 1 0 0 1 = 1 , 1 0 REAU ( 5 , F M T ) TEMPI I) , 0 IS T{I ) , TI M E ( I ) , E P S ( I I ) , I P C T R IF ( I D C T R . M E . 0 ) GO TO 10 IF ( T' M ( I ) . ;. ). ) GO TO 2 0 0 0 ICO CONTINUE 10 C-UL MUCAL NTE S T ( I I ) = 1 SUM = 0 SUMSQA=0. DO 2 0 0 K = 1 , I U(K)=DIST(K)/TIf!C(K) UNU(K. ) = U ( K ) * N U ( K ) wRITE ( 6 , F M 0 U T 1 ) T E M P ( K ) , 0 1 S T ( K ) , T I M F ( K ) , U ( K ) ,U J U ( K ) , EPS ( I I ) SUMSCA=SUMSQA + U N U ( K ) * * 2 D  r  5C 51 52 53 54 55  56 57 60 61 62  200  l  201  L G E P S ( I I)= AL0<710(CPS ( II ) )  1C00 CUNT 1 iviL^ 2000 11=11-1 SLUNU=0. S L G F = 0.0 SLUNU?=0.0 SLUNLE=0.0  63  64 65 66 67 70 71 72 73 74 75 76 77 ICO 101 1C2 103 104 105 106 107 110 111 11 2 113  30  114  115 116 117 120 121 122 123 124 12 5 126 127 130 131  SUM=SUM+U NU ( K) U N U A ( II ) - S U M / F L G\ T ( I ) I I ( l . f ' I . l ) -Ti TO 201 STNDD (I I )=SCRT( I SUM SO A- S-JM* *2 /FLOAT ( I ) ) / FLOAT ( I-1 ) ) LGUNUA ( I I ) = ALOG I 0 ( UWUA ( I I ) )  SLGL2 =0 . J 00 30 1 = 1,11 SLUNU=SLUHJ + LGUNUA( I > SLGL = SLGE + L G L P S ( I 5 SLUNU?=SLUNU2 + LGUNUA ( I ) *»2 SLLNL£=SLIJNLE + LGUNUA( I ) * L G E P S ( I ) SLGE?=SLGE2+LGEPS<I)**2 CONTINUE N=( FLOA r(I I ) * S L U N L E - S L G E * S L U N U ) / ( F L O A T ( I I ) * S L G E ? - S L G E * * 2 ) LGU a 0 = ( SLU;\IU-N*SLGE ) /FLOAT ( I I ) UNUQ=10.0**LGUMUO REAL LGEAVE L G E A V E = S L G E/F L 0 A T( I I ) S0LUN2=( SLUNU2-LGUNU0*SLUNU-N*SLiJNLE) / ( FLOAT ( I I ) - 2 . ) ) SDLUN=SCRT(S0LUN2) SLELE2=SLGE?-SLGE**2/FLOAI( I I) CFD.vi-T ( I 1-2 ) *SDLUN/SQRT( j L E L E 2 ) CFDLUM=T ( I I - 2 ) * 3 D L IJ N * S 0 • \ T ( 1 . 0 /FLOAT ( I I ) +LGEAVE**2/SLELE2 ) VAR.M = SDLUr)2/SLELE2 SON=S0RI(VARN) I! N U G = 1 C .0 ** LG UN U 0 U M U 01 = 1 G . 9 * * ( L G U N U 0 - C F I) L U N) UNU:i2 = l 0. u * * ( LGU NUO + CFPLU -J) . PHYPRU=0.18*DFNLI0/( (DEN°-D fcMLI 3 ) * 9 8 0 . ) DPSQ=UNUG*PHYPRa  DPE1SQ=JNU01*PHYPRG UPE2 3(J = UNUU2*PHYPRU DPEXT=SORT(DPSQ) U P E X U = SQRT(fJPElSQ) 0PEXT2=SQRT{DPE2S3) CURFAC=1.0+2.104*DRATI0 CQRF=SCKT(CORFAC) DPEXCO=DPEXT*CORF R E 0 MIM = 0 E X T * U N U 0/M U M A X * * 2 * 10 0 . 0 REOMAX = QPEXT*UNUC/NUMIN**?*lQ0.t.< PR I f! T 2 , RUN , P TC , DENP , L I C , DE ML I G , DV , DT , DRAT 1 0 , SCR E EN PRINT 2 2 , R E U M I N , R E 0 M A X FORMAT ( 2 3 X , 5 H R E ( 0 ) t 4 X , f 6 . 3 , 1 H - , F 6 . 3 / / 2 3 X , 3 H E P S , 2 X , 9 H U * N U ( A V L ) , l ? X , 7 H L G ( F P S ) , ? X , 0 H L G ( U * N U ) , 2 X , 3 H S T U . f ) E V . , l X 5 H N J 0 F / 3 2 X , 1 2 H 0. G 1 2/SEG ,1 ? X,1 3 H T ST /) vy!'I T;- (7,221 ) NUM I N , NUM A X FORMAT ( 2 F 1 0 . 3 ) Jr  22  f  C  132 133 134  135 136 137  221  DO  iCOQ K = l , I I  IF (NTFST(K).EQ.1 ) GO To 110 VIR I TB ( 6 , F M 0 U T 2 ) E P S ( K ) , UNUA ( K ) , L G F P 3 ( K ) , LGUNU A ( K ) , STNDD (K) ,NTE IK) WRITE ( 7 , F M O U T 2 ) E P S ( K ) , UNU A ( K ) , L S £ P S ( K ) ,LGUNU *\ I<) , STNDD(K),  140 141 142 143 144 145  146 147  IK ) GO To 3 C 0 ' j W P I TE ( , 6 FMOUT i) E P S ( K ) ,DNUA( K,) •L3EPS(Y.) »L GUOU A ( K ) , N T E S T ( K. ) 110 WRI T . (,7F MOUT 3 ) •: PS ( K ) , 1INUA {K ) ,LG F P S ( K ) , LGUNU A(K ) , N F EST(K ) 3C00 CONTI NU c 6 , LGUMUO , N , UNUU , N » N » C Fr>M » L GU WO, CFULuN , U 4U01 , UNUG 2 F 0 R M \ r ( /23X,24HLEAST SOUARfS EST [MATES 8 / 2 IX , 1 HLOG < U*N'J )F=7 t. 4 , 2 IH +,F6. 2,9H*L0G(E°S) /27X, 6HU*NU =,F8.3,6H*EPS**,F5.2 /27X, 19 HI; ON 2F I DE 'JCE INTERVAL /?8X,2HN=,!.!X,F5. ?» 3X,F5.2 /?8X, 10HLOG(J*NU) Li, F 7 3» 1 X t F 7 -t ./28X,9H(U*NU)EXT , F 3 . 3 , I H - , F 8 . 3 ) PRINT 9 »U JUG » DP E X T t DP E XCO,UNUOl»U NU02 » D PE X T1»DPuXT2 NU) I- XT /?7X,10H(U* FORMAT (/23 * , U H O I A . OF SPHERE CORRESPONDING TO 9 3H ? 7 1=,FH.3, 14X,F7.4,3H CM/27X , 1 8HCDRR EC TED FOR W ALL , 14X , F 7 . M- ,CM/ 2X,12H(U *NU)FXT GF F.n.^,lH-»F8.3,lH, t 2 X , F 7 . 4 , 1H-, F 7 . 4, 2HC M ) GO TO 1 COCO E AO f  150 151  C.  152 153 154 155 156 157 160 161 162 163 164 165 166 167 170  SUBROUTINE *••!' J C A L. KEAL NU,NUS,NUMIM NUM1X F  COMMON  TEMP t  0 IME M S T J N  I , N U t TT  T E M P (20)  0U 2 2 K = 1 , I 00  11 12  11  RATIO NU IF  iv-=l,l? . G T . T F h P S ( M ) . A M D . TEMPI  +( T FMP ( « ) - T LMPS ( M ( N U ( K ) . L T . N U M I N ) NUMIN=NU(K)  CONTINUE RFTU*M  K)  ,UNUM?0)  .LE.TEMP.>(M+1 ) )  =(NUS(M+l)-NUS(M))/(TEMPS(M+l)-TEMPS(M))  < K) =NUS (M)  END  $ENTRY  A , M U M I N , N'JMAX  IF (TEM-P(K) CONTINUE  I F ( N U ( K ) . G T . N U M A X )  22  MPS\, N U S , U.NU  ,MU(2C) , T E M R S ( 2 0 ) , N U S ( 2 0 )  NJVAX=NU(K)  ) ) *RA T I 0  GO  TO  12  EASE RETURN TO THE CHEMICAL JOB NUMBER JOB START QB  16116  35  I FE  3  ORTRAN  PROGRAM B  4 5 6 7 10 11 12 13 14 15 16 17  20 21 22 23 24 25 26 27 30 31 32 33 34 35 36 37 40 41 42 43 44  16116  BUI LP IMG  CATEGORY F  OIHRS 50MIN 06.45EC  USER'S NAME- YU-SEM CHOMG V9M011  USER OFF-  CHUNG YU-SEN  AGE  1 2 3  ENGINEERING  REAL NU,N,NGS,LGUMUA,LGEPS ,LGUNUO,NUMIN,NUMAX INTEGER DI SCAR DIMENSION T I M E ( I O ) , D I S T(10) ,E P S ( I 5) , U ( 1 0 ) , U N U ( 1 5 ) , 1TEMP120) ,MU(20) , TEMPS(20),NUS(20) ,UNUA(20),LGUMUA(15),LGEPS(15) DIMENSION P T C ( 3 ) , L I Q ( 4 ) , S C R E E N ( 1 2 ) , R U N ( 2 ) DIMENSION T ( 1 4 ) DATA T ( 2 ) , T ( 3 ) , T ( 4 ) , T ( 5 ) , T ( 6 ) , T ( 7 ) , T ( 8 ) , T ( 9 ) , T ( 1 0 ) , r ( l l ) , T ( 1 2 ) , T ( 1 1 3 ) , T ( l 4 ) / 4 . 3 0 3 , 3 . 1 8 2 , 2 . 7 7 6 , 2 . 5 7 0 , 2 . 4 4 7 , 2 . 3 6 5 , 2 . 3 0 6 , 2 . 2 6 2 , 2 . 2 2 8,2.? 201,2.179,2.160,2.145/ DIMENSION F M T ( 1 6 ) , F M 0 U T 1 ( 1 6 ) , F M G U T 2 ( 1 6 ) , F M 0 U T 3 ( 1 6 ) , F M 0 U T 4 ( 1 6 ) , FNOl 1T5116) DIMENSION STNOD(15)»NTEST( 15) 1CCC0 READ 114,RUN,PTC,DEMP,LIQ,DENLI 0,DVtDT SCREEN,NUMIN,NUMAX 114 FORMAT ( 2 A 6 , 3 A 6 , F 6 . 0 , 4 A 6 , F 1 0 . 0 / 2 F 1 0 . 0 / 1 2 A 6 /2F10.0 ) READ 1, FM0UT2,FM0UT3,FM0UT4,FM0UT5 1 FORMAT(16A5 ) DR A T10 = D V/D T PRINT 2,RUN,PTC,DENP,LIQ,DEML10,DV,DT,DRAT 10,SCREEN FORMAT { 1 H 1 , 2 2 X , 2 A 6 / 2 3 X , U H P A R T I C L E S = ,3A6,8X,8HDENSITY= ,F6.3,7H 2 1GM/CM /23X,11HLIQUID= ,4A6,2X,8H0ENSITY= ,F6.3,7H GM/CM /23X,1 2HPARTICLE SIZE D = ,F7.4,9H CM, D =,F6.2,12H CM, D /D = ,F7.4/?3; 3,12A6 /) PRINT 21 FORMAT ( 28X,3HEPS,2X,9HU*NU(AVE),2X,7HLG(EPS)» 2X,8HLG(U*NU),2X,8! 21 1STD.DEV.,IX,5HNC.0F /32X,12H0.01 CM /SEC ,19X,14H TESTS/ SLUNU=0. SLGE=0.0 SLUNU2=C.0 SLUNLE=0.0 SLGE2=0.0 1=0 DO 30 J = l , 1 4 1=1+1 READ ( 5 , 3 1 ) EPS( I ) ,UNUA(I),LGEPS( I),LGUNUA( I ) , STNDD( I ) , N T E S T ( I ) 1ISCAR FORMAT (2 6 X , F 9 . 0 , F 9 . 0 , F 1 0 . 0 , F 9 . 0 , F 1 1 . 0 , I 1 , 4 X , 1 1 ) 31 IF ( E P S ( I ) . L T . O . C O C l ) GO TO 40 IF (DISCAR.NE.O) GO TU 32 IF ( N T E S T ( I ) . E Q . l ) GO TO 110 WRITE ( 6 , F M 0 U T 2 ) E P S ( I ) , U N U A ( I ) , L G E P S ( I),LGUNUA(I ) , STNDD( I ),N T E o T 11 ) GO TO 3 5 WRITE(6.FM0UT3) E P S < I ) , U N U A ( I ) , L G E P S ( I),LGUNUA( I),NTEST( I ) 110 SLUMU=SLUMU+LGUNUA(I) 35 SLGE = SLGE + LGEPS( I ) SLUNU2=SLUNU2+LGUNUA(I)**2 f  45 46 47 5C 51 52 53 54 55 56 57 60 61 62 63 64 65 66 67 70 71 72 73 74 75 76 77 100 101 1C2 103 104 105 106 107 110 111 112 113 I 14 115 116 117 120  121 122  123 124  SLUNLE=SLUNLE+LGUNUA(I)*LGEPS(I) SLGE2=SLGE2+LGEPS<I)**2 GO TO 30 32 I F ( N T E S T ( I ) . E Q . 1 ) GO TO 33 WRITE (6,FM0UT4 ) EPS ( I ) ,UNUA( I ) t LGEPS( I ) ,LGUNUAf I ) , S IN D f) ( 11 ) 1 = 1-1 GO TO 30 WRITE(6,FM0UT5) E S ( I ) ,UNUA< I ) , L G E P S ( I ) ,LGUNUA( I ) ,NTEST( I ) 33 1 = 1-1 30 CONTINUE 40 11=1-1 N=(FLOAT(II)*SLUNLE-SLGE*SLUNU)/(FLOAT( II)*SLGE2-SLGE**2) LGUNUO=(SLUNU-N*SLGE)/FLOAT(II) UNUO=lC.C**LGUNUO REAL LGEAVE LGEAVE = SLGE/FLOAT( I I ) SOLUN2=(SLUNU2-LGUNUO*SLUNU-N*SLUNLE)/(FLOA T(I I ) - 2 . 0 ) SDLUN=SORT{SDLUN2) SLELE2=SLGE2-SLGE**2/FL0AT(II) CFDN = T ( I 1-2)*SDLUN/SORT(SLELE2) C FDLUN=T(I I - 2 ) * S D L U N * S Q R T ( 1 . 0 / F L O A T ( I I ) + L G E A V E * * 2 / S L E L E 2 ) VARN=SPLUN2/SLELC2 SDN=SQRT(VARN) UNUO=10.0**LGUNUU UNU01=1G.0**(LGUNUO-CFOLUN) UNUQ2=10.0**(LGUNUO+CFDLUN) PHYPRO=0.18*0ENLI0/((DENP-DENLIQ)*980.) DPSQ = UNUO*PHYPRQ DPE1SQ=LNU01*PHYPR0 UPE2SQ=LNU02*PHYPR0 DPEXT=SQRT(DPSQ) 0PEXT1=SQRT(DPE1SQ) DPEXT2=SQRT(0PE2SQ) CORF AC = 1.0+2. 104*PRATIU CORF=SQRT(CORFAC) DPEXCO=DPEXT*CORF DPEIC0=DPEXT1*C0RF DPE2C0=DPEXT2*C0RF REOMIN=DPEXT*UNL0/NUMAX**2*100.0 KEOMAX=DPEXT*UNU0/NUMIN**2*100.0 PRINT 22,REOMIN,REOMAX FORMAT(/2 3 X , 5 H R E ( 0 ) , 7 X , F 6 . 3 , 1 H - , F 6 . 3 ) 22 PRINT 8 » LGU NUO »Nt UNUC,N N » CFDN »LGUNUO» CFDLUN »UNUO1 UNUO 2 8 FURMAT (/23X.24HLEAST SQUARES ESTIMATES /27X,1OHLOG(U*NU)=,F7.4, IH +,F6.2,9H*L0G(FPS) /27X, 6HU+NU =»F8.3,6H*E°S**,F5.2 /27X,19HC0 2FIDENCE INTERVAL /2 8 X , 2HN= , 3 X, F5. 2 , 3X , F 5 . 2 / 2.8X , 1 OHLOG ( U*NU 3,1X,F7.4 /28X,9H(U*NU)EXT ,F8.3,1H-,F8.3 ) PRINT 9,UNU0,l)PEXT,DPFXC0,UNU01 , UNU02 , DPEXT 1 DP E X T2 , OP E 1 CO , DP E 2 C 9 FORMAT (/23X,31HDIA. CF SPHERE CORRESPONDING TO /27X,10H(U*NU)EX 1=,F8.3,14X,F7.4,3H CM/27X,18HC0RRFCTED FOR WALL,14X,F7.4,3H CM/ ? 2X,12H(U*NU)EXT OF,F8.3,1H-,F8.3,IH,,2X,F7.4,1H-,F7.4,2HCM/2 7X,l&H 30RRECTED FOR WALL ,14X,F7.4,IH-,F7.4,2HCM ) GO TO 1CCC0 END SEN TRY D  t  1  1  

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