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Contact angle measurements on fine coal particles He, Ying Bin 1989

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CONTACT ANGLE MEASUREMENTS  ON FINE COAL PARTICLES  BY YING BIN HE B.A.Sc, Heilongjiang Institute of M i n i n g & T e c h . , P.R.C, 1982  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE (Department o f M i n i n g  STUDIES  and M i n e r a l P r o c e s s  We a c c e p t t h i s t h e s i s a s  Engineering)  conforming  to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA A u g u s t 1989 ©Ying  B i n He, 1989  In  presenting this  degree at the  thesis  in  University of  partial  fulfilment  British Columbia,  of  the  requirements for  an advanced  I agree that the Library shall make it  freely available for reference and study. I further agree that permission for extensive copying  of this thesis for scholarly purposes may be granted by the  department  or  by  his  or  her  representatives.  It  is  understood  that  head of my copying  or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of H J "  > n C  l  Q  ^  Mt"e» ft|  The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  Oct.  13 ,  tHf  ,  Process  Engineering  ABSTRACT  This angle one  study  investigates  measurement  direct  and  on  fine  coal  one  indirect,  direct  contact  the  techniques  particles. have  of  Two  been  contact  techniques,  investigated  and  modified. In high a  the  pressure  pellet  employed  i s employed  and in  the  angle versus are  the  angle  to  compress  artificial  contact  t i m e and  surface  the  pellet  model  and  properties  a method  are  powder  the  measurements.  pellet  technique,  coal  of  d r o p s i z e on  examined. In a d d i t i o n , t h e  affecting  the  surface  angle  versus  measurement  pellet The  is  contact  pellet  surface  p r o p e r t i e s and  factors  also  for contact  the  into  studied.  angle  A  pellet  correction  are  proposed. In  the  calculated to The  employ  from the high  holding  powder  the  liquid contact  penetration  behaviour The  pressure  penetration  is  t o p r o d u c e h i g h l y compact  columns.  longer  the  in  as w e l l  angle  modified  properties applied  contact method i s  no of  the  r a t e . The  tube t r a d i t i o n a l l y  therefore,  investigated.  measurement,  pressures  glass  is,  penetration  of  indirect  as  used  f o r the  column  of  needed.  The  change  in  liquid  within  such  columns  is  of  columns  the  their other  formation  and on  the the  phenomena a r e  angle c a l c u l a t i o n procedure i s a l s o  impact rate  studied.  proposed.  of A  TABLE OF CONTENTS  ABSTRACT  i i  TABLE OF CONTENTS  i i i  LIST OF TABLES  v i i  LIST OF FIGURES  ix  ACKNOWLEDGEMENT  xiv  CHAPTER 1. INTRODUCTION  1  CHAPTER 2. LITERATURE REVIEW  4  2.1  General Concept 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5  2.2  Contact Angle Measurements 2.2.1 2.2.2  2.3  Contact Angle On An I d e a l Surface Contact Angle H y s t e r e s i s H e t e r o g e n e i t y and C a s s i e ' s Equation Roughness and Wenzel's E q u a t i o n Composite C o n f i g u r a t i o n and Cassie-Baxter Equation  D i r e c t Contact Angle Measurements I n d i r e c t Contact Angle Measurements  Other Techniques t o C h a r a c t e r i z e Wettability 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 2.3.6 2.3.7  H y d r o p h i l i c i t y Index I n d u c t i o n Time Heat o f Immersion Rate o f Immersion Film Flotation C r i t i c a l Surface Tension of Flotation Other Techniques  CHAPTER 3. COAL  5 5 6 7 10 13 16 16 21 29 29 30 32 34 37 39 43 44  3.1 I n t r o d u c t i o n  44 iii  3.1.1  Classification  44  3.1.2  Chemical Composition  47  3.2 Homogenization  49  3.3 C o a l S t u d i e d  50  CHAPTER 4. OBJECTIVE CHAPTER 5. DIRECT CONTACT ANGLE MEASUREMENTS AND EXPERIMENTAL  55 57  5.1  Introduction  57  5.2  Theory and Techniques  59  5.3  5.2.1  Background  59  5.2.2  Techniques  63  E x p e r i m e n t a l and Apparatus  67  5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 5.3.6  Sink-and-Float Test Comminution o f C o a l Samples P a r t i c l e Size Analysis Pellet-Making P o r o s i t y Measurement P e l l e t S u r f a c e Examination  CHAPTER 6. RESULTS AND DISCUSSIONS <I>  67 ....68 68 69 71 73 74  6.1  Contact Angle Measurements  75  6.2  Comparison  78  6.3  T e s t i n g The Computation Method  84  6.3  Contact Angle Versus Drop S i z e  91  6.5  Contact Angle Versus Time  101  6.6  Factors Affecting  105  6.7 6.8 6.9  o f The Two Techniques  C o n t a c t Angle  6.6.1 O x i d a t i o n 105 6.6.2 Pellet-Making Pressure I l l Porosity 117 S u r f a c e Examination and Assumption F o r F r a c t i o n a l Area o f Pores 125 A Model  134  iv  6.9.1 6.9.2  CHAPTER 7.  133 137  6.10 Summary and D i s c u s s i o n  143  THE RATE OF PENETRATION TECHNIQUE  148  7.1  Introduction  148  7.2  Theory and Techniques  151  7.2.1 7.2.2 7.3  B a s i c Theory Techniques  Experimental 7.3.1 7.3.2 7.3.3 7.3.4  CHAPTER 8.  A Compressed P e l l e t S u r f a c e Model Contact Angle C o r r e c t i o n And Comparison  151 155 157  Materials Column-Making Rate o f P e n e t r a t i o n Measurement V i s c o s i t y and S u r f a c e T e n s i o n  157 158 158 161  RESULTS AND DISCUSSIONS <II>  163  8.1  163  A p p l i c a b i l i t y Test 8.1.1 8.1.2 8.1.3  8.2  Column-Making P r e s s u r e 8.2.1 8.2.2 8.2.3 8.2.4  8.3  Some F e a t u r e s P r e c i s i o n and L i n e a r i t y Height L i m i t  173  The E f f e c t o f P r e s s u r e on R e p r o d u c i b i l i t y and L i n e a r i t y ..173 E f f e c t on Rate o f P e n e t r a t i o n 189 S i d e E f f e c t o f High P r e s s u r e ..193 Lower L i m i t o f P r e s s u r e 194  P h y s i c a l P r o p e r t i e s o f Columns 8.3.1 8.3.2 8.3.3 8.3.4  163 165 170  Column Column Column Column  196  Height v e r s u s P r e s s u r e ..196 Height v e r s u s Weight ...198 Porosity 200 Expansion 201  8.4  E f f e c t of F r i c t i o n  203  8.5  Contact Angle C a l c u l a t i o n s  213  8.5.1 8.5.2 8.5.3 8.5.4  Introduction A New Approach Numerical C a l c u l a t i o n s Evaluation v  213 214 217 225  8.6  Summary and D i s c u s s i o n  230  CHAPTER 9. CONCLUSIONS  236  REFERENCES  241  APPENDIX 1.  A FLOWSHEET FOR SIMPLEX SEARCH PROGRAM  250  APPENDIX 2.  CONTACT ANGLE CALCULATION PROGRAM  251  vi  LIST OF TABLES Table 3.1.1  Page Coals arranged  i n an ascending  o r d e r o f carbon  45  content. 3.3.1  Q u a l i t y c h a r a c t e r i s t i c s of L i n e Creek c l e a n  52  coal 3.3.2  Proximate a n a l y s i s o f ROM  Bullmoose seam C c o a l  52  dry b a s i s . 6.6.1  The  c o n t a c t angle on p e l l e t of o x i d i z e d  c o a l - the -1.3 6.6.2  107  of the Bullmoose c o a l  Comparison of the c o n t a c t angles w i t h the r a t e  108  o f p e n e t r a t i o n measured on d i f f e r e n t c o a l s . 8.1.1  T e s t f o r the ruggedness of p e n e t r a t i o n f r o n t on the 1.4-1.5 d e n s i t y  8.2.1  8.2.2  c o a l , pressure  i s 6.9  i s 13.8  8.2.4  The  and and  penetration  186  MPa.  e f f e c t o f column-making p r e s s u r e on  accuracy  185  MPa.  S t a t i s t i c a n a l y s i s of p e n e t r a t i o n data f o r BM c o a l , p r e s s u r e i s 20.7  184  MPa.  S t a t i s t i c a n a l y s i s o f p e n e t r a t i o n data f o r BM c o a l , pressure  8.2.3  fraction.  S t a t i s t i c a n a l y s i s o f p e n e t r a t i o n data f o r BM  168  187  l i n e a r i t y of the r a t e o f  line.  8.3.1  S w e l l o f columns a f t e r p e n e t r a t e d  8.5.1  Rate of p e n e t r a t i o n e q u a t i o n matrix. vii  by l i q u i d .  202 218  8.5.2  The  slopes f o r d i f f e r e n t density f r a c t i o n s  219  under v a r i o u s p r e s s u r e . 8.5.3  A g e n e r a l c o n t a c t angle and t o r t u o s i t y c o n s t a n t calculation  8.5.4  The  results.  f i n a l c o n t a c t angle and t o r t u o s i t y c o n s t a n t  calculation  223  results.  viii  226  LIST OF FIGURES  2.1.1  E q u i l i b r i u m contact vapour  angle formed by water,  8  (gas), and s o l i d phases.  2.1.2  Models o f heterogeneous s u r f a c e s .  8  2.1.3  A model o f i d e a l i z e d rough s u r f a c e .  12  2.1.4  An i l l u s t r a t i o n o f composite c o n f i g u r a t i o n .  14  2.1.5  Contact angle h y s t e r e s i s on a model porous  14  surface. 2.2.1  Constructing  a tangent t o t h e p r o f i l e .  2.2.2  The t i l t e d p l a t e method f o r c o n t a c t  17  angle  18  measurement. 2.2.3  The c y l i n d r i c a l r o d method f o r c o n t a c t  angle  18  measurement. 2.2.4  The Wilhelmy method.  22  2.2.5  Capillary rise at v e r t i c a l plate.  25  2.2.6  The microscope i n t e r f e r e n c e method.  25  2.3.1  Rate o f immersion t e c h n i q u e .  36  2.3.2  Film flotation.  38  2.3.3  C r i t i c a l surface tension of f l o t a t i o n .  41  3.1.1  A m o l e c u l a r model o f c o a l proposed by Wiser.  48  3.3.1  The s i n k - a n d - f l o a t t e s t f o r t h e L i n e Creek c o a l .  53  3.3.2  The s i n k - a n d - f l o a t t e s t f o r t h e Bullmoose c o a l .  53  5.2.1  The d e f i n i t i o n o f t h e c o o r d i n a t e  61  ix  system f o r a  s e s s i l e drop p r o f i l e . 5.2.2  The set-up o f a Rame-Hart model 100 c o n t a c t  64  angle goniometer. 5.3.1  A MET-A-TEST specimen mounting p r e s s .  70  6.1.1  A s e s s i l e drop image observed through t h e  77  goniometer. 6.2.1  A comparison o f t h e measured and t h e computed c o n t a c t angles on a p e l l e t  (-1.3  79  L i n e Creek  coal). 6.2.2  An i d e a l i z e d heterogeneous s u r f a c e model.  82  6.3.1  The p o s i t i o n i n g  86  o f the drop b a s e l i n e and i t s  e f f e c t on computed angle v a l u e . 6.3.2  The p o s i t i o n i n g  o f the apex p o i n t and i t s  87  e f f e c t on t h e computed angle v a l u e . 6.3.3  The measurement o f s c a l i n g  f a c t o r and i t s  88  e f f e c t on t h e computed angle v a l u e . 6.3.4  The accuracy o f l i q u i d d e n s i t y measurement and  6.4.1  89  i t s e f f e c t on the computed angle v a l u e .  The e f f e c t o f drop volume on t h e c o n t a c t  93  angle - drop volume i n c r e a s e d i n two ways. 6.4.2  Drop s i z e e f f e c t on c o n t a c t angle (1.3-1.4 Density f r a c t i o n  6.4.3  95  P=31.1 MPa).  Drop s i z e e f f e c t on c o n t a c t angle ( o x i d i z e d  96  -1.3 Bullmoose c o a l t=150°C) 6.4.4  Drop s i z e e f f e c t on c o n t a c t angle ( o x i d i z e d  97  -1.3 Bullmoose c o a l t=200°C) 6.4.5  Drop s i z e e f f e c t on c o n t a c t angle ( o x i d i z e d x  98  -1.3 6.5.1  Bullmoose c o a l t=250°C)  Contact angle v s . time f o r d i f f e r e n t d e n s i t y  102  f r a c t i o n s o f L i n e Creek c o a l . 6.6.1  Contact angle v e r s u s o x i d a t i o n time - o x i d i z e d i n water and  6.6.2  in air.  Contact angle v s . p e l l e t - m a k i n g p r e s s u r e f o r the L i n e Creek c o a l -1.3  6.6.3  The  6.6.4  The  (-1.3  114  d e n s i t y f r a c t i o n o f Bullmoose c o a l )  i n f l u e n c e o f p e l l e t - m a k i n g p r e s s u r e on  angle r e p r o d u c i b i l i t y 6.7.1  113  density fraction.  e f f e c t of p e l l e t - m a k i n g p r e s s u r e on c o n t a c t  angle  110  (-1.3  115  of Bullmoose c o a l ) .  The p e l l e t p o r o s i t y v s . p r e s s u r e f o r d i f f e r e n t  120  d e n s i t y f r a c t i o n s of the L i n e Creek c o a l . 6.7.2  The p e l l e t p o r o s i t y v s . p r e s s u r e f o r d i f f e r e n t  121  d e n s i t y f r a c t i o n s of the L i n e Creek c o a l . 6.7.3  Characteristic particle sizes for different  123  d e n s i t y f r a c t i o n s o f the L i n e Creek c o a l . 6.8.1  A t e s t f o r the f r a c t i o n a l pore area on  129  d i f f e r e n t cross sectional surface. 6.8.2  SEM  photograph of a p e l l e t s u r f a c e .  6.9.1  A model of compressed p e l l e t s u r f a c e .  134  6.9.2  Contact angle v s . ash content and c o r r e c t e d  140  c o n t a c t angle f o r LC 6.9.3  130  coal.  Measured and c o r r e c t e d c o n t a c t angle v a l u e s  141  v e r s u s p r e s s u r e f o r L i n e Creek c o a l . 7.3.1  The  columns made f o r the r a t e of p e n e t r a t i o n  test. xi  160  8.1.1  A p p l i c a b i l i t y o f t h e Washburn e q u a t i o n .  171  8.2.1  Rate o f p e n e t r a t i o n curves  174  f o r columns o f  -1.3 BM c o a l made under d i f f e r e n t 8.2.2  Rate o f p e n e t r a t i o n curves  pressures.  f o r columns o f  1.3- 1.4 BM c o a l made under d i f f e r e n t 8.2.3  Rate o f p e n e t r a t i o n curves  8.2.4  Rate o f p e n e t r a t i o n curves  Rate o f p e n e t r a t i o n curves  8.2.6  Rate o f p e n e t r a t i o n curves  8.2.7  8.2.8  Rate o f p e n e t r a t i o n f o r d i f f e r e n t  182  (columns made under 13.8 MPa). 183  (columns made under 20.7 MPa).  The e f f e c t o f column-making p r e s s u r e on t h e slope of the rate of penetration  8.3.1  specific  Rate o f p e n e t r a t i o n f o r d i f f e r e n t s p e c i f i c density fractions  8.2.10  181  (columns made under 6.9 MPa).  density fractions 8.2.9  179  pressure.  Rate o f p e n e t r a t i o n f o r d i f f e r e n t d e n s i t y fractions  178  pressure.  f o r columns o f  +1.8 BM c o a l made under d i f f e r e n t  177  pressures.  f o r columns o f  1.6- 1.8 BM c o a l made under d i f f e r e n t  176  pressures.  f o r columns o f  1.5- 1.6 BM c o a l made under d i f f e r e n t 8.2.5  pressures.  f o r columns o f  1.4- 1.5 BM c o a l made under d i f f e r e n t  175  curve.  The e f f e c t o f column-making p r e s s u r e on t h e column-packing d e n s i t y  190  197  (Bullmoose c o a l -1.3  density fraction) 8.3.2  Column weight versus fraction  8.4.1  i t s height  (+1.8 d e n s i t y  199  pressure=13.8 MPa).  Change i n t h e r a t e o f p e n e t r a t i o n behaviour xii  204  when columns p l a c e d u p s i d e down. 8.4.2  The f o r c e s a c t i n g on t h e column w i t h i n t h e  206  mould. 8.4.3  The t h e o r e t i c a l e f f e c t o f column h e i g h t on t h e  209  i n t e g r a l p o r o s i t y o f t h e column. 8.4.4  Column h e i g h t v e r s u s i n t e g r a l p o r o s i t y - v a l u e s  210  o b t a i n e d from a c t u a l measurement I . 8.4.5  Column h e i g h t v e r s u s i n t e g r a l p o r o s i t y - v a l u e s  211  o b t a i n e d from a c t u a l measurement I I . 8.5.1  An i l l u s t r a t i o n o f t h e two dimensional simplex  222  search process. 8.5.2  The t o r t u o s i t y c o n s t a n t v e r s u s p a c k i n g d e n s i t y .  xiii  228  ACKNOWLEDGEMENT  The Dr.  author wishes t o express h i s deepest g r a t i t u d e t o  Janusz  S.  Laskowski  under  whose  kind  direction  and  guidance t h i s work was undertaken.  The  t e c h n i c a l a s s i s t a n c e p r o v i d e d by Mrs. S. F i n o r a ,  and Mr. F. Schmidiger i s g r a t e f u l l y acknowledged.  The  author  a l s o wishes  t o express  h i s gratitude to  P r o f e s s o r A.L Mular f o r h i s v a l u a b l e t e a c h i n g interesting students (UBC),  and  useful  i n Dept. o f Mining  especially  t o Mr. K.  reading t h i s  thesis.  My s p e c i a l encouraging  love,  and t o a l l t h e f e l l o w  and M i n e r a l Process  t o Mrs. Maria  discussions;  for  courses,  Lund  Holuzko  Engineering  f o r many v a l u a b l e  and Mr. B. K l e i n  thanks a r e g i v e n  me w i t h  i n some v e r y  t o my w i f e ,  understanding,  care,  f o r proof  Y i n g Wang,  and  and f o r s h a r i n g i n t h e happiness and h a r d s h i p s  past years.  xiv  enduring of the  CHAPTER  1  INTRODUCTION  The h y d r o p h i l i c - h y d r o p h o b i c c h a r a c t e r i s t i c o f a s o l i d p l a y s a predominant r o l e  i n diverse technological  such as f r o t h  lithographic printing,  textile  flotation,  manufacturing,  resistance methods  cell  adhesion  and  processes  detergency,  the  thrombo-  o f b i o - m a t e r i a l s , e t c . One o f t h e most  f o r determining  the hydrophobicity  of  common  a  solid  s u r f a c e has been through t h e c o n t a c t angle measurements.  Some m a t e r i a l s on which t h e c o n t a c t angles a r e t o be measured, polished  are not a v a i l a b l e  i n sizes  t o accommodate t h e s e s s i l e  large  drops.  enough  t o be  I n t h e case o f  c o a l , a d d i t i o n a l problems a r i s e because c o a l i s a mixture o f the Wide  degradation  products  variations  in  o f p l a n t s and o f m i n e r a l  their  genesis,  h y d r o p h o b i c i t y make c o a l h i g h l y  In  order  to  accomplish  matter.  composition,  and  heterogeneous.  meaningful  contact  angle  measurements, two techniques have been s t u d i e d . One i s t h e Compressed  Pellet  Method  1  a  direct  contact  angle  measurement  technique;  Method - an  indirect  o r i g i n a l sample was  For pellet  i s the  technique.  Rate  of  Penetration  In both cases,  a very  fine  utilized.  direct  method),  another  contact  angle  measurement  i t i s desirable to  obtain  a  (compressed flat  surface  which should be m a c r o s c o p i c a l l y homogeneous as compared w i t h the  dimension o f the s e s s i l e drop and  entire  coal  under h i g h inch) and measured this  sample  tested.  pressure 5 t o 8 mm  on  the  technique  contact  c o a l powder was  into pellets h e i g h t . The  pellet and  angle  The  a  upper variety  measurement  representative of  of  25.4  mm  the  compressed  diameter  (one  c o n t a c t angles were d i r e c t l y surface.  The  of  factors  on  pellet  feasibility  of  influencing  the  surface  were  investigated.  The apparent  measured ones.  correction measured  A  contact  pellet  angles  surface  were  model  considered  and  contact  method were t e n t a t i v e l y proposed t o c o n v e r t  contact  angle  values  to  the  true  contact  the angle the angle  values.  T h i s technique direct.  However,  s m a l l , the  liquid  when  has the  the  advantage o f b e i n g  contact  angle  values  from the s e s s i l e drop s t a r t s t o  quick are  very  penetrate  i n t o the p e l l e t and e q u i l i b r i u m can not be e s t a b l i s h e d . 2  and  Contact  angles  have  also  been  measured  from t h e r a t e o f p e n e t r a t i o n The technique t h i s work by making the columns u s i n g a  indirectly  was m o d i f i e d i n  machine-controlled  h i g h p r e s s u r e p r e s s . T h i s made p o s s i b l e t o overcome problems in  the  traditional  reproducibility scattering the  method  in  column  e t c . . The  liquid  physical  effects  penetration  resulting  from  the  poor  properties,  data  o f column-making  rate  and  column  pressure  properties  on  were  s t u d i e d . A new c a l i b r a t i o n method was proposed.  S i n c e i n t h e d i r e c t method o n l y those p a r t i c l e s which form while  the  pellet  surface  a l l particles  participate  i n t h e column  have  p e n e t r a t i o n r a t e , the l a t t e r technique reliable. the d i r e c t  I t s accuracy  i n the an  3  effect  on t h e  i s s t a t i s t i c a l l y more  and r e p r o d u c i b i l i t y  method.  measurement,  are higher  than  CHAPTER 2  LITERATURE REVIEW  The  w e t t a b i l i t y of a s o l i d surface i s very  i n many t e c h n o l o g i c a l p r o c e s s e s . on  the s o l i d  the  The c o n t a c t angle o f l i q u i d  s u r f a c e i s t h e most commonly used parameter i n  wettability  usually  important  measured  study on f l a t  process.  The  surfaces,  contact  angles  are  and l e s s f r e q u e n t l y on  p a r t i c u l a t e s o l i d s <Good, 1979>.  The  surface  characterization  and  contact  angle  measurement on f i n e l y d i v i d e d p a r t i c u l a t e s o l i d s u r f a c e s has become more and more important and has developed i n t o a new field  f o r study. A v a r i e t y o f techniques  have emerged i n t h e  l a s t twenty y e a r s . Some r e l e v a n t b a s i c t h e o r i e s and r e c e n t l y developed  modifications  will  be  following sections.  4  briefly  reviewed  i n the  2.1  GENERAL CONCEPTS  2.1.1  Contact Angle On An I d e a l S u r f a c e  The property  angle  and a u s e f u l  idealized free  contact  smooth,  liquid  drop  liquid  on  the  measure o f s o l i d  homogeneous,  The e q u i l i b r i u m  idealized  a  surface  macroscopic  wettability.  nondeformable  t a k e s t h e shape which  energy o f t h e system. by  i s , intrinsically,  On an  surface,  the  minimizes t h e f r e e  contact  angle  i s a unique  formed  quantity  <Neumann and Good, 1972>.  The  c o n t a c t angle was f i r s t  linked to surface  energy  by Thomas Young <1855>. I t was demonstrated by Gibbs, <1928> t h a t m i n i m i z i n g t h e f r e e energy r e q u i r e s t h e m i n i m i z a t i o n o f the  sum  Tlv^lv  +  7  s v  *sv  +  Tsl^sl  2.1.1  where 7 i s a s u r f a c e o r i n t e r f a c i a l area,  and  the  liquid/vapour,  subscripts  solid/  lv,  vapour  and  sv,  t e n s i o n , A i s an  and  si  solid/liquid  refer  to  interfaces,  r e s p e c t i v e l y . The m i n i m i z a t i o n y i e l d s t h e f o l l o w i n g e q u a t i o n  "YigCOSfl  = 7  5  - 7  s  i  2.1.2  where  6  i s the  Young's  contact  equation.  three-phase  line  angle.  Figure of  2.1.1  contact  smooth nondeformable s o l i d assumes  on  the  between the air/solid  7  solid  This  illustrates  between  water,  s u r f a c e . The  surface  i s the  forces at a i r / l i q u i d 7 i n t e r f a c e as  s l  equation  result  ,  l g  angle  i s known the  classical  vapour,  and  which a of  a  liquid/solid  shown i n the  as  a  drop  balance y ,  and  B l  above e q u a t i o n  and  F i g u r e 2.1.1.  2.1.2  Contact  For contact the  a  Angle H y s t e r e s i s  real  angles  liquid/solid  can be  Young e q u a t i o n .  system,  a number o f  assumed, i n apparent c o n t r a d i c t i o n t o  Two  relatively  reproducible  the l a r g e s t and the s m a l l e s t . These are c a l l e d angle,  8 , and a  the  receding  when  surface,  and  back.  The  the  the  periphery  receding  difference  a  angle is  g  are  the advancing  r  t h a t the advancing angle of  d -6  angles  0 , respectively. Their  angle,  names are d e r i v e d from the f a c t measured  stable  a  drop  advances  i s measured by termed  the  over  pulling  contact  is a it  angle  hysteresis.  Two  major  factors  which  h y s t e r e s i s are s u r f a c e h e t e r o g e n e i t y  are  attributed  the  and roughness. D e t a i l e d  review o f both w i l l f o l l o w i n the next two 6  to  sections.  The contact  symbols  angle,  6  and  e  and  composition  heterogeneous or  contact  the  equilibrium  respectively.  6  y  while  s u r f a c e s and  8  may  e  i t may  not  i s o b t a i n e d from  e  exist  on  conform  to  experiment.  H e t e r o g e n e i t y And The C a s s i e E q u a t i o n  One  of  the  major  causes  heterogeneous nature o f s o l i d 1964>.  The  surface  compositions. an adsorbed  They may  mosaic. The energy  2.1.2.  local  of the  islands  regions  on  of  hysteresis  consists  of  varying  be p r e s e n t as a d i s t i n c t  shows two  regions of  c o n t a c t angle w i l l  r e g i o n w i t h which the in  the  Fig.2.1.2(a) s u r f a c e . As  is  the  s u r f a c e s <Johnson and D e t t r e ,  f i l m which can not be i d e n t i f i a b l e  Figure  The  angle,  structure,  Young's e q u a t i o n . Commonly, 6  2.1.3  for  a smooth, homogeneous s u r f a c e of  and  rough  stand  y  Young  obeys Young's e q u a t i o n on specific  d  phase o r as  as a phase.  a  solid  surface  depend on t h e s u r f a c e liquid  represent  a drop  chemical  i s i n contact.  high-contact-angle  p e r i p h e r y advances  over  such a s u r f a c e , the edge of the l i q u i d tends t o stop a t the boundaries that  of  the  advancing  intrinsic surfaces.  angle  islands. angles of  Similarly,  the  I t was  should  suggested  be  <Pease,  associated  high-contact-angle  receding 7  angles  should  be  1945>  with  the  regions  of  associated  Figure  2.1.1  Equilibrium contact vapour(gas),  angle  and s o l i d  f o r m e d by w a t e r  phases.  PLAN  (a)  A general  Figure  2.1.2  model;  (b)  An i d e a l i z e d model  Models o f heterogeneous  8  VIEW  surfaces  w i t h the low-contact-angle  C a s s i e <Cassie, contact  angle  consisting  of  of a  areas.  1948> suggested  a  smooth  t h a t the e q u i l i b r i u m  micro-heterogeneous  "patchwork" arrangement of two  surface  homogeneous  elements c o u l d be d e s c r i b e d by  COS0 =  where  ai  i s the  c o n t a c t angle e , x  a  1  - C O S 9  fraction and a  2  of  +  1  a  the  2  - C O S 9  surface  2.1.4  z  c h a r a c t e r i z e d by  i s the f r a c t i o n h a v i n g angle  < 7  1  + < 7  = 2  8  2  1  2.1.5  When the number of elements i s more than two,  this  equation  can be g e n e r a l i z e d as  cosfl >= 2 < r - c o s * 1  Embodied i n t h i s e q u a t i o n two  components  patches  occur  as  2.1.6  i  i s the assumption t h a t the  discrete,  uniformly  distributed  a t the s u r f a c e which are s m a l l compared t o the  area  o f the drop o r bubble used t o measure the c o n t a c t angle. Cassie in  equation  various  al.,  1977;  has  been confirmed  situations Lamb and  <Cassie  Furlong,  and 1977;  e x p e r i m e n t a l l y and Baxter, and  1944;  Blake  and  The used  Oliver  et  Ralston,  1985>. Johnson and D e t t r e <1964> analyzed an i d e a l i z e d model 9  consisting intrinsic  of  contact  The the  concentric  results  liquid  t o be  The  e  and  x  of  c o n f i g u r a t i o n and  wettability  behaviour  This  Johnson 1964;  For of  composite  alternating  the  vibrational  been  a  to  a  state  s i z e s of the  real  smaller real  that  Cassie's  surface  the  experimentally  angles  equation.  permits  should  more The  still  concentric  verified  of  hetero-  energy b a r r i e r s .  surface  of  2.1.2  be  circular  <Dettre  and  Crawford and Koopal, 1987>.  the  pellet,  of  similar  has  of  shown i n F i g u r e  o r as the  meta-stable  model.  as  2  t h a t p r e d i c t e d by  heterogeneity  quantitatively  regions  s u r f a c e become s m a l l e r , the c o n t a c t  closer to  random  6  r e v e a l t h a t as  becomes g r e a t e r ,  g e n e i t i e s on the tend  angle  circular  composite s u r f a c e w i t h  the  region  of  c o n s i s t i n g of  pores as  pores  can  be  a i r , and  the  Cassie  i n the  considered  case as  equation  a can  s t i l l be a p p l i e d .  2.1.4  Roughness And  The  contact  The Wenzel  angles  of  Equation  a  liquid  with  the  solid  d i r e c t l y dependent on the macroscopic geometry o f the Wenzel<1936>  developed  a  relation  between  roughness o f a s o l i d s u r f a c e and the c o n t a c t 10  the  are  solid.  macroscopic  angle:  cose  ' = r-cos0  2.1.7  where 8 ' i s the measured or apparent c o n t a c t angle, true  contact  coefficient.  angle, The  and  r  is  the  surface  8 i s the roughness  s i m p l e s t parameter f o r d e s c r i b i n g roughness  i s the roughness r a t i o  r = A/a  where A  i s the  true  surface  area  2.1.8  and  a i s the  apparent  or  envelope area on a plane p a r a l l e l t o the apparent s u r f a c e .  Certain Johnson and chosen by  idealized  c o n f i g u r a t i o n have been s t u d i e d  D e t t r e <1964>, and E i c k e t al.<1975>.  Johnson and  Dettre  (Figure  The  by  model  2.1.3) c o n s i s t e d of  a  drop of l i q u i d on a s u r f a c e o f c o n c e n t r i c grooves which were large  with  respect  to  molecular  dimensions,  but  compared w i t h macroscopic l a b o r a t o r y apparatus. The of t h i s  idealized  surface  small  analysis  showed t h a t roughness l e a d s t o a  l a r g e number o f meta-stable c o n f i g u r a t i o n s . Each meta-stable state  was  barrier.  separated The  approximately a s p e r i t i e s and  from  heights directly  an of  adjacent the  proportional  independent of t h e i r  state  energy to  the  by  an  energy  barriers height  were of  the  separation.  There are, however, s i g n i f i c a n t d i f f e r e n c e s between 11  Figure  2.1.3  A model o f i d e a l i z e d r o u g h s u r f a c e  (Johnson  and Dettre<1964>)  the a  i d e a l i z e d model o f rough s u r f a c e and r e a l  thermodynamic  model  to  a  standpoint,  random  meta-stable  states  them.  and  Huh  going  from  hill-and-valley and  lowers  the  Mason<1977>  a  model  circular  From  groove  introduces  energy  modified  surfaces.  barriers  Wenzel's  more  between original  r o u g h n e s s e q u a t i o n t o a c c o u n t f o r t h e c a s e o f random s u r f a c e roughness by  introducing a surface t e x t i l e  cosfl  Concentric possible  textures  influence the that -  grooves  height  = (r  1  and for  when t h e  a  radial  which  r  Gaussian  drop s i z e i s  *  + (r-l)tf)•cosfl  grooves could  on e be q u i t e d i f f e r e n t . follows  factor  large  0. 12  be  2.1.9  would the  present same  but  For a roughness i n  distribution, compared t o  it the  two  was  the which  found  roughness,  Objections concerning the  have  Wenzel's e q u a t i o n .  geometry i n the  t h e drop,  raised  from  Because the  immediate v i c i n i t y  time angle  to  time  depends  on  of the p e r i p h e r y of  Wenzel's d e s c r i p t i o n i s not u s e f u l i f the s u r f a c e  i s non-uniformly  One Bracke  been  of  et  rough.  the  most  al.<1988>.  recent  They  criticisms  demonstrated  by  was  raised  means  of  by the  c a l c u l u s o f v a r i a t i o n s t h a t even on rough s u r f a c e s the Young equation  still  Wenzel e q u a t i o n hysteresis, and  applies.  however,  claimed  that  r e l i e s on a f a l s e assumption. Contact  i . e . the  receding  They,  angles,  d i f f e r e n c e i n the  the angle  apparent  advancing  f o r homogeneous rough s o l i d  substrate  i s due t o the l o c a l s l o p e o f the s o l i d a t the t h r e e phase of contact-line. arithmetic  The  thermodynamic  mean between these  Young  advancing  and  angle  is  receding  the angle  values.  2.1.5  Composite C o n f i g u r a t i o n And  The  Cassie-Baxter  Equation  L i q u i d s w i t h h i g h i n t r i n s i c angles may penetrate  into  c r a c k s and  c r e v i c e s of v e r y rough or porous  s u r f a c e s . These i n c o m p l e t e l y p e n e t r a t e d composite.  not be a b l e t o  s u r f a c e s are  called  An i d e a l i z e d composite i s shown i n F i g u r e 2.1.4. 13 (  r = 2.67  LIQUID  -SOLID  /-AIR  r = 1.61  LIQUID 1  Figure  2  2.1.4  3  100  Figure  2.1.5  5  6  r= 1.09  An i l l u s t r a t i o n  configuration  ~i  4  ^-SOLID  1  of  (Johnson and  1  r  T  1  Dettre)  1  30' 80 70 60 50 40 30 20 PER CENT SOLID AREA IN SURFACE  Contact  porous surface  composite  r  10  angle h y s t e r e s i s (Cassie  14  and  0  on a model  Baxter)  C a s s i e and  Baxter<1944> have d e r i v e d an e q u a t i o n  for  composite i n t e r f a c e s  COS0 =  ffj-cos^u  -  a  2.1.10  z  where <7 =A /A, a =A /A, A i s apparent s u r f a c e area, h x  contact  sl  2  area  liquid-air  A  of  liquid  with  solid,  and  A  is  l g  the  composite  consists  reduces  of  to  interface  is  air  equation  (0=180°),  obviously  2.1.10.  the  a  family of contact  2.1.5  f o r the  angle  and  o f the from  model porous  contact  solid  area  Cassie's  represent  angle  particular  possible  corresponding  different  roughness w i t h  the  centre  wettability  line. of  angle  curves  surfaces.  The the  this  I t shows how  centre l i n e  curves  above  angles  receding less  equation  i s shown i n F i g u r e  h y s t e r e s i s v a r y w i t h the  The  (2.1.4)  2  advancing  represent  equation  region  a =0.  i n s u r f a c e . The  equation.  Cassie  Particularly,  reduces t o Wenzel equation when  A  free  i n t e r f a c e under the drop.  example o f a heterogeneous s u r f a c e . By assuming t h a t 2  is  Bl  lg  percentage  i s calculated  Cassie's  and  angles  contact  on  those  curve below  surfaces  rough s u r f a c e b e i n g  close  r e c e d i n g angle depends s t r o n g l y on solid  portion  i n s e n s i t i v e to surface porosity. 15  of  a  surface  and  of to the is  2.2  CONTACT ANGLE MEASUREMENTS  Some major  techniques  that  have  been  measurement o f c o n t a c t angles a r e reviewed.  used  for  In general, the  t e c h n i q u e s o f c o n t a c t angle measurements can be d i v i d e d two  major c a t e g o r i e s ; t h e d i r e c t  from  which  indirect  t h e angle  value  the  into  c o n t a c t angle measurement  i s directly  obtained,  and t h e  c o n t a c t angle measurements from which t h e v a l u e o f  c o n t a c t angle i s c a l c u l a t e d .  2.2.1  D i r e c t Contact Angle Measurements  2.2.1.1  S e s s i l e Drop and A i r Bubble  Of a l l t h e methods which were developed,  the s e s s i l e  and pendent drop method, and t h e adhesion a i r bubble method are  t h e most  Good,  1979>.  involving liquid  general The  direct  drop  experimental  method  of  measurement  techniques<Neumann and  measuring  contact  on t h e p r o f i l e  or, alternatively,  angles  of a  sessile  o f t h e a d h e r i n g a i r bubble,  i s t h e most commonly employed technique.  The  contact  angle  is  determined  by  directly  c o n s t r u c t i n g a tangent t o t h e p r o f i l e a t t h e p o i n t o f  16  V////////////  /Y7777777777?  a  '/////////////  Figure a.  sessile  contact  drop method;  directly  goniometer the  2.2.1.2  b.  phases by  eyepiece,  drop p r o f i l e .  generally  adhering a i r  (Figure 2.2.1).  using  or  to the  a  An a c c u r a c y  b u b b l e method  The a n g l e c a n be  telescope  on a p r o j e c t e d  fitted  image  o f ±2°  profile  or  with  a  photograph  f o r t h e s e methods  is  claimed.  T i l t e d P l a t e Method  The  tilted  Jsssop  <1925>.  Figure  2.2.2.  liquid  which  the  Constructing a tangent  of the three  measured  of  2.2.1  '////////////,  plate.  method i s  method  The p r i n c i p l e A  solid  will  The  disappears.  plate  plate  a is  devised  o f t h e method i s  plate  form  was  is  partially  concaved tilted  or  The most i m p o r t a n t a d v a n t a g e  the  simplicity  of the 17  the  Adams  immersed  in  meniscus  curved  in the  near  meniscus  of the t i l t e d  apparatus.  and  illustrated  convex  until  by  plate  Figure  2.2.2  T i l t e d p l a t e method f o r  contact  angle  measurement  Figure  2.2.3  C y l i n d r i c a l r o d method f o r c o n t a c t measurement  18  angle  2.2.1.3  C y l i n d r i c a l Rod  As  a  Method  modification  of  the  c y l i n d r i c a l r o d method e n c l o s e s , which  can  be  rotated.  The  tilted  plate  i n a glass c e l l ,  level  of  the  method,  a cylinder  liquid  around  p a r t i a l l y immersed h o r i z o n t a l c y l i n d e r can be a d j u s t e d it  touches the  shows a The  cross  c y l i n d e r without s e c t i o n of  c o n t a c t angle  the  any  curvature.  i s c a l c u l a t e d from the  cos0 = 2h/d  until  Figure  c y l i n d e r immersed  in  a  2.2.3  liquid.  equation  - 1  2.2.1  where d i s the diameter o f the c y l i n d e r and h i s the  height  o f the l i q u i d s u r f a c e above the bottom o f the c y l i n d e r .  2.2.1.4  Compressed p e l l e t method  The  surface  scopically size  of  high. and  It  glossy  powder was  of and  is  compressed  pellet  smooth, e s p e c i a l l y  fine  or  demonstrated  the  i s u s u a l l y macrowhen the  pellet-making  thermodynamically  particle  pressure  is  <Shuttleworth  B a i l e y , 1948> t h a t the c o n t a c t angle on a porous s u r f a c e  will  be  higher  composition Baxter  than  i s the  equation  on  a  smooth  same. T h i s  2.1.10. 19  can  surface be  even  explaned  by  if  the  Cassie-  It  was  concluded  <Neumann  and  Good,  1979>  c o n t a c t angles measured on compressed p e l l e t s , although may reach a l i m i t i n g v a l u e if  t h e compressing  value),  are  they  ( i . e . , they do n o t change f u r t h e r  pressure  determined  that  i s increased  by  above  microscopic  certain  roughness  and  porosity.  An modify  the preparation  contact the  attempt was made by Kossen and H e e r t j e s <1965> t o  angle  o f t h e compressed  measurement  i n cases  pellet  where l i q u i d  t o allow penetrates  compressed powder. I t was observed t h a t p r e s o a k i n g t h e  pellet  with  the  measuring  liquid  could  produce  solid  s u r f a c e s on which drops p l a c e d t o measure t h e c o n t a c t  angles  are q u i t e s t a b l e .  The Kossen  contact  angles  and H e e r t j e s  on  <1965>  solids  from  were  c a l c u l a t e d by  t h e observed  angle  using  C a s s i e ' s method, which r e l a t e s t h e c o n t a c t angle measurement on  a heterogeneous  angles.  The  implicit  of  particles  surfaces oriented pellet.  solid  parallel Doubt  concerning  surface  assumption were  was  that  (a) p e r f e c t l y  to the o v e r a l l  has been  to the i n t r i n s i c  surface  contact  the flat  exposed and (b)  o f t h e compacted  r a i s e d by Neumann and Good  the v a l i d i t y of t h i s  20  assumption.  (1979)  2.2.2  I n d i r e c t Contact Angle Measurements  2.2.2.1  The wilhelmy Method  As shown i n F i g u r e 2.2.4, i f a smooth, v e r t i c a l  plate  i s brought i n t o c o n t a c t w i t h a l i q u i d , the l i q u i d w i l l  exert  a downward f o r c e on the p l a t e  f = P-7 -COS0 - V - A p - g  2.2.2  lv  where  P  is  displaced, fluids  Lp  perimeter  i s the  ( a i r and the  To liquid  the  of  the  plate,  V  i s the  d i f f e r e n c e i n d e n s i t y between the  liquid).  and  f  is  plotted  of contact  against  time.  Prior  between the  p l a t e and  the r e c o r d e r i n d i c a t e constant weight  ( l i n e AB).  contact,  the  capillary  rise  2.2.4.b).  As  balance angle during  along  recorder  of  the  decreases  the  two  c a l c u l a t e 6 , the p l a t e i s s l o w l y lowered i n t o the  establishment  after  volume  the  the  jumps  liquid  immersion again line  immersion, around  the  but  contorted  line  BC,  the f o r c e i n equation  at  the  continues,  (line  of  from  the  chart  does line  not will  From the  21  liquid,  (see  weight average  to  the  Figure on  the  contact  remain  constant  not  straight  be  l e n g t h o f the  above i s o b t a i n e d  the  Immediately  C due  plate  CD) . I f the  contact  CD.  B to  the  to  line  (a)  Device  f o r Wilhelmy  technique  11  1.measuring device,  -.6-z-z'7C  or  10  rod,  cell,  5.measuring  platform,  7.movable  8.screw or gear mechanism to or  lower  the  platform,  10.clamp and support,  b)  Weight  of the plate  a s a method  f u n c t i o n o f t h e depth o f immersion Figure  2.2.4  22  Wilhelmy  fibre  3 . eleotrobalance,  A.recorder, 6.liquid,  2.glass  method  raise  9.motor,  11.lid.  2.2.3  f = AM-g  where AM i s i n grams.  In t h i s method, t h e measurement o f a c o n t a c t angle i s reduced  to  performed  the  measurement  of  a  weight,  which  w i t h much h i g h e r accuracy than t h e d i r e c t  can  be  reading  of an angle w i t h a goniometer.  The  disadvantages  of  this  method  perimeter  o f t h e p l a t e must be s t r i c t l y  part  the  of  morphology. time  plate  must  have  I n measurements  intervals,  the  that  swelling or d i s s o l u t i o n  that  the  c o n s t a n t , and each  same  extend  are  composition over  and  appreciable  of the s o l i d  may  become a problem.  2.2.2.2  The C a p i l l a r y R i s e a t a V e r t i c a l P l a t e  As a v a r i a n t o f Wilhelmy method, t h e c a p i l l a r y at  a vertical  at  the v e r t i c a l  infinitely  p l a t e method o n l y needs t h e c a p i l l a r y  wide  rise  rise h  s u r f a c e t o be measured ( F i g u r e 2.2.5). F o r plate,  an  integration  of  the  Laplace  equation y i e l d s  sinfl = 1 - Apgh /2y 23  lv  2.2.4  where Ap  i s density  d i f f e r e n c e between the two  fluids.  p r a c t i c a l purposes, p l a t e s t h a t a r e about 2 cm wide the t h e o r e t i c a l and is  7  requirement  of " i n f i n i t e "  width.  For  satisfy  I f g,  Ap,  a r e known, the t a s k o f d e t e r m i n i n g a c o n t a c t angle  l v  reduced  t o measuring  the  capillary  rise,  which  may  be  determined o p t i c a l l y w i t h a cathetometer. T h i s t e c h n i q u e has been  broadly  measuring and  used  and  found  c o n t a c t angles as  a  particularly function  effective  of r a t e  of  for  advance  retreat.  2.2.2.3  I n t e r f e r e n c e Microscopy  The p r i n c i p l e o f t h i s method i s i l l u s t r a t e d i n F i g u r e 2.2.6. when  Destructive the  optical  interference path  (dark  fringes)  difference  between  will  occur  adjacent  i n t e r f e r i n g beams i s g i v e n by  t = x/2n  where  n  i s the  wavelength.  refractive  index  2.2.5  of  the  liquid  x  is  A the  From the geometry i n F i g u r e 2.2.6, we have  6 = arctan(t/x)  where  and  the  distance  between 24  dark  2.2.6  fringes.  Combining  +  h  Figure 2.2.5  ^/  Capillary  r i s e at v e r t i c a l  plate  F  C  >  Figure 2.2.6  B  I n t e r f e r e n c e M i c r o s c o p e Method  A . l i g h t source, B.lens, C . h a l f - s i l v e r e d glass mirror, D.liquid-vapour interface, E.substrate-liquid interface, F.microscope.  25  above two  equations  yields  6 = arctan(x/2ux)  T h i s method can  2.2.7  o n l y be used f o r s m a l l c o n t a c t  measurements. I t uses a v e r y s m a l l amount o f  2.2.2.4  angle  liquid.  C a p i l l a r y R i s e Method  Given the h e i g h t  of l i q u i d  rise  (or depression)  in a  c a p i l l a r y tube, the c o n t a c t angle can be c a l c u l a t e d from the equation  cosfl = h r p g / 2 7  where h  i s the  l i q u i d height,  2.2.8  lv  r i s the  radius, p  capillary  i s l i q u i d d e n s i t y . Advancing or r e c e d i n g angles are  obtained  a f t e r l o w e r i n g o r r a i s i n g the l i q u i d l e v e l i n the tube.  The transparent capillary.  method r e q u i r e s t h a t the capillary It  is  tube,  or  restricted  to  narrow t h a t the meniscus may For  wide tubes,  correction  must  i n which be  as  a  small  to  sphericity. 26  a v a i l a b l e as  coating tubes  be c o n s i d e r e d  the  applied  s o l i d be  which  t o be  meniscus i s not account  for  within are  a a so  spherical.  spherical,  deviation  a  from  2.2.2.5  Rate o f P e n e t r a t i o n  In t h e method, t h e l i q u i d i s allowed t o r i s e unopposed through  a  column  Wooldridge,  of  this  law  than  Bruil  the  rate  direct  technique  that  powder  1967;  Statistically, accurate  of  glass  and  van  of  tube  developed  <Crowl  Aarsten,  penetration  c o n t a c t angle  was  governs  in a  method  and  1974>. is  measurement. The  more  theory  by a g e n e r a l i z a t i o n o f t h e  penetration  into  capillaries  given  by  Washburn e q u a t i o n  h  where 7  =  K« 7•t«cose 2  2.2.9  M  i s the surface tension of l i q u i d ,  viscosity, and  2  n  i s the l i q u i d  and K i s a c o n s t a n t f o r a g i v e n p a c k i n g o f podwer  i t can be c a l l e d  t o r t u o s i t y constant. D e t a i l e d d i s c u s i o n  on t h i s e q u a t i o n i s g i v e n i n S e c t i o n 7.2.1.  The <Studebaker Bruil  experimental and  Snow,  and van A a r s t e n ,  procedure  1955; 1974>  Crowl  commonly and  Wooldridge,  adopted 1967;  i s as f o l l o w s ; a known weight  of  t h e d r i e d powder i s p l a c e d i n a g l a s s tube o f about  cm  i . d . with  an a t t a c h e d  scale,  0.8  and c o n s o l i d a t e d by manual  t a p p i n g . The lower end o f t h e tube i s c l o s e d w i t h a g l a s s o r 27  paper f i l t e r column time lamp  supported  by a s m a l l p l u g o f c o t t o n wool. The  i s placed v e r t i c a l l y  a t which w e t t i n g the  position  of  i n the wetting  started the  liquid  i s recorded.  liquid  level  and t h e  By means o f a is  periodically  recorded.  S t a t i s t i c a l l y , t h e r a t e o f p e n e t r a t i o n method i s more a c c u r a t e than d i r e c t penetration  is  c o n t a c t angle measurement. The r a t e o f  obtained  c a p i l l a r i e s surrounded the  c o n t a c t angle  (usually  t h e angle  from  a  flow  of  liquid  through  by a l a r g e number o f p a r t i c l e s ,  measurement  i s carried  i s measured  on  out f o r one  various  places  while spot  on t h e  specimen, and t h e average v a l u e i s c a l c u l a t e d ) .  The technique,  problem  associated  as c l a i m e d  with  present  experimental  by Good and L i n <1976>, i s t h a t t h e  d a t a measured g e n e r a l l y e x h i b i t a l a r g e s t a t i s t i c a l  28  scatter.  2.3  OTHER TECHNIQUES  I n a d d i t i o n t o t h e d i r e c t and i n d i r e c t c o n t a c t angle measurements, t h e r e a r e many o t h e r t e c h n i q u e s  developed t o  characterize the w e t t a b i l i t y of p a r t i c u l a t e s o l i d surfaces. They  a l l use o t h e r  parameters  than  contact  angle  as the  i n d i c a t o r s and u s u a l l y r e f l e c t some a s p e c t s o f s o l i d s u r f a c e properties.  2.3.1  H y d r o p h i l i c i t y Index  Solid  surface  s u r f a c e compositions. considered levels,  properties  main  of, kinds  hydrophobic  un-oxidized  hydrophilic  coal  the  mineral  coal  surface  various these  patches  matter  at  molecular  of  components:  patches  i s neglected,  <Painter,  groups  on  and  macro-size  i)  naturally bearing,  the w e t t a b i l i t y  i t s surface.  o f pure  abundances o f In respect t o  of h y d r o p h i l i c i t y  by Ye e t al.<1987> u s i n g FTIR  index has  spectroscopy  1983; Yuh and Wolf, 1983;84; J i n e t a l . , 1987> t o  analyze the r a t i o (hydroxyl  their  m i n e r a l matter. I f  by t h e r e l a t i v e  p r o p e r t i e s , t h e concept  been f o r m u l a t e d  by  (HO), i i ) oxygen  (HL), and i i i )  i s controlled  functional  governed  The s u r f a c e o f a c o a l p a r t i c l e can be  consisting  three  are  o f t h e s u r f a c e h y d r o p h i l i c group  and c a r b o x y l  groups) 29  t o t h e content  content  of surface  hydrophobic groups ( a l i p h a t i c and aromatic  CH  S k (HL) 4  H y d r o p h i l i c i t y Index =  groups),  t  2.3.1  s kj (HO),  where ( H L ) i i s a measure o f the h y d r o p h i l i c f u n c t i o n a l group i  content,  and  (HO)j a measure o f the hydrophobic f u n c t i o n a l  group j content a t c o a l s u r f a c e , r e s p e c t i v e l y , k i and k j are corresponding  coefficients.  S i n c e , a l i p h a t i c and  aromatic  hydrophobic f u n c t i o n a l groups and groups are index  can  values  the be  of  simplified  by  absorption claimed <Ye  only  h y d r o x y l i e and c a r b o x y l i c  o n l y h y d r o p h i l i c groups, the  the  groups. I t was  CH groups are the  substituting intensities  hydrophilicity  the of  corresponding  the  functional  e t a l . , 1987> t h a t t h i s index,  as  determined from FTIR s p e c t r a , p r o v i d e s a r a t h e r good measure of  hydrophobicity  /  hydrophilicity  balance  at  a  coal  surface.  2.3.2  I n d u c t i o n Time  Induction in  1934.  to  first  introduced  by  Sven-Nillson  I t i s d e f i n e d as the minimum time r e q u i r e d f o r the  disjoining drain  time was  water such  a  film  between  thickness  that 30  a  particle rupture  of  and the  a  bubble water  to  film  takes p l a c e . T h e r e f o r e hydrophobic p a r t i c l e s possess s h o r t e r induction  time;  while  the induction  time  f o r hydrophilic  s o l i d s would be l o n g e r .  The  induction  time  method  has been  used  r e s e a r c h e r s < E i g e l e s and Volova, 1960; Laskowski 1970; Ye  by  many  and I s k r a ,  L e k k i and Laskowski, 1971; Blake and K i t e c h e n e r , 1972;  et  a l . , 1986;  Yordan  and  Yoon,  1988>.  The  factors  i n f l u e n c i n g t h e i n d u c t i o n time, such as f l o t a t i o n reagents, pH,  temperature,  inorganic s a l t s ,  have been s t u d i e d by many  workers <Laskowski, 1974; Yordan and Yoon, 1986>.  The b a s i c procedure o f t h i s t e c h n i q u e i s t h a t a l a y e r of  p a r t i c l e s t o be t e s t e d i s formed i n a r e c t a n g u l a r o p t i c a l  cell.  The  reagent  cell,  containing  solution,  approximately  ml  of the  i s then p l a c e d on t h e moving stage o f a  microscope. An a i r bubble approximately 2 mm formed  20  i n diameter i s  a t t h e t i p o f a g l a s s c a p i l l a r y tube u s i n g a m i c r o -  s y r i n g e . By l o w e r i n g t h e g l a s s c a p i l l a r y tube, t h e bubble i s kept  i n touch w i t h t h e p a r t i c l e  time  period.  Then,  layer f o r a preset contact  the c a p i l l a r y  tube  i s returned t o the  o r i g i n a l p o s i t i o n separating the a i r - s o l i d contact.  The  bubble  i s examined through t h e microscope t o see  i f any p a r t i c l e s a r e p i c k e d up by t h e bubble. I f t h e c o n t a c t time  i s too short,  experiment  is  no p a r t i c l e s  repeated  a t t a c h t o t h e bubble. The  changing 31  the  contact  time  incrementally. which out  In t h i s  at l e a s t  one  way,  the minimum c o n t a c t time,  particle  o f t e n c o n t a c t s , was  i s a c t u a l l y p i c k e d up  determined.  for  i n five  T h i s c o n t a c t time i s  taken as the i n d u c t i o n time.  Contact angle measurements show whether the is  thermodynamically  dynamic  nature  Induction  time  possible,  of  the  can  but  cannot  describe  particle-to-bubble  provide  kinetic  adhesion the  attachment.  i n f o r m a t i o n . Both  thermodynamic and k i n e t i c c r i t e r i a must be f u l f i l l e d  the  f o r the  f l o t a t i o n t o be p o s s i b l e .  2.3.3  Heat o f Immersion  Heat o f immersion  i s the n e g a t i v e o f the heat e v o l v e d  p e r square c e n t i m e t r e (or p e r gram) o f powder immersed i n a l i q u i d . I t has been shown<Good and G i r i f a l c o , heat  of  immersion  temperature  i s related  1958> t h a t the  t o the c o n t a c t angle and i t s  derivative  AH = 7 • d ( c o s 0 ) / d ( l n T ) - e - c o s 0 L v  where e  l v  l v  i s the t o t a l s u r f a c e energy o f the  e  iv  = 7iv + d  32  7 l v  /d(lnT)  2.3.2  liquid  2.3.3  In by  this  passing  a given  method, the  calorimeter  i s f i r s t calibrated  a known c u r r e n t through a p r e c i s i o n r e s i s t o r f o r  time. The  sample powder  (150-200 mg)  i s weighed t o  the n e a r e s t t e n t h m i l l i g r a m and p l a c e d i n s m a l l , g l a s s tubes w i t h b r e a k - o f f t i p s . The a pressure under  of approximately  vacuum.  The  1 mPa  evacuated  tubes were evacuated a t  f o r 15 min  and  cylindrical  sealed  and then s e a l e d  sample  tubes  are  p l a c e d i n s i d e s t a i n l e s s - s t e e l v e s s e l s c o n t a i n i n g about 3 of  the  the  wetting  micro  liquid.  calorimeter  The  whole assembly  which  i s lowered  i s maintained  at  a  cm  3  into  constant  temperature and allowed t o a t t a i n thermal e q u i l i b r i u m . A f t e r steady-state each  tube  had is  liberated  been  broken  heat  is  established, by  remote  detected  i n t e g r a t i o n o f the d e t e c t o r  Heat  of  immersion  and  the  break-off  mechanical recorded  tips  action. by  of The  electronic  signal.  can  provide  information  on  hydro-  p h o b i c i t y o f s o l i d s u r f a c e s ; the e n e r g i e s o f i n t e r a c t i o n f o r system  i n cases  <Zettlemoyer,  of  spreading  1964>.  In  wetting  addition,  o r zero c o n t a c t it  can  determine  average p o l a r i t y o f s o l i d s u r f a c e s , h e t e r o g e n e i t i e s on surfaces, wetting specific  by  interaction  s u r f a c t a n t s , and  angle the solid  thermodynamics of  o f molecules from s o l u t i o n onto  the  solid  s u r f a c e s <Zettlemoyer, 1965>.  Initially, area  of  this  inorganic  method  was  mainly  minerals<Zettlemoyer, 33  employed 1964  and  in  the 1965;  Cochrane  and  basically  hydrophilic  hydrophobic this  Hendriksen,  1967;  i n n a t u r e and  materials<Cokill  method  to  coal  Wightman<1980>. Heat  Taylor,  had  1967>  to a  which  lesser  were  extent to  e t a l . , 1967>. A p p l i c a t i o n  been  studied  o f immersion  was  by  Glanville  proved  t o be  of and  one  of  the v a l u a b l e methods f o r i n v e s t i g a t i o n .  2.3.4  Rate o f Immersion  Walker  The  immersion  et  al.<1952>  time to  measurement  test  surface  was  initiated  by  active  agents.  The  procedure c o n s i s t s o f dropping c o a l p a r t i c l e s  individually,  from  progressively  approximately  more d i l u t e  1  cm,  solutions  on  until  the  surface  a dilution  of  was  found  at  which  the p a r t i c l e s were not i n s t a n t a n e o u s l y wetted.  T h i s procedure has been adopted and m o d i f i e d <Garhsva et a l . ,  1978;  Marmur, e t a l . ,  1986;  Fuerstenau e t a l . 1986>  to  t e s t i n g the w e t t a b i l i t y o f m i n e r a l s u r f a c e s and employed  by  many  others<Glanville  and  Wightman,  1980;  Laskowski,  1986>.  In 1976>,  150  one mg  o f the of  m o d i f i e d procedures  the  powdered  <Garbsva e t a l . ,  narrow-sized  material  is  g e n t l y p l a c e d on the s u r f a c e o f a mixture o f s o l v e n t s w i t h different  percentages  of  water 34  in a  number  of  16x150  mm  Pyrex t e s t tubes without the  material  to  sink  s t i r r i n g . The  i s determined  time taken f o r 3/4  and  i s plotted  of  against  the percentage of water. At c e r t a i n c o n c e n t r a t i o n s o f water, immersion  time  abruptly  increases.  For  change i n s l o p e occurs a t a constant 2.3.1(a)).  This  t e n s i o n ; and  value  is  tend  use  some  concentration the  (Figure  critical  surface  of powder as w e l l as  researchers  more parameters t o  p r o p e r t i e s . Data has  and  the  the  i t i s t y p i c a l f o r each s o l i d .  hysteresis, to  solid,  surface tension  called  Because o f h e t e r o g e n e i t y angle  a given  of  lowest  <Marmur  of  surface  i n terms o f the  which a l l the  concentration  a l . , 1986>  characterize s o l i d  been presented  alcohol at  et  contact  alcohol  highest  particles  at  which  float  a l l the  p a r t i c l e s sink.  In  Figure  concentration,  2.3.1  at  (b) , the  which  lowest  a l l the  particles  the " T o t a l S i n k i n g C o n c e n t r a t i o n " (methanol) c o n c e n t r a t i o n , is  termed  "Total Float  ethanol  (methanol)  sink,  i s termed  (TSC). The h i g h e s t  ethanol  a t which a l l the p a r t i c l e s  Concentrate"  (TFC).  I t was  float, claimed  <Marmur e t al.,1986> t h a t t h i s method of c h a r a c t e r i z a t i o n of the  wettability  surface  energy  difference  in  of  particles  than the  contact  contact  various  s u r f a c e can be  the TFC  o r TSC  is angle  angle  more  measurements. and  associated with  values. 35  sensitive  surface  to A  energy  the small for  large differences i n  2500  (min}  1500  500  80  i0 .  x—y - »  50  »-»  i  V. H 0 2  a.  .i  100  I m m e r s i o n t i m e s o f m e t h y l a t e d q u a r t z powder i n d i f f e r e n t w a t e r / a l c o h o l m i x t u r e s as a f u n c t i o n o f c o n c e n t r a t i o n o f water, o methanol/water; x ethanol/water; $ propanol/water; A butanol/water (Garbsva e t a l . ) 100  o  • o  90  ao  O- 3 0 •  10  20  30  40  50  60  70  60  Volume. Percent Ethanol  FIG. 2. Floatability of PMMA-coated glass beads on ethanol-water mixtures: (•) 74.1>m, (O) 127 jim.  b.  f l o a t a b i l i t y o f t h e p o l y m e t h y l m e t h a c r y l a t e (PMMA)c o a t e d b e a d s on E t h a n o l - w a t e r m i x t u r e s : ( ® ) 7 4 . 1 /xm, ( o ) 12 7 /xm. (Marmur e t a l . ) Figure  2 . 3 . 1 Rate o f immersion t e c h n i q u e  36  2.3.5  Film Flotation  Another referred  as  modification  film  of  flotation  the  Walker  (developed  technique  by  is  Fuerstenau  and  W i l l i a m s <1987>). T h i s method uses a s e t of t h r e e parameters to describe  s u r f a c e p r o p e r t i e s . A monolayer o f t e s t e d  particles  (about  placed  on  the  25  diameter  mm  0.06  to  0.3  gram i n the  case o f c o a l )  s u r f a c e o f a s o l u t i o n i n a shallow and  20  or  30  mm  depth.  fine  The  is  v e s s e l of  closely  sized  s o l i d e i t h e r remains on the l i q u i d s u r f a c e o r i s immediately imbibed;  and  fractions.  splits  The  i n t o lyophobic  surface  tension  of  and  lyophilic  the  liquid  (imbibed)  i s varied  by  the a d d i t i o n o f methanol t o t r i p l y d i s t i l l e d water.  The percentage of p a r t i c l e s not imbibed by the is  plotted  liquid  as  function  i n Figure  quasi-Gausian describing be  a  the  Two  w e t t a b i l i t y and  from  surface  tension  2.3.2. They approximately  distributions.  the  obtained  of  Figure  2.3.3  of  the  of  the  conform t o  the  three  heterogeneity ( a ) , the  the s o l u t i o n t h a t wets a l l p a r t i c l e s , 7  m i n  parameters  o f powder  surface  0  liquid  tension  , and the  s o l u t i o n i n which none o f the p a r t i c l e s  wetted,  and  r a a x c  ;  (b)  the  mass f r a c t i o n  of  the  of  surface  t e n s i o n of the 7  can  are  particles  p l o t t e d a g a i n s t the s u r f a c e t e n s i o n of the imbibing s o l u t i o n allows  calculation  deviation  a.  a  of  is a  the  third  measure 37  of  parameter the  -  the  heterogeneity  standard of  the  LIQUID SURFACE TENSION, mN/m  (b) Figure  2.3.2  (a)  (b)  Film flotation  (Fuerstenau  and W i l l i a m )  Accumulative percentage of m a t e r i a l Frequency histogram  38  floating  material.  Three surface  f a c t o r s : the s i z e  energies  reasons  for difference  concentration) Rate  and c o n t a c t  of  Flotation.  Study  angle  between  and t h e TFC  Immersion,  distribution,  o r between  by Marmur  hysteresis  the  (total 7  variation i n  TSC  float m  i  (total  sinking  concentration)  and  n  c  can be t h e  e t a l . <1986>  7  m  a  x  c  shows  in  i n Film that the  e f f e c t of s i z e d i s t r i b u t i o n i s n e g l i g i b l e while v a r i a t i o n i n s u r f a c e energy has a major e f f e c t .  2.3.6  C r i t i c a l S u r f a c e Tension  The developed wetting  concept  of  of F l o t a t i o n  Critical  Surface  by Zisman <1964>, i s t h e s u r f a c e  liquid  t h a t would  g i v e complete w e t t i n g .  just  spread  A convenient  Tension, tension  7 , C  of the  on t h e s u b s t r a t e t o  way o f i l l u s t r a t i n g t h e  concept i s t h e adhesion t e n s i o n diagram, 7 c o s 0 l v  versus 7  l v  ,  as shown i n F i g u r e 2.3.3(a). On such a diagram, t h e measured contact  angles  represented  give  a  straight  line,  which  may  be  by t h e equation  7 l v  COS0  = 0-7iv  +  <l-0)7  c  2.3.3  Hornsby and Leja<1980, 83, and 84> extended Zisman's concept  of c r i t i c a l  surface  tension 39  t o dynamic  flotation  c o n d i t i o n s <Gaudin, 1957; Tomlinson and Fleming, 1963; Reay and  Ratcliff,  Kitchener,  1973; L e k k i  1971; Blake and  1972; Laskowski, 1974; Jameson e t a l . , 1977> and  distinguished critical  and Laskowski,  critical  surface  tension  o f adhesion, 7  surface tension o f particle-bubble s t a b i l i t y , 7  and c r i t i c a l s u r f a c e t e n s i o n o f f l o a t a b i l i t y , 7  The  c  a  ;  0 S  ;  c  .  f  c r i t i c a l s u r f a c e t e n s i o n o f adhesion,  7  C a  , i s the  minimum s u r f a c e t e n s i o n o f l i q u i d i n c o n t a c t w i t h t h e t e s t e d solid  f o r which t h e adhesion o f a i r bubble from t h e l i q u i d  onto t h e s o l i d solid  i s p o s s i b l e . Apparently  surface  critical  properties,  surface  same s i z e  tension,  and should  in a solution of  7  However properties, y  c  C  may be separated  ca  i f y'  c a  <  7 c  < " 7  f o r particles  c &  be g r e a t e r  7 . Hydrophobic p a r t i c l e s  d b u t y' <y" , ca  i t i s determined by  size.  On t h i s  with  t h e same  i s due t o t h e k i n e t i c account,  the c r i t i c a l  stability  y  same y  the l a r g e r the p a r t i c l e  7  C s  the  c a  ,  value  2.3.3(b), the  was i n t r o d u c e d .  will  relevant  into fractions  surface  , but with d i f f e r e n t s i z e s , smaller p a r t i c l e s  This  cs  of the  .  c a  may be f l o a t a b l e whereas t h e l a r g e s i z e floatable.  than  8 '  Obviously size  particle  a r e non-  effect  of particle  surface  tension of  for particles  with  i s , the greater the  be. Two p a r t i c l e s o f s i z e s d'<d" would have C  B  < 9 "  C  8  and 7 '  i f a solution of 7  smaller-size  particles  C  0 S  <7"  .  was used  would 40  C S  As shown  i n Figure  and y' <y  be f l o a t e d  c s  1  w  <y"  c  s  ,  whereas t h e  SURFACE  a.  T E N S I O N ,  v  dyne/cm  Adhesion t e n s i o n diagram i l l u s t r a t i n g t h e c o n c e p t . o f c r i t i c a l surface tension of adhesion, i , f o r a low energy s o l i d w i t h w e t t a b i l i t y l i n e B i n aqueous s o l u t i o n s o f a s h o r t c h a i n n - a l c o h o l (Hornsby and L e j a ) . c  a  £  UJ o  SURFACE  TENSION ,  y^  dyne  /cm  b. A d h e s i o n t e n s i o n diagram i l l u s t r a t i n g p o s s i b l e d i f f e r ences i n c r i t i c a l s u r f a c e t e n s i o n o f f l o a t a b i l i t y f o r t h r e e low energy solids of different w e t t a b i l i t y i n aqueous s o l u t i o n s o f a s h o r t c h a i n n - a l c o h o l (Hornsby and L e j a ) . F i g u r e 2.3.3  C r i t i c a l surface tension of 41  flotation  l a r g e r - s i z e p a r t i c l e would be n o n - f l o a t a b l e . T h i s means t h a t wettability  and  under c e r t a i n  All called  floatability circumstances.  above  factors  critical  According  to  surface  this  concept  its  7  i s smaller  7 l v  ( F i g u r e 2.3.3(b))  C f  The  values if  the  may  7  C  exist of  Such  floatability  tension  in  of  a particle  critical  a  general  term  y  floatability  will  be  liquid-vapour  between two their  although  value.  of  included  a  t h e r e may  be  difference  little would  r e g i o n , where s e p a r a t i o n  are  .  tension  tension  i n h e r e n t l y hydrophobic  wettability lines  f  floatable i f  surface  surface  c  of  y  indicates that a s i g n i f i c a n t difference i n  slope  different,  are  than the  concept  floatability  are not n e c e s s a r i l y synonymous  cf  solids  significantly  o r no d i f f e r e n c e i n provide  of the  a two  selective solids  by  f l o t a t i o n should be t h e o r e t i c a l l y p o s s i b l e .  The has  been  Kelebek,  concept o f c r i t i c a l employed 1987>  in  by  surface tension of  others  <Kelebek  characterization  i n h e r e n t l y hydrophobic m i n e r a l s .  42  and and  flotation  Smith, flotation  1985; of  2.3.7  Other Techniques  In  a d d i t i o n t o above mentioned t e c h n i q u e s , a v a r i e t y  of o t h e r t e c h n i q u e s have a l s o been developed. Among them are partition 1981>,  between  salt  kerosene and water  flotation  <Laskowski,  <Adams-Viola  1965  and  1974;  et a l . , Yoon  Sabey, 1989> e t a l . They w i l l not be d i s c u s s e d here.  43  and  CHAPTER 3  COAL  3.1  INTRODUCTION  The such  m a t e r i a l s used  as  Teflon  and  i n surface w e t t a b i l i t y  Quartz,  are  commonly  homogeneous.  Measures can be taken t o a c q u i r e a v e r y c l e a n , chemically  consistent  measurements. F a i r l y Nonetheless, Butler, Coal  surface  for  angle  measurements  e t a l . 1986> show t h a t t h i s  has  a  very  complex  smooth,  contact  reproducible results  contact  studies,  can on  be  and  angle  obtained.  coal  <Vargha-  i s not t r u e f o r c o a l .  composition  and  heterogeneous  s u r f a c e . Some o f the c o a l p r o p e r t i e s are unique and  deserve  d e t a i l e d summary.  3.1.1  Classification  Coal indicates occurred content  is  the and  as  graphite,  first extent  classified  by  rank.  The  to  which  coalification  i s arranged  i n an  ascending  shown i n T a b l e which  i s the  p r o c e s s ; the lowest one  3.1.1. The  final  product  coal process  o r d e r of  h i g h e s t rank o f the  rank has  carbon coal i s  coalification  i s woody m a t e r i a l peat, f o l l o w e d by 44  lignite.  T a b l e 3.1.1 C o a l s Arranged i n an Ascending of Carbon Content Coal Rank Bituminous Sub bituminous  Peat l i g n i t e  Order  Anthracite  %c  60  70  75  80  93  %0  35  25  20  15  3  Calorific value MC/ka  28  30  31  32.5  The to  properties  of the coal w i t h i n  36.5  each  rank  depend,  some e x t e n t , on t h e n a t u r e o f t h e v a r i o u s components i n  the o r i g i n a l on  both  o r g a n i c accumulation; s p e c i f i c a l l y they depend  the  degradation macerals,  forms  prior are  than  to  aggregates  distinctive  physical  of  and  degree  components,  the  by t h e i r  the  different  organic chemical  called mineral  They a r e o r g a n i c  botanic structure  properties.  of  rather  They a r e o p t i c a l l y  substances, properties  possessing <Winans  and  1984>.  Macerals  are  1982>: I.  The  to  crystallographic  homogeneous  Crelling,  burial.  and  i n i n o r g a n i c sediments.  characterized  their  vegetation  analogous  c o n s t i t u e n t s found minerals,  of  Vitrinite,  classified  in  three  groups  <Stach,  II.  Exinite,  III.  Inertinite.  Coal more  macerals  usually  associations vitrite, and  rarely  associated  occur  with  by themselves;  other  maceral  are c a l l e d micro-lithotypes.  liptite,  inertite,  clarite,  groups.  Such  They a r e mainly:  vitrinertite,  durite,  trimacerite.  These  micro-lithotypes  further  combine  t o form t h e  mass o f a banded bituminous c o a l . These combined are  they are  visible  ingredients  t o t h e eye and a r e known as l i t h o t y p e s .  They  are: I.  fusain  ( c h a r c o a l - l i k e fragments - s o f t  lithotype) II.  durain  ( d u l l hard c o a l type - t h e h a r d e s t  lithotype) III.  clarain  IV.  vitrain  These specific  four  gravity,  > together the equivalent type  banded ash  ingredients content,  hardness, and c o k i n g p r o p e r t i e s properties.  46  of bright  differ  chemical  in  coal  their  composition,  as w e l l as i n t h e i r w e t t i n g  3.1.2  Chemical  Composition  Change i n c o a l in  chemical  mineral  rank  composition  of  constant  i s reflected  and c a l o r i f i c  composition,  sedimentary  rock  composed  debris.  has  substantially  It  inorganic carbon  minerals.  chemistry,  Due  these  is  but  an of  organo-clastic lithified  different  macerals  cannot  plant  properties  i t s extraordinarily  any u n i q u e l y d e f i n e d chemical  Pure c o a l  v a l u e . Coal i s not a  essentially  to  by a steady change  from  complex  be r e p r e s e n t e d by  structure.  i s t h e combustible  o r g a n i c m i n e r a l , which  a h i g h l y c r o s s - l i n k e d polymer, c o n s i s t i n g o f a number o f  stable  fragments  connected  by r e l a t i v e l y  week  cross-links  <VanKrevelen, 1961>. The remaining components, which have no heating  value,  a r e regarded  as i m p u r i t y m i n e r a l s  including  s h a l e , k a o l i n , s u l p h a t e s , carbonates, and c h l o r i d e s .  Coal  i s a polymeric  h i g h m o l e c u l a r weight  solid,  molecules.  i . e . i t c o n s i s t s o f many I t c o n t a i n s mainly  hydrogen and oxygen a l o n g w i t h s m a l l q u a n t i t i e s and  n i t r o g e n . The m o l e c u l a r  ultimate  elemental  information functional statistical  such  models  analysis as  variety  and of  proposed large  of sulphur  a r e based  amount  spectroscopic  group a n a l y s i s , m o l e c u l a r weight  carbon,  of  on  other  analyses,  determinations,  c o n s t i t u t i o n a n a l y s i s e t c . . The m o l e c u l a r model 47  48  of Wiser<1975>  i s given  i n Figure  model i n d i c a t e t h e week p o i n t s also includes various functional  groups  hydroxylic, The  3.1.1. The arrows i n t h e  o f t h e s t r u c t u r e . T h i s model  f u n c t i o n a l groups found i n c o a l s . Most  contain  carbonylic,  oxygen  and appear  and c a r b o x y l i c  Mineral composition.  well  phenolic,  functional  groups.  r e s t o f t h e oxygen i s thought t o l i n k aromatic n u c l e i o r  t o be p r e s e n t i n a fused p o l y n u c l e a r  the  as  matter  is  I t i s termed,  inorganic  an  skeleton.  important  part  i n i t s widest  sense,  of  coal  as a l l o f  components found i n c o a l as m i n e r a l phases as  as t h e elements i n c o a l  <Mraw e t a l . , 1983>. M i n e r a l  that  are considered  matter p l a y s  inorganic  an important  role  i n a l l coal u t i l i z a t i o n processes.  3.2  HOMOGENIZATION  As rock  s t a t e d above, c o a l i s a v e r y heterogeneous o r g a n i c  comprised  of inorganic  m i n e r a l s and o r g a n i c  macerals.  I t would be i n t e r e s t i n g t o i s o l a t e these i n d i v i d u a l macerals for  coal  wettability  practically enough  impossible  characterization. to  f o r characterization.  separate  them  To o b t a i n  However, and  i t is  accumulate  an a c c u r a t e  picture  o f t h e w e t t a b i l i t y o f c o a l , i t has t o be s e p a r a t e d i n t o l e s s heterogeneous  portions.  These  portions,  w e t t a b i l i t y , need t o be c h a r a c t e r i z e d 49  differing  separately.  in  Homogenization coal  surface  studies  on  of coal  wettability  i s the f i r s t  s t e p needed f o r  characterization.  such a heterogeneous  Otherwise,  mixture as a whole may  be  very misleading.  There a r e many ways o f homogenizing most p r a c t i c a b l e of  way  i t s physical  specific  t o homogenize c o a l ,  or  gravity,  physiochemical  surface  c o a l . I t i s the  a c c o r d i n g t o some  properties,  wettability,  such  as  macro-lithotype,  e t c . , c r e a t i n g f r a c t i o n s which are l e s s heterogeneous.  S i n c e t h i s work i s mainly focused on t h e of the c h a r a c t e r i z a t i o n and-float further  method  was  studies.  methodology  of coal w e t t a b i l i t y , only employed  The  to  coal  prepare  surface  the  fractions  sinkfor  characterization  t e c h n i q u e s developed i n t h i s work can be a p p l i e d t o any c o a l fractions regardless  3.3  of the separation  method used.  COALS STUDIED  Coal  samples  used  Creek and t h e Bullmoose  The Coalfield  Line  i n t h i s work were  (Seam "C")  Creek c o a l d e p o s i t  i n the E a s t  Kootenays,  from  the  Line  mines.  i s p a r t o f t h e Upper E l k B.C..  It i s  characterized  as a low s u l p h u r , medium v o l a t i l e bituminous c o a l and i s a h i g h q u a l i t y b l e n d c o k i n g c o a l . Some o f t h e c h a r a c t e r i s t i c of  the  Line  Creek  coal  are l i s t e d  i n Table  3.3.1.  The  proximate a n a l y s i s o f ROM Bullmoose c o a l i s g i v e n i n T a b l e 3.3.2.  The and  results  Bullmoose  3.3.2, against  of sink-and-float  coals  respectively,  are presented i n which  density f r a c t i o n .  51  tests  f o r Line  i n Figures  t h e ash content  3.3.1  Creek and  i s plotted  T a b l e 3.3.1  QUALITY CHARACTERISTICS OF LINE CREEK CLEAN COAL  PARAMETER  QUANTITY  BASIS  MOISTURE % total residual  A.D.  PROXIMATE % ash volatile sulphur  A.D.  ULTIMATE % carbon hydrogen nitrogen sulphur oxygen  D.A.F.  6.0 - 8.0 0.4 - 0.6 9.5 21. - 22. 0.3 - 0.4 85.85 4.67 1.10 0.37 8.01  HARDGROVE GRINDABILITY INDEX  75.0  GROSS CALORIFIC VALUE  7700  KCAL/KG.A.D.  Notes: A.D. stands f o r A i r D r i e d D.A.F. stands f o r Dry Ash Free b a s i s  T a b l e 3.3.2 Proximate A n a l y s i s Of ROM Bullmoose Seam "C" Coal Dry B a s i s M.A.F.  A.D.  Notes:  %Moisture  0.95  %Volatile  20.37  %Ash  25.05  %FIXED C  54.58  27.18  72.82  M.A.F. stands f o r M o i s t u r e and Ash Free b a s i s A.D. stands f o r A i r Dry b a s i s  52  SINK-AND-FLOAT TEST OF LINE CREEK COAL F i g u r e 3.3.1  80  N  C o c o  70  -  60  -  50  -  40  -  Ash content versus density fraction  '  u  JS  co in  30  20  10  -  Density fraction (g/cnr) j f  A S H CONTENT  SINK-AND-FLOAT TEST OF BULLMOOSE COAL Figure 3.3.2  Ash content versus density fraction  Density fraction (g/cn?) ASH CONTENT  CHAPTER 4  OBJECTIVE  The  major  objective  develope b e t t e r techniques fine  coal  particles.  of  the  present  work  is  to  f o r c o n t a c t angle measurements on  Two  techniques,  one  direct  and  one  i n d i r e c t , have been m o d i f i e d and i n v e s t i g a t e d .  In the  coal  34.5  MPa  0.8  cm  the  direct  powder to  contact  angle  i s compressed  form the p e l l e t s  height.  The  pellet,  measurement  under h i g h of  with  2.54  cm  technique,  pressures  20  diameter and  its artificial  employed f o r c o n t a c t angle measurements. The  0.5-  surface, i s  behaviour  of a  water drop i n c o n t a c t w i t h the p e l l e t such as the e f f e c t drop  size  on  contact  angle,  the  stability  of  to  the  of  sessile  drop are examined. In a d d i t i o n , the p r o p e r t i e s o f the p e l l e t and the f a c t o r s a f f e c t i n g The  contact  apparent  angle  angle  values  are  measured  value.  a c c o r d i n g t o t h e SEM  the measurement are a l s o s t u d i e d .  A  on  pellet  examination.  corrected  using  the  pellet  surface The  surface  model  is  i s proposed  apparent c o n t a c t  Cassie-Baxter  an  equation  to  angle the  r e a l angle v a l u e s .  In the  indirect  contact 55  angle  measurement, the  rate  of  l i q u i d penetration  Pressures  ranging  technique  from  3.5  employed t o make h i g h l y tube  traditionally  therefore,  no  longer  equation  different  coal density  of  the  the  (500  column  The  highly  holding of  applicability  applied as  l i q u i d within  in their well  as  glass is,  of  the  columns  for  change i n  such columns i s  columns and  formation other  are  powder  compacted  of the  modified.  - 4000 p s i )  f r a c t i o n s are s t u d i e d . The  properties  penetration  MPa  the  needed.  to  The  pressure  liquid  for  behaviour of the  investigated.  28  and  compact columns. The  used  Washburn  penetration  to  i s employed  on  the the  phenomena  impact rate  are  of  also  studied.  An particle  assumption i s made t h a t f o r m a t e r i a l s h a v i n g same s i z e s and  pressure,  possess the  assumption, a new  The development particles. these  shapes,  More  columns,  work  contact work  i f made a t  same t o r t u o s i t y c o n s t a n t .  c a l i b r a t i o n method i s  present for  their  i s mainly angle  needs  to  techniques.  56  aimed  done  this  introduced.  at  measurements be  Under  same  to  methodological on  fine  further  coal verify  CHAPTER  5  DIRECT CONTACT ANGLE MEASUREMENTS AND  5.1  INTRODUCTION  Among the d i r e c t the  EXPERIMENTAL  sessile  adhering  air  solubility easily  drop  with  adhering  sessile  bubble  has  methods.  swelling,  the  air  technique  bubble  and  c o n t a c t angle measurement methods, many  advantages  Complications,  can  usually  drop  method  methods.  be  However,  bubble method has the advantage  than  the  the  to  the  due  dealt  rather  over  with  more  with  the  adhering  air  of minimizing contamination  from a i r b o r n e substances.  Contact angle measurements are g e n e r a l l y performed c o a l lumps <Horsley and Smith, Gutierrez-Rodrigues been e s t a b l i s h e d  and  1957,  Apian,  1984>.  f o r the s e l e c t i o n  c o n t a c t angle measurement. The  Parekh and Apian, Some  on  1978,  criteria  have  o f sample specimens f o r  p r e - s e l e c t i o n o f samples (or  t h e a r e a o f a c o a l specimen) l i k e l y produces b i a s e d r e s u l t s . Although  the w e l l - e s t a b l i s h e d  specimen  has  suitable  f o r the measurement, p o l i s h i n g may  the  s u r f a c e markedly.  advantage  of  practice  of p o l i s h i n g  providing  a  coal  smooth s u r f a c e change the c o a l  V a r g h a - B u t l e r e t al.<1986> have 57  a  carefully  studied  the d i r e c t  contact  angle  measurements  on p o l i s h e d  s e c t i o n s o f c o a l lumps. They i n d i c a t e d t h a t t h e i n f o r m a t i o n obtained the  from  this  method  i s not very  reliable  because o f  heterogeneity.  Coal  surfaces  are  a  mosaic  with  elements h a v i n g v a r y i n g dimensions. Cracks  the  different  are often v i s i b l e  on  c o a l s u r f a c e s . As i n d i c a t e d by Neumann and Good <1979>,  if  t h e dimension  relative  to  microscopic contact  the  dimension  heterogeneity  angle  solution  o f t h e primary  will  the  effect  i s t o crush  the  of  i s very  sessile  not a f f e c t  measurements.  to  heterogeneity  of  elements  and g r i n d c o a l  the  t h e macroscopic  Therefore, chemical  drop,  small  one and  possible mechanical  particles  t o an  average diameter o f 10 microns. Such a f i n e powder, though microscopically  heterogeneous,  may  be  considered  m a c r o s c o p i c a l l y homogeneous.  For t h e s u r f a c e c h a r a c t e r i z a t i o n , i t i s d e s i r a b l e t o work w i t h the  fine  surface under  a flat  s u r f a c e made o f a f i n e powder. Compressing  powder under h i g h i s an obvious  high  pressure  pressure  solution.  t o form  an  artificial  The p r e p a r a t i o n o f p e l l e t s  and t h e d e t e r m i n a t i o n  of the contact  angle on t h e p e l l e t s u r f a c e a r e d i s c u s s e d here as w e l l as i n the f o l l o w i n g c h a p t e r s .  58  5.2  THEORY AND TECHNIQUES  5.2.1  Background  There a r e two methods o f o b t a i n i n g t h e c o n t a c t angle from t h e measurement w i t h a s e s s i l e drop. One method i s t o construct contact angle  a tangent t o t h e drop p r o f i l e  line with  a t t h e three-phase  ( F i g u r e 2.2.1) and t o measure t h e v a l u e o f t h e a  mathematically  goniometer.  The  another  method  calculating  the  contact  angle  involves from  the  p r o f i l e o f t h e drop <Bashforth and Adams, 1892; H a r t l a n d and Hartley, al.,  1976; Malcolm  1982>. Depending  and Paynter, 1981; and Rotenberg e t on t h e drop s i z e , d i f f e r e n t e q u a t i o n s  may be needed.  I f a drop s i z e i s s m a l l enough (10" m l ) , so t h a t t h e 4  drop  i s indeed  employed.  One  a  spherical  connects  cap,  two  the contact  equations  angle  with  may  the  be base  diameter, D, and h e i g h t o f t h e drop, h, (Mack, 1936)  2h = tan0/2  5.2.1  D and  the  calculates  second  equation  (Johnson  and  Dettre,  1969)  t h e angle, 6 , through t h e base diameter and the  drop volume, v, 59  D  24 s i n 6  3  3  = V  The  5.2.2 TT(2  -  + cos B ) 3  3COS0  l i m i t a t i o n s f o r these two equations a r e t h a t (1) D and h  or v cannot be measured w i t h h i g h accuracy, and (2) t h e drop must be a s p h e r i c a l cap.  When t h e drop s i z e i s so l a r g e t h a t t h e h e i g h t o f t h e drop  i s independent  o f t h e drop s i z e , t h e c o n t a c t angle can  be c a l c u l a t e d from: d«g«h  2  cose = 1  5.2.3 2  where  h  i s the l i m i t i n g  height  density; g the g r a v i t a t i o n a l surface  7  t e n s i o n . In order  o f drop;  i s theoretically  the  liquid  a c c e l e r a t i o n ; and y t h e l i q u i d  for this  equation  drop must be v e r y l a r g e . F o r water, a drop diameter  d  t o apply, t h e  o f one meter i n  required. I t i s impracticable to  produce such a l a r g e s o l i d s u r f a c e t o accommodate t h e l i q u i d drop.  In two  most cases, t h e drop volume r e s i d e s between these  extremities.  sufficiently homogeneous difference classical  large film across  When  the  compared  radii  curvature  t o the thickness  s e p a r a t i n g two b u l k a curved  of  interface  Laplace equation  60  phases,  are  o f a non-  the pressure  i s d e s c r i b e d by t h e  7(1/1*! + 1 / R ) = AP  5.2.4  2  where two  7  i s the i n t e r f a c i a l  principle  difference  In  of  curvature,  across the interface  the  gravity,  radii  tension,  absence  of  RT_ a n d R2 and  i s the  (see F i g u r e  external  the pressure difference  AP  represent the pressure  5.2.1.).  forces,  other  i s a linear function  than of the  elevation  AP = AP where  AP  0  i s the pressure  0  + Ap»gZ  difference  5.2.5 at  a  selected  datum  The d e f i n i t i o n o f t h e c o o r d i n a t e f o r a s e s s i l e drop p r o f i l e  system  plane,  Figure  Ap  is  phases,  the g  5.2.1  difference  in  the  i s the g r a v i t a t i o n a l  densities  of  the  two  acceleration  and  Z  bulk  i s the  v e r t i c a l h e i g h t measured from t h e datum p l a n e .  From  t h e above  two  equations,  Bashforth  <1892> d e r i v e d t h e f o l l o w i n g g e n e r a l e q u a t i o n describing  the s e s s i l e  drop  and s e s s i l e  and Adams  mathematically  bubble i n t e r f a c e  p r o f i l e under g r a v i t y 7(1/1*! + Sin$/X) = 27/R where  R^  rotates and  turns  i n t h e plane  i n a plane  about  the  curvature  of  apex  o f t h e paper  perpendicular  axis  of  5.2.6 and R2=x/sin$  t o the plane  symmetry;  and $  + Ap'-yZ  0  o f t h e paper  R Q i s the radius  i s the turning  angle  of  measured  between t h e tangent t o t h e i n t e r f a c e a t t h e p o i n t  (x,z)  and  the datum p l a n e .  Many developed  graphical  <Malcolm  curve  and  fitting  Paynter,  techniques  have  1981, Rotenberg  been  et a l . ,  1982>. The one developed by Rotenberg, Boruvka, and Neumann employs which  the strategy  expresses  theoretical  t o construct  the e r r o r  Laplacian  between  curve,  an  objective  function  t h e observed  and t h e  i . e . , equation  5.2.6.  The  o b j e c t i v e f u n c t i o n i s minimized n u m e r i c a l l y u s i n g t h e method of  incremental  loading  Raphson method. Apart  i n conjunction  from  local  with  t h e Newton-  g r a v i t y and d e n s i t i e s o f  l i q u i d and f l u i d phases, t h e o n l y i n p u t i n f o r m a t i o n r e q u i r e d to  determine  information  the l i q u i d - f l u i d  interfacial  tension  i s the  on t h e shape o f t h e meniscus and t h e v e r t i c a l 62  c o o r d i n a t e o f t h e three-phase  5.2.2  Techniques  The They  line.  c o n t a c t angle v a l u e s were o b t a i n e d i n two ways.  were  goniometer,  either or  directly  the  measured  values  of  the  with  the  contact  c a l c u l a t e d from t h e axisymmetric s e s s i l e drop  5.2.3.1  use  of  angle  a  were  profiles.  D i r e c t Measurement  A Rame-Hart Model 100 c o n t a c t angle goniometer (see Figure  5.2.2)  was  utilized  i n the  direct  contact  angle  measurements. I t has a s t a t i o n a r y t e l e s c o p e . The p o s i t i o n o f t h e stage i s c o n t r o l l e d by graduated that  the  edge  vertically hairs.  of  a  to bring  drop  can be  micrometer  moved  screws,  horizontally  so and  i t t o the axis of the telescope cross  The m i c r o - s y r i n g e f o r t h i s  instrument  i s mounted so  t h a t t h e needle can be h e l d s t a t i o n a r y r e l a t i v e t o t h e stage and moved v e r t i c a l l y r e l a t i v e t o t h e stage by a screw. is  a v a l u a b l e f e a t u r e f o r t h e measurement o f advancing and  receding micrometer An  This  contact  I t i s also  possible  t o use t h e  screws t o measure t h e h e i g h t and width o f a drop.  environmental  attachment  angles.  used  chamber to  is  prevent  provided  the 63  liquid  as  an  optional  evaporation.  The  Figure  5.2.2  The s e t - u p o f a Rame-Hart m o d e l 100 angle goniometer 64  contact  humidity  i n t h e chamber was maintained  a t 100% by  filling  the sample chamber w i t h d i s t i l l e d water. The temperature not  controlled  and v a r i e d  was  between 20 and 25 °C. To i n s u r e  r e p r o d u c i b i l i t y , a c o n s t a n t drop s i z e was maintained.  F o r r o u t i n e measurements, t h e p e l l e t s were mounted on the  horizontal  oxidation,  stage  i n contact with  t h e measurements  f o r m a t i o n . The temperature is  were  atmosphere. To a v o i d  made  coefficient  shortly  after  drop  o f t h e c o n t a c t angle  c l a i m e d t o be s m a l l enough so t h a t t h e r m o s t a t i n g i s not  n e c e s s a r y <Adam, 1964; Neumann and Good, 1979>  To  illuminate  with a f i l t e r  5.2.3.2  t h e drop,  a source  equipped  t o minimize h e a t i n g was f i x e d behind t h e drop.  C a l c u l a t i o n From Axisymmetric  The  of l i g h t  profile  of the s e s s i l e  Drop I n t e r f a c e  drop  through t h e t e l e s c o p e o f t h e goniometer  was  photographed  using a horizontally  mounted camera. The p i p e t t e o f t h e m i c r o - s y r i n g e w i t h known diameter  was  included  i n the picture;  this  served  as an  a c c u r a t e s c a l i n g r e f e r e n c e . The image o f t h e drop p r o f i l e i n the photograph  The computer  was e n l a r g e d approximately 36 times.  curve program,  fitting  technique  developed  by 65  and  Rotenberg,  corresponding Boruvka,  and  Neumann The  (1982) as d e s c r i b e d  computer  program,  i n s e c t i o n 5.2.1, was employed.  already  UBC, a c q u i r e s t h e p r o f i l e  stored  i n MTS  mainframe i n  c o o r d i n a t e data on t h e photograph  through a T a l o s CYBERGRAPH d i g i t i z e r which was connected t o MTS w i t h About  t h e Z e n i t h 158 microcomputer a c t i n g as a t e r m i n a l .  30 t o 40 p o i n t s were generated from each p r o f i l e f o r  computer p r o c e s s i n g .  66  5.3  EXPERIMENTAL AND  5.3.1  APPARATUS  Sink-and F l o a t T e s t  First density  the  fractions  f r a c t i o n was mill.  coal  The  sample was  samples were separated  by  a  sink-and-float  ground t o v e r y  characterized using  the  1.6,  an E l z o n e s i z e a n a l y z e r .  i n p l a s t i c bags and  sink-and-float  1.8  stored  procedure,  The in a  aqueous  zinc  f o l l o w i n g d e n s i t i e s : 1.3,  1.35,  were used. S i n k i n g  f r a c t i o n s from  t e s t were t r a n s f e r r e d t o the next l i q u i d o f h i g h e r The  rod  use.  c h l o r i d e s o l u t i o n s w i t h the 1.5,  Each  s i z e d i s t r i b u t i o n of each ground d e n s i t y f r a c t i o n  r e f r i g e r a t o r for future  1.4,  procedure.  f i n e powder i n a l a b o r a t o r y  ground samples were s e a l e d  In  into different  each  density.  f l o a t i n g p r o d u c t s were r i n s e d w i t h f r e s h water, and a i r -  dried.  5.3.2  Comminution of Coal  The separately  separated using  a  Samples  coal 195x318  fractions mm  laboratory  maximum sample s i z e f e d t o the m i l l was was  used  either  for  one  stage 67  were  300  grinding  rod  pulverized mill.  grams. The or  for  The mill  primary  grinding  followed  performed  i n a mortar g r i n d e r .  To  by  the  study the e f f e c t  secondary  grinding  of p a r t i c l e  which  was  size distribution  on  the c o n t a c t angle measurements, the WEKOB mortar g r i n d e r was employed  to  further  reduce  the  size  of  coal  powder.  The  t o t a l volume o f ground m a t e r i a l i n one b a t c h was  kept below  150  the  ml.  In  instrument nitrogen was  the  was  process  covered  t o prevent  stopped  of  mortar  a  plastic  by  oxidation.  f o r a period of  grinding, bag  and  In a d d i t i o n ,  five  minutes  whole  purged  the after  with  instrument each  two-  minute g r i n d t o prevent e x c e s s i v e h e a t i n g .  5.3.3  Particle Size Analysis  Particle affect  size  the p e l l e t  i s an  porosity  important and  parameter  consequently  the  which  may  fractional  area o f pores on the p e l l e t s u r f a c e .  The Celloscope particles which  also  size  conducted  u s i n g an E l e c t r o z o n e  ( E l z o n e ) . In t h i s d e v i c e , the suspension of in  an  electrolyte  passes  traversing resistance  a n a l y s i s was  through change  Corresponding  to  an  i s drawn  electric the  this  c u r r e n t . Each  orifice,  proportional change, 68  through  to an  causes the  an  orifice  particle, a  particle  electrical  fine  in  momentary volume. pulse  is  generated.  A l l the  electric  pulses  are  processed  by  a  computer t o y i e l d p a r t i c l e count and s i z e d i s t r i b u t i o n d a t a .  A d i s p e r s i n g agent were  required  particle  i n order  t o prevent  size  relative  volume  distribution percent  characteristic sizes procedure  agitation  the f o r m a t i o n  of c o a l  results  against  are p l o t t e d  i t s log  as the  size.  Three  ( i n c e n t i - m i c r o n ) were o b t a i n e d i n t h i s  i n c l u d i n g l o g mean, mode, and median s i z e s .  Pellet-Making  The p e l l e t - m a k i n g  i s one o f t h e most important  i n t h e p r o c e s s . The instrument press  and v i g o r o u s  aggregation.  The  5.3.4  (Calgon)  as shown i n F i g u r e  steps  used was MET-A-TEST mounting  5.3.1.  I t has a b u i l t - i n  manual  h y d r a u l i c gauge and t i m e r w i t h an a u d i b l e beep a t t h e end o f each  run.  The  high  pressure  was  provided  by  a  manual  h y d r a u l i c pump w i t h a working p r e s s u r e up t o 34.5 MPa p s i ) . The mould diameter  After alcohol  and  introduced. slowly  i s 25.4 mm  t h e mold was degreased  cotton,  The mold was  increased  by  carefully  then  (one i n c h ) .  cleaned  3 grams  by u s i n g  ethyl  o f c o a l powder  was  c l o s e d and t h e p r e s s u r e  was  h y d r a u l i c pumping. 69  (5000  When  the  pressure  Figure  5.3.1  A MET-A-TEST s p e c i m e n m o u n t i n g  70  press  reached  a  pre-set  point,  timing  was  started,  which  was  u s u a l l y s e t a t 5 minutes. P r e c a u t i o n s were taken t o c o n t r o l the  pressure  closely;  frequent  adjustments  were  required  since the pressure could d e c l i n e i n the p r e s s i n g process.  The from 3.45 the  pressure  t o 34.5 MPa  effect  Most  i n making t h e p e l l e t  angle  p e l l e t s prepared  was  measurements  on t h e c o n t a c t  were  carried  angle.  out on t h e  a t p r e s s u r e s o f 27.6 t o 34.5 MPa.  The P o r o s i t y Measurement  The  porosity  of  a  pellet  is  a  very  important  parameter both i n d i r e c t c o n t a c t angle measurement (this  varied  (500 t o 5000 p s i ) i n o r d e r t o study  of pellet-making pressure  contact  5.3.5  used  technique  i n c l u d e s two d i f f e r e n t methods: d i r e c t o b s e r v a t i o n o r  calculation  from  the p r o f i l e  of the l i q u i d  r a t e o f p e n e t r a t i o n measurement which w i l l Chapters  7  and  distribution,  8.  I t i s determined  pellet-making  by  pressure,  inherent p o r o s i t y of the material i t s e l f . pellet  method, p o r o s i t y a f f e c t s  pores  on  penetration  the  pellet  process,  affects  p e n e t r a t i o n w i t h i n a column.  71  be d i s c u s s e d i n  the p a r t i c l e as  well  while the  size  as  the  I n t h e compressed  the f r a c t i o n a l  surface, i t  drop) , and i n  in  area  the  rate  of  of a i r  rate  of  liquid  The p o r o s i t y was determined by s a t u r a t i n g t h e p e l l e t with a c e r t a i n l i q u i d the  compressed  analytical The  liquid, the  pellet  balance  weight  (kerosene i n t h i s c a s e ) . The weight o f was  before  accurately  determined  using  an  and a f t e r t h e s a t u r a t i o n p r o c e s s .  d i f f e r e n c e was  the weight  of the  penetrating  t h e volume o f which was assumed t o be t h e volume o f  pores  i n the p e l l e t .  The  total  volume  of the  pellet  c o u l d be o b t a i n e d by a c c u r a t e l y measuring i t s two dimensions - h e i g h t and diameter u s i n g a v e r n i e r gauge. The p o r o s i t y o f the p e l l e t can be subsequently  P  c a l c u l a t e d from  (Wi -  W) 0  Q  »r • r • h« p 2  where  P  Q  - Porosity  Wi and W Q - The p e l l e t weights (gram) b e f o r e and after penetration  ( a i r - d r y and s a t u r a t e d  pellet) r - p e l l e t diameter h - p e l l e t height  (cm)  (cm)  p - the penetrating l i q u i d density  5.3.6  P e l l e t Surface  In  order  (g/cm ) 3  Examination  t o examine possible  the p e l l e t  particle  surface  roughness  and  pressure.  The Scanning E l e c t r o n Microscope 72  crushing  f o r pores,  caused  by  high  (SEM H i t a c h i S-  570)  was  used. The  magnification  employed ranged from 20  10000 times. Under such a h i g h m a g n i f i c a t i o n , the particles  and  their  packing  Prior was  coated  under  very  repeated  t o the  with  surface  three  The  the  s u r f a c e examination, the p e l l e t  surface  clearly.  carbon. In order  high  on  individual  pellet  c o u l d be s t u d i e d v e r y  states  to  magnification,  t o o b t a i n good the  coating  resolution  process  was  times.  pellet  surfaces,  at  were photographed.  73  different  magnifications,  CHAPTER 6  RESULTS AND  The  freshly  macroscopically considered  DISCUSSIONS  prepared  pellet  smooth. S u r f a c e  to  be  a  surface  major  effect  For such a macroscopic process asperity  relatively  to  size  on  liquid  take  place  in  glossy  not  pellet  drop on  size  events  which  wetting  f r o n t passes over them may  the  angle.  naked It  eyes,  could  has  been  <Shuttleworth and  generally  contact  angle  Bracke, e t a l . , 1989>.  surface that  individual  is  the  so  small  microscopic  particles  as  the  be masked.  The p o r o s i t y on p e l l e t s u r f a c e , though not to  and  as c o n t a c t angle measurement,  the  the  was  roughness was  measurements <Nuemann and Good, 1979;  the  <I>  seriously  alter  demonstrated  the  observable  real  contact  thermodynamically  B a i l e y , 1948> t h a t the c o n t a c t angle  on  a  porous s u r f a c e w i l l be h i g h e r than on a smooth s u r f a c e t h a t has  the  same  composition.  p e l l e t s u r f a c e was  In  this  work,  a  proposed and c o r r e s p o n d i n g  the c o n t a c t angle v a l u e s was  introduced.  74  model  for  the  correction for  6.1  CONTACT ANGLE MEASUREMENTS  Practically, hysteresis. is  There  t o develope  can  be  angle  angle  systems  exhibit  a r e two ways o f h a n d l i n g h y s t e r e s i s .  One  a simple method by which r e p r o d u c i b l e data  obtained  single  a l l contact  i n spite  f o r any  of hysteresis,  liquid  approach  was  adopted  exploit  the  phenomenon,  on  in this  and t o r e p o r t  a particular  work.  The  recognizing  solid.  second  that  way  i t  a  This i s to  furnishes  a d d i t i o n a l i n f o r m a t i o n about t h e s o l i d .  As a l r e a d y p o i n t e d out, t h e c o n t a c t angle d a t a were o b t a i n e d e i t h e r by d i r e c t  r e a d i n g through goniometer,  o r by  c a l c u l a t i n g t h e angle v a l u e from t h e p r o f i l e o f axisymmetric meniscus.  U n l e s s otherwise i n d i c a t e d , o n l y advancing c o n t a c t  angles were measured i n t h i s work, and t h e u n i t o f a l l t h e angle v a l u e s i n t e x t this  i s that  roughness angle  the  and f i g u r e s i s degree. receding  and heterogeneous  <Bartell  reproducible  angle  Ruch,  1956>.  results  for 9  than  a  i s more  effects  and  The reason f o r  than It  sensitive  i s the  is  advancing  easier  f o r e . Also, z  e  to  to  a  get  i s much  e a s i e r t o measure.  In  the process  experimenter reflection  of contact  can n o t i c e ,  o f t h e drop  angle  measurements, the  through t h e goniometer,  profile 75  on t h e p e l l e t  the c l e a r  surface.  The  reflectivity smoothness.  is  obviously  F o r drops  with  a  manifestation  large  contact  of  angle,  image may l o o k l i k e an 8-shaped p r o f i l e having middle because o f r e f l e c t i o n  t h e drop  a t i p i n the  (see F i g u r e 6.1.1). T h i s e f f e c t  i s v e r y u s e f u l f o r determining which i s v i t a l  surface  t h e three-phase c o n t a c t  line  i n c o n t a c t angle measurement.  Vibration  by manual  tapping  was  also  tried  i n the  p r e s e n t c o n t a c t angle measurements w i t h t h e e x p e c t a t i o n t h a t it  would  make  help  t o overcome  t h e advancing  contact  obtained  angle  e . Nevertheless,  angle  measured  contact  hysteresis  without  way  were  less  measured  contact  the  advancing and r e c e d i n g angle. by Neumann  right was  sides often  observation  and  the equilibrium  found  reproducible  angles  that  angles  than  those  were l o c a t e d somewhere between  and Good  I t i s probably  <1979>  o f t h e drop may not be e q u a l . on  was r e j e c t e d  the  coal  i f this  degrees.  76  against  results.  o f h y s t e r e s i s , t h e angles  observed  b e t t e r , as  to insulate  v i b r a t i o n i n o r d e r t o produce r e p r o d u c i b l e  Because  barrier,  t h e v i b r a t i o n . When v i b r a t i o n was a p p l i e d ,  the  indicated  approach i t was  g  i n this  energy  pellet  a t the l e f t  and  This inequality surfaces.  The  d i f f e r e n c e exceeded  four  Figure  6.1.1  A s e s s i l e d r o p image o b s e r v e d the  goniometer  77  through  6.2  COMPARISON OF THE TWO TECHNIQUES  For made  each  with  value  drop,  t h e goniometer  on both  angles  sessile  was  sides  taken  a direct  r e a d i n g was  first  by measuring  the contact  angle  o f t h e drop.  The average  as t h e measured  o f t h e two  c o n t a c t angle  value. A  photograph was taken o f t h e same drop r i g h t a f t e r t h e d i r e c t measurement. computed  From t h e drop  angle  i n t h i s photograph, t h e  v a l u e was o b t a i n e d l a t e r  developed by Rotenberg,  The comparison different  profile  density  Boruvka,  u s i n g t h e program  and Neumann <1982>.  was made on t h e p e l l e t s prepared  fractions.  c o r r e l a t e d w i t h t h e computed  The d i r e c t  from  measured angle was  one f o r t h e same s e s s i l e  drop  as shown i n F i g u r e 6.2.1. The f i g u r e r e v e a l s t h a t n e a r l y a l l of  the points f a l l  beneath  the l i n e  and show f a i r l y  large  differences.  It lower  appears  than  the  that  the d i r e c t  computed  measurement  angles.  One  gives values  probable  reason  r e s p o n s i b l e f o r t h i s d e v i a t i o n might be t h e s y s t e m a t i c e r r o r introduced section conducted drop  by e i t h e r  that  o r by both  follows,  to test  technique.  a  o f t h e procedures.  series  of  the r e p r o d u c i b i l i t y Different  In the  measurements  were  o f t h e axisymmetric  perturbation  effects  such  as  l i q u i d d e n s i t y , s c a l i n g f a c t o r , p o s i t i o n i n g o f t h e drop apex 78  Comparison of the measured & computed  computed angle (degree) •  Measured vs. Calc.  diagonal  e t c . , were d e l i b e r a t e l y i n t r o d u c e d i n t o t h e computer program t o examine t h e consequent d e v i a t i o n . The r e s u l t s showed t h a t the  angle  confined  d e v i a t i o n i n the actual operation within  differences  1.5°.  between  6.2.1. T h e r e f o r e ,  This value  the  two  i s much  techniques  i t i s very  unlikely  e r r o r i s i n t r o d u c e d by t h e axisymmetric  The accuracy  lower than  shown  in  that the drop  the  Figure  systematic  technique.  o f d i r e c t r e a d i n g through goniometer was  also  tested  drop  and on t h e photographic  Again,  by  c o u l d be w e l l  repeated  t h e standard  measurements profile  both  on  the  sessile  of the s e s s i l e  drop.  d e v i a t i o n was below 2 ° . T h e r e f o r e ,  the  d e v i a t i o n between t h e two methods can not be a t t r i b u t e d t o the  measurement  error.  Some  other  factors  must  then  i n f l u e n c e t h e c o n t a c t angle measurements.  The h y p o t h e s i s  suggested  i n t h e p r e s e n t work i s t h a t  the d e v i a t i o n between t h e d i r e c t l y measured and the computed angle  values  have mainly  heterogeneity,  and  r e s u l t e d from t h e p e l l e t  the s e s s i l e  drop  distortion  surface  caused  by  heterogeneity.  B a s i c a l l y , t h e p e l l e t s u r f a c e can be c o n s i d e r e d t o be an u n i f o r m l y  d i s t r i b u t e d heterogeneous s u r f a c e . The  hetero-  geneous model proposed by Neumann and Good <1972> i n F i g u r e 6.2.2(a) surface  may  be  employed t o i l l u s t r a t e  heterogeneity  on  the two 80  the e f f e c t  contact  angle  o f the  measuring  methods. The s o l i d s u r f a c e i n the model c o n s i s t s o f strips  o f two  equilibrium solid  t y p e s , on which  c o n t a c t angles  surface  would  liquid-vapour  lead  interface  edge o f the drop may cross section (b) . The figure)  and  on  the  to microscopic d i s t o r t i o n  of  the  that  the  Young's e q u a t i o n l o c a l l y .  The  near  the  that  o f the  drop  6.  assumes d i f f e r e n t patches  x  o f F i g u r e 6.2.2  portion  line)  6  satisfy  The  Z  solid  i n order  (a) i s shown i n F i g u r e profile  (dashed  line  in profile.  i s t h a t p a r t o f the l i q u i d  contortion  line and  would  extend  from  upward t o the curved l i q u i d die  out  surface. fall  An  s u r f a c e which  merging  into  extrapolation  the  directly line,  e  2  the  direct  X  a  smooth,  of  the  three-phase-contact  spheroidal  main  r e a d i n g through  i s totally  drop method, t h e data p o i n t s  drop  main  surface  goniometer,  drop would  line.  what  i s t h e angle o f  i g n o r e d . For t h e from  is in  s u r f a c e f o r some d i s t a n c e  measures through goniometer , while 6  (the  surface.  somewhere between the s o l i d l i n e and the broken  In  i n the  The v i s i b l e p r o f i l e  c o n t a c t w i t h the high-energy patches o f the s o l i d The  6.2.2  comes down t o the lower-energy patches o f the  s u r f a c e i s not v i s i b l e solid  the l i q u i d  parallel  one  solid  axisymmetric  the main p r o f i l e  o f the  s e s s i l e drop are f e d i n t o d i g i t i z e r . The c o n t o r t i o n near the three-phase c o n t a c t l i n e might have d i e d out b e f o r e r e a c h i n g the  main p r o f i l e .  computer profile  should  The then  extrapolated  c o n t a c t angle thus c a l c u l a t e d on the be  the  angle  assumed  a t the three-phase 81  by  the  main  contact l i n e .  This  .I;I;I  3,  i>|l(li';  A ISJil iTI  ill!! I i I ill ijiil i i ' !l ' i i " !! !' '; ! i i i i iii ii'ii i ii'i  i  1  |! 1  WALL  1 1 1  1  1  TI  Hi :i  'i i 'I'I'I'I  ! hill!  'I' ' 'l'V -  MENISCUS  vis;. o^S^fS^SSiSs.,  a. An a r t i s t ' s conception  o f a meniscus i n c o n t a c t  with  a s t r i p w i s e heterogeneous w a l l  b. A view o f c r o s s s e c t i o n i n t h e s t r i p w i s e d i r e c t i o n  F i g u r e 6.2.2  An i d e a l i z e d heterogeneous s u r f a c e model 82  angle  6  r e s i d e s between  and  X  9  2  as  shown  i n Figure  6.2.2  (b). So i t i s always g r e a t e r measured angle 6 • 2  Because cooperative  effect  angle might be Cassie  the  main  profile  o f both  strips:  is a  determined  and  x  a , this 2  c o n s i d e r e d t o be C a s s i e ' s angle  equation)  which  reflects  the  by  a  contact  (confirms  overall  to  surface  wettability.  From above d i s c u s s i o n , i t can be concluded heterogeneous three-phase high  surface:  contact  a)  line  energy component, b)  the  contact  angle  t h a t on  measured  at  through a goniometer r e f l e c t s Cassie's contact  measured a t a t h r e e phase-contact main p r o f i l e o f the s e s s i l e drop.  83  angle  cannot  l i n e but o n l y through  a a  the be the  6.3  TESTING THE  The  COMPUTATION METHOD  direct  v u l n e r a b l e t o the  contact effect  angle  measurement  of h e t e r o g e n e i t y  and  is  more  reflects  the w e t t a b i l i t y o f h i g h e r energy component. The  only  axisymmetric  drop method c a l c u l a t e s the angle  from the main p r o f i l e ,  reflects  the  w e t t a b i l i t y o f the  overall  of  It  i s , therefore,  one.  axisymmetric drop technique  more  applying  the  appropriate  to  instead use  the  t o measure the c o n t a c t angle  a heterogeneous s u r f a c e . In t h i s of  composites  axisymmetric  section, different  drop  technique  and  on  aspects  are  further  investigated.  The  use  of  the  Rotenberg, Boruvka and  computer  program  developed  Neumann <1983> r e q u i r e s the  by  accurate  p o s i t i o n i n g o f the p r o f i l e b a s e l i n e (the three-phase c o n t a c t line) The  and  the p o s i t i o n i n g o f the apex p o i n t on the  importance  intentionally  of  p o s i t i o n i n g the  drifting  r e s u l t s i n F i g u r e 6.3.1 greater upward  than into  baseline  possible is  ±1.25°  real  the  profile,  the  baseline  ones  downward.  when and  from the  the  tested  by  one.  The  real  b a s e l i n e was  i n the  shown i n F i g u r e 84  baseline  become  Normally  e r r o r associated with as  was  show t h a t the c a l c u l a t e d angles were  the  move  positioning  the  baseline  profile.  the  was  smaller  when  the  uncertainty  in  range o f ±0.5  p o s i t i o n i n g o f the  6.3.1. The  moved  mm,  the  baseline  enlargement o f  the  drop p r o f i l e was error  in  the  34.6.  I f the s c a l i n g f a c t o r was  computed  angle  value  p o s i t i o n i n g of the b a s e l i n e would be  The  effect  tested  by  point.  The  point  of  was  r e s u l t s are removed,  associated  apex  i t away  shown i n F i g u r e  along  the  drop  with  point  was  also  the  real  apex  the  apex  from  6.3.2. As  profile,  away  from  r e a l apex p o i n t , the computed v a l u e d i d not show any change. The  conclusion  i s t h a t the  p o i n t o f the drop p r o f i l e i s not  The repeating standard ±2°  r e p r o d u c i b i l i t y of the  measurement  d e v i a t i o n was  f o r the  the  notable  p o s i t i o n i n g o f the  apex  important.  this  on  the  smaller.  p o s i t i o n i n g the  d e l i b e r a t e l y moving  l a r g e r , the  t e c h n i q u e was  the  same  tested  photograph.  by The  as s m a l l as 0.32°; i n comparison w i t h  d i r e c t contact  angle r e a d i n g  obtained  using  the  requires  the  goniometer.  The  use  of  the  computer  also  accurate  measurement of the  (scaling  f a c t o r ) o f the drop p r o f i l e on photograph, and  liquid the  density.  contact  angle  tension,  sessile  drop.  liquid  by  and  other  surface  The  (1.0)  the with  of  real  and these  enlargement  required to  q u a n t i t i e s such as  area,  effects  replacing  density  parameters: the  These measurements are  surface  tested  two  program  contact factors  scaling  the  radius were  factor  compute liquid of  the  further  (34.6)  some a r b i t r a r y v a l u e s . R e s u l t s 85  the  and in  The positioning of drop baseline and  138  its effect on computed angle  F i g u r e 6.3.1  140  ii 137.8  136  a 135.6  134  i H33.1  132  a 130.9  130 Sb o  128  "3)  126  c O  6 o U  124  ii 123.8  122 120 118 116 114 112 110 2  i -  i 1  i 0  I  Deviation from the true baseline (mm) H  Computed values  i 1  i  2  00  Positioning of the apex point of a drop F i g u r e 6.3.2  »  1 3 3  m 132.5  and its effect on computed angle value  B 1 3 3  -  2 B  m4  "132.7  "133  -8137.3  oo  i  r  -1  Deviation from real apex point (mm) Computed angle  1  r  Measurement of scaling factor and its 140.0  Figure  effect on the computed angles  6.3.3  139.0 138.0 137.0 136.0  H 135.3  135.0  JJ "to  c  CS T3 O  4—»  3 O.  S  o CJ  1135.4  a 134.3  134.0 o o to o -a •  1  133.0 132.0 131.0 130.0 129.0  CO co  128.0 127.0 126.0 125.0 124.0 123.0 122.0 121.0 120.0 26•.0  1  i  -22.0  i  i  -18.0  i  i  -14.0  i  i  i  -10.0  Deviation from true scaling value computed angle  i  -6.0  i  i  -2.0  2.  Accuracy of liquid density measurement F i g u r e 6.3.4  H  and its effect on computed angle  . „.  133.9  a  • 133  H 134.4  0  133.8  ' H33.1  CM  oo  -0.12  -0.08  -0.04  0.04  Deviation from the true liquid density •  Computed values  0.08  0.12  F i g u r e s 6.3.3 and 6.3.4  show t h a t t h e two parameters have no  s i g n i f i c a n t i n f l u e n c e on t h e computed angle  In above  conclusion,  indicate  that,  the  series  between  of the  value.  the t e s t s two  discussed  contact  angle  measurement methods, t h e computation method has much h i g h e r p r e c i s i o n than t h e d i r e c t r e a d i n g method. I n l a t e r work, t h e computation method was employed u n l e s s noted.  90  6.4  CONTACT ANGLE AND  DROP SIZE  Theoretically, affect and  one,  contact  situation. that  equilibrium angle  I t has  when the  solid  sessile  drop  size  should  not  the c o n t a c t angle on an i d e a l s u r f a c e . There i s one,  only  real  the  by  contact  the  < S h a f r i n and  system, been  contact sessile  angle  contact  is  Zisman,  i s rarely,  known e m p i r i c a l l y , angle o f a l i q u i d drop  a  this  a n g l e . However  or  captive  function 1952;  of  L e j a and  i f ever,  the  f o r many y e a r s , i s measured  bubble  drop  f o r the  (or  on  method, bubble)  a  the size  Poling,  1960;  Herzberg  effect,  the  advancing  and Marian, 1970; Good, 1979>.  For contact was  the  study  of  drop  size  angle i s u s u a l l y measured v e r s u s the drop s i z e . I t  observed i n a t y p i c a l experiment t h a t the c o n t a c t angle  of water on T e f l o n TFE <Herzberg  and Marian, 1970> i n c r e a s e s  w i t h the i n c r e a s e  For the c a p t i v e a i r bubble  method,  a  similar  <1960>.  They  i n drop s i z e . result  found  that  polymethymeth-acrylate  was the  (Lucite)  o b t a i n e d by contact  Leja  angle  increased  and  of  Poling  water  on  from 50° t o about  70° when the diameter o f a i r bubble decreases from 2 t o  0.8  mm.  To e x p l a i n t h i s phenomenon, L e j a and P o l i n g assumed, that  a drop  o r a bubble  i n contact with a 91  solid  could  be  treated  as  effect  a  was  spherical  due  cap and suggested  t o the influence  that  of gravity.  the  size  While  Good  <1979> and Good and Koo <1979> a t t r i b u t e d t h e s i z e e f f e c t t o heterogeneity  which  could  i n t e r f a c e near t h e s o l i d  lead  to  contortion  of  drop  surface.  To observe t h e behaviour o f c o n t a c t angle v e r s u s drop size  on a p e l l e t ,  two procedures o f forming d i f f e r e n t  size  drops were used i n t h i s work. In t h e f i r s t procedure, drops w i t h v a r i o u s predetermined volumes (1.0 t o 20.0 p l i t r e ) were first the  formed  a t the c a l i b r a t e d  whole s y r i n g e  lowered s l o w l y surface.  m i c r o - s y r i n g e t i p and then  set with the l i q u i d  and smoothly  until  The whole s y r i n g e  drop on i t s t i p was  t h e drop met w i t h p e l l e t  s e t was a g a i n r a i s e d  and l e f t a f r e e s e s s i l e drop on t h e p e l l e t  The sessile  second  drop  procedure  employed  up  slowly  surface.  was  t o increase the  s i z e by i n c r e m e n t a l a d d i t i o n  o f t h e l i q u i d (1  M l i t r e ) t o t h e p r e v i o u s l y formed one. The d r o p l e t was  first  formed on t h e s y r i n g e t i p and then was lowered t o g e t h e r w i t h the  s y r i n g e on t o t h e apex o f t h e p r e v i o u s l y formed  drop s i t t i n g on t h e p e l l e t  sessile  surface.  F i g u r e 6.4.1 shows t h e r e s u l t s p l o t t e d on t h e c o n t a c t angle  versus  Bullmoose  coal.  drop  size  I t can be  o b t a i n e d by t h e f i r s t  f o r -1.3 seen  that  density  fraction  t h e advancing  of  angle  procedure i n c r e a s e s w i t h drop volume 92  Effect of drop volume on contact angle F i g u r e 6.4.1  Drop volume increased in two ways  180 170  -  160  -  150 + 140 130 120 110 100  -  90 80 70 60 6  0  8  Sessile drop volume (microlitre) By incremental add  +  drops of diff. size  s l o w l y u n t i l the drop volume reached about 8 ulitres. this,  the  contact  These r e s u l t s  are  angle  value  was  essentially  i n a good accordance  In contact  the  angle v e r s u s drop  contact  1970;  obtained  Good,  1979;  1979>.  contrast to  procedure  constant.  w i t h those  p r e v i o u s l y by o t h e r s <Herzberg and Marian, Good and Koo,  Beyond  above size  result,  as  the  plot  o b t a i n e d from  of  the  the  second  i s q u i t e d i f f e r e n t . As shown i n F i g u r e 6.4.1, the  angle  first  decreased  with  the  increase of  a  drop  volume, then s t a r t e d r i s i n g a g a i n forming a minimum v a l u e a t around  6 //.litres.  This result  i s very  different  from  what  has been r e p o r t e d b e f o r e .  I t i s worthy of mention t h a t the c o n t a c t angle v a l u e s in The  F i g u r e 6.4.1  were o b t a i n e d by  c o n t a c t angle v a l u e s  known  until  calculated  their all  for different  photographs  in  a  axisymmetric  batch.  drop  drop  method.  s i z e s were not  were  digitized  This  excluded  and  angles  possible  s u b j e c t i v e i n f l u e n c e i n the measurement.  In o r d e r t o c o n f i r m t h i s phenomenon's r e p r o d u c i b i l i t y s e v e r a l s e t s o f t e s t s were conducted fraction  ( F i g u r e 6.4.2) and  fraction  ( F i g u r e 6.4.3  on t h e 1.3-1.4 d e n s i t y  on the oven-heated -1.3  t o 6.4.5). A l l the  two major f e a t u r e s .  94  density  figures revealed  Drop volume (micronlitre) H  Contact angle  Drop size effect on contact angle F i g u r e 6.4.3  130  oxidized-1.3 BM coal t=150C  "  128 126  H  106 H 104 102 100 -| 2  1  1  4  1  1  6  1  1  8  1  1  1  10  Drop volume (microlilre) •  contact angle  1  12  1  1  14  i  r  16  Drop size effect on contact angle Figure 6.4.4  2  4  oxidized -1.3 BM coal t=200C  6  8  10  Drop volume (microlilre) •  contact angle  12  14  Drop size effect on contact angle Figure 6.4.5  oxidized-1.3 BM coal t=250C  o u N  '  f—H  O  c o o  bo  .a  > •o <  Drop volume (microlitre) •  contact angle  First, angles  exhibit  beginning. the  be  a  angle  generally  decrease  V-shaped.  versus  drop  beginning  All  contact  volume  at  (8 t o 17  the  /^litres)  s t a r t s t o i n c r e a s e a g a i n . T h i s phenomenon  explained  gravitational  very  are  Then, beyond a c e r t a i n volume  contact  may  they  force  as  a  and  joint  effect  contact  angle  of  two  factors:  h y s t e r e s i s . At  the  when s e s s i l e drop volume on the p e l l e t s u r f a c e i s  small,  each  incremental  addition  substantially  i n c r e a s e s the s e s s i l e drop h e i g h t , and the g r a v i t a t i o n f o r c e moves the  s e s s i l e drop p r o f i l e downward t o assume a  c o n t a c t a n g l e . A continuous volume  a d d i t i o n o f the l i q u i d t o the s e s s i l e drop does not  increase  only  sessile  continues  to  Beyond  a  certain  versus further  the  observed.  decrease i n c o n t a c t angle volume,  notably  is  smaller  drop h e i g h t expand  any  more. The  h o r i z o n t a l l y . As  sessile  a  drop  result,  the  curve e x h i b i t s a c l e a r minimum.  A f t e r the minimum i s reached, the f u r t h e r i n c r e a s e i n sessile  drop  expansion. The  volume  can  only  lead  to  its  horizontal  second f a c t o r , the c o n t a c t angle h y s t e r e s i s ,  becomes a major e f f e c t . I t attempts t o o b s t r u c t the  advance  of  contact  the  three-phase  contact  line.  As  a result,  the  angle began t o i n c r e a s e .  The  second f e a t u r e presented  all  cu rves  are  sawtooth-shaped.  the  h y s t e r e s i s energy  barrier. 99  by these  This An  can  figures i s that  be  incremental  attributed to increase  in  the s e s s i l e by  an  drop  size  expansion  expansion  of  on t h e p e l l e t the  s u r f a c e i s accompanied  three-phase  o f t h e three-phase  contact  contact line  line.  was  The  opposed  by  the h y s t e r e s i s energy b a r r i e r . T h i s may l e a d t o an i n c r e a s e o f t h e c o n t a c t angle v a l u e .  The subsequent be  energy accumulated w i t h i n t h e s e s s i l e drop  after  a d d i t i o n s o f one o r two i n c r e m e n t a l d r o p l e t s may  sufficient  i s accompanied  t o overcome t h e energy b a r r i e r .  This process  by a decrease i n t h e c o n t a c t a n g l e . The whole  c y c l e , when more i n c r e m e n t a l l i q u i d  i s added t o t h e s e s s i l e  drop, r e p e a t s c o n t i n u o u s l y . A sawtooth-shaped  c o n t a c t angle  v e r s u s drop volume curve r e s u l t s .  Apparently energy  small  introduced energy  a  phenomenon  i n t r o d u c e d by each d r o p l e t  hysteresis very  f o r such  energy  barrier.  (1 nlitre by each  barrier,  That  i n this droplet  that  appear,  the  s h o u l d be lower than t h e i s , the droplet  case).  Otherwise  i s so l a r g e  the e f f e c t  to  s h o u l d be t h e energy  relatively  o f energy  barrier  to the may  be  overshadowed.  The  p r e s e n t methodology  may be f u r t h e r developed t o  study t h e h y s t e r e s i s energy b a r r i e r by c o r r e l a t i n g t h e sawt e e t h h e i g h t w i t h energy.  100  6.5  CONTACT ANGLE VERSUS TIME  It  was  p e r c e i v e d t h a t c o n t a c t angles measured i n the  open a i r and  i n an  However, i t was  enclosed  thermostated  chamber may  vary.  not known whether e q u i l i b r i u m , or, a t  meta-equilibrium  of  the  sessile  drop  least  on  the  pellet  was  e s t a b l i s h e d w i t h i n c e r t a i n p e r i o d . I f not,  the  question i s  how  l o n g i t w i l l take t o reach such an e q u i l i b r i u m . In o r d e r  to  answer  carried  such  a  question,  additional  experiments  were  out.  The  first  observation  was  aimed  at  testing  the  r e l a t i o n s h i p between the c o n t a c t angle a t a s e s s i l e drop and its  life  time  thermostated w i t h i n the  on the p e l l e t .  The  chamber a t ambient chamber was  filled  t e s t s were performed i n a temperature.  with  The  distilled  reservoir  water t o keep  the humidity c o n s t a n t . A f t e r l o w e r i n g the t e s t e d p e l l e t onto the  stage  w i t h i n the  minutes  later,  surface  through  chamber was angle  a  sessile  a  small  equipped  could  be  of  Line  drop hole  with  taken  d i s t u r b i n g the s e s s i l e  The  chamber, the  Coal  was on  without  placed  top  viewing  of  on  the  windows, so  touching  the  closed. the  pellet  chamber. the  10  The  contact  chamber  and  drop.  r e s u l t s obtained Creek  main l i p was  are  for different density  presented 101  in  Figure  fractions  6.5.1.  For  CONTACT ANGLE vs. TIME F i g u r e 6.5.1  FOR DIFF. DENSITY FRACTIONS OF LC COAL  1  0  4  9  15  i i r 20 16200 34200 44280 63000 66600 68400 75600 82800 90000111600 1  1  1  1  1  time (second)  +  1.4-1.5  O  1.5-1.6  A  1.6-1.8  density very  fractions  stable  lower  than  1.5,  and o n l y v a r i e d  very  t h e c o n t a c t angles slightly  were  even over  a two  day p e r i o d , Then a q u i c k d e c l i n e f o l l o w e d .  L i q u i d e v a p o r a t i o n , p e l l e t s u r f a c e o x i d a t i o n , and the penetration  of l i q u i d  into  the p e l l e t  can be  the  factors  r e s p o n s i b l e f o r such a behaviour. For low d e n s i t y f r a c t i o n s , the  effect  of l i q u i d  The  slow decrease  p e n e t r a t i o n was  i n c o n t a c t angle  initially  was  negligible.  principally  due t o  the s e s s i l e drop e v a p o r a t i o n . The reason i s t h a t t h e s e s s i l e drop  interface  reservoir  and  the  possessed  surface  different  of  bulk  liquid  curvatures  i n the  (see  Kelvin's  equation).  Therefore, volume  s u r f a c e o x i d a t i o n becomes s i g n i f i c a n t , and t h e l i q u i d  begins  into  the  time.  As  pellet.  time  proceeds,  drop  pellet  penetrate  with  that the s e s s i l e the  to  decreases  i t can be expected  Consequently,  the  contact  angle s t a r t s d e c r e a s i n g q u i c k l y .  The reveal coal  horizontal  parts  that the equilibrium  sample  can e s t a b l i s h  of  the  state very  f o r t h e -1.5  quickly,  minute. So i n t h e a c t u a l measurement, wait angle  curves  ( F i g . 6.5.1) f r a c t i o n of  i . e . , within  one  i t i s not necessary t o  l o n g f o r t h e e s t a b l i s h m e n t o f e q u i l i b r i u m . The c o n t a c t i n open a i r was  6.5.1. I t was  observed  compared  with  the r e s u l t  t h a t t h e angle 103  values  i n Figure  i n open a i r  were part  approximately of  the  researchers' Ralston,  equal  curve.  This  observationy  1987>.  thermostated  t o the values was  <R.  According  chamber  agreement  to  this  i s not c o n s i d e r e d  t o be necessary  all  c o n t a c t angles were measured i n open a i r .  angles  measurements, and,  angle  because  of  on  the  pellet  the in  therefore,  o f water on t h e p e l l e t s were much  s m a l l e r than 90° f o r t h e +1.5 contact  other  observation,  practical  contact  angle  with  Crawford, L.K. Koopal and J .  the  The  contact  in  at the h o r i z o n t a l  g/cm  3  surface  significant  liquid  pellet.  104  density fractions. decreases  very  penetration  The  quickly into  the  6.6  FACTORS AFFECTING CONTACT ANGLE  In contact  this  angle  section, on  a  the  pellet  o x i d a t i o n and p e l l e t - m a k i n g  6.6.1  factors  were  that  tested.  influence  They  are  the  pellet  pressure.  Oxidation  O x i d a t i o n was found t o decrease t h e h y d r o p h o b i c i t y coal  surface.  Sun's e a r l y s t u d i e s  oxidation  on  coal  proceeds,  coal  flotation  becomes  <1954> o f t h e e f f e c t  indicated  progressingly  that  more  as  of of  oxidation  hydrophilic. It  was a l s o noted <Iskra and Laskowski, 1967> t h a t r e d u c t i o n i n hydrophobicity  of  lower  rank  coals  o x i d a t i o n than was t h a t o f h i g h e r  To  evaluate  the  change  was  one  i n hydrophobicity  beaker  the and  of  coal  angle and t h e r a t e  i n d e t a i l i n Chapters 7 and 8.  o x i d a t i o n procedures have been c o n s i d e r e d .  procedure recommended  <1986>,  by  t e c h n i q u e s were used. The r a t e o f p e n e t r a t i o n  t e c h n i q u e w i l l be d i s c u s s e d  Various  affected  rank bituminous c o a l s .  powder due t o o x i d a t i o n , both t h e c o n t a c t of penetration  more  powdered oxidized  In  by Fuerstenau, Yang and Laskowski  Bullmoose in a  coal  was  fan ventilated 105  contained oven  at  in a 150 °C,  200°C,  and  After  250°C,  respectively, for a period  oxidation,  pressure  of  27.6  the  coal  MPa  into pellets  were measured as a l r e a d y  The  results  change i n c o n t a c t test,  shown  angles  was,  compressed  under  the  contact  penetrating  by  p e n e t r a t i o n curve Chapter of  and  the  liquid  6.6.1. Although  was  the  of  trend  still  coal  penetration  kerosene.  directly  For  the  the  a c c o r d i n g t o the s i g n i f i c a n c e  un-oxidized  rate  was  7) .  angles  can  be  increase  observed.  oxidized  tested  instead  hours.  anomaly appeared a t 250°C where a s l i g h t  These  (see  and  i n Table  insignificant,  i n c o n t a c t angle was  again  was  8  discussed.  are  statistically  seen. An  powder  of  The  powders  were  technique.  slope  value  of  r e l a t e d t o the c o n t a c t  simplicity,  calculated  only  angles  the  were  slope  The the angle  values  presented  for  comparison s i n c e t h i s i s o n l y a q u a l i t a t i v e comparison. They were t a b u l a t e d angles  together  with  the  d i r e c t l y measured  i n T a b l e 6.6.2.  Kerosene  can  penetrate  i n t o a column o f  hydrophobic  m a t e r i a l more q u i c k l y than i n t o a h y d r o p h i l i c one. table, coal  the  slope value  should  Following value  contact  the  became  be  of penetration value  greater  same t r e n d smaller  for  than as  the  the 106  that  for  contact coals  So i n the  f o r un-oxidized oxidized angle,  oxidized  at  the 150  coal. slope and  The c o n t a c t angle on p e l l e t o f o x i d i z e d c o a l Table  6.6.1  the -1.3 d e n s i t y f r a c t i o n Bullmoose c o a l  Pellet No.  Unoxidized  1st  2nd  3rd  Average: Std  Deviatn:  150* C  200* C  250* C  130 .5 127 .5 128 .5 125 .5 127 .0 129 .0 130 .5 126 .0  131 .5 129 .0 132 .0 131 .5 127 .0 132 .0 136 .0 132 .5  129 .8 135 .5 129 .8 128 .8 126 .0 129 .3 128 .5 127 .5  130.5 130.5 133.5 135.0 127.0 129.8 132.8 125.8  125.0 132.8 131.0 134.0 132.3 133.0 127.3 131.5  132 .5 127 .5 128 .5 129 .5 127 .0 131 .0 130 .5  129 .5 135 .0 133 .0 135 .5 135 .5 130 .0 130 .0  129 .3 126 .5 127 .3 128 .3 127 .3 123 .8 129 .0 127 .0  121.0 125.0 125.5 127.8 130.5 126.5 122.0 124.5  128.8 127.5 132.3 130.8 130.0 129.0 131.3  131 .0 131 .0 132 .5 128 .5 135 .5 129 .5 128 .5  132 .5 127 .5 126 .6 133 .5 130 .5 131 .0 126 .0  125 .5 129 .3 125 .8 136 .5 126 .3 126 .0 126 .3 125 .8 129 .3  123.8 127.5 129.8 129.0 132.8  128.0 128.8 129.5 129.5 130.3 132.3 129.8 129.0 129.8  130.34  128.18  128.18  130.15  2.75  2.79  3.71  2.06  * The p e r i o d o f o x i d a t i o n time i s 8 hours * P e l l e t - m a k i n g p r e s s u r e i s 27.6 MPa  107  Table 6.6.2 Comparison o f the c o n t a c t angles w i t h the r a t e o f p e n e t r a t i o n measured on d i f f e r e n t c o a l s  method  unoxidized  measured angle degree rate of pene t r a t n slope  150*C  200"C  250*C  130.34  128.18  128.18  130.15  0.945  0.904  0.864  0.958  The d i r e c t c o n t a c t angle measurement v a l u e s are quoted from chapter 5  *  Bullmoose c o a l  -1.3 d e n s i t y f r a c t i o n  Column making p r e s s u r e i s 13.8 MPa  200°C. The anomaly f o r t h e c o a l powder o x i d i z e d again  observed.  greater  than  The  slope  others.  value  This  was  means  0.958  that  a t 250°C was  and  the  apparently  coal  powder  o x i d i z e d a t 250°C became more hydrophobic.  The  s i m i l a r r e s u l t s obtained  t e c h n i q u e s confirmed t h a t the  coal  reason  powder heated  f o r t h i s may  breakup  of  the  1986>.  Even  functional surface  an i n c r e a s e a t 250°C  hydrophilic  though  i n hydrophobicity f o r  d i d occur.  be a t t r i b u t e d  groups) on c o a l s u r f a c e  from t h e two d i f f e r e n t  The  possible  t o t h e decomposition o r  functional  groups  (carboxyl  i n t h e h e a t i n g p r o c e s s <Ye, e t a l . ,  oxidation  groups c o u l d  was  still  going  be e f f e c t i v e l y s p l i t  on,  the  from t h e c o a l  and evaporated a t h i g h e r temperature. While a t lower  temperature, effectively  the functional  groups  could  n o t be  split  as a t h i g h temperature. The c o a l s u r f a c e  so  became  more and more h y d r o p h i l i c .  A s i m i l a r phenomenon was observed b e f o r e by Ye, J i n , and  M i l l e r <1986>  low-rank They  coal  found  improve  study  on thermal  and i t s r e l a t i o n s h i p  that  coal  in their  properly  flotation  controlled and  treatment o f  t o f l o t a t i o n response. heating  i t s separation  can a c t u a l l y from  mineral  matter, e s p e c i a l l y f o r l o w - r a n k - c o a l .  It  was  alleged  by Yordon  and Yoon <1988>  and many  o t h e r s t h a t t h e o x i d a t i o n mechanism o f c o a l and t h e r e a c t i o n 109  CONTACT ANGLE vs. OXIDATION TIME F i g u r e 6.6.1  Oxidized in water and in air  Oxidation time (hour) •  Oxidized in water  +  Oxidized in air  p r o d u c t s under d r y c o n d i t i o n s can be s i g n i f i c a n t l y from those o f the low-temperature i n a moist o r wet  the  process,  o x i d a t i o n t h a t take p l a c e  environment.  In t h i s work, wet In  different  a  o x i d a t i o n of c o a l was  pellet  o f the  f o l l o w i n g the same procedure  also  L i n e Creek c o a l  tested.  was  made  as mentioned above and h e l d on  a s m a l l h o l d e r w i t h i t s s u r f a c e exposed t o water. Then, the whole  set  temperature  For  was  immersed  in  distilled  water  and  the  oven  was maintained a t 100°C.  comparison,  another  t o g e t h e r w i t h the above p e l l e t  pellet  was  dry-heated  i n the same oven i n the a i r .  A f t e r a p e r i o d of time, the two p e l l e t s were taken out oven  to  determine  back  into  procedure  the  c o n t a c t angle.  the  oven t o c o n t i n u e the  was  repeated.  A  curve  were  put  oxidation process.  The  of  Then,  contact  o x i d a t i o n time c o u l d be o b t a i n e d f o r each  The  results  the r a t e o f wet  6.6.2  are  given  they  from  angle  versus  pellet.  i n F i g u r e 6.6.1.  Apparently,  o x i d a t i o n i s much l a r g e r than d r y o x i d a t i o n .  Contact Angle v e r s u s P r e s s u r e  Contact  angles  measured  on  the  porous  pellet  s u r f a c e s a r e not t h e t r u e c o n t a c t a n g l e s . The p e l l e t - m a k i n g p r e s s u r e can i n f l u e n c e t h e c o n t a c t angle on a p e l l e t s u r f a c e through changing i t s f r a c t i o n a l area o f pores.  To series  test  of  this  pellets  hypothesis, made  the contact  under  different  t e s t e d . R e s u l t s f o r t h e -1.3 g/cm  3  Line and  pressures, pressure  respectively.  pressures  were  i n Figures  As shown i n F i g u r e  t h e c o n t a c t angle (3.4 -  on a  d e n s i t y f r a c t i o n o f both  Creek and Bullmoose c o a l s a r e g i v e n 6.6.3,  angles  decreases  17.2 MPa). F u r t h e r  with  6.6.2,  6.6.2 a t low  an i n c r e a s e i n  increases  i n pressure  above 17.2 MPa have o n l y a v e r y s m a l l impact on t h e c o n t a c t angle v a l u e .  In influences Figure  addition,  pellet-making  the r e p r o d u c i b i l i t y  6.6.3  deviations  the  were  pressure  of the data.  statistically  analyzed.  The  also  data i n  The  standard  a r e shown i n F i g u r e 6.6.4. As t h e p e l l e t - m a k i n g  p r e s s u r e i n c r e a s e s , t h e r e p r o d u c i b i l i t y o f t h e c o n t a c t angle d a t a becomes b e t t e r .  The value of  influence of the pellet-making pressure  o f t h e c o n t a c t angle may  solid  surface  result  properties,  on t h e  from t h e a l t e r a t i o n s  surface  roughness,  and  f r a c t i o n a l area o f pores on p e l l e t s u r f a c e .  The  SEM  photographs  (Section 112  6.8)  show  that  the  CONTACT ANGLE vs.PELLET-MAKING PRESSURE  100 H  90 H 2  \  1  6  1  \  10  1  i  i  1  14  1  18 Pressure MPa  S  Measured angle  1  22  1  1  26  i  i  30  i  r  34  Effect of pellet-making pressure on contact angle -1.3 fraction BM coal  Figure 6.6.3  180 170 160 H 150 H 140 1)  •  o •a  + <t> • 130 ^ +  bo  120  o  110  -4-» g  • ;  i  i ° 5•  +  * - ?"  A  + • 9  + 5 o •  +  + * •  ° •  o  • +• f  100 90 80 70 H 60  "i—i—r  10.34  "1—I—I—I  "i—i—r  17.24  24.11  n—i—r  1—i—i—i—r 31.03  Pressure (MPa) •  1st pellet  +  2nd pellet  O  3rd pellet  Standard deviation in degree  o Lo  r—  If* to  •ff^-;-}Kpf'-"v----"-u^  11111111181111 ^^^^  pellet-making  pressure  of  27.6  MPa  caused  only  negligible  p a r t i c l e c r u s h i n g on the p e l l e t s u r f a c e . I t i s u n l i k e l y t h a t t this  static  properties In contact pores  a  force  would  alter  the  coal  surface  noticeably. fact,  the  pellet-making  pressure  influenced  the  angle mainly through changing the f r a c t i o n a l area on  a  reduce both of  pressing  pellet  fractional  pellet.  surface  surface.  The  roughness  results has  h y s t e r e s i s , whereas the factor.  area  a  The  increase  o f pores and in  section  minor  fraction  effect area  i n pressure surface  6.9 on  show  can  roughness that  contact  the angle  o f pores i s the major  D e t a i l e d d i s c u s s i o n of t h i s e f f e c t w i l l be g i v e n  the f o l l o w i n g s e c t i o n s .  116  of  in  6.7  POROSITY  The  compressed p e l l e t s u r f a c e s looked g l o s s y and were  macroscopically the  pellet  flat.  surface  Although t i n y  a i r voids  are not detectable  and pores on  t o t h e naked  these pores e x e r t a s i g n i f i c a n t e f f e c t on t h e c o n t a c t on p e l l e t  the  angles  surfaces.  C a s s i e and Baxter on  eyes,  <1944> c o n s i d e r e d t h e c o n t a c t  a composite s u r f a c e as an o v e r a l l components  i n contact  with  angle  c o n t r i b u t i o n s from a l l  the l i q u i d  drop,  including  the a i r pores as one o f t h e components. The c o n t a c t angle o f water on these a i r pores i s 180°. The e f f e c t o f pores can be quantitatively  corrected  from  t h e measured  contact  angle  (the apparent c o n t a c t angle) by u t i l i z i n g t h e C a s s i e - B a x t e r equation  (see Chapter 2 ) .  COSe  However,  such  = a -COSe 1  correction  - a  0  requires  2.1.10  2  the f r a c t i o n a l  area  of  pores on p e l l e t s u r f a c e , a , be q u a n t i t a t i v e l y known. 2  There has been no d i r e c t measure t h e f r a c t i o n a l while  the p e l l e t  bulk  area  technique,  o f pores  porosity  through some simple t e c h n i q u e s . 117  i n practice, to  on a p e l l e t  surface,  can be d i r e c t l y  measured  I t was c o n s i d e r e d t h a t t h e r e  must of  exist  certain  pores on  the  study,  surface  the  was  types the  of  trapped  in  porosity within individual minerals, amount  coal  of  microns  is  tiny  in  diameter  t o t a l volume of  the  measurement  of  the  c o a l powder, t h e r e are  two  6.8).  of  porosity  particles,  and  caused  and  porous.  There  capillaries  within  coal  these pores and  intra-particle  are  with  tremendous  only  particles.  several  However,  voids within coal  i s , therefore,  controlled  by  the  particles  i s much s m a l l e r than t h a t trapped in-between p a r t i c l e s . pellet porosity  by  p a r t i c l e s . Unlike other inorganic  extremely  pores  In  on  the  of  inter-particle  between  area  pores  section  the  area  from  compressed p e l l e t s  fractional  p e l l e t bulk porosity.  fractional  (see  porosities:  air  the  estimated  p e l l e t bulk porosity  For  between the  p e l l e t s u r f a c e and  present  pellet  correlation  The  inter-particle  porosity.  In the liquid.  The  trapped  in  p r e s e n t work, kerosene was volume of the  converted into  In with  the  it.  pores  process,  kerosene.  from  kerosene needed t o within  a  pellet  displace  the  can  directly  be  air  porosity.  penetrates into, air  used as a r e p l a c i n g  Because and The  the of  p e l l e t was the  capillary  s a t u r a t e s the pellet  weights 118  brought  effect,  p e l l e t by before  into  contact kerosene  displacing and  after  the the  p e n e t r a t i o n were determined. of  kerosene  penetrated  The  into  d i f f e r e n c e was  the  pellet;  which  the  weight  volume  is  equal t o t h e volume o f pores w i t h i n a p e l l e t .  Kerosene was the  coal  density  surface  used and  i n s t e a d of water because  can  penetrate  into  f r a c t i o n o f c o a l v e r y q u i c k l y . The  kerosene t o p e n e t r a t e  a pellet  pellets  i t wets of  any  time r e q u i r e d by  from bottom t o top was  less  than 10 minutes. In o r d e r t o ensure complete s a t u r a t i o n , the p e l l e t was  left  o v e r n i g h t i n c o n t a c t w i t h kerosene u n t i l  f u r t h e r i n c r e a s e i n the p e l l e t weight was  The  p o r o s i t y t e s t s were conducted  no  observed.  on a l l t h e d e n s i t y  f r a c t i o n s o f L i n e Creek c o a l s . R e s u l t s are shown i n F i g u r e s 6.7.1  to  6.7.2. At  low  pellet-making  MPa) , t h e p o r o s i t y decreases more  quickly  reached in was  the  than  that  a c e r t a i n value p r e s s u r e had  at  w i t h the high  a negligible  pressure  at  this  c o u l d not  the p r e s s u r e  was  pressure. change such  extremely  p l a c e , no f u r t h e r decrease  It  can be  observed  p o r o s i t y versus  13.8  increase i n pressure  pressures.  (above 24.1  (below  MPa),  When  pressure  further increases  i n f l u e n c e on p o r o s i t y . I t  b e l i e v e d t h a t the p e l l e t had reached the c l o s e s t  condition  the  pressure  Further a packing  h i g h and  increases  packing in  the  s t r u c t u r e . Unless  particle  crushing  took  i n p o r o s i t y was p o s s i b l e .  from F i g u r e s 6.7.1  pressure 119  curve  shifts  and  6.7.2  downward  that to  a  THE PELLET POROCITY vs. PRESSURE F i g u r e 6.7.1  For diff. density fractions of LC coal  o  o  CM  Pressure MPa -1.3  +  1.3-1.35  1.35-1.4  THE PELLET POROCITY vs. PRESSURE For diff. density fractions of LC coal  F i g u r e 6.7.2  Pressure MPa 1.4-1.5  +  1.5-1.6  O  1.6-1.8  A +1.8  lower p o s i t i o n  as  the  coal  density  increases  and  they  are  parallel.  In  the  powders  grinding  for  controlled  all  to  coal  for  are  the  as  presented  fraction,  two  in  different  as  The  density  particle sizes  fractions  they had  possible.  different  the  density  ensure t h a t  distributions results  process,  were  coal  closely  narrow p a r t i c l e  particle  fractions  Figure  of  of  6.7.3.  characteristic  size the  For  analysis Line  each  sizes  size  Creek  density  ( l o g mean  and  median) of the powder were determined.  As the  described  same p r e s s u r e  similar  size  fact  that  The  porosity  While porosity  particle  the  pellet-making  intercepts  above  changed  parallel  pressure  (intra-particle),  porosity.  the  are  be  same  or  by  the  characterized  indicated  i t can  p e l l e t s made under  m a t e r i a l s w i t h the  should be  porosity  curves  the  i s the  by  inter-  pressure.  (Figures  The  6.7.1  and  change  the  supported such a c o n c l u s i o n .  f r a c t i o n exhibited  If  from the  and  a l l the  6.7.2) s t r o n g l y  coal  and  distributions,  same p o r o s i t y . particle  i n Chapter 8.5,  The  particles  it of  cannot  only  affects  the  lower  interdensity  higher i n t r a - p a r t i c l e p o r o s i t i e s .  curves  are  extrapolated  to  the  are the p o r o s i t i e s when powders are 122  Y-axis, loosely  the  piled  CHARACTERISTIC PARTICLE SIZES F i g u r e 6.7.3  For diff. densityfractionsof LC coal  v  - "> £•!*!•!•!•»  'mm  without making  any compression. pressures  reproducibility  above  pellet  scattered.  20.7 MPa  for pellet  When p e l l e t - m a k i n g the  I t was observed  properties  pressure  properties  were  t h a t when p e l l e t -  employed, could  i s decreased  such  as  be  very  good  obtained.  down t o 6.9 MPa,  porosity  were  severely  R e p r o d u c i b i l i t y i s , therefore, b e t t e r a t higher  p e l l e t - m a k i n g p r e s s u r e s . I n chapter 8, a d e t a i l e d d i s c u s s i o n on  the e f f e c t  given. still  of pressure  on  The c o n c l u s i o n s o b t a i n e d applicable to pellets.  124  column  properties w i l l  from those  be  experiments a r e  6.8  SURFACE EXAMINATION AND AREA OF  As  was  has  already  been mentioned, between the  a p e l l e t s u r f a c e and proposed t o  such a  FRACTIONAL  PORES  there i s a correlation on  ASSUMPTION FOR  the  i t was  assumed  fractional  area of  p e l l e t b u l k p o r o s i t y . The  o b t a i n the  fractional  p e n e t r a t i o n behaviour of  through c a p i l l a r y  effect  g i v e s the  a  liquid  hint.  into  Pellets  porous. In o r d e r t o e x p l a i n the  phenomenon,  pores  the  e q u a l i z e d as the  utilized  column's in solving  thin  inside  axis  pellet  the  along  its  fractional  inside  pellet  compressed penetration  statistically  can By  pores  of  the  ratio  tubes  This  tortuous  methodology  c o n d i t i o n , a bundle of  was  axis  be  direction, pores and  easily  definition, the  (pores) t o  straight  p a r a l l e l p e r f o r a t i n g through a  area of  geometry d e r i v a t i o n .  capillary  are  pellet  p r e s e n t problem.  idealized  between the  is  pellet  direction.  c a p i l l a r y tubes are  the  the  a  a bundle of c a p i l l a r y tubes which are  I f under an  solid  method  area of pores through  from powders are  and  pores  correlation.  The  along  that  total  the  s u r f a c e . That i s 125  the the  obtained the  correlation bulk  from  porosity a  simple  fractional  cross  section  whole area of  area  of  area  of  pellet  bottom  4> = n • n • r /n • R 2  <f> = n - r / R 2  where  i s the  capillary the  fractional  tubes  capillary  2  6.8.1  2  area  of pores,  p e r f o r a t i n g through tubes,  and  R  the  n  the  the p e l l e t ,  r a d i u s of  number  of  r r a d i u s of  the  pellet.  The  p o r o s i t y o f the p e l l e t i s g i v e n by  (P  = n•  TT  • r • h/n  = nr /R 2  where  <P i s the  pellet.  pellet  Combining Equations  i s , the  2  6.8.2  2  p o r o s i t y , and  <f> =  That  •R •h  2  fractional  6.8.1  and  h  the  height  6.8.2, one  can  of  the  get  6.8.3  (P  area  of  pores  on  pellet  bottom  s u r f a c e i s equal t o the b u l k p o r o s i t y i n s i d e a p e l l e t  i n an  idealized condition.  For capillary Under  such  a  tubes a  pellet inside  case,  the  made  of  compressed  i t are t o r t u o u s question  the above c o n c l u s i o n s t i l l  t o be  h o l d s . One 126  powder,  and v a r y  the  i n radius.  answered i s whether  can c o n s i d e r t h a t the  pellet one  i s composed o f a l a r g e  number o f t h i n l a y e r s  piled  over another. They a r e so t h i n and t h e c a p i l l a r y  tubes  inside  i t a r e so  considered  short  that  the c a p i l l a r y  tubes  are  s t r a i g h t and t h e i r r a d i i uniform. T h e r e f o r e , f o r  these  individual  holds.  A d d i t i o n a l l y , t h e f r a c t i o n a l areas o f pores on those  thin  layers'  thin  surfaces  layers  t h e above  conclusion  should be s t a t i s t i c a l l y  still  equal t o one  another. And so a r e t h e b u l k p o r o s i t i e s i n s i d e those l a y e r s . When a l l those pellet,  that  is,  Eq.6.8.3 s t i l l  One  thin  layers  for a  compressed  possible  top  of p e l l e t  sections.  t o form  a  o f powder t h e  during  and l e a d  above  assumption  a c t i o n t h a t may o c c u r on t h e outmost compressing p r o c e s s . The breakage  new i n t e r f a c e s b u t a l s o  surface  pellet  problem which renders  o f p a r t i c l e s on t h e t o p s u r f a c e reveal  together  applies.  i n v a l i d i s the crushing surface  are p i l e d  of the p e l l e t  smear s o f t m a t e r i a l  t o t h e blockage  I f this  occurs,  examine  the  can n o t o n l y  t h e above  on t h e  of capillary assumption  cross  will  be  rate  of  invalid.  To penetration  possible  experiment was designed  breakage,  the  ( f o r d e t a i l see Chapters  7 and 8) , i n which two groups o f columns were made under exactly that  t h e same c o n d i t i o n s .  i f the breaking  fractional  The b a s i c  and smearing  idea  actions  f o r t h i s was  d i d occur, t h e  area o f pores on t h e t o p and bottom s u r f a c e s o f 127  the  pellet  should  be  smaller  than  that  on  any  cross  s e c t i o n a l s u r f a c e i n s i d e t h e column. The p e n e t r a t i o n r a t e o f a  liquid  into  t h e column  will  be  slower  because  existence of the t h i n layer i n h i b i t i n g the process. this to  i d e a , one group o f t h e columns was s p e c i a l l y remove  pellet  the t h i n  using  layer  abrasive.  on  t h e outmost  The p e n e t r a t i o n  of the Based on  processed  surface  rate  of the  should  become  h i g h e r f o r these columns i f t h e b r e a k i n g a c t i o n occur.  The  experimental  results  f o r t h e +1.8  Bullmoose c o a l a r e shown i n F i g u r e  f r a c t i o n of  6.8.1. The data  points  f o r t h e two groups o f columns have f a l l e n on t h e same This  i n d i c a t e s that the postulated breaking  line.  a c t i o n d i d not  happen.  To Microscopic surface  confirm  this  conclusion,  t h e Scanning E l e c t r o n  (SEM) i n s p e c t i o n was c a r r i e d out t o examine t h e  state  of  the  pellet  surface  under  different  magnifications.  The  SEM  photographs  are given  i n Figure  6.8.2. As  the m a g n i f i c a t i o n goes up, t h e g l o s s y p e l l e t s u r f a c e becomes more and more v i s i b l y porous. When t h e m a g n i f i c a t i o n reached above  3000, t h e p a c k i n g  state of p a r t i c l e s  become  clearly  visible.  I t can be seen from t h e photographs t h a t t h e c r u s h i n g 128  Test for fractional area of pores F i g u r e 6.8.1  on different cross sectional surfaces  Time (second) surface erased  +  surface not erased  014699  Figure  6.8.2(a)  £0KV  X30:0"i:00mm  SEM p h o t o g r a p h o f a p e l l e t  surface  m a g n i f i e d by 30 t i m e s .  The 1.4-1.5 d e n s i t y  fraction  pellet-making pressure  is  130  of Bullmoose  2 7 . 6 mPa  (4000  coal, psi)  Figure  6.8.2  (b)  SEM p h o t o g r a p h o f t h e  same p e l l e t  M a g n i f i e d by 2500 t i m e s  131  surface  action  has r a r e l y happened. Only  some p l a s t i c deformations  o c c u r r e d a t some s p o t s ; and t h e a s p e r i t y has been f l a t t e n e d . If  any c r u s h i n g  action  had happened,  a cluster  o f small  p a r t i c l e s p i l e d t o g e t h e r would be found i n t h e photographs.  132  6.9  A MODEL  6.9.1  A Compressed P e l l e t S u r f a c e Model  The  SEM  capillary  photographs  properties  compressed p e l l e t  shown  of  a  i n Figure  pellet  6.8.2  led to  a  and t h e model  of  s u r f a c e shown i n F i g u r e 6.9.1. There a r e  two domains on t h e model s u r f a c e : s o l i d and a i r p o r e s . Under the  pellet-making  particles between The  pressure  are c l o s e l y  squeezed  large particles  particles  as  will  high  as  together  be f i l l e d  on t h e outermost  protruding to  match  flat  plane.  pores.  they  are  magnified uneven,  pellet  surface  surface  can  thus  SEM  5  surface  be  small  microns.  photograph  the p e l l e t  i s very  on t h e p e l l e t  considered  as  a  o f two domains i . e . s o l i d and  Such domains a r e v e r y than  locally  account.  surface consisting  less  are  a t a p l a n e ; and some  i f t h e a i r c r a t e r s and pores d i s t r i b u t e d  The  ones.  of the p e l l e t  Thus t h e compressed  s u r f a c e a r e not taken i n t o  air  smaller  edges a r e p l a s t i c l y deformed o r crushed this  composite  MPa, a l l  and t h e c r e v i c e s with  surface  o r i e n t e d w i t h one s i d e o r edge touched  27.6  Although  the p e l l e t is still  flat. 133  (see F i g u r e 6.8.2), under  surface  highly  looks  macro-scopically  very very  Figure  6.9.1  A model of compressed p e l l e t  134  surface  The  distinction  between macroscopic and  microscopic  s t a t e s i s a r b i t r a r y . Good <1979> s e t the l i m i t o f macro i n a range o f mm.  r e s o l u t i o n of  The  scanning  l i n e s separated  by  electron microscopic  about 0.02  examinations  8.2.12) showed t h a t the s i z e s o f p a r t i c l e s and p e l l e t s u r f a c e are normally  s m a l l e r than 0.05  -  0.1  (Figure  a i r pores  mm.  on  Therefore,  the compressed p e l l e t s u r f a c e i s m a c r o s c o p i c a l l y homogeneous and  flat.  As by  two  i t i s known (Chapter  major  factors:  surface  roughness.  Therefore,  the p e l l e t  s u r f a c e can be  contact  angle  hysteresis;  both  could  while  and  and  surface  heterogeneity  of  i n v e s t i g a t e d by the examining the It  more  the  heterogeneity,  roughness  hysteresis.  heterogeneity  2), the h y s t e r e s i s i s caused  was  observed  significantly  surface  roughness  that  the  influence  the  exhibited  only  a  minor e f f e c t .  To first surface  test  the  effect  o f the  s u r f a c e roughness, i t was  isolated  from  heterogeneity  with  very  thin  a  wettability  of  monolayer  the  and  packing  nature  organic r a d i c a l s , atoms i n the  and  solid  layer coated  of  the  of  by  kerosene.  surfaces outmost  not by the nature  substrate  10  coating  t o 20  the  Because  i s determined surface  and  atoms  the by or  arrangements of  Angstroms below  s u r f a c e l a y e r <Zisman, 1964>, the p e l l e t ' s u r f a c e thus 135  pellet  the  coated  became  homogeneous  unchanged. affecting  The  and  i t s surface  surface  the contact  roughness  angle  roughness  became  remained  the only  factor  h y s t e r e s i s and c o u l d be  easily  detected.  The cotton  c o a t i n g was prepared  bed s a t u r a t e d  kerosene through  with  spontaneously capillary  kerosene. Upon t h e c o n t a c t , t h e  penetrates  effects  and  surface.  The  kerosene  and t h e p a r t i c l e s  coated  with  surface, angle  pores  a  then,  within  very  thin  becomes  measurement.  by p l a c i n g t h e p e l l e t on a  upward  eventually  the p e l l e t  layer  of  a  pellet  the  reaches  become  on t h e p e l l e t  homogeneous  Such  into  the top  filled  with  top surface are  kerosene.  The  i n respect  to  was  pellet  used  to  pellet contact  test  the  c o n t a c t angle h y s t e r e s i s .  The  observation  hysteresis very  showed  that  on a l l t h e kerosene-coated  small.  I t ranged  from  the  contact  pellet  angle  surfaces  was  3 t o 8 degrees. I n comparison,  the h y s t e r e s i s on t h e un-coated p e l l e t s u r f a c e s a l l exceeded 90  degrees.  hysteresis roughness  The  significant  values played  difference  confirmed an  that  insignificant  h y s t e r e s i s with heterogeneity  being  136  the role  between  the  pellet i n contact  t h e predominant  two  surface angle factor.  6.9.2  Contact Angle C o r r e c t i o n And  As  mentioned  significant contact  above, the  i n f l u e n c e on the  angle  on  contributions  a  of  Therefore,  the  surface heterogeneity  contact  contact  surface  components  surface  Figure  6.9.1,  proposed  measured  be  pellet  on  surface  a  composite  established.  Therefore,  1  where  a  and  a  2  s L  liquid; A liquid and  a pellet  air  surface  corrected.  model  proposed  configuration the  in this  will  Cassie-Baxter  = A  x  -  1  s L  a  2  /A •  = A /A' lg  i s the t o t a l area o f the s o l i d i n c o n t a c t w i t h l g  i s the  drop;  the  the  (2.1.10) can be r e a d i l y a p p l i e d  cose•= o -cosd  where A  The from  l i q u i d drop comes i n c o n t a c t w i t h  surface,  a  (see l i t e r a t u r e review 5.1.2).  angle  the  if a  model  undoutedly equation  to  results  (especially  (the apparent c o n t a c t angle) needs t o be  According  has  angle measurement.  heterogeneous  a l l the  pores) on the p e l l e t  Comparison  and  contact  the  f r e e l i q u i d - a i r i n t e r f a c e area under the  6*  and  angle  e  x  on  are the the  respectively. 137  measured c o n t a c t  solid  without  any  angle pores,  S i n c e the dimension of a i r pores on a p e l l e t is  extremely  the  small  ( l e s s than  free l i q u i d - a i r  neglected  and  10 m i c r o n s ) ,  i n t e r f a c e under the  c o n s i d e r e d t o be  surface  the curvature  liquid  drop can a  f l a t . Therefore,  of be  i s equal  2  t o the f r a c t i o n a l area o f pores o f the p e l l e t s u r f a c e . Under the  assumption made i n S e c t i o n  can  be  directly  obtained  6.8,  from  the  a)  i t (and  therefore  pellet  bulk  porosity  and  corrected  x  measurement.  In  Figure  c o n t a c t angles versus  ash  6.9.2,  both  the  measured  o f water on the L i n e Creek c o a l were p l o t t e d  content.  i n F i g u r e 6.6.2  The  contact  angle  versus  pressure  data  were a l s o c o r r e c t e d and r e - p l o t t e d i n F i g u r e  6.9.3.  In fractions pressure  Figure of of  correponding 6.7.1  and  the 27.6  6.9.2, the Line MPa  pellets  Creek  coal  for different were  (4000 p s i ) . The  made  the  same  p e l l e t p o r o s i t y value  t o each d e n s i t y f r a c t i o n can be read i n F i g u r e s  6.7.2.  In F i g u r e  6.9.3, the  pellets  o f the  -1.3  c o a l were m i l e a t d i f f e r e n t p r e s s u r e s ; and the pellet  p o r o s i t y values  can  observed,  be  at  density  are  obtained  from F i g u r e  d i r e c t l y measured decreases  from  L i n e Creek  corresponding  Figure  6.7.1. I t  6.9.2, t h a t the c o n t a c t  noticeably with 138  angle  i n c r e a s e of  the  pellet-making  pressure.  Apparently,  this  is  due  to  the  e f f e c t s o f both a i r pores and s u r f a c e roughness.  The  corrected  value  of  changes o n l y a t low p r e s s u r e s pressures,  the  a t low p r e s s u r e , very  rapidly  Once  the  pressure  however, At  higher  angle v a l u e s do not  change  i s further increased. This indicates that, the s u r f a c e roughness o f a p e l l e t decreases  with  increase  pressure  reaches  20.7  MPa,  change  the  pellet  does  angle,  ( l e s s than 14 MPa).  corrected contact  when the p r e s s u r e  contact  not  i n the  pellet-making further  pressure.  increase  surface  of  roughness  notably.  For on  the  comparison,  polished  chunks o f L i n e were p o l i s h e d  the  surface  contact of  Line  angle  was  Creek  coal.  Creek c o a l were s e l e c t e d , and on  these  large p a r t i c l e s .  The  a l s o measured Some  flat  surfaces  contact  v a l u e s measured on these s u r f a c e s are shown below  Contact  angles measured on p o l i s h e d  L i n e Creek c o a l s u r f a c e  77.4  76.5  78.0  78.3  76.3  79.5  Average:  74.8  76.9  139  77.5  (degree)  78.4  73.2  large  75.9  angle  CONTACT ANGLE vs ASH CONTENT OF LC COAL 130 - i  Figure 6.9.2  0  both the measured and the corrected —  2  0  -  4  0  Ash content (%) MEASURED ANGLE  +  CORRECTED ANGLE  60  80  CONTACT ANGLE vs.PELLET-MAKING PRESSURE 140  F i g u r e 6.9.3  Line Creek coal-1.3 density fraction  -i  H  80  2  1  1  6  —  1  1  10  1  1  14  1  1  1  18  1  1  22  Pressure MPa •  Measured angle  +  Corrected angle  1  26  1  1  30  i  r 34  The  average  angle  value  on  polished  coal  surface  76.9  degrees.  According  t o the r e s u l t s  shown i n F i g u r e  6.9.3, t h e  apparent c o n t a c t angle on t h e p e l l e t s u r f a c e o f -1.3 d e n s i t y f r a c t i o n o f L i n e Creek c o a l i s as l a r g e as 107 degree. While the  corresponding  still  greater  surface.  corrected contact  than  I t should  chunk was  randomly  t h e angle be  value  angle  measured  remembered t h a t  selected  from  i s 84.2 which i s on  polished  the polished  t h e sample.  I t may  coal be a  m i x t u r e o f t h e d i f f e r e n t d e n s i t y f r a c t i o n s . On average, i t s density  i s greater  than  1.3  g/cm . 3  Therefore  the contact  angle on t h e p o l i s h e d c o a l chuck i s lower than t h e c o r r e c t e d angle on t h e p e l l e t s u r f a c e o f -1.3 d e n s i t y  142  fraction.  6.10  SUMMARY AND  DISCUSSIONS  The c o n t a c t angle on f i n e c o a l p a r t i c l e s was in  this  0.3  project  t o 0.5  An  cm  by  making p e l l e t s  cm  i n diameter  and  (6.9 t o 28  MPa)  i n h e i g h t under h i g h p r e s s u r e  artificial  s u r f a c e formed on  the p e l l e t was  accommodate  liquid  sessile  drop  angle.  pellet  surface  was  The  2.54  and  measured  measure  u t i l i z e d to the  macroscopically  contact flat  and  glossy.  The  contact  angles  were  measured  in  two  different  ways, e i t h e r d i r e c t l y through the goniometer by c o n s t r u c t i n g a  tangent  contact  to  point,  goniometer drop  the  sessile  or with  telescope  profile.  The  drop  the  to  profile  use  take  standard  of  a  at  camera  d e v i a t i o n of  digitizer. calculated Rotenberg, The  profile According by et  to  using  on  the  these a  of  data,  this  of  the  the  Boruvka,  and  method  was  to  the  sessile  angle  values  degrees.  were  contact  program  phase  the  t o 3.71  photograph  computer  al.<Rotenberg,  reproducibility  standard  data  three  attached  photograph  measured on the p e l l e t s ranged from 2.06  The  the  taken  by  angle  was  developed  by  Neumann, high  1983>.  with  the  d e v i a t i o n of the measured angle v a l u e s b e i n g ±0.32  degrees.  143  Because  o f the  roughness,  the  different.  While  reflects  the  effect  angles  measured  the  value  contact  o f h e t e r o g e n e i t y and by  the  o b t a i n e d by  angle o f water  on  surface  two  methods  the  first  were  method  the higher  energy  s u r f a c e a r e a , the v a l u e o b t a i n e d by the second method i s the weighed average o f the angle v a l u e s on a l l the components o f the  heterogeneous  The  surface.  effect  o f the s e s s i l e drop s i z e on the advancing  c o n t a c t angle was size  was  first,  increased  a  syringe  drop  To  followed larger  of  in  lowered  the  to  another  by  In  procedures. formed  with  the  on  the  drop  size,  the  whole  sessile  procedure,  addition  of  the  set  the  of  sessile  drop  drop  the  micro-  same procedure  independent  second  incremental  the  drop  In  on the p e l l e t s u r f a c e as a f r e e  increase form  different  volume was  i t was  rested  size.  enlarged  two  preset  t i p . Then  s y r i n g e and drop.  a l s o t e s t e d i n the p r e s e n t work. The  was with  size  was  to  the  liquid  p r e v i o u s s e s s i l e drop.  The following the  results the  first  show  that  procedure  s i z e o f the drop.. A f t e r  certain angle  v a l u e , the drop changes  phenomenon  only  the  increases  angle  measured  continuously  with  the drop s i z e i s i n c r e a s e d t o a  size  randomly  i s attributed  contact  to  effect  d i m i n i s h e s and  around  a  the  a r i s i n g from the s u r f a c e roughness. 144  certain  contact  angle  contact  value.  This  hysteresis  I n the second procedure, the c o n t a c t angle d e c r e a s e s w i t h the drop resulting surface  i n a V-shaped roughness,  increasing  the  drop  size,  but then s t a r t s  initially  to  increase  curve. The g r a v i t a t i o n a l f o r c e , the  and  kinetic  size  by  energy  introduced  incremental a d d i t i o n  when  play  the  major r o l e s i n the p r o c e s s .  At  the  b e g i n n i n g when  sessile  drop  size  is  small,  each a d d i t i o n o f the i n c r e m e n t a l drop i n c r e a s e s t h e drop h e i g h t s u b s t a n t i a l l y . The g r a v i t a t i o n a l  sessile  f o r c e tends t o  push the s e s s i l e drop downwards. The k i n e t i c energy which i s l a r g e r e l a t i v e l y t o the energy b a r r i e r h e l p s the t h r e e phase c o n t a c t l i n e t o overcome the energy b a r r i e r and expand. Thus the s e s s i l e drop assumes a lower v a l u e o f the c o n t a c t a n g l e . F u r t h e r i n c r e a s e i n the drop s i z e o n l y makes the drop horizontally. energy  The  effect  diminishes,  predominant. the drop  of g r a v i t a t i o n a l  and  the  surface  f o r c e and roughness  the s e s s i l e  drop  and  s t a b l e even a f t e r s e v e r a l hours they  are  becomes  size.  t e s t e d v e r s u s time. For lower d e n s i t y f r a c t i o n s  1.4-1.5),  kinetic  In t h i s range, the c o n t a c t angle i n c r e a s e s w i t h  The c o n t a c t angle o f water on the c o a l p e l l e t was  expand  not  stable  on  the c o n t a c t  surface (-1.3  to  angle a r e v e r y  (see F i g u r e 6.5.1). However,  higher density  fractions  of  coal  (1.5-1.6 t o +1.8). Because the c o n t a c t angle on h i g h e r c o a l 145  density  fractions  i s small,  the  water  drop  starts  to  p e n e t r a t e i n t o t h e p e l l e t d u r i n g t h e experiment.  Although  the  pellet  surface  was  glossy  and  flat  v i s u a l l y , t h e p e l l e t i s a c t u a l l y v e r y porous both i n s i d e and on i t s s u r f a c e . The p o r o s i t y o f t h e p e l l e t i s r e p r e s e n t e d by the v a l u e  of the p e l l e t  b u l k p o r o s i t y . The p e l l e t p o r o s i t y  i s composed o f two p a r t s : i n t r a - p a r t i c l e p o r o s i t y and i n t e r particle porosity higher  porosity. inside  The  intra-particle  an i n d i v i d u a l  f o r lower  porosity  coal particle.  i s the  I t s value i s  c o a l d e n s i t y f r a c t i o n s and becomes s m a l l e r  for higher density fractions.  The i n t e r - p a r t i c l e p o r o s i t y i s  t h e space between p a r t i c l e s .  The p e l l e t - m a k i n g p r e s s u r e has  a  major  effect  on t h e i n t e r - p a r t i c l e  porosity; the i n t e r -  p a r t i c l e p o r o s i t y decreases when t h e p r e s s u r e i s i n c r e a s e d .  With  t h e use o f t h e data  E l e c t r o n Microscope  a pellet  orient  deformation surface  is  distributed  Under  themselves  t o match very  Scanning  o r experience Thus  provided  some l o c a l  plastic  t h e compressed that  the  air  pellet pores  on t h e p e l l e t s u r f a c e a r e n e g l e c t e d .  t h e Scanning  s u r f a c e was found and  a  on t h e outmost s u r f a c e o f t h e  a plane.  flat,  from  s u r f a c e model was proposed. In  the model, t h e c o a l p a r t i c l e s pellet  obtained  E l e c t r o n Microscope,  the p e l l e t  t o c o n s i s t o f two major components:  a i r . The d i r e c t l y measured c o n t a c t angle 146  solid  (the apparent  contact  angle)  wettability pellet  of  results both  surface  from  components.  model,  a  C a s s i e - B a x t e r e q u a t i o n was air  component on  apparent solid  contact  the  the  to  the  procedure  the  proposed applying  employed t o c o r r e c t the e f f e c t of  c o n t a c t angle v a l u e and  angle  from  into  the  real  contact  transform angle  on  the the  alone.  degree on  a  coal.  contact  more  According  correction  The c o r r e c t e d angle v a l u e  the  contributions  The  -1.3  g/cm"  3  angle  density  fraction  measured on  c o a l chunk was  about 76  comparable  the  and  ( r e a l angle value) was  difference  147  Bullmoose  a polished surface  degrees.  acceptable.  of the  84.2  These two seems  to  values be  of are  quite  CHAPTER 7  THE RATE OF PENETRATION TECHNIQUE  7.1  INTRODUCTION  From  a more p r a c t i c a l  point  hydrophobicity/hydrophilicity  o f view,  through  the  assessment study  of  of the  w e t t i n g c h a r a c t e r i s t i c s o f a mass o f p a r t i c l e s may p r o v i d e a more r e a l i s t i c technological only  correlation  w i t h t h e performance  p r o c e s s e s . C o a l i s a heterogeneous  i t s overall  composition can r e f l e c t be  must  penetration  i s one o f such measurement. Many  derived theoretical  into  with  account.  interfacial  the v e l o c i t y  parameters  rate  methods have t h e advantage  over t h e o p t i c a l  angle measurement) i n t h a t  obtained  for a  large  number  polished  and a r e not contaminated  of  authors have <Bruil  of the r i s i n g  such as c o n t a c t a n g l e s .  measurements o f c o n t a c t angles by such  contact  The  and s e m i - e m p i r i c a l r e l a t i o n s h i p s  Good, 1979> t o i n t e r r e l a t e  liquid The  taken  material,  i t s behaviour and,  therefore,  and  of various  capillary method  rise  (direct  i t g i v e s a "mean" v a l u e  of p a r t i c l e s from  which  a r e not  t h e a b r a s i v e agent  used i n t h e p o l i s h i n g .  Compression  o f powder i n t o 148  a pellet,  on t h e o t h e r  hand, can r a i s e the p o r o s i t y problem. When the c o n t a c t on t h e compressed p e l l e t  surface  angle  i s much s m a l l e r than 90°,  p e n e t r a t i o n o f t h e l i q u i d i n t o the p e l l e t i s s i g n i f i c a n t and sessile  drop  established. angle al.  equilibrium  Under  technique  such  can  not  conditions,  is likely  the  consequently  dynamic  contact  t o be more r e l i a b l e <Crawford e t  1987>.  As one o f t h e dynamic c o n t a c t rate  of  penetration  method  shows  been  employed  extensively.  angle  techniques,  considerable  However, i n s p i t e o f t h e s i m p l i c i t y not  be  promise.  o f t h i s method,  The  publications  i t has on  this  method a r e r e l a t i v e l y few compared w i t h d i r e c t c o n t a c t measurements  on  t h e r a t e o f p e n e t r a t i o n technique  the unopposed  penetration  compressed column o f powder, technique the  i s needed  constant;  method times  the density  studied.  of a  liquid  and i s regarded  to  influence and  calibrate of  many  particle  size  the  as a  column  factors has  such  not been  I n a d d i t i o n , major problems a s s o c i a t e d  a r e i n c o m p a r a b i l i t y of r e s u l t s o b t a i n e d by  different  persons  is  through  a  relative  f o r t h a t a l i q u i d w i t h a known c o n t a c t angle  solid  packing  angle  over the p a s t decade.  Conventionally, based  the  with  tortuosity as  column  carefully with  this  at different  o r i g i n a t i n g from t h e f a c t  that  the columns were packed by manual t a p p i n g . The e f f e c t o f the difference  i n w e t t a b i l i t y between 149  t h e powder m a t e r i a l  and  the  wall  of holding  penetration  column  which  can a f f e c t  f r o n t and make t h e a c c u r a t e  t h e column  penetration  front  measurement d i f f i c u l t has n o t been e v a l u a t e d e i t h e r .  In t h e p r e s e n t penetration  method  High p r e s s u r e s  work, a new approach f o r t h e r a t e o f  i s studied  t o overcome these  (up t o 27.6 MPa) were a p p l i e d and p r e c i s e l y  c o n t r o l l e d t o produce c l o s e l y compacted column strong t o withstand  In  problems.  handling  sufficiently  and f a c i l i t a t e t h e experiment.  a d d i t i o n , a new approach t o c a l i b r a t e  t h e column  t o r t u o s i t y c o n s t a n t was i n t r o d u c e d i n t h e p r e s e n t work. T h i s new approach may make t h e r a t e o f p e n e t r a t i o n method from a r e l a t i v e technique a  zero  contact  t o a a b s o l u t e one, s i n c e t h e l i q u i d s  angle  on a l l t h e t e s t e d  r e q u i r e d any more.  150  solid  with  may n o t be  7.2  THEORY AND TECHNIQUES  7.2.1  B a s i c Theory  The  capillary  driving  force  for a  liquid  in a  c y l i n d r i c a l tube o f r a d i u s r i s  AP = 2 7 - c o s 0 / r  7.2.1  lv  where  AP  is  interface,  71 v  the  LaPlace  pressure  across  the  curved  i s t h e l i q u i d s u r f a c e t e n s i o n , and 6 a r e t h e  l i q u i d c o n t a c t angle on t h e c a p i l l a r y .  One  application  of t h i s  theory  i s t o measure t h e  p r e s s u r e , P , necessary t o balance t h e L a P l a c e p r e s s u r e , AP, 1  which d r i v e s t h e l i q u i d  i n t o a c a p i l l a r y bed <White, 1982>;  the c o n t a c t angle can then be c a l c u l a t e d u s i n g Eq.5.2.1.  Washburn <1921> combined t h e c a p i l l a r y d r i v i n g f o r c e for  a cylindrical  Poisseulle steady  equation  tube  of radius  f o r viscous  r  (Eq. 5.2.1) w i t h t h e  drag  under  conditions of  flow  8 • h / r • dh/dt = AP 2  M  151  7.2.2  where  M  i s viscosity  penetration  i n time  of  the  fluid,  t, r capillary  h  the  length  of  r a d i u s , AP t h e p r e s s u r e  drop and o b t a i n e d  r  271V•cose  2  d(h )/dt =  (  2  Apgh)  7.2.3  r  4M  where Ap i s t h e d i f f e r e n c e i n d e n s i t y between t h e l i q u i d and the s u r r o u n d i n g medium, g t h e g r a v i t a t i o n a l a c c e l e r a t i o n , 6 contact angle.  If length  the c a p i l l a r y  i s small,  i s horizontal  t h e term  Apqh  or the penetration  i n equation  above  can be  n e g l e c t e d , and one can o b t a i n :  r-7 •cose l v  d(h )/dt=  7.2.4  2  2M  The a p p l i c a b i l i t y o f t h i s e q u a t i o n t o a powder column has  been  <1967>  theoretically  and S z e k e l y  radii  by  Crowl  and Wooldridge  e t a l . <1971>. I n t h e case  column, t h e c a p i l l a r i e s their  justified  inside  are not constant  o f a powder  t h e column a r e t o r t u o u s and and v a r y  from  point to point  w i t h i n t h e column. The o v e r a l l column p e n e t r a t i o n p r o c e s s i s an  average  on a l l these  individual  r a t e d ( h ) / d t must correspond 2  process.  t o an average  The  value of r " i n  the p l a c e o f r i n Eq.5.2.4. T h e r e f o r e a t o r t u o s i t y 152  observed  constant  K was  introduced  i n p l a c e o f r <Ely and  Pepper, 1944>,  and  Eq.5.2.4 becomes  d(h )/dt =  K-  • cose  7 l v  7.2.5  2  The  t o r t u o s i t y c o n s t a n t K i s a h y p o t h e t i c a l mean r a d i u s . T h e o r e t i c a l l y , the a d s o r p t i o n of some f l u i d molecules  can  take  place  onto  the  shown t h a t <Good, 1973,  column p a r t i c l e  Good and  surfaces.  L i n , 1976  and  i f a porous body i s i n i t i a l l y d e v o i d o f any the  liquid  fluid rate  are by  faster  that not  penetrate  transported  diffusion, than  i t , and  then  ahead the  rate  t h a t p r e d i c t e d by  the of  was  White, 1982>  adsorbed f i l m  i f the  of  It  molecules of liquid  at  penetration  Washburn e q u a t i o n  a  of the  rapid  will  because  be of  the s p r e a d i n g p r e s s u r e . That i s  r  7  l  v  • cose/2/i  where n  g  < d(h )/dt < r ( 7  i s the  cose  2  l  v  e q u i l i b r i u m spreading  + jr  e  -  7r )/2/i  pressure,  7.2.6  0  and  n  0  the  s p r e a d i n g p r e s s u r e a t zero time  w  e  *o  The  =  7  = 7  7 v  _  S  S  S  "  7  S  (t=0)  major drawback of a p p l y i n g the Washburn 153  7.2.7  7.2.8  equation  t o t h e powder column i s t h a t t h e r e has been no d i r e c t means t o o b t a i n t h e v a l u e o f t o r t u o s i t y constant K. U s i n g equation,  White<1982>  defining  the  obtained  effective  column by thermodynamic  a  radius  of  Laplace  quantitative the  equation  compressed  powder  derivation  r  =  e  2(P/(l-(P)/9*  7.2.9  where <P i s t h e column p o r o s i t y , p i s t h e mass d e n s i t y o f t h e powder i n t h e column, and * i s t h e s p e c i f i c per  gram.  vertical of  I f the  porous  capillaries p,  density  column  of radius r  one  can  e  area o f powder  consists  of  identical  through a s o l i d  substrate  derive  the  same  f o r the P o i s e u l l e  drag  on  relationship  geometrically.  However, liquid  in  compressed  validity  of  tested.  Once  compressed  Eq.7.2.9  powder for r  could  the  i n Eq.7.2.2  e  the a p p l i c a t i o n  column  column,  hydrodynamic  has  o f Eq.7.2.9  be  t h e permeating  never  been  t o Eq.7.2.2 f o r  justified,  the  tortuosity  c o n s t a n t K i n Eq.7.2.5 c o u l d c o n v e n i e n t l y be c a l c u l a t e d from Eq.7.2.9.  I n t h e common a p p l i c a t i o n o f t h e Washburn the  tortuosity  constant  K was  which t h e same measurement w i t h have  zero  contact  angle  is 154  obtained  by  a liquid taken,  equation,  calibration i n  t h a t i s known t o  assuming  the  pore  s t r u c t u r e and the  runs  the  with  penetration  penetration  different  value  and  process  liquids.  cosO=l  t o be The  inserted  the  same as  measured  in  rate  i n t o Eq.7.2.4  of  allow  the K t o be c a l c u l a t e d .  7.2.2  Techniques  In  a c t u a l a p p l i c a t i o n o f the  Washburn equation  to  porous column, a known weight of the d r i e d powder was in  a 0.8  cm  diameter g l a s s tube w i t h an a t t a c h e d  c o n s o l i d a t e d by manual t a p p i n g . was  lower end  placed  scale,  o f the  and  column  supported on a s m a l l p l u g o f c o t t o n wool covered w i t h  d i s c of f i l t e r was  The  a  dipped  paper. The  into  a  dish  packed tube c o n t a i n i n g the powder of  the  corresponding  penetrating  t e c h n i q u e has  been used w i t h  1946>,  carbon  blacks  a  liquid  height  and  are  the  time  recorded.  g l a s s powder <Ely and  <Studerbaker  and  Snow,  and This  Pepper,  1955>,  and  pigments <Crowl and Wooldridge, 1967>.  It data  in  was  studies  statistical the  observed<Good of  this  scatter. A  non-uniformity  of  kind  major the  change i n s t r u c t u r e o f the and  and  Lin,  1976>  generally reasons  column  exhibit a  for this  packing  packed bed  that  with  the  serious  scatter  density  rate  and  are the  wetting<Neumann  Good, 1979>. Another drawback o f t h i s t e c h n i q u e i s the  difficulties  associated  with 155  obtaining  the  tortuosity  constant  K  in  calibration  the  Washburn  method,  equation.  i t is difficult  In  to  the  find  traditional a  particular  l i q u i d which should have zero c o n t a c t angle on the s o l i d be  tested.  applicable quartz  This to  etc.  requirement  a  limited  Since  has  number o f  for  made  the  specific  majority  of  method  only  materials  solids,  it  to  like  is  an  i m p o s s i b l e t a s k t o f i n d such a l i q u i d .  To  overcome  above  mentioned  problems,  in  the  m o d i f i c a t i o n d i s c u s s e d i n t h i s work, the h y d r a u l i c mounting press  to  make more c l o s e l y  controlled  higher  packed  pressures  was  made were much more uniform reproducibility t e c h n i q u e was  In  and  substantially  the  of  the  rate  columns  of  penetration  improved.  tortuosity  been  brought  constant under  K  control  in  equation  modified  technique,  and  has  been c a l c u l a t e d  w i t h the  c o n t a c t angle.  The  o l d c a l i b r a t i o n method was  used any  more and  The  thus  s t r u c t u r e . The  Washburn  exist.  has  employed. The  in i t s interior  accuracy  addition,  column under a c c u r a t e l y  in  discussion w i l l  following sections.  156  be  the  simultaneously  the problems a s s o c i a t e d w i t h i t ceased  detailed  the  presented  in  not to the  7.3  EXPERIMENTAL  7.3.1  Materials  The  materials  tested  and  the  initial  sample  p r e p a r a t i o n procedure f o r t h e r a t e o f p e n e t r a t i o n method a r e the  same as t h a t  The  same  contact  i n the d i r e c t  pulverized angle  coal  contact  samples  measurements  angle measurements.  as used  were  again  i n the d i r e c t  utilized  in  this  kerosene  and  section.  The water.  penetration  The  deodorized  liquids  used  kerosene  include  used  was  the product  of  J.T.Baker Chemical Co., P h i l l i p s b u r g , NJ. The i m p l i c a t i o n t o use  kerosene  addition  as t h e major  t o i t s lower  penetration  hazardous  degree  chemicals,  i t i s e x t e n s i v e l y used  flotation  as  importantly, of  by  lyophicity  effective  of d i f f e r e n t  kerosene. towards  flotation  The  coal  compared  cheap  when  collector.  157  t o other  collector.  coal More  i s a q u a n t i t a t i v e measure f r a c t i o n s of coal fractions  kerosene c o u l d be f l o a t e d  processes  i s that, i n  i n t h e contemporary  and  rate of penetration  the c a p a b i l i t y  wetted  real  an  liquid  kerosene  having  t o be higher  b e t t e r i n the  i s utilized  as a  7.3.2  Column-Making  A MET-A-TEST mounting p r e s s was column under h i g h p r e s s u r e s The  ranging  column made i n such a way  experimental  employed t o make the  from  3.4  to  20.7  MPa.  i s s t r o n g enough t o w i t h s t a n d  h a n d l i n g without  the  h o l d i n g g l a s s tube;  the p a c k i n g d e n s i t y can be a c c u r a t e l y c o n t r o l l e d and  and  easily  varied.  A s e r i e s of c o a l powder samples r a n g i n g from  3 to  grams were weighed. They were i n d i v i d u a l l y put i n t o the  15 MET-  A-TEST mounting p r e s s mould which was  c a r e f u l l y cleaned with  degreased  close  cotton.  cylindrical pumping  cover,  the  started.  The  the  the t i m e r was  the  upper and was  pressing  to  pressing  pressure  drops  packed  of  s e t f o r f i v e minutes,  hydraulic  p r e s s i n g p e r i o d due closely  Following  pre-set  pressure  slowly  during  the  t o the squeezing o f p a r t i c l e s t o a more  configurations.  This  may  need  frequent  adj ustment.  7.3.3  Rate of P e n e t r a t i o n Measurement  For  each  columns w i t h were  made  columns  different  under  with  coal  sample,  a  weights  ranging  e x a c t l y the  different  same  heights 158  group  of  four  from  3 to  c o n d i t i o n s so  but  the  same  to  eight  12  grams  that  the  properties  (packing d e n s i t y ) were o b t a i n e d as shown i n F i g u r e 7.3.1.  The ranging  column  from  5  diameter  to  25  was  mm,  were  25.4  mm.  accurately  v e r n i e r gauge w i t h p r e c i s i o n of ±0.025  A and mm  porous  fitted  bed  made of  and  heading  penetration  upward  illumination  can  was  surface that liquid  end  area  line  be  along  required.  The  i s , the  a c c u r a t e l y measured  the No  liquid  to  flow  through  same procedure  was  number o f  points  data  height the  equal  visible  cylindrical  wall  additional  strong  would  slowly  flow  top.  each column, versus  the  one  time  whole column was  repeated  bed;  s e l e c t e d when h a l f o f the  wetted. For  column  40  penetration  started. A clearly  observed.  o f t i m i n g was  was  prepared  i n h e i g h t and  through the column and e v e n t u a l l y reach the  The  using  v e r t i c a l l y r e s t e d g e n t l y on the  a t the same time, t i m i n g was  horizontal  was  saturated with  column, a f t e r i t s h e i g h t was  w i t h v e r n i e r gauge, was  measured  cotton  i n t o a s m a l l c o n t a i n e r o f 10 mm  l i q u i d . The  heights,  mm.  degreased  i n diameter; then the bed was  Their  for to  other the  data  top  point,  required  for  recorded.  The  columns.  Finally  a  number o f columns were  a c q u i r e d . I t should be emphasized t h a t these columns, though having  different  heights,  must  be  made under  exactly  the  same c o n d i t i o n s ( i . e . same p r e s s u r e ) . For each data p o i n t , a straight  line  connecting  this 159  point  and  original  of  H2  F i g u r e 7.3.1  The columns made f o r t h e r a t e penetration  test  160  of  versus  T  coordinate  measurement be  i n comparison  considered  l i n e s thus  could  be  Therefore  each  t o t h e c o n v e n t i o n a l method  could  as an i n d i v i d u a l l y  drawn.  repeated  r u n because t h e  o b t a i n e d were f o r d i f f e r e n t columns. A f t e r  p o i n t s were r e g r e s s e d ,  the l i n e a r i t y  these  of the regressed  line  c o u l d be c o n s i d e r e d a r e p r e s e n t a t i o n o f t h e r e p r o d u c i b i l i t y f o r t h e experiment.  Columns must be made a t a minimum o f two d i f f e r e n t pressures  because t h e r a t e o f p e n e t r a t i o n from t h e columns  made under d i f f e r e n t p r e s s u r e s were e s s e n t i a l p a r t s o f t h i s technique  7.3.4  i n the c a l c u l a t i o n of contact angles.  V i s c o s i t y and S u r f a c e  The viscosity  Ostwald of l i q u i d .  Tension  viscometer According  g i v e n volume V o f t h e l i q u i d tube  under  was  the influence  used  to  t o t h e time  through  measure o f flow  a vertical  of gravity,  the of a  capillary  the v i s c o s i t y  was  c a l c u l a t e d by P o i s e u l l e ' s law i n t h e form  Tr«(Pi-P )  dV  2  =  7.3.1  dt  8/iL  where dV/dt i s t h e r a t e o f l i q u i d flow through  a cylindrical  tube o f r a d i u s r and l e n g t h L and (P1-P2) i s t h e d i f f e r e n c e 161  in  p r e s s u r e between t h e two ends o f t h e tube. In p r a c t i c e ,  above e q u a t i o n , a t c o n s t a n t temperature, i s s i m p l i f i e d g i v e n t o t a l volume o f l i q u i d and a g i v e n c y l i n d r i c a l  fi/p  fora tube  = Bt  7.3.2  where t i s t h e time r e q u i r e d f o r t h e upper meniscus t o f a l l from  t h e upper  t o t h e lower  apparatus c o n s t a n t which  i s determined  w i t h a l i q u i d o f known v i s c o s i t y The  liquid  fiducial  surface  162  and B  through  i s an  calibration  (e.g. w a t e r ) .  tension  Cenco-du Nouy Tensiometer.  mark  was  measured  using  a  CHAPTER 8  RESULTS AND DISCUSSIONS <II>  8.1  APPLICABILITY TEST  The column  conventional  i s by manually  method  tapping  of  making  a  penetration  t h e t e s t e d powder h e l d i n a  g l a s s tube i n t o a column<Crowl and Wooldridge, 1967, Szekely et  a l . , 1971, B r u i l  1976>. Very  and van A a r t s e n ,  low p r e s s u r e s  1973, Good  (below 3.5 MPa) were  and L i n ,  e x e r t e d on  t h e powdered m a t e r i a l w i t h i n t h e h o l d i n g g l a s s tube tapping.  Whether  t h e Washburn  equation  is still  during  applicable  t o t h e columns made under v e r y h i g h p r e s s u r e s up t o 27.6 MPa has  n o t been t e s t e d . I n t h i s  section, the a p p l i c a b i l i t y of  the Washburn e q u a t i o n has been f i r s t  8.1.1  verified.  Some Features  Some p r e l i m i n a r y o b s e r v a t i o n s the  features  and behaviour  were  of the l i q u i d  columns compacted under h i g h p r e s s u r e . in  the p e n e t r a t i o n process  lines  were  clearly  made t o examine penetrating  into  Because t h e columns  were unwrapped, t h e p e n e t r a t i n g  observable. 163  The  periphery  of the  penetrating  front  surface  was  apparently  within  a  well  defined h o r i z o n t a l plane.  The also  penetration  examined. S i n c e  i n the i n t e r i o r  o f t h e columns  t h e column diameter i s 25.4 mm  and i s  much g r e a t e r than diameter o f a c o n v e n t i o n a l one (8 mm), crosswise  penetration  manifested.  Observing  difference could from  the  be more p e r c e p t i b l y  t h e top s u r f a c e  one c o u l d f i n d t h a t the w e t t i n g  was  o f t h e column,  front surface, a f t e r c e r t a i n  time o f p e n e t r a t i o n , would not reach the t o p s u r f a c e o f the column a l l over a t t h e same time; i n s t e a d , i t emerges  in a  local  non-  flat  area  first  penetration  surface  emerges  concentrically  and q u i c k l y spreads.  This  f r o n t s u r f a c e . Sometimes from  t h e c e n t r a l area  implies  the wetting  and  spreads  observed  Occasionally,  front  outward  which i n d i c a t e s a dome shaped w e t t i n g  w i t h i n t h e column; on t h e o t h e r hand t h e w e t t i n g also  a  to  emerge  the w e t t i n g  p e r i p h e r a l l y and f r o n t may  start  front  f r o n t was  spread  inward.  from one s i d e o f  the t o p s u r f a c e o f t h e column and f i n i s h e d a t another, which means a t i l t e d w e t t i n g f r o n t .  The magnitude o f the l a t i t u d e d i f f e r e n c e s between the highest  point  surface  i s not o n l y  the  column  numerical  and t h e lowest  interior index  one  a matter  of probing  penetration  indicating  on t h e p e n e t r a t i o n  the  the uniformity of  behaviour,  but  also  precision of  the  method.  These d e t a i l s w i l l be d i s c u s s e d i n the next s e c t i o n . 164  front  a  Other possible  features  swelling  penetrating  concerning  of  liquid;  the  columns  t h e lowest  p o s s i b l e breakage o f p a r t i c l e s these  v a r i a b l e s were  tested  the  method  after  applicable  are: the  soaking  with  pressure;  and  i n the pressing process. A l l  and w i l l  be d i s c u s s e d  i n the  following sections.  One o f t h e advantages o f t h i s  technique i s that the  t o t a l s u r f a c e area p e n e t r a t e d  by l i q u i d w i t h i n a u n i t h e i g h t  of  than  column  i s much  method. T h e r e f o r e In  greater  that  in a  i t i s more s t a t i s t i c a l l y  addition, the t o t a l height  cm. Thus t h e p e n e t r a t i o n process  8.1.2  representative.  can be lowered t o a range o f  0.5 t o 2 cm compared w i t h t h e c o n v e n t i o n a l  l e s s extent,  conventional  range o f 4 t o 10  c o u l d be s u b j e c t , t o a much  t o the e f f e c t of g r a v i t a t i o n a l force.  P r e c i s i o n and L i n e a r i t y  Since  i t i s more  difficult  t o measure  accurately  p e n e t r a t i o n d i s t a n c e s on s h o r t columns, a d i f f e r e n t approach as  described  i n section  7.3  was  employed.  v e r n i e r c o u l d reach a b s o l u t e accuracy undoubtedly q u i t e  The use o f a  o f ±0.0025 cm which i s  sufficient.  However, another aspect which a f f e c t s t h e accuracy i s the  estimation  o f ending  time 165  point  which  was taken  when  half  of the top surface  the  liquid  only  wetting  area  front  t h e judgement  o f t h e column was wetted. I f  zigzagged  o f t h e ending  a l s o t h e method i t s e l f  up and s e r i o u s l y , not time  o f p e n e t r a t i o n but  i s questionable.  In o r d e r t o answer these q u e s t i o n s , t h e time when t h e wetting  f r o n t s t a r t s t o emerge from t h e t o p s u r f a c e , and t h e  time when t h e whole t o p s u r f a c e was wetted, were measured. From  the  altitude point)  time  span,  difference  the  ruggedness  between  o f t h e imaginary  (i.e.  the  maximum  and  the  highest  t h e lowest  penetration  f r o n t s u r f a c e c o u l d be  calculated.  The  experiment was conducted on t h e 1.4-1.5 d e n s i t y  f r a c t i o n o f t h e Bullmoose c o a l . F i v e columns w i t h heights  were made  experiment. T  i n s e r i e s and kerosene was used  x  i s t h e time f o r t h e whole t o p s u r f a c e o f t h e  column t o be wetted. The p e n e t r a t i o n to T  1  i n the  i s t h e time a f t e r which t h e p e n e t r a t i n g f r o n t  0  emerges; and T  different  would be t h e a l t i t u d e  distance  from time T  0  d i f f e r e n c e between t h e h i g h e s t  p o i n t and lowest p o i n t on t h e p e n e t r a t i o n f r o n t s u r f a c e . The magnitude o f t h i s d i s t a n c e i s a numerical  representation of  the ruggedness o f t h e p e n e t r a t i o n f r o n t s u r f a c e .  The  middle  point  between  T  0  and T , i n t h e a c t u a l x  measurement, was taken as t h e ending p o i n t o f p e n e t r a t i o n , T.  The  T  values  and  corresponding 166  column  heights  Were  tabulated was  (Table 8.1.1). The  0  versus  2  T regression  result  shown i n the lower p a r t o f the t a b l e . A c c o r d i n g t o  regression T  H  to T  equation,  the  this  p e n e t r a t i o n d i s t a n c e between  time  c o u l d be c a l c u l a t e d . Here  x  H so  = 0.625T  2  Ruggedness = H(T )  - H(T )  X  8.1.1  0  = 7(0.625-1! ) - J (0.625-T ) 0  The ruggedness i s d e f i n e d as the maximum a l t i t u d e d i f f e r e n c e on  the  penetration  front  surfaces.  The  ruggedness  shown i n T a b l e 8.1.1, are i n the range from 0.18  results  t o 0.6  mm.  T h i s i n d i c a t e s t h a t the p e n e t r a t i o n f r o n t s u r f a c e s are q u i t e flat  c o n s i d e r i n g the v e r y  diameter o f 25.4  Since when  one  with  mm.  i n the r e a l  half  l a r g e p e n e t r a t i o n f r o n t area  of  the  o b s e r v a t i o n , the r e a d i n g was total  penetration  front  taken surface  emerged, the o b s e r v a t i o n e r r o r o f the p e n e t r a t i o n f r o n t  was  limited  0.3  mm.  to  This  a half is  a t t a i n e d by the  quite  ruggedness, t h a t i s , 0.09  high  the c o n v e n t i o n a l  graduation  can be  a  o f the  accuracy  which  graduation  may  to  hardly  method. In a d d i t i o n  method o n l y the p e r i p h e r a l p e n e t r a t i o n  observed w h i l e  be  line  the i n t e r i o r p e n e t r a t i o n behaviour i s  ignored.  The  applicability  of  the 167  Washburn  equation  to  this  Table  T e s t f o r the ruggedness o f p e n e t r a t i o n on 1.4 - 1.5 d e n s i t y f r a c t i o n P - 13.8 MPa  8.1.1  H mm 0.00 6.63 7.30 16.70 23.66 34.61  HxH  Measured data TO Tl sec sec  0 43.96 53.29 278.89 559.79 1197.85  T1-T0  0 77 100 464 901 1955  0 73 93 454 871 1882  * H i n mm  0 4 7 10 30 73  HO mm  front  Calculated reesults HI-HO HI mm  0.,00 6.,76 7..63 16. ,85 23..34 34, .30  i s the l i q u i d p e n e t r a t i o n  0..00 6..94 7..91 17, .03 23,.73 34 .96  height  ** TO i n second i s the time when p e n e t r a t i o n f r o n t emerge from the top s u r f a c e o f the column *** T l i s the time when the whole p e n e t r a t i o n f r o n t emerges out  Regression  Output  Constant Std dvtn o f HxH E s t R Squared No o f O b s e r v a t i o n Degrees o f Freedom T Coefficient Std dvtn o f Coef.  HxH = 0.625 T  168  0 4.171126 0.999918 6 5 0.625173 0.001927  0.00 0.18 0.28 0.18 0.40 .0.66  method  can  be  simply  reproducibility whether  A  of  density  fractions  of  p e n e t r a t i o n data  through  T  curves  linearity  and  materials  experiments  the  of  rate  column-making  Figures  versus  observing  and  by  observing  have  different  lines.  linearity  constant  by  wettability  series  different  in  H  different  penetration  the  of  tested  has  the  of  been  Bullmoose c o a l t o  penetration  pressure  conducted  of  6.9  to  curves, 20.7  test under  MPa.  The  f o r a l l s i x d e n s i t y f r a c t i o n s were p l o t t e d  8.2.1  to  8.2.3. E s s e n t i a l l y  the o r i g i n . The  a l l the  lines  pass  l i n e a r i t y of the p e n e t r a t i o n curves,  which i s n u m e r i c a l l y r e p r e s e n t e d by the R squared v a l u e R < 1), and o t h e r r e g r e s s i o n r e s u l t s are p r e s e n t e d 8.2.1 the  on  (0 <  i n Tables  t o 8.2.4. As can be seen, a l l s i x R squared v a l u e s f o r regression lines  are  close to unit  value  illustrating  v e r y good l i n e a r i t y .  In terms o f r e p r o d u c i b i l i t y , t h a t the data a c q u i s i t i o n procedure quite  different  conventional penetration the  reading  from t h a t of  method, curve of  the  a l l the  A c c o r d i n g l y , the experimental  emphasized  i n the p r e s e n t method i s conventional  experimental  were o b t a i n e d penetration  i t should be  from one  length  at  one.  In  points  on  169  a  column by  taking  different  times.  r e p r o d u c i b i l i t y was  t e s t e d by  examining d e v i a t i o n of the p e n e t r a t i o n curves o b t a i n e d d i f f e r e n t columns.  the  from  In t h e p r e s e n t method, o n l y one p o i n t was o b t a i n e d on a column. To draw a p e n e t r a t i o n l i n e i n c l u d i n g 5 d a t a p o i n t s on i t ,  an equal number o f columns w i t h d i f f e r e n t h e i g h t s a r e  needed  t o c a r r y out f i v e  separate  penetration tests.  d a t a p o i n t c o u l d be c o n s i d e r e d independently run.  Therefore,  the l i n e a r i t y  denoted  by  Each  as a repeated R  squared  and  s t a n d a r d d e v i a t i o n , a t t h e same time, were a l s o t h e measures o f t h e experimental  Judging  reproducibility.  from  both  the R  squared  standard d e v i a t i o n o f the c o e f f i c i e n t s ,  value  and t h e  i t can be confirmed  t h a t t h e Washburn e q u a t i o n i s w e l l a p p l i c a b l e t o t h e columns made under v e r y h i g h p r e s s u r e s .  8.1.3  Height  As versus  T  Limit  t h e column reaches begins  to  c e r t a i n height, the H  deviate  from  linearity;  2  plotted this  is  e s p e c i a l l y t r u e f o r columns made under lower p r e s s u r e s (see Figure  8.1.1).  Several  factors  may  attribute  to  this  phenomenon. The g r a v i t a t i o n a l f o r c e c o u l d be one o f them. By r e c a l l i n g the general r a t e of c a p i l l a r y p e n e t r a t i o n equation 7.2.3  r d(h )/dt = —  2  2  Ay,  (  27 «cos0  170  lv  r  Apgh)  7.2.3  APPLICABILITY TEST OF WASHBURN EQUATION 600 -i  0  F i g u r e 8.1.1  PRESSURE 17.2 MPa,+1.8 FRACT'N BM COAL —  20  40  60  Penetration time (second) •  Squared height  80  100  one  can  notice  that,  Washburn equation neglected was  under  to  in  the  the  the  actual  packed  a p p l i c a t i o n of  column, the  condition that  term Apgh  penetration  with  the  above e q u a t i o n  o f f . I t was  lower  pressures  packed  under  influence  lower  height  pressures. column  the  the  T curve that  distribution  increases,  in  observed  had  the  term  versus  2  higher  of  diameters  first  and H  level  height,  can  the  h,  in  the  lose l i n e a r i t y  and  columns packed  limits  This  packing  than  could  column.  radii,  r's,  the  be  pressure  i n s i d e the  capillary  parenthesis  on  As  in  Apgh.  Therefore  pressure  the  the  greater  relative  column  height  to  limit  pressure  column  the  the  become  parenthesis second  raises  term  up  when  i s increased.  The and  becomes  to  capillary  the  lv  Eq.7.2.3  under  columns  due  s m a l l e r , w h i l e the f i r s t term 2 7 « c o s 0 / r i n the  be  was  s m a l l . Once h i s l a r g e , the term Apgh i s comparable i n  magnitude  of  the  f r i c t i o n between the mould o f a MET-A-TEST p r e s s  column w i t h i n i t i n the column-making p r o c e s s  another  affecting  factor  of  column  height  f r i c t i o n , when the column i s h i g h enough, c o u l d a l t e r the p a c k i n g  could  limit.  The  considerably  d e n s i t i e s a t d i f f e r e n t p a r t s of the column  and,  as a consequence, change the p e n e t r a t i o n behaviour  and  make  the  The  influence section  rate of  of the  penetration friction  line  will  8.5.  172  be  to  be  non-linear.  further  discussed  in  8.2  COLUMN-MAKING PRESSURE  I t was claimed<Good and L i n , 1976, Neumann and Good, 1979>  that  t h e column-making  pressure  had no p e r c e p t i b l e  e f f e c t on t h e p e n e t r a t i o n r a t e . T h i s c o n c l u s i o n was o b t a i n e d from  t h e columns  However,  i t may  which  were  packed  not be t r u e  by  manual  i n t h e case  compressed column. The column-making p r e s s u r e pronounced e f f e c t into  the  change (or  and  The  the equivalent  the  measurement  rationality  i n column-making  and consequently,  o f a machineshould have a  on both t h e r a t e o f p e n e t r a t i o n o f l i q u i d  columns  reproducibility.  tapping.  pressure  capillary  behind  accuracy, this  and  i s that  a  c o u l d change t h e p o r o s i t y  diameter) w i t h i n t h e column,  as shown i n Eqs.7.2.4 and 7.2.5, a l t e r t h e  r a t e o f p e n e t r a t i o n . Under h i g h e r p r e s s u r e , t h e column c o u l d be  more  uniformly  packed  and measurement  accuracy  and  r e p r o d u c i b i l i t y should be h i g h e r .  8.2.1  The E f f e c t o f Pressure on R e p r o d u c i b i l i t y and Linearity  In pressures several fractions  order  to  study  the  effect  of  on t h e experiment r e p r o d u c i b i l i t y series were  of  columns  from  different  column-making and l i n e a r i t y , coal  compressed under v a r i o u s p r e s s u r e s 173  density and were  penetration height (mm) squared  o o  o o  O O  o o  o o  ON O O  O •  7  OS  II  to »  8^  > +  + x II  X  o  o o  o o  3  o.  4i. T3  II  bo  ON  o o  X  oo o o  174  O O  Rate of penetra. curves for columns of 700  F i g u r e 8.2.2  1.3-1.4 made under dif. pressures  600  500  400  300  200  100 H  Time in second •  P=6.9 MPa  +  p=13.8  O  p=20.7  Rate of penetra. curves for columns Figure 8.2.3  800  0 P=6.9MPa  T 0.2  of 1.4-1.5 made under dif. pressures  0.4 +  0.6 (Thousands) Time in second P=13.79  0.8 O P=20.7  Rate of penetra. curves for columns of 700  Figure 8.2.4  1.5-1.6 made under different pressures  600  -a  500  3  cr  a  s.  400  '3 J3  C  O  300  .—1  C3  s  200  100 H  0.6  0.8 (Thousands) Time in second  •  P=6.9 MPa  +  P=13.8  1.4  O  P=20.7  Rate of penetra. curves for columns of F i g u r e 8.2.5  600  1.6-1.8 made under different pressures  500  T3  p  3  400 H  a  S. 50 'o .C  300 H  a is o a o a.  00  200  H  100  1—  ;  0.2 p=6.9 MPa  0.4  1  T  0.6  0.8 (Thousands) Time in second + p=13.8  O  p=20.7  Rate of penetra. curves for columns of F i g u r e 8 .2 . 6  +1-8 made under different pressures  0.6 (Thousands) Time in second •  p=6.9 MPa  + A  p=17.2  p=10.3 X  O  p=20.7  p=l3.8  t e s t e d s e p a r a t e l y . F i g u r e s 8.2.1 a  g r a p h i c a l form.  Clearly,  t o 8.2.6  f o r each  are the r e s u l t s i n  density  fraction  and  under a c o n s t a n t p r e s s u r e , a corresponding s t r a i g h t l i n e o b t a i n e d . However, i f the column making-pressure was  was  changed  f o r the same sample, the r a t e of p e n e t r a t i o n l i n e would have different  slopes.  different  slopes  A  group  can  be  of  penetration  obtained  if  column-making p r e s s u r e g r a d u a l l y . The making  pressure,  the  slower  ( s m a l l e r s l o p e v a l u e of H 8.2.9 all  were  re-plotted  higher  the  from  Figures  of  penetration  F i g u r e s 8.2.7  8.2.1  to  8.2.6  to  placing fractions  graph.  T a b l e s 8.2.1 these  the  i s t h e column-  rate  versus T l i n e ) .  2  with  increases  the r a t e of penetration l i n e s f o r s i x d e n s i t y  t o g e t h e r i n one  t o 8.2.3  g i v e the r e g r e s s i o n r e s u l t s f o r  data.  The  experimental  evaluated  from  coefficients. the  is  one  lines  table,  R  standard  error  decrease  as  fractions.  squared  They  one  reproducibility  are  can of  2  R  a  (or  the p r e s s u r e The  standard  given  find H  and  i n c r e a s e toward  pressure.  A l l this  i n Table  d e v i a t i o n of 8.2.4. By  general  tendency  Y)  the  and  accuracy  are these  examining  t h a t both  standard  the  deviation  i n c r e a s e s f o r a l l the s i x d e n s i t y  squared  fractions  and  values unit  suggests  the  column-making p r e s s u r e s . 180  value  for with  positive  all the  six  density  increase i n  effect  of  higher  penetration height (mm) squared  o o  O  o  o o  o o  oo o o  -J  ON  o o  o o  o o  ON  x> o  +  >  X  X r4^  H  §  +  ON  +  ha  p bo  X  o  181  penetration height (mm) squared  o o  to o o  CO  o o  o o  o o  o o  -0 o o  53  © a r  Si o O* S C/3  182  Rate of Penetra. for Diff. SG Fractions 700  Figure 8.2.9  columns made under 20.7 MPa  +  A  600 H o 500 H  X  400  A  +  300 H  A  x  200 +  A X  o  a  100 H p  A  * x  v  0  • A  i  -1.3 1.5-1.6  1 0.2  1  +  1 0.4  1  1 1 1 0.6 0.8 (Thousands) Time in second  1.3-1.4 X 1.6-1.8  O  1  1r  1.4-1.5 V +1.8  1.2  1.4  Table  8.2.1  STATISTIC ANALYSIS OF PENETRATION DATA For BM c o a l , Pressure i s 6.9 MPa Density Fraction  Regression Equation  -1.3  Y - -4.05 + 1.21 X  20.61  0.059  0.993  1.3- 1.4  Y = 8.92 + 0.946 X  7.45  0.012  0.9995  1.4- 1.5  Y - -10.0 + 0.743 X  21,81  0.025  0.997  1.5- 1.6  Y - -5.38 + 0.684 X  22.45  0.031  0.9896  1.6- 1.8  Y - -0.30 + 0.603 X  3.52  0.0049  0.9998  Y - -3.64 + 0.306 X  5.92  0.009  +1.8  S t d dvtn o f S t d dvtn o f R Y estimate slope v a l u e s Squared  0.997  * S t d dvtn - Standard d e v i a t i o n ** The u n i t o f d e n s i t y i n t h i s t a b l e and f o l l o w i n g t a b l e s i s gram p e r c u b i c centimeter  T a b l e . 8.2.2 STATISTIC ANALYSIS OF PENETRATION DATA f o r BM c o a l , p r e s s u r e i s 13.8 MPa density fraction  Regression Equation  S t d dvtn o f Y estimate  -1.3  Y = -4.98 + 0.945 X  6.54  1.3- 1.4  Y = -6.75 + 0.829 X  5.88  0.009  1.4- 1.5  Y = -15.1 + 0.592 X  17.78  0.02  1.5- 1.6  Y - -4.21 + 0.53 X  7.75  0.0076  1.6- 1.8  Y = -5.17 + 0.195 X  18.61  Y - 5.62 + 0.195 X  6.69  +1.8  S t d dvtn o f slope v a l u e s '  0.016  0.02 0.008  Table  8.2.3  STATISTIC ANALYSIS OF PENETRATION DATA For BM c o a l , P r e s s u r e i s 20.7 MPa density fraction -1.3  Regresion Equation  S t d dvtn o f Y estimate  S t d dvtn o f R slope v a l u e s Squared  Y - -9.82 + 0.836 X  7.58  0.013  0.9992  1.3- 1.4  Y = -4.03 + 0.703 X  5.47  0.0076  0.9996  1.4- 1.5  Y = -5.66 + 0.499 X  4.49  0.0051  0.9997  1.5- 1.6  Y - -8.52 + 0.458 X  6.15  0.0053  0.9993  1.6- 1.8  Y - -2.11 + 0.337 X  2.55  0.0025  0.9998  Y - 0.250 + 0.163 X  0.29  0.0003  +1.8  1.0000  Table  8.2.4  density fraction  The e f f e c t o f column-making p r e s s u r e on a c c u r a c y and l i n e a r i t y o f the r a t e o f p e n e t r a t i o n l i n e Std  dvtn o f Y estimate  P-6.9 MPa -1.3  13.8  20.7  Std  dvtn o f slope v a l u e s  P-6.9 MPa  13.8  20.7  R squared P-6.9 MPa  13.8  20.7  20.61  6.54  7.58  0.0590  0.0160  0.0130  0.9930  0.9992  1.3- 1.4  7.45  5.88  5.47  0.0120  0.0090  0.0076  0.9995  0.9996  1.4- 1.5  21.81  17.78  4.49  0.0250  0.0200  0.0015  0.9970  0.9997  1.5- 1.6  22.45  7.75  6.15  0.0310  0.0076  0.0053  0.9896  0.9993  1.6- 1.8  3.52  18.61  2.55  0.0049  0.0200  0.0025  0.9998  0.9998  +1.8  5.92  6.69  0.29  0.0090  0.0080  0.0003  0.9970  1.0000  The  low p r e s s u r e  manual packing, the  o f 3.5 MPa, which i s comparable w i t h  was a l s o  experimental  data  tested.  Under t h i s  are s i g n i f i c a n t l y  low  pressure,  scattered.  This  might be t h e reason why Good and L i n <1976> and Neumann and Good<1979>  concluded  that  the rate  of penetration  data i n  the s t u d i e s g e n e r a l l y e x h i b i t a s e r i o u s s t a t i s t i c a l s c a t t e r . They have a t t r i b u t e d t h i s s c a t t e r t o t h e change i n s t r u c t u r e o f t h e packed column w i t h w e t t i n g . reason. Another reason, the  inconsistency  as i m p l i e d  i n structure  E s p e c i a l l y under lower p r e s s u r e themselves p r o p e r l y  T h i s c o u l d be p a r t o f t h e by t h i s  study, might be  o f packed  column  itself.  t h e p a r t i c l e s do n o t o r i e n t  f o r the best  packing density  and t h e i r  i r r e g u l a r c o n f i g u r a t i o n would t r a p l a r g e amount o f i r r e g u l a r air  pockets  within  significantly of  penetration  column.  These  configurations  from one t o another. T h e r e f o r e  can be d i f f e r e n t  When h i g h  configurations to  vary  t h e column.  pressure  collapse  i n various  was a p p l i e d ,  and p a r t i c l e s  form b e t t e r packed c o n f i g u r a t i o n s  the rate  parts  these  can  of the  air-trapped  re-orient  themselves  which tend t o be more  uniform.  By that  checking  the published  the penetration  lines  literature,  one may  f o r t h e same m a t e r i a l  find  from t h e  r e p e a t e d runs d i d not observe t h e same s l o p e even though an individual  line,  had  good l i n e a r i t y <Crowl and Wooldridge, 1967>. The  a very  which was measured  188  from  a s i n g l e column,  poor  reproducibility,  likely  to  be  produce  due  the  to  according the  columns  configurations.  The  kept  constant  inability with  of  to  analysis, i s  manual  tapping  reproducible  column-packing p r e s s u r e  an e x c e p t i o n a l l y important and  t o t h e above  interior  i s , therefore,  f a c t o r . I t should be h i g h  attain  high  to  reproducibility  enough of  the  change  the  experiments.  8.2.2  E f f e c t on Rate o f P e n e t r a t i o n  The  column-making  experimental  accuracy  above, but a l s o a l t e r Figures H  2  8.2.1  versus  T  be answered  and  reproducibility,  smaller  the  origin  slope value.  i s what i s t h e g e n e r a l  delineated  by  of  can r o t a t e  coordinate  The q u e s t i o n  t o the  which  r e l a t i o n s h i p between the  testing  the  on the r a t e o f p e n e t r a t i o n  columns  made  under  various  p r e s s u r e s . The s l o p e v a l u e , S, f o r each p e n e t r a t i o n l i n e c a l c u l a t e d by s t a t i s t i c a l r e g r e s s i o n o f the p e n e t r a t i o n and was the  p l o t t e d versus  effect  of  pressure  pressure  s u b s t a n t i a l . According  will  P, and what i t stands f o r .  The i n f l u e n c e o f p r e s s u r e studied  as  the r a t e o f p e n e t r a t i o n . As shown i n  around  s l o p e , S, and p r e s s u r e ,  was  can not o n l y  t o 8.2.6, t h e i n c r e a s e i n p r e s s u r e line  p o s i t i o n with  pressure  on  i n F i g u r e 8.2.10.  the  rate  of  189  line  Obviously  penetration  t o the Washburn e q u a t i o n  was  7.2.5  is  The effect of column-making pressure on Figure 8.2.10  SLOPE of the rate of penetr. curve  4) 3  -a >  o cr>  o .—I  CO  Pressure in MPa -1.3 1.5-1.6  +  1.3-1.4 X 1.6-1.8  O  1.4-1.5 V +1.8  d(H )/dt = 2  The  A  general  values,  tendency  S's,  lower  in  for  decreasing with at  7  s l o p e of p e n e t r a t i o n l i n e should  S  -  be  K-7-COSC?/2M  Figure  all  the  i s wider  8.2.1  8.2.10 six  and  is  that  density  increasing pressure.  pressure  7.2.5  K- COSc5/2/i  The  the  slope  fractions  band o f the  becomes  narrower  are lines  as  the  pressure increases.  In Eq.8.2.1, 6 i s what we n  are the p e n e t r a t i o n l i q u i d  accurate  measurements;  regression  S  p r o p e r t i e s and  could  o f measured d a t a .  i n t e n d t o determine; 7  be  are known from  obtained  If tortuosity  and  through  constant  the  K were  known, 6 v a l u e c o u l d be r e a d i l y c a l c u l a t e d . U n f o r t u n a t e l y K i s unknown.  In the experimental pressure unchanged regarded tested solid  on  rate  f o r the unchanged  i f the  of  p r o c e s s f o r t e s t i n g t h e e f f e c t of  penetration, 7  same l i q u i d . f o r the  pressure  And  and e  M were  was  also  same l i q u i d - s o l i d  i s not  high  enough  considered presumably  system t o to  change  be the  s u r f a c e p r o p e r t i e s ( t h i s w i l l be d i s c u s s e d i n s e c t i o n  8.2.3). T h e r e f o r e  a c c o r d i n g t o Eq.8.2.1, the 191  change i n the  s l o p e v a l u e , S, v e r s u s p r e s s u r e , the  P, was o n l y a s s o c i a t e d w i t h  change i n t o r t u o s i t y constant,  K. That i s , t h e p r e s s u r e  was o n l y i n f l u e n c i n g t h e l i q u i d p e n e t r a t i o n through changing the column t o r t u o s i t y constant,  The  t o r t u o s i t y constant  capillary columns. surface  radius  r , i s only  It i s , like  size  to  i f two  say,  distribution  quite  distribution, columns  constant  different  value  physical radius  property  density,  d e n s i t y , they  i t i s p o s s i b l e t o procure  without  the reference  material  particle  size  should have t h e  K, even though these properties.  by  of  e t c . . That i s  a r e o f t h e same  surface  of the  r , independent  determined  packing  and same packing  useful conclusion,  a  and i s o n l y  same t o r t u o s i t y constant have  K, which i s an e q u i v a l e n t o f  capillary  wettabilities  particle  K.  two m a t e r i a l  Based  on  this  the t o r t u o s i t y  t o the  calibration  liquid.  There i s s t i l l of  no way t o f i n d out d i r e c t l y t h e v a l u e  t h e t o r t u o s i t y constant,  K  from  Fig.8.2.10.  But F i g .  8.2.10, Eq.7.4.1, and above c o n s i d e r a t i o n s do p r o v i d e clue  how  above  t o c a l c u l a t e the K value.  idea  entirely  will  devoted  be  presented  entirely  new  i n section  approach 8.5.2  to the c a l c u l a t i o n  under v a r i o u s column-making p r e s s u r e s values  A  192  using  which i s  of K  and t h e c o n t a c t  f o r d i f f e r e n t density fractions of coal.  some  values angle  8.2.3  S i d e E f f e c t o f High  The present  a p p l i c a t i o n o f h i g h e r column-making p r e s s u r e s may-  many advantages i n t h e r a t e o f p e n e t r a t i o n t e s t s as  illustrated high  Pressure  above. N e v e r t h e l e s s ,  pressure  particles  i s that  to finer  a major  i t may  cause  concern  with the  crushing  s i z e s and then p o s s i b l y a l t e r  of  coal  the coal  surface properties.  The  possibility  column-making process  of  crushing  of the coal  can be d e t e c t e d  p o s s i b l e way i s through p a r t i c l e  i n s e v e r a l ways. One  size distribution analysis  before  and a f t e r t h e column-making p r o c e s s .  action  has o c c u r r e d ,  the of  i n the  size distribution  within  column a f t e r r e - d i s p e r s i o n would i n d i c a t e h i g h e r  yields  fine  sizes  than  the p a r t i c l e  I f any c r u s h i n g  prior  t o t h e column  preparation.  The  p o s s i b l e s h i f t i n s i z e d i s t r i b u t i o n toward f i n e r s i z e s would suggest t h e occurrence  o f t h e c r u s h i n g a c t i o n . The p a r t i c l e  s i z e a n a l y s i s r e s u l t s showed t h a t no apparent s h i f t  i n size  d i s t r i b u t i o n has o c c u r r e d .  Another was  way t o d e t e c t  t o examine d i r e c t l y  the possible  the p e l l e t  surface  crushing using  action  Scanning  E l e c t r o n Microscope (SEM) under v e r y h i g h m a g n i f i c a t i o n . The  surfaces  photographed  o f columns  (Figures  6.8.2). 193  made  under  The p i c t u r e  27.6 MPa magnified  were 3000  times  in  Figure  crushing  6.8.2,  action  Otherwise,  has  groups  breakage o f  ocurred  of  larger  clearly  small  shows on  the  particles  particles  can  that  be  no  obvious  pellet  surface.  produced  seen p i l e d  from up  the  a t some  random s p o t s .  The present 27.6  column-making  work ranged  MPa  as  used  pressure  from 6.9  i n the  t o 20.7  Lower L i m i t o f  The tested this  lower  to  technique.  which  comparable  fragile was  is  and  the  As  needed  the  I t i s f a r below p o s s i b l e crushing  excluded.  lowest  However, the  value.  in  o f column-making p r e s s u r e s was  find  clear-cut  The  used  Pressure  limit  i n order  MPa.  above t e s t .  a c t i o n w i t h i n a column should be  8.2.4  usually  the  pressure  with  t o be  f u r t h e r decreased  tests  manual handled  down  to  pressure  also  feasible  show t h a t t h e r e was was  reduced  tapping, with  2.8  to  the  the  no MPa,  column  c a r e . When  MPa,  3.5  for  was  pressure  column  could  h a r d l y h o l d and loosened i n s t a n t a n e o u s l y a f t e r r e l e a s e d from the mould.  In therefore, Pressures  the  present  was  chosen  down t o 3.5  work, i n the  the range  and up t o 34.5 194  column-making from MPa  6.9  to  pressure, 20.7  MPa.  were a l s o employed  i n t h e s e experiments  i n o r d e r t o study i t s i n f l u e n c e on the  column p r o p e r t i e s and on the r a t e of  195  penetration.  8.3  PHYSICAL PROPERTIES OF COLUMNS  The columns compacted under h i g h p r e s s u r e s e x h i b i t e d many d i s t i n c t p r o p e r t i e s . The study o f these p r o p e r t i e s may be  an  integrate  part  of t h i s  technique.  Some  of  these  o b s e r v a t i o n s may be used i n l a t e r s e c t i o n s t o i n t e r p r e t t h e r e s u l t s and e v a l u a t e t h e assumptions.  8.3.1  Column Height v e r s u s  The parameters value  column  height  i n the rate  was i n e v i t a b l y  Pressure  i s one  o f t h e most  of penetration  tests.  important  However i t s  i n f l u e n c e d by t h e column  compressing  p r e s s u r e . F o r t h e same amount o f m a t e r i a l , t h e column h e i g h t i s s m a l l e r under h i g h e r p r e s s u r e .  In  order  t o examine t h e g e n e r a l c o r r e l a t i o n  between  column h e i g h t and p r e s s u r e , columns o f c o n s t a n t weight were pressed Figure  under  different  pressures.  8.3.1. As t h e p r e s s u r e  decreases,  Results  a r e shown i n  i n c r e a s e s t h e column  height  b u t n o n - l i n e a r l y . A t lower p r e s s u r e s , an i n c r e a s e  i n p r e s s u r e can reduce t h e column h e i g h t more s u b s t a n t i a l l y . As  the pressure  increases,  the influence of pressure  column h e i g h t d i m i n i s h e s .  196  on  Effect of column-making pressure on Figure 8.3.1  column packing density (BM-1.3 fract'n)  column-making pressure (MPa) •  Height/gram powder  It  is  worthy  measured a t lower  of  mention  that  compacting p r e s s u r e  the  column  height  i s more l i k e l y  to  be  s c a t t e r e d because a s m a l l random e r r o r or d i s t u r b a n c e would have l a r g e r at  lower  effect  pressure  the reasons  why  on  the  interior  s t r u c t u r e o f the  column  (than a t h i g h e r p r e s s u r e ) . T h i s i s one  h i g h compressing  p r e s s u r e was  of  preferred for  the sake o f p r e c i s i o n .  As  the  (27.6 MPa), on  the  8.3.1  column-packing p r e s s u r e  reaches  a high  a f u r t h e r i n c r e a s e i n p r e s s u r e has l i t t l e  column h e i g h t . The  tail  p a r t o f the curve  level effect  i n Figure  t h e r e f o r e tends t o l e v e l o f f . Working i n t h i s area  possibly  have  some advantages  effect  of  compressing  possibility destruction  of  pressure.  changing  becomes  more  of b e i n g  coal likely  independent  of  Nevertheless,  may the the  surface  properties  by  f o r higher  pressures  and  p r o h i b i t s the use o f v e r y h i g h p r e s s u r e .  8.3.2  Column Height v e r s u s Weight  In density, material  order  to  guaranty  a  constant  column  some r e s e a r c h e r s have packed a c o n s t a n t into  a  glass  tube;  and  always  kept  packing  weight the  column  h e i g h t c o n s t a n t . However t h i s p r a c t i c e c o u l d not r e a d i l y applied different  to  coal  because  of  the  coal density fractions. 198  density  variation  In t h i s work, a  of  be  among  constant  Figure 8.3.2  Column weight vs. its height +1.8 density fraction P=13.8 MPa  cri  Sample weight in gram Column height in mm  packing making  d e n s i t y was secured  a constant  column-  pressure.  Under a constant  pressure,  different  weights were  measured.  As shown  relationship observed. makes  by a p p l y i n g  and t h e i r  i n Figure  between  However,  made  column  a number o f columns  8.3.2, height  further increase  i t s height  out  of  weight  accurately  an a c c e p t a b l e and  with  linear  i t s weight  was  i n column weight  only  proportion  and  higher  than  predicted.  It column  was  made  proportional  initially under  wall  next  process  mould  f o r c e s , which w i l l  that  pressure weight.  i t was  of the f r i c t i o n  of the holding  friction  constant  t o t h e column  column-making existence  perceived  the height  of the  should  always  However  not true,  forces  decrease  real  of the  the c y l i n d r i c a l  and t h e column  s e c t i o n , produce a g r a d i e n t  i n the  because  between  be d i s c u s s e d  be  within  i n detail  i t . The i n the  of the pressure  through t h e column and, as a r e s u l t , may y i e l d a n o n - l i n e a r column h e i g h t versus weight r e l a t i o n s h i p .  8.3.3  Column P o r o s i t y  Although  t h e column-making  same as t h e p e l l e t - m a k i n g  process, 200  process  i s e x a c t l y the  t h e column e x h i b i t s q u i t e  different between  their  uniform. under  p r o p e r t i e s because o f t h e s u b s t a n t i a l d i f f e r e n c e heights.  Firstly,  I t changes along  t h e same  different porosities.  i t s perpendicular axis.  column-making  heights  t h e column p o r o s i t y i s n o t  pressure,  are characterized  Detailed  Secondly,  t h e columns  by d i f f e r e n t  discussion w i l l  be g i v e n  with  average  i n section  8.4.  8.3.4  Column Expansion  The s i g n i f i c a n c e o f column expansion  after the l i q u i d  p e n e t r a t i o n p r o c e s s was t e s t e d . The s u b s t a n t i a l expansion o f the  column  during  penetration  affects  t h e measurement o f  column h e i g h t and column p o r o s i t y .  In T a b l e is  8.3.1, H  t h e column h e i g h t  0  i s t h e o r i g i n a l column h e i g h t ; H  a f t e r penetrated  by l i q u i d ;  i n c r e a s e i n h e i g h t . The r e l a t i v e column expansion is  presented  made  from  different columns expansion However,  i n the l a s t t h e -1.3  pressures made than  column  fraction  higher  dH i s t h e i n height  o f t h e t a b l e . The columns of  t h e Bullmoose  were t e s t e d . The r e s u l t s  under  x  pressures  coal at  show t h a t t h e  experienced  greater  d i d t h e columns made under lower p r e s s u r e .  the largest  average r e l a t i v e  0.71 p e r c e n t and c o u l d be n e g l e c t e d .  201  expansion  was  only  S w e l l o f columns a f t e r p e n e t r a t e d by l i q u i d  Pressure MPa  P-6..9  P=13..8  P=20..7  HO mm  HI mm  dH mm  24.55 19.60 17.15 13.00 12.80 8.65 6.75  24..65 19..70 17..35 13..00 12..90 8..65 6..75  0..10 0..10 0..20 0..00 0.,10 0..00 0..00  0.,41% 0.,51% 1..17% 0.,00% 0..78% 0..00% 0..00%  0..41%  24.60 20.20 18.10 15.85 12.00 8.25 6.30  .80 " 24. 20..40 18..20 15..95 12..10 8..25 6..30  0..20 0..20 0..10 0..10 0..10 0..00 0..00  0.,81% 0..99% 0..55% 0..63% 0..83% 0..00% 0..00%  0..55%  24.00 19.75 17.60 15.40 12.30 11.50 8.85 7.00  24..30 19..80 17..90 15..50 12..35 11..50 8..85 7..10  0..30 0..05 0..30 0..10 0..05 0..00 0..00 0..10  1..25% 0,.25% 1..70% 0,.65% 0,.41% 0,.00% 0 .00% 1..43%  0,.71%  HO i s HI i s by dH i s  %  Average  the o r i g i n a l column h i g h t i n mm the column h e i g h t (mm) a f t e r p e n e t r a t e d kerosene the i n c r e a s e i n column h e i g h t (mm)  202  8.4  The E f f e c t o f F r i c t i o n  When t h e p r e s s u r e  e x e r t e d on the column i s h i g h , the  f o r c e e x e r t e d by column on t h e c y l i n d r i c a l w a l l o f t h e mould is  also  significant  friction column force  in  f o r c e between of  particles  prevents  the  column-making  cylinder wall  can  not be  the propagation  process.  o f t h e mould  neglected.  of pressure  This  The  and the friction  throughout  the  column, generates a p r e s s u r e g r a d i e n t throughout t h e column, and  consequently  packing  density.  even be v i s u a l l y brightness  influences The  the  packing  consistency  density  of  column's  inconsistency  could  observed through t h e change i n c o l o u r and  i n the column's a x i s d i r e c t i o n .  As demonstrated  b e f o r e , t h e column-making p r e s s u r e had a s t r o n g i n f l u e n c e on the  r a t e o f p e n e t r a t i o n . The e x i s t e n c e o f p r e s s u r e  gradient  may a l t e r t h e r a t e o f p e n e t r a t i o n behaviour w i t h i n a column.  The most d i r e c t m a n i f e s t a t i o n  o f t h i s phenomenon was  observed when columns were put upside penetration material  tests.  were  penetration  Two  compacted  experiments  sets  of  under were  a  down and used i n t h e  columns  from  constant  carried  on  manners: one s e t o f columns were p e n e t r a t e d  the  pressure.  i n two  same The  different  i n a normal way;  but i n another s e t , t h e columns were p l a c e d u p s i d e down. The results  ( F i g u r e 8.4.1) show t h a t two p e n e t r a t i o n l i n e s  different  s l o p e s were  obtained. 203  with  Change in Rate of Penetration Behavior 130  F i g u r e 8.4^1  when columns placed upside down  120 H 110 100 90 H o 80 70 60 H 50 40 penetration time in second as usual  +  upside down  Suppose t h a t i n F i g u r e 8.4.2 is  f,  the  present  circumference  of  work), the p r e s s u r e  the  the f r i c t i o n column  is c  coefficient (7.98  cm  in  a t any p o i n t w i t h i n the column  i s p, a d i f f e r e n t i a l e q u a t i o n can be d e r i v e d dp = -p«c»f«dx  8.4.2  A f t e r i n t e g r a t i n g above equation from x=0 t o h, we can g e t  [lnp]  p  =  Po  [-cfx]  h 0  p = Po»exp(-cfh) where Po  8.4.3  i s t h e p r e s s u r e e x e r t e d on t h e column's bottom ( i t  i s kept c o n s t a n t i n column-making p r o c e s s ) . A c c o r d i n g t o t h e above e q u a t i o n , t h e p r e s s u r e decreases  from column's bottom,  t o t h e column's t o p s u r f a c e e x p o n e n t i a l l y .  It linearly  has  been  decreases  known  that  the  porosity  w i t h column-packing p r e s s u r e  of  a  column  linearly in  a r e l a t i v e l y narrow range o f p r e s s u r e s . That i s  q = Q - k«p  8.4.4  where q i s t h e column p o r o s i t y , Q i s i n t e r c e p t a t q a x i s and p the pressure  exerted  on column. By s u b s t i t u t i n g  i n t o Eq.8.4.4, one can get  205  Eq.8.4.3  D  —  If  1 dxI  X  1  !  —  \  P  p  0  P  F i g u r e 8.4.2  0  The f o r c e s a c t i n g on the column w i t h i n the mould  P  0  i s the pressure  (MPa)  exerted  on t h e column bottom  by t h e h y d r a u l i c p r e s s , p  i s the pressure  (MPa) a t a p o i n t w i t h i n t h e column,  f  i s the f r i c t i o n  coefficient. 206  q = Q - kPo • exp(-cfh)  where  q  within  is a the  differential  column  porosity  of  a t h. A p p a r e n t l y  column i s i n c r e a s i n g i n x - a x i s  8.4.5  a very  thin  layer  the p o r o s i t y w i t h i n  a  d i r e c t i o n toward t h e top o f  the column i n a p a t t e r n g i v e n by Eq.8.4.5.  The  increase  suggests an i n c r e a s e  in  porosity  along  i n equivalent  column's  capillary  X-axis  radius  i n the  same d i r e c t i o n . V a r i a t i o n o f t h e e q u i v a l e n t c a p i l l a r y  radius  w i t h i n a column can i n f l u e n c e t h e r a t e o f p e n e t r a t i o n .  There along  a r e many ways t o t e s t  X-axis.  layers  from  practice,  The most d i r e c t a  column  however,  and  way  to  the p o r o s i t y  i s t o chop up some t h i n  measure  i t is difficult  is  that  friction  under  same  When  column  in  porosities  a the  porosity presence  one  of  In  layers  experimentally.  different  height  i n t h e absence  idea were  o f the  f o r a l l t h e columns should  gradient  f o r columns w i t h  i n t e g r a t i n g Eq.8.4.5  column,  pressure  force, the porosity  equal.  By  the  porosity.  employed here. The b a s i c  i f a number o f columns w i t h  compacted  their  t o c u t such t h i n  from a column and t o measure i t s q v a l u e  An i n d i r e c t method was  gradient  i s produced  friction  force,  different  heights  within the  be the  average  should  vary.  from the bottom t o t h e top o f t h e  can get t h e average 207  (or i n t e g r a l ) p o r o s i t y o f  the whole column h  Qa  Q  a  =  q.dx/(h-0)  0  = Q  8.4.6  <1 - exp(-cfh)>  8.4.7  c-f-h where  Q  a  i s t h e average p o r o s i t y o f t h e whole column, h i s  the column h e i g h t , P i s column-making p r e s s u r e , and c, f , k, and  Q a r e c o n s t a n t s . As i n d i c a t e d  porosity,  by Eq.8.4.7,  Q , o f a column made under c o n s t a n t a  t h e average pressure  P  changes w i t h column h e i g h t h. T h i s can be r e a d i l y t e s t e d .  The g e n e r a l shape o f Eq.8.4.7 was  first  examined. Q  a  was p l o t t e d a g a i n s t h by a s s i g n i n g some a r b i t r a r y v a l u e s t o the were  constants  i n the e q u a t i o n .  I n F i g u r e 8.4.3, two  curves  o b t a i n e d by a s s i g n i n g two s e t s o f d i f f e r e n t v a l u e s t o  f r i c t i o n c o e f f i c i e n t f i n Eq.8.4.7. The f i g u r e c l e a r l y shows that  among t h e columns made under c o n s t a n t p r e s s u r e P , the  average p o r o s i t y f o r the t a l l e r that with  column w i l l  f o r t h e s h o r t e r one. To t e s t various  weights  were  this,  compacted  be l a r g e r  a s e t o f columns under  a  constant  p r e s s u r e . T h e i r p o r o s i t i e s were measured and p l o t t e d t h e i r height  i n F i g u r e s 8.4.4  than  versus  and 8.4.5. The s i m i l a r i t y i n  the curve shapes between the t h e o r e t i c a l l y p r e d i c t e d and the actually  measured  porosity  versus  r e v e a l s t h e e x i s t e n c e o f the f r i c t i o n  208  column effect.  height  curves  Column Height cm B  f=0.2  +  {=0.1  The effect of column height on integral Figure 8.4.4  porosity avged on four pressure points  31 H  7  9  11  Column height mm ^  Porosity  13  15  H  Integral Porosity  It  could  compressed porosity  thus  column  concluded  i s not  gradient  exponentially,  be  uniform  and  it;  the  within  according  that  the  that  p o r o s i t y of there  porosity  exists a increases  t o Eq.8.4.5, from bottom t o top  a column. Because an i n c r e a s e o f p o r o s i t y means an of  tortuosity  penetration, penetration  d(h )/dt,  K  in  should  2  force  effect  on  (see  the  Eq.7.2.5,  exhibit  f r o n t moves upward.  gravitational porosity  constant  It  other  Eq.7.2.3).  As  an  hand the  the  rate  of  as  the  be  noticed  that  can  offset  this  penetration  s u r f a c e moves upward, the term Apgh i n c r e a s e s l i n e a r l y on  the  contrary  to  K,  tends t o drag  the  penetration  back. T h i s phenomenon i n d i c a t e s t h a t the h e i g h t column made under h i g h  pressure  column made by manual t a p p i n g .  212  of  increase  increase  i s to  a  limit  front and, front for a  i s g r e a t e r than t h a t f o r a  8.5  CONTACT ANGLE CALCULATIONS  8.5.1  Introduction  As from  noted  the  experimental  calibration. the  fact  The  is  measurement, contact  packing  e,  column, and  can  it  reference l i q u i d  can  the can  not  be  Without  not  be  K,  the  i n the  attained knowing  constant  calculated  column  results  from  i s chosen f o r which 0=0°  by  direct  K  For K  from  Washburn  the  determined.  tortuosity be  calculation  necessitated  constant,  calculation.  angle,  of  constant,  or  and  angle  for calibration  tortuosity  unknown  contact  data  requirement  t h a t the  Eq.7.2.5  the  p r e v i o u s l y , the  value, a  given  should  Eq.7.2.5  (complete  be  if  a  wetting  or spreading).  Since  coal  hydrophobicity  wettability  f o r low  density  for high density fractions. select  the  fulfilled.  liquid As  assume cos0=l  In the K  and  by  very  fractions  to  widely  hydrophilicity  0=0°  condition w i l l  Harper  <1967>  f o l l o w i n g s e c t i o n s , a new simultaneously 213  will  be  be  always  i t i s risky  i n order t o compute the t o r t u o s i t y  6 values  from  I t i s p r a c t i c a l l y impossible to  f o r which  indicated  ranges  to  constant.  approach t o compute i n t r o d u c e d based  on  the proposed assumption.  8.5.2  A New Approach  In  t h e new  tortuosity  constant  coal density  stressed  equivalent property particle packing  of  of the  0's f o r d i f f e r e n t  equations.  before,  o f t h e packed  the t o r t u o s i t y radius,  column.  distribution,  density.  angle  values  a r e r e s o l v e d a t t h e same time from a  capillary  size  the absolute  K, and c o n t a c t  fractions  s e t o f simultaneous  As  approach,  I t should  constant  i s purely  I t i s only  particle  a  K, an  geometric  associated  shape,  and  with  column  be independent o f w e t t a b i l i t y o f  the m a t e r i a l i n v e s t i g a t e d .  Suppose,  under  idealized  conditions,  that  two  d i f f e r e n t m a t e r i a l s a r e both composed o f s p h e r i c a l p a r t i c l e s all  with  identical  diameter o f , say, 5 microns.  under t h e same p r e s s u r e , should may  possess  be  particle  shapes  distributions, assumption,  t h e columns f o r t h i s two m a t e r i a l s  t h e same t o r t u o s i t y  generalized  t o apply and  e.g.  constant,  to materials  approximately  coal  powders.  o n l y one c a l i b r a t i o n  materials of different  I f packed  surface 214  K. T h i s having  the According  idea  similar  same to  size this  i s r e q u i r e d f o r a group o f  wettabilities.  Assume possessing shapes.  that  there  similar  Two  size  columns  are  two  different  distributions  a r e made  and s i m i l a r  respectively  m a t e r i a l s under e x a c t l y t h e same p r e s s u r e . should  have  penetrating  the  these  same  tortuosity  materials particle  from  t h e two  These two columns  constant,  K.  two columns w i t h t h e same l i q u i d ,  After one can  get  d(h )/dt 2  and  = S  x  = K-  S  2  = K-7  7 l v  L v  •cosc? /2 1  8.4.8  M  • cos0 /2/i  8.4.9  2  where S i and S2 a r e t h e s l o p e s o f t h e p e n e t r a t i o n l i n e s f o r two  columns  penetration corresponding  respectively B  test,  x  and 0  and  materials, 7  can  be  obtained  the contact  Z  angles  from  the  on t h e  t h e l i q u i d s u r f a c e t e n s i o n , and  l v  n the v i s c o s i t y of the l i q u i d .  After  the  column-packing  densities  are  equally  changed, by e q u a l l y changing t h e column-making p r e s s u r e , t o another equations  and  Thus,  tortuosity  constant  can be s i m i l a r l y  value  K',  another  s e t of  obtained  S  3  = K'-7  S  4  = K •7  l v  • cos 9 /2/i  8.4.10  • COS0 /2A*  8.4.11  1  l v  a s e t o f f o u r equations 215  c  1  2  with  f o u r unknown v a l u e s ,  K,  K',  e  of  the  and  lt  e  obtained. Unfortunately, only three  f o u r equations are  of s o l u t i o n s is  are  2  needed  Another  independent. An  i n s t e a d of one  in  order  useful  to  can  put  restraint  a  be  for  the  real  applications,  g r i n d i n g process to the  size  making  becomes  packing  same p r e s s u r e  packing  density,  measurement, and  The subject to and  the  same. differ,  the  fractions difference.  might  if  which  In  the  the  the  in  general  same  for  possessing by  can  not  individual the  column-  small  will  the  the  the  same  porosity  constant  K.  constant  be  K  the  particles  not  may  density  show  particle  much sizes  shape e f f e c t  diminish  to  i n s i g n i f i c a n t degree under a h i g h column-making p r e s s u r e .  216  is  column  exactly  different  would  such  the  Columns made under  micrometers, both the deviation  Under  shapes w i t h i n the  origin  have  controlling  tortuosity  for  the  to  the  same t o r t u o s i t y  distributions  addition,  distribution  factor  testified  for  that  in  fractions  distribution,  particle  shapes  is  made  possible.  columns.  was  of  size  a v e r a g i n g around ten small  equations  were  considered  i s that  effect  shapes from  of  be  as  only  t h e r e f o r e the  particle Even  the  density  intricacy the  efforts  size  solutions.  90°.  similar  identical  pressure  volumetric the  of  as  calibration  these  keep v a r i o u s d e n s i t y  distributions  precondition  on  above  c o n t a c t angle must range from 0 t o In  i n d e f i n i t e number  o b t a i n e d . One  restraint  out  and an  8.5.3  Numerical C a l c u l a t i o n s  In columns under 20.7  applying  approach  for a l l six different  a s e t of three  should  be  columns: K , K x  density  2  t o the present  were made  6.9,  1 3 . 8 , and  pressures:  Corresponding  three  tortuosity  t o these  constant  a r e d\,  8,  and t h r e e  8.5.1.  f o r those f o r the  and 6 . The t o t a l  Z  6  (K's and 0 ' s ) .  A l l t h e r a t e o f p e n e t r a t i o n equations  Table  K  3  number o f unknown v a r i a b l e s would be n i n e  fractions  pressures,  and K . Suppose t h e c o n t a c t angles  fractions  different  pressures  I n t h e t a b l e , Xi = 7 S  the p e n e t r a t i o n l i n e ,  L  l  v  f o r s i x density  were t a b u l a t e d i n  • c o s 0 i / 2 / i . The s l o p e s o f  i n Table- 8 . 5 . 1 were o b t a i n e d  the r a t e o f p e n e t r a t i o n t e s t . They a r e g i v e n i n T a b l e Among t h e t o t a l are  eighteen  independent, w h i l e  case,  density fractions  different  MPa, r e s p e c t i v e l y .  there  six  this  equations  i n Table  8.5.1,  from  8.5.2. eight  t h e number o f t h e unknowns i s n i n e .  So t h e number o f s o l u t i o n s i s i n d e f i n i t e , and a r e s t r a i n i s r e q u i r e d t o g e t one p a r t i c u l a r s o l u t i o n out o f them.  The advantage o f employing t h e redundant e q u a t i o n s i s that can  they  can encompass more experimental  be o b t a i n e d .  redundant exactly,  as much as  Though t h e s o l u t i o n s r e s o l v e d  equations they  data  may n o t be f i t t e d  i n every  can be p u t i n a l l t h e equations 217  from t h e equation with the  Table 8.5.1 Rate o f p e n e t r a t i o n e q u a t i o n  Density fractions  P-6.9 HPa KI  matrix  P-13.8 MPa K2  P-20.7 MPa K3  S l l = KI XI  S12 - K2 XI  S13 - K3 XI  1.3- 1.4  S21  - KI X2  S22 - K2 X2  S23 - K3 X2  1.4- 1.5  S31  - KI X3  S32  = K2 X3  S33 = K3 X3  1.5- 1.6  S41  = KI X4  S42 - K2 X4  S43 = K3 X4  1.6- 1.8  S51  = KI X5  S52 = K2 X5  S53 - K3 X5  S61  = KI X6  S62 = K2 X6  S63 = K3 X6  -1.3  +1.8  8.52  Table The  slopes f o r d i f f e r e n t density f r a c t i o n s under v a r i o u s p r e s s u r e s  density fractions  p r e s s u r e MPa 13.8  6.9  20.7  1.17  0.9446  0.8246  1.3-1. 4  0..9643  0.829  0.7033  1.4-1. 5  0..7544  0.5922  0.499  1.5-1. 6  0..6845  0.5308  0.4586  1.6-1. 8  0..6028  0.4246  0.3373  0..3029  0.2074  0.163  -1.3  +1.8  219  minimum  overall  deviation.  Therefore  the  solution's  r e l i a b i l i t y i s higher.  To  s o l v e these  equations, simplex  s e a r c h method  was  employed. A b r i e f d e s c r i p t i o n o f t h i s method i s g i v e n below; detailed  description  publications Mular,  of  <Spandley  this  method  e t c . , 1962,  can  be  Nelder  found  and  i n many  Meed,  1965,  1972>.  The begins  simplex  with  vertices  n-dimensional  i n n-dimensional  variables, function  a  method i s a d i r e c t  i n our  case  general  space  simplex  with  (n+1)  (n i s the number o f unknown  n=9) . The  (here R e s i d u a l Sum  search strategy that  values  of  o f Squares RSS)  the are  objective calculated  on a l l v e r t i c e s of the simplex and compared. The v e r t e x w i t h the  h i g h e s t RSS  value  which i s chosen by formed. The  i s r e p l a c e d by  reflection.  above procedure  itself  surface,  the  approaching  t o the  'local  simplex w i l l the  bottom  illustrative  two  the  On  basin,  a  long  simplex  inclined  expansion.  the  simplex  u n t i l a minimum RSS  dimensional  will  s u r f a c e , and i s f o r c e d t o  e l o n g a t e down by of  vertex point  i s repeated so the simplex  landscape'.  c o n t r a c t i n the neighborhood An  new  Then an a d j a c e n t simplex i s  move on the o b j e c t i v e f u n c t i o n RSS adapt  a  Upon will  i s reached.  search process  is  shown i n F i g u r e 8.5.1.  The u t i l i z a t i o n of simplex s e a r c h method i s o n l y made 220  p o s s i b l e by u s i n g computer because o f t h e tremendous amount of  iterative  written one.  computation  The  i n FORTRAN and i t s flowsheet  I n t h e program,  nine.  involved.  t h e number  t o Xi  correspond  program  a r e g i v e n i n Appendix  of search  v a r i a b l e s was  t o K 3 and C(4) t o C(9)  Ki  C ( l ) t o C(3) r e p r e s e n t  computer  t o X6 r e s p e c t i v e l y .  The v a l u e s  o f C(I)  c o u l d be a r b i t r a r i l y g i v e n . They should f i n a l l y converge a t the same p o i n t .  The computed r e s u l t s a r e p r e s e n t e d the  Table,  function  T3  to  and T be  are the values  minimized.  As  i n T a b l e 8.5.3. I n  o f program  expected,  the  objective tortuosity  c o n s t a n t K becomes s m a l l e r w i t h an i n c r e a s e i n column-making pressure.  In t h e lower  part  of the table,  i n t h e second  column a r e t h e measured r a t e o f p e n e t r a t i o n v a l u e s ; i n t h e third  column  are the values  c o r r e s p o n d i n g equations  calculated  according  i n T a b l e 8.5.1.  In T a b l e 8.5.1, t h e r e a r e e i g h t independent and  nine  solutions  unknowns,  there  should  f o r t h e equations.  i s presented  t o the  Only  be  indefinite  equations number  of  one s e t o f t h e s o l u t i o n s  i n T a b l e 8.5.3. By m u l t i p l y i n g a l l t h e K v a l u e s  by a c o e f f i c i e n t N, and a t t h e same time d i v i d i n g a l l t h e X v a l u e s by t h e same c o e f f i c i e n t , N, one can o b t a i n K'S  1.53NX10" ,  Xi's  797.97/N, 676.39/N, 499.58/N, 453.09/N,  5  1.18NX10" , 5  221  0.98NX10"  5  8.4.12  F i g u r e 8.5.1  An  i l l u s t r a t i o n of  simplex s e a r c h  222  the two  process  dimensional  T a b l e 8.5.3  A General Contact Angle And TortuosityConstant C a l c u l a t i o n R e s u l t s  CYCL. TIMES 501 T3= 0.26980E-05  T= 0.26980E-05  THE TORTUOSITY CONSTANTS KI, K2, K3 0.000027065 0.000020889 0.000017361 THE X VALUES FOR SIX DENSITY FRACTIONS 452.40 383.25 283.22 256.83 205.37  100.58  CONTACT ANGLES ON SIX DENSITY RFACTIONS 55.45 61.28 69.20 71.22 75.08  82.76  DENSITY  SLOPE VALUES MEASURED CALCULATED  DIFFERENCE  RELATIVE%  -0.00056 -0.00074 -0.00012 -0.00011 0.00046 0.00030  -4.78038 -7.65562 -1.,63480 -1..54287 7. 70454 10.03356  -0.00001 0.00028 0.00001 -0.00005 -0.00005 -0.00003  -0.09892 3.41586 0.14100 -0.99584 -1.06134 -1.34038  0.00039 0.00038 0.00008 0.00013 -0.00019 -0.00012  4.71980 5.40061 1.52551 2.86652 -5.71031 -7.14510  6.9 MPa -1.3 1.3- 1.4 1.4- 1.5 1.5- 1.6 1.6- 1.8 +1.8  0.01170 0.00964 0.00754 0.00685 0.00603 0.00303  0.01226 0.01038 0.00767 0.00695 0.00556 0.00273 13.8 MPa  -1.3 1.3- 1.4 1.4- 1.5 1.5- 1.6 1.6- 1.8 +1.8  0.00945 0.00829 0.00592 0.00531 0.00425 0.00207  0.00946 0.00801 0.00591 0.00536 0.00429 0.00210 20.7 MPa  -1.3 1.3- 1.4 1.4- 1.5 1.5- 1.6 1.6- 1.8 +1.8  0.00825 0.00703 0.00499 0.00459 0.00337 0.00163  0.00786 0.00665 0.00491 0.00445 0.00357 0.00175  223  362.37/N, 173.62/N  8.4.13  Above a r e t h e g e n e r a l s o l u t i o n s o f equations i n T a b l e 8.5.1. M a t h e m a t i c a l l y , N can be any r e a l v a l u e . However, one o f the restraints kerosene 90°  i n real  on c o a l  situation  i s t h a t t h e c o n t a c t angle o f  can not be l e s s  (If greater  than  than  90°, kerosene  0° and g r e a t e r will  than  not p e n e t r a t e ) .  T h e r e f o r e , t h e N v a l u e i s l i m i t e d i n t h e range from 1.13 t o 2.0.  Once t h e exact N v a l u e i s o b t a i n e d , a l l t h e K's and 8 's can be c a l c u l a t e d .  In p r e s e n t work, t h i s was done w i t h  quartz.  Quartz,  on which  contact  angle, was ground  water  was  known  t o have a  i n mortar t o t h e same s i z e  zero range  as c o a l powder. The quartz powder was p r e s s e d under p r e s s u r e of  12.7  MPa  procedure  as  constant  into  columns.  that  f o r coal  f o r t h e quartz  Exactly was  t h e same  followed.  column was  easily  experimental  The  tortuosity  calculated  from  Eq.7.2.5 2S-M/7  K =  where n  i s viscosity  o f water, 7 i s t h e s u r f a c e t e n s i o n o f  water.  The  tortuosity  constant  K  f o r quartz  column  made  under p r e s s u r e o f 12.7 MPa was found t o be 1.451x10" . T h i s 5  v a l u e was  a l s o c o n s i d e r e d , a c c o r d i n g t o t h e assumption,  be t h e K v a l u e  f o r a l l coal  columns made under  224  12.7  to MPa.  That  i s , 1.18N  xlO"  5  =  1.451  xicr , 5  and N=1.23.  After  s u b s t i t u t i n g N=1.23 i n t o t h e g e n e r a l s o l u t i o n s i n Eqs.8.4.12 and  8.4.13, one can g e t t h e f i n a l  c o n t a c t angle v a l u e s as  shown i n T a b l e 8.5.4.  The  contact  calculated  through  angles,  as  indirect  discussed  calibration.  assumption made p r e v i o u s l y i n t h i s constant size  above,  According  section,  were t o the  the t o r t u o s i t y  o f a column i s o n l y dependent on p a r t i c l e shapes,  distributions  constant  K  will  and i t s p a c k i n g be  same  m a t e r i a l s w i t h approximately  d e n s i t y . The t o r t u o s i t y  f o r a l l columns  of  different  t h e same s i z e d i s t r i b u t i o n s and  shapes i f they a r e compacted under t h e same p r e s s u r e .  T h i s i m p l i e s how t o f i n d t h e c o r r e l a t i o n between t h e column t o r t u o s i t y  constant  Once t h e c o r r e l a t i o n  and p a r t i c l e s i z e  distribution.  i s d e f i n e d , t o r t u o s i t y c o n s t a n t can be  o b t a i n e d simply from p a r t i c l e s i z e d i s t r i b u t i o n .  8.5.4  Evaluation  The  assumption  that  t h e columns  materials,  b u t under  t h e same  made  pressures,  of different  have  t h e same  t o r t u o s i t y c o n s t a n t K, needed t o be v e r i f i e d . There a r e many ways o f d o i n g t h i s . Cross examination of  this  assumption  i s simply 225  i n which t h e v a l i d i t y  t e s t e d by r e p e a t i n g t h e same  T a b l e 8.5.4  The F i n a l Contact Angle And T o r t u o s i t y Constant C a l c u l a t i o n R e s u l t s (  CYCL. TIMES 5001 T3= 0.13141E-06  T= 0.13141E-06  THE TORTUOSITY CONSTANTS K l , K2, K3 0.000016662 0.000012852  0.000010691  THE X VALUES FOR SIX DENSITY FRACTIONS 734.14 622.91 459.85 417.30 333.77  163.49  CONTACT ANGLES ON SIX DENSITY RFACTIONS 23.02 38.66 54.80 58.46 65.26  78.17  DENSITY  SLOPE VALUES MEASURED CALCULATED  DIFFERENCE  RELATIVE%  6.9 MPa -1.3 1.3- 1.4 1.4- 1.5 1.5- 1.6 1.6- 1.8 +1.8  0.01170 0.00964 0.00754 0.00685 0.00603 0.00303  0.01223 0.01038 0.00766 0.00695 0.00556 0.00272  •0.00053 -0.00074 •0.00012 •0.00011 0.00047 0.00030  -4.55185 -7.63957 -1.56433 -1.60030 7.72557 10.06571  0.00001 0.00028 0.00001 -0.00006 -0.00004 -0.00003  0.11730 3.42823 0.20814 -1.05509 -1.04044 -1.30631  0.00040 0.00037 0.00007 0.00012 -0.00020 -0.00012  4.82406 5.31168 1.48661 2.70571 -5.80134 -7.22349  13.8 MPa -1.3 1.3- 1.4 1.4- 1.5 1.5- 1.6 1.6- 1.8 +1.8  0.00945 0.00829 0.00592 0.00531 0.00425 0.00207  0.00943 0.00801 0.00591 0.00536 0.00429 0.00210 P = 20.7 MPa  +1.3 .3-1.4 .4-1.5 ,5-1.6 .6-1.8 +1.8  0.00825 0.00703 0.00499 0.00459 0.00337 0.00163  0.00785 0.00666 0.00492 0.00446 0.00357 0.00175  226  rate of penetration t e s t with d i f f e r e n t kinds of l i q u i d s i s probably  the  tortuosity different  simplest.  constants, liquids  If  the  K's,  will  keep  t e s t e d . Because  r e p e a t e d t e s t s , t h i s method was  By  assumption  of  is  true,  unchanged the  the  for a l l  l a r g e number  not, a t p r e s e n t ,  of  used.  t a k i n g a l o o k a t the r e l a t i o n s h i p between column  p a c k i n g d e n s i t y and  column-making p r e s s u r e i n F i g u r e 8.3.1,  one can f i n d t h a t a v e r y s i m i l a r r e l a t i o n s h i p e x i s t s between tortuosity  constant  and  column-making  pressure  in  8.5.4. T h i s g i v e s a c l u e t h a t t h e r e must be a c e r t a i n relation  between the  c o n s t a n t . As expected, 8.5.4  plotted  against  8.3.1  gives,  as  column-packing d e n s i t y and  Table linear  tortuosity  the t o r t u o s i t y c o n s t a n t data i n T a b l e the  packing  expected,  a  d e n s i t y data  very  good  in  linear  Figure  relation  ( F i g u r e 8.5.2).  Because are both based there  column-packing  on the same concept,  i s a linear  porosities. above  of  column  particles.  As  different  types  i t can be concluded t h a t  is  made  discussed  obtain K  packing  A t t e n t i o n should be  assumption  column p o r o s i t y  T h i s i s an important  make p o s s i b l e i n f u t u r e t o  measurement  and  r e l a t i o n s h i p between column p o r o s i t y and  t o r t u o s i t y c o n s t a n t K. will  density  of p o r o s i t i e s : 227  values  densities  p a i d t o the  based in  correlation. It  on  the  section the  6.7,  from  or fact  column that  non-porous there  the  are  the  solid two  inner-particle porosity  Packing density mm/gram ^  Packing density  and i n t e r - p a r t i c l e different  types  inter-particle capillary particle compacted  tubes  p o r o s i t y . C o r r e s p o n d i n g l y , t h e r e a r e two  of c a p i l l a r y  tubes: t h e i n n e r - p a r t i c l e  c a p i l l a r y tubes. The r a d i i a r e much more s m a l l e r  of  than  and  inner-particle that  of inter-  c a p i l l a r y tubes. The r a t e o f p e n e t r a t i o n through a column i s mainly c o n t r o l l e d  capillaries.  The p o r o s i t y  by t h e i n t e r - p a r t i c l e  of the material  prominent e f f e c t on t h e r a t e o f p e n e t r a t i o n .  229  does not have a  8.6  SUMMARY AND  The Washburn  DISCUSSION  rate  of  equation  penetration  penetration which  height  p e n e t r a t i o n time.  the  that  linearly  contact  the slope of t h i s l i n e a r  In  states  is  The  technique  angle  the  can  tube  is  tapped  calibrated  penetration  height  method  procedure,  to  on  ensure  its  reading.  was  the  a  cm  a  highly  from t h e fall  handling. height  compacted  T h i s method  and The  i n diameter. packing.  ranges from 0.5  penetration  The vernier.  in  the  of  fine The The  surface  for  the  suffers  from  poor  accuracy.  present  the  (or p i l l a r ) .  work.  The  When r e l e a s e d  c o a l column h o l d i n g does  i s s t r o n g enough t o r e s i s t diameter  the  employed t o compress c o a l powder  column  mounting p r e s s ,  apart  to  tested  uniform  external  modified  specimen mounting p r e s s was into  liquid  c a l c u l a t e d from  r e p r o d u c i b i l i t y and not v e r y good experimental  The  the  relationship.  conventional  i s manually  be  on  squared  proportional  p a r t i c l e s are p l a c e d i n a g l a s s tube 0.8 tube  i s based  the  t o 3 cm.  column  the  experimental  i s 2.54  Kerosene was  not  cm,  and  utilized  the as  a  liquid.  column Because  height  the  was  column  accurately  diameter  230  measured  i s quite  large,  with the  time  i s read when h a l f o f t h e column t o p s u r f a c e i s wetted.  Thus f o r each column, o n l y one p a i r o f data i s o b t a i n e d . F o r each c o a l sample, f o u r t o s i x columns w i t h d i f f e r e n t h e i g h t s were  prepared  and p e n e t r a t e d  t o g e t t h e same  number o f  experimental p o i n t s .  The is  experiments  still  r e v e a l e d t h a t t h e Washburn e q u a t i o n  applicable t o the highly  compacted  column.  The  l i n e a r i t y o f t h e p e n e t r a t i o n l i n e , which i s r e p r e s e n t e d by R squared,  can be as h i g h as 0.9992 t o 1.000 f o r columns made  under p r e s s u r e o f 20.7 MPa. The accuracy i s a l s o v e r y h i g h . The  s t a n d a r d d e v i a t i o n s o f t h e s l o p e v a l u e s a r e o n l y 0.0003  and  0.013  f o r the  respectively  The  slope  values  of  0.163  and  0.8246,  (see T a b l e s 8.2.4 and 8.5.2).  column-making p r e s s u r e has a p o s i t i v e  e f f e c t on  experimental r e p r o d u c i b i l i t y and accuracy. R e s u l t s f o r a -1.3  density  indicate  fraction  t h a t when  of  Bullmoose  coal  a column-making p r e s s u r e  (Table  8.2.4)  increases  from  6.9 t o 20.7 MPa, t h e standard d e v i a t i o n o f t h e s l o p e v a l u e decreases  from  0.059  t o 0.013,  and t h e R  squared  value  i n c r e a s e s from 0.9930 t o 0.9992.  It under  i s possible that  the  However,  influence of  examination  coal  particles  the high  under  can be  column-making  Scanning  Electron  crushed  pressure. Microscope  showed t h a t t h e c r u s h i n g o f c o a l p a r t i c l e s under p r e s s u r e o f 231  up  t o 27.6 MPa i s n e g l i g i b l e .  columns  d i d not exceed  The a p p l i e d p r e s s u r e s  20.7 MPa.  The  minimum  t o make pressure  r e q u i r e d t o make s t r o n g enough columns cannot be lower than 2.8 MPa.  For  a  certain  amount  of coal,  the height  column decreases a p p r e c i a b l y w i t h p r e s s u r e . in  pressure  height  beyond  20 MPa has o n l y  At height as  a  constant  increases with  t h e weight  +1.8 d e n s i t y will  fraction  on t h e  i n t h e column have  packing.  column-making  pressure,  t h e column weight  increases  increase  a slight effect  ( F i g u r e 8.3.1) because p a r t i c l e s  a l r e a d y reached a v e r y c l o s e  Further  of the  to a certain  i n Figure  t h e column  l i n e a r l y . However,  value  (16 grams f o r  8.3.2), t h e column  height  be out o f p r o p o r t i o n and g r e a t e r than p r e d i c t e d .  This  i s because o f t h e f r i c t i o n a l f o r c e s which e x i s t between t h e column and mounting p r e s s mold i n t h e column-making p r o c e s s .  In t h e l i q u i d p e n e t r a t i o n p r o c e s s , some  swelling.  experience  a  The  greater  under  lower p r e s s u r e .  after  liquid  pressure The  columns  made  expansion  under  than  The r e l a t i v e  penetration  i s 0.41%  columns higher  experience pressure  do t h e columns  made  column h e i g h t  increase  f o r columns  made a t  o f 6.9 MPa, and 0.71% f o r columns made.at 20.7 MPa.  expansion i s v e r y s m a l l and can be i g n o r e d .  232  Following (slope)  values  7.2.5)  is  determination from  of  the  test,  to  calculate  employed  the  the  penetration  Washburn the  rate  equation  contact  (Eq.  angles  of  kerosene on the f i n e c o a l p a r t i c l e s . The t o r t u o s i t y  constant  K  unknown.  which  appears  Conventionally, particles  in the  i s used  the  equation  second  to  i s , however,  liquid  obtain  K  which  in a  perfectly  parallel  wets  experiment.  Having K, the c o n t a c t angle can be c a l c u l a t e d . T h i s p r a c t i c e i s not  r e a d i l y a p p l i c a b l e t o c o a l because c o a l i s  heterogeneous and  i t s wettability  extremely  i s widely d i s t r i b u t e d .  l i q u i d can be found t o have a zero c o n t a c t angle on  In the p r e s e n t work, an assumption was  coal.  made t h a t f o r  the m a t e r i a l s w i t h the same p a r t i c l e s i z e d i s t r i b u t i o n , shape,  their  columns,  i f made  under  the  same  possess the same t o r t u o s i t y c o n s t a n t . Under t h i s t h e columns f o r d i f f e r e n t  No  and  pressure,  assumption,  coal density fractions  a l s o have  the same t o r t u o s i t y c o n s t a n t . Washburn equation's m a t r i x f o r different  density  fractions  pressures  i s given  i n Table  program values  was of  used  to  kerosene  of  8.5.1, and  solve t h i s on  coal,  different  and the  matrix. density  at  different  simplex  The  search  contact  fractions  angle of  the  Bullmoose c o a l were c a l c u l a t e d as shown i n T a b l e 8.5.4.  One  o f the  advantages o f t h i s  technique  i s t h a t the  t o t a l s u r f a c e area p e n e t r a t e d by l i q u i d w i t h i n a u n i t h e i g h t of  the  column  i s much g r e a t e r than 233  that i n a  conventional  method. T h e r e f o r e ,  i t i s more s t a t i s t i c a l l y r e p r e s e n t a t i v e .  In a d d i t i o n , the column h e i g h t was to  2 cm  compared t o the  lowered t o a range o f  c o n v e n t i o n a l range o f 4 t o  T h e r e f o r e , the p e n e t r a t i o n p r o c e s s was  cm.  force.  work needed t o be done i n f u t u r e i s t o f i n d  relationship parameters column  10  s u b j e c t e d , t o a much  l e s s e x t e n t , t o the e f f e c t o f g r a v i t a t i o n a l  The  0.5  between  such  as  porosity,  the  tortuosity  particle  and  shape  packing  constant and  size  density.  In  and  the  various  distribution, addition,  the  a p p l i c a b i l i t y of t h i s technique t o d i f f e r e n t combinations  of  l i q u i d s and m a t e r i a l s should a l s o be t e s t e d .  The  q u a n t i t a t i v e comparison  of  the  contact  angle  o b t a i n e d f o r the same c o a l by the "column" method on the  one  hand, and by t h e " p e l l e t " method on the o t h e r , i s i m p o s s i b l e because size.  of  the  dependence  of  the  In a d d i t i o n , kerosene was  and water i n the l a t t e r  Since which  in  form  the  the  contact  used  angles  i n the  on  drop  former method,  one.  direct  method,  pellet  surface  only  those  particles  participate  in  the  measurement, w h i l e a l l the p a r t i c l e s i n the column take p a r t in  affecting  the p e n e t r a t i o n r a t e ,  technique  is  statistically  deviation  of  the  pellets  ranges  from  more  contact 2.06  angle to  3.71  234  the  rate of penetration  reliable. values  The  measured  standard on  degrees c o r r e s p o n d i n g  the to  the  angle  value  measurement deviation  of  error  about  is  1.7  -  corresponding  to  relative  The  degrees.  3.1%.  of the slope values  0.0003 t o 0.013 0.8246.  120  While  The  relative  the  standard  measured on t h e columns i s t o t h e s l o p e v a l u e s o f 0.163  measurement  error  i s 0.2  -  1.6%.  C l e a r l y , t h e measurement accuracy i n t h e r a t e o f p e n e t r a t i o n technique i s higher.  235  CHAPTER 9  CONCLUSIONS  The d i r e c t  a.  On  c o n t a c t angle measurements  a heterogeneous  coal  surface,  the contact  angle  measured by c o n s t r u c t i n g a tangent t o t h e drop p r o f i l e at  t h e three-phase c o n t a c t l i n e and t h e c o n t a c t angle  calculated different. the  through  t h e whole  drop  profile  are  The former one r e f l e c t s t h e c o n t a c t angle on  h i g h e r s u r f a c e energy a r e a , w h i l e t h e l a t t e r one  r e p r e s e n t s t h e average c o n t a c t angle on t h e o v e r a l l heterogeneous value one  surface.  The  i s , on t h e average, calculated  from  directly  five  measured  angle  degrees lower than t h e  t h e same  drop  profile  (Figure  6.2.1).  b.  The c o n t a c t depend  angle on t h e p e l l e t  on t h e drop  size  s u r f a c e was found t o  and t h e way t h e s i z e  of the  drop was manipulated. The c o n t a c t angle o f a l i q u i d on the  s o l i d does not n e c e s s a r i l y i n c r e a s e s w i t h t h e s i z e  of t h e drop. I t can a l s o decrease when t h e drop s i z e i s e n l a r g e d by i n c r e m e n t a l a d d i t i o n s . 236  The  s u r f a c e of a compressed c o a l p e l l e t  macroscopically  flat.  microscopically surface.  The  fractional  very  the  can  porosity  cannot.  6.8,  fractional  the  is  s u r f a c e p o r o s i t y i s c h a r a c t e r i z e d by  porosity  to  pellet  the  its  be  of  pellet  porous  and  on  area  the  However,  i s glossy  both  pores.  inside  While  experimentally  and  the  pellet  measured,  the  bulk  surface  Under the assumption made i n S e c t i o n  bulk  area  o f pores  i s equal,  p o r o s i t y . The  pellet  i n value,  porosity i s  composed o f two p o r t i o n s : i n t r a - p a r t i c l e p o r o s i t y which is  the  porosity  inter-particle particles;  inside  an  individual  p o r o s i t y which  i t i s controlled  and p e l l e t - m a k i n g p r e s s u r e  i s the by  particle,  and  p o r o s i t y between  particle  ( F i g u r e s 6.7.1  size, and  shape,  6.7.2).  The c o n t a c t angle measured d i r e c t l y on the s u r f a c e of a compressed  coal  determined  pellet  is  an  apparent  the  fractional  area  of  a i r pores  can  be  quantitatively  effect  Cassie-Baxter contact  angle  apparent  equation i n t o the  contact  to real  on  fraction  on  the  o f the  pellet  angles  the  pellet  via  the  c o n t a c t angle of  a  -1.3  L i n e Creek c o a l range from 109  the  apparent  angle v a l u e on t h e  surfaces  the  surface.  corrected using  transform  For example i n F i g u r e 6.9.3, the measured  angle  by s o l i d and a i r . The p e l l e t - m a k i n g p r e s s u r e  influences  This  contact  solid. values density to  133  degrees depending on the p e l l e t - m a k i n g correction,  the  contact  angle  pressure.  value  After  become  84.2  degrees.  e.  I t was  found t h a t  than 27.6  MPa  a pellet-making  this  f.  The  of  (and  t h e r e f o r e , does not r e l e a s e  does not  i n f l u e n c e the  applicability  of  r e p r o d u c i b i l i t y o f the c o n t a c t angle measured on  the  coal pellets  as  g i v e n by  the  standard  d e v i a t i o n of the angle v a l u e s ranges from 2.06 degrees.  The  deviation  heterogeneity contact  of  angle  carried  Butler,  Kashi,  t o 4.2  the  mainly  coal  measurements  surfaces  confidence  a.  new  technique).  directly  The  lower  cannot r e s u l t i n the p e r c e i v a b l e c r u s h i n g  o f c o a l p a r t i c l e s and, surfaces  pressure  limit  out  by  resulted  pellet on  and  o f the  contact  3.71  from  the  surface.  finely  Vargha-Butler  Hamza,  to  polished  the coal  e t a l . <Vargha-  Neumann, angle  In  1986>,  ranges from  the 0.5  degrees.  r a t e o f p e n e t r a t i o n method  The  Washburn equation  compacted  column  demonstrated  by  i s w e l l a p p l i c a b l e t o the h i g h l y  made the  of  fine  linearity 238  of  coal.  This  is  the  rate  of  p e n e t r a t i o n r e l a t i o n s h i p . The R squared m u l t i p l e determination)  values f a l l  ( c o e f f i c i e n t of  between  0.9992 and  1.0000. The l i n e a r i t y i s v e r y h i g h .  b.  I t was found t h a t when working w i t h f i n e c o a l particles,  the  modified  gave b e t t e r accuracy the  original  penetration  rate  of  penetration  and r e p r o d u c i b i l i t y  method.  The  slope values  standard ranges  method  than t h a t o f  d e v i a t i o n of  from  0.0003 t o  the 0.013  c o r r e s p o n d i n g t o 0.163 t o 0.8246 o f t h e s l o p e v a l u e s .  c.  The  experimental  accuracy  and  reproducibility  also  depend on t h e f l a t n e s s o f the p e n e t r a t i o n f r o n t w i t h i n the column. The l i q u i d p e n e t r a t i o n f r o n t i n t h e h i g h l y compacted which point  column was  i s the  found  vertical  and t h e lowest  very  flat.  distance  The  between  p o i n t i s lower  than  ruggedness  the  highest  0.06  cm f o r  the columns 2.54 cm i n diameter.  d.  A column made under h i g h e r p r e s s u r e  experiences  a g r e a t e r s w e l l i n g a f t e r p e n e t r a t i o n . The s w e l l i n g f o r all  the  columns,  however,  was  found  t o be  so  small  ( l e s s than 0.71% r e l a t i v e ) , t h a t i t c o u l d be n e g l e c t e d .  e.  The p r e s s u r e i s the most important  factor i n affecting  t h e column p r o p e r t i e s and the p e n e t r a t i o n p r o c e s s . The physical  p r o p e r t i e s o f t h e column become more uniform 239  and r e p r o d u c i b l e under h i g h e r p r e s s u r e . As t h e p r e s s u r e i n c r e a s e s , t h e p e n e t r a t i o n r a t e becomes s m a l l e r f o r t h e same s o l i d - l i q u i d system.  f.  The t o r t u o s i t y constant the  solid  particle making  surface  o f a column i s independent o f  properties. I t s value  shapes and s i z e d i s t r i b u t i o n , pressure.  similar  particle  column  tortuosity  column-making particle identical  For d i f f e r e n t shapes  and  constants  pressure,  deformation  column-making  size  that  there  the by  i s no  applied. At  a l l these  are c h a r a c t e r i z e d by t h e same t o r t u o s i t y  240  controlled  the pressure  pressures,  possessing  distributions,  are only  by  and by column-  materials  provided  under  i s given  columns  constants.  REFERENCES  Adam, N.K., and Jessop, G., (1925) "Angles o f Contact and P o l a r i t y o f S o l i d S u r f a c e s " , J . Chem. Soc.. Vol.127, p.1863. Adam, N.K., (1964) "The Chemical S t r u c t u r e o f S o l i d S u r f a c e s as Deduced From Contact Angle", Contact Angle W e t t a b i l i t y and Adhesion Advances i n Chemistry S e r i e s 43., American Chemical S o c i e t y , Washington, D.C. p.52. 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Zisman, W.A., (1964) " R e l a t i o n o f E q u i l i b r i u m Contact Angle t o L i q u i d and S o l i d C o n s t i t u t i o n " , Contact Angle W e t t a b i l i t y and Adhesion, American Chemical S o c i e t y A p p l i e d P u b l i c a t i o n , Washington, D.C.  249  APPENDIX I  (1)  A FLOWSHEET FOR SIMPLEX SEARCH PROGRAM  CALC. X, A N D (flSS), »  FIND h, S, L. FORM X, "  (1  + a) X, - aX,  CALCULATE (RSS),  IS (RSS), < (nSS)  IS (RSS), > (RSS),  L  \  YES  IS (RSS), > (RSS)„  YES  NO  YES  \ FORM X. o  (1  ' NO •  REPLACE +  r) X, -  X. BY X,  r X,  I IS (RSS), < (RSS)  T t  NO FORM X. -  fi\  +  (1  - fi) X .  YES IS (RSS). > (RSS)„  _L REPLACE  REPLACE  X„ BY X.  X  K  -*•  DY X,  REPLACE NO  ALL X, BY  1/2  REPLACE X . BY X .  HAS MIN. BEEN REACHED  NO  YES  YES  »- PRINTOUT  STOP  (X, + X )  L  APPENDIX 2  Contact Angle C a l c u l a t i o n  Program  ***************************************************** *  *  *  *  *  CONTACT ANGLE CALCULATION PROGRAM  *  * * * * ****************************************************************  * * * *  *  * * * * * * * * * * * * * * * * * *  T h i s i s a program w r i t e n i n FORTRAN f o r t h e c o n t a c t angle r e s u l t c a l c u l a t i o n . I t uses simplex o p t i m i z a t i o n t e c h n i q u e t o s e a r c h the b e s t v a l u e s o f unknown v a r i a b l e s i n t h e s e t o f redundant e q u a t i o n s .  TABLE OF PARAMETERS  N - - t h e number o f s e a r c h v a r i a b l e s Z9 -- t h e s u b r o u t i n e computation c y c l e times RSS and Y ( I ) -- t h e R e s i d u l e Sum o f Squares 1=1 t o N+l H -- t h e p o i n t on t h e simplex where RSS i s the h i g h e s t S -- t h e p o i n t on the simplex where RSS i s t h e second highest L -- t h e p o i n t on t h e simplex where RSS i s the lowest A - - the r e f l e c t i o n c o e f f i c i e n t V - - t h e expansion c o e f f i c i e n t B -- t h e c o n t r a c t i o n c o e f f i c i e n t S L ( I , J ) -- SLope v a l u e s a c t u a l l y measured. S P ( I , J ) -- Slope v a l u e s P r e d i c t e d a c c o d i n g t o t h e e q u a t i o n s I -- the number o f d e n s i t y f r a c t i o n s J -- the number o f column-making p r e s s u r e s used X ( I , J ) -- t h e simplex m a t r i x -- 1=1 t o N+l and J = l t o N GAMA -- the l i q u i d s u r f a c e t e n s i o n MU -- l i q u i d v i s c o s i t y COS - - a t r a n s i t v a r i a b l e  251  INTEGER N, Z9, H, L, S REAL T,T1,T2,T3,C2,RSS,A,V,B, GAMA.MU.COS, N2 DIMENSION D ( 9 ) , C ( 9 ) , X ( 1 0 , 9 ) , Z ( 9 ) , Y ( 1 0 ) , Q ( 9 ) , + SL(6,3),SP(6,3),THETA(6) OPEN (UNIT=12, FILE='SLOPE.DAT', STATUS='OLD') OPEN (UNIT=13, FILE='ANGLE.DAT', STATUS='NEW') READ (12, *) ( S L ( I , 1 ) , 1=1, 6) READ (12, *) ( S L ( I , 2 ) , 1=1, 6) READ (12, *) ( S L ( I , 3 ) , 1=1, 6)  GAMA=27.36 MU=0.01715  N=9 A-l. V=2. B=.5  *****************************************************  * S e t up i n i t i a l simplex -- C a l c u l a t e and s e t up the s t a r t * * values of search v a r i a b l e s C ( I ) 1=1 TO 9 * ***************************************************************  30  32 33  N2=l.1340000032 N2=2. C(1)=0.000013535*N2 C(2)=0.000010450*N2 C(3)=0.000008691*N2 C(4)=903.04/N2 C(5)=767.68/N2 C(6)=564.63/N2 C(7)=513.84/N2 C(8)=410.68/N2 C(9)=200.88/N2 DO 30 J=1,N D(J)=0.1*C(J) CONTINUE DO 31 J = l , N DO 32 1=1, N+l X(I, J)=C(J)-(2./(J+D)*D(J) IF(I.EQ.(J+1)) GO TO 33 CONTINUE X(I, J)=C(J)+((2./(J+l))*D(J))*J DO 34 I=J+2, N+l X(I, J)=C(J) 252  34 31  CONTINUE CONTINUE  ******************************************** *  C a l c u l a t e the s t a n d a r d  error of objective function  *  **************************************************************** Z9=0 T3=1.E9  * 101  70  * 91  92  93  C a l c u l a t e t h e r e s i d u a l sum o f (RSS)i DO 70 K=l, N+l H=K CALL SUBRSS(N, X, H, RSS, Z9, SL, SP) Y(K)=RSS CONTINUE  To f i n d out the H, L, S CALL SUBLHS(Y, N, H, L, S, RSSH, RSSL, RSSS) T1=0. T2=0. DO 92 1=1, N+l T1=T1+Y(I) CONTINUE DO 93 1=1, N+l T2=T2+(Y(I)-Tl/(N+1))**2 CONTINUE T=SQRT(T2/N)  **************************************************************** * Judge minimum o r c y c l e mnumber b e i n g r e a r c h e d o r n o t * **************************************************************** I F (T.LT.1.E-10.OR.Z9.GT.500) GO TO 81 I F (T.GT.T3) GO TO 41 T3=T  253  ************************************* * Reflection Xr=(l+A)Xo-AXh  *  **************************************************************** 41  42  43  *  88  DO 43 J - l , N P=0 DO 42 1=1, N+l IF(I.EQ.H) GO TO 42 P=P+X(I, J ) / N CONTINUE Q(J)-X(H, J ) Z(J)=(1.+A)*P-A*X(H, J ) X(H, J ) - Z ( J ) D(J)-P CONTINUE  Calculate  (RSS)r  CALL SUBRSS(N, X, H, RSS, Z9, SL, SP) R=RSS IF(RSS.LT.Y(L)) GO TO 71 IF(RSS.LT.Y(S)) GO TO 91 IF(RSS.LT.Y(H)) THEN Y(H)=RSS GO TO 51 ELSE DO 88 J = l , N X(H, J ) - Q ( J ) CONTINUE ENDIF  **************************************************************** * Contration Xc=BXh+(l-B)*Xo, Replacement o f Xh by Xc * **************************************************************** 51  52  *  J=0 DO 52 J - l , N Q(J)=X(H, J ) X(H, J)=B*X(H, J ) + ( l . - B ) * D ( J ) CONTINUE  Calculate  (RSS)c  254  CALL SUBRSS(N, X, H, RSS, Z9, SL, SP) IF(RSS.GT.Y(H)) GO TO 55 Y(H)=RSS GO TO 91  *************************************** *  Reduce the s i z e o f simplex  *  **************************************************************** 55  56 57  * 25  26  1=0 J=0 DO 57 J - l , N X(H, J ) - Q ( J ) DO 56 1=1, N+l X ( I , J ) - ( X ( I , J)+X(L, J ) ) / 2 CONTINUE CONTINUE GO TO 101  Replace Xh by X r J=0 DO 26 J - l , N X(H, J ) = Z ( J ) CONTINUE Y(H)=R GO TO 91  **************************************************************** *Expansion, X e = ( l + v ) * Z ( l , J ) - v * D ( l , J ) , replacement o f Xh by Xe* **************************************************************** 71  72  *  J=0 DO 72 J - l , N X(H, J)=(1.+V)*Z(J)-V*D(J) CONTINUE  Calculate  (RSS)e  CALL SUBRSS(N, X, H, RSS, Z9, SL, SP) IF(RSS.GT.Y(L)) GOTO 25 Y(H)=RSS GO TO 91 255  ********************************************* * C o n t a c t Angle C a l c u l a t i o n * * d(HxH)/dT = K.Gama.Cos(Theta)/(2.Mu) * **************************************************************** 81  5  C0S=GAMA/2./MU DO 5 1=1, 6 THETA(I)=X(L,1+3)/COS IF(THETA(I).LE.1.0) THEN THETA(I)=AC0S(THETA(I))*180./3.1416 ELSE THETA(I)=0.0 ENDIF CONTINUE  **************************************************************** *  P r i n t out the r e s u l t  *  ****************************************************************  78 77  2 3  124 120  125 126  PRINT * WRITE(13, 78) FORMAT(5X, 5HCYCL., IX, 5HTIMES) WRITE(13, 77) Z9 FORMAT(5X, 15) WRITE(13, *) WRITE(13, 2) FORMAT(5X, 3HT3=, 16X, 2HT=) WRITE(13, 3) T3, T FORMAT(5X, 2E13.5) WRITE(13, *)  WRITE(13, 124) FORMAT(5X, 35HTHE TORTUOSITY CONSTANTS KI, K2, K3) WRITE(13, 120) ( X ( L , I ) , 1=1,3) FORMAT(5X, 3F16.9) WRITE(13, *)  WRITE(13, 125) FORMAT(5X, 38HTHE X VALUES FOR SIX DENSITY FRACTIONS) WRITE(13, 126) ( X ( L , I ) , 1=4, 9) FORMAT(5X, 6F9.2) WRITE(13, *) 256  WRITE(13, 129) FORMAT(5X, 39HCONTACT ANGLES ON SIX DENSITY WRITE(13,128) (THETA(I), 1=1, 6) FORMAT(5X, 6F9.2) WRITE(13, *)  129 128  127 +  + 121 122  123  RFACTIONS)  WRITE(13, 127) FORMAT(7X, 8HMEASURED, 4X, 10HCALCULATED, 3X, 10HDIFFERENCE, 5X, 9HRELATIVE%) WRITE(13, *) DO 123 J = l , 3 DO 122 1=1, 6 WRITE(13, 121) S L ( I , J ) , S P ( I , J ) , S L ( I , J ) - S P ( I , J ) , (SL(I,J)-SP(I,J))/SL(I,J)*10O. FORMAT(IX, 4F13.5) CONTINUE WRITE(13, *) WRITE(13, *) CONTINUE STOP END  ****************************  * SUBROUTINE I * * T h i s s u b r o u t i n e i s used f o r c a l c u l a t i n g (RSS) * **************************************************************** SUBROUTINE SUBRSS(N, X, H, RSS, Z9, SL, SP) INTEGER H, Z9, I , J REAL C2, RSS, X(N+1, N), SL(6,3), SP(6,3)  *  4 2  *  C a l c u l a t e the p r e d i c t e d  values  DO 2 J = l , 3 DO 4 1=1, 6 SP(I,J)=X(H,J)*X(H,3+I) CONTINUE CONTINUE  C a l c u l a t e the r e s i d u a l sum o f squares  257  8 6  C2=0 DO 6 J = l , 3 DO 8 1-1, 6 C2=C2+(SL(I,J)-SP(I,J))**2/SL(I,J)**2 CONTINUE CONTINUE RSS=C2 Z9=Z9+1 RETURN END  ****************************************** * SUBROUTINE I I * * The s u b r o u t i n e f o r f i n d i n g out H^L, S * ****************************************************************  21  23  SUBROUTINE SUBLHS(Y, N, H, L, S, RSSH, RSSL, RSSS ) REAL Y(N+l), RSSH, RSSL, RSSS INTEGER L, H, S H=l S-l L=l DO 21 1=2, N+l I F ( Y ( I ) . G T . Y ( H ) ) THEN H=I ELSE I F ( Y ( I ) . L T . Y ( L ) ) THEN L=I ELSE END I F END I F CONTINUE RSSH=Y(H) RSSL=Y(L) Y(H)=0. DO 23 1=2, N+l I F ( Y ( I ) . G T . Y ( S ) ) THEN S=I ELSE END I F CONTINUE Y(H)=RSSH RETURN END  258  

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