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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, H e i l o n g j i a n g I n s t i t u t e o f Mining & Tech., P.R.C, 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of Mining and M i n e r a l Process Engineering) We accept t h i s t h e s i s as conforming t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA August 1989 © Y i n g B i n He, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, 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 head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of HJ" > n C l Q ^ Mt"e» ,ft| Process Engineer ing The University of British Columbia Vancouver, Canada Date Oct. 13 , tHf  DE-6 (2/88) ABSTRACT T h i s study i n v e s t i g a t e s the t e c h n i q u e s of c o n t a c t angle measurement on f i n e c o a l p a r t i c l e s . Two t e c h n i q u e s , one d i r e c t and one i n d i r e c t , have been i n v e s t i g a t e d and m o d i f i e d . In the d i r e c t c o n t a c t angle measurement technique, h i g h p r e s s u r e i s employed t o compress the c o a l powder i n t o a p e l l e t and the a r t i f i c i a l s u r f a c e o f the p e l l e t i s employed i n t h e c o n t a c t angle measurements. The c o n t a c t angle v e r s u s time and v e r s u s drop s i z e on the p e l l e t s u r f a c e are examined. In a d d i t i o n , the p e l l e t p r o p e r t i e s and f a c t o r s a f f e c t i n g t h e p e l l e t p r o p e r t i e s are a l s o s t u d i e d . A p e l l e t s u r f a c e model and a method f o r c o n t a c t angle c o r r e c t i o n are proposed. In the i n d i r e c t measurement, the c o n t a c t angle i s c a l c u l a t e d from the p e n e t r a t i o n r a t e . The method i s m o d i f i e d t o employ h i g h p r e s s u r e s t o produce h i g h l y compact columns. The h o l d i n g g l a s s tube t r a d i t i o n a l l y used f o r the column of powder i s , t h e r e f o r e , no l o n g e r needed. The change i n p e n e t r a t i o n behaviour of the l i q u i d w i t h i n such columns i s i n v e s t i g a t e d . The p r o p e r t i e s of the columns and the impact of the p r e s s u r e a p p l i e d i n t h e i r f o r m a t i o n on the r a t e of l i q u i d p e n e t r a t i o n as w e l l as o t h e r phenomena are s t u d i e d . A c o n t a c t angle c a l c u l a t i o n procedure i s a l s o proposed. TABLE OF CONTENTS ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES v i i LIST OF FIGURES i x ACKNOWLEDGEMENT xiv CHAPTER 1. INTRODUCTION 1 CHAPTER 2. LITERATURE REVIEW 4 2.1 General Concept 5 2.1.1 Contact Angle On An Ideal Surface 5 2.1.2 Contact Angle Hysteresis 6 2.1.3 Heterogeneity and Cassie's Equation 7 2.1.4 Roughness and Wenzel's Equation 10 2.1.5 Composite Configuration and Cassie-Baxter Equation 13 2.2 Contact Angle Measurements 16 2.2.1 Direct Contact Angle Measurements 16 2.2.2 Indirect Contact Angle Measurements 21 2.3 Other Techniques to Characterize Wettability 29 2.3.1 Hy d r o p h i l i c i t y Index 29 2.3.2 Induction Time 30 2.3.3 Heat of Immersion 32 2.3.4 Rate of Immersion 34 2.3.5 Film F l o t a t i o n 37 2.3.6 C r i t i c a l Surface Tension of Fl o t a t i o n 39 2.3.7 Other Techniques 43 CHAPTER 3. COAL 44 3.1 Introduction 44 i i i 3.1.1 C l a s s i f i c a t i o n 44 3.1.2 Chemical Composition 47 3.2 Homogenization 49 3.3 Coal Studied 50 CHAPTER 4. OBJECTIVE 55 CHAPTER 5. DIRECT CONTACT ANGLE MEASUREMENTS AND EXPERIMENTAL 57 5.1 Introduction 57 5.2 Theory and Techniques 59 5.2.1 Background 59 5.2.2 Techniques 63 5.3 Experimental and Apparatus 67 5.3.1 Sink-and-Float Test 67 5.3.2 Comminution of Coal Samples ....68 5.3.3 P a r t i c l e Size Analysis 68 5.3.4 Pellet-Making 69 5.3.5 Porosity Measurement 71 5.3.6 P e l l e t Surface Examination 73 CHAPTER 6. RESULTS AND DISCUSSIONS <I> 74 6.1 Contact Angle Measurements 75 6.2 Comparison of The Two Techniques 78 6.3 Testing The Computation Method 84 6.3 Contact Angle Versus Drop Size 91 6.5 Contact Angle Versus Time 101 6.6 Factors A f f e c t i n g Contact Angle 105 6.6.1 Oxidation 105 6.6.2 Pellet-Making Pressure I l l 6.7 Porosity 117 6.8 Surface Examination and Assumption For Fracti o n a l Area of Pores 125 6.9 A Model 134 i v 6.9.1 A Compressed P e l l e t Surface Model 133 6.9.2 Contact Angle Correction And Comparison 137 6.10 Summary and Discussion 143 CHAPTER 7. THE RATE OF PENETRATION TECHNIQUE 148 7.1 Introduction 148 7.2 Theory and Techniques 151 7.2.1 Basic Theory 151 7.2.2 Techniques 155 7.3 Experimental 157 7.3.1 Materials 157 7.3.2 Column-Making 158 7.3.3 Rate of Penetration Measurement 158 7.3.4 V i s c o s i t y and Surface Tension 161 CHAPTER 8. RESULTS AND DISCUSSIONS <II> 163 8.1 A p p l i c a b i l i t y Test 163 8.1.1 Some Features 163 8.1.2 Precision and L i n e a r i t y 165 8.1.3 Height Limit 170 8.2 Column-Making Pressure 173 8.2.1 The E f f e c t of Pressure on Reproducibility and L i n e a r i t y ..173 8.2.2 E f f e c t on Rate of Penetration 189 8.2.3 Side E f f e c t of High Pressure ..193 8.2.4 Lower Limit of Pressure 194 8.3 Physical Properties of Columns 196 8.3.1 Column Height versus Pressure ..196 8.3.2 Column Height versus Weight ...198 8.3.3 Column Porosity 200 8.3.4 Column Expansion 201 8.4 E f f e c t of F r i c t i o n 203 8.5 Contact Angle Calculations 213 8.5.1 Introduction 213 8.5.2 A New Approach 214 8.5.3 Numerical Calculations 217 8.5.4 Evaluation 225 v 8.6 Summary and Discussion 230 CHAPTER 9. CONCLUSIONS 236 REFERENCES 241 APPENDIX 1. A FLOWSHEET FOR SIMPLEX SEARCH PROGRAM 250 APPENDIX 2. CONTACT ANGLE CALCULATION PROGRAM 251 v i LIST OF TABLES Table Page 3.1.1 Coals arranged i n an ascending order of carbon 45 content. 3.3.1 Quality c h a r a c t e r i s t i c s of Line Creek clean 52 coal 3.3.2 Proximate analysis of ROM Bullmoose seam C coal 52 dry basis. 6.6.1 The contact angle on p e l l e t of oxidized 107 coal - the -1.3 of the Bullmoose coal 6.6.2 Comparison of the contact angles with the rate 108 of penetration measured on d i f f e r e n t coals. 8.1.1 Test f o r the ruggedness of penetration front 168 on the 1.4-1.5 density f r a c t i o n . 8.2.1 S t a t i s t i c analysis of penetration data f o r 184 BM coal, pressure i s 6.9 MPa. 8.2.2 S t a t i s t i c analysis of penetration data f o r BM 185 coal, pressure i s 13.8 MPa. 8.2.3 S t a t i s t i c analysis of penetration data f o r BM 186 coal,pressure i s 20.7 MPa. 8.2.4 The e f f e c t of column-making pressure on 187 accuracy and and l i n e a r i t y of the rate of penetration l i n e . 8.3.1 Swell of columns a f t e r penetrated by l i q u i d . 202 8.5.1 Rate of penetration equation matrix. 218 v i i 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 various pressure. 8.5.3 A general contact angle and t o r t u o s i t y constant 223 c a l c u l a t i o n r e s u l t s . 8.5.4 The f i n a l contact angle and t o r t u o s i t y constant 226 c a l c u l a t i o n r e s u l t s . v i i i LIST OF FIGURES 2.1.1 Equilibrium contact angle formed by water, 8 vapour (gas), and s o l i d phases. 2.1.2 Models of heterogeneous surfaces. 8 2.1.3 A model of i d e a l i z e d rough surface. 12 2.1.4 An i l l u s t r a t i o n of composite configuration. 14 2.1.5 Contact angle hysteresis on a model porous 14 surface. 2.2.1 Constructing a tangent to the p r o f i l e . 17 2.2.2 The t i l t e d plate method for contact angle 18 measurement. 2.2.3 The c y l i n d r i c a l rod method f o r contact angle 18 measurement. 2.2.4 The Wilhelmy method. 22 2.2.5 C a p i l l a r y r i s e at v e r t i c a l plate. 25 2.2.6 The microscope interference method. 25 2.3.1 Rate of immersion technique. 3 6 2.3.2 Film f l o t a t i o n . 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 molecular model of coal proposed by Wiser. 48 3.3.1 The sink-and-float t e s t for the Line Creek coal . 53 3.3.2 The sink-and-float t e s t for the Bullmoose coal. 53 5.2.1 The d e f i n i t i o n of the coordinate system f o r a 61 ix s e s s i l e drop p r o f i l e . 5.2.2 The set-up of a Rame-Hart model 100 contact 64 angle goniometer. 5.3.1 A MET-A-TEST specimen mounting press. 70 6.1.1 A s e s s i l e drop image observed through the 77 goniometer. 6.2.1 A comparison of the measured and the computed 79 contact angles on a p e l l e t (-1.3 Line Creek co a l ) . 6.2.2 An i d e a l i z e d heterogeneous surface model. 82 6.3.1 The posi t i o n i n g of the drop baseline and i t s 86 e f f e c t on computed angle value. 6.3.2 The posi t i o n i n g of the apex point and i t s 87 e f f e c t on the computed angle value. 6.3.3 The measurement of sc a l i n g factor and i t s 88 e f f e c t on the computed angle value. 6.3.4 The accuracy of l i q u i d density measurement 89 and i t s e f f e c t on the computed angle value. 6.4.1 The e f f e c t of drop volume on the contact 93 angle - drop volume increased i n two ways. 6.4.2 Drop s i z e e f f e c t on contact angle (1.3-1.4 95 Density f r a c t i o n P=31.1 MPa). 6.4.3 Drop s i z e e f f e c t on contact angle (oxidized 96 -1.3 Bullmoose coal t=150°C) 6.4.4 Drop s i z e e f f e c t on contact angle (oxidized 97 -1.3 Bullmoose coal t=200°C) 6.4.5 Drop s i z e e f f e c t on contact angle (oxidized 98 x -1.3 Bullmoose coal t=250°C) 6.5.1 Contact angle vs. time for d i f f e r e n t density 102 f r a c t i o n s of Line Creek coal . 6.6.1 Contact angle versus oxidation time - oxidized 110 i n water and i n a i r . 6.6.2 Contact angle vs. pellet-making pressure f o r 113 the Line Creek coal -1.3 density f r a c t i o n . 6.6.3 The e f f e c t of pellet-making pressure on contact 114 angle (-1.3 density f r a c t i o n of Bullmoose coal) 6.6.4 The influence of pellet-making pressure on 115 angle r e p r o d u c i b i l i t y (-1.3 of Bullmoose c o a l ) . 6.7.1 The p e l l e t porosity vs. pressure f o r d i f f e r e n t 120 density f r a c t i o n s of the Line Creek coal . 6.7.2 The p e l l e t porosity vs. pressure f o r d i f f e r e n t 121 density f r a c t i o n s of the Line Creek coal . 6.7.3 C h a r a c t e r i s t i c p a r t i c l e sizes f o r d i f f e r e n t 123 density f r a c t i o n s of the Line Creek coal . 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 surface. 130 6.9.1 A model of compressed p e l l e t surface. 134 6.9.2 Contact angle vs. ash content and corrected 140 contact angle for LC coa l . 6.9.3 Measured and corrected contact angle values 141 versus pressure for Line Creek coal. 7.3.1 The columns made for the rate of penetration 160 t e s t . x i 8.1.1 A p p l i c a b i l i t y of the Washburn equation. 171 8.2.1 Rate of penetration curves for columns of 174 -1.3 BM coal made under d i f f e r e n t pressures. 8.2.2 Rate of penetration curves for columns of 175 1.3- 1.4 BM coal made under d i f f e r e n t pressures. 8.2.3 Rate of penetration curves for columns of 176 1.4- 1.5 BM coal made under d i f f e r e n t pressures. 8.2.4 Rate of penetration curves f o r columns of 177 1.5- 1.6 BM coal made under d i f f e r e n t pressures. 8.2.5 Rate of penetration curves f o r columns of 178 1.6- 1.8 BM coal made under d i f f e r e n t pressure. 8.2.6 Rate of penetration curves f o r columns of 179 +1.8 BM coal made under d i f f e r e n t pressure. 8.2.7 Rate of penetration for d i f f e r e n t density 181 fra c t i o n s (columns made under 6.9 MPa). 8.2.8 Rate of penetration f o r d i f f e r e n t s p e c i f i c 182 density f r a c t i o n s (columns made under 13.8 MPa). 8.2.9 Rate of penetration for d i f f e r e n t s p e c i f i c 183 density fract i o n s (columns made under 20.7 MPa). 8.2.10 The e f f e c t of column-making pressure on the 190 slope of the rate of penetration curve. 8.3.1 The e f f e c t of column-making pressure on the 197 column-packing density (Bullmoose coal -1.3 density fraction) 8.3.2 Column weight versus i t s height (+1.8 density 199 f r a c t i o n pressure=13.8 MPa). 8.4.1 Change i n the rate of penetration behaviour 204 x i i when columns placed upside down. 8.4.2 The forces acting on the column within the 206 mould. 8.4.3 The t h e o r e t i c a l e f f e c t of column height on the 209 in t e g r a l porosity of the column. 8.4.4 Column height versus i n t e g r a l porosity - values 210 obtained from actual measurement I. 8.4.5 Column height versus i n t e g r a l porosity - values 211 obtained from actual measurement I I . 8.5.1 An i l l u s t r a t i o n of the two dimensional simplex 222 search process. 8.5.2 The t o r t u o s i t y constant versus packing density. 228 x i i i ACKNOWLEDGEMENT The author wishes to express h i s deepest gratitude to Dr. Janusz S. Laskowski under whose kind d i r e c t i o n and guidance t h i s work was undertaken. The technical assistance provided by Mrs. S. Finora, and Mr. F. Schmidiger i s g r a t e f u l l y acknowledged. The author also wishes to express h i s gratitude to Professor A.L Mular f o r h i s valuable teaching i n some very i n t e r e s t i n g and useful courses, and to a l l the fellow students i n Dept. of Mining and Mineral Process Engineering (UBC), e s p e c i a l l y to Mrs. Maria Holuzko f o r many valuable discussions; to Mr. K. Lund and Mr. B. K l e i n f o r proof reading t h i s t h e s i s . My sp e c i a l thanks are given to my wife, Ying Wang, for encouraging me with understanding, care, and enduring love, and f o r sharing i n the happiness and hardships of the past years. xiv CHAPTER 1 INTRODUCTION The hydrophilic-hydrophobic c h a r a c t e r i s t i c of a s o l i d plays a predominant r o l e i n diverse technological processes such as fr o t h f l o t a t i o n , lithographic p r i n t i n g , detergency, t e x t i l e manufacturing, c e l l adhesion and the thrombo-resistance of bio-materials, etc. One of the most common methods f o r determining the hydrophobicity of a s o l i d surface has been through the contact angle measurements. Some materials on which the contact angles are to be measured, are not availa b l e i n sizes large enough to be polished to accommodate the s e s s i l e drops. In the case of coal, a d d i t i o n a l problems a r i s e because coal i s a mixture of the degradation products of plants and of mineral matter. Wide v a r i a t i o n s i n t h e i r genesis, composition, and hydrophobicity make coal highly heterogeneous. In order to accomplish meaningful contact angle measurements, two techniques have been studied. One i s the Compressed P e l l e t Method - a d i r e c t contact angle 1 measurement technique; another i s the Rate of Penetration Method - an i n d i r e c t technique. In both cases, a very f i n e o r i g i n a l sample was u t i l i z e d . For d i r e c t contact angle measurement (compressed p e l l e t method), i t i s desirable to obtain a f l a t surface which should be macroscopically homogeneous as compared with the dimension of the s e s s i l e drop and representative of the e n t i r e coal sample tested. The coal powder was compressed under high pressure into p e l l e t s of 25.4 mm diameter (one inch) and 5 to 8 mm height. The contact angles were d i r e c t l y measured on the p e l l e t upper surface. The f e a s i b i l i t y of t h i s technique and a v a r i e t y of factors influencing the contact angle measurement on p e l l e t surface were investigated. The measured contact angles were considered the apparent ones. A p e l l e t surface model and contact angle correc t i o n method were t e n t a t i v e l y proposed to convert the measured contact angle values to the true contact angle values. This technique has the advantage of being quick and d i r e c t . However, when the contact angle values are very small, the l i q u i d from the s e s s i l e drop s t a r t s to penetrate into the p e l l e t and equilibrium can not be established. 2 Contact angles have also been measured i n d i r e c t l y from the rate of penetration The technique was modified i n t h i s work by making the columns using a machine-controlled high pressure press. This made possible to overcome problems i n the t r a d i t i o n a l method r e s u l t i n g from the poor r e p r o d u c i b i l i t y i n column physical properties, data sca t t e r i n g etc.. The e f f e c t s of column-making pressure on the l i q u i d penetration rate and column properties were studied. A new c a l i b r a t i o n method was proposed. Since i n the d i r e c t method only those p a r t i c l e s which form the p e l l e t surface p a r t i c i p a t e i n the measurement, while a l l p a r t i c l e s i n the column have an e f f e c t on the penetration rate, the l a t t e r technique i s s t a t i s t i c a l l y more r e l i a b l e . I t s accuracy and r e p r o d u c i b i l i t y are higher than the d i r e c t method. 3 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 important i n many technological processes. The contact angle of l i q u i d on the s o l i d surface i s the most commonly used parameter i n the w e t t a b i l i t y study process. The contact angles are usually measured on f l a t surfaces, and les s frequently 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 divided p a r t i c u l a t e s o l i d surfaces has become more and more important and has developed into a new f i e l d f o r study. A v a r i e t y of techniques have emerged i n the l a s t twenty years. Some relevant basic theories and recently developed modifications w i l l be b r i e f l y reviewed i n the following sections. 4 2.1 GENERAL CONCEPTS 2.1.1 Contact Angle On An Ideal Surface The contact angle i s , i n t r i n s i c a l l y , a macroscopic property and a useful measure of s o l i d w e t t a b i l i t y . On an i d e a l i z e d smooth, homogeneous, nondeformable surface, the free l i q u i d drop takes the shape which minimizes the free energy of the system. The equilibrium contact angle formed by l i q u i d on the i d e a l i z e d surface i s a unique quantity <Neumann and Good, 1972>. The contact angle was f i r s t linked to surface energy by Thomas Young <1855>. I t was demonstrated by Gibbs, <1928> that minimizing the free energy requires the minimization of the sum T l v ^ l v + 7 s v * s v + T s l ^ s l 2.1.1 where 7 i s a surface or i n t e r f a c i a l tension, A i s an area, and the subscripts l v , sv, and s i r e f e r to liquid/vapour, s o l i d / vapour and s o l i d / l i q u i d interfaces, r e s p e c t i v e l y . The minimization y i e l d s the following equation "YigCOSfl = 7 - 7 s i 2.1.2 5 where 6 i s the contact angle. This equation i s known as Young's equation. Figure 2.1.1 i l l u s t r a t e s the c l a s s i c a l three-phase l i n e of contact between water, vapour, and a smooth nondeformable s o l i d surface. The angle which a drop assumes on the s o l i d surface i s the r e s u l t of a balance between the forces at a i r / l i q u i d 7 l g , l i q u i d / s o l i d y B l , and a i r / s o l i d 7 s l interface as shown i n the above equation and Figure 2.1.1. 2.1.2 Contact Angle Hysteresis For a r e a l l i q u i d / s o l i d system, a number of stable contact angles can be assumed, i n apparent contradiction to the Young equation. Two r e l a t i v e l y reproducible angles are the largest and the smallest. These are c a l l e d the advancing angle, 8a , and the receding angle, 0 r , respectively. Their names are derived from the fa c t that the advancing angle i s measured when the periphery of a drop advances over a surface, and the receding angle i s measured by p u l l i n g i t back. The difference da-6g i s termed the contact angle hysteresis. Two major factors which are a t t r i b u t e d to the hysteresis are surface heterogeneity and roughness. Detailed review of both w i l l follow i n the next two sections. 6 The symbols 6e and dy stand f o r the equilibrium contact angle, and Young contact angle, respectively. 6y obeys Young's equation on a smooth, homogeneous surface of s p e c i f i c composition and structure, while 8e may e x i s t on heterogeneous or rough surfaces and i t may not conform to Young's equation. Commonly, 6e i s obtained from experiment. 2.1.3 Heterogeneity And The Cassie Equation One of the major causes of hysteresis i s the heterogeneous nature of s o l i d surfaces <Johnson and Dettre, 1964>. The surface consists of varying chemical compositions. They may be present as a d i s t i n c t phase or as an adsorbed f i l m which can not be i d e n t i f i a b l e as a phase. Figure 2.1.2. shows two regions of a s o l i d surface mosaic. The l o c a l contact angle w i l l depend on the surface energy of the region with which the l i q u i d i s i n contact. The islands i n Fig.2.1.2(a) represent high-contact-angle regions on the surface. As a drop periphery advances over such a surface, the edge of the l i q u i d tends to stop at the boundaries of the islands. I t was suggested <Pease, 1945> that advancing angles should be associated with the i n t r i n s i c angle of the high-contact-angle regions of surfaces. S i m i l a r l y , receding angles should be associated 7 F i g u r e 2 .1 .1 E q u i l i b r i u m con t a c t angle formed by water v apou r (gas ) , and s o l i d phases . PLAN VIEW (a) A g e n e r a l mode l ; (b) An i d e a l i z e d model F i g u r e 2 .1 .2 Models o f heterogeneous s u r f a c e s 8 with the low-contact-angle areas. Cassie <Cassie, 1948> suggested that the equilibrium contact angle of a smooth micro-heterogeneous surface co n s i s t i n g of a "patchwork" arrangement of two homogeneous elements could be described by COS0 = a 1 - C O S 9 1 + a 2 - C O S 9 z 2.1.4 where ai i s the f r a c t i o n of the surface characterized by contact angle ex, and a2 i s the f r a c t i o n having angle 82 < 7 1 + < 7 2 = 1 2.1.5 When the number of elements i s more than two, t h i s equation can be generalized as cosfl >= 2 < r 1-cos* i 2.1.6 Embodied i n t h i s equation i s the assumption that the two components occur as discrete, uniformly d i s t r i b u t e d patches at the surface which are small compared to the area of the drop or bubble used to measure the contact angle. The Cassie equation has been confirmed experimentally and used i n various si t u a t i o n s <Cassie and Baxter, 1944; O l i v e r et a l . , 1977; Lamb and Furlong, 1977; and Blake and Ralston, 1985>. Johnson and Dettre <1964> analyzed an i d e a l i z e d model 9 c o n s i s t i n g of concentric c i r c u l a r regions of a l t e r n a t i n g i n t r i n s i c contact angle ex and 62 as shown i n Figure 2.1.2 The r e s u l t s reveal that as the v i b r a t i o n a l state of the l i q u i d becomes greater, or as the sizes of the hetero-geneities on the surface become smaller, the contact angles tend to be c l o s e r to that predicted by Cassie's equation. The random heterogeneity of a r e a l surface permits more meta-stable configuration and smaller energy b a r r i e r s . The w e t t a b i l i t y behaviour of a r e a l surface should s t i l l be q u a n t i t a t i v e l y s i m i l a r to that of the concentric c i r c u l a r model. This has been experimentally v e r i f i e d <Dettre and Johnson 1964; Crawford and Koopal, 1987>. For the composite surface with pores as i n the case of p e l l e t , the region of pores can be considered as a composite consisting of a i r , and the Cassie equation can s t i l l be applied. 2.1.4 Roughness And The Wenzel Equation The contact angles of a l i q u i d with the s o l i d are d i r e c t l y dependent on the macroscopic geometry of the s o l i d . Wenzel<1936> developed a r e l a t i o n between the macroscopic roughness of a s o l i d surface and the contact angle: 10 cose ' = r-cos0 2.1.7 where 8 ' i s the measured or apparent contact angle, 8 i s the true contact angle, and r i s the surface roughness c o e f f i c i e n t . The simplest parameter fo r describing roughness i s the roughness r a t i o r = A/a 2.1.8 where A i s the true surface area and a i s the apparent or envelope area on a plane p a r a l l e l to the apparent surface. Certain i d e a l i z e d configuration have been studied by Johnson and Dettre <1964>, and Eick et al.<1975>. The model chosen by Johnson and Dettre (Figure 2.1.3) consisted of a drop of l i q u i d on a surface of concentric grooves which were large with respect to molecular dimensions, but small compared with macroscopic laboratory apparatus. The analysis of t h i s i d e a l i z e d surface showed that roughness leads to a large number of meta-stable configurations. Each meta-stable state was separated from an adjacent state by an energy b a r r i e r . The heights of the energy b a r r i e r s were approximately d i r e c t l y proportional to the height of the a s p e r i t i e s and independent of t h e i r separation. There are, however, s i g n i f i c a n t differences between 11 F i g u r e 2 .1 .3 A model o f i d e a l i z e d rough s u r f a c e (Johnson and Dettre<1964>) the 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 s u r f a c e s . From a thermodynamic s t a n d p o i n t , go ing from a c i r c u l a r groove model t o a random h i l l - a n d - v a l l e y model i n t r o d u c e s more me ta-s t ab l e s t a t e s and lowers the energy b a r r i e r s between them. Huh and Mason<1977> m o d i f i e d Wenze l ' s o r i g i n a l roughness e q u a t i o n t o account f o r the case o f random s u r f a c e roughness by i n t r o d u c i n g a s u r f a c e t e x t i l e f a c t o r * cos f l 1 = (r + (r-l)tf)•cosfl 2 .1 .9 C o n c e n t r i c grooves and r a d i a l grooves would p r e sen t two p o s s i b l e t e x t u r e s f o r which r c o u l d be the same but the i n f l u e n c e on e be q u i t e d i f f e r e n t . Fo r a roughness i n which the h e i g h t f o l l o w s a Gauss ian d i s t r i b u t i o n , i t was found t h a t when the drop s i z e i s l a r g e compared t o the roughness , - 0. 12 Objections have been raised from time to time concerning Wenzel's equation. Because the angle depends on the geometry i n the immediate v i c i n i t y of the periphery of the drop, Wenzel's description i s not useful i f the surface i s non-uniformly rough. One of the most recent c r i t i c i s m s was raised by Bracke et al.<1988>. They demonstrated by means of the calculus of v a r i a t i o n s that even on rough surfaces the Young equation s t i l l applies. They, however, claimed that the Wenzel equation r e l i e s on a f a l s e assumption. Contact angle hysteresis, i . e . the difference i n the apparent advancing and receding angles, f o r homogeneous rough s o l i d substrate i s due to the l o c a l slope of the s o l i d at the three phase of contact-line. The thermodynamic Young angle i s the arithmetic mean between these advancing and receding angle values. 2.1.5 Composite Configuration And The Cassie-Baxter Equation Liquids with high i n t r i n s i c angles may not be able to penetrate into cracks and crevices of very rough or porous surfaces. These incompletely penetrated surfaces are c a l l e d composite. An i d e a l i z e d composite i s shown i n Figure 2.1.4. 13 ( r = 2.67 LIQUID /-AIR -SOLID r = 1.61 1 2 3 4 r= 1.09 LIQUID ^-SOLID 5 6 F i g u r e 2 .1 .4 An i l l u s t r a t i o n o f compos i te c o n f i g u r a t i o n (Johnson and De t t re ) ~i 1 1 r T 1 1 r 100 30' 80 70 60 50 40 30 20 10 0 PER CENT SOLID AREA IN SURFACE F i g u r e 2 .1 .5 Contact angle h y s t e r e s i s on a model porous su r f a ce (Cass ie and Baxter ) 14 Cassie and Baxter<1944> have derived an equation for composite interfaces COS0 = ffj-cos^u - az 2.1.10 where <7x=Asl/A, a 2=A l g/A, A i s apparent surface area, hBl i s contact area of l i q u i d with s o l i d , and A l g i s the free l i q u i d - a i r i nterface under the drop. A composite interface i s obviously a p a r t i c u l a r example of a heterogeneous surface. By assuming that region 2 consists of a i r (0=180°), the Cassie equation (2.1.4) reduces to equation 2.1.10. P a r t i c u l a r l y , t h i s equation reduces to Wenzel equation when a2=0. A family of contact angle curves i s shown i n Figure 2.1.5 for the model porous surfaces. I t shows how contact angle and contact angle hysteresis vary with the percentage of the s o l i d area i n surface. The centre l i n e i s calculated from Cassie's equation. The curves above Cassie's curve represent possible advancing angles and those below represent corresponding receding angles on surfaces of d i f f e r e n t roughness with l e s s rough surface being close to the centre l i n e . The receding angle depends strongly on the w e t t a b i l i t y of the s o l i d portion of a surface and i s i n s e n s i t i v e to surface porosity. 15 2.2 CONTACT ANGLE MEASUREMENTS Some major techniques that have been used for the measurement of contact angles are reviewed. In general, the techniques of contact angle measurements can be divided into two major categories; the d i r e c t contact angle measurement from which the angle value i s d i r e c t l y obtained, and the i n d i r e c t contact angle measurements from which the value of contact angle i s calculated. 2.2.1 Direct Contact Angle Measurements 2.2.1.1 S e s s i l e Drop and A i r Bubble Of a l l the methods which were developed, the s e s s i l e and pendent drop method, and the adhesion a i r bubble method are the most general experimental techniques<Neumann and Good, 1979>. The method of measuring contact angles involving d i r e c t measurement on the p r o f i l e of a s e s s i l e l i q u i d drop or, a l t e r n a t i v e l y , of the adhering a i r bubble, i s the most commonly employed technique. The contact angle i s determined by d i r e c t l y constructing a tangent to the p r o f i l e at the point of 16 V//////////// /Y7777777777? a '///////////// '////////////, F i g u r e 2 .2 .1 C o n s t r u c t i n g a tangent t o the p r o f i l e a . s e s s i l e drop method; b. adhe r ing a i r bubb le method c o n t a c t o f t he t h r e e phases ( F igure 2 . 2 . 1 ) . The ang le can be measured d i r e c t l y by u s i n g a t e l e s c o p e f i t t e d w i th a gon iomete r e y e p i e c e , o r on a p r o j e c t e d image o r photograph o f the d rop p r o f i l e . An accuracy o f ±2° f o r t hese methods i s g e n e r a l l y c l a i m e d . 2 . 2 . 1 . 2 T i l t e d P l a t e Method The t i l t e d p l a t e method was d e v i s e d by Adams and J s s s o p <1925>. The p r i n c i p l e o f the method i s i l l u s t r a t e d i n F i g u r e 2 . 2 . 2 . A s o l i d p l a t e i s p a r t i a l l y immersed i n the l i q u i d wh ich w i l l form a concaved o r convex meniscus near t he p l a t e . The p l a t e i s t i l t e d u n t i l the cu rved meniscus d i s a p p e a r s . The most impor tant advantage o f the t i l t e d p l a t e method i s the s i m p l i c i t y o f the appara tus . 17 F i g u r e 2 .2 .2 T i l t e d p l a t e method f o r c o n t a c t ang le measurement F i g u r e 2 .2 .3 C y l i n d r i c a l rod method f o r con t a c t angle measurement 18 2.2.1.3 C y l i n d r i c a l Rod Method As a modification of the t i l t e d p late method, c y l i n d r i c a l rod method encloses, i n a glass c e l l , a cylinder which can be rotated. The l e v e l of the l i q u i d around a p a r t i a l l y immersed horizontal cylinder can be adjusted u n t i l i t touches the cylinder without any curvature. Figure 2.2.3 shows a cross section of the c y l i n d e r immersed i n l i q u i d . The contact angle i s calculated from the equation cos0 = 2h/d - 1 2.2.1 where d i s the diameter of the c y l i n d e r and h i s the height of the l i q u i d surface above the bottom of the c y l i n d e r . 2.2.1.4 Compressed p e l l e t method The surface of compressed p e l l e t i s usually macro-s c o p i c a l l y glossy and smooth, e s p e c i a l l y when the p a r t i c l e s i z e of powder i s f i n e or the pellet-making pressure i s high. I t was demonstrated thermodynamically <Shuttleworth and Bailey, 1948> that the contact angle on a porous surface w i l l be higher than on a smooth surface even i f the composition i s the same. This can be explaned by Cassie-Baxter equation 2.1.10. 19 I t was concluded <Neumann and Good, 1979> that contact angles measured on compressed p e l l e t s , although they may reach a l i m i t i n g value ( i . e . , they do not change further i f the compressing pressure i s increased above c e r t a i n value), are determined by microscopic roughness and porosity. An attempt was made by Kossen and Heertjes <1965> to modify the preparation of the compressed p e l l e t to allow contact angle measurement i n cases where l i q u i d penetrates the compressed powder. I t was observed that presoaking the p e l l e t with the measuring l i q u i d could produce s o l i d surfaces on which drops placed to measure the contact angles are quite stable. The contact angles on s o l i d s were calculated by Kossen and Heertjes <1965> from the observed angle using Cassie's method, which rel a t e s the contact angle measurement on a heterogeneous s o l i d surface to the i n t r i n s i c contact angles. The i m p l i c i t assumption was that the exposed surfaces of p a r t i c l e s were (a) p e r f e c t l y f l a t and (b) oriented p a r a l l e l to the o v e r a l l surface of the compacted p e l l e t . Doubt has been raised by Neumann and Good (1979) concerning the v a l i d i t y of t h i s assumption. 20 2.2.2 Indirect Contact Angle Measurements 2.2.2.1 The wilhelmy Method As shown i n Figure 2.2.4, i f a smooth, v e r t i c a l plate i s brought into contact with a l i q u i d , the l i q u i d w i l l exert a downward force on the plate f = P-7lv-COS0 - V - A p-g 2.2.2 where P i s the perimeter of the plate, V i s the volume displaced, Lp i s the difference i n density between the two f l u i d s ( a i r and the l i q u i d ) . To c a l c u l a t e 6 , the plate i s slowly lowered into the l i q u i d and f i s plotted against time. P r i o r to the establishment of contact between the plate and the l i q u i d , the recorder indicate constant weight ( l i n e AB). Immediately a f t e r contact, the recorder jumps from B to C due to the c a p i l l a r y r i s e of the l i q u i d at the plate (see Figure 2.2.4.b). As the immersion continues, the weight on the balance decreases again ( l i n e CD) . I f the average contact angle along the l i n e of contact does not remain constant during the immersion, the chart l i n e w i l l not be s t r a i g h t but contorted around l i n e CD. From the length of the l i n e BC, the force i n equation above i s obtained 21 11 (a) Dev i ce f o r Wi lhelmy t e chn ique -.6-z-z'-7 C 10 1.measuring device, 2.glass fibre or rod, 3 . eleotrobalance, A.recorder, 5.measuring c e l l , 6.liquid, 7.movable platform, 8.screw or gear mechanism to raise or lower the platform, 9.motor, 10.clamp and support, 11. l id . b) Weight o f the p l a t e as a method f u n c t i o n o f the depth o f immersion F i g u r e 2 .2 .4 Wi lhelmy method 22 f = AM-g 2.2.3 where AM i s i n grams. In t h i s method, the measurement of a contact angle i s reduced to the measurement of a weight, which can be performed with much higher accuracy than the d i r e c t reading of an angle with a goniometer. The disadvantages of t h i s method are that the perimeter of the plate must be s t r i c t l y constant, and each part of the plate must have the same composition and morphology. In measurements that extend over appreciable time i n t e r v a l s , swelling or d i s s o l u t i o n 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 Rise at a V e r t i c a l Plate As a variant of Wilhelmy method, the c a p i l l a r y r i s e at a v e r t i c a l plate method only needs the c a p i l l a r y r i s e h at the v e r t i c a l surface to be measured (Figure 2.2.5). For i n f i n i t e l y wide plate, an integration of the Laplace equation y i e l d s sinfl = 1 - Apgh /2ylv 2.2.4 23 where Ap i s density difference between the two f l u i d s . For p r a c t i c a l purposes, plates that are about 2 cm wide s a t i s f y the t h e o r e t i c a l requirement of " i n f i n i t e " width. I f g, Ap, and 7 l v are known, the task of determining a contact angle i s reduced to measuring the c a p i l l a r y r i s e , which may be determined o p t i c a l l y with a cathetometer. This technique has been broadly used and found p a r t i c u l a r l y e f f e c t i v e for measuring contact angles as a function of rate of advance and r e t r e a t . 2.2.2.3 Interference Microscopy The p r i n c i p l e of t h i s method i s i l l u s t r a t e d i n Figure 2.2.6. Destructive interference (dark fringes) w i l l occur when the o p t i c a l path difference between adjacent i n t e r f e r i n g beams i s given by t = x/2n 2.2.5 where n i s the r e f r a c t i v e index of the l i q u i d and A the wavelength. From the geometry i n Figure 2.2.6, we have 6 = arctan(t/x) 2.2.6 where x i s the distance between dark fringes. Combining 24 + h ^ / F i g u r e 2 .2 .5 C a p i l l a r y r i s e a t v e r t i c a l p l a t e F C > B F i g u r e 2 .2 .6 I n t e r f e r e n c e Mic roscope Method A.l ight source, B.lens, C.half-si lvered glass mirror, D.liquid-vapour interface, E.substrate-liquid interface, F.microscope. 25 above two equations y i e l d s 6 = arctan(x /2ux) 2.2.7 This method can only be used f o r small contact angle measurements. I t uses a very small amount of l i q u i d . 2.2.2.4 C a p i l l a r y Rise Method Given the height of l i q u i d r i s e (or depression) i n a c a p i l l a r y tube, the contact angle can be calculated from the equation cosfl = hrpg/27 l v 2.2.8 where h i s the l i q u i d height, r i s the c a p i l l a r y radius, p i s l i q u i d density. Advancing or receding angles are obtained a f t e r lowering or r a i s i n g the l i q u i d l e v e l i n the tube. The method requires that the s o l i d be a v a i l a b l e as a transparent c a p i l l a r y tube, or as a coating within a c a p i l l a r y . I t i s r e s t r i c t e d to small tubes which are so narrow that the meniscus may be considered to be sph e r i c a l . For wide tubes, i n which the meniscus i s not spherical, a correc t i o n must be applied to account f o r deviation from s p h e r i c i t y . 26 2.2.2.5 Rate of Penetration In the method, the l i q u i d i s allowed to r i s e unopposed through a column of powder i n a glass tube <Crowl and Wooldridge, 1967; B r u i l and van Aarsten, 1974>. S t a t i s t i c a l l y , the rate of penetration method i s more accurate than d i r e c t contact angle measurement. The theory of t h i s technique was developed by a generalization of the law that governs penetration into c a p i l l a r i e s given by Washburn equation K« 7•t«cose h 2 = 2.2.9 2 M where 7 i s the surface tension of l i q u i d , n i s the l i q u i d v i s c o s i t y , and K i s a constant f o r a given packing of podwer and i t can be c a l l e d t o r t u o s i t y constant. Detailed discusion on t h i s equation i s given i n Section 7.2.1. The experimental procedure commonly adopted <Studebaker and Snow, 1955; Crowl and Wooldridge, 1967; B r u i l and van Aarsten, 1974> i s as follows; a known weight of the dried powder i s placed i n a glass tube of about 0.8 cm i . d . with an attached scale, and consolidated by manual tapping. The lower end of the tube i s closed with a glass or 27 paper f i l t e r supported by a small plug of cotton wool. The column i s placed v e r t i c a l l y i n the wetting l i q u i d and the time at which wetting started i s recorded. By means of a lamp the p o s i t i o n of the l i q u i d l e v e l i s p e r i o d i c a l l y recorded. S t a t i s t i c a l l y , the rate of penetration method i s more accurate than d i r e c t contact angle measurement. The rate of penetration i s obtained from a flow of l i q u i d through c a p i l l a r i e s surrounded by a large number of p a r t i c l e s , while the contact angle measurement i s c a r r i e d out f o r one spot (usually the angle i s measured on various places on the specimen, and the average value i s calculated). The problem associated with present experimental technique, as claimed by Good and L i n <1976>, i s that the data measured generally exhibit a large s t a t i s t i c a l scatter. 28 2.3 OTHER TECHNIQUES In addition to the d i r e c t and i n d i r e c t contact angle measurements, there are many other techniques developed to 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 other parameters than contact angle as the indica t o r s and usually r e f l e c t some aspects of s o l i d surface properties. 2.3.1 H y d r o p h i l i c i t y Index S o l i d surface properties are governed by t h e i r surface compositions. The surface of a coal p a r t i c l e can be considered consisting of, at molecular and macro-size l e v e l s , three main kinds of components: i) na t u r a l l y hydrophobic un-oxidized patches (HO), i i ) oxygen bearing, hydrophilic coal patches (HL), and i i i ) mineral matter. I f the mineral matter i s neglected, the w e t t a b i l i t y of pure coal surface i s cont r o l l e d by the r e l a t i v e abundances of various functional groups on i t s surface. In respect to these properties, the concept of h y d r o p h i l i c i t y index has been formulated by Ye et al.<1987> using FTIR spectroscopy <Painter, 1983; Yuh and Wolf, 1983;84; J i n et a l . , 1987> to analyze the r a t i o of the surface hydrophilic group content (hydroxyl and carboxyl groups) to the content of surface 29 hydrophobic groups ( a l i p h a t i c and aromatic CH groups), S k 4 (HL) t H y d r o p h i l i c i t y Index = 2.3.1 s kj (HO), where (HL)i i s a measure of the hydrophilic functional group i content, and (HO)j a measure of the hydrophobic functional group j content at coal surface, respectively, k i and kj are corresponding c o e f f i c i e n t s . Since, a l i p h a t i c and aromatic CH groups are the only hydrophobic functional groups and hydroxylie and carboxylic groups are the only hydrophilic groups, the h y d r o p h i l i c i t y index can be s i m p l i f i e d by su b s t i t u t i n g the corresponding values of the absorption i n t e n s i t i e s of the functional groups. I t was claimed <Ye et a l . , 1987> that t h i s index, as determined from FTIR spectra, provides a rather good measure of hydrophobicity / h y d r o p h i l i c i t y balance at a coal surface. 2.3.2 Induction Time Induction time was f i r s t introduced by Sven-Nillson i n 1934. I t i s defined as the minimum time required f o r the d i s j o i n i n g water f i l m between a p a r t i c l e and a bubble to drain to such a thickness that rupture of the water f i l m 30 takes place. Therefore hydrophobic p a r t i c l e s possess shorter induction time; while the induction time f o r hydrophilic s o l i d s would be longer. The induction time method has been used by many researchers <Eigeles and Volova, 1960; Laskowski and Iskra, 1970; Lekki and Laskowski, 1971; Blake and Kitechener, 1972; Ye et a l . , 1986; Yordan and Yoon, 1988>. The factors influencing the induction time, such as f l o t a t i o n reagents, pH, temperature, inorganic s a l t s , have been studied by many workers <Laskowski, 1974; Yordan and Yoon, 1986>. The basic procedure of t h i s technique i s that a layer of p a r t i c l e s to be tested i s formed i n a rectangular o p t i c a l c e l l . The c e l l , containing approximately 20 ml of the reagent solution, i s then placed on the moving stage of a microscope. An a i r bubble approximately 2 mm i n diameter i s formed at the t i p of a glass c a p i l l a r y tube using a micro-syringe. By lowering the glass c a p i l l a r y tube, the bubble i s kept i n touch with the p a r t i c l e layer f o r a preset contact time period. Then, the c a p i l l a r y tube i s returned to 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 the microscope to see i f any p a r t i c l e s are picked up by the bubble. I f the contact time i s too short, no p a r t i c l e s attach to the bubble. The experiment i s repeated changing the contact time 31 incrementally. In t h i s way, the minimum contact time, for which at l e a s t one p a r t i c l e i s a c t u a l l y picked up i n f i v e out of ten contacts, was determined. This contact time i s taken as the induction time. Contact angle measurements show whether the adhesion i s thermodynamically possible, but cannot describe the dynamic nature of the particle-to-bubble attachment. Induction time can provide k i n e t i c information. Both the 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 for the f l o t a t i o n to be possible. 2.3.3 Heat of Immersion Heat of immersion i s the negative of the heat evolved per square centimetre (or per gram) of 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 , 1958> that the heat of immersion i s related to the contact angle and i t s temperature deri v a t i v e AH = 7 L v•d(cos0)/d(lnT) - e l v-cos0 2.3.2 where e l v i s the t o t a l surface energy of the l i q u i d e i v = 7 i v + d 7 l v / d ( l n T ) 2.3.3 32 In t h i s method, the calorimeter i s f i r s t c a l i b r a t e d by passing a known current through a p r e c i s i o n r e s i s t o r for a given time. The sample powder (150-200 mg) i s weighed to the nearest tenth milligram and placed i n small, c y l i n d r i c a l glass tubes with break-off t i p s . The tubes were evacuated at a pressure of approximately 1 mPa for 15 min and then sealed under vacuum. The evacuated and sealed sample tubes are placed inside s t a i n l e s s - s t e e l vessels containing about 3 cm3 of the wetting l i q u i d . The whole assembly i s lowered into the micro calorimeter which i s maintained at a constant temperature and allowed to a t t a i n thermal equilibrium. A f t e r steady-state had been established, the break-off t i p s of each tube i s broken by remote mechanical action. The l i b e r a t e d heat i s detected and recorded by e l e c t r o n i c integration of the detector s i g n a l . Heat of immersion can provide information on hydro-phobicity of s o l i d surfaces; the energies of i n t e r a c t i o n f o r system i n cases of spreading wetting or zero contact angle <Zettlemoyer, 1964>. In addition, i t can determine the average p o l a r i t y of s o l i d surfaces, heterogeneities on s o l i d surfaces, wetting by surfactants, and thermodynamics of the s p e c i f i c i n t e r a c t i o n of molecules from s o l u t i o n onto s o l i d surfaces <Zettlemoyer, 1965>. I n i t i a l l y , t h i s method was mainly employed i n the area of inorganic minerals<Zettlemoyer, 1964 and 1965; 33 Cochrane and Hendriksen, 1967; Taylor, 1967> which were b a s i c a l l y hydrophilic i n nature and to a l e s s e r extent to hydrophobic materials<Cokill et a l . , 1967>. Application of t h i s method to coal had been studied by G l a n v i l l e and Wightman<1980>. Heat of immersion was proved to be one of the valuable methods f o r investigation. 2.3.4 Rate of Immersion The immersion time measurement was i n i t i a t e d by Walker et al.<1952> to t e s t surface active agents. The procedure consists of dropping coal p a r t i c l e s i n d i v i d u a l l y , from approximately 1 cm, on the surface of progressively more d i l u t e solutions u n t i l a d i l u t i o n was found at which the p a r t i c l e s were not instantaneously wetted. This procedure has been adopted and modified <Garhsva et a l . , 1978; Marmur, et a l . , 1986; Fuerstenau et a l . 1986> to t e s t i n g the w e t t a b i l i t y of mineral surfaces and employed by many others<Glanville and Wightman, 1980; Laskowski, 1986>. In one of the modified procedures <Garbsva et a l . , 1976>, 150 mg of the powdered narrow-sized material i s gently placed on the surface of a mixture of solvents with d i f f e r e n t percentages of water i n a number of 16x150 mm 34 Pyrex t e s t tubes without s t i r r i n g . The time taken for 3/4 of the material to sink i s determined and i s p l o t t e d against the percentage of water. At c e r t a i n concentrations of water, immersion time abruptly increases. For a given s o l i d , the change i n slope occurs at a constant surface tension (Figure 2.3.1(a)). This value i s c a l l e d the c r i t i c a l surface tension; and i t i s t y p i c a l for each s o l i d . Because of heterogeneity of powder as well as contact angle hysteresis, some researchers <Marmur et a l . , 1986> tend to use more parameters to characterize s o l i d surface properties. Data has been presented i n terms of the highest concentration of alcohol at which a l l the p a r t i c l e s f l o a t and the lowest concentration of alcohol at which a l l the p a r t i c l e s sink. In Figure 2.3.1 (b) , the lowest ethanol (methanol) concentration, at which a l l the p a r t i c l e s sink, i s termed the "Total Sinking Concentration" (TSC). The highest ethanol (methanol) concentration, at which a l l the p a r t i c l e s f l o a t , i s termed "Total Float Concentrate" (TFC). I t was claimed <Marmur et al.,1986> that t h i s method of characterization of the w e t t a b i l i t y of p a r t i c l e s i s more s e n s i t i v e to the surface energy than contact angle measurements. A small difference i n the contact angle and surface energy for various surface can be associated with large differences i n the TFC or TSC values. 35 2500 (min} 1500 500 80 i0 . x — y - » »-» i .i V. H 2 0 100 a . Immersion t imes o f methy la ted quar tz powder i n d i f f e r e n t w a t e r / a l c o h o l mix tures 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 e thano l /wa t e r ; $ p ropano l/wate r ; A butano l/wate r (Garbsva e t a l . ) 50 100 90 ao o • o O- 30 • 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 the po l ymethy lmethac ry l a t e (PMMA)-coa t ed beads on Ethanol-water m i x t u r e s : (®) 74.1 /xm, (o) 12 7 /xm. (Marmur e t a l . ) F i g u r e 2 .3 .1 Rate o f immersion t e chn ique 36 2.3.5 Film F l o t a t i o n Another modification of the Walker technique i s referr e d as f i l m f l o t a t i o n (developed by Fuerstenau and Williams <1987>). This method uses a set of three parameters to describe surface properties. A monolayer of tested f i n e p a r t i c l e s (about 0.06 to 0.3 gram i n the case of coal) i s placed on the surface of a s o l u t i o n i n a shallow vessel of 25 mm diameter and 20 or 30 mm depth. The c l o s e l y sized s o l i d e i t h e r remains on the l i q u i d surface or i s immediately imbibed; and s p l i t s into lyophobic and l y o p h i l i c (imbibed) f r a c t i o n s . The surface tension of the l i q u i d i s varied by the addition of methanol to 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 l i q u i d i s p l o t t e d as a function of the surface tension of the l i q u i d i n Figure 2.3.2. They approximately conform to the quasi-Gausian d i s t r i b u t i o n s . Two of the three parameters describing the w e t t a b i l i t y and heterogeneity of powder can be obtained from Figure 2.3.3 (a), the surface tension of the s o l u t i o n that wets a l l p a r t i c l e s , 7 0 m i n , and the surface tension of the solution i n which none of the p a r t i c l e s are wetted, 7 c r a a x ; and (b) the mass f r a c t i o n of the p a r t i c l e s p l o t t e d against the surface tension of the imbibing s o l u t i o n allows c a l c u l a t i o n of the t h i r d parameter - the standard deviation a. a i s a measure of the heterogeneity of the 37 LIQUID SURFACE TENSION, mN/m (b) F i g u r e 2 .3 .2 F i l m f l o t a t i o n (Fuerstenau and W i l l i am) (a) Accumu la t i ve percentage o f m a t e r i a l f l o a t i n g (b) Frequency h i s togram 38 material. Three factors: the s i z e d i s t r i b u t i o n , v a r i a t i o n i n surface energies and contact angle hysteresis can be the reasons f o r difference between the TSC ( t o t a l sinking concentration) and the TFC ( t o t a l f l o a t concentration) i n Rate of Immersion, or between 7 c m i n and 7 c m a x i n Film F l o t a t i o n . Study by Marmur et a l . <1986> shows 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 surface energy has a major e f f e c t . 2.3.6 C r i t i c a l Surface Tension of F l o t a t i o n The concept of C r i t i c a l Surface Tension, 7 C , developed by Zisman <1964>, i s the surface tension of the wetting l i q u i d that would j u s t spread on the substrate to give complete wetting. A convenient way of i l l u s t r a t i n g the concept i s the adhesion tension diagram, 7 l v c o s 0 versus 7 l v , as shown i n Figure 2.3.3(a). On such a diagram, the measured contact angles give a str a i g h t l i n e , which may be represented by the equation 7 l vCOS0 = 0 - 7 i v + < 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 to dynamic f l o t a t i o n 39 conditions <Gaudin, 1957; Tomlinson and Fleming, 1963; Reay and R a t c l i f f , 1973; Lekki and Laskowski, 1971; Blake and Kitchener, 1972; Laskowski, 1974; Jameson et a l . , 1977> and distinguished c r i t i c a l surface tension of adhesion, 7 c a ; c r i t i c a l surface tension of particle-bubble s t a b i l i t y , 7 0 S ; and c r i t i c a l surface tension of f l o a t a b i l i t y , 7 c f . The c r i t i c a l surface tension of adhesion, 7 C a , i s the minimum surface tension of l i q u i d i n contact with the tested s o l i d f o r which the adhesion of a i r bubble from the l i q u i d onto the s o l i d i s possible. Apparently i t i s determined by s o l i d surface properties, and should be greater than c r i t i c a l surface tension, 7 C . Hydrophobic p a r t i c l e s of the same s i z e d but y'ca<y"ca, may be separated into f r a c t i o n s i n a sol u t i o n of 7 c i f y' c a < 7 c < 7 " c a . However f o r p a r t i c l e s with the same surface properties, y c & , 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 may be fl o a t a b l e whereas the large s i z e p a r t i c l e are non-fl o a t a b l e . This i s due to the k i n e t i c e f f e c t of p a r t i c l e s i z e . On t h i s account, the c r i t i c a l surface tension of s t a b i l i t y ycs was introduced. Obviously f o r p a r t i c l e s with same y c a , the larger the p a r t i c l e s i z e i s , the greater the 7 C s value w i l l be. Two p a r t i c l e s of sizes d'<d" would have the relevant 8 ' C B < 9 " C 8 and 7 ' 0 S < 7 " C S . As shown i n Figure 2.3.3(b), i f a solution of 7 C was used and y' c s<y1 w<y"c s , the smaller-size p a r t i c l e s would be flo a t e d whereas the 40 S U R F A C E T E N S I O N , v d y n e / c m a. Adhesion t e n s i o n diagram i l l u s t r a t i n g t he concept.of c r i t i c a l s u r f a c e t e n s i o n of adhesion, i c a , 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 ) . £ UJ o SURFACE TENSION , y^ dyne /cm b. Adhesion 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 of f l o a t a b i l i t y f o r t h r e e low energy s o l i d s o f d i f f e r e n t w e t t a b i l i t y i n aqueous s o l u t i o n s of 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 s u r f a c e t e n s i o n o f f l o t a t i o n 4 1 l a r g e r - s i z e p a r t i c l e would be non-floatable. This means that w e t t a b i l i t y and f l o a t a b i l i t y are not necessarily synonymous under c e r t a i n circumstances. A l l above factors are included i n a general term c a l l e d c r i t i c a l surface tension of f l o a t a b i l i t y yc f . According to t h i s concept a p a r t i c l e w i l l be f l o a t a b l e i f i t s 7 C f i s smaller than the liquid-vapour surface tension 7 l v (Figure 2.3.3(b)) The concept of c r i t i c a l surface tension of f l o a t a b i l i t y indicates that a s i g n i f i c a n t d ifference i n ycf values may e x i s t between two inherently hydrophobic s o l i d s i f the slope of t h e i r w e t t a b i l i t y l i n e s are s i g n i f i c a n t l y d i f f e r e n t , although there may be l i t t l e or no difference i n 7 C value. Such a difference would provide a s e l e c t i v e f l o a t a b i l i t y region, where separation of the two s o l i d s 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 possible. The concept of c r i t i c a l surface tension of f l o t a t i o n has been employed by others <Kelebek and Smith, 1985; Kelebek, 1987> i n characterization and f l o t a t i o n of inherently hydrophobic minerals. 42 2.3.7 Other Techniques In addition to above mentioned techniques, a v a r i e t y of other techniques have also been developed. Among them are p a r t i t i o n between kerosene and water <Adams-Viola et a l . , 1981>, s a l t f l o t a t i o n <Laskowski, 1965 and 1974; Yoon and Sabey, 1989> et a l . They w i l l not be discussed here. 43 CHAPTER 3 COAL 3.1 INTRODUCTION The materials used i n surface w e t t a b i l i t y studies, such as Teflon and Quartz, are commonly homogeneous. Measures can be taken to acquire a very clean, smooth, and chemically consistent surface f o r contact angle measurements. F a i r l y reproducible r e s u l t s can be obtained. Nonetheless, contact angle measurements on coal <Vargha-Butler, et a l . 1986> show that t h i s i s not true f o r coal. Coal has a very complex composition and heterogeneous surface. Some of the coal properties are unique and deserve d e t a i l e d summary. 3.1.1 C l a s s i f i c a t i o n Coal i s f i r s t c l a s s i f i e d by rank. The coal rank indicates the extent to which c o a l i f i c a t i o n process has occurred and i s arranged i n an ascending order of carbon content as shown i n Table 3.1.1. The highest rank coal i s graphite, which i s the f i n a l product of the c o a l i f i c a t i o n process; the lowest one i s woody material peat, followed by 44 l i g n i t e . Table 3.1.1 Coals Arranged i n an Ascending Order of Carbon Content Coal Rank Peat l i g n i t e Sub bituminous Bituminous Anthracite %c 60 70 75 80 93 %0 35 25 20 15 3 C a l o r i f i c value MC/ka 28 30 31 32.5 36.5 The properties of the coal within each rank depend, to some extent, on the nature of the various components i n the o r i g i n a l organic accumulation; s p e c i f i c a l l y they depend on both the forms of vegetation and the degree of degradation p r i o r to b u r i a l . The components, c a l l e d macerals, are analogous to the d i f f e r e n t mineral constituents found i n inorganic sediments. They are organic minerals, characterized by t h e i r botanic structure rather than t h e i r c r y s t a l l o g r a p h i c properties. They are o p t i c a l l y homogeneous aggregates of organic substances, possessing d i s t i n c t i v e physical and chemical properties <Winans and C r e l l i n g , 1984>. Macerals are c l a s s i f i e d i n three groups <Stach, 1982>: I. V i t r i n i t e , I I . E x i n i t e , I I I . I n e r t i n i t e . Coal macerals r a r e l y occur by themselves; they are more usually associated with other maceral groups. Such associations are c a l l e d micro-lithotypes. They are mainly: v i t r i t e , l i p t i t e , i n e r t i t e , c l a r i t e , v i t r i n e r t i t e , durite, and trimacerite. These micro-lithotypes further combine to form the mass of a banded bituminous coal. These combined ingredients are v i s i b l e to the eye and are known as lit h o t y p e s . They are: I. fusain (charcoal-like fragments - s o f t lithotype) I I . durain ( d u l l hard coal type - the hardest lithotype) I I I . c l a r a i n > together the equivalent of bright coal IV. v i t r a i n type These four banded ingredients d i f f e r i n t h e i r s p e c i f i c gravity, ash content, chemical composition, hardness, and coking properties as well as i n t h e i r wetting properties. 46 3.1.2 Chemical Composition Change i n coal rank i s r e f l e c t e d by a steady change i n chemical composition and c a l o r i f i c value. Coal i s not a mineral of constant composition, but an organo-clastic sedimentary rock composed e s s e n t i a l l y of l i t h i f i e d plant debris. I t has s u b s t a n t i a l l y d i f f e r e n t properties from inorganic minerals. Due to i t s e x t r a o r d i n a r i l y complex carbon chemistry, these macerals cannot be represented by any uniquely defined chemical structure. Pure coal i s the combustible organic mineral, which i s a highly cross-linked polymer, consisting of a number of stable fragments connected by r e l a t i v e l y week cr o s s - l i n k s <VanKrevelen, 1961>. The remaining components, which have no heating value, are regarded as impurity minerals including shale, kaolin, sulphates, carbonates, and chlorides. Coal i s a polymeric s o l i d , i . e . i t consists of many high molecular weight molecules. I t contains mainly carbon, hydrogen and oxygen along with small quantities of sulphur and nitrogen. The molecular models proposed are based on ultimate elemental analysis and large amount of other information such as v a r i e t y of spectroscopic analyses, functional group analysis, molecular weight determinations, s t a t i s t i c a l c o n s t i t u t i o n analysis etc.. The molecular model 47 48 of Wiser<1975> i s given i n Figure 3.1.1. The arrows i n the model indicate the week points of the structure. This model also includes various functional groups found i n coals. Most functional groups contain oxygen and appear as phenolic, hydroxylic, carbonylic, and carboxylic functional groups. The r e s t of the oxygen i s thought to l i n k aromatic n u c l e i or to be present i n a fused polynuclear skeleton. Mineral matter i s an important part of coal composition. I t i s termed, i n i t s widest sense, as a l l of the inorganic components found i n coal as mineral phases as well as the elements i n coal that are considered inorganic <Mraw et a l . , 1983>. Mineral matter plays an important r o l e i n a l l coal u t i l i z a t i o n processes. 3.2 HOMOGENIZATION As stated above, coal i s a very heterogeneous organic rock comprised of inorganic minerals and organic macerals. I t would be i n t e r e s t i n g to i s o l a t e these i n d i v i d u a l macerals for coal w e t t a b i l i t y characterization. However, i t i s p r a c t i c a l l y impossible to separate them and accumulate enough f o r characterization. To obtain an accurate picture of the w e t t a b i l i t y of coal, i t has to be separated into less heterogeneous portions. These portions, d i f f e r i n g i n w e t t a b i l i t y , need to be characterized separately. 49 Homogenization of coal i s the f i r s t step needed for coal surface w e t t a b i l i t y characterization. Otherwise, studies on such a heterogeneous mixture as a whole may be very misleading. There are many ways of homogenizing coal . I t i s the most pr a c t i c a b l e way to homogenize coal, according to some of i t s physical or physiochemical properties, such as s p e c i f i c gravity, surface w e t t a b i l i t y , macro-lithotype, etc., creating f r a c t i o n s which are less heterogeneous. Since t h i s work i s mainly focused on the methodology of the characterization of coal w e t t a b i l i t y , only the sink-and-float method was employed to prepare f r a c t i o n s for further studies. The coal surface characterization techniques developed i n t h i s work can be applied to any coal f r a c t i o n s regardless of the separation method used. 3.3 COALS STUDIED Coal samples used i n t h i s work were from the Line Creek and the Bullmoose (Seam "C") mines. The Line Creek coal deposit i s part of the Upper Elk C o a l f i e l d i n the East Kootenays, B.C.. I t i s characterized as a low sulphur, medium v o l a t i l e bituminous coal and i s a high q u a l i t y blend coking coal. Some of the 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 analysis of ROM Bullmoose coal i s given i n Table 3.3.2. The r e s u l t s of sink-and-float t e s t s f o r Line Creek and Bullmoose coals are presented i n Figures 3.3.1 and 3.3.2, respectively, i n which the ash content i s plotted against density f r a c t i o n . 51 Table 3.3.1 QUALITY CHARACTERISTICS OF LINE CREEK CLEAN COAL PARAMETER BASIS QUANTITY MOISTURE % A.D. t o t a l r e s i d u a l PROXIMATE % A.D. ash v o l a t i l e sulphur ULTIMATE % D.A.F. carbon hydrogen nitrogen sulphur oxygen HARDGROVE GRINDABILITY INDEX GROSS CALORIFIC KCAL/KG.A.D. VALUE  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 75.0 7700 Notes: A.D. stands for A i r Dried D.A.F. stands f o r Dry Ash Free basis Table 3.3.2 Proximate Analysis Of ROM Bullmoose Seam "C" Coal Dry Basis A.D. M.A.F. %Moisture 0.95 % V o l a t i l e 20.37 27.18 %Ash 25.05 %FIXED C 54.58 72.82 Notes: M.A.F. stands f o r Moisture and Ash Free basis A.D. stands f o r A i r Dry basis 52 SINK-AND-FLOAT TEST OF LINE CREEK COAL N ' C o c o u JS 80 70 -60 -50 -40 -30 20 10 -Figure 3.3.1 Ash content versus density fraction co in Density fraction (g/cnr) j f ASH CONTENT SINK-AND-FLOAT TEST OF BULLMOOSE COAL F i g u r e 3 . 3 . 2 Ash content versus density fraction Density fraction (g/cn?) ASH CONTENT CHAPTER 4 OBJECTIVE The major objective of the present work i s to develope better techniques for contact angle measurements on f i n e coal p a r t i c l e s . Two techniques, one d i r e c t and one i n d i r e c t , have been modified and investigated. In the d i r e c t contact angle measurement technique, the coal powder i s compressed under high pressures 20 to 34.5 MPa to form the p e l l e t s of 2.54 cm diameter and 0.5-0.8 cm height. The p e l l e t , with i t s a r t i f i c i a l surface, i s employed fo r contact angle measurements. The behaviour of a water drop i n contact with the p e l l e t such as the e f f e c t of drop s i z e on contact angle, the s t a b i l i t y of the s e s s i l e drop are examined. In addition, the properties of the p e l l e t and the factors a f f e c t i n g the measurement are also studied. The contact angle measured on the p e l l e t surface i s an apparent angle value. A p e l l e t surface model i s proposed according to the SEM examination. The apparent contact angle values are corrected using Cassie-Baxter equation to the r e a l angle values. In the i n d i r e c t contact angle measurement, the rate 55 of l i q u i d penetration technique i s employed and modified. Pressures ranging from 3.5 to 28 MPa (500 - 4000 psi) are employed to make highly compact columns. The holding glass tube t r a d i t i o n a l l y used f o r the column of powder i s , therefore, no longer needed. The a p p l i c a b i l i t y of the Washburn equation to the highly compacted columns for d i f f e r e n t coal density f r a c t i o n s are studied. The change i n penetration behaviour of the l i q u i d within such columns i s investigated. The properties of the columns and the impact of the pressure applied i n t h e i r formation on the rate of l i q u i d penetration as well as other phenomena are also studied. An assumption i s made that for materials having same p a r t i c l e sizes and shapes, t h e i r columns, i f made at same pressure, possess the same t o r t u o s i t y constant. Under t h i s assumption, a new c a l i b r a t i o n method i s introduced. The present work i s mainly aimed at methodological development fo r contact angle measurements on f i n e coal p a r t i c l e s . More work needs to be done to further v e r i f y these techniques. 56 CHAPTER 5 DIRECT CONTACT ANGLE MEASUREMENTS AND EXPERIMENTAL 5.1 INTRODUCTION Among the d i r e c t contact angle measurement methods, the s e s s i l e drop technique has many advantages over the adhering a i r bubble methods. Complications, due to the s o l u b i l i t y and swelling, can usually be dealt with more e a s i l y with the s e s s i l e drop method rather than with the adhering a i r bubble methods. However, the adhering a i r bubble method has the advantage of minimizing contamination from airborne substances. Contact angle measurements are generally performed on coal lumps <Horsley and Smith, 1957, Parekh and Apian, 1978, Gutierrez-Rodrigues and Apian, 1984>. Some c r i t e r i a have been established f o r the s e l e c t i o n of sample specimens for contact angle measurement. The pre-selection of samples (or the area of a coal specimen) l i k e l y produces biased r e s u l t s . Although the well-established p r a c t i c e of p o l i s h i n g a coal specimen has the advantage of providing a smooth surface su i t a b l e f o r the measurement, po l i s h i n g may change the coal surface markedly. Vargha-Butler et al.<1986> have c a r e f u l l y 57 studied the d i r e c t contact angle measurements on polished sections of coal lumps. They indicated that the information obtained from t h i s method i s not very r e l i a b l e because of the heterogeneity. Coal surfaces are a mosaic with the d i f f e r e n t elements having varying dimensions. Cracks are often v i s i b l e on coal surfaces. As indicated by Neumann and Good <1979>, i f the dimension of the primary elements i s very small r e l a t i v e to the dimension of the s e s s i l e drop, the microscopic heterogeneity w i l l not a f f e c t the macroscopic contact angle measurements. Therefore, one possible s o l u t i o n to the e f f e c t of chemical and mechanical heterogeneity i s to crush and grind coal p a r t i c l e s to an average diameter of 10 microns. Such a f i n e powder, though microscopically heterogeneous, may be considered macroscopically homogeneous. For the surface characterization, i t i s desirable to work with a f l a t surface made of a f i n e powder. Compressing the f i n e powder under high pressure to form an a r t i f i c i a l surface i s an obvious solution. The preparation of p e l l e t s under high pressure and the determination of the contact angle on the p e l l e t surface are discussed here as well as i n the following chapters. 58 5.2 THEORY AND TECHNIQUES 5.2.1 Background There are two methods of obtaining the contact angle from the measurement with a s e s s i l e drop. One method i s to construct a tangent to the drop p r o f i l e at the three-phase contact l i n e (Figure 2.2.1) and to measure the value of the angle with a goniometer. The another method involves mathematically c a l c u l a t i n g the contact angle from the p r o f i l e of the drop <Bashforth and Adams, 1892; Hartland and Hartley, 1976; Malcolm and Paynter, 1981; and Rotenberg et a l . , 1982>. Depending on the drop s i z e , d i f f e r e n t equations may be needed. I f a drop s i z e i s small enough (10" 4 ml), so that the drop i s indeed a spherical cap, two equations may be employed. One connects the contact angle with the base diameter, D, and height of the drop, h, (Mack, 1936) 2h = tan0/2 5.2.1 D and the second equation (Johnson and Dettre, 1969) calc u l a t e s the angle, 6 , through the base diameter and the drop volume, v, 59 D3 24 s i n 3 6 = 5.2.2 V TT(2 - 3 C O S 0 + cos 3 B ) The l i m i t a t i o n s f o r these two equations are that (1) D and h or v cannot be measured with high accuracy, and (2) the drop must be a spherical cap. When the drop s i z e i s so large that the height of the drop i s independent of the drop s i z e , the contact angle can be calculated from: d«g«h 2 cose = 1 5.2.3 2 7 where h i s the l i m i t i n g height of drop; d the l i q u i d density; g the g r a v i t a t i o n a l acceleration; and y the l i q u i d surface tension. In order f o r t h i s equation to apply, the drop must be very large. For water, a drop of one meter i n diameter i s t h e o r e t i c a l l y required. I t i s impracticable to produce such a large s o l i d surface to accommodate the l i q u i d drop. In most cases, the drop volume resides between these two extremities. When the r a d i i of curvature are s u f f i c i e n t l y large compared to the thickness of a non-homogeneous f i l m separating two bulk phases, the pressure diff e r e n c e across a curved interface i s described by the c l a s s i c a l Laplace equation 60 7(1/1*! + 1/R 2 ) = AP 5.2.4 where 7 i s the i n t e r f a c i a l t e n s i o n , RT_ and R2 r e p r e s e n t the two p r i n c i p l e r a d i i o f curvature, and AP i s the p r e s s u r e d i f f e r e n c e a c r o s s the i n t e r f a c e (see F i g u r e 5.2.1.). In the absence of e x t e r n a l f o r c e s , o t h e r than g r a v i t y , the p r e s s u r e d i f f e r e n c e i s a l i n e a r f u n c t i o n o f the e l e v a t i o n AP = AP 0 + Ap»gZ 5.2.5 where AP 0 i s the p r e s s u r e d i f f e r e n c e a t a s e l e c t e d datum p l a n e , F i g u r e 5.2.1 The d e f i n i t i o n o f the c o o r d i n a t e system f o r a s e s s i l e drop p r o f i l e Ap i s the d i f f e r e n c e i n the d e n s i t i e s o f the two b u l k phases, g i s the 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 and Z i s the v e r t i c a l height measured from the datum plane. From the above two equations, Bashforth and Adams <1892> derived the following general equation mathematically describing the s e s s i l e drop and s e s s i l e bubble interface p r o f i l e under gravity 7(1/1*! + Sin$/X) = 27/R0 + Ap'-yZ 5.2.6 where R^ turns i n the plane of the paper and R2=x/sin$ rotates i n a plane perpendicular to the plane of the paper and about the axis of symmetry; R Q i s the radius of curvature of apex and $ i s the turning angle measured between the tangent to the interface at the point (x,z) and the datum plane. Many graphical curve f i t t i n g techniques have been developed <Malcolm and Paynter, 1981, Rotenberg et a l . , 1982>. The one developed by Rotenberg, Boruvka, and Neumann employs the strategy to construct an objective function which expresses the error between the observed and the t h e o r e t i c a l Laplacian curve, i . e . , equation 5.2.6. The objective function i s minimized numerically using the method of incremental loading i n conjunction with the Newton-Raphson method. Apart from l o c a l gravity and den s i t i e s of l i q u i d and f l u i d phases, the only input information required to determine the l i q u i d - f l u i d i n t e r f a c i a l tension i s the information on the shape of the meniscus and the v e r t i c a l 62 coordinate of the three-phase l i n e . 5.2.2 Techniques The contact angle values were obtained i n two ways. They were ei t h e r d i r e c t l y measured with the use of a goniometer, or the values of the contact angle were calculated from the axisymmetric s e s s i l e drop p r o f i l e s . 5.2.3.1 Direct Measurement A Rame-Hart Model 100 contact angle goniometer (see Figure 5.2.2) was u t i l i z e d i n the d i r e c t contact angle measurements. I t has a stationary telescope. The p o s i t i o n of the stage i s cont r o l l e d by graduated micrometer screws, so that the edge of a drop can be moved h o r i z o n t a l l y and v e r t i c a l l y to bring i t to the axis of the telescope cross h a i r s . The micro-syringe f o r t h i s instrument i s mounted so that the needle can be held stationary r e l a t i v e to the stage and moved v e r t i c a l l y r e l a t i v e to the stage by a screw. This i s a valuable feature f o r the measurement of advancing and receding contact angles. I t i s also possible to use the micrometer screws to measure the height and width of a drop. An environmental chamber i s provided as an optional attachment used to prevent the l i q u i d evaporation. The 63 F i g u r e 5.2.2 The set-up of a Rame-Hart model 100 c o n t a c t ang le goniometer 64 humidity i n the chamber was maintained at 100% by f i l l i n g the sample chamber with d i s t i l l e d water. The temperature was not c o n t r o l l e d and varied between 20 and 25 °C. To insure r e p r o d u c i b i l i t y , a constant drop s i z e was maintained. For routine measurements, the p e l l e t s were mounted on the horizontal stage i n contact with atmosphere. To avoid oxidation, the measurements were made shortly a f t e r drop formation. The temperature c o e f f i c i e n t of the contact angle i s claimed to be small enough so that thermostating i s not necessary <Adam, 1964; Neumann and Good, 1979> To illuminate the drop, a source of l i g h t equipped with a f i l t e r to minimize heating was fix e d behind the drop. 5.2.3.2 Calculation From Axisymmetric Drop Interface The p r o f i l e of the s e s s i l e drop was photographed through the telescope of the goniometer using a h o r i z o n t a l l y mounted camera. The pipette of the micro-syringe with known diameter was included i n the picture; t h i s served as an accurate s c a l i n g reference. The image of the drop p r o f i l e i n the photograph was enlarged approximately 36 times. The curve f i t t i n g technique and corresponding computer program, developed by Rotenberg, Boruvka, and 65 Neumann (1982) as described i n section 5.2.1, was employed. The computer program, already stored i n MTS mainframe i n UBC, acquires the p r o f i l e coordinate data on the photograph through a Talos CYBERGRAPH d i g i t i z e r which was connected to MTS with the Zenith 158 microcomputer acting as a terminal. About 30 to 40 points were generated from each p r o f i l e f or computer processing. 66 5.3 EXPERIMENTAL AND APPARATUS 5.3.1 Sink-and Float Test F i r s t the coal samples were separated into d i f f e r e n t density f r a c t i o n s by a sink-and-float procedure. Each f r a c t i o n was ground to very f i n e powder i n a laboratory rod m i l l . The s i z e d i s t r i b u t i o n of each ground density f r a c t i o n sample was characterized using an Elzone s i z e analyzer. The ground samples were sealed i n p l a s t i c bags and stored i n a r e f r i g e r a t o r for future use. In the sink-and-float procedure, aqueous zinc chloride solutions with the following d e n s i t i e s : 1.3, 1.35, 1.4, 1.5, 1.6, 1.8 were used. Sinking f r a c t i o n s from each t e s t were transferred to the next l i q u i d of higher density. The f l o a t i n g products were rinsed with fresh water, and a i r -dried. 5.3.2 Comminution of Coal Samples The separated coal f r a c t i o n s were pulverized separately using a 195x318 mm laboratory rod m i l l . The maximum sample s i z e fed to the m i l l was 300 grams. The m i l l was used e i t h e r f o r one stage grinding or f o r primary 67 grinding followed by the secondary grinding which was performed i n a mortar grinder. To study the e f f e c t of p a r t i c l e s i z e d i s t r i b u t i o n on the contact angle measurements, the WEKOB mortar grinder was employed to further reduce the s i z e of coal powder. The t o t a l volume of ground material i n one batch was kept below 150 ml. In the process of mortar grinding, the whole instrument was covered by a p l a s t i c bag and purged with nitrogen to prevent oxidation. In addition, the instrument was stopped f o r a period of f i v e minutes a f t e r each two-minute grind to prevent excessive heating. 5.3.3 P a r t i c l e Size Analysis P a r t i c l e s i z e i s an important parameter which may a f f e c t the p e l l e t porosity and consequently the f r a c t i o n a l area of pores on the p e l l e t surface. The s i z e analysis was conducted using an Electrozone Celloscope (Elzone). In t h i s device, the suspension of fi n e p a r t i c l e s i n an e l e c t r o l y t e i s drawn through an o r i f i c e which also passes an e l e c t r i c current. Each p a r t i c l e , i n traversing through the o r i f i c e , causes a momentary resistance change proportional to the p a r t i c l e volume. Corresponding to t h i s change, an e l e c t r i c a l pulse i s 68 generated. A l l the e l e c t r i c pulses are processed by a computer to 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 data. A dispersing agent (Calgon) and vigorous a g i t a t i o n were required i n order to prevent the formation of coal p a r t i c l e aggregation. The s i z e d i s t r i b u t i o n r e s u l t s are p l o t t e d as the r e l a t i v e volume percent against i t s log s i z e . Three c h a r a c t e r i s t i c sizes (in centi-micron) were obtained i n t h i s procedure including log mean, mode, and median s i z e s . 5.3.4 Pellet-Making The pellet-making i s one of the most important steps i n the process. The instrument used was MET-A-TEST mounting press as shown i n Figure 5.3.1. I t has a b u i l t - i n manual hydraulic gauge and timer with an audible beep at the end of each run. The high pressure was provided by a manual hydraulic pump with a working pressure up to 34.5 MPa (5000 p s i ) . The mould diameter i s 25.4 mm (one inch). A f t e r the mold was c a r e f u l l y cleaned by using ethyl alcohol and degreased cotton, 3 grams of coal powder was introduced. The mold was then closed and the pressure was slowly increased by hydraulic pumping. When the pressure 69 F i g u r e 5.3.1 A MET-A-TEST specimen mount ing p r e s s 70 reached a pre-set point, timing was started, which was usually set at 5 minutes. Precautions were taken to control the pressure c l o s e l y ; frequent adjustments were required since the pressure could decline i n the pressing process. The pressure used i n making the p e l l e t was varied from 3.45 to 34.5 MPa (500 to 5000 psi) i n order to study the e f f e c t of pellet-making pressure on the contact angle. Most contact angle measurements were c a r r i e d out on the p e l l e t s prepared at pressures of 27.6 to 34.5 MPa. 5.3.5 The Porosity Measurement The porosity of a p e l l e t i s a very important parameter both i n d i r e c t contact angle measurement technique (this includes two d i f f e r e n t methods: d i r e c t observation or c a l c u l a t i o n from the p r o f i l e of the l i q u i d drop) , and i n rate of penetration measurement which w i l l be discussed i n Chapters 7 and 8. I t i s determined by the p a r t i c l e s i z e d i s t r i b u t i o n , pellet-making pressure, as well as the inherent porosity of the material i t s e l f . In the compressed p e l l e t method, porosity a f f e c t s the f r a c t i o n a l area of a i r pores on the p e l l e t surface, while i n the rate of penetration process, i t a f f e c t s the rate of l i q u i d penetration within a column. 71 The porosity was determined by saturating the p e l l e t with a c e r t a i n l i q u i d (kerosene i n t h i s case). The weight of the compressed p e l l e t was accurately determined using an a n a l y t i c a l balance before and a f t e r the saturation process. The weight difference was the weight of the penetrating l i q u i d , the volume of which was assumed to be the volume of the pores i n the p e l l e t . The t o t a l volume of the p e l l e t could be obtained by accurately measuring i t s two dimensions - height and diameter using a vernier gauge. The porosity of the p e l l e t can be subsequently calculated from (Wi - W0) P Q  »r • r 2 • h« p where P Q - Porosity Wi and WQ - The p e l l e t weights (gram) before and a f t e r penetration (air-dry and saturated p e l l e t ) r - p e l l e t diameter (cm) h - p e l l e t height (cm) p - the penetrating l i q u i d density (g/cm3) 5 . 3 . 6 P e l l e t Surface Examination In order to examine the p e l l e t surface f o r pores, roughness and possible p a r t i c l e crushing caused by high pressure. The Scanning Electron Microscope (SEM Hit a c h i S-72 570) was used. The magnification employed ranged from 20 to 10000 times. Under such a high magnification, the i n d i v i d u a l p a r t i c l e s and t h e i r packing states on the p e l l e t surface could be studied very c l e a r l y . P r i o r to the surface examination, the p e l l e t surface was coated with carbon. In order to obtain good resolution under very high magnification, the coating process was repeated three times. The p e l l e t surfaces, at d i f f e r e n t magnifications, were photographed. 73 CHAPTER 6 RESULTS AND DISCUSSIONS <I> The f r e s h l y prepared p e l l e t surface was glossy and macroscopically smooth. Surface roughness was not generally considered to be a major e f f e c t i n contact angle measurements <Nuemann and Good, 1979; Bracke, et a l . , 1989>. For such a macroscopic process as contact angle measurement, the asperity s i z e on the p e l l e t surface i s so small r e l a t i v e l y to the l i q u i d drop s i z e that the microscopic events which take place on i n d i v i d u a l p a r t i c l e s as the wetting front passes over them may be masked. The porosity on p e l l e t surface, though not observable to the naked eyes, could seri o u s l y a l t e r the r e a l contact angle. I t has been demonstrated thermodynamically <Shuttleworth and Bailey, 1948> that the contact angle on a porous surface w i l l be higher than on a smooth surface that has the same composition. In t h i s work, a model fo r the p e l l e t surface was proposed and corresponding correction for the contact angle values was introduced. 74 6.1 CONTACT ANGLE MEASUREMENTS P r a c t i c a l l y , a l l contact angle systems exhibit hysteresis. There are two ways of handling hysteresis. One i s to develope a simple method by which reproducible data can be obtained i n spi t e of hysteresis, and to report a single angle for any l i q u i d on a p a r t i c u l a r s o l i d . This approach was adopted i n t h i s work. The second way i s to ex p l o i t the phenomenon, recognizing that i t furnishes add i t i o n a l information about the s o l i d . As already pointed out, the contact angle data were obtained e i t h e r by d i r e c t reading through goniometer, or by c a l c u l a t i n g the angle value from the p r o f i l e of axisymmetric meniscus. Unless otherwise indicated, only advancing contact  angles were measured i n t h i s work, and the unit of a l l the angle values i n text and figures i s degree. The reason for t h i s i s that the receding angle i s more s e n s i t i v e to roughness and heterogeneous e f f e c t s than i s the advancing angle <Bartell and Ruch, 1956>. I t i s easier to get reproducible r e s u l t s f o r 9a than for ez . Also, ea i s much easier to measure. In the process of contact angle measurements, the experimenter can notice, through the goniometer, the cle a r r e f l e c t i o n of the drop p r o f i l e on the p e l l e t surface. The 75 r e f l e c t i v i t y i s obviously a manifestation of surface smoothness. For drops with large contact angle, the drop image may look l i k e an 8-shaped p r o f i l e having a t i p i n the middle because of r e f l e c t i o n (see Figure 6.1.1). This e f f e c t i s very useful f o r determining the three-phase contact l i n e which i s v i t a l i n contact angle measurement. Vib r a t i o n by manual tapping was also t r i e d i n the present contact angle measurements with the expectation that i t would help to overcome hysteresis energy b a r r i e r , and make the advancing contact angle approach the equilibrium contact angle eg . Nevertheless, i t was found that angles measured i n t h i s way were less reproducible than those obtained without the v i b r a t i o n . When v i b r a t i o n was applied, the measured contact angles were located somewhere between the advancing and receding angle. I t i s probably better, as indicated by Neumann and Good <1979> to insulate against v i b r a t i o n i n order to produce reproducible r e s u l t s . Because of hysteresis, the angles at the l e f t and r i g h t sides of the drop may not be equal. This inequality was often observed on the coal p e l l e t surfaces. The observation was rejected i f t h i s difference exceeded four degrees. 76 F i g u r e 6 .1 .1 A s e s s i l e drop image obse rved th rough the goniometer 77 6.2 COMPARISON OF THE TWO TECHNIQUES For each s e s s i l e drop, a d i r e c t reading was f i r s t made with the goniometer by measuring the contact angle value on both sides of the drop. The average of the two angles was taken as the measured contact angle value. A photograph was taken of the same drop r i g h t a f t e r the d i r e c t measurement. From the drop p r o f i l e i n t h i s photograph, the computed angle value was obtained l a t e r using the program developed by Rotenberg, Boruvka, and Neumann <1982>. The comparison was made on the p e l l e t s prepared from d i f f e r e n t density f r a c t i o n s . The d i r e c t measured angle was correlated with the computed one f o r the same s e s s i l e drop as shown i n Figure 6.2.1. The figure reveals that nearly 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. I t appears that the d i r e c t measurement gives values lower than the computed angles. One probable reason responsible f o r t h i s deviation might be the systematic error introduced by eithe r or by both of the procedures. In the section that follows, a series of measurements were conducted to t e s t the r e p r o d u c i b i l i t y of the axisymmetric drop technique. Different perturbation e f f e c t s such as l i q u i d density, s c a l i n g factor, p o s i t i o n i n g of the drop apex 78 Comparison of the measured & computed computed angle (degree) • Measured vs. Calc. diagonal etc., were d e l i b e r a t e l y introduced into the computer program to examine the consequent deviation. The r e s u l t s showed that the angle deviation i n the actual operation could be well confined within 1.5°. This value i s much lower than the differences between the two techniques shown i n Figure 6.2.1. Therefore, i t i s very u n l i k e l y that the systematic error i s introduced by the axisymmetric drop technique. The accuracy of d i r e c t reading through goniometer was also tested by repeated measurements both on the s e s s i l e drop and on the photographic p r o f i l e of the s e s s i l e drop. Again, the standard deviation was below 2°. Therefore, the deviation between the two methods can not be at t r i b u t e d to the measurement error. Some other factors must then influence the contact angle measurements. The hypothesis suggested i n the present work i s that the deviation between the d i r e c t l y measured and the computed angle values have mainly resulted from the p e l l e t surface heterogeneity, and the s e s s i l e drop d i s t o r t i o n caused by heterogeneity. B a s i c a l l y , the p e l l e t surface can be considered to be an uniformly d i s t r i b u t e d heterogeneous surface. The hetero-geneous model proposed by Neumann and Good <1972> i n Figure 6.2.2(a) may be employed to i l l u s t r a t e the e f f e c t of the surface heterogeneity on the two contact angle measuring 80 methods. The s o l i d surface i n the model consists of p a r a l l e l s t r i p s of two types, on which the l i q u i d assumes d i f f e r e n t equilibrium contact angles 6x and 6Z. The patches on the s o l i d surface would lead to microscopic d i s t o r t i o n of the liquid-vapour interface near the s o l i d i n order that the edge of the drop may s a t i s f y Young's equation l o c a l l y . The cross section of Figure 6.2.2 (a) i s shown i n Figure 6.2.2 (b) . The portion of the drop p r o f i l e (dashed l i n e i n the figure) that comes down to the lower-energy patches of the surface i s not v i s i b l e i n p r o f i l e . The v i s i b l e p r o f i l e (the s o l i d l ine) i s that part of the l i q u i d surface which i s i n contact with the high-energy patches of the s o l i d surface. The contortion would extend from the three-phase-contact l i n e upward to the curved l i q u i d surface f o r some distance and die out merging into a smooth, spheroidal main drop surface. An extrapolation of the main drop surface would f a l l somewhere between the s o l i d l i n e and the broken l i n e . In the d i r e c t reading through goniometer, what one d i r e c t l y measures through goniometer i s the angle of s o l i d l i n e , e2 , while 6X i s t o t a l l y ignored. For the axisymmetric drop method, the data points from the main p r o f i l e of the s e s s i l e drop are fed into d i g i t i z e r . The contortion near the three-phase contact l i n e might have died out before reaching the main p r o f i l e . The contact angle thus calculated on the computer should then be the angle assumed by the main p r o f i l e extrapolated at the three-phase contact l i n e . This 81 iTI i 1 T I Hi :i 'i i 'I'I'I'I ! h i l l ! .I;I;I 3, i>|l(li'; A I S J i l ill!! I i I i l l i j i i l i i ' !l ' i i " !! !' '; | ! 1 ! 1 1 1 i i i 1 i iii ii'ii 1 i ii'i 'I' ' 'l ' -WALL V MENISCUS vis;. o^S^fS^SSiSs., a. An a r t i s t ' s conception of a meniscus i n contact with a stripwise heterogeneous wall b. A view of cross section i n the stripwise d i r e c t i o n Figure 6.2.2 An idealized heterogeneous surface model 82 angle resides between 6X and 92 as shown i n Figure 6.2.2 (b). So i t i s always greater measured angle 62 • Because the main p r o f i l e i s determined by a cooperative e f f e c t of both s t r i p s : ax and a 2 , t h i s contact angle might be considered to be Cassie's angle (confirms to Cassie equation) which r e f l e c t s the o v e r a l l surface w e t t a b i l i t y . From above discussion, i t can be concluded that on a heterogeneous surface: a) the contact angle measured at a three-phase contact l i n e through a goniometer r e f l e c t s the high energy component, b) Cassie's contact angle cannot be measured at a three phase-contact l i n e but only through the main p r o f i l e of the s e s s i l e drop. 83 6.3 TESTING THE COMPUTATION METHOD The d i r e c t contact angle measurement i s more vulnerable to the e f f e c t of heterogeneity and r e f l e c t s only the w e t t a b i l i t y of higher energy component. The axisymmetric drop method calculates the angle from the main p r o f i l e , and r e f l e c t s the w e t t a b i l i t y of the o v e r a l l composites instead of one. I t i s , therefore, more appropriate to use the axisymmetric drop technique to measure the contact angle on a heterogeneous surface. In t h i s section, d i f f e r e n t aspects of applying the axisymmetric drop technique are further investigated. The use of the computer program developed by Rotenberg, Boruvka and Neumann <1983> requires the accurate p o s i t i o n i n g of the p r o f i l e baseline (the three-phase contact line) and the p o s i t i o n i n g of the apex point on the p r o f i l e . The importance of positioning the baseline was tested by i n t e n t i o n a l l y d r i f t i n g the baseline from the r e a l one. The r e s u l t s i n Figure 6.3.1 show that the calculated angles were greater than the r e a l ones when the baseline was moved upward into the p r o f i l e , and become smaller when the baseline move downward. Normally the uncertainty i n p o s i t i o n i n g the baseline was i n the range of ±0.5 mm, the possible error associated with p o s i t i o n i n g of the baseline i s ±1.25° as shown i n Figure 6.3.1. The enlargement of the 84 drop p r o f i l e was 34.6. I f the s c a l i n g factor was larger, the error i n the computed angle value associated with the p o s i t i o n i n g of the baseline would be smaller. The e f f e c t of p o s i t i o n i n g the apex point was also tested by d e l i b e r a t e l y moving i t away from the r e a l apex point. The r e s u l t s are shown i n Figure 6.3.2. As the apex point was removed, along the drop p r o f i l e , away from the r e a l apex point, the computed value did not show any notable change. The conclusion i s that the p o s i t i o n i n g of the apex point of the drop p r o f i l e i s not important. The r e p r o d u c i b i l i t y of t h i s technique was tested by repeating the measurement on the same photograph. The standard deviation was as small as 0.32°; i n comparison with ±2° f o r the d i r e c t contact angle reading obtained using the goniometer. The use of the computer program also requires the accurate measurement of the two parameters: the enlargement (scaling factor) of the drop p r o f i l e on photograph, and the l i q u i d density. These measurements are required to compute the contact angle and other quantities such as the l i q u i d surface tension, surface area, and contact radius of the s e s s i l e drop. The e f f e c t s of these factors were further tested by replacing the r e a l s c a l i n g factor (34.6) and l i q u i d density (1.0) with some a r b i t r a r y values. Results i n 85 The positioning of drop baseline and Sb o "3) c O 6 o U 140 138 136 134 132 130 128 126 124 122 120 118 116 114 112 110 Figure 6.3.1 its effect on computed angle ii 137.8 a 135.6 i H33.1 a 130.9 ii i i i 2 - 1 0 I i i 1 2 123.8 00 Deviation from the true baseline (mm) H Computed values Positioning of the apex point of a drop Figure 6.3.2 and its effect on computed angle value -1 » 1 3 3 m 132.5 B 1 3 3 - 2 B m 4 "132.7 "133 i r -8137.3 1 r oo Deviation from real apex point (mm) Computed angle o o to o -a • JJ "to c CS T 3 O 4—» 3 O. S o CJ 140.0 139.0 138.0 137.0 136.0 135.0 134.0 133.0 132.0 131.0 130.0 129.0 128.0 127.0 126.0 125.0 124.0 123.0 122.0 121.0 120.0 F i g u r e 6 . 3 . 3 Measurement of scaling factor and its effect on the computed angles H 135.3 1 1135.4 a 134.3 26 1 i i i i i i i i i i i •.0 -22.0 -18.0 -14.0 -10.0 -6.0 -2.0 2. CO co Deviation from true scaling value computed angle Accuracy of liquid density measurement Figure 6.3.4 and its effect on computed angle . „. 0 H 134.4 H 133.9 • 133 ' a 133.8 H33.1 CM oo -0.12 -0.08 -0.04 0.04 0.08 0.12 Deviation from the true liquid density • Computed values Figures 6.3.3 and 6.3.4 show that the two parameters have no s i g n i f i c a n t influence on the computed angle value. In conclusion, the series of the t e s t s discussed above indicate that, between the two contact angle measurement methods, the computation method has much higher p r e c i s i o n than the d i r e c t reading method. In l a t e r work, the computation method was employed unless noted. 90 6.4 CONTACT ANGLE AND DROP SIZE The o r e t i c a l l y , the s e s s i l e drop s i z e should not a f f e c t the contact angle on an i d e a l surface. There i s one, and only one, equilibrium contact angle. However fo r the r e a l contact angle system, t h i s i s r a r e l y , i f ever, the s i t u a t i o n . I t has been known empirically, f o r many years, that when the contact angle of a l i q u i d i s measured on a s o l i d by the s e s s i l e drop or captive bubble method, the contact angle i s a function of drop (or bubble) si z e <Shafrin and Zisman, 1952; Leja and Poling, 1960; Herzberg and Marian, 1970; Good, 1979>. For the study of drop s i z e e f f e c t , the advancing contact angle i s usually measured versus the drop s i z e . I t was observed i n a t y p i c a l experiment that the contact angle of water on Teflon TFE <Herzberg and Marian, 1970> increases with the increase i n drop s i z e . For the captive a i r bubble method, a s i m i l a r r e s u l t was obtained by Leja and Poling <1960>. They found that the contact angle of water on polymethymeth-acrylate (Lucite) increased from 50° to about 70° when the diameter of a i r bubble decreases from 2 to 0.8 mm. To explain t h i s phenomenon, Leja and Poling assumed, that a drop or a bubble i n contact with a s o l i d could be 91 treated as a spherical cap and suggested that the s i z e e f f e c t was due to the influence of gravity. While Good <1979> and Good and Koo <1979> attr i b u t e d the s i z e e f f e c t to heterogeneity which could lead to contortion of drop in t e r f a c e near the s o l i d surface. To observe the behaviour of contact angle versus drop s i z e on a p e l l e t , two procedures of forming d i f f e r e n t s i z e drops were used i n t h i s work. In the f i r s t procedure, drops with various predetermined volumes (1.0 to 20.0 p l i t r e ) were f i r s t formed at the ca l i b r a t e d micro-syringe t i p and then the whole syringe set with the l i q u i d drop on i t s t i p was lowered slowly and smoothly u n t i l the drop met with p e l l e t surface. The whole syringe set was again raised up slowly and l e f t a free s e s s i l e drop on the p e l l e t surface. The second procedure employed was to increase the s e s s i l e drop s i z e by incremental addition of the l i q u i d (1 Mlitre) to the previously formed one. The droplet was f i r s t formed on the syringe t i p and then was lowered together with the syringe on to the apex of the previously formed s e s s i l e drop s i t t i n g on the p e l l e t surface. Figure 6.4.1 shows the r e s u l t s p l o t t e d on the contact angle versus drop s i z e f o r -1.3 density f r a c t i o n of Bullmoose coal . I t can be seen that the advancing angle obtained by the f i r s t procedure increases with drop volume 92 180 170 -160 -150 140 130 120 110 100 -90 -80 70 60 Effect of drop volume on contact angle Figure 6.4.1 Drop volume increased in two ways + 0 By incremental add 6 8 Sessile drop volume (microlitre) + drops of diff. size slowly u n t i l the drop volume reached about 8 ulitres. Beyond t h i s , the contact angle value was e s s e n t i a l l y constant. These r e s u l t s are i n a good accordance with those obtained previously by others <Herzberg and Marian, 1970; Good, 1979; Good and Koo, 1979>. In contrast to the above r e s u l t , the p l o t of the contact angle versus drop s i z e as obtained from the second procedure i s quite d i f f e r e n t . As shown i n Figure 6.4.1, the contact angle f i r s t decreased with the increase of a drop volume, then started r i s i n g again forming a minimum value at around 6 //.litres. This r e s u l t i s very d i f f e r e n t from what has been reported before. I t i s worthy of mention that the contact angle values i n Figure 6.4.1 were obtained by axisymmetric drop method. The contact angle values f o r d i f f e r e n t drop sizes were not known u n t i l t h e i r photographs were d i g i t i z e d and angles calculated a l l i n a batch. This excluded possible subjective influence i n the measurement. In order to confirm t h i s phenomenon's r e p r o d u c i b i l i t y several sets of t e s t s were conducted on the 1.3-1.4 density f r a c t i o n (Figure 6.4.2) and on the oven-heated -1.3 density f r a c t i o n (Figure 6.4.3 to 6.4.5). A l l the figures revealed two major features. 94 Drop volume (micronlitre) H Contact angle Drop size effect on contact angle Figure 6.4.3 oxidized-1.3 BM coal t=150C 130 " 128 -126 H 106 H 104 -102 -100 -| 1 1 1 1 1 1 1 1 1 1 1 1 i r 2 4 6 8 10 12 14 16 Drop volume (microlilre) • contact angle Drop size effect on contact angle Figure 6.4.4 oxidized -1.3 BM coal t=200C 2 4 6 8 10 12 14 Drop volume (microlilre) • contact angle 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 F i r s t , they are generally V-shaped. A l l contact angles e x h i b i t a decrease versus drop volume at the beginning. Then, beyond a c e r t a i n volume (8 to 17 /^litres) the contact angle s t a r t s to increase again. This phenomenon may be explained as a j o i n t e f f e c t of two factors: g r a v i t a t i o n a l force and contact angle hysteresis. At the beginning when s e s s i l e drop volume on the p e l l e t surface i s very small, each incremental addition s u b s t a n t i a l l y increases the s e s s i l e drop height, and the g r a v i t a t i o n force moves the s e s s i l e drop p r o f i l e downward to assume a smaller contact angle. A continuous decrease i n contact angle versus volume i s observed. Beyond a c e r t a i n volume, further addition of the l i q u i d to the s e s s i l e drop does not increase notably the s e s s i l e drop height any more. The s e s s i l e drop only continues to expand h o r i z o n t a l l y . As a r e s u l t , the curve exhibits a c l e a r minimum. Af t e r the minimum i s reached, the further increase i n s e s s i l e drop volume can only lead to i t s horizontal expansion. The second factor, the contact angle hysteresis, becomes a major e f f e c t . I t attempts to obstruct the advance of the three-phase contact l i n e . As a r e s u l t , the contact angle began to increase. The second feature presented by these figures i s that a l l curves are sawtooth-shaped. This can be a t t r i b u t e d to the hysteresis energy b a r r i e r . An incremental increase i n 99 the s e s s i l e drop s i z e on the p e l l e t surface i s accompanied by an expansion of the three-phase contact l i n e . The expansion of the three-phase contact l i n e was opposed by the hysteresis energy b a r r i e r . This may lead to an increase of the contact angle value. The energy accumulated within the s e s s i l e drop a f t e r subsequent additions of one or two incremental droplets may be s u f f i c i e n t to overcome the energy b a r r i e r . This process i s accompanied by a decrease i n the contact angle. The whole cycle, when more incremental l i q u i d i s added to the s e s s i l e drop, repeats continuously. A sawtooth-shaped contact angle versus drop volume curve r e s u l t s . Apparently f o r such a phenomenon to appear, the energy introduced by each droplet should be lower than the hysteresis energy b a r r i e r . That i s , the droplet should be very small (1 nlitre i n t h i s case). Otherwise the energy introduced by each droplet i s so large r e l a t i v e l y to the energy b a r r i e r , that the e f f e c t of energy b a r r i e r may be overshadowed. The present methodology may be further developed to study the hysteresis energy b a r r i e r by c o r r e l a t i n g the saw-teeth height with energy. 100 6.5 CONTACT ANGLE VERSUS TIME I t was perceived that contact angles measured i n the open a i r and i n an enclosed thermostated chamber may vary. However, i t was not known whether equilibrium, or, at l e a s t meta-equilibrium of the s e s s i l e drop on the p e l l e t was established within c e r t a i n period. I f not, the question i s how long i t w i l l take to reach such an equilibrium. In order to answer such a question, additional experiments were ca r r i e d out. The f i r s t observation was aimed at t e s t i n g the r e l a t i o n s h i p between the contact angle at a s e s s i l e drop and i t s l i f e time on the p e l l e t . The t e s t s were performed i n a thermostated chamber at ambient temperature. The re s e r v o i r within the chamber was f i l l e d with d i s t i l l e d water to keep the humidity constant. A f t e r lowering the tested p e l l e t onto the stage within the chamber, the main l i p was closed. 10 minutes l a t e r , a s e s s i l e drop was placed on the p e l l e t surface through a small hole on top of the chamber. The chamber was equipped with viewing windows, so the contact angle could be taken without touching the chamber and disturbing the s e s s i l e drop. The r e s u l t s obtained for d i f f e r e n t density fract i o n s of Line Creek Coal are presented i n Figure 6.5.1. For 101 CONTACT ANGLE vs. TIME F i g u r e 6.5.1 FOR DIFF. DENSITY FRACTIONS OF LC COAL 1 1 1 1 1 1 i i r 0 4 9 15 20 16200 34200 44280 63000 66600 68400 75600 82800 90000111600 + 1.4-1.5 time (second) O 1.5-1.6 A 1.6-1.8 density f r a c t i o n s lower than 1.5, the contact angles were very stable and only varied very s l i g h t l y even over a two day period, Then a quick decline followed. Liquid evaporation, p e l l e t surface oxidation, and the penetration of l i q u i d into the p e l l e t can be the factors responsible f o r such a behaviour. For low density f r a c t i o n s , the e f f e c t of l i q u i d penetration was i n i t i a l l y n e g l i g i b l e . The slow decrease i n contact angle was p r i n c i p a l l y due to the s e s s i l e drop evaporation. The reason i s that the s e s s i l e drop in t e r f a c e and the surface of bulk l i q u i d i n the res e r v o i r possessed d i f f e r e n t curvatures (see Kelvin's equation). Therefore, i t can be expected that the s e s s i l e drop volume decreases with time. As time proceeds, the p e l l e t surface oxidation becomes s i g n i f i c a n t , and the l i q u i d begins to penetrate into the p e l l e t . Consequently, the contact angle s t a r t s decreasing quickly. The horizontal parts of the curves (Fig. 6.5.1) reveal that the equilibrium state for the -1.5 f r a c t i o n of coal sample can e s t a b l i s h very quickly, i . e . , within one minute. So i n the actual measurement, i t i s not necessary to wait long f o r the establishment of equilibrium. The contact angle i n open a i r was compared with the r e s u l t i n Figure 6.5.1. I t was observed that the angle values i n open a i r 103 were approximately equal to the values at the horizontal part of the curve. This was i n agreement with other researchers' observationy <R. Crawford, L.K. Koopal and J . Ralston, 1987>. According to t h i s observation, the thermostated chamber i s not considered to be necessary i n the p r a c t i c a l contact angle measurements, and, therefore, a l l contact angles were measured i n open a i r . The contact angles of water on the p e l l e t s were much smaller than 90° f o r the +1.5 g/cm3 density f r a c t i o n s . The contact angle on p e l l e t surface decreases very quickly because of the s i g n i f i c a n t l i q u i d penetration into the p e l l e t . 104 6.6 FACTORS AFFECTING CONTACT ANGLE In t h i s section, the factors that influence the contact angle on a p e l l e t were tested. They are p e l l e t oxidation and pellet-making pressure. 6.6.1 Oxidation Oxidation was found to decrease the hydrophobicity of coal surface. Sun's early studies <1954> of the e f f e c t of oxidation on coal f l o t a t i o n indicated that as oxidation proceeds, coal becomes progressingly more hydrophilic. I t was also noted <Iskra and Laskowski, 1967> that reduction i n hydrophobicity of lower rank coals was more affected by oxidation than was that of higher rank bituminous coals. To evaluate the change i n hydrophobicity of coal powder due to oxidation, both the contact angle and the rate of penetration techniques were used. The rate of penetration technique w i l l be discussed i n d e t a i l i n Chapters 7 and 8. Various oxidation procedures have been considered. In one procedure recommended by Fuerstenau, Yang and Laskowski <1986>, the powdered Bullmoose coal was contained i n a beaker and oxidized i n a fan v e n t i l a t e d oven at 150 °C, 105 200°C, and 250°C, respectively, for a period of 8 hours. A f t e r oxidation, the coal powder was compressed under pressure of 27.6 MPa into p e l l e t s and the contact angles were measured as already discussed. The r e s u l t s are shown i n Table 6.6.1. Although the change i n contact angles was, according to the s i g n i f i c a n c e t e s t , s t a t i s t i c a l l y i n s i g n i f i c a n t , the trend s t i l l can be seen. An anomaly appeared at 250°C where a s l i g h t increase i n contact angle was observed. These oxidized and un-oxidized coal powders were again tested by the rate of penetration technique. The penetrating l i q u i d was kerosene. The slope value of the penetration curve was d i r e c t l y r elated to the contact angle (see Chapter 7) . For s i m p l i c i t y , only the slope values instead of the calculated angles were presented f o r comparison since t h i s i s only a q u a l i t a t i v e comparison. They were tabulated together with the d i r e c t l y measured contact angles i n Table 6.6.2. Kerosene can penetrate into a column of hydrophobic material more quickly than into a hydrophilic one. So i n the table, the slope value of penetration value f o r un-oxidized coal should be greater than that f o r oxidized coal. Following the same trend as the contact angle, the slope value became smaller for the coals oxidized at 150 and 106 The contact angle on p e l l e t of oxidized coal Table 6.6.1 the -1.3 density f r a c t i o n Bullmoose coal P e l l e t No. Unoxidized 150* C 200* C 250* C 130 .5 131 .5 129 .8 130.5 125.0 127 .5 129 .0 135 .5 130.5 132.8 128 .5 132 .0 129 .8 133.5 131.0 125 .5 131 .5 128 .8 135.0 134.0 1st 127 .0 127 .0 126 .0 127.0 132.3 129 .0 132 .0 129 .3 129.8 133.0 130 .5 136 .0 128 .5 132.8 127.3 126 .0 132 .5 127 .5 125.8 131.5 132 .5 129 .5 129 .3 121.0 128.8 127 .5 135 .0 126 .5 125.0 127.5 128 .5 133 .0 127 .3 125.5 132.3 129 .5 135 .5 128 .3 127.8 130.8 2nd 127 .0 135 .5 127 .3 130.5 130.0 131 .0 130 .0 123 .8 126.5 129.0 130 .5 130 .0 129 .0 122.0 131.3 127 .0 124.5 131 .0 132 .5 125 .5 123.8 128.0 131 .0 127 .5 129 .3 127.5 128.8 132 .5 126 .6 125 .8 129.8 129.5 128 .5 133 .5 136 .5 129.0 129.5 3rd 135 .5 130 .5 126 .3 132.8 130.3 129 .5 131 .0 126 .0 132.3 128 .5 126 .0 126 .3 129.8 125 .8 129.0 129 .3 129.8 Average: Std Deviatn: 130.34 2.75 128.18 2.79 128.18 3.71 130.15 2.06 * The period of oxidation time i s 8 hours * Pellet-making pressure i s 27.6 MPa 107 Table 6.6.2 Comparison of the contact angles with the rate of penetration measured on d i f f e r e n t coals method unoxidized 150*C 200"C 250*C measured angle degree 130.34 128.18 128.18 130.15 rate of pene tratn slope 0.945 0.904 0.864 0.958 The d i r e c t contact angle measurement are quoted from chapter 5 values * Bullmoose coal -1.3 density f r a c t i o n Column making pressure i s 13.8 MPa 200°C. The anomaly for the coal powder oxidized at 250°C was again observed. The slope value was 0.958 and apparently greater than others. This means that the coal powder oxidized at 250°C became more hydrophobic. The s i m i l a r r e s u l t s obtained from the two d i f f e r e n t techniques confirmed that an increase i n hydrophobicity for the coal powder heated at 250°C d i d occur. The possible reason f o r t h i s may be attr i b u t e d to the decomposition or breakup of the hydrophilic functional groups (carboxyl groups) on coal surface i n the heating process <Ye, et a l . , 1986>. Even though oxidation was s t i l l going on, the functional groups could be e f f e c t i v e l y s p l i t from the coal surface and evaporated at higher temperature. While at lower temperature, the functional groups could not be s p l i t so e f f e c t i v e l y as at high temperature. The coal surface became more and more hydrophilic. A s i m i l a r phenomenon was observed before by Ye, J i n , and M i l l e r <1986> i n t h e i r study on thermal treatment of low-rank coal and i t s re l a t i o n s h i p to f l o t a t i o n response. They found that properly c o n t r o l l e d heating can a c t u a l l y improve coal f l o t a t i o n and i t s separation from mineral matter, e s p e c i a l l y for low-rank-coal. I t was alleged by Yordon and Yoon <1988> and many others that the oxidation mechanism of coal and the reaction 109 CONTACT ANGLE vs. OXIDATION TIME Figure 6.6.1 Oxidized in water and in air Oxidation time (hour) • Oxidized in water + Oxidized in air products under dry conditions can be s i g n i f i c a n t l y d i f f e r e n t from those of the low-temperature oxidation that take place i n a moist or wet environment. In t h i s work, wet oxidation of coal was also tested. In the process, a p e l l e t of the Line Creek coal was made following the same procedure as mentioned above and held on a small holder with i t s surface exposed to water. Then, the whole set was immersed i n d i s t i l l e d water and the oven temperature was maintained at 100°C. For comparison, another p e l l e t was dry-heated together with the above p e l l e t i n the same oven i n the a i r . A f t e r a period of time, the two p e l l e t s were taken out from oven to determine the contact angle. Then, they were put back into the oven to continue the oxidation process. The procedure was repeated. A curve of contact angle versus oxidation time could be obtained f o r each p e l l e t . The r e s u l t s are given i n Figure 6.6.1. Apparently, the rate of wet oxidation i s much larger than dry oxidation. 6.6.2 Contact Angle versus Pressure Contact angles measured on the porous p e l l e t surfaces are not the true contact angles. The pellet-making pressure can influence the contact angle on a p e l l e t surface through changing i t s f r a c t i o n a l area of pores. To t e s t t h i s hypothesis, the contact angles on a ser i e s of p e l l e t s made under d i f f e r e n t pressures were tested. Results f o r the -1.3 g/cm3 density f r a c t i o n of both Line Creek and Bullmoose coals are given i n Figures 6.6.2 and 6.6.3, respectively. As shown i n Figure 6.6.2, at low pressures, the contact angle decreases with an increase i n pressure (3.4 - 17.2 MPa). Further increases i n pressure above 17.2 MPa have only a very small impact on the contact angle value. In addition, the pellet-making pressure also influences the r e p r o d u c i b i l i t y of the data. The data i n Figure 6.6.3 were s t a t i s t i c a l l y analyzed. The standard deviations are shown i n Figure 6.6.4. As the pellet-making pressure increases, the r e p r o d u c i b i l i t y of the contact angle data becomes better. The influence of the pellet-making pressure on the value of the contact angle may r e s u l t from the a l t e r a t i o n s of s o l i d surface properties, surface roughness, and f r a c t i o n a l area of pores on p e l l e t surface. The SEM photographs (Section 6.8) show that the 112 CONTACT ANGLE vs.PELLET-MAKING PRESSURE 100 H 90 H \ 1 1 \ 1 i 1 i 1 1 1 1 i i i r 2 6 10 14 18 22 26 30 34 Pressure MPa S Measured angle 1) o •a bo o -4-» g 180 170 Figure 6.6.3 Effect of pellet-making pressure on contact angle -1.3 fraction BM coal 160 H 150 H 140 130 ^ 120 110 100 90 80 70 H 60 • + <t> • + " i— i—r 10.34 • ; i i ° 5 • + + A + • * - ? " 9 ° • + 5 o • + * • o • + • f "1—I—I—I 17.24 "i—i—r n—i—r 24.11 1—i—i—i—r 31.03 • 1st pellet Pressure (MPa) + 2nd pellet O 3rd pellet Standard deviation in degree o Lo to r— I f * •ff^-;-}Kpf'-"v----"-u^ 11111111181111 ^ ^ ^ ^ pellet-making pressure of 27.6 MPa caused only n e g l i g i b l e p a r t i c l e crushing on the p e l l e t surface. I t i s u n l i k e l y that t t h i s s t a t i c pressing force would a l t e r the coal surface properties noticeably. In fact, the pellet-making pressure influenced the contact angle mainly through changing the f r a c t i o n a l area of pores on a p e l l e t surface. The increase i n pressure can reduce both f r a c t i o n a l area of pores and surface roughness of a p e l l e t . The r e s u l t s i n section 6.9 show that the surface roughness has a minor e f f e c t on contact angle hysteresis, whereas the f r a c t i o n area of pores i s the major factor. Detailed discussion of t h i s e f f e c t w i l l be given i n the following sections. 116 6.7 POROSITY The compressed p e l l e t surfaces looked glossy and were macroscopically f l a t . Although t i n y a i r voids and pores on the p e l l e t surface are not detectable to the naked eyes, these pores exert a s i g n i f i c a n t e f f e c t on the contact angles on p e l l e t surfaces. Cassie and Baxter <1944> considered the contact angle on a composite surface as an o v e r a l l contributions from a l l the components i n contact with the l i q u i d drop, including the a i r pores as one of the components. The contact angle of water on these a i r pores i s 180°. The e f f e c t of pores can be qua n t i t a t i v e l y corrected from the measured contact angle (the apparent contact angle) by u t i l i z i n g the Cassie-Baxter equation (see Chapter 2). COSe = a 1 - C O S e 0 - a 2 2.1.10 However, such correction requires the f r a c t i o n a l area of pores on p e l l e t surface, a2 , be qu a n t i t a t i v e l y known. There has been no d i r e c t technique, i n pra c t i c e , to measure the f r a c t i o n a l area of pores on a p e l l e t surface, while the p e l l e t bulk porosity can be d i r e c t l y measured through some simple techniques. I t was considered that there 117 must e x i s t c e r t a i n c o r r e l a t i o n between the f r a c t i o n a l area of pores on p e l l e t surface and the p e l l e t bulk porosity. In the present study, the f r a c t i o n a l area of pores on the p e l l e t surface was estimated from the measurement of the p e l l e t bulk porosity (see section 6.8). For compressed p e l l e t s of coal powder, there are two types of p o r o s i t i e s : the i n t e r - p a r t i c l e porosity caused by the a i r trapped i n between p a r t i c l e s , and i n t r a - p a r t i c l e porosity within i n d i v i d u a l p a r t i c l e s . Unlike other inorganic minerals, coal i s extremely porous. There are tremendous amount of t i n y pores and c a p i l l a r i e s with only several microns i n diameter within coal p a r t i c l e s . However, the t o t a l volume of these pores and voids within coal p a r t i c l e s i s much smaller than that trapped in-between p a r t i c l e s . The p e l l e t porosity i s , therefore, co n t r o l l e d by i n t e r - p a r t i c l e porosity. In the present work, kerosene was used as a replacing l i q u i d . The volume of kerosene needed to displace the a i r trapped i n the pores within a p e l l e t can be d i r e c t l y converted into porosity. In the process, the p e l l e t was brought into contact with kerosene. Because of the c a p i l l a r y e f f e c t , kerosene penetrates into, and saturates the p e l l e t by d i s p l a c i n g the a i r from i t . The p e l l e t weights before and a f t e r the 118 penetration were determined. The difference was the weight of kerosene penetrated into the p e l l e t ; which volume i s equal to the volume of pores within a p e l l e t . Kerosene was used instead of water because i t wets the coal surface and can penetrate into p e l l e t s of any density f r a c t i o n of coal very quickly. The time required by kerosene to penetrate a p e l l e t from bottom to top was less than 10 minutes. In order to ensure complete saturation, the p e l l e t was l e f t overnight i n contact with kerosene u n t i l no further increase i n the p e l l e t weight was observed. The porosity t e s t s were conducted on a l l the density f r a c t i o n s of Line Creek coals. Results are shown i n Figures 6.7.1 to 6.7.2. At low pellet-making pressure (below 13.8 MPa) , the porosity decreases with the increase i n pressure more quickly than that at high pressures. When pressure reached a c e r t a i n value (above 24.1 MPa), further increases i n the pressure had a n e g l i g i b l e influence on porosity. I t was believed that the p e l l e t had reached the cl o s e s t packing condition at t h i s pressure. Further increases i n the pressure could not change such a packing structure. Unless the pressure was extremely high and p a r t i c l e crushing took place, no further decrease i n porosity was possible. I t can be observed from Figures 6.7.1 and 6.7.2 that the porosity versus pressure curve s h i f t s downward to a 119 o THE PELLET POROCITY vs. PRESSURE Figure 6.7.1 For diff. density fractions of LC coal Pressure MPa o CM -1.3 + 1.3-1.35 1.35-1.4 THE PELLET POROCITY vs. PRESSURE Figure 6.7.2 For diff. density fractions of LC coal 1.4-1.5 + 1.5-1.6 Pressure MPa 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 p a r a l l e l . In the grinding process, the p a r t i c l e s i z e s of coal powders for a l l the density f r a c t i o n s were c l o s e l y c o n t r o l l e d to ensure that they had as narrow p a r t i c l e s i z e d i s t r i b u t i o n s as possible. The p a r t i c l e s i z e analysis r e s u l t s f o r d i f f e r e n t density f r a c t i o n s of the Line Creek coal are presented i n Figure 6.7.3. For each density f r a c t i o n , two d i f f e r e n t c h a r a c t e r i s t i c sizes (log mean and median) of the powder were determined. As described i n Chapter 8.5, the p e l l e t s made under the same pressure and from the materials with the same or s i m i l a r s i z e d i s t r i b u t i o n s , should be characterized by the same porosity. The porosity indicated above i s the i n t e r -p a r t i c l e porosity and i t can be changed by pressure. The f a c t that a l l the curves are p a r a l l e l (Figures 6.7.1 and 6.7.2) strongly supported such a conclusion. While the pellet-making pressure cannot change the coal porosity ( i n t r a - p a r t i c l e ) , i t only a f f e c t s i n t e r -p a r t i c l e porosity. The p a r t i c l e s of the lower density f r a c t i o n exhibited higher i n t r a - p a r t i c l e p o r o s i t i e s . I f the curves are extrapolated to the Y-axis, the intercepts are the p o r o s i t i e s when powders are loosely p i l e d 122 CHARACTERISTIC PARTICLE SIZES Figure 6.7.3 For diff. density fractions of LC coal  v - "> £•!*!•!•!•» 'mm without any compression. I t was observed that when p e l l e t -making pressures above 20.7 MPa were employed, very good r e p r o d u c i b i l i t y f o r p e l l e t properties could be obtained. When pellet-making pressure i s decreased down to 6.9 MPa, the p e l l e t properties such as porosity were severely scattered. Reproducibility i s , therefore, better at higher pellet-making pressures. In chapter 8, a de t a i l e d discussion on the e f f e c t of pressure on column properties w i l l be given. The conclusions obtained from those experiments are s t i l l applicable to p e l l e t s . 124 6.8 SURFACE EXAMINATION AND ASSUMPTION FOR FRACTIONAL AREA OF PORES As has already been mentioned, i t was assumed that there i s a c o r r e l a t i o n between the f r a c t i o n a l area of pores on a p e l l e t surface and the p e l l e t bulk porosity. The method was proposed to obtain the f r a c t i o n a l area of pores through such a c o r r e l a t i o n . The penetration behaviour of a l i q u i d into a p e l l e t through c a p i l l a r y e f f e c t gives the h i n t . P e l l e t s compressed from powders are porous. In order to explain the penetration phenomenon, the pores inside the p e l l e t are s t a t i s t i c a l l y equalized as a bundle of c a p i l l a r y tubes which are tortuous along the column's axis d i r e c t i o n . This methodology was u t i l i z e d i n solving the present problem. I f under an i d e a l i z e d condition, a bundle of s t r a i g h t and t h i n c a p i l l a r y tubes are p a r a l l e l perforating through a s o l i d p e l l e t along i t s axis d i r e c t i o n , the c o r r e l a t i o n between the f r a c t i o n a l area of pores and the bulk porosity inside the p e l l e t can be e a s i l y obtained from a simple geometry derivation. By d e f i n i t i o n , the f r a c t i o n a l area of pores i s the r a t i o of the t o t a l cross section area of c a p i l l a r y tubes (pores) to the whole area of p e l l e t bottom surface. That i s 125 4> = n • n • r 2 /n • R2 <f> = n-r 2/R 2 6.8.1 where i s the f r a c t i o n a l area of pores, n the number of c a p i l l a r y tubes perforating through the p e l l e t , r radius of the c a p i l l a r y tubes, and R the radius of the p e l l e t . The porosity of the p e l l e t i s given by (P = n • TT • r 2 • h/n • R2 • h = n r 2 / R 2 6.8.2 where <P i s the p e l l e t porosity, and h the height of the p e l l e t . Combining Equations 6.8.1 and 6.8.2, one can get <f> = (P 6.8.3 That i s , the f r a c t i o n a l area of pores on p e l l e t bottom surface i s equal to the bulk porosity inside a p e l l e t i n an i d e a l i z e d condition. For a p e l l e t made of compressed powder, the c a p i l l a r y tubes inside i t are tortuous and vary i n radius. Under such a case, the question to be answered i s whether the above conclusion s t i l l holds. One can consider that the 126 p e l l e t i s composed of a large number of t h i n layers p i l e d one over another. They are so t h i n and the c a p i l l a r y tubes inside i t are so short that the c a p i l l a r y tubes are considered s t r a i g h t and t h e i r r a d i i uniform. Therefore, for these i n d i v i d u a l t h i n layers the above conclusion s t i l l holds. A d d i t i o n a l l y , the f r a c t i o n a l areas of pores on those t h i n layers' surfaces should be s t a t i s t i c a l l y equal to one another. And so are the bulk p o r o s i t i e s inside those layers. When a l l those t h i n layers are p i l e d together to form a p e l l e t , that i s , f o r a compressed p e l l e t of powder the Eq.6.8.3 s t i l l applies. One possible problem which renders above assumption i n v a l i d i s the crushing action that may occur on the outmost surface of p e l l e t during compressing process. The breakage of p a r t i c l e s on the top surface of the p e l l e t can not only reveal new interfaces but also smear s o f t material on the top surface and lead to the blockage of c a p i l l a r y cross sections. I f t h i s occurs, the above assumption w i l l be i n v a l i d . To examine the possible breakage, the rate of penetration experiment was designed (for d e t a i l see Chapters 7 and 8) , i n which two groups of columns were made under exactly the same conditions. The basic idea f o r t h i s was that i f the breaking and smearing actions d i d occur, the f r a c t i o n a l area of pores on the top and bottom surfaces of 127 the p e l l e t should be smaller than that on any cross s e c t i o n a l surface inside the column. The penetration rate of a l i q u i d into the column w i l l be slower because of the existence of the t h i n layer i n h i b i t i n g the process. Based on t h i s idea, one group of the columns was s p e c i a l l y processed to remove the t h i n layer on the outmost surface of the p e l l e t using abrasive. The penetration rate should become higher f o r these columns i f the breaking action occur. The experimental r e s u l t s f o r the +1.8 f r a c t i o n of Bullmoose coal are shown i n Figure 6.8.1. The data points fo r the two groups of columns have f a l l e n on the same l i n e . This indicates that the postulated breaking action d i d not happen. To confirm t h i s conclusion, the Scanning Electron Microscopic (SEM) inspection was c a r r i e d out to examine the surface state of the p e l l e t surface under d i f f e r e n t magnifications. The SEM photographs are given i n Figure 6.8.2. As the magnification goes up, the glossy p e l l e t surface becomes more and more v i s i b l y porous. When the magnification reached above 3000, the packing state of p a r t i c l e s become c l e a r l y v i s i b l e . I t can be seen from the photographs that the crushing 128 Figure 6.8.1 Test for fractional area of pores on different cross sectional surfaces surface erased + Time (second) surface not erased 0 1 4 6 9 9 £0KV X 3 0 : 0 " i : 0 0 m m F i g u r e 6 .8 .2 (a ) SEM photograph of a p e l l e t s u r f a c e 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 f r a c t i o n o f Bul lmoose c o a l , 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 (4000 p s i ) 130 F i g u r e 6 .8 .2 (b) SEM photograph o f the same p e l l e t s u r f a c e Magn i f i ed by 2500 t imes 131 action has r a r e l y happened. Only some p l a s t i c deformations occurred at some spots; and the asperity has been flattened. I f any crushing action had happened, a c l u s t e r of small p a r t i c l e s p i l e d together would be found i n the photographs. 132 6.9 A MODEL 6.9.1 A Compressed P e l l e t Surface Model The SEM photographs shown i n Figure 6.8.2 and the c a p i l l a r y properties of a p e l l e t l e d to a model of compressed p e l l e t surface shown i n Figure 6.9.1. There are two domains on the model surface: s o l i d and a i r pores. Under the pellet-making pressure as high as 27.6 MPa, a l l p a r t i c l e s are c l o s e l y squeezed together and the crevices between large p a r t i c l e s w i l l be f i l l e d with smaller ones. The p a r t i c l e s on the outermost surface of the p e l l e t are oriented with one side or edge touched at a plane; and some protruding edges are p l a s t i c l y deformed or crushed l o c a l l y to match t h i s plane. Thus the compressed surface i s very f l a t i f the a i r craters and pores d i s t r i b u t e d on the p e l l e t surface are not taken into account. The p e l l e t surface can thus be considered as a composite surface consisting of two domains i . e . s o l i d and a i r pores. Such domains are very small (see Figure 6.8.2), they are les s than 5 microns. Although under highly magnified SEM photograph the p e l l e t surface looks very uneven, the p e l l e t surface i s s t i l l macro-scopically very f l a t . 133 Figure 6.9.1 A model of compressed p e l l e t surface 134 The d i s t i n c t i o n between macroscopic and microscopic states i s a r b i t r a r y . Good <1979> set the l i m i t of macro i n a range of resolution of l i n e s separated by about 0.02 - 0.1 mm. The scanning electron microscopic examinations (Figure 8.2.12) showed that the sizes of p a r t i c l e s and a i r pores on p e l l e t surface are normally smaller than 0.05 mm. Therefore, the compressed p e l l e t surface i s macroscopically homogeneous and f l a t . As i t i s known (Chapter 2), the hysteresis i s caused by two major factors: surface heterogeneity, and surface roughness. Therefore, both roughness and heterogeneity of the p e l l e t surface can be investigated by the examining the contact angle hysteresis. I t was observed that the heterogeneity could more s i g n i f i c a n t l y influence the hysteresis; while the surface roughness exhibited only a minor e f f e c t . To t e s t the e f f e c t of the surface roughness, i t was f i r s t i s o l a t e d from heterogeneity by coating the p e l l e t surface with a very t h i n layer of kerosene. Because the w e t t a b i l i t y of monolayer coated surfaces i s determined by the nature and packing of the outmost surface atoms or organic r a d i c a l s , and not by the nature and arrangements of atoms i n the s o l i d substrate 10 to 20 Angstroms below the surface layer <Zisman, 1964>, the p e l l e t ' surface thus coated 135 became homogeneous and i t s surface roughness remained unchanged. The surface roughness became the only factor a f f e c t i n g the contact angle hysteresis and could be e a s i l y detected. The coating was prepared by placing the p e l l e t on a cotton bed saturated with kerosene. Upon the contact, the kerosene spontaneously penetrates upward into the p e l l e t through c a p i l l a r y e f f e c t s and eventually reaches the top surface. The pores within the p e l l e t become f i l l e d with kerosene and the p a r t i c l e s on the p e l l e t top surface are coated with a very t h i n layer of kerosene. The p e l l e t surface, then, becomes homogeneous i n respect to contact angle measurement. Such a p e l l e t was used to t e s t the contact angle hysteresis. The observation showed that the contact angle hysteresis on a l l the kerosene-coated p e l l e t surfaces was very small. I t ranged from 3 to 8 degrees. In comparison, the hysteresis on the un-coated p e l l e t surfaces a l l exceeded 90 degrees. The s i g n i f i c a n t difference between the two hysteresis values confirmed that the p e l l e t surface roughness played an i n s i g n i f i c a n t r o l e i n contact angle hysteresis with heterogeneity being the predominant factor. 136 6.9.2 Contact Angle Correction And Comparison As mentioned above, the surface heterogeneity has a s i g n i f i c a n t influence on the contact angle measurement. The contact angle on a heterogeneous surface r e s u l t s from contributions of a l l the components (especially the a i r pores) on the p e l l e t surface (see l i t e r a t u r e review 5.1.2). Therefore, the contact angle measured on a p e l l e t surface (the apparent contact angle) needs to be corrected. According to the p e l l e t surface model proposed i n Figure 6.9.1, i f a l i q u i d drop comes i n contact with t h i s proposed model surface, a composite configuration w i l l undoutedly be established. Therefore, the Cassie-Baxter equation (2.1.10) can be r e a d i l y applied cose•= o1-cosd1 - a2 where a x = As L /A • and a 2 = A l g/A' where As L i s the t o t a l area of the s o l i d i n contact with the l i q u i d ; A l g i s the free l i q u i d - a i r interface area under the l i q u i d drop; and 6* and ex are the measured contact angle and the contact angle on the s o l i d without any pores, res p e c t i v e l y . 137 Since the dimension of a i r pores on a p e l l e t surface i s extremely small (less than 10 microns), the curvature of the free l i q u i d - a i r interface under the l i q u i d drop can be neglected and considered to be f l a t . Therefore, a2 i s equal to the f r a c t i o n a l area of pores of the p e l l e t surface. Under the assumption made i n Section 6.8, i t (and therefore ax) can be d i r e c t l y obtained from the p e l l e t bulk porosity measurement. In Figure 6.9.2, both the measured and corrected contact angles of water on the Line Creek coal were plotted versus ash content. The contact angle versus pressure data i n Figure 6.6.2 were also corrected and re-plotted i n Figure 6.9.3. In Figure 6.9.2, the p e l l e t s f o r d i f f e r e n t density f r a c t i o n s of the Line Creek coal were made at the same pressure of 27.6 MPa (4000 p s i ) . The p e l l e t porosity value correponding to each density f r a c t i o n can be read i n Figures 6.7.1 and 6.7.2. In Figure 6.9.3, the p e l l e t s of the -1.3 Line Creek coal were mi le at d i f f e r e n t pressures; and the corresponding p e l l e t porosity values are obtained from Figure 6.7.1. I t can be observed, from Figure 6.9.2, that the contact angle d i r e c t l y measured decreases noticeably with increase of the 138 pellet-making pressure. Apparently, t h i s i s due to the e f f e c t s of both a i r pores and surface roughness. The corrected value of contact angle, however, changes only at low pressures (less than 14 MPa). At higher pressures, the corrected contact angle values do not change when the pressure i s further increased. This indicates that, at low pressure, the surface roughness of a p e l l e t decreases very r a p i d l y with increase i n the pellet-making pressure. Once the pressure reaches 20.7 MPa, further increase of pressure does not change the p e l l e t surface roughness notably. For comparison, the contact angle was also measured on the polished surface of Line Creek coal. Some large chunks of Line Creek coal were selected, and f l a t surfaces were polished on these large p a r t i c l e s . The contact angle values measured on these surfaces are shown below Contact angles measured on polished Line Creek coal surface (degree) 77.4 76.5 78.0 74.8 77.5 78.4 73.2 75.9 78.3 76.3 79.5  Average: 76.9 139 CONTACT ANGLE vs ASH CONTENT OF LC COAL F i g u r e 6 . 9 . 2 both the measured and the corrected 130 - i — 0 2 0 - 4 0 60 80 MEASURED ANGLE Ash content (%) + CORRECTED ANGLE CONTACT ANGLE vs.PELLET-MAKING PRESSURE F i g u r e 6.9.3 Line Creek coal-1.3 density fraction 140 - i — 80 H 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i r 2 6 10 14 18 22 26 30 34 • Measured angle Pressure MPa + Corrected angle The average angle value on polished coal surface 76.9 degrees. According to the r e s u l t s shown i n Figure 6.9.3, the apparent contact angle on the p e l l e t surface of -1.3 density f r a c t i o n of Line Creek coal i s as large as 107 degree. While the corresponding corrected contact angle i s 84.2 which i s s t i l l greater than the angle value measured on polished surface. I t should be remembered that the polished coal chunk was randomly selected from the sample. I t may be a mixture of the d i f f e r e n t density f r a c t i o n s . On average, i t s density i s greater than 1.3 g/cm3. Therefore the contact angle on the polished coal chuck i s lower than the corrected angle on the p e l l e t surface of -1.3 density f r a c t i o n . 142 6.10 SUMMARY AND DISCUSSIONS The contact angle on f i n e coal p a r t i c l e s was measured i n t h i s project by making p e l l e t s 2.54 cm i n diameter and 0.3 to 0.5 cm i n height under high pressure (6.9 to 28 MPa) An a r t i f i c i a l surface formed on the p e l l e t was u t i l i z e d to accommodate l i q u i d s e s s i l e drop and measure the contact angle. The p e l l e t surface was macroscopically f l a t and glossy. The contact angles were measured i n two d i f f e r e n t ways, ei t h e r d i r e c t l y through the goniometer by constructing a tangent to the s e s s i l e drop p r o f i l e at the three phase contact point, or with the use of camera attached to the goniometer telescope to take a photograph of the s e s s i l e drop p r o f i l e . The standard deviation of the angle values measured on the p e l l e t s ranged from 2.06 to 3.71 degrees. The p r o f i l e data on the photograph were taken by d i g i t i z e r . According to these data, the contact angle was calculated by using a computer program developed by Rotenberg, et al.<Rotenberg, Boruvka, and Neumann, 1983>. The r e p r o d u c i b i l i t y of t h i s method was high with the standard deviation of the measured angle values being ±0.32 degrees. 143 Because of the e f f e c t of heterogeneity and surface roughness, the angles measured by the two methods were d i f f e r e n t . While the value obtained by the f i r s t method r e f l e c t s the contact angle of water on the higher energy surface area, the value obtained by the second method i s the weighed average of the angle values on a l l the components of the heterogeneous surface. The e f f e c t of the s e s s i l e drop s i z e on the advancing contact angle was also tested i n the present work. The drop s i z e was increased i n two d i f f e r e n t procedures. In the f i r s t , a drop of preset volume was formed on the micro-syringe t i p . Then i t was lowered with the whole set of syringe and rested on the p e l l e t surface as a free s e s s i l e drop. To increase the drop s i z e , the same procedure was followed to form another independent s e s s i l e drop with larger s i z e . In the second procedure, the drop s i z e was enlarged by incremental addition of the l i q u i d to the previous s e s s i l e drop. The r e s u l t s show that the contact angle measured following the f i r s t procedure increases continuously with the s i z e of the drop.. After the drop s i z e i s increased to a c e r t a i n value, the drop si z e e f f e c t diminishes and contact angle changes only randomly around a c e r t a i n value. This phenomenon i s att r i b u t e d to the contact angle hysteresis a r i s i n g from the surface roughness. 144 In the second procedure, the contact angle i n i t i a l l y decreases with the drop s i z e , but then s t a r t s to increase r e s u l t i n g i n a V-shaped curve. The g r a v i t a t i o n a l force, the surface roughness, and k i n e t i c energy introduced when increasing the drop s i z e by incremental addition play the major ro l e s i n the process. At the beginning when s e s s i l e drop s i z e i s small, each addition of the incremental drop increases the s e s s i l e drop height 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 force tends to push the s e s s i l e drop downwards. The k i n e t i c energy which i s large r e l a t i v e l y to the energy b a r r i e r helps the three phase contact l i n e to 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 value of the contact angle. Further increase i n the drop s i z e only makes the drop expand h o r i z o n t a l l y . The e f f e c t of g r a v i t a t i o n a l force and k i n e t i c energy diminishes, and the surface roughness becomes predominant. In t h i s range, the contact angle increases with the drop s i z e . The contact angle of water on the coal p e l l e t surface was tested versus time. For lower density f r a c t i o n s (-1.3 to 1.4-1.5), the s e s s i l e drop and the contact angle are very stable even a f t e r several hours (see Figure 6.5.1). However, they are not stable on higher density f r a c t i o n s of coal (1.5-1.6 to +1.8). Because the contact angle on higher coal 145 density f r a c t i o n s i s small, the water drop s t a r t s to penetrate into the p e l l e t during the experiment. Although the p e l l e t surface was glossy and f l a t v i s u a l l y , the p e l l e t i s a c t u a l l y very porous both inside and on i t s surface. The porosity of the p e l l e t i s represented by the value of the p e l l e t bulk porosity. The p e l l e t porosity i s composed of two parts: i n t r a - p a r t i c l e porosity and i n t e r -p a r t i c l e porosity. The i n t r a - p a r t i c l e porosity i s the porosity inside an in d i v i d u a l coal p a r t i c l e . I t s value i s higher f o r lower coal density fract i o n s and becomes smaller f o r higher density f r a c t i o n s . The i n t e r - p a r t i c l e porosity i s the space between p a r t i c l e s . The pellet-making pressure has a major e f f e c t on the 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 porosity decreases when the pressure i s increased. With the use of the data obtained from a Scanning Electron Microscope a p e l l e t surface model was proposed. In the model, the coal p a r t i c l e s on the outmost surface of the p e l l e t o r i e n t themselves or experience some l o c a l p l a s t i c deformation to match a plane. Thus the compressed p e l l e t surface i s very f l a t , provided that the a i r pores d i s t r i b u t e d on the p e l l e t surface are neglected. Under the Scanning Electron Microscope, the p e l l e t surface was found to consist of two major components: s o l i d and a i r . The d i r e c t l y measured contact angle (the apparent 146 contact angle) r e s u l t s from the contributions from the w e t t a b i l i t y of both components. According to the proposed p e l l e t surface model, a correction procedure applying Cassie-Baxter equation was employed to correct the e f f e c t of a i r component on the contact angle value and transform the apparent contact angle into the r e a l contact angle on the s o l i d alone. The corrected angle value (real angle value) was 84.2 degree on a -1.3 g/cm"3 density f r a c t i o n of the Bullmoose coal. The contact angle measured on a polished surface of the coal chunk was about 76 degrees. These two values are more comparable and the difference seems to be quite acceptable. 147 CHAPTER 7 THE RATE OF PENETRATION TECHNIQUE 7.1 INTRODUCTION From a more p r a c t i c a l point of view, assessment of hydrophobicity/hydrophilicity through the study of the wetting c h a r a c t e r i s t i c s of a mass of p a r t i c l e s may provide a more r e a l i s t i c c o r r e l a t i o n with the performance of various technological processes. Coal i s a heterogeneous material, only i t s o v e r a l l composition can r e f l e c t i t s behaviour and, therefore, must be taken into account. The rate of penetration i s one of such measurement. Many authors have derived t h e o r e t i c a l and semi-empirical r e l a t i o n s h i p s <Bruil and Good, 1979> to i n t e r r e l a t e the v e l o c i t y of the r i s i n g l i q u i d with i n t e r f a c i a l parameters such as contact angles. The measurements of contact angles by such c a p i l l a r y r i s e methods have the advantage over the o p t i c a l method (direct contact angle measurement) i n that i t gives a "mean" value obtained f o r a large number of p a r t i c l e s which are not polished and are not contaminated from the abrasive agent used i n the pol i s h i n g . Compression of powder into a p e l l e t , on the other 148 hand, can r a i s e the porosity problem. When the contact angle on the compressed p e l l e t surface i s much smaller than 90°, penetration of the l i q u i d into the p e l l e t i s s i g n i f i c a n t and s e s s i l e drop equilibrium can not be consequently established. Under such conditions, the dynamic contact angle technique i s l i k e l y to be more r e l i a b l e <Crawford et a l . 1987>. As one of the dynamic contact angle techniques, the rate of penetration method shows considerable promise. However, i n s p i t e of the s i m p l i c i t y of t h i s method, i t has not been employed extensively. The publications on t h i s method are r e l a t i v e l y few compared with d i r e c t contact angle measurements over the past decade. Conventionally, the rate of penetration technique i s based on the unopposed penetration of a l i q u i d through a compressed column of powder, and i s regarded as a r e l a t i v e technique f o r that a l i q u i d with a known contact angle with the s o l i d i s needed to c a l i b r a t e the column t o r t u o s i t y constant; the influence of many factors such as column packing density and p a r t i c l e s i z e has not been c a r e f u l l y studied. In addition, major problems associated with t h i s method are incomparability of r e s u l t s obtained at d i f f e r e n t times by d i f f e r e n t persons o r i g i n a t i n g from the fa c t that the columns were packed by manual tapping. The e f f e c t of the dif f e r e n c e i n w e t t a b i l i t y between the powder material and 149 the wall of holding column which can a f f e c t the column penetration front and make the accurate penetration front measurement d i f f i c u l t has not been evaluated e i t h e r . In the present work, a new approach f o r the rate of penetration method i s studied to overcome these problems. High pressures (up to 27.6 MPa) were applied and p r e c i s e l y c o n t r o l l e d to produce c l o s e l y compacted column s u f f i c i e n t l y strong to withstand handling and f a c i l i t a t e the experiment. In addition, a new approach to c a l i b r a t e the column t o r t u o s i t y constant was introduced i n the present work. This new approach may make the rate of penetration method from a r e l a t i v e technique to a absolute one, since the l i q u i d s with a zero contact angle on a l l the tested s o l i d may not be required any more. 150 7.2 THEORY AND TECHNIQUES 7.2.1 Basic Theory The c a p i l l a r y d r i v i n g force f o r a l i q u i d i n a c y l i n d r i c a l tube of radius r i s AP = 27 l v-cos0/r 7.2.1 where AP i s the LaPlace pressure across the curved interface, 71 v i s the l i q u i d surface tension, and 6 are the l i q u i d contact angle on the c a p i l l a r y . One ap p l i c a t i o n of t h i s theory i s to measure the pressure, P 1, necessary to balance the LaPlace pressure, AP, which drives the l i q u i d into a c a p i l l a r y bed <White, 1982>; the contact angle can then be calculated using Eq.5.2.1. Washburn <1921> combined the c a p i l l a r y d r i v i n g force for a c y l i n d r i c a l tube of radius r (Eq. 5.2.1) with the Poiss e u l l e equation for viscous drag under conditions of steady flow 8M• h/r 2 • dh/dt = AP 7.2.2 151 where M i s v i s c o s i t y of the f l u i d , h the length of penetration i n time t , r c a p i l l a r y radius, AP the pressure drop and obtained r 2 271V•cose d(h 2)/dt = ( Apgh) 7.2.3 4M r where Ap i s the difference i n density between the l i q u i d and the surrounding medium, g the g r a v i t a t i o n a l acceleration, 6 contact angle. I f the c a p i l l a r y i s horizontal or the penetration length i s small, the term Apqh i n equation above can be neglected, and one can obtain: r - 7 l v • c o s e d ( h 2 ) / d t = 7.2.4 2M The a p p l i c a b i l i t y of t h i s equation to a powder column has been t h e o r e t i c a l l y j u s t i f i e d by Crowl and Wooldridge <1967> and Szekely et a l . <1971>. In the case of a powder column, the c a p i l l a r i e s inside the column are tortuous and t h e i r r a d i i are not constant and vary from point to point within the column. The o v e r a l l column penetration process i s an average on a l l these i n d i v i d u a l process. The observed rate d (h 2) /dt must correspond to an average value of r " i n the place of r i n Eq.5.2.4. Therefore a t o r t u o s i t y constant 152 K was introduced i n place of r <Ely and Pepper, 1944>, and Eq.5.2.4 becomes K- 7 l v • cose d(h 2)/dt = 7.2.5 The t o r t u o s i t y constant K i s a hypothetical mean radius. Th e o r e t i c a l l y , the adsorption of some f l u i d molecules can take place onto the column p a r t i c l e surfaces. I t was shown that <Good, 1973, Good and Lin, 1976 and White, 1982> i f a porous body i s i n i t i a l l y devoid of any adsorbed f i l m of the l i q u i d that penetrate i t , and i f the molecules of the f l u i d are not transported ahead of the l i q u i d at a rapid rate by d i f f u s i o n , then the rate of penetration w i l l be f a s t e r than that predicted by Washburn equation because of the spreading pressure. That i s r 7 l v • cose/2/i < d(h 2)/dt < r ( 7 l v c o s e + jre - 7 r 0)/2 / i 7.2.6 where ng i s the equilibrium spreading pressure, and n0 the spreading pressure at zero time we = 7 S _ 7 S v 7.2.7 *o = 7 S " 7 S (t=0) 7.2.8 The major drawback of applying the Washburn equation 153 to the powder column i s that there has been no d i r e c t means to obtain the value of t o r t u o s i t y constant K. Using Laplace equation, White<1982> obtained a quantitative equation defining the e f f e c t i v e radius of the compressed powder column by thermodynamic derivation r e = 2 ( P/(l - ( P)/9* 7.2.9 where <P i s the column porosity, p i s the mass density of the powder i n the column, and * i s the s p e c i f i c area of powder per gram. I f the porous column consists of i d e n t i c a l v e r t i c a l c a p i l l a r i e s of radius r e through a s o l i d substrate of density p, one can derive the same re l a t i o n s h i p geometrically. However, f o r the Poiseulle drag on the permeating l i q u i d i n compressed powder column, the hydrodynamic v a l i d i t y of Eq.7.2.9 f o r r e i n Eq.7.2.2 has never been tested. Once the app l i c a t i o n of Eq.7.2.9 to Eq.7.2.2 for compressed column could be j u s t i f i e d , the t o r t u o s i t y constant K i n Eq.7.2.5 could conveniently be calculated from Eq.7.2.9. In the common ap p l i c a t i o n of the Washburn equation, the t o r t u o s i t y constant K was obtained by c a l i b r a t i o n i n which the same measurement with a l i q u i d that i s known to have zero contact angle i s taken, assuming the pore 154 structure and the penetration process to be the same as i n the runs with d i f f e r e n t l i q u i d s . The measured rate of penetration value and cosO=l inserted into Eq.7.2.4 allow the K to be calculated. 7.2.2 Techniques In actual a p p l i c a t i o n of the Washburn equation to a porous column, a known weight of the dried powder was placed i n a 0.8 cm diameter glass tube with an attached scale, and consolidated by manual tapping. The lower end of the column was supported on a small plug of cotton wool covered with a d i s c of f i l t e r paper. The packed tube containing the powder was dipped into a dish of the l i q u i d and the time and corresponding penetrating height are recorded. This technique has been used with glass powder <Ely and Pepper, 1946>, carbon blacks <Studerbaker and Snow, 1955>, and pigments <Crowl and Wooldridge, 1967>. I t was observed<Good and Lin, 1976> that the rate data i n studies of t h i s kind generally e x h i b i t a serious s t a t i s t i c a l scatter. A major reasons f o r t h i s scatter are the non-uniformity of the column packing density and the change i n structure of the packed bed with wetting<Neumann and Good, 1979>. Another drawback of t h i s technique i s the d i f f i c u l t i e s associated with obtaining the t o r t u o s i t y 155 constant K i n the Washburn equation. In the t r a d i t i o n a l c a l i b r a t i o n method, i t i s d i f f i c u l t to f i n d a p a r t i c u l a r l i q u i d which should have zero contact angle on the s o l i d to be tested. This requirement has made the method only applicable to a l i m i t e d number of s p e c i f i c materials l i k e quartz etc. Since for majority of s o l i d s , i t i s an impossible task to f i n d such a l i q u i d . To overcome above mentioned problems, i n the modification discussed i n t h i s work, the hydraulic mounting press to make more c l o s e l y packed column under accurately c o n t r o l l e d higher pressures was employed. The columns thus made were much more uniform i n i t s i n t e r i o r structure. The r e p r o d u c i b i l i t y and accuracy of the rate of penetration technique was s u b s t a n t i a l l y improved. In addition, the t o r t u o s i t y constant K i n the Washburn equation has been brought under control i n the modified technique, and has been calculated simultaneously with the contact angle. The old c a l i b r a t i o n method was not used any more and the problems associated with i t ceased to e x i s t . The d e t a i l e d discussion w i l l be presented i n the following sections. 156 7.3 EXPERIMENTAL 7.3.1 Materials The materials tested and the i n i t i a l sample preparation procedure f o r the rate of penetration method are the same as that i n the d i r e c t contact angle measurements. The same pulverized coal samples as used i n the d i r e c t contact angle measurements were again u t i l i z e d i n t h i s section. The penetration l i q u i d s used include kerosene and water. The deodorized kerosene used was the product of J.T.Baker Chemical Co., P h i l l i p s b u r g , NJ. The implication to use kerosene as the major penetration l i q u i d i s that, i n addition to i t s lower hazardous degree compared to other chemicals, i t i s extensively used i n the contemporary coal f l o t a t i o n as an e f f e c t i v e and cheap c o l l e c t o r . More importantly, rate of penetration i s a quantitative measure of the c a p a b i l i t y of d i f f e r e n t f r a c t i o n s of coal to be wetted by kerosene. The coal f r a c t i o n s having higher l y o p h i c i t y towards kerosene could be floated better i n the r e a l f l o t a t i o n processes when kerosene i s u t i l i z e d as a c o l l e c t o r . 157 7.3.2 Column-Making A MET-A-TEST mounting press was employed to make the column under high pressures ranging from 3.4 to 20.7 MPa. The column made i n such a way i s strong enough to withstand experimental handling without the holding glass tube; and the packing density can be accurately c o n t r o l l e d and e a s i l y varied. A ser i e s of coal powder samples ranging from 3 to 15 grams were weighed. They were i n d i v i d u a l l y put into the MET-A-TEST mounting press mould which was c a r e f u l l y cleaned with degreased cotton. Following the close of the upper c y l i n d r i c a l cover, the timer was set f o r f i v e minutes, and pumping the hydraulic pressing to pre-set pressure was started. The pressing pressure drops slowly during the pressing period due to the squeezing of p a r t i c l e s to a more c l o s e l y packed configurations. This may need frequent adj ustment. 7.3.3 Rate of Penetration Measurement For each coal sample, a group of four to eight columns with d i f f e r e n t weights ranging from 3 to 12 grams were made under exactly the same conditions so that the columns with d i f f e r e n t heights but the same properties 158 (packing density) were obtained as shown i n Figure 7.3.1. The column diameter was 25.4 mm. Their heights, ranging from 5 to 25 mm, were accurately measured using vernier gauge with p r e c i s i o n of ±0.025 mm. A porous bed made of degreased cotton was prepared and f i t t e d into a small container of 10 mm i n height and 40 mm i n diameter; then the bed was saturated with penetration l i q u i d . The column, a f t e r i t s height was accurately measured with vernier gauge, was v e r t i c a l l y rested gently on the bed; and at the same time, timing was started. A c l e a r l y v i s i b l e h o r izontal penetration l i n e along the c y l i n d r i c a l wall heading upward can be observed. No a d d i t i o n a l strong i l l u m i n a t i o n was required. The l i q u i d would flow slowly through the column and eventually reach the top. The end of timing was selected when h a l f of the top surface area was wetted. For each column, one data point, that i s , the column height versus the time required for l i q u i d to flow through the whole column was recorded. The same procedure was repeated f o r other columns. F i n a l l y a number of data points equal to the number of columns were acquired. I t should be emphasized that these columns, though having d i f f e r e n t heights, must be made under exactly the same conditions ( i . e . same pressure). For each data point, a s t r a i g h t l i n e connecting t h i s point and o r i g i n a l of H2 159 F i g u r e 7.3.1 The columns made f o r the r a t e o f p e n e t r a t i o n t e s t 160 versus T coordinate could be drawn. Therefore each measurement i n comparison to the conventional method could be considered as an i n d i v i d u a l l y repeated run because the l i n e s thus obtained were for d i f f e r e n t columns. A f t e r these points were regressed, the l i n e a r i t y of the regressed l i n e could be considered a representation of the r e p r o d u c i b i l i t y f o r the experiment. Columns must be made at a minimum of two d i f f e r e n t pressures because the rate of penetration from the columns made under d i f f e r e n t pressures were e s s e n t i a l parts of t h i s technique i n the c a l c u l a t i o n of contact angles. 7.3.4 V i s c o s i t y and Surface Tension The Ostwald viscometer was used to measure the v i s c o s i t y of l i q u i d . According to the time of flow of a given volume V of the l i q u i d through a v e r t i c a l c a p i l l a r y tube under the influence of gravity, the v i s c o s i t y was calculated by Poiseulle's law i n the form dV T r « ( P i - P 2 ) = 7.3.1 dt 8/iL where dV/dt i s the rate of l i q u i d flow through a c y l i n d r i c a l tube of radius r and length L and (P1-P2) i s the difference 161 i n pressure between the two ends of the tube. In practice, above equation, at constant temperature, i s s i m p l i f i e d f o r a given t o t a l volume of l i q u i d and a given c y l i n d r i c a l tube fi/p = Bt 7.3.2 where t i s the time required for the upper meniscus to f a l l from the upper to the lower f i d u c i a l mark and B i s an apparatus constant which i s determined through c a l i b r a t i o n with a l i q u i d of known v i s c o s i t y (e.g. water). The l i q u i d surface tension was measured using a Cenco-du Nouy Tensiometer. 162 CHAPTER 8 RESULTS AND DISCUSSIONS <II> 8.1 APPLICABILITY TEST The conventional method of making a penetration column i s by manually tapping the tested powder held i n a glass tube into a column<Crowl and Wooldridge, 1967, Szekely et a l . , 1971, B r u i l and van Aartsen, 1973, Good and Lin, 1976>. Very low pressures (below 3.5 MPa) were exerted on the powdered material within the holding glass tube during tapping. Whether the Washburn equation i s s t i l l applicable to the columns made under very high pressures up to 27.6 MPa has not been tested. In t h i s section, the a p p l i c a b i l i t y of the Washburn equation has been f i r s t v e r i f i e d . 8.1.1 Some Features Some preliminary observations were made to examine the features and behaviour of the l i q u i d penetrating into columns compacted under high pressure. Because the columns i n the penetration process were unwrapped, the penetrating l i n e s were c l e a r l y observable. The periphery of the 163 penetrating front surface was apparently within a well defined horizontal plane. The penetration i n the i n t e r i o r of the columns was also examined. Since the column diameter i s 25.4 mm and i s much greater than diameter of a conventional one (8 mm), the crosswise penetration difference could be more perceptibly manifested. Observing from the top surface of the column, one could f i n d that the wetting front surface, a f t e r c e r t a i n time of penetration, would not reach the top surface of the column a l l over at the same time; instead, i t emerges i n a l o c a l area f i r s t and quickly spreads. This implies a non-f l a t penetration front surface. Sometimes the wetting front surface emerges from the central area and spreads outward co n c e n t r i c a l l y which indicates a dome shaped wetting front within the column; on the other hand the wetting front was also observed to emerge pe r i p h e r a l l y and spread inward. Occasionally, the wetting front may s t a r t from one side of the top surface of the column and fi n i s h e d at another, which means a t i l t e d wetting front. The magnitude of the l a t i t u d e differences between the highest point and the lowest one on the penetration front surface i s not only a matter of probing the uniformity of the column i n t e r i o r penetration behaviour, but also a numerical index i n d i c a t i n g the p r e c i s i o n of the method. These d e t a i l s w i l l be discussed i n the next section. 164 Other features concerning the method are: the possible swelling of the columns a f t e r soaking with penetrating l i q u i d ; the lowest applicable pressure; and possible breakage of p a r t i c l e s i n the pressing process. A l l these variables were tested and w i l l be discussed i n the following sections. One of the advantages of t h i s technique i s that the t o t a l surface area penetrated by l i q u i d within a u n i t height of column i s much greater than that i n a conventional method. Therefore i t i s more s t a t i s t i c a l l y representative. In addition, the t o t a l height can be lowered to a range of 0.5 to 2 cm compared with the conventional range of 4 to 10 cm. Thus the penetration process could be subject, to a much less extent, to the e f f e c t of g r a v i t a t i o n a l force. 8.1.2 Precisio n and L i n e a r i t y Since i t i s more d i f f i c u l t to measure accurately penetration distances on short columns, a d i f f e r e n t approach as described i n section 7.3 was employed. The use of a vernier could reach absolute accuracy of ±0.0025 cm which i s undoubtedly quite s u f f i c i e n t . However, another aspect which a f f e c t s the accuracy i s the estimation of ending time point which was taken when 165 h a l f of the top surface area of the column was wetted. I f the l i q u i d wetting front zigzagged up and seriously, not only the judgement of the ending time of penetration but also the method i t s e l f i s questionable. In order to answer these questions, the time when the wetting front s t a r t s to emerge from the top surface, and the time when the whole top surface was wetted, were measured. From the time span, the ruggedness ( i . e . the maximum a l t i t u d e difference between the lowest and the highest point) of the imaginary penetration front surface could be calculated. The experiment was conducted on the 1.4-1.5 density f r a c t i o n of the Bullmoose coal. Five columns with d i f f e r e n t heights were made i n series and kerosene was used i n the experiment. T 0 i s the time a f t e r which the penetrating front emerges; and T x i s the time f o r the whole top surface of the column to be wetted. The penetration distance from time T 0 to T1 would be the a l t i t u d e difference between the highest point and lowest point on the penetration front surface. The magnitude of t h i s distance i s a numerical representation of the ruggedness of the penetration front surface. The middle point between T 0 and T x , i n the actual measurement, was taken as the ending point of penetration, T. The T values and corresponding column heights Were 166 tabulated (Table 8.1.1). The H2 versus T regression r e s u l t was shown i n the lower part of the table. According to t h i s regression equation, the penetration distance between time T 0 to T x could be calculated. Here H2 = 0.625T so Ruggedness = H(T X) - H(T 0) 8.1.1 = 7(0.625-1! ) - J (0.625-T0 ) The ruggedness i s defined as the maximum a l t i t u d e difference on the penetration front surfaces. The ruggedness r e s u l t s shown i n Table 8.1.1, are i n the range from 0.18 to 0.6 mm. This indicates that the penetration front surfaces are quite f l a t considering the very large penetration front area with diameter of 25.4 mm. Since i n the r e a l observation, the reading was taken when one h a l f of the t o t a l penetration front surface emerged, the observation error of the penetration front was l i m i t e d to a h a l f of the ruggedness, that i s , 0.09 to 0.3 mm. This i s a quite high accuracy which may hardly be attained by the conventional graduation method. In addition the graduation method only the peripheral penetration l i n e can be observed while the i n t e r i o r penetration behaviour i s ignored. The a p p l i c a b i l i t y of the Washburn equation to t h i s 167 Table 8.1.1 Test for the ruggedness of penetration front on 1.4 - 1.5 density f r a c t i o n P - 13.8 MPa Measured data Calculated r e e s u l t s H HxH TO T l T1-T0 HO HI HI-HO mm sec sec mm mm 0.00 0 0 0 0 0. ,00 0. .00 0.00 6.63 43.96 73 77 4 6. ,76 6. .94 0.18 7.30 53.29 93 100 7 7. .63 7. .91 0.28 16.70 278.89 454 464 10 16. ,85 17, .03 0.18 23.66 559.79 871 901 30 23. .34 23, .73 0.40 34.61 1197.85 1882 1955 73 34, .30 34 .96 .0.66 * H i n mm i s the l i q u i d penetration height ** TO i n second i s the time when penetration front emerge from the top surface of the column *** T l i s the time when the whole penetration front emerges out Regression Output Constant Std dvtn of HxH Est R Squared No of Observation Degrees of Freedom T Co e f f i c i e n t Std dvtn of Coef. HxH = 0.625 T 0 4.171126 0.999918 6 5 0.625173 0.001927 168 method can be simply tested by observing l i n e a r i t y and r e p r o d u c i b i l i t y of H versus T curves and by observing whether d i f f e r e n t w e t t a b i l i t y materials have d i f f e r e n t penetration l i n e s . A s e r i e s of experiments has been conducted on d i f f e r e n t density f r a c t i o n s of the Bullmoose coal to t e s t the l i n e a r i t y of the rate of penetration curves, under constant column-making pressure of 6.9 to 20.7 MPa. The penetration data f o r a l l s i x density f r a c t i o n s were plotted i n Figures 8.2.1 to 8.2.3. E s s e n t i a l l y a l l the l i n e s pass through the o r i g i n . The l i n e a r i t y of the penetration curves, which i s numerically represented by the R squared value (0 < R < 1), and other regression r e s u l t s are presented i n Tables 8.2.1 to 8.2.4. As can be seen, a l l s i x R squared values for the regression l i n e s are close to uni t value i l l u s t r a t i n g very good l i n e a r i t y . In terms of r e p r o d u c i b i l i t y , i t should be emphasized that the data a c q u i s i t i o n procedure i n the present method i s quite d i f f e r e n t from that of the conventional one. In the conventional method, a l l the experimental points on a penetration curve were obtained from one column by taking the reading of penetration length at d i f f e r e n t times. Accordingly, the experimental r e p r o d u c i b i l i t y was tested by examining deviation of the penetration curves obtained from d i f f e r e n t columns. 169 In the present method, only one point was obtained on a column. To draw a penetration l i n e including 5 data points on i t , an equal number of columns with d i f f e r e n t heights are needed to carry out f i v e separate penetration t e s t s . Each data point could be considered independently as a repeated run. Therefore, the l i n e a r i t y denoted by R squared and standard deviation, at the same time, were also the measures of the experimental r e p r o d u c i b i l i t y . Judging from both the R squared value and the standard deviation of the c o e f f i c i e n t s , i t can be confirmed that the Washburn equation i s well applicable to the columns made under very high pressures. 8.1.3 Height Limit As the column reaches c e r t a i n height, the H 2 plotted versus T begins to deviate from l i n e a r i t y ; t h i s i s es p e c i a l l y true f o r columns made under lower pressures (see Figure 8.1.1). Several factors may a t t r i b u t e to t h i s phenomenon. The g r a v i t a t i o n a l force could be one of them. By r e c a l l i n g the general rate of c a p i l l a r y penetration equation 7.2.3 r 2 27 l v«cos0 d(h 2)/dt = — ( Apgh) 7.2.3 Ay, r 170 APPLICABILITY TEST OF WASHBURN EQUATION Figure 8.1.1 PRESSURE 17.2 MPa,+1.8 FRACT'N BM COAL 600 -i — 0 20 40 60 80 100 Penetration time (second) • Squared height one can notice that, i n the actual a p p l i c a t i o n of the Washburn equation to the packed column, the term Apgh was neglected under the condition that penetration height, h, was small. Once h i s large, the term Apgh i s comparable i n magnitude with the f i r s t term i n the parenthesis i n the above equation and H 2 versus T curve can lose l i n e a r i t y and l e v e l o f f . I t was observed that the columns packed under lower pressures had lower height l i m i t s than the columns packed under higher pressures. This could be due to the influence of the column packing pressure on c a p i l l a r y diameters d i s t r i b u t i o n inside the column. As the pressure increases, the c a p i l l a r y r a d i i , r's, i n column become smaller, while the f i r s t term 27 l v«cos0/r i n the parenthesis of Eq.7.2.3 becomes greater r e l a t i v e to the second term Apgh. Therefore the column height l i m i t r a i s e s up when pressure i s increased. The f r i c t i o n between the mould of a MET-A-TEST press and the column within i t i n the column-making process could be another a f f e c t i n g factor of column height l i m i t . The f r i c t i o n , when the column i s high enough, could considerably a l t e r the packing densities at d i f f e r e n t parts of the column and, as a consequence, change the penetration behaviour and make the rate of penetration l i n e to be non-linear. The influence of the f r i c t i o n w i l l be further discussed i n section 8.5. 172 8.2 COLUMN-MAKING PRESSURE I t was claimed<Good and Lin, 1976, Neumann and Good, 1979> that the column-making pressure had no perceptible e f f e c t on the penetration rate. This conclusion was obtained from the columns which were packed by manual tapping. However, i t may not be true i n the case of a machine-compressed column. The column-making pressure should have a pronounced e f f e c t on both the rate of penetration of l i q u i d into the columns and the measurement accuracy, and r e p r o d u c i b i l i t y . The r a t i o n a l i t y behind t h i s i s that a change i n column-making pressure could change the porosity (or the equivalent c a p i l l a r y diameter) within the column, and consequently, as shown i n Eqs.7.2.4 and 7.2.5, a l t e r the rate of penetration. Under higher pressure, the column could 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 higher. 8.2.1 The E f f e c t of Pressure on Reproducibility and Li n e a r i t y In order to study the e f f e c t of column-making pressures on the experiment 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 , several se r i e s of columns from d i f f e r e n t coal density f r a c t i o n s were compressed under various pressures and were 173 penetration height (mm) squared o o O O o o o o o o ON O O O O 7 OS II to » 8 ^ x II o o o 3 o. o o 4i. T3 II bo ON o o O • > + + X X oo o o 174 700 600 500 400 300 200 100 H Rate of penetra. curves for columns of Figure 8.2.2 1.3-1.4 made under dif. pressures • P=6.9 MPa Time in second + p=13.8 O p=20.7 800 Rate of penetra. curves for columns Figure 8.2.3 of 1.4-1.5 made under dif. pressures T 0 0.2 0.4 0.6 0.8 (Thousands) Time in second P=6.9MPa + P=13.79 O P=20.7 -a 3 cr a s. '3 J3 C O .—1 C3 s 700 600 500 400 300 200 100 H Rate of penetra. curves for columns of F i g u r e 8 . 2 . 4 1.5-1.6 made under different pressures 0.6 0.8 (Thousands) Time in second 1.4 • P=6.9 MPa + P=13.8 O P=20.7 T3 p 3 a S. 50 'o .C a is o a o a. 600 500 400 H 300 H 200 H 100 Rate of penetra. curves for columns of F i g u r e 8.2.5 1.6-1.8 made under different pressures 0.2 p=6.9 MPa 0.4 1—; 1 T 0.6 0.8 (Thousands) Time in second + p=13.8 00 O p=20.7 Rate of penetra. curves for columns of Figure 8 .2 .6 +1-8 made under different pressures • p=6.9 MPa A p=17.2 0.6 (Thousands) Time in second + p=10.3 X p=20.7 O p=l3.8 tested separately. Figures 8.2.1 to 8.2.6 are the r e s u l t s i n a graphical form. Clearly, for each density f r a c t i o n and under a constant pressure, a corresponding s t r a i g h t l i n e was obtained. However, i f the column making-pressure was changed for the same sample, the rate of penetration l i n e would have d i f f e r e n t slopes. A group of penetration l i n e s with d i f f e r e n t slopes can be obtained i f one increases the column-making pressure gradually. The higher i s the column-making pressure, the slower i s the rate of penetration (smaller slope value of H 2 versus T l i n e ) . Figures 8.2.7 to 8.2.9 were re-plotted from Figures 8.2.1 to 8.2.6 placing a l l the rate of penetration l i n e s for s i x density f r a c t i o n s together i n one graph. Tables 8.2.1 to 8.2.3 give the regression r e s u l t s for these data. The experimental r e p r o d u c i b i l i t y and accuracy are evaluated from R squared and standard deviation of these c o e f f i c i e n t s . They are given i n Table 8.2.4. By examining the table, one can f i n d a general tendency that both the standard error of H 2 (or Y) and the standard deviation decrease as the pressure increases f o r a l l the s i x density f r a c t i o n s . The R squared values f o r a l l s i x density f r a c t i o n s increase toward unit value with the increase i n pressure. A l l t h i s suggests the p o s i t i v e e f f e c t of higher column-making pressures. 180 penetration height (mm) squared o o O o o o o o o o ON o o - J o o oo o o ON x> o + > X X r-4^  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/3 182 700 Rate of Penetra. for Diff. SG Fractions Figure 8.2.9 columns made under 20.7 MPa 600 H 500 H 400 300 H 200 100 H + A + o X a p * A x A x + A v i 1 1 1 1 1 1 1 1 r o A X 0 0.2 0.4 0.6 0.8 1 1.2 1.4 (Thousands) Time in second • -1.3 + 1.3-1.4 O 1.4-1.5 A 1.5-1.6 X 1.6-1.8 V +1.8 T a b l e 8.2.1 STATISTIC ANALYSIS OF PENETRATION DATA For BM coal , Pressure i s 6.9 MPa Density Regression Equation Std dvtn of Std dvtn of R Fra c t i o n Y estimate slope values Squared -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 +1.8 Y - -3.64 + 0.306 X 5.92 0.009 0.997 * Std dvtn - Standard deviation ** The unit of density i n this table and following tables i s gram per cubic centimeter Table. 8.2.2 STATISTIC ANALYSIS OF PENETRATION DATA for BM coal, pressure i s 13.8 MPa density Std dvtn of Std dvtn of f r a c t i o n Regression Equation Y estimate slope values -1.3 Y = -4.98 + 0.945 X 6.54 ' 0.016 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 0.02 +1.8 Y - 5.62 + 0.195 X 6.69 0.008 Table 8.2.3 STATISTIC ANALYSIS OF PENETRATION DATA For BM coal, Pressure i s 20.7 MPa density Std dvtn of Std dvtn of R f r a c t i o n Regresion Equation Y estimate slope values Squared -1.3 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 +1.8 Y - 0.250 + 0.163 X 0.29 0.0003 1.0000 Table 8.2.4 The e f f e c t of column-making pressure on accuracy and l i n e a r i t y of the rate of penetration l i n e density f r a c t i o n Std dvtn of Y estimate P-6.9 MPa 13.8 20.7 Std dvtn of slope values P-6.9 MPa 13.8 20.7 0.0590 0.0160 0.0130 0.0120 0.0090 0.0076 0.0250 0.0200 0.0015 0.0310 0.0076 0.0053 0.0049 0.0200 0.0025 0.0090 0.0080 0.0003 R squared P-6.9 MPa 13.8 20.7 -1.3 1.3- 1.4 1.4- 1.5 1.5- 1.6 1.6- 1.8 +1.8 20.61 7.45 21.81 22.45 3.52 5.92 6.54 5.88 17.78 7.75 18.61 6.69 7.58 5.47 4.49 6.15 2.55 0.29 0.9930 0.9995 0.9970 0.9896 0.9998 0.9970 0.9992 0.9996 0.9997 0.9993 0.9998 1.0000 The low pressure of 3.5 MPa, which i s comparable with manual packing, was also tested. Under t h i s low pressure, the experimental data are s i g n i f i c a n t l y scattered. This might be the reason why Good and L i n <1976> and Neumann and Good<1979> concluded that the rate of penetration data i n the studies generally exhibit a serious s t a t i s t i c a l scatter. They have att r i b u t e d t h i s scatter to the change i n structure of the packed column with wetting. This could be part of the reason. Another reason, as implied by t h i s study, might be the inconsistency i n structure of packed column i t s e l f . E s p e c i a l l y under lower pressure the p a r t i c l e s do not orient themselves properly for the best packing density and t h e i r i r r e g u l a r configuration would trap large amount of i r r e g u l a r a i r pockets within the column. These configurations can s i g n i f i c a n t l y vary from one to another. Therefore the rate of penetration can be d i f f e r e n t i n various parts of the column. When high pressure was applied, these air-trapped configurations collapse and p a r t i c l e s re-orient themselves to form better packed configurations which tend to be more uniform. By checking the published l i t e r a t u r e , one may f i n d that the penetration l i n e s f or the same material from the repeated runs d i d not observe the same slope even though an in d i v i d u a l l i n e , which was measured from a single column, had a very good l i n e a r i t y <Crowl and Wooldridge, 1967>. The 188 poor r e p r o d u c i b i l i t y , according to the above analysis, i s l i k e l y to be due to the i n a b i l i t y of manual tapping to produce the columns with reproducible i n t e r i o r configurations. The column-packing pressure i s , therefore, an exceptionally important factor. I t should be high enough and kept constant to a t t a i n high r e p r o d u c i b i l i t y of the experiments. 8.2.2 E f f e c t on Rate of Penetration The column-making pressure can not only change the experimental accuracy and r e p r o d u c i b i l i t y , as delineated above, but also a l t e r the rate of penetration. As shown i n Figures 8.2.1 to 8.2.6, the increase i n pressure can rotate H 2 versus T l i n e around the o r i g i n of coordinate to the p o s i t i o n with smaller slope value. The question which w i l l be answered i s what i s the general r e l a t i o n s h i p between the slope, S, and pressure, P, and what i t stands f o r . The influence of pressure on the rate of penetration was studied by t e s t i n g the columns made under various pressures. The slope value, S, f o r each penetration l i n e was calcula t e d by s t a t i s t i c a l regression of the penetration l i n e and was plotted versus pressure i n Figure 8.2.10. Obviously the e f f e c t of pressure on the rate of penetration i s sub s t a n t i a l . According to the Washburn equation 7.2.5 189 4) 3 -a > o .—I CO The effect of column-making pressure on Figure 8 .2 .10 SLOPE of the rate of penetr. curve -1.3 1.5-1.6 Pressure in MPa + 1.3-1.4 O 1.4-1.5 X 1.6-1.8 V +1.8 o cr> d(H 2)/dt = K - 7 C O S c 5 / 2 / i 7.2.5 The slope of penetration l i n e should be S - K - 7 - C O S C ? / 2 M 8.2.1 A general tendency i n Figure 8.2.10 i s that the slope values, S's, for a l l the s i x density f r a c t i o n s are decreasing with increasing pressure. The band of the l i n e s at lower pressure i s wider and becomes narrower as the pressure increases. In Eq.8.2.1, 6 i s what we intend to determine; 7 and n are the penetration l i q u i d properties and are known from accurate measurements; S could be obtained through the regression of measured data. I f t o r t u o s i t y constant K were known, 6 value could be r e a d i l y calculated. Unfortunately K i s unknown. In the experimental process for t e s t i n g the e f f e c t of pressure on rate of penetration, 7 and M were considered unchanged fo r the same l i q u i d . And e was also presumably regarded unchanged for the same l i q u i d - s o l i d system to be tested i f the pressure i s not high enough to change the s o l i d surface properties (this w i l l be discussed i n section 8.2.3). Therefore according to Eq.8.2.1, the change i n the 191 slope value, S, versus pressure, P, was only associated with the change i n t o r t u o s i t y constant, K. That i s , the pressure was only influencing the l i q u i d penetration through changing the column t o r t u o s i t y constant, K. The t o r t u o s i t y constant K, which i s an equivalent of c a p i l l a r y radius r, i s only a physical property of the columns. I t i s , l i k e c a p i l l a r y radius r, independent of surface w e t t a b i l i t i e s and i s only determined by material p a r t i c l e s i z e d i s t r i b u t i o n , packing density, etc.. That i s to say, i f two columns are of 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 and same packing density, they should have the same t o r t u o s i t y constant K, even though these two material have quite d i f f e r e n t surface properties. Based on t h i s useful conclusion, i t i s possible to procure the t o r t u o s i t y constant value without the reference to the c a l i b r a t i o n l i q u i d . There i s s t i l l no way to f i n d out d i r e c t l y the value of the 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 considerations do provide some clue how to calc u l a t e the K value. A new approach using above idea w i l l be presented i n section 8.5.2 which i s e n t i r e l y devoted e n t i r e l y to the c a l c u l a t i o n of K values under various column-making pressures and the contact angle values f o r d i f f e r e n t density f r a c t i o n s of coal. 192 8.2.3 Side E f f e c t of High Pressure The a p p l i c a t i o n of higher column-making pressures may-present many advantages i n the rate of penetration t e s t s as i l l u s t r a t e d above. Nevertheless, a major concern with the high pressure i s that i t may cause crushing of coal p a r t i c l e s to f i n e r sizes and then possibly a l t e r the coal surface properties. The p o s s i b i l i t y of crushing of the coal i n the column-making process can be detected i n several ways. One possible way i s through p a r t i c l e s i z e d i s t r i b u t i o n analysis before and a f t e r the column-making process. I f any crushing action has occurred, the p a r t i c l e s i z e d i s t r i b u t i o n within the column a f t e r re-dispersion would indicate higher y i e l d s of f i n e s i z e s than p r i o r to the column preparation. The possible 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 the occurrence of the crushing action. The p a r t i c l e s i z e analysis r e s u l t s showed that no apparent s h i f t i n s i z e d i s t r i b u t i o n has occurred. Another way to detect the possible crushing action was to examine d i r e c t l y the p e l l e t surface using Scanning Electron Microscope (SEM) under very high magnification. The surfaces of columns made under 27.6 MPa were photographed (Figures 6.8.2). The picture magnified 3000 193 times i n Figure 6.8.2, c l e a r l y shows that no obvious crushing action has ocurred on the p e l l e t surface. Otherwise, groups of small p a r t i c l e s produced from the breakage of larger p a r t i c l e s can be seen p i l e d up at some random spots. The column-making pressure usually used i n the present work ranged from 6.9 to 20.7 MPa. I t i s f a r below 27.6 MPa as used i n the above t e s t . The possible crushing action within a column should be excluded. 8.2.4 Lower Limit of Pressure The lower l i m i t of column-making pressures was also tested i n order to f i n d the lowest pressure f e a s i b l e for t h i s technique. However, the t e s t s show that there was no clear-cut value. As the pressure was reduced to 3.5 MPa, which i s comparable with manual tapping, the column was f r a g i l e and needed to be handled with care. When pressure was further decreased down to 2.8 MPa, the column could hardly hold and loosened instantaneously a f t e r released from the mould. In the present work, the column-making pressure, therefore, was chosen i n the range from 6.9 to 20.7 MPa. Pressures down to 3.5 and up to 34.5 MPa were also employed 194 i n these experiments i n order to study i t s influence on the column properties and on the rate of penetration. 195 8.3 PHYSICAL PROPERTIES OF COLUMNS The columns compacted under high pressures exhibited many d i s t i n c t properties. The study of these properties may be an integrate part of t h i s technique. Some of these observations may be used i n l a t e r sections to int e r p r e t the r e s u l t s and evaluate the assumptions. 8.3.1 Column Height versus Pressure The column height i s one of the most important parameters i n the rate of penetration t e s t s . However i t s value was ine v i t a b l y influenced by the column compressing pressure. For the same amount of material, the column height i s smaller under higher pressure. In order to examine the general c o r r e l a t i o n between column height and pressure, columns of constant weight were pressed under d i f f e r e n t pressures. Results are shown i n Figure 8.3.1. As the pressure increases the column height decreases, but non-linearly. At lower pressures, an increase i n pressure can reduce the column height more s u b s t a n t i a l l y . As the pressure increases, the influence of pressure on column height diminishes. 196 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 I t i s worthy of mention that the column height measured at lower compacting pressure i s more l i k e l y to be scattered because a small random error or disturbance would have larger e f f e c t on the i n t e r i o r structure of the column at lower pressure (than at higher pressure). This i s one of the reasons why high compressing pressure was preferred for the sake of p r e c i s i o n . As the column-packing pressure reaches a high l e v e l (27.6 MPa), a further increase i n pressure has l i t t l e e f f e c t on the column height. The t a i l part of the curve i n Figure 8.3.1 therefore tends to l e v e l o f f . Working i n t h i s area may possibly have some advantages of being independent of the e f f e c t of compressing pressure. Nevertheless, the p o s s i b i l i t y of changing coal surface properties by destruction becomes more l i k e l y for higher pressures and p r o h i b i t s the use of very high pressure. 8.3.2 Column Height versus Weight In order to guaranty a constant column packing density, some researchers have packed a constant weight of material into a glass tube; and always kept the column height constant. However t h i s p ractice could not r e a d i l y be applied to coal because of the density v a r i a t i o n among d i f f e r e n t coal density f r a c t i o n s . In t h i s work, a constant 198 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 density was secured by applying a constant column-making pressure. Under a constant pressure, a number of columns with d i f f e r e n t weights were made and t h e i r weight accurately measured. As shown i n Figure 8.3.2, an acceptable l i n e a r r e l a t i o n s h i p between column height and i t s weight was observed. However, further increase i n column weight only makes i t s height out of proportion and higher than predicted. I t was i n i t i a l l y perceived that the height of the column made under constant pressure should be always proportional to the column weight. However i n the r e a l column-making process i t was not true, because of the existence of the f r i c t i o n forces between the c y l i n d r i c a l wall of the holding mould and the column within i t . The f r i c t i o n forces, which w i l l be discussed i n d e t a i l i n the next section, produce a gradient decrease of the pressure through the column and, as a r e s u l t , may y i e l d a non-linear column height versus weight r e l a t i o n s h i p . 8.3.3 Column Porosity Although the column-making process i s exactly the same as the pellet-making process, the column exhibits quite 200 d i f f e r e n t properties because of the substantial difference between t h e i r heights. F i r s t l y , the column porosity i s not uniform. I t changes along i t s perpendicular axis. Secondly, under the same column-making pressure, the columns with d i f f e r e n t heights are characterized by d i f f e r e n t average p o r o s i t i e s . Detailed discussion w i l l be given i n section 8.4. 8.3.4 Column Expansion The s i g n i f i c a n c e of column expansion a f t e r the l i q u i d penetration process was tested. The substantial expansion of the column during penetration a f f e c t s the measurement of column height and column porosity. In Table 8.3.1, H0 i s the o r i g i n a l column height; Hx i s the column height a f t e r penetrated by l i q u i d ; dH i s the increase i n height. The r e l a t i v e column expansion i n height i s presented i n the l a s t column of the table. The columns made from the -1.3 f r a c t i o n of the Bullmoose coal at d i f f e r e n t pressures were tested. The r e s u l t s show that the columns made under higher pressures experienced greater expansion than did the columns made under lower pressure. However, the largest average r e l a t i v e expansion was only 0.71 percent and could be neglected. 201 Swell of columns after penetrated by l i q u i d Pressure HO HI dH % Average MPa mm mm mm 24.55 24. .65 0. .10 0. ,41% 19.60 19. .70 0. .10 0. ,51% 17.15 17. .35 0. .20 1. .17% P-6. .9 13.00 13. .00 0. .00 0. ,00% 12.80 12. .90 0. ,10 0. .78% 8.65 8. .65 0. .00 0. .00% 6.75 6. .75 0. .00 0. .00% 0. .41% 24.60 " 24. 80 0. .20 0. ,81% 20.20 20. .40 0. .20 0. .99% 18.10 18. .20 0. .10 0. .55% P=13. .8 15.85 15. .95 0. .10 0. .63% 12.00 12. .10 0. .10 0. .83% 8.25 8. .25 0. .00 0. .00% 6.30 6. .30 0. .00 0. .00% 0. .55% 24.00 24. .30 0. .30 1. .25% 19.75 19. .80 0. .05 0, .25% 17.60 17. .90 0. .30 1. .70% 15.40 15. .50 0. .10 0, .65% P=20. .7 12.30 12. .35 0. .05 0, .41% 11.50 11. .50 0. .00 0, .00% 8.85 8. .85 0. .00 0 .00% 7.00 7. .10 0. .10 1. .43% 0, .71% HO i s the o r i g i n a l column hight i n mm HI i s the column height (mm) a f t e r penetrated by kerosene dH i s the increase i n column height (mm) 202 8.4 The E f f e c t of F r i c t i o n When the pressure exerted on the column i s high, the force exerted by column on the c y l i n d r i c a l wall of the mould i s also s i g n i f i c a n t i n the column-making process. The f r i c t i o n force between cylinder wall of the mould and the column of p a r t i c l e s can not be neglected. This f r i c t i o n force prevents the propagation of pressure throughout the column, generates a pressure gradient throughout the column, and consequently influences the consistency of column's packing density. The packing density inconsistency could even be v i s u a l l y observed through the change i n colour and brightness i n the column's axis d i r e c t i o n . As demonstrated before, the column-making pressure had a strong influence on the rate of penetration. The existence of pressure gradient may a l t e r the rate of penetration behaviour within a column. The most d i r e c t manifestation of t h i s phenomenon was observed when columns were put upside down and used i n the penetration t e s t s . Two sets of columns from the same material were compacted under a constant pressure. The penetration experiments were c a r r i e d on i n two d i f f e r e n t manners: one set of columns were penetrated i n a normal way; but i n another set, the columns were placed upside down. The r e s u l t s (Figure 8.4.1) show that two penetration l i n e s with d i f f e r e n t slopes were obtained. 203 130 Change in Rate of Penetration Behavior Figure 8.4^1 when columns placed upside down 120 H 110 100 90 H 80 70 60 H 50 40 o as usual penetration time in second + upside down Suppose that i n Figure 8.4.2 the f r i c t i o n c o e f f i c i e n t i s f, the circumference of the column i s c (7.98 cm i n present work), the pressure at any point within the column i s p, a d i f f e r e n t i a l equation can be derived dp = -p«c»f«dx 8.4.2 A f t e r integrating above equation from x=0 to h, we can get p h [lnp] = [-cfx] Po 0 p = Po»exp(-cfh) 8.4.3 where Po i s the pressure exerted on the column's bottom ( i t i s kept constant i n column-making process). According to the above equation, the pressure decreases from column's bottom, to the column's top surface exponentially. I t has been known that the porosity of a column l i n e a r l y decreases with column-packing pressure l i n e a r l y i n a r e l a t i v e l y narrow range of pressures. That i s q = Q - k«p 8.4.4 where q i s the column porosity, Q i s intercept at q axis and p the pressure exerted on column. By s u b s t i t u t i n g Eq.8.4.3 into Eq.8.4.4, one can get 205 X — D 1 I If 1 ! — P dx \ p 0 P 0 Figure 8.4.2 The forces acting on the column within the mould P0 i s the pressure (MPa) exerted on the column bottom by the hydraulic press, p i s the pressure (MPa) at a point within the column, f i s the f r i c t i o n c o e f f i c i e n t . 206 q = Q - kPo • exp(-cfh) 8.4.5 where q i s a d i f f e r e n t i a l porosity of a very t h i n layer within the column at h. Apparently the porosity within a column i s increasing i n x-axis d i r e c t i o n toward the top of the column i n a pattern given by Eq.8.4.5. The increase i n porosity along column's X-axis suggests an increase i n equivalent c a p i l l a r y radius i n the same d i r e c t i o n . V a r i a t i o n of the equivalent c a p i l l a r y radius within a column can influence the rate of penetration. There are many ways to t e s t the porosity gradient along X-axis. The most d i r e c t way i s to chop up some t h i n layers from a column and to measure t h e i r porosity. In prac t i c e , however, i t i s d i f f i c u l t to cut such t h i n layers from a column and to measure i t s q value experimentally. An i n d i r e c t method was employed here. The basic idea i s that i f a number of columns with d i f f e r e n t height were compacted under the same pressure i n the absence of the f r i c t i o n force, the porosity for a l l the columns should be equal. When a porosity gradient i s produced within the column i n the presence of f r i c t i o n force, the average p o r o s i t i e s f o r columns with d i f f e r e n t heights should vary. By integ r a t i n g Eq.8.4.5 from the bottom to the top of the column, one can get the average (or integral) porosity of 207 the whole column Qa = h q.dx/(h-0) 8.4.6 0 Q a = Q <1 - exp(-cfh)> 8.4.7 c-f-h where Q a i s the average porosity of the whole column, h i s the column height, P i s column-making pressure, and c, f, k, and Q are constants. As indicated by Eq.8.4.7, the average porosity, Q a , of a column made under constant pressure P changes with column height h. This can be r e a d i l y tested. The general shape of Eq.8.4.7 was f i r s t examined. Q a was p l o t t e d against h by assigning some a r b i t r a r y values to the constants i n the equation. In Figure 8.4.3, two curves were obtained by assigning two sets of d i f f e r e n t values to 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 figure c l e a r l y shows that among the columns made under constant pressure P , the average porosity f o r the t a l l e r column w i l l be larger than that f o r the shorter one. To t e s t t h i s , a set of columns with various weights were compacted under a constant pressure. Their p o r o s i t i e s were measured and plo t t e d versus t h e i r height i n Figures 8.4.4 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 predicted and the a c t u a l l y measured porosity versus column height curves reveals the existence of the f r i c t i o n e f f e c t . 208 B f=0.2 Column Height cm + {=0.1 The effect of column height on integral F i g u r e 8 . 4 . 4 porosity avged on four pressure points 31 H 7 9 11 13 15 Column height mm ^ Porosity H Integral Porosity I t could thus be concluded that the porosity of a compressed column i s not uniform and that there e x i s t s a porosity gradient within i t ; the porosity increases exponentially, according to Eq.8.4.5, from bottom to top of a column. Because an increase of porosity means an increase of t o r t u o s i t y constant K i n Eq.7.2.5, the rate of penetration, d(h 2)/dt, should exhibit an increase as the penetration front moves upward. I t i s to be noticed that g r a v i t a t i o n a l force on the other hand can o f f s e t t h i s porosity e f f e c t (see Eq.7.2.3). As the penetration front surface moves upward, the term Apgh increases l i n e a r l y and, on the contrary to K, tends to drag the penetration front back. This phenomenon indicates that the height l i m i t f o r a column made under high pressure i s greater than that f o r a column made by manual tapping. 212 8.5 CONTACT ANGLE CALCULATIONS 8.5.1 Introduction As noted previously, the contact angle c a l c u l a t i o n from the experimental data necessitated the column c a l i b r a t i o n . The requirement f o r c a l i b r a t i o n r e s u l t s from the f a c t that the t o r t u o s i t y constant, K, i n the Washburn Eq.7.2.5 i s unknown and can not be attained by d i r e c t measurement, or c a l c u l a t i o n . Without knowing the K value, the contact angle, e, can not be determined. For a given packing of column, the t o r t u o s i t y constant K should be constant, and i t can be calculated from Eq.7.2.5 i f a reference l i q u i d i s chosen f o r which 0=0° (complete wetting or spreading). Since coal w e t t a b i l i t y ranges very widely from hydrophobicity f o r low density fract i o n s to h y d r o p h i l i c i t y f o r high density f r a c t i o n s . I t i s p r a c t i c a l l y impossible to s e l e c t the l i q u i d for which 0=0° condition w i l l be always f u l f i l l e d . As indicated by Harper <1967> i t i s r i s k y to assume cos0=l i n order to compute the t o r t u o s i t y constant. In the following sections, a new approach to compute K and 6 values simultaneously w i l l be introduced based on 213 the proposed assumption. 8.5.2 A New Approach In the new approach, the absolute values of the t o r t u o s i t y constant K, and contact angle 0's f o r d i f f e r e n t coal density f r a c t i o n s are resolved at the same time from a set of simultaneous equations. As stressed before, the t o r t u o s i t y constant K, an equivalent of c a p i l l a r y radius, i s purely a geometric property of the packed column. I t i s only associated with p a r t i c l e s i z e d i s t r i b u t i o n , p a r t i c l e shape, and column packing density. I t should be independent of w e t t a b i l i t y of the material investigated. Suppose, under i d e a l i z e d conditions, that two d i f f e r e n t materials are both composed of spherical p a r t i c l e s a l l with i d e n t i c a l diameter of, say, 5 microns. I f packed under the same pressure, the columns f o r t h i s two materials should possess the same t o r t u o s i t y constant, K. This idea may be generalized to apply to materials having s i m i l a r p a r t i c l e shapes and approximately the same siz e d i s t r i b u t i o n s , e.g. coal powders. According to t h i s assumption, only one c a l i b r a t i o n i s required f o r a group of materials of d i f f e r e n t surface w e t t a b i l i t i e s . 214 Assume that there are two d i f f e r e n t materials possessing s i m i l a r s i z e d i s t r i b u t i o n s and s i m i l a r p a r t i c l e shapes. Two columns are made respectively from the two materials under exactly the same pressure. These two columns should have the same t o r t u o s i t y constant, K. After penetrating these two columns with the same l i q u i d , one can get d(h 2)/dt = Sx = K- 7 l v •cosc? 1/2 M 8.4.8 and S 2 = K-7 L v • cos0 2/2/i 8.4.9 where S i and S2 are the slopes of the penetration l i n e s f or two columns respectively and can be obtained from the penetration t e s t , Bx and 0Z the contact angles on the corresponding materials, 7 l v the l i q u i d surface tension, and n the v i s c o s i t y of the l i q u i d . A f t e r the column-packing de n s i t i e s are equally changed, by equally changing the column-making pressure, to another t o r t u o s i t y constant value K', another set of equations can be s i m i l a r l y obtained S3 = K'-7 l v • cos c9 1/2/i 8.4.10 and S4 = K1 • 7 l v • C O S0 2/2A* 8.4.11 Thus, a set of four equations with four unknown values, K, 215 K', elt and e2 are obtained. Unfortunately, only three out of the four equations are independent. An i n d e f i n i t e number of solutions instead of one can be obtained. One c a l i b r a t i o n i s needed i n order to put a r e s t r a i n t on these solutions. Another useful r e s t r a i n t for the above equations i s that contact angle must range from 0 to 90°. In r e a l applications, e f f o r t s were made i n the grinding process to keep various density f r a c t i o n s to have the s i z e d i s t r i b u t i o n s as s i m i l a r as possible. Under the precondition of i d e n t i c a l s i z e d i s t r i b u t i o n , the column-making pressure becomes the only factor c o n t r o l l i n g the volumetric packing density of columns. Columns made under the same pressure might be considered possessing the same packing density, which was t e s t i f i e d by the porosity measurement, and therefore the same t o r t u o s i t y constant K. The i n t r i c a c y i s that the t o r t u o s i t y constant K i s subject to the e f f e c t of p a r t i c l e shapes within the column and the p a r t i c l e s i z e d i s t r i b u t i o n s can not be exactly the same. Even i f the shapes for i n d i v i d u a l p a r t i c l e s may d i f f e r , the shapes i n general for the d i f f e r e n t density f r a c t i o n s from the same o r i g i n would not show much differ e n c e . In addition, f o r such small p a r t i c l e sizes averaging around ten micrometers, both the shape e f f e c t and small d i s t r i b u t i o n deviation w i l l diminish to an i n s i g n i f i c a n t degree under a high column-making pressure. 216 8.5.3 Numerical Calculations In applying t h i s approach to the present case, columns f o r a l l s i x d i f f e r e n t density f r a c t i o n s were made under a set of three d i f f e r e n t pressures: 6.9, 13.8, and 20.7 MPa, respectively. Corresponding to these pressures, there should be three t o r t u o s i t y constant K f o r those columns: Kx , K2 and K3 . Suppose the contact angles for the s i x density f r a c t i o n s are d\, 8Z, and 66 . The t o t a l number of unknown variables would be nine (K's and 0's). A l l the rate of penetration equations f o r s i x density f r a c t i o n s and three d i f f e r e n t pressures were tabulated i n Table 8 .5 .1 . In the table, Xi = 7 l v • cos0i/2/i. The slopes of the penetration l i n e , SL i n Table- 8.5.1 were obtained from the rate of penetration t e s t . They are given i n Table 8 .5 .2 . Among the t o t a l eighteen equations i n Table 8 .5 .1 , eight are independent, while the number of the unknowns i s nine. So the number of solutions i s i n d e f i n i t e , and a r e s t r a i n i s required to get one p a r t i c u l a r s o l u t i o n out of them. The advantage of employing the redundant equations i s that they can encompass more experimental data as much as can be obtained. Though the solutions resolved from the redundant equations may not be f i t t e d i n every equation exactly, they can be put i n a l l the equations with the 217 T a b l e 8.5.1 Rate of penetration equation matrix Density f r a c t i o n s P-6.9 HPa KI P-13.8 MPa K2 P-20.7 MPa K3 -1.3 1.3- 1.4 1.4- 1.5 1.5- 1.6 1.6- 1.8 +1.8 S l l = KI XI S21 - KI X2 S31 - KI X3 S41 = KI X4 S51 = KI X5 S61 = KI X6 S12 - K2 XI S22 - K2 X2 S32 = K2 X3 S42 - K2 X4 S52 = K2 X5 S62 = K2 X6 S13 - K3 XI S23 - K3 X2 S33 = K3 X3 S43 = K3 X4 S53 - K3 X5 S63 = K3 X6 Table 8.52 The slopes for different density f r a c t i o n s under various pressures density pressure MPa fr a c t i o n s 6.9 13.8 20.7 -1.3 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 +1.8 0. .3029 0.2074 0.163 219 minimum o v e r a l l deviation. Therefore the solution's r e l i a b i l i t y i s higher. To solve these equations, simplex search method was employed. A b r i e f description of t h i s method i s given below; d e t a i l e d d e s c r i p t i o n of t h i s method can be found i n many publications <Spandley etc., 1962, Nelder and Meed, 1965, Mular, 1972>. The simplex method i s a d i r e c t search strategy that begins with a n-dimensional general simplex with (n+1) v e r t i c e s i n n-dimensional space (n i s the number of unknown vari a b l e s , i n our case n=9) . The values of the objective function (here Residual Sum of Squares RSS) are calculated on a l l v e r t i c e s of the simplex and compared. The vertex with the highest RSS value i s replaced by a new vertex point which i s chosen by r e f l e c t i o n . Then an adjacent simplex i s formed. The above procedure i s repeated so the simplex w i l l move on the objective function RSS surface, and i s forced to adapt i t s e l f to the ' l o c a l landscape'. On a long i n c l i n e d surface, the simplex w i l l elongate down by expansion. Upon approaching the bottom of the basin, the simplex w i l l contract i n the neighborhood u n t i l a minimum RSS i s reached. An i l l u s t r a t i v e two dimensional simplex search process i s shown i n Figure 8.5.1. The u t i l i z a t i o n of simplex search method i s only made 220 possible by using computer because of the tremendous amount of i t e r a t i v e computation involved. The computer program written i n FORTRAN and i t s flowsheet are given i n Appendix one. In the program, the number of search variables was nine. C(l) to C(3) represent Ki to K 3 and C(4) to C(9) correspond to Xi to X6 respectively. The values of C(I) could be a r b i t r a r i l y given. They should f i n a l l y converge at the same point. The computed r e s u l t s are presented i n Table 8.5.3. In the Table, T3 and T are the values of program objective function to be minimized. As expected, the t o r t u o s i t y constant K becomes smaller with an increase i n column-making pressure. In the lower part of the table, i n the second column are the measured rate of penetration values; i n the t h i r d column are the values calculated according to the corresponding equations i n Table 8.5.1. In Table 8.5.1, there are eight independent equations and nine unknowns, there should be i n d e f i n i t e number of solutions f o r the equations. Only one set of the solutions i s presented i n Table 8.5.3. By multiplying a l l the K values by a c o e f f i c i e n t N, and at the same time d i v i d i n g a l l the X values by the same c o e f f i c i e n t , N, one can obtain K'S 1.53NX10"5, 1.18NX10"5, 0.98NX10"5 8.4.12 Xi's 797.97/N, 676.39/N, 499.58/N, 453.09/N, 221 Figure 8.5.1 An i l l u s t r a t i o n of the two dimensional simplex search process 222 Table 8.5.3 A General Contact Angle And Tortuosity-Constant Calculation Results CYCL. TIMES 501 T3= T= 0.26980E-05 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% 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 -0.00056 -0.00074 -0.00012 -0.00011 0.00046 0.00030 -4.78038 -7.65562 ,63480 .54287 70454 -1. -1. 7. 10.03356 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 -0.00001 0.00028 0.00001 -0.00005 -0.00005 -0.00003 -0.09892 3.41586 0.14100 -0.99584 -1.06134 -1.34038 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 0.00039 0.00038 0.00008 0.00013 -0.00019 -0.00012 4.71980 5.40061 1.52551 2.86652 -5.71031 -7.14510 223 362.37/N, 173.62/N 8.4.13 Above are the general solutions of equations i n Table 8.5.1. Mathematically, N can be any r e a l value. However, one of the r e s t r a i n t s i n r e a l s i t u a t i o n i s that the contact angle of kerosene on coal can not be les s than 0° and greater than 90° (If greater than 90°, kerosene w i l l not penetrate). Therefore, the N value i s li m i t e d i n the range from 1.13 to 2.0. Once the exact N value i s obtained, a l l the K's and 8 's can be calculated. In present work, t h i s was done with quartz. Quartz, on which water was known to have a zero contact angle, was ground i n mortar to the same s i z e range as coal powder. The quartz powder was pressed under pressure of 12.7 MPa into columns. Exactly the same experimental procedure as that f o r coal was followed. The t o r t u o s i t y constant f o r the quartz column was e a s i l y calculated from Eq.7.2.5 K = 2S - M/7 where n i s v i s c o s i t y of water, 7 i s the surface tension of water. The t o r t u o s i t y constant K for quartz column made under pressure of 12.7 MPa was found to be 1.451x10"5. This value was also considered, according to the assumption, to be the K value for a l l coal columns made under 12.7 MPa. 224 That i s , 1.18N xlO" 5 = 1.451 x i c r 5 , and N=1.23. After s u b s t i t u t i n g N=1.23 into the general solutions i n Eqs.8.4.12 and 8.4.13, one can get the f i n a l contact angle values as shown i n Table 8.5.4. The contact angles, as discussed above, were calcula t e d through i n d i r e c t c a l i b r a t i o n . According to the assumption made previously i n t h i s section, the t o r t u o s i t y constant of a column i s only dependent on p a r t i c l e shapes, s i z e d i s t r i b u t i o n s and i t s packing density. The t o r t u o s i t y constant K w i l l be same for a l l columns of d i f f e r e n t materials with approximately the same s i z e d i s t r i b u t i o n s and shapes i f they are compacted under the same pressure. This implies how to f i n d the c o r r e l a t i o n between the column t o r t u o s i t y constant and p a r t i c l e s i z e d i s t r i b u t i o n . Once the c o r r e l a t i o n i s defined, t o r t u o s i t y constant can be obtained 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 the columns made of d i f f e r e n t materials, but under the same pressures, have the same t o r t u o s i t y constant K, needed to be v e r i f i e d . There are many ways of doing t h i s . Cross examination i n which the v a l i d i t y of t h i s assumption i s simply tested by repeating the same 225 Table 8.5.4 The F i n a l Contact ( Angle And Tortuosity Constant Calculation Results CYCL. TIMES 5001 T3= T= 0.13141E-06 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 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 0.00001 0.00028 0.00001 -0.00006 -0.00004 -0.00003 0.11730 3.42823 0.20814 -1.05509 -1.04044 -1.30631 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 0.00040 0.00037 0.00007 0.00012 -0.00020 -0.00012 4.82406 5.31168 1.48661 2.70571 -5.80134 -7.22349 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 simplest. I f the assumption i s true, the t o r t u o s i t y constants, K's, w i l l keep unchanged f o r a l l d i f f e r e n t l i q u i d s tested. Because of the large number of repeated t e s t s , t h i s method was not, at present, used. By taking a look at the r e l a t i o n s h i p between column packing density and column-making pressure i n Figure 8.3.1, one can f i n d that a very 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 t o r t u o s i t y constant and column-making pressure i n Table 8.5.4. This gives a clue that there must be a c e r t a i n l i n e a r r e l a t i o n between the column-packing density and t o r t u o s i t y constant. As expected, the t o r t u o s i t y constant data i n Table 8.5.4 pl o t t e d against the packing density data i n Figure 8.3.1 gives, as expected, a very good l i n e a r r e l a t i o n (Figure 8.5.2). Because column-packing density and column porosity are both based on the same concept, i t can be concluded that there i s a l i n e a r r e l a t i o n s h i p between column porosity and t o r t u o s i t y constant K. This i s an important c o r r e l a t i o n . I t w i l l make possible i n future to obtain K values from the measurement of column packing densities or column p o r o s i t i e s . Attention should be paid to the f a c t that the above assumption i s made based on the non-porous s o l i d p a r t i c l e s . As discussed i n section 6.7, there are two d i f f e r e n t types of p o r o s i t i e s : the i n n e r - p a r t i c l e porosity 227 Packing density mm/gram ^ Packing density and i n t e r - p a r t i c l e porosity. Correspondingly, there are two d i f f e r e n t types of c a p i l l a r y tubes: the i n n e r - p a r t i c l e and i n t 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 of i n n e r - p a r t i c l e c a p i l l a r y tubes are much more smaller than that of i n t e r -p a r t i c l e c a p i l l a r y tubes. The rate of penetration through a compacted column i s mainly con t r o l l e d by the i n t e r - p a r t i c l e c a p i l l a r i e s . The porosity of the material does not have a prominent e f f e c t on the rate of penetration. 229 8.6 SUMMARY AND DISCUSSION The rate of penetration technique i s based on the Washburn equation which states that the squared l i q u i d penetration height i s l i n e a r l y proportional to the penetration time. The contact angle can be calculated from the slope of t h i s l i n e a r r e l a t i o n s h i p . In the conventional procedure, the tested f i n e p a r t i c l e s are placed i n a glass tube 0.8 cm i n diameter. The tube i s manually tapped to ensure a uniform packing. The tube i s c a l i b r a t e d on i t s external surface f o r the penetration height reading. This method suffers from poor r e p r o d u c i b i l i t y and not very good experimental accuracy. The method was modified i n the present work. The specimen mounting press was employed to compress coal powder into a highly compacted column (or p i l l a r ) . When released from the mounting press, the coal column holding does not f a l l apart and i s strong enough to r e s i s t the experimental handling. The diameter of the column i s 2.54 cm, and the height ranges from 0.5 to 3 cm. Kerosene was u t i l i z e d as a penetration l i q u i d . The column height was accurately measured with vernier. Because the column diameter i s quite large, the 230 time i s read when h a l f of the column top surface i s wetted. Thus f o r each column, only one p a i r of data i s obtained. For each coal sample, four to s i x columns with d i f f e r e n t heights were prepared and penetrated to get the same number of experimental points. The experiments revealed that the Washburn equation i s s t i l l applicable to the highly compacted column. The l i n e a r i t y of the penetration l i n e , which i s represented by R squared, can be as high as 0.9992 to 1.000 f o r columns made under pressure of 20.7 MPa. The accuracy i s also very high. The standard deviations of the slope values are only 0.0003 and 0.013 for the slope values of 0.163 and 0.8246, respectively (see Tables 8.2.4 and 8.5.2). The column-making pressure 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. Results f o r a -1.3 density f r a c t i o n of Bullmoose coal (Table 8.2.4) indicate that when a column-making pressure increases from 6.9 to 20.7 MPa, the standard deviation of the slope value decreases from 0.059 to 0.013, and the R squared value increases from 0.9930 to 0.9992. I t i s possible that coal p a r t i c l e s can be crushed under the influence of the high column-making pressure. However, examination under Scanning Electron Microscope showed that the crushing of coal p a r t i c l e s under pressure of 231 up to 27.6 MPa i s n e g l i g i b l e . The applied pressures to make columns d i d not exceed 20.7 MPa. The minimum pressure required to make strong enough columns cannot be lower than 2.8 MPa. For a ce r t a i n amount of coal, the height of the column decreases appreciably with pressure. Further increase i n pressure beyond 20 MPa has only a s l i g h t e f f e c t on the height (Figure 8.3.1) because p a r t i c l e s i n the column have already reached a very close packing. At a constant column-making pressure, the column height increases with the column weight l i n e a r l y . However, as the weight increases to a c e r t a i n value (16 grams for +1.8 density f r a c t i o n i n Figure 8.3.2), the column height w i l l be out of proportion and greater than predicted. This i s because of the f r i c t i o n a l forces which e x i s t between the column and mounting press mold i n the column-making process. In the l i q u i d penetration process, columns experience some swelling. The columns made under higher pressure experience a greater expansion than do the columns made under lower pressure. The r e l a t i v e column height increase a f t e r l i q u i d penetration i s 0.41% f o r columns made at pressure of 6.9 MPa, and 0.71% for columns made.at 20.7 MPa. The expansion i s very small and can be ignored. 232 Following determination of the penetration rate (slope) values from the t e s t , the Washburn equation (Eq. 7.2.5) i s employed to cal c u l a t e the contact angles of kerosene on the f i n e coal p a r t i c l e s . The t o r t u o s i t y constant K which appears i n the equation i s , however, unknown. Conventionally, the second l i q u i d which p e r f e c t l y wets p a r t i c l e s i s used to obtain K i n a p a r a l l e l experiment. Having K, the contact angle can be calculated. This practice i s not r e a d i l y applicable to coal because coal i s extremely heterogeneous and i t s w e t t a b i l i t y i s widely d i s t r i b u t e d . No l i q u i d can be found to have a zero contact angle on coa l . In the present work, an assumption was made that f o r the materials with 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 , and shape, t h e i r columns, i f made under the same pressure, possess the same t o r t u o s i t y constant. Under t h i s assumption, the columns fo r d i f f e r e n t coal density f r a c t i o n s also have the same t o r t u o s i t y constant. Washburn equation's matrix f o r d i f f e r e n t density fract i o n s of coal, and at d i f f e r e n t pressures i s given i n Table 8.5.1, and the simplex search program was used to solve t h i s matrix. The contact angle values of kerosene on d i f f e r e n t density f r a c t i o n s of the Bullmoose coal were calculated as shown i n Table 8.5.4. One of the advantages of t h i s technique i s that the t o t a l surface area penetrated by l i q u i d within a uni t height of the column i s much greater than that i n a conventional 233 method. Therefore, i t i s more s t a t i s t i c a l l y representative. In addition, the column height was lowered to a range of 0.5 to 2 cm compared to the conventional range of 4 to 10 cm. Therefore, the penetration process was subjected, to a much le s s extent, to the e f f e c t of g r a v i t a t i o n a l force. The work needed to be done i n future i s to f i n d the r e l a t i o n s h i p between the t o r t u o s i t y constant and various parameters such as p a r t i c l e shape and s i z e d i s t r i b u t i o n , column porosity, and packing density. In addition, the a p p l i c a b i l i t y of t h i s technique to d i f f e r e n t combinations of l i q u i d s and materials should also be tested. The quantitative comparison of the contact angle obtained for the same coal by the "column" method on the one hand, and by the " p e l l e t " method on the other, i s impossible because of the dependence of the contact angles on drop s i z e . In addition, kerosene was used i n the former method, and water i n the l a t t e r one. Since i n the d i r e c t method, only those p a r t i c l e s which form the p e l l e t surface p a r t i c i p a t e i n the measurement, while a l l the p a r t i c l e s i n the column take part i n a f f e c t i n g the penetration rate, the rate of penetration technique i s s t a t i s t i c a l l y more r e l i a b l e . The standard deviation of the contact angle values measured on the p e l l e t s ranges from 2.06 to 3.71 degrees corresponding to 234 the angle value of about 120 degrees. The r e l a t i v e measurement error i s 1.7 - 3.1%. While the standard deviation of the slope values measured on the columns i s 0.0003 to 0.013 corresponding to the slope values of 0.163 to 0.8246. The r e l a t i v e measurement error i s 0.2 - 1.6%. Cle a r l y , the measurement accuracy i n the rate of penetration technique i s higher. 235 CHAPTER 9 CONCLUSIONS The d i r e c t contact angle measurements a. On a heterogeneous coal surface, the contact angle measured by constructing a tangent to the drop p r o f i l e at the three-phase contact l i n e and the contact angle calculated through the whole drop p r o f i l e are d i f f e r e n t . The former one r e f l e c t s the contact angle on the higher surface energy area, while the l a t t e r one represents the average contact angle on the o v e r a l l heterogeneous surface. The d i r e c t l y measured angle value i s , on the average, f i v e degrees lower than the one calculated from the same drop p r o f i l e (Figure 6.2.1). b. The contact angle on the p e l l e t surface was found to depend on the drop siz e and the way the si z e of the drop was manipulated. The contact angle of a l i q u i d on the s o l i d does not necessarily increases with the si z e of the drop. I t can also decrease when the drop s i z e i s enlarged by incremental additions. 236 The surface of a compressed coal p e l l e t i s glossy and macroscopically f l a t . However, the p e l l e t i s microscopically very porous both inside and on i t s surface. The surface porosity i s characterized by the f r a c t i o n a l area of pores. While the p e l l e t bulk porosity can be experimentally measured, the surface porosity cannot. Under the assumption made i n Section 6.8, the f r a c t i o n a l area of pores i s equal, i n value, to the p e l l e t bulk porosity. The p e l l e t porosity i s composed of two portions: i n t r a - p a r t i c l e porosity which i s the porosity inside an i n d i v i d u a l p a r t i c l e , and i n t e r - p a r t i c l e porosity which i s the porosity between p a r t i c l e s ; i t i s controlled by p a r t i c l e s i z e , shape, and pellet-making pressure (Figures 6.7.1 and 6.7.2). The contact angle measured d i r e c t l y on the surface of a compressed coal p e l l e t i s an apparent contact angle determined by s o l i d and a i r . The pellet-making pressure influences the apparent contact angles v i a the f r a c t i o n a l area of a i r pores on the p e l l e t surface. This e f f e c t can be q u a n t i t a t i v e l y corrected using the Cassie-Baxter equation to transform the apparent contact angle into the r e a l angle value on the s o l i d . For example i n Figure 6.9.3, the contact angle values measured on the p e l l e t surfaces of a -1.3 density f r a c t i o n of the Line Creek coal range from 109 to 133 degrees depending on the pellet-making pressure. After correction, the contact angle value become 84.2 degrees. e. I t was found that a pellet-making pressure of lower than 27.6 MPa cannot r e s u l t i n the perceivable crushing of coal p a r t i c l e s and, therefore, does not release new surfaces (and does not influence the a p p l i c a b i l i t y of t h i s technique). f. The r e p r o d u c i b i l i t y of the contact angle measured d i r e c t l y on the coal p e l l e t s as given by the standard deviation of the angle values ranges from 2.06 to 3.71 degrees. The deviation mainly resulted from the heterogeneity of the coal p e l l e t surface. In the contact angle measurements on f i n e l y polished coal surfaces c a r r i e d out by Vargha-Butler et a l . <Vargha-Butler, Kashi, Hamza, and Neumann, 1986>, the confidence l i m i t of the contact angle ranges from 0.5 to 4.2 degrees. The rate of penetration method a. The Washburn equation i s well applicable to the highly compacted column made of f i n e c o a l . This i s demonstrated by the l i n e a r i t y of the rate of 238 penetration r e l a t i o n s h i p . The R squared ( c o e f f i c i e n t of multiple determination) values f a l l between 0.9992 and 1.0000. The l i n e a r i t y i s very high. b. I t was found that when working with f i n e coal p a r t i c l e s , the modified rate of penetration method gave better accuracy and r e p r o d u c i b i l i t y than that of the o r i g i n a l method. The standard deviation of the penetration slope values ranges from 0.0003 to 0.013 corresponding to 0.163 to 0.8246 of the slope values. c. The experimental accuracy and r e p r o d u c i b i l i t y also depend on the flatness of the penetration front within the column. The l i q u i d penetration front i n the highly compacted column was found very f l a t . The ruggedness which i s the v e r t i c a l distance between the highest point and the lowest point i s lower than 0.06 cm f o r the columns 2.54 cm i n diameter. d. A column made under higher pressure experiences a greater swelling a f t e r penetration. The swelling for a l l the columns, however, was found to be so small (less than 0.71% r e l a t i v e ) , that i t could be neglected. e. The pressure i s the most important factor i n a f f e c t i n g the column properties and the penetration process. The physical properties of the column become more uniform 239 and reproducible under higher pressure. As the pressure increases, the penetration rate becomes smaller f o r the 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 of a column i s independent of the s o l i d surface properties. I t s value i s given by p a r t i c l e shapes and s i z e d i s t r i b u t i o n , and by column-making pressure. 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Zisman, W.A., (1964) "Relation of Equilibrium Contact Angle to Liquid and S o l i d Constitution", Contact Angle -Wettab i l i t y and Adhesion, American Chemical Society Applied Publication, Washington, D.C. 249 APPENDIX I A FLOWSHEET FOR SIMPLEX SEARCH PROGRAM o (1) CALC. X, AND (flSS), » FIND h, S, L. FORM X, " (1 + a) X, - aX, CALCULATE (RSS), IS (RSS), < (nSS)L \ YES \ FORM X. - (1 + r) X, - r X, I IS (RSS), < (RSS) t YES _L NO REPLACE X„ BY X. IS (RSS), > (RSS), NO REPLACE XK DY X, HAS MIN. BEEN REACHED NO YES IS (RSS), > (RSS)„ YES ' NO • REPLACE X. BY X, T FORM X. - fi\ + (1 - fi) X. IS (RSS). > (RSS)„ -*• YES NO REPLACE ALL X, BY 1/2 (X, + X) L REPLACE X. BY X. YES »- PRINTOUT STOP APPENDIX 2 Contact Angle Calculation Program ***************************************************** * * * * * CONTACT ANGLE CALCULATION PROGRAM * * * * * **************************************************************** * This i s a program writen i n FORTRAN f o r the contact angle * r e s u l t c a l c u l a t i o n . I t uses simplex optimization technique * to search the best values of unknown v a r i a b l e s i n the set * of redundant equations. * TABLE OF PARAMETERS * N - - the number of search v a r i a b l e s * Z9 -- the subroutine computation cycle times * RSS and Y(I) -- the Residule Sum of Squares 1=1 to N+l * H -- the point on the simplex where RSS i s the highest * S -- the point on the simplex where RSS i s the second * highest * L -- the point on the 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 - - the expansion c o e f f i c i e n t * B -- the contraction c o e f f i c i e n t * SL(I,J) -- SLope values a c t u a l l y measured. * SP(I,J) -- Slope values Predicted accoding to the equations * I -- the number of density f r a c t i o n s * J -- the number of column-making pressures used * X(I,J) -- the simplex matrix -- 1=1 to N+l and J=l to N * GAMA -- the l i q u i d surface tension * 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(10,9),Z(9),Y(10),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, *) (SL(I,1), 1=1, 6) READ (12, *) (SL(I,2), 1=1, 6) READ (12, *) (SL(I,3), 1=1, 6) GAMA=27.36 MU=0.01715 N=9 A - l . V=2. B=.5 ***************************************************** * Set up i n i t i a l simplex -- Calculate and set 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 * *************************************************************** 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) 30 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 32 CONTINUE 33 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 CONTINUE 31 CONTINUE ******************************************** * Calculate the standard error of objective function * **************************************************************** Z9=0 T3=1.E9 * Calculate the r e s i d u a l sum of (RSS)i 101 DO 70 K=l, N+l H=K CALL SUBRSS(N, X, H, RSS, Z9, SL, SP) Y(K)=RSS 70 CONTINUE * To f i n d out the H, L, S 91 CALL SUBLHS(Y, N, H, L, S, RSSH, RSSL, RSSS) T1=0. T2=0. DO 92 1=1, N+l T1=T1+Y(I) 92 CONTINUE DO 93 1=1, N+l T2=T2+(Y(I)-Tl/(N+1))**2 93 CONTINUE T=SQRT(T2/N) **************************************************************** * Judge minimum or cycle mnumber being rearched or not * **************************************************************** IF (T.LT.1.E-10.OR.Z9.GT.500) GO TO 81 IF (T.GT.T3) GO TO 41 T3=T 253 ************************************* * R e f l e c t i o n Xr=(l+A)Xo-AXh * **************************************************************** 41 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 42 CONTINUE Q(J)-X(H, J) Z(J)=(1.+A)*P-A*X(H, J) X(H, J)-Z(J) D(J)-P 43 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) 88 CONTINUE ENDIF **************************************************************** * Contration Xc=BXh+(l-B)*Xo, Replacement of Xh by Xc * **************************************************************** 51 J=0 DO 52 J - l , N Q(J)=X(H, J) X(H, J)=B*X(H, J)+(l.-B)*D(J) 52 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 of simplex * **************************************************************** 55 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 56 CONTINUE 57 CONTINUE GO TO 101 * Replace Xh by Xr 25 J=0 DO 26 J - l , N X(H, J)=Z(J) 26 CONTINUE Y(H)=R GO TO 91 **************************************************************** *Expansion, Xe=(l+v)*Z(l, J ) - v * D ( l , J ) , replacement of Xh by Xe* **************************************************************** 71 J=0 DO 72 J - l , N X(H, J)=(1.+V)*Z(J)-V*D(J) 72 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 ********************************************* * Contact Angle C a l c u l a t i o n * * d(HxH)/dT = K.Gama.Cos(Theta)/(2.Mu) * **************************************************************** 81 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 5 CONTINUE **************************************************************** * P r i n t out the r e s u l t * **************************************************************** PRINT * WRITE(13, 78) 78 FORMAT(5X, 5HCYCL., IX, 5HTIMES) WRITE(13, 77) Z9 77 FORMAT(5X, 15) WRITE(13, *) WRITE(13, 2) 2 FORMAT(5X, 3HT3=, 16X, 2HT=) WRITE(13, 3) T3, T 3 FORMAT(5X, 2E13.5) WRITE(13, *) WRITE(13, 124) 124 FORMAT(5X, 35HTHE TORTUOSITY CONSTANTS KI, K2, K3) WRITE(13, 120) (X(L,I), 1=1,3) 120 FORMAT(5X, 3F16.9) WRITE(13, *) WRITE(13, 125) 125 FORMAT(5X, 38HTHE X VALUES FOR SIX DENSITY FRACTIONS) WRITE(13, 126) (X(L,I), 1=4, 9) 126 FORMAT(5X, 6F9.2) WRITE(13, *) 256 WRITE(13, 129) 129 FORMAT(5X, 39HCONTACT ANGLES ON SIX DENSITY RFACTIONS) WRITE(13,128) (THETA(I), 1=1, 6) 128 FORMAT(5X, 6F9.2) WRITE(13, *) WRITE(13, 127) 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) SL(I,J), SP(I,J), SL(I,J)-SP(I,J), + (SL(I,J)-SP(I,J))/SL(I,J)*10O. 121 FORMAT(IX, 4F13.5) 122 CONTINUE WRITE(13, *) WRITE(13, *) 123 CONTINUE STOP END **************************** * SUBROUTINE I * * This subroutine i s used f or 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) * Calculate the predicted values DO 2 J=l, 3 DO 4 1=1, 6 SP(I,J)=X(H,J)*X(H,3+I) 4 CONTINUE 2 CONTINUE * Calculate the r e s i d u a l sum of squares 257 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 8 CONTINUE 6 CONTINUE RSS=C2 Z9=Z9+1 RETURN END ****************************************** * SUBROUTINE II * * The subroutine f o r f i n d i n g out H^L, S * **************************************************************** 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 IF(Y(I).GT.Y(H)) THEN H=I ELSE IF(Y(I).LT.Y(L)) THEN L=I ELSE END IF END IF 21 CONTINUE RSSH=Y(H) RSSL=Y(L) Y(H)=0. DO 23 1=2, N+l IF(Y(I).GT.Y(S)) THEN S=I ELSE END IF 23 CONTINUE Y(H)=RSSH RETURN END 258 

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