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Effect of salt concentration and cation valence on maximum yield of a bentonite claypaste Hu, Chien-Sheng 1972

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EFFECT OF SALT CONCENTRATION AND CATION VALENCE ON MAXIMUM YIELD STRESS OF A BENTONITE CLAY PASTE by CHIEN-SHENG HU B.A.Sc, Cheng Kung Un i v e r s i t y , 1963 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of CHEMICAL ENGINEERING We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1972. In present ing t h i s . t h e s i s in pa r t i a l f u l f i lmen t of the requirements for an advanced degree at the Un ive rs i t y of B r i t i s h Columbia, I agree that the L ib ra ry sha l l make it f r ee l y ava i l ab le for reference and study. I fu r ther agree that permission for extensive copying o f th i s thes i s fo r s cho l a r l y purposes may be granted by the Head of my Department or by h is representa t i ves . It is understood that copying or pub l i c a t i on o f th i s thes i s fo r f inanc ia l gain sha l l not be allowed without my wr i t ten permiss ion . Department of The Un i ve rs i t y of B r i t i s h Columbia Vancouver 8, Canada Date "A-Uffl . 3 ABSTRACT A review i s given on the f a c t o r s important to the build-up of a g e l s t r u c t u r e i n clay suspensions. The e f f e c t of s a l t i s e s p e c i a l l y stressed. The maximum y i e l d stress of a 19.06 weight per cent washed Bentonite clay paste was measured with a Rotovisco viscometer as a function of the concentration of f i v e s a l t s which were added i n d i v i d u a l l y to the paste. The s a l t concentration was va r i e d from .002 m o l a l i t y up to the coagulation concentration. Two groups of s a l t s were studied; those which had cations i n common with the caly: NaCl and CaC^, and those found only i n trace amounts i n clay: CuCl, MnC^ and CeCl^. The behavior of the two groups of s a l t was quite d i f f e r e n t . The l a t t e r group produced a maximum developable y i e l d value i n the clay which was inv e r s e l y p r o p o r t i o n a l to the valence of the cation. Sodium Chloride produced the l a r g e s t maximum y i e l d value at a high s a l t con-centration while no y i e l d value could be found f o r clay with concen-t r a t i o n s of C a C l 2 above 0.002M. ACKNOWLEDGEMENTS I wish to place on record my sincere gratitude to Dr. Kenneth Pinder, under whom th i s i n v e s t i g a t i o n was conducted, f o r hi s guidance i n helping to carry out th i s p r o j ect. I am e s p e c i a l l y indebted to him f o r h i s kindness i n taking the microscopic photographs and i n correcting the thesis w r i t i n g , ensuring the aut h e n t i c i t y of the material. I would l i k e to thank the National Research Council of Canada and The University of B r i t i s h Columbia f o r t h e i r f i n a n c i a l support of t h i s research. I would l i k e to express my deep appreciation for the assistance of Mr ;N;.Nv Walker of Metallurgy i n taking electron microscope photographs and f o r the assistance of my classmate M.S. L i u i n u t i l i z i n g atomic absorption spectroscopy i n B.C. Research Council; to B.D. Bowen i n using micro-electrophoresis apparatus; to V.R. P h i l l i p s i n operating the Vernier Microscope and i n helping i n various ways during the years as my room mate. My g r a t e f u l acknowledgements are also due to the many others who , by t h e i r kind co-operation have a s s i s t e d i n the accomplishment of th i s task. i i i TABLE OF CONTENTS Page Chapter 1 INTRODUCTION .. . . . . .. .. , ..' .. 1 1.1. Reason f o r Studying the Flow Behavior of Thixo-t r o p i c Systems . . . . .. 1 1.2. Test F l u i d - Bentonite Clay . . . . 2 2 REVIEW OF RHEOLOGICAL STUDIES 2.1. Review of Fundamental Studies of Thixo-t r o p i c Behaviour 2 A. D e f i n i t i o n of Thixotropy . . . . 4 B. Theory of Thixotropy 4 1. Mechanical Approach .. .. 5 2. Continuum Mechanics Approach . . . . ... 5 3. Empirical Approach .. . . . . . . . . 5 C. Factors Influencing Rheological (Include Thixotropic) Properties of Dispersions of S o l i d P a r t i c l e s i n F l u i d Media . . . . 6 1. Dispersed Phase .. ., 6 2. Continuous Phase 6 3. Surface A c t i v e Agents 7 4. A d d i t i o n a l S t a b i l i z i n g Agents .. .. ... 7 2.2. Pinder's Work . . . . . . . . .. 7 2.3. Brown's Work 8 i v Chapter Page 2.4. Nicholson's Work 8 2.5. I n i t i a l Work .. 8 2.6. Bentonite Clay Suspension - Exchangeable Ion - Thixotropic 9 2.7. Review of Main Studies on Bentonite Clay .. 9 A. Much Higher Than 20% by Weight . . . . 9 B. Below 10% by weight .. • .. 10 3 REVIEW OF GENERAL THEORETICAL CONSIDERATION .. 11 3.1. Y i e l d Stress and Maximum Y i e l d Stress .. 11 A. D e f i n i t i o n of Y i e l d Stress 11 B. Maximum Y i e l d Stress . . . . . . . . . . . 13 C. Measurement Methods and Devices . . . . 14 1. General D i f f i c u l t i e s Encountered i n Y i e l d Stress Measurement . . . . .. 14 a) Shear Stress D i s t r i b u t i o n Not Uniform .. .. .. .. . . . . . . 14 b) Local Y i e l d Stress Not Uniform . . . . 14 c) Concentration Gradients .. . . . . .. 15 d) P a r t i c l e Orientation 15 2. Types of Instruments 16 a) Capillary-Tube . . . . .. . . . . .. 16 b) P a r a l l e l - P l a t e 17 c) Rotational Concentric Cylinder .. .. 17 d) Cone and Plate Viscometer . . . . . . 18 e) P u l l i n g Viscometer ........ 18 Chapter Page 3. Measuring Methods f o r Y i e l d Stress . . . . 19 a) Dynamic Methods .. .. 19 (1) Extrapolation of Flow Curve to Zero Shear Rate . . .. 19 (2) Analysis of the Torque Decay Curve .. 20 b) S t a t i c Methods .. .. 20 (1) Boardman and Whitmore's S t a t i c Method .. 20 (2) Volcadlo and Charles' S t a t i c Method .. 21 D. P r a c t i c a l Method . . . . .. 23 E. Bingham Y i e l d Stress and P l a s t i c i t y . . . . 24 1. Bingham Y i e l d Stress . . . . ..... .. 24 2. P l a s t i c i t y 26 3.2. (Cat)ion Exchange .. .. .. 26 A. The Phenomena of Ion Exchange of Clay Minerals . . . . . . . . . . .. 26 B. Commonest Exchangeable Ions 27 C. Base Exchange, Cation Exchange and Ion Exchange i . ' • 27 D. Cation Exchange 28 1. History and Exchange Reactions .. . . . . 28 2. Rate of Reactions 30 3. Causes of Cation Exchange and O r i g i n of P a r t i c l e Charge 31 a) Broken Bonds 31 b) Substitution Within the L a t t i c e Structure 33 . c) The Hydrogen of Exposed HydroxyIs . . . . 34 v i Chapter Page 4. Cation Exchange Capacity . . . . . . . .. 34 a) Factors Influencing Cation Exchange Capacity 34 b) Determination of Cation Exchange Capacity and Exchangeable Cations ..... 38 5. Cation E f f e c t on Swelling of Clay . . . . 39 E. Anion Exchange . . . . 41 1. Replacement of OH Ions 41 2. Geometry of the Anion .. 42 3. Anion-Exchange Spots .. .. 42 3.3. O r i g i n of Y i e l d Stress of Clay Suspension .. 43 A. O r i g i n of Y i e l d Stress .. 43 B. O r i g i n of P a r t i c l e Charge .. 45 C. Possible Bonding Forces .. .. 46 1. Van der Waals A t t r a c t i o n . . . . . . . . 46 2. E l e c t r i c Double Layer 47 a) Gouy Model of the E l e c t r i c Double Layer.. 47 b) Stern's Model of the E l e c t r i c Double Layer 48 c) Corrections,3 of the Gouy Theory According to B o l t • 50 d) E f f e c t of .Electrolytes on the Configuration of the E l e c t r i c Double Layer 50 e) . Zeta P o t e n t i a l .. 51 3/ Double Layer Repulsion 52 4. The Summation of Repulsion and A t t r a c t i o n 53 5. Secondary Minimum . ... ... .. .. 57 v i i Chapter Page D. O r i g i n of Cross-linked Gel Structure i n Clay Suspension . . . . .. 57 1. Negative Double Layer on the F l a t Unit-Layer Surfaces 58 2. P o s i t i v e Double Layer on the Edge Surfaces of Clay Plates . . . . . . . . ,. . 58 3. Models of P a r t i c l e Association and Cross-linked Gel Structure .. .. .. .. 59 E. Cross-linked Gel Structure .. 60 3.4. Clay Sample Preparation . . . . . . . . .. 64 A. Ideal Clay Sample .. 64 1. For S c i e n t i f i c Investigation . . . . .. 64 2. For I n d u s t r i a l Purpose .. .. 64 B. Disadvantages of Conversion Methods .. .. 64 1. Disadvantages of the Displacing Method .. 65 2. Disadvantages of E l e c t r o d i a l y s i s . . .. .. 66 3. Hydrogen Clay .. 67 C. Preparation of Clay Sample i n t h i s Work .. 67 4 PRESENT WORK . . . . . . . . 69 4.1. Variables Studied .. .. ... 69 A. Dependent Variable . . . . .. 69 B. Independent Variable .. 69 4.2. S p e c i a l Features of This Work . . . . .. .. 12 A.A Feasible Method to Measure Y i e l d Stress .. ?2 B. Simple Paddle Randomly Destroys Gel Structure v i i i Chapter Page 5 EXPERIMENTAL 73 5.1. Materials .. .. .. .'. 73 A. Bentonite Clay .. .. . . . . 73 B. Chemicals 74 5.2. Main Apparatus 74 A. -Haake Rotovisco Viscometer 74 B. A l t e r a t i o n Made to Basic Viscometer .. 76 1. Speed Reducer .. .. .. 76 2. Grooved Bob SVPII and Cylinder SVP .. 76 3. Gold P l a t i n g 78 4. Gum Sealing 79 5. Cap to Prevent Evaporation . . . . .. 79 6. Mixing Paddle 79 C. Centrifuge ... .. ... 79 5.3. Experimental Accuracy .. 79 5.4. C a l i b r a t i o n Procedures . . . . . . . . .. 82 A. Thermometer 82 B. Bob Speed While Rotovisco Using Reducer ZG10 82 C. Chart Speed of Recorder 82 D. Stress Conversion Factor 82 5.5. Experimental Procedures • 83 A. Procedures f o r Washing Out Soluble Salts i n Clay . . 83 B. Determination of (Hygroscopic) Moisture Content of Clay by Weighing Method . . . . 85 Chapter Page C. Sample Preparation f o r Y i e l d Stress Measurement . .> 86 1. Without.Salt . . . . . 86 2. With S a l t .. .. .. .. 86 D. Y i e l d . Stress Measurement .. 86 E. Aging Test f o r Maximum Y i e l d Stress . . . . 88 F. Determination of Exchangeable Cations .. 88 1. Procedures f o r Unwashed Clay . . . . . . 88 2. Procedures f o r Washed Clay 89 G. Determination of Soluble S a l t 89 H. Zeta P o t e n t i a l .. .. .. .. 89 I. Photographs .. 90 1. Electron Microscope Photographs . . . . 90 2. Microscopic Photographs 91 6 RESULTS AND DISCUSSION .. .. 92 6.1. Preliminary Experiment for Washing Out Soluble S a l t 92 6.2. Exchangeable Cations of Beaver-Bond Western Bentonite 94 A. Chemical Composition and Exchangeable Cation of Unwashed Clay 94 B. Exchangeable Cations i n Washed and Un-washed Clay 95 6.3. Size and Shape of P a r t i c l e s and P a r t i c l e Agglomerates .. 95 6.4. E l e c t r o p h o r e t i c V e l o c i t y of the Clay P a r t i c l e 97 X Chapter Page A. Speed of the P a r t i c l e 97 B. Charge Sign of the Clay P a r t i c l e gg 6.5. A T y p i c a l Y i e l d Stress Result 90. 6.6 Re p r o d u c i b i l i t y of Y i e l d Stress Measurement .. 99 6.7. Moisture Content Based on Maximum Y i e l d Stress 101 6.8'. Aging Test of Clay Paste (Without Salt) .. .. 103 6.9. E f f e c t of Rotational Speed of Bob on Y i e l d Stress 105 6.10. Grooved Bob and Y i e l d Stress 107 6.11. S a l i n a t i o n and Cation Valence on Maximum Y i e l d Stress . . . . 107 , . A. M o l a l i t y of S a l t .. .. 107 B. M i l l i e q u i v a l e n t s per 100 gm Clay at Maximum Y i e l d Stress 117 £. Microphotographs 118 7 CONCLUSIONS 126 8 RECOMMENDATIONS .. 128 . LITERATURE CITED .. ..... .. 130 1 NOMENCLATURE 135 Chapter Page APPENDICES: I Bentonite Clay ,. . .. 137 II Radioactive Tracer Technique 140 II I Computer Programs .. .. 141 IV C a l i b r a t i o n of Conversion Factors of Haake'. Rotovisco Viscometer 154 V Density and V i s c o s i t y Match 164 x i i LIST OF FIGURES Figure Page 1 Flow curve of Bingham p l a s t i c clay suspension .. .. 25 2 Repulsive and a t t r a c t i v e energy as a function of p a r t i c l e separation of three e l e c t r o l y t e concentrations. .. . .• 54 3 Net i n t e r a c t i o n energy as a function of p a r t i c l e separation' of,three e l e c t r o l y t e concentrations .. 55 4 Modes of p a r t i c l e association i n clay sus-pensions .. .. ..... . . 61 5 Haake Rotovisco viscometer . . . . . . . . .. .. .. 75 6 Bottom view of the SVPII bob . . . .• . . . . 77 7 The p l e x i g l a s s cap . . . . . . .. .. .. .. .. .. 80 8 The p l e x i g l a s s mixing paddle .. .. . . 81 9 Flow chart of procedures to wash out soluble s a l t i n clay .. . . . . . . . . 84 10 T o t a l ion concentration of clay f i l t r a t e i n washing out soluble s a l t 93 11 Electron microscopic photos of Beaver-Bond Western Bentonite p a r t i c l e s . . .. 96 12 A t y p i c a l shear stress recording . . .. 100 13 Moisture content e f f e c t on maximum y i e l d stress .. .. 102 14 Aging t e s t of clay paste 104 15 Log-log p l o t of co versus . . . . . . 106 16 Extrapolation of flow curve to zero shear rate .. .. 108 17 Torque M Q versus the geometric factors 8 f o r suspensions of Ti0„, k a o l i n and MgO 2' 109 i n water .. . . .. ^ x i i i Figure Page 18 E f f e c t of m o l a l i t y of s a l t on y i e l d stress H I 19 Am p l i f i c a t i o n p l o t of the lower concentration. Part of Figure 18 1 1 2 20 Microphotos of washed clay suspension and c a l i b r a t i o n . . . . 21 Microphotographs of CaC^ system 1^0 22 Microphotos of NaCl system .. .. . . . . . . . . ^.21 23 Microphotos of MnC^ system before saturation point 122 24 Microphotos of MnC^ system at saturation point 123 25 Microphotos of MnC^ system beyond saturation point . . . . . . . . .. 124 26 Diagrammatic edge view of moritmorillonite 139 27 Bob r o t a t i n g i n cup of rotovisco viscometer 156 28 Stress behavior during shearing of a t h i x o t r o p i c ^ system .. .. 165 x i v LIST OF TABLES Table Page I Ionic Radii of Cations Used.in the Experiment .. .. 71 II Chemical Cbmpositon of Beaver-Bond Western Bentonite ..' 73 III Dimensions and Stress Conversion Factor f o r the Cup and Bob Set SVP and SVPII .. .. ...... 78 IV T o t a l Ion Concentration of Clay F i l t r a t e i n Washing Out Soluble Salt .. . . ..- .. 92 V ' Exchangeable Cations and Soluble Salt of Washed and Unwashed Clays . . . . .. . . .. .. 94 VI E l e c t r o p h o r e t i c Speed of Beaver-Bond Western Bentonite P a r t i c l e s .. .. . . .. . . .. .. . . 98 VII Moisture Content on Maximum Y i e l d Stress .. ... .. 101 VIII Aging Test of Clay Paste . . . . . . .. 103 IX Rotating Speed of Bob on Y i e l d Stress .. 105 X Maximum Y i e l d Stress of CaCl2 System at Di f f e r e n t Concentration of CaC^ .. .. .. .. .. H 3 XI Maximum Y i e l d Stress of NaCl System at Di f f e r e n t Concentration of NaCl .. 114 XII Maximum Y i e l d Stress of CuCl System at Di f f e r e n t Concentration of CuCl .. 115 XIII Maximum Y i e l d Stress of MnC^ System at Di f f e r e n t Concentration of MnC^ 115 XIV Maximum Y i e l d Stress of CeCl^ System at Di f f e r e n t Concentration of CeCl^ .. .. .. .. 116 XV Usage of Combinations of Main Program and Subprogram • 151 xv'' Table Page XVI C a l i b r a t i o n Data'of K,' and A of SVPII i n SVP Clip--(with c l u t c h , brake r i n g , speed reducer, head 50 and n i c k l e plated SVPII) .. .. .. . . . . . . . 162 XVII C a l i b r a t i o n of Data of K, M Q and A of SVPII i n SVP Cup (without c l u t c h , Drake r i n g ; with speed reducer, head 500 and gold plated SVPII) .. .. 163 XVIII C a l i b r a t i o n Data of wFactor . . . . 163 XIX Density and V i s c o s i t y Data of CMC i n C a C l 2 (0.02M) - Corn Syrup (82.7 wt. %) Solution 166 XX Density and V i s c o s i t y Data of Fructose, Dextrose and Salts i n 35 wt. % PEG Solution 167 Chapter 1  INTRODUCTION 1.1. Reason for Studying the Flow Behaviour of Thlxotropic Systems Thixotropy, a time dependent v i s c o s i t y which decreases with time at a constant shear rate and which recovers i t s o r i g i n a l values a f t e r a period of s t a n d s t i l l , i s . _ a phenomenon which i s encountered quite frequently i n two phase systems. In many i n d u s t r i a l applications a be t t e r understanding of t h i x o t r o p i c behaviour could be of considerable economic b e n e f i t , not only i n the planning and design of new processes, but also i n gaining the maximum e f f i c i e n c y from processes presently i n use. Face cream or many other cosmetic and pharmaceutical products have properties imparted to them, " / so that they can be smoothed on to the skin as a f l u i d and w i l l then c l i n g as a g e l . The existence of a structure breakdown of p e n i c i l l i n suspensions i s e s s e n t i a l f o r i t s i n t e r -muscular i n j e c t i o n through a hypodermic needle. A f t e r i n j e c t i o n , the quick g e l l i n g of the suspension to form a compact depot i s responsible for i t s prolonged therapeutic action. The p r i n t i n g industry has had problems maintaining the. flow c h a r a c t e r i s t i c s of inks, since i n the production of a printed page, an ink i s compressed, stretched, sheared, fractured and kissed i n a few seconds, and f i n a l l y when i t meets the paper, i t i s 2 t r a n s f e r r e d and s e t d r i e d i n a f r a c t i o n o f a second. P a i n t manu-(1-3) f a c t u r e r s use t h i x o t r o p y t o o b t a i n b e t t e r b l o t outs and smooth s u r f a c e s , m i n i m i z i n g h a r d s e t t i n g , s a g g i n g and t h e f l o w of p a i n t a f t e r a p p l i c a t i o n . Many c l a y s l u r r i e s e x h i b i t t h i x o t r o p y , and e x t e n s i v e (4) damage has been caused by l a r g e t r a c t s o f l a n d f l o w i n g , because of v i s c o s i t y r e d u c t i o n by v i b r a t i o n s . I t a l s o a f f e c t s the q u a l i t y o f g l a z e s and may be c o r r e l a t e d t o the p o r o s i t y o f c r u c i b l e s . The t r e n d i n the c h e m i c a l i n d u s t r y has been to the t r a n s p o r t a t i o n of o i l s and s l u r r i e s (5—8) i n p i p e l i n e s . - D i f f i c u l t i e s have been encountered i n p i p e l i n e d e s i g n f o r non-Newtonian f l u i d s . Many m a t e r i a l s a t low temperatures have been found to be time dependent, forming g e l s , w hich i n c r e a s e p r e s -s u r e drop and cause b l o c k a g e s . I n s p i t e of the importance and l o n g h i s t o r y o f t h e study of the f l o w b e h a v i o u r of the t h i x o t r b p i c system, i t i s s t i l l i n i t s e a r l y e m p i r i c a l s t a g e , hence i t i n d e e d o f f e r s a v e r y i n t e r e s t i n g as w e l l as c h a l l e n g i n g - r e s e a r c h s u b j e c t . 1.2. T e s t F l u i d - B e n t o n i t e C l a y P r e v i o u s workers have met d i f f i c u l t i e s i n c o r r e l a t i n g s i z e (9) and shape f a c t o r s u s i n g n a t u r a l systems. F o r t h i s r e a s o n Brown and N i c h o l s o n ^ ^ u t i l i z e d an a r t i f i c i a l c e l l u l o s e p a r t i c l e s u s p e n s i o n . An attempt was made to use such a system, but u n f o r t u n a t e l y poor y i e l d s t r e s s v a l u e s were o b t a i n e d because of th e l a r g e s i z e o f the p a r t i c l e s . I t was then d e c i d e d to work w i t h th e B e n t o n i t e c l a y system i n view of i t s huge range of a p p l i c a t i o n s - as a bonding agent i n f o u n d r y m o l d i n g s ; as an i n g r e d i e n t i n p e l l e t s o f a n i m a l f e e d made from c o a r s e ground com-ponents; i n d r i l l i n g mud for rotary d r i l l s ; as a f i r e retardant g e l ; as a medium for suspending materials which include medicines that are taken i n t e r n a l l y , to lumps of coal as part of a f l o a t - s i n k ore sep.aratory pro-cess; as c a r r i e r materials f o r chemicals, such as i n s e c t i c i d e s ; as an emulsion s t a b i l i z e r ; as c l a r i f y i n g agents for products such as wine and beer - thus embracing almost a l l i n d u s t r i e s . 4 Chapter 2 REVIEW OF RHEOLOGICAL STUDIES 2.1. Review of Fundamental Studies of Thixotroplc Behaviour A. D e f i n i t i o n of,Thixotropy The early l i t e r a t u r e i s complicated by many authors mis-using the term thixotropy to define other non-Newtonian behaviours. Freundlich and J u l i u s b u r g e r f i r s t defined thixotropy as "the r e v e r s i b l e isothermal g e l / s o l / g e l transformations induced by shear and subsequent r e s t " . The present day accepted d e f i n i t i o n i s by Alves, (6) • Boucher and Pigford , "Thixotropic f l u i d s possess a structure, the breakdown of which i s a function of time as w e l l as rate of shear. This structure can r e b u i l d i t s e l f i f not prevented from doing so by externally applied forces". Most confusion has arisen between t h i x o t r o p i c and f a l s e body behaviours since both exhibit s i m i l a r decay curves. Thixotropic dispersions decay to an equilibrium state which i s Newtonian; independent of shear rate. False body dispersions decay to an equilibrium state which i s pseudoplastic; dependent on shear rate. 5 B. Theory of Thixotropy The construction of a theory with the capability of des-cribing the characteristics of the thixotropic behaviour should ideally start with basic microscopic variables such as particle size, particle shape, interparticle forces etc. At the other extreme a suitable theory could be arrived at simply by manipulating mathematical forms until an equation capable of describing the characteristic behaviour is obtained. Most of the equations already reported have been obtained by combinations of the above two methods. (12) (13) (9) Casey , Sherman , and Brown have done a good job of reviewing the general theories. The constitutive equations have been (12) commonly arrived at by one of the following three approaches :-1. Mechanical Approach Several workers (5,12,14.19) p 0 s t u i a t e ( j t h a t there is a cer-tain linkage structure formed by the solid particles which w i l l be des-troyed by shearing (and the effect of Brownian motion) and which w i l l be redeveloped following a reversible mechanism. 2. Continuum; Mechanics Approach Slibar and P a s l e y ^ ^ and Bouge^^ modified certain continuum mechanics theories to include the case of thixotropy. 3. Empirical Approach (22 23) Green and Weltmann ' used the area of the hysteresis loop, produced in stress vs. angular velocity diagrams, as a measure of thixotropy. 6 C. Factors Influencing Rheolgical. (Including Thixotropic) Properties  of Dispersions of S o l i d P a r t i c l e s i n F l u i d Media (13) Sherman summarized them as follows:-1. Dispersed Phase a) Volume Concentration Influences hydrodynamic i n t e r a c t i o n between p a r t i c l e s ; and f l o c c u l a t i o n leading to formation of aggregates. b) P a r t i c l e . Size, P a r t i c l e Size D i s t r i b u t i o n and P a r t i c l e Shape Influence; v i s c o s i t y over whole range of shear ra t e s , and also the v i s c o - e l a s t i c properties of the more concentrated dispersions; since p a r t i c l e s i z e etc. influence the number of p a r t i c l e s / u n i t volume, they also influence the rate of f l o c c u l a t i o n . c) Chemical Constitution . Influences i n t e r a c t i o n forces between p a r t i c l e s . 2. Continuous Phase a) V i s c o s i t y Direct p r o p o r t i o n a l i t y with dispersion v i s c o s i t y . b) Chemical Constitution, P o l a r i t y , pH E f f e c t on p o t e n t i a l energy of i n t e r a c t i o n between p a r t i c l e s . c) E l e c t r o l y t e Concentration ( i f polar medium) Influences surface charge on p a r t i c l e s ; may also a f f e c t s o l u b i l i t y of surface active agents i n continuous phase. 3. Surface Active Agents a) Chemical Constitution Influences s o l u b i l i t y i n continuous phase; also adsorption at the s o l i d - l i q u i d i n t e r f a c e . b) Concentration Influences v i s c o s i t y of the continuous phase. c) Adsorbed Film at Interface Thickness influences e f f e c t i v e p a r t i c l e dimensions; i t also influences i n t e r a c t i o n between p a r t i c l e s . d) Electroviscous E f f e c t s Leads to an extra d i s s i p a t i o n of energy and an increased v i s c o s i t y of the dispersion through d i s t o r t i o n of symmetry of e l e c t r i c double layer around each p a r t i c l e . 4. A d d i t i o n a l S t a b i l i z i n g Agents (Pigments, Hydrocolloids,  Hydrous Oxides etc.) Modify p o t e n t i a l energy of i n t e r a c t i o n between p a r t i c l e s through e f f e c t on surfaces of p a r t i c l e s , g e l a t i o n etc., also modify hydrodynamic i n t e r a c t i o n . 2.2. Pinder's W o r k ^ Realizing the importance of the gas hydrate method of water des a l i n a t i o n , he c o l l e c t e d some data on the flow properties of hydrate 8 s l u r r i e s . During the course of h i s i n v e s t i g a t i o n , he experienced, as J.J ^ (1,2,5,11,24-30) . ^ C , dxd many others .  » d i f f i c u l t i e s i n the measurement of the e f f e c t s caused by p a r t i c l e properties because of the v a r i a t i o n of the shape and s i z e i n known t h i x o t r o p i c dispersions. 2-3. Brown's W o r k ( 9 , 3 1 ) Using a r t i f i c i a l c e l l u l o s e p a r t i c l e dispersions, Brown got some information on y i e l d value v i s c o s i t y by using an extrapolation technique proposed by P i n d e r ^ . With large p a r t i c l e s , Brown also ob-served a ragged decay curve. I t indicated that a breakdown of an e l e c t r o s t a t i c structure or p a r t i c l e interference was taking place. To check t h i s was the aim of Nicholson's w o r k ^ ^ . 2.4. Nicholson's Work^"^ Af t e r study of s a l t s of d i f f e r e n t cation valence i n Brown's suspension, he found: that the degree of raggedness of the decay curve increased with increased " c a t i o n " strength. I t showed that the break-down of the e l e c t r o s t a t i c structure must at l e a s t be one of the forces responsible f o r the raggedness of the decay curve. 2.5. I n i t i a l Work (see also Appendix V) To continue the forgoing work, the i n i t i a l study on t h i s project was designed to investigate the e f f e c t s of cation valence, s a l t concentration, p a r t i c l e s i z e and p a r t i c l e shape on the zero flow y i e l d s tress of the a r t i f i c i a l c e l l u l o s e p a r t i c l e suspension. 9 That i t did not succeed might be due to the e f f e c t of the large s i z e of the p a r t i c l e on the y i e l d s t r e s s . I t was then decided to examine the e f f e c t s of cation valence and s a l t concentration on the zero flow y i e l d stress of a known t h i x o t r o p i c system - Bentonite clay suspension -because of i t s i n d u s t r i a l usefulness (see 1.2). 2.6. Bentonite Clay Suspension - Exchangeable Ion - Thixotropic Bentonite, as i s known, i s one of the minerals which produces a t h i x o t r o p i c suspension when mixed with water. However, i f one removes by e l e c t r o d i a l y s i s f or example, the a l k a l i s a l t s (as w e l l as part of the a l k a l i earths) which are adsorbed on the Bentonite, i t loses t h i s pro-(35) perty, that i s the suspensions are no longer t h i x o t r o p i c . Obviously the e l e c t r o l y t e s held by cation (and/or anion) exchange (see 3.2 and 3.3)* do influence the i n t e r a c t i v e forces between Bentonite clay p a r t i c l e s . 2.7. Review of Main Studies on Bentonite Clay As f a r as the published papers on t h i s subject are concerned, there are too many to be considered separately. However, they can be c l a s s i f i e d i n t o two large groups according to the range of concentrations of clay i n water. Reference w i l l be made i n Chapter 3 to s p e c i f i c r e s u l t s from such studies. A, Much Higher Than 20% by Weight Most of the work done i n the ceramic industry f a l l s i n t o t h i s category. Measurements of p l a s t i c i t y and exploration of the r e l a t i o n (32 33) between f l o c c u l a t i o n phenomena and molding are the common topics ' 10 B. Below 10% by Weight Mainly examined by the petroleum industry i n so lv ing app l i c a t i on problems of d r i l l i n g muds. S t a b i l i t y of suspension and t ranspor ta t ion of c lay s l u r r y (Bingham y i e l d values are the main design data) i s the p r e v a i l i n g r e -search d i r e c t i o n . As for the s a l t e f f e c t on the rheo log i ca l p roper t i es of c l a y , the s a l t s genera l l y used are with cat ions of H + (only except ion , not a s a l t ) , L i , Na , K , Cs , NH^, Mg , Ca , Ba , La , A l or Th s and with anions of C l or other ion which f u l f i l s two requirements.. One i s that the anion has ne i the r phys i c a l nor chemical e f f e c t on the c l a y ; the other i s such that the s a l t has reasonable s o l u b i l i t y w i th in +u • (34-36) the i n ves t i ga t i on range Chapter 3 REVIEW OF GENERAL THEORETICAL CONSIDERATION 3.1. Y i e l d Stress and Maximum Y i e l d Stress A. D e f i n i t i o n of Y i e l d Stress (37) Vocadlo and Charles gave a very c l e a r discussion on t h i s subject. The y i e l d stress i s usually defined as the s t r e s s which must be applied to a substance i n order to i n i t i a t e flow. I t implies that i f a substance has a y i e l d s t r e s s then the substance may be considered as a s o l i d . A problem thus occurs i n placing a material i n e i t h e r the category of " s o l i d " or " f l u i d " . Such a choice i s only possible through personal judgement based on time of observation, time of service,predicted permanent deformation, etc. I t i s not s u r p r i s i n g , therefore, that whenever a material has r h e o l o g i c a l properties which make i t d i f f i c u l t to bracket i t with one of the three groups: gas, l i q u i d (both are f l u i d s ) and s o l i d , the temptation arises to c a l l i t a "fourth state of aggregation". Van Iterson (1945) who studied the flow properties of clay bodies under pressure, emphasized that t h e i r r h e o l o g i c a l properties d i f f e r from the p l a s t i c i t y of s o l i d s , i n p a r t i c u l a r of metals, and of l i q u i d s . 12 He suggested that a p l a s t i c c l a y body be c a l l e d a f o u r t h s t a t e of aggregation, a suggestion which reminds one of the time when p h y s i c a l chemists began to be i n t e r e s t e d i n the rheology of g l a s s e s . They a l s o proposed that glasses represent the f o u r t h s t a t e of aggregation. A f t e r considering a l l the d i f f i c u l t i e s of such a d e f i n i t i o n , there was produced the f o l l o w i n g t o l e r a b l e formal d e f i n i t i o n s f o r a f l u i d and y i e l d s t r e s s by the c o u n c i l of Group Francois de Rheologie (1965) (38) and p u b l i s h e d subsequently by the B r i t i s h Society of Rheology "A f l u i d i s a body which can remain i n e q u i l i b r i u m only when the imposed s t r e s s i s s p h e r i c a l . I f a s t r e s s d e v i a t o r e x i s t s , however s m a l l , , the body w i l l deform i n d e f i n i t e l y , there not e x i s t i n g a l i m i t i n g value at d e f i n i t e s t r a i n s " . "The y i e l d s t r e s s i s the value of the load ... above which permanent deformations appear. I t may depend on the p r e c i s i o n w i t h which the deformations can be detected. I t may depend on the loa d i n g h i s t o r y , the temperature, and, i n the case of an element, on the mean s t r e s s , the o r i e n t a t i o n s and r a t i o s of the p r i n c i p a l s t r e s s e s e t c . " As regards to m a t e r i a l s t u d i e d i n t h i s work, the c l a y paste i s t h e o r e t i c a l l y assumed to be one of those v i s c o p l a s t i c , incompressible i s o t r o p i c homogeneous substances c h a r a c t e r i z e d by the f o l l o w i n g general A i(37) model During a steady or even quasiasteady flow process P. . = - p6l. / + T. . , T. . = T:. . (T , C , D. .) w i t h 1/2 T. . T. . > T 2 (1) and at r e s t D. . = 0, 1/2 T.'. T. . < T 2 (2) 13 where: P.. = stress tensor p = i s o t r o p i c pressure 5 . . = Kronecker d e l t a i j T.. = str e s s deviator x = y i e l d stress o a d d i t i o n a l parameters D.. = rate of s t r a i n tensor B. Maximum Y i e l d Stress The y i e l d stress of a t h i x o t r o p i c system depends on the amount of time dependent t h i x o t r o p i c build-up i t has undergone; that i s f o r the same t h i x o t r o p i c system, the. y i e l d stress can be compared only under the same degree of build-up. of g e l structure. When the g e l structure i s f u l l y developed, the y i e l d stress i s c a l l e d the maximum y i e l d stress of the given system. The measuring" method for i t s determination i s the same as that for y i e l d stress except there i s a minimum aging" time re-quired f o r the maximum y i e l d stress measurement. The i d e n t i f i c a t i o n of the time f o r complete build-up of the g e l structure, i s made by an "aging" t e s t of y i e l d stress vs. time of rest (see 5.5 and 6.8). The minimum "aging" time when the g e l structure i s e n t i r e l y restored can'-be f i x e d so that the maximum y i e l d stress i s measured at s p e c i f i c aging time a f t e r loading i n the measuring device. In t h i s work, d i f f e r e n t systems, namely, Bentonite clay paste and clay paste with many kinds of s a l t and various s a l t concentration are to be studied. The re s t o r a t i o n rate of the g e l structure of the diverse systems w i l l supposely vary from one to another. So the question arises 14 whether aging experiments f o r each of the systems are necessary? Thanks to the nature of the system under study, when the s a l t concentration increases, the s i z e of the r e s i d u a l energy b a r r i e r i n the p a r t i c l e - i n t e r a c t i o n p o t e n t i a l curve i s reduced, and the rate of (34) p a r t i c l e l i n k i n g and s t i f f e n i n g of the suspensions increases . This means the minimum aging time for the system of clay paste without s a l t w i l l be longer than that f or systems with s a l t . Therefore, only one aging experiment for the former w i l l give an adequate aging time for a l l the other systems. C. Measurement Methods and Devices There are a large number of commercial viscometers on the (39) market. Van Wazer c o l l e c t e d a vast amount of information about most of them. I t w i l l only be necessary here to discuss general problems en-countered i n y i e l d stress measurements - types of instruments, measurement methods and t h e i r imperfections. 1. General D i f f i c u l t i e s Encountered i n Y i e l d Stress  Measurement (of clay suspension) a) Shear Stress D i s t r i b u t i o n Not Uniform In nearly a l l experimental deformations the shear stress d i s t r i b u t i o n i s not uniform. Thus, as the o v e r a l l stress i s increased, y i e l d i n g tends to occur not suddenly but progressively through the (32) specimen b) Local Y i e l d Stress Not Uniform A clay suspension, f o r example, i s composed of several 15 minerals with a wide v a r i e t y of p a r t i c l e sizes and shapes i n numerous d i f f e r e n t arrangements. Therefore, on a microscopic l e v e l i t may be expected that the l o c a l y i e l d stress w i l l vary considerably from point to point. When the weaker p a r t i c l e bonds have y i e l d e d the stress w i l l be transmitted only by the p a r t i c l e arrangements with higher y i e l d values. c) Concentration Gradients - Rate of Shear Relative movement of the s o l i d phase and f l u i d phase occurs when stresses are applied, f l u i d migrating from the higher - to the lower - stressed areas. Thus, the measured value of y i e l d stress de-(32) pends on the rate of stress applications d) P a r t i c l e Orientation Clay and any other platy type of p a r t i c l e s , unless f l o c c u l a t e d i n t o an edge-to-face str u c t u r e , tend to develop a degree of p a r a l l e l o r i e n t a t i o n ' , p a r a l l e l to any adjacent s o l i d surface that presses or s l i d e s against them. Hence, the^boundary layer of the sub--, stance may exhibit p h y s i c a l properties d i f f erenfrjf rom those of the bulk substance.? 5 Often t h i s layer i s predominantly f l u i d only and consequently the measured value of y i e l d stress i s an underestimate of the actual y i e l d stress of the material. I f we denote the components of the stress tensor a., and cl the forces of adhesion by cr„ then, i f i n the case of simple shear, > °i2 a s l i p P a S e w i l l occur, whatever the nature of surface forces and i f a^ £  a\2' t n e . substance adheres to the surface and no slippage (37) occurs 16 Another trouble encountered i n early e f f o r t s to measure the rh e o l o g i c a l properties of clay bodies was due to the fac t that any de-formation of a clay water mixture produces two i r r e v e r s i b l e changes: (1) o r i e n t a t i o n of the p a r t i c l e r e l a t i v e to the d i r e c t i o n of the com-pressive stresses and (2) increase of the strength due to the or i e n t a t i o n . Thus, a y i e l d stress measurement should s t a r t out with randomly oriented clay mixture and not with one which was predeformed through handling and which, therefore, was "shear-hardened"^^. 2. Types of Instruments There e x i s t many i n d u s t r i a l methods which at best allow some factors r e l a t e d to the y i e l d stress value to be determined. Most of the methods which provide such quantities' as hardness, r i g i d i t y , p l a s t i c i t y , consistency, etc. belong to t h i s category. They are s u i t -able as comparative, q u a l i t a t i v e methods but most of them cannot be analysed i n a quantitative or absolute sense. For r h e o l o g i c a l purposes, an instrument should be constructed i n which the deformation or flow pattern and boundary conditions are such that the required kinematic and dynamic quantities which appear i n a mathematical analysis of the problem can be measured. In consideration of t h i s , only the following types of instruments are discussed. a) Capillary-tube C a p i l l a r y viscometers of varied design are commonly used to measure the v i s c o s i t y of Newtonian or Bingham p l a s t i c (Newtonian with a y i e l d s t r e s s , see 3.1) l i q u i d s . In ca p i l l a r y - t u b e flow, the rate of shear and the shearing stress are not constant throughout the liquid; they vary between zero in the center of the tube and a f i n i t e value at the wall of the capillary ' b) Parallel-plate Parallel-plate viscometers, in which the plates are moved with respect to each other in one direction, meet the requirement that shear rate' is uniform, but i t is usually more practical to use a vis-cometer in which the plates are rolled up to form a set of concentric cylinders. c) . Rotational Concentric Cylinder At a given rate of rotation, the rate of shear in the sample between the cylinders is not s t r i c t l y constant, but i t varies only between narrow limits, particularly when the diameters of the cylinders are large and their clearance small. In plastic systems, slip of the bulk of the mass at the walls of cylinders may be pre-(42) vented by grooved cylinder(s) (45) Finke and Heinz explained the function of grooves from a semi-microscopic point of view. Byuusing grooved cylinders, the sub-stances in the grooves is excluded from the shear flow, and is therefore at rest with respect to the cylinder. The tangential stress of the cylinder is transmitted to the substance in the measuring gap from substance to substance at transition points which are the points where the grooves go over into the measuring gap. While with smooth cylinders, the tangential stress is transmitted to the substance in the measuring gap at the surface of contact between cylinder material and the test 18 substance. The cylinder w a l l surfaces cause inhomogeneity i n the sub-stance. In the.center of the gap each p a r t i c l e i s surrounded o n _ a l l sides by other i d e n t i c a l p a r t i c l e s , but this i s not the case i n the substance immediately adjoing the cylinder walls. Through these i r r e g u l a r i t i e s the smooth cylinder walls a l t e r the flow behaviour and cause slippage. ( 3 7 ) Vocadlo and Charles suggested the width of grooves be 10-40 times the.size of p a r t i c u l a t e aggregates and the depth s u f f i c i e n t to guarantee shear at the cylinder surface. The grooves must not be top narrow, otherwise the material may become modified. I t might be argued that the e f f e c t of a grooved surface may be s i m i l a r to that of a rough surface. However, t h i s i s not so. (43) Morrison and Harper showed that on an.inner cy l i n d e r covered with width "100 g r i t " abrasive paper a layer about 1 mm formed adjacent to the surface i n which p a r t i c l e s simply rotate. d) Cone and Plate Viscometer For small angles, the rate of shear across the c o n i c a l ( 3 9 ) gap may be considered constant . This holds for most p r a c t i c a l p l a t e -cone viscometers. No tedious cal c u l a t i o n s are required, but the e s s e n t i a l disadvantage i s that the plate-cone viscometer cannotl eliminate slippage e f f e c t s l i k e the r o t a t i o n a l concentric c y l i n d e r v i s -meter. e) P u l l i n g Viscometer Slippage s t i l l i s a problem. For d e t a i l s see Boardman and Whitemore's s t a t i c method i n the next section. 19 Owing to the above arguments, a r o t a t i o n a l concentric grooved cylinder viscometer i s the most f e a s i b l e instrument f or the measurement of y i e l d stress of a clay paste. 3. Measuring Methods f o r Y i e l d Stress Only the methods for r o t a t i o n a l concentric grooved cy l i n d e r viscometers w i l l be discussed. Boardman and Whitmore's s t a t i c method i s the exception because of i t s p r e v a i l i n g use i n R u s s i a ^ ^ . a) Dynamic Methods (1) Extrapolation of Flow Curve to Zero Shear Rate Using Data  Obtained at Higher Shear Rates (see 6.9) The l i n e a r extrapolation should be based on the actual flow curve, i . e . the r e l a t i o n s h i p between shear stress and shear rate. I f the i n s i d e cylinder i s rot a t i n g and the outside one i s (39) stationary, the shear rate" equation for simple power law i s derived i n as follows:-Shear rate = (co/lne) [1 + mine + (mine) 2:/3^ - (mlne)V45] (3) where: 'Ss = angular v e l o c i t y of the inner cylinder (bob), rad./sec. _ radius of cylinder (the outer cylinder) ,. n e = R /R; = T: .. , J,—7—r r T~-—J S »dimensionless c D radius of bob (the inner c y l i n d e r J 2 T = shear stress at the surface of bob, dyne/cm b ' d l h to., ,. . .. m = -r—z , dimensionless d In T b I f a log-log p l o t of co versus T i s a s t r a i g h t l i n e i t i n d i -b cates the flow follows a simple power law. When a f l o w c u r v e has been e s t a b l i s h e d , the u n c e r t a i n t i e s i n v o l v e d i n e x t r a p o l a t i o n t o z e r o s h e a r r a t e s h o u l d be checked f o r p o s s i b l e s i g n i f i c a n t change i n c u r v a t u r e i n t h e / u n i n v e s t i g a t e d range of s h e a r r a t e . As the s l i p p a g e i s p r e v e n t e d by grooved c y l i n d e r s the o c c u r e n c e of p l u g flow a t low s h e a r r a t e and the e x i s t e n c e of concen-t r a t i o n g r a d i e n t w i l l be e l i m i n a t e d . (2) A n a l y s i s o f t h e Torque Decay Curve The t o r q u e decay c u r v e i s o f t e n used t o determine y i e l d s t r e s s by c a l c u l a t i n g the s t r e s s c o r r e s p o n d i n g to the r e s i d u a l t o r q u e r e m a i n i n g when the v i s c o m e t e r i s s t o p p e d a f t e r a p e r i o d o f slow . r o t a t i o n . (37) However, V o c a d l o and C h a r l e s have s u g g e s t e d t h a t t h e sum o f the k i n e t i c and p o t e n t i a l energy o f the s e n s i n g system, f o r example the bob and s p r i n g , may i n f l u e n c e the t o r q u e decay c u r v e . b ) S t a t i c Methods I n o r d e r t o o b t a i n more r e l i a b l e v a l u e s of y i e l d s t r e s s , measurements under s t a t i c c o n d i t i o n s a r e p r e f e r a b l e . There a r e two methods t o be examined. (1) Boardman and Whitmore's S t a t i c Method f o r Y i e l d S t r e s s The a u t h o r s s u g g e s t e d the use of an a p p a r a t u s , i n which a body, e i t h e r a s phere o r a r e c t a n g u l a r l a m i n a , i s suspended i n the s u b s t a n c e t o be measured, from the end of a h o r i z o n t a l s p r i n g by means o f a t h r e a d . The o t h e r end of the s p r i n g i s a t t a c h e d r i g i d l y t o a b r a c k e t which can be moved v e r t i c a l l y u n t i l the body s t a r t s moving. This method has several disadvanges:-(a) the method determines some r e s i d u a l stress value which i s not w e l l defined, (b) i f the suspended body has some other shape than that of a lamina, the actual force i s not a simple function of the surface area. (c) even i n the case of a lamina the "creep" due to the ad-jacent layer may cause a r e d i s t r i b u t i o n of forces acting on the surfaces, (d) for p l a s t i c materials, Archimedes' p r i n c i p l e cannot be interpreted i n i t s c l a s s i c a l way. From Equation (1), i t i s obvious that forces acting on a body at rest are composed of two parts - one due to the i s o t r o p i c pressure and the other due to the stress deviator bounded 2 by the conditions that 1/2 T.. T.. < T . Consequently, i t i s rather d i f f i c u l t to determine the apparent weight experimentally. (37) (2) Vocadlo and Charles' S t a t i c method for Y i e l d Stress The apparatus used i s a s i m p l i f i e d Haake Rotovisco r o t a t i n g cylinder viscometer. (a) Moment Equation Mq = kARj^h [P T q + (1 - 3) x g] (4) where: M '= .'torque, on grooved cylinder k -1 + £<V'V2 b = depth of groove h = height of bob immersed i n f l u i d R^*= distance from center of bob to bottom of groove R^  = distance from centre of bob to r i b surface T G = shear force at surface of smooth cylinder 3 = y A A = A .+ An & s A = area of grooves per unit height, calculated at R A g = surface area of r i b s per unit height as calculated by summing i n d i v i d u a l arc length at R Equation (4) becomes M T = i n I. when x -> 0 (5) o k3AR^h s M T = , .n u when 3 = 1 or T = T (6) o kAR bh s o (b) Experimental Procedure i ) T = T No.slip occurs at the cylinder surfaces. The same values c .torqueMQ are.^obtaihed f o r the smooth cylinder and any of the grooved cy l i n d e r s . The y i e l d stress can be calculated from Equation (6). i i ) T < T Rough Method S' . o  x g should be f i r s t determined using the smooth cylinder. Subsequently, the torque measured, at a grooved cylinder w i l l allow the y i e l d stress to be calculated from Equation (4). i i i ) T < T Fine Method s o Values of the torque measured when the substance s t a r t s to 23 shear are p l o t t e d against the corresponding values of 3. Extrapolation of the data to 3 = 1, w i l l give the value of torque corresponding to the y i e l d s t r e s s x acting at radius R . o b v i ) x < T Super Fine Method s o v  For each 3, a set of r e s i d u a l s t r a i n values are p l o t t e d against the i n i t i a l torque values. The y i e l d stress i s then r e l a t e d to that value of Mq obtained by extrapolating the r e s i d u a l s t r a i n -torque data to zero r e s i d u a l s t r a i n . Then follow method i i i ) . In the procedures i ) , i i ) and i i i ) of Vacadlo and Charles'" method, the assessment of torque i s s t i l l by a semi-dynamic method. Their super f i n e method, academically speaking, i s an i d e a l one, but i t i s a very time consuming procedure. In t h i s method since three (or more) d i f f e r e n t 3 values and for each 3, f i v e s t r a i n values are generated, thus a time period of f i f t e e n aging periods i s needed for one y i e l d stress measurement. For a system i n which the minimum aging period required for maximum y i e l d stress i s twelve hours, as was the case i n t h i s work, i t would take more than a week to get one y i e l d stress value. D. P r a c t i c a l Method Considering the above techniques, a p r a c t i c a l method was constructed. 1. Grooved Bob and Cylinder with g ->• 1 (45) It was shown by Finke and Heinz's experiment that the e f f e c t i v e radius of the grooved cylinders with 3 1 i n the measuring -1 2 -range, shear rate = 0 - 6 0 sec and = 10 - 5,000.dynes/cm , i s not d i f f e r en t from the true radius , hence M x = r — (see Appendix IV) (7) 2 ^ h 2. Low Speed of Bob Bob speed i s such that there i s no plug-f low, the e x t r a -po l a t i on to zero shear rate i s not necessary and a y i e l d s t ress can be assessed w i th in experimental e r ro r (see 6.9) . 3. Hard Spring Hard spr ing w i l l g ive more sharp y i e l d s t ress point because (47) the load r e l axa t i on increases (see 6.5) . E. Bingham y i e l d Stress and P l a s t i c i t y These terms f requent ly occur i n the c lay l i t e r a t u r e , but are d i f f e r e n t i n nature from what was discussed as y i e l d s t r e s s . 1. Bingham y i e l d Stress A system d i sp lay ing a rheo log i ca l behavior represented by the curve i n F igure 1 i s s a id to exh ib i t Bingham p l a s t i c f low. I t i s very commonly observed i n d ispersed systems. When the s t r a i g h t - l i n e por t ion of the curve i s extrapolated to low shear r a t e s , i t i n t e r sec t s the shear-stress ordinate at a po int marked x , which i s c a l l the a Bingham y i e l d s t r e s s . X q i s the (true) y i e l d s t r e s s . Figure 1. Flow curve of Bingham plastic clay suspension (schematic). 26 2. P l a s t i c i t y (32) Moore defined p l a s t i c i t y as "the property that enables a material to be changed i n shape by the a p p l i c a t i o n of an external force without rupturing and to r e t a i n that shape when the force i s removed or reduced below a ce r t a i n value". Therefore, besides the concept of y i e l d stress there i s that of deformation without rupture i n the d e f i n i t i o n of p l a s t i c i t y . I t i s a very important q u a l i t y i n the ceramic industry. 3.2. (Cat)ioni. Exchange A. The Phenomena of Ion Exchange of Clay Minerals The property of ion exchange i s of very great fundamental and p r a c t i c a l importance i n a l l f l u i d s i n which clay materials are studied and used. Some s i g n i f i c a n t applications of ion exchange are given i n the following:-In the f i e l d of s o i l s , ease of t i l l i n g of s o i l i s frequently determined by the character of the exchangeable ion, and i t may be con-t r o l l e d by an exchange reacti o n . Thus, the presence of appreciable Na + i n a s o i l makes i t unsuitable for a g r i c u l t u r e . The replacement of the + 2+ Na by another i o n , usually Ca , w i l l generally make the s o i l s u i t a b l e for a g r i c u l t u r e . In oceanography the concentration of sodium i n sea water i s to a considerable extent a consequence of the cation-exchange pro-p e r t i e s of clay minerals which have accumulated i n the sea. The re-l a t i v e exchangeability of the common cations brought to sea and the pro-perty of some clay minerals to f i x K would lead to a concentration of sodium. In a l l the applied arts where clay minerals are used, or where the properties of clays are important, ion exchange i s of very great importance, because the p h y s i c a l properties of clay minerals are dependent to a large extent on the exchangeable ions c a r r i e d by a clay. For instance, the p l a s t i c properties of a clay or s o i l are very + 2+ d i f f e r e n t , depending on whether Na or Ca i s the exchangeable cation. Therefore, i t i s common p r a c t i c e i n the^brick industry to add soda ash to the p l a s t i c clay to improve i t s properties. Sometimes the construction engineer inadvertently causes an ion-exchange reaction by a s h i f t of water table or an emplacement of a mass of concrete, e t c . , r e s u l t i n g i n an unexpected change i n the properties of the s o i l . I f the changes i n the p l a s t i c , compaction and shrinkage properties from such exchange reactions are not foreseen, the consequences may be disastrous. B. Commonest Exchangeable Ions "f"2 -J~2 4~ In clay minerals the commonest cations are Ca , Mg , H , K +, NE* and Na +; anions are SO2", C l " , PO^" and N0~ ( 4 8 ) . C. Base Exchange, Cation Exchange and Ion Exchange Soon a f t e r the discovery was made i n 1850 that s o i l s have the property of exchanging calcium, magnesium and to a l e s s e r extent, ammonium and potassium, the term "base exchange" began to be applied to the process. 28 I t was many y e a r s a f t e r the p u b l i c a t i o n o f A r r h e n i u s 1 E l e c t r o l y t i c D i s s o c i a t i o n Theory i n 1887 t h a t s o i l s c i e n t i s t s began t o ap p l y t h i s concept t o s o i l r e a c t i o n s . Thus, i t became known t h a t the hydrogen i o n may tak&,part i n the exchange r e a c t i o n . I n view o f t h e im-p o r t a n c e o f the Hydrogen i o n i n the exchange p r o c e s s , and the f a c t t h a t c a t i o n exchange i s s i m i l a r i n p r i n c i p l e , whether the exchange i s between m e t a l l i c c a t i o n s o r whether hydrogen i o n s o r some organic c a t i o n s ex-change w i t h m e t a l l i c c a t i o n s , the term " c a t i o n exchange" i s t h e more a p p r o p r i a t e . (49 ) Not u n t i l 1931,did M a t t s o n show t h a t the c o n s t i t u e n t m i n e r a l s of many s o i l c l a y s a l s o e x h i b i t a n i o n exchange r e a c t i o n s . S i n c e then the g e n e r a l term " i o n exchange" has been used t o co v e r b o t h phenomena. V a s t l y more i n f o r m a t i o n i s a v a i l a b l e r e g a r d i n g c a t i o n ex-change than a n i o n exchange, and a l t h o u g h they w i l l be c o n s i d e r e d s e p a r a t e l y , o n l y a s h o r t d i s c u s s i o n o f a n i o n exchange i s g i v e n . D. C a t i o n Exchange 1. H i s t o r y and Exchange R e a c t i o n s As i n d i c a t e d by K e l l y ^ r e v i e w e d the h i s t o r y of c a t i o n exchange i r i d e t a i l , the d i s c o v e r y t h a t s o i l s have the power o f exchanging c a t i o n s w i t h s o l u t i o n s c o n t a i n i n g o t h e r c a t i o n s was the outgrowth o f o b s e r v a t i o n s d a t i n g back i n t o the remote p a s t . F o r example, i t has been known f o r c e n t u r i e s t h a t l i q u i d manures become i d e c o l o r i z e d and d e o d o r i z e d when f i l t e r e d through s o i l s . Thompson (1850) is g e n e r a l l y c r e d i t e d w i t h b e i n g the f i r s t p e r s o n who s y s t e m a t i c a l l y s t u d i e d c a t i o n exchange. S i n c e 1854, when Thomas Way f o r m u l a t e d the concept of base exchange, the p h y s i c a l and c h e m i c a l n a t u r e of the f o r c e s by which c a t i o n s 29 are held has been debated. Way favored the chemical view. L i e b i g , on the other hand, argued that the absorption of gases by charcoal provided a closer analogy^"^. Since 1930, the trend has been toward formulation i n physicochemical terms, although much empiricism has s t i l l been needed. The l a t t e r group designated the exchangeable cations as adsorbed. I n i t i a l l y Freundlich's, adsorption equation was used to c a l -culate the adsorption isotherms. Later, c e r t a i n modifications of t h i s equation were found that express the data more p e r f e c t l y . In the chemical approach, the law of mass action was used to give a good explanation of the exchange phenomena^^. i Some attempts were also made to explain the exchange by s t a -t i s t i c a l models and thermodynamic formulations. Another very d i f f e r e n t mechanism - d i r e c t exchange - was suggested by K e l l y ^ " ^ and by Jenny and O v e r s t r e e t ^ 2 ) a n ( j proven l a t e r (53) by Jenny and h i s co-workers , using tracer elements. They claim that ion exchange can take place d i r e c t l y between plant roots and clays with-out the intermediate s o l u t i o n of the ions., The cation moves d i r e c t l y from the clay to the plant i n return for another ion, which moves d i r e c t l y from the plant to the clay. This probably requires that ions be able to migrate on clay-mineral surfaces from exchange spot to exchange spot. (54) Jenny postulated that exchangeable ions are i n a continuous state of thermal a g i t a t i o n , and when neighboring zones of a g i t a t i o n overlap, there should be an opportunity f o r a given cation to jump from one spot to another, provided that there i s another ion of l i k e charge simultaneously jumping i n the opposite d i r e c t i o n . 30 It may be that d i r e c t exchange can take place between clay minerals and inorganic materials as w e l l as between clay mineral and plants. This was proved by many investigators ^"^'"^ . 2. Rate of Reactions a) Rate of Reactions Up to the present, cation exchange reactions i n clay systems have proven to be rapid b) Factors A f f e c t i n g the Rate of Reaction (1) The Clay Mineral (for the d e f i n i t i o n of Bentonite, k a o l i n i t e , montmorillonite and smectite, see Appendix I ) . (a) P o s i t i o n of Exchangeable Ions (see also section 3) Exchange on the edge of the p a r t i c l e s , as i n k a o l i n i t e can take place quickly, but penetration between the sheets of montmorillonite requires more time. (b) L a t t i c e Generally, reactions involving l a t t i c contraction are more d i f f i c u l t to push to completion than those jreactions involving l a t t i c e repulsion. When the exchange reaction i s accompanied by swelling e.g., i n montmorillonite, the change from one stable i n t e r l a y e r . distance to another requires a c e r t a i n a c t i v a t i o n energy and a hysteresis phenomena may be observed. (2) M o b i l i t y of Ions Ion exchange i s a d i f f u s i o n process, and i t s rate depends on the ions. Thus,ion-exchange k i n e t i c s has no resemblance to chemical reaction k i n e t i c s i n i t s usual sense. L o w ^ ^ studied the influence of adsorbed water on exchange-able-ion movement i n montmorillonite clays and concluded that e l e c t r i c a l i n t e r a c t i o n between ions and clays appears to have l i t t l e e f f e c t on the a c t i v a t i o n energy and the most important factor governing exchangeable-ion movement i n the pores of clay-water system i s the structure of the adsorbed water. (3) Temperature (58)' Wilklander stated that temperature increases s l i g h t l y the rate of rapid exchange. For slow exchange, temperature i s l i k e l y to have a greater e f f e c t . 3. Causes of Cation Exchange and O r i g i n of P a r t i c l e Change G r i n / 4 ^ gives a very d e t a i l d e s c r i p t i o n of t h i s phenomena. There are three general causes:-a) Broken Bonds (1) O r i g i n The valences of the l a t t i c e atoms which are exposed at the surface are balanced by adsorbed cations. Since they are not completely compensated as they are i n the i n t e r i o r of the l a t t i c , these surfaces are c a l l e d "broken bonds" surfaces. (2) P o s i t i o n Usually around the edges of the s i l i c a - a l u m i n a units. Broken bonds are probably the major cause of exchange capacity in^the k a o l i n i t e minerals, and are responsible f or a r e l a t i v e l y small portion (± 20%) of cation-exchange capacity i n smectites and ver-mi c u l i t e s (the remainder might r e s u l t from s u b s t i t u t i o n within?the l a t t i c e ) (3) Character (58) Wilklander reviewed much of the work on the broken bonds on clay mineral u n i t s . He concluded that hydroxyls would be attached to the s i l i c a t e s of broken tetrahedral units and that the hydroxyls would be ioni z e d s i m i l a r l y to ordinary s i l i c i c a c i d , that i s , SiOH + ^ 0 =.SiO + H^0+, causing a negative charge on the l a t t i c e . The p o s i t i v e charges may o r i g i n a t e from exposed octahedral groups which react as base by accepting protons, thus requiring a p o s i t i v e charge. (4) Factors i n Relation to Broken Bonds (a) £H The negative charge would grow and the p o s i t i v e charge de-crease with r i s i n g pH as a r e s u l t of increasing i o n i z a t i o n of the acid groups and decreasing proton addition to the basic groups. (b) P a r t i c l e Size. Decreasing p a r t i c l e s i z e would increase the number of broken bonds and hence the exchange capacity due to; t h i s cause. (c) L a t t i c e D i s t o r t i o n and Degree of C r y s t a l l i n i t y L a t t i c e d i s t o r t i o n would tend to increase the number of broken bonds, and the exchange-^ capacity would be expected to increase as the de-gree of c r y s t a l l i n i t y decreased. 33 b) Substitution Within the. L a t t i c e Structure (1) O r i g i n Substitution of t r i v a l e n t aluminum for quadrivalent s i l i c o n i n the tetrahedral sheet and of ions of lower valence, p a r t i c u l a r l y magnesium, for t r i v a l e n t aluminum i n the octahedral sheet r e s u l t i n un-balanced changes i n the s t r u c t u r a l units of some clay minerals. Some-times such substitutions are balanced by other l a t t i c e charges, for example, OH for 0, or by f i l l i n g more than two-thirds of the possible octahedral p o s i t i o n s , but frequently they are balanced by adsorbed cations. (2) P o s i t i o n Exchangeable cations r e s u l t i n g from l a t t i c e s u b s t i t u t i o n s are to be found mostly on cleavage surfaces, e.g., the basal cleavage surfaces of the layer clay minerals. Since the charges r e s u l t i n g from substitutions i n the octahedral sheet would act through a greater distance than the charges r e s u l t i n g from substitutions i n the tetrahedral sheet, i t would be expected that cations held because of the l a t t i c e s ubstitutions would be bounded by a stronger force than those held by forces r e s u l t i n g from substitutions i n the octahedral sheet. In some cases, cations held by forces due to s ub st it ut ions of aluminum for s i l i c o n seem to be s u b s t a n t i a l l y non-exchangeable, e.g., the potassium i n the micas. In the clay minerals, replacements i n the octahedral layer are probably the major substitutions causing cation-exchange capacity. In montmorillonite,subistitutions w i t h i n the l a t t i c e . c a u s e about 80 per cent of the t o t a l cation-exchange capacity. 34 c) The Hydrogen of Exposed Hydroxyls The hydrogen of exposed hydroxyls (which are an i n t e g r a l part of the structure rather than due to broken bonds) may be replacedby a . cation which might be exchangeable. However, i t seems probable that such hydrogen would be r e l a t i v e l y t i g h t l y held as compared with those associated with broken bonds and hence, i n the main, would not be re-placeable. This cause of exchange capacity would be important for k a o l i n i t e because of the presence of the sheet of hydroxyls on one side of the basal cleavage plane. 4. Cation Exchange Capacity M a r s h a l l o f f e r e d a very i n t e r e s t i n g discussion on t h i s subject. a) Factors Influencing Cation Exchange Capacity As shown i n the l a s t section, the factors are:-(1) pH. (2) P a r t i c l e s i z e . (3) L a t t i c e d i s t r i b u t i o n and degree of c r y s t a l l i n i t y . (4) Cationic bonding force. In addition to these, many others a f f e c t the apparent exchange capacity:-(5) F i x a t i o n of Cations and of Anions (high c a t i o n i c bonding force i s one of the reasons for f i x a t i o n ) . (6) . Geometrical Hindrance by blocking of exchange s i t e s . (7) Anchorage of Cations by a d d i t i o n a l forces superimposed upon coulumbic e f f e c t s . * 35 (8) Special Properties of Framework Structures i n r e l a t i o n s to p a r t i c u l a r cations or to s a l t molecules. (9) Temperature The exchange capacity i s reduced by heating, but the reduction i s not uniform and varies with the cation present. The phenomena i s interpreted to mean that, when the clay i s heated, the exchangeable cations tend to move insi d e the l a t t i c e . (10) R e p l a c e a b i l i t y of Exchangeable Cations Under a given set of conditions, various cations are not equally replaceable and do not have the same replacing power. The re-placement seri e s v a r i e s , depending not only on the experimental conditions but also on the cations involved,and on the kind of clay material. R e p l a c e a b i l i t y i s not yet completely understood, but i t i s known that i t i s c o n t r o l l e d by a considerable number of f a c t o r s . Much has been learned about the nature and the influence of each of the f a c t o r s . (a) E f f e c t of Concentration In general, increased, concentration of the replacing cation causes greater exchange by that cation. The e f f e c t s of concentration de-pend on the kind of cation that i s being replaced and also on the valence of the cation, as w e l l as on other f a c t o r s . This factor i s hence very com-plex. (b) Population of Exchange Positions Jenny and Ayers and l a t e r Wilklander i n considerable d e t a i l , showed that the ease of release of an ion depends not only on the nature of the ion i t s e l f , but also upon the nature of the complimentary 36 ions f i l l i n g the remainder of the exchangeable p o s i t i o n s , and on the degree to which the replaced ion saturates the exchange spots. Therefore, Wilklander showed that, as the amount of exchangeable calcium on the clay mineral becomes l e s s , the calcium becomes more and more d i f f i c u l t to re-lease. Sodium, on the other hand, tends to become easier to release as the degree of saturation with sodium become l e s s . (c) Nature of Anion i n Replacing Solution M a r s h a l l r e p o r t e d that considerable v a r i a t i o n i n cation-exchange capacity i s obtained by leaching with d i f f e r e n t neutral s a l t s of a given ion. The whole matter of the e f f e c t of anion i s complicated by the p o s s i b i l i t y of the formation of "basic" s a l t s with the clay and a soluble anion. (d) Nature of the Ion i ) Valence of the Ion Other things being equal, the. higher the valence of the ion, the greater i s i t s replacing power and the more d i f f i c u l t i t i s to d i s -place when already present on the clay. Hydrogen i s an exception since for the most part i t behaves l i k e a divalent or t r i v a l e n t ion. i i ) Atomic Number of the Ion K e l l y p o i n t e d out that the replacing power increases q u a l i t a t i v e l y with atomic number i n ions of the same valence. i i i ) Size of the Nonhydrated Ion In ions of the same valence, replacing power tends to i n -crease as the s i z e of the ion increases, i . e . , the smaller ions are less 37 t i g h t l y held than the larger ones. An exception to the e f f e c t of ion s i z e occurs i n those ions which have almost the correct s i z e and co-ordination properties to f i t on the ba s a l oxygen sheet of the larger clay minerals. iv) Size of the Hydrated Ion It was suggested that the s i z e of the hydrated ion, rather than the s i z e of the nonhydrated ion,controls r e p l a c e a b i l i t y , but no con-c l u s i o n can be drawn at the present time, because the matter o f the hy-dration of the adsorbed ions i n clay-water systems i s a matter of much con-troversy. v) P o l a r i z a t i o n of the Ion Rep l a c e a b i l i t y i s r e l a t e d to the p o l a r i z a t i o n of the ion, with increasing p o l a r i z a t i o n being accompanied by increasing d i f f i c u l t y of exchange. Also, highly polar ions are thought to be held closer to the adsorbing surface. P o l a r i z a t i o n increases as the valence increases and as the : s i z e of the ion decreases. v i ) E f f e c t of Heating I t was indicated that heating to moderate temperatures re-duces the cation-exchange capacity but changes the r e l a t i v e r e p l a c e a b i l i t y of the cations. It seems l i k e l y that the exchange i n r e p l a c e a b i l i t y of cations when heated would be r e l a t i v e l y greater f o r the expanding-lattice minerals than f o r those minerals i n which the capacity i s due l a r g e l y to broken bonds. At elevated temperatures, when there i s l i t t l e or no water present between basal layers i n addition to the sorbed cations, the s i z e of the ion and i t s geometrical f i t into the structure of the oxygen layers are probably major factors i n determining r e p l a c e a b i l i t y . v i i ) Nature of the Clay Mineral There was not a s i n g l e r e p l a c e a b i l i t y s e r i e s c h a r a c t e r i s t i c of a l l clay minerals, but rather separate r e p l a c e a b i l i t y series f or the various clay minerals. b) Determination of Cation Exchange Capacity and Exchangeable  Cations In view of the foregoing mentioned complications, accurate determinations of cation exchange capacity and exchangeable cations are very d i f f i c u l t to accomplish. L i t e r a l l y dozens of methods have been suggested, and a tremendous amount of time has been spent on t h i s problem. K e l l y and Peech et a l ^ " * " ' ^ 2 ^ considered i n d e t a i l the various methods and pointed out various p i t f a l l s . The determination of cation exchange capacity i s at best a more or le s s a r b i t r a r y matter, and no high degree of accuracy can be claimed W e i s s d i s c u s s e d minutely the problem of accurate deter-minations of cation-exchange capacity and showed the wide v a r i a t i o n s i n values obtained by using d i f f e r e n t methods. (49 73) This i s exactly what was emphasized by Mattson ' who stated that exchange capacity denotes the t o t a l amount of cations that can be exchanged under a given set of conditions and not n e c e s s a r i l y the amount that could be exchanged under other conditions. However, K e l l y l a i d down the f o l l o w i n g g e n e r a l p r i n c i p l e s R e g a r d l e s s o f the k i n d o f exchange m a t e r i a l b e i n g d e a l t w i t h , whether s o i l o r any o t h e r k i n d o f s u b s t a n c e , the q u a n t i t a t i v e d e t e r -m i n a t i o n o f the exchangeable c a t i o n depends on the f u l f i l m e n t o f t h r e e c o n d i t i o n s : -(1) i Complete r e p l a c e m e n t o f a l l exchangeable c a t i o n s by some c a t i o n s which a r e n o t p r e s e n t i n the sample. (2) A c c u r a t e a n a l y s i s o f the s o l u t i o n o b t a i n e d . (3} D e t e r m i n a t i o n o f , and s u i t a b l e c o r r e c t i o n f o r , t h e c a t i o n a t h a t pass i n t o s o l u t i o n from s o l u b l e s u b s t a n c e s o r by d e c o m p o s i t i o n o f some s u b s t a n c e s i n the sample. In any c a s e , the amount o f NH* adsorbed upon l e a c h i n g the s o i l t h o r o u g h l y w i t h a n e u t r a l normal ammonium s a l t s o l u t i o n , w i t h the p o s s i b l e e x c e p t i o n o f s o i l r i c h i n humus, i s p r o b a b l y as a c c u r a t e a measure o f c a t i o n - e x c h a n g e c a p a c i t y a t pH'7 as can be found. The c l a s s i c a l method o f l e a c h i n g , washing, and subsequent a n a l y s i s always i n v o l v e s a t l e a s t two c a t i o n s , each o f which may impose s p e c i a l c h a r a c t e r i s t i c s ^ ^ . B e s i d e s t h i s , t h e a n a l y t i c a l method i s g e n e r a l l y v e r y t e d i o u s . The use o f s p e c t r o s c o p y f o r the a n a l y s i s o f the i o n s i n t h e r e p l a c i n g s o l u t i o n has i n r e c e n t y e a r s p r o v i d e d s a t i s -' t o r y d a t a i n a - v e r y s h o r t t i m e , p a r t i c u l a r l y f o r some o f t h e a l k a l i i o n s and c a l c i u m . 5. C a t i o n E f f e c t on S w e l l i n g o f C l a y In g e n e r a l , the i n t e r p a r t i c l e m o l e c u l a r s w e l l i n g d e -m o n s t r a t e d by X-ray d i f f r a c t i o n o f m o n t m o r i l l o n i t e c l a y s does not account for the t o t a l swelling observed. Thus a considerable and of ten dominant component i s that of the i n t e r p a r t i c l e water. Both components are s e n s i t i v e l y affected by:-a) Nature of the Exchange Cation b) P o l a r i t y of the L i q u i d Taken Up C 6 2 63} Winterkorn and Bayer ' showed the magnitudes of the differences they found. Uptake by the non-polar carbon t e t r a c h l o r i d e was assumed to be c a p i l l a r y only. Values above t h i s were ascribed to swelling. Water intake (c.c./gm) by L i - , Na-, Ba-, Ca- and H-Bentonites are 10.77, 11.08, 8.55, 2.50, 2.20. Except the two factors mentioned i n the foregoing, there are s t i l l a few others which w i l l influence the i n t e r l a y e r hydration, namely, c) S i t e of Negative Charge A predominant charge on the s i l i c a , with i t s strong p o l a r i z i n g e f f e c t , would tend to favor v e r m i c u l i t e - l i k e layers having a r e l a t i v e l y small tendency to separate. A corresponding charge on the inner octahedral layer would be less capable of holding the s i l i c a t e , layers together, so that a higher hydration and ultimate dispersion should r e s u l t . d) Strength of the Individual Linkage This i s the linkage which operates from one s i l i c a t e sheet, through the interleaved cation and water layer, to the next. When the clay i s f i r s t formed i n nature, the structure w i l l accommodate i t s e l f as nearly as possible to the conditions c a l l e d for under Pauling's r u l e ; that i s , the charges should be n e u t r a l i z e d over the shortest possible distances. The valence' of the interleaved cation w i l l then influence the s p a t i a l .^distribution of charges on the s i l i c a t e l a y e r s . I f the cation i s diva l e n t , the charges on the s i l i c a t e layers w i l l tend to occur i n p a i r s . This s i t u a t i o n w i l l s t i l l p r e v a i l when the o r i g i n a l divalent cation i s l o s t by exchange and two monovalent cations take- i t s place. Such a surface might be expected to show a smaller i o n i c d i s s o c i a t i o n than one with the same cation but which had o r i g i n a l l y been sythesized i n the presence of a monovalent exchange ion. E. Anion Exchange M a t t s o n ( 4 9 ) , R a v i k o v i t c h ( 6 4 ) , S c a r s e t h ( 6 5 ) T o t h ( 6 6 ) and many others have shown that the constituent minerals of many s o i l clays exhibit anion-exchange reactions. . The i n v e s t i g a t i o n of anion-exchange reactions i n s o i l s i s very d i f f i c u l t , p r i m a r i l y because of the p o s s i b i l i t y of the decomposition of the clay minerals i n the course of the reaction. There seem to be three types of anion exchange i n clay minerals, as follows:-1. Replacement of OH Ions McAuliffe and co-workers using deuterium-tagged hydroxyls, showed conclusively that the OH ions of a clay mineral surface can enter ( 68^ i n t o exchange reactions. Dickmanand Bray presented very c l e a r evidence f o r the replacement of hydroxyls by f l u o r i n e i n k a o l i n i t e . Contrary to the case with chlorides, bromides and iodides, the f l u o r i d e ion i s strongly s p e c i f i c i n t h i s uptake. Here i s a c l a s s i c a l case of geometrical accommodation, the f l u o r i d e ion being very close to hydroxyl 42 i n s i z e . In the case of exchange due to replacement of OH ions, and i n general the only factor preventing complete s u b s t i t u t i o n i s the f a c t that many OH ions are with i n the l a t t i c e and therefore, not accessible. 2. Geometry of the Anion i n r e l a t i o n to the geometry of the clay-mineral structure u n i t s . Anions such as..' phosphate, arsenate, borate, etc., which have about the same s i z e and geometry as the s i l i c a tetrahedron, may be ad-sorbed by f i t t i n g on to the edges of the s i l i c a tetrahedra sheets and growing as extensions of these sheets. Other anions such as s u l f a t e , c h l o r i d e , n i t r a t e , etc., because t h e i r geometry do not f i t that of the s i l i c a tetrahedra sheets, cannot be adsorbed. For both types of anion exchange, anion exchange would take place around the edges of the clay minerals and i n the case of the clay minerals l i k e k a o l i n i t e i n which cation exchange i s due to broken bonds, the cation-and anion-exchange capacities should be s u b s t a n t i a l l y equal. In the case of smectite and vermiculite i n which cation capacity i s due mostly to l a t t i c e s u b s t i t u t i o n s , anion capacity should be only a small f r a c t i o n of the cation exchange capacity. 3. Anion-Exchange Spots as w e l l as cation-exchange spots on basal plane surfaces of the clay minerals. Schofield^ 9'~^® J indicated that i i i strongly acid s o l u t i o n s , clays can takeeup both potassium and chloride ions, the former g r e a t l y predominating, and that both the K + and C l are. exchangeable f o r other 43 cations and anions. He explained that such a c t i v e anion-exchange positions would be due to unbalanced charges wi t h i n the l a t t i c e , e.g., an excess of aluminum i n the octahedral p o s i t i o n s . G r i m ^ ^ commented that i t i s d i f f i c u l t to see how t h i s could be, since p o s i t i v e and negative d e f i c i e n c i e s would tend to balance each other, unless they occurred at considerable distances from each other. A further f a c t o r complicating anion-exchange studies i s that any free or exchangeable i r o n , aluminum, or a l k a l i n e earths present i n the clay may form insoluble s a l t s with anions, and i t i s very d i f f i c u l t to separate the e f f e c t s due to such reactions which may be due to re-actions with the clay minerals. 3.3. O r i g i n of Y i e l d Stess of Clay Suspension A. O r i g i n of Y i e l d Stress Some p l a s t i c systems have a y i e l d stress which decreases i f the system i s subject to mild v i b r a t i o n . This phenomenon, as was mentioned before, i s c a l l e d "thixotropy". The shear stress i s r e l a t e d to the gel structure formed by the t h i x o t r o p i c suspension a f t e r a c e r t a i n period of s t a n d s t i l l . So f a r as an explanation of g e l structure i s concerned, there are e s s e n t i a l l y three schools of thought. One group of s c i e n t i s t s , i n ('41) p a r t i c u l a r F r e u d l i c h , von Engelhart and Hauser -' , assume long range e l e c t r i c a l forces which permit the i n d i v i d u a l p a r t i c l e s to i n t e r a c t over distances i n the order of 1000 angstroms. Another group, Usher, Kuhn and Hofmann^-^ prefer a mechanical 44 p i c t u r e according to which the p a r t i c l e s touch one another, adhere on contact, .and b u i l d up a spacious network resembling a house of cards. A t h i r d group explains the rheology of the clay-water mixture by assuming th a t the water which surrounds the clay p a r t i c l e s becomes r i g i d . This view i s shared by Marcey^"^, M c B a i n ^ ^ , Grim and C u t h b e r t ^ ^ . (78) E l e c t r i c a l conductivity measurement by McDowell and Usher of a suspension of graphite i n an organic medium showed that the s o l i d i -f i c a t i o n of the suspension was caused by d i r e c t contact of the p a r t i c l e s (79) or t h e i r forming a house of cards. Hofmann and others claimed a proof of p a r t i c l e contact i n clay gels. Aerogels were made of a Bentonite hydrogel by freeze drying, i n which the o r i g i n a l structure of the hydrogel i s thought to be undistrubed since the pores are not collapsed by the receding meniscus as i s the case i n the normal drying of a g e l . The aerogels had indeed good adherence and p r a c t i c a l l y the same volume as hydrogels, but van O l p h e n ^ ^ indicated by experiment that secondary changes had taken place i n the gels during the freeze drying pro-cess. Therefore, Hofmann's experiment does not supply the d e f i n i t e proof of p a r t i c l e contact i n hydrogels. The strongly anisodimensional character of clay minerals make i t p o s s i b l e for a few per cent of s o l i d matter to form a house of cards structure which has a very large volume. This explanation, however, does not explain why t h i s phenomenon can also appear i n a 0.05% montmorillonite _ (81) suspension i n water (41) Hauser and h i s associates have greatly contributed to the e l u c i d a t i o n of the mechanism of the s o l - g e l transformation by ob-serving the process by the ultramicroscope. The Brownian molecular motion comes to a s t a n d s t i l l and i n t r u l y t h i x o t r o p i c systems of highly dispersed Bentonite f r a c t i o n s , the p a r t i c l e s which have ceased to move seem to be c l e a r l y separated from each other by the water. The f i n d i n g of Hauser are i n no way i n contradiction to the (26) findings of Hofmann who studied suspensions which contained higher con-centration of clay, a condition which i s conducive to the formation of a "house of cards" structure. As f o r the t h i r d group's explanation, van Olphen argued that the o r i e n t a t i o n e f f e c t of the charged p a r t i c l e s on the water dipoles can be expected to be s i g n i f i c a n t only up to a few water-molecular d i a -meters, away from the surface. However, the i n t e r p a r t i c l e distances i n gels are often very large and beyond any sensible range of hydration forces emanating from the surfaces. In consideration of these theories, i t would be preferable to follow the f i r s t theory for the very d i l u t e suspensions and the second theory f o r the concentrated suspensions. How^the g e l structure i s formed by the platy clay p a r t i c l e s through various forces w i l l be discussed i n the subsequent sections. B.' O r i g i n of p a r t i c l e Charge It was analysed i n d e t a i l , i n 3.2 that the p a r t i c l e charge i s caused by "broken bonds", by substitutions within the l a t t i c e and by hydrogen of exposed hydroxyls. 46 C. Possible Bonding Forces P a r t i c l e association i n s a l t solutions i s caused by general van der Waals a t t r a c t i o n forces which operate between the atoms of the two p a r t i c l e s . The t o t a l a t t r a c t i v e force between the p a r t i c l e s i s obtained by the summation of a l l a t t r a c t i v e forces" between a l l atom p a i r s . Since t h i s force i s p r a c t i c a l l y independent of the s a l t content of the l i q u i d , i t i s equally e f f e c t i v e i n fresh-water systems. However, p a r t i c l e a s s o c i -a t i o n i n a fresh-water s o l u t i o n i s prevented by repulsive forces between the p a r t i c l e s . These forces are a r e s u l t of the e l e c t r i c charges on the surfaces of the p a r t i c l e s . They are c a l l e d double-layer repulsion forces. Besides these two long-range forces, there i s another short-range re-p u l s i v e force to which there are two possible contributions. One, the Born repulsion, becomes e f f e c t i v e as soon as protruding l a t t i c e points or regions come into contact. I t r e s i s t s the interpenetration of the c r y s t a l l a t t i c e s . A second short-range repulsive i s the r e s u l t of s p e c i f i c ad-sorptive forces between the c r y s t a l l a t t i c e and the molecules of the l i q u i d medium, i . e . , water. Owing to such adsorptive forces, usually one or two monomolecular layers of water are held rather t i g h t l y by the p a r t i c l e sur-face. These water layers must be desorbed when the p a r t i c l e s approach each other so c l o s e l y that there i s no longer room for the adsorbed water layers. Since the desorption requires work, the dehydration of the surface mani-fests i t s e l f by a short-range rep u l s i o n - s o l v a t i o n repulsion. 1. yan, der Waals A t t r a c t i o n The a t t r a c t i o n arises from the temporary dipoles set up by the r e l a t i v e vibrations of the electrons and n u c l e i of the atoms near the surface. For two atoms, the van der Waals a t t r a c t i o n force i s i n v e r s e l y 47 proportional to the seventh power of the distance, (or to the sixth power for the attractive energy), but for two spherical particles, the force is inversely proportional to the third power of the distance he-rs ^ay>4/~ o^ ~ tween the surfaces, and the attractive energy therefore to the second of that distance (see Figure 2 in section 3 ) . 2. Electric Double Layer The el e c t r i c a l charge of small particles suspended in water (82) was discovered by Quincke in (1861) when he observed that these particles migrate toward one pole of a battery (cataphdresis or electrophoresis). (83) Twenty years later von Helmholtz developed his theory of the electrical double layer. In order to account for the various electrokinetic phenomena, Gouy^^ and Freundlich and Rona^"^ proposed a modification of the Helmholtz concept. a) Gouy Model of the Electric Double Layer Gouy (1910) suggested that the electric double layer consists of a surface charge and a compensating counter-ion charge. The counter-ions of the double layer are subject to two opppsThg'tendencies. Electro-static forces attract them to the charged surface, whereas diffusion tends to bring them away from the surface toward the equilibrium solution, where their concentration is smaller. Simultaneously, ions of the same sign as the surface charge are repelled by the surface and back diffusion from the equilibrium solution toward the surface counteracts the electric re-pulsion like an atmospheric distribution, the concentration of the counter-ions near the particle surface is high, and i t decreases with increasing 48 distance from the surface. More p r e c i s e l y formulated, the " d i f f u s e l a y e r " does not merely include an excess of ions of opposite sign; simultaneously, there i s a deficiency of ions of the same sign i n the neighbourhood of the surface since these ions are e l e c t r o s t a t i c a l l y r e p e l l e d by the p a r t i c l e . There-fore, one speaks of the adsorption of counter-ions and the negative adsorption of ions of the same sign. The Gouy model contains some u n r e a l i s t i c elements. For example, the ions are treated as point charges, and any s p e c i f i c e f f e c t s r e l a t e d to ion s i z e are neglected. S p e c i f i c i n t e r a c t i o n s between the surface and the counter-ions and the medium are not taken into consideration. Although many c o l l o i d chemical phenomena can be s u c c e s s f u l l y interpreted i n a general wayton the basis of the Gouy model, deviations from the general conclusions of the theory are frequently encountered with s p e c i f i c c o l l o i d a l systems. Evidently, the double-layer model must be r e f i n e d i n order to explain such deviations. Some of these refinements are given i n the following: b) Stern's Model of the E l e c t r i c Double Layer Stern considers that, contrary to the Gouy model, the distance of closest approach of a counter-ion to the charge surface i s l i m i t e d by the s i z e of these ions. Between the plane i n which the surface charge i s located and the plane of the centers of the counter-ions which are clo s e s t to the surface, there i s no charge. The part of the double layer be-tween these planes may be considered as a molecular condenser. In t h i s "Stern-layer" the e l e c t r i c a l p o t e n t i a l decreases l i n e a r l y with the distance from the surface, from a value $ at the surface to a value $ , which i s ' o s' c a l l e d the "Stern p o t e n t i a l " . The counter-ions are s t a t i s t i c a l l y d i s t r i b u t e d over the Stern layer charge closest to the surface and a Gouy d i f f u s e layer outside the Stern layer i n the s o l u t i o n . A s p e c i f i c a t t r a c t i o n between the surface and the counter-ions may be introduced i n the form of a s p e c i f i c ad-sorption p o t e n t i a l of the counter-ions at the surface. Usually, i n the Stern model, a decrease of the d i e l e c t r i c constant of the medium i n the high f i e l d strength of the molecular con-denser i s accounted f o r . The computation of the energy of i n t e r a c t i o n of two Stern-Gouy layers i s somewhat more complicated than that for Gouy layers be-cause of the changes occurring i n the charge d i s t r i b u t i o n and i n $ g. /•QC\ However, i t has been shown by Mackor that, for moderate- i n t e r a c t i o n , the r e p l u l s i v e energy can be computed to a good approximation as though one i s merely dealing with the i n t e r a c t i o n of two Gouy layers with a constant p o t e n t i a l which i s equal to the value of § when the p a r t i c l e s are at i n f i n i t e separation. This r e s u l t explains why the theory based on the simple Gouy mo'del i s s t i l l s a t i s f a c t o r y in^many cases. However, when s p e c i f i c adsorption of counter-ions occurs, the Stern model must be applied. There are i n d i c a t i o n s that s p e c i f i c counter-ion adsorption often occurs i n clay systems, therefore, Stern's model i s of i n t e r e s t i n clay c o l l o i d chemistry. Obviously, s p e c i f i c i n t e r a c t i o n s between a surface and d i f f e r e n t species of counter-ions w i l l be of considerable consequence for the counter-ion exchange equilibrium. c) Corrections of the Gouy Theory According to Bolt Another approach which gives the Gouy theory more p h y s i c a l (86) r e a l i t y has been presented by Bolt . He corrected the o r i g i n a l Gouy theory f or several secondary energy e f f e c t s , e.g.,the Coulombic i n t e r -action energy between the; ions ,;the energy of p o l a r i z a t i o n of the ions i n the e l e c t r i c f i e l d , and the. repulsive energy caused by non-Coulombic i n t e r a c t i o n between the ions. The e f f e c t of the f i e l d strength on the d i e l e c t r i c con-stant of the medium, which i s most important near the surface where the f l u i d strength i s highest, i s taken care of by an empirical expression re-l a t i n g the d i e l e c t r i c constant and the l o c a l f i e l d strength. Short-range i n t e r a c t i o n between the surface and the ions i s taken care of by introducing a distance of -closest approach, as i n the Stern model. Any s p e c i f i c i n t e r a c t i o n between surface and ion (the s p e c i f i c adsorption p o t e n t i a l i n the Stern theory) i s not introduced i n the general treatment. By evaluating several correction terms, Bolt could show that the corrections, which compensate each other p a r t l y , are of l i t t l e con-sequence i n the computation of the repulsive energy between two p a r t i c l e s carrying Gouy layers. However, Bolt points out that the corrections are of f i r s t - o r d e r s i g n i f i c a n c e for the treatment of the ion d i s t r i b u t i o n i n the ion exchange equilibrium. d) E f f e c t of E l e c t r o l y t e s on the Configuration of the E l e c t r i c  Double Layer The computation of the ion d i s t r i b u t i o n in.the d i f f u s e double layer as a function of the electrolyte content of the bulk solution shows that the diffuse counter-ion atmosphere is compressed towards the surface (34) when the bulk electrolyte concentration is increased The degree of compression of the double layer is governed by the concentration and valence of the ions of opposite sign from that of the surface charge, while the effect of ions of the same sign is compara-tively small. The higher the concentration and the higher the valence of the ions of opposite sign, the more the double layer is compressed. In the case where the surface charge of the particle, which is determined by interior l a t t i c imperfections, does not change with increasing electrolyte concentration, the diffuse double layer is s t i l l compressed, however, the surface potential decreases with Increasing electrolyte concentration. e) Zeta Potential The zeta potential i s the electric potential i n the double layer at the shearing plane between a particle which moves in an electric f i e l d and the surrounding liquid. The zeta potential i s computed from the electrophoretic mobility of the sol particle. Its magnitude is considered as a measure of the particle repulsion. Upon the addition of an electrolyte, the zeta potential usually decreases, and at the floccu-lation value of the electrolyte i t is considered to have reached a c r i t i c a l value, below which the particle repulsion w i l l no longer be strong enough to prevent flocculation. Since the position of the shearing plane is not known, the zeta potential represents the e l e c t r i c a l potential at an unknown dis-tance from the surface i n the double layer. Therefore, the zeta p o t e n t i a l i s not equal to the surface p o t e n t i a l , but i t i s to some ex-tent, comparable with the Stern p o t e n t i a l , although i t i s not nec e s s a r i l y i d e n t i c a l with that p o t e n t i a l . Like the Stern model, the zeta p o t e n t i a l may be expected to decrease with increasing e l e c t r o l y t e concentration because of a s h i f t of counter-ions toward the Stern layer when the d i f f u s e double layer i s compressed. It i s hence not s u r p r i s i n g that a r e l a t i o n exists between c o l l o i d a l s t a b i l i t y and the magnitude of the.zeta p o t e n t i a l . However, because of i t s i l l - d e f i n e d character, the zeta p o t e n t i a l i s not a u s e f u l quantitative c r i t e r i o n of s t a b i l i t y . Moreover, the computation of the zeta p o t e n t i a l from the.observed e l e c t r o -phoretic mobility i s subject to several corrections which are d i f f i c u l t , to evaluate q u a n t i t a t i v e l y . The recognition of the existence of such cor r e c t i o n terms has s t i l l further reduced the usefulness of the zeta p o t e n t i a l as a quantitative s t a b i l i t y c r i t e r i o n and, as such, t h i s (34) parameter has l o s t i t s s i g n i f i c a n c e 3. Double Layer Repulsion When two, p a r t i c l e s approach each other owing to t h e i r Brownian motion, t h e i r d i f f u s e counter-ion atmospheres begin to i n t e r -fere. The free energy of the system i s increased, because the i n t e r -ference leads to changes i n the d i s t r i b u t i o n of the ions i n the double layer of both p a r t i c l e s . To br i n g about the changes, work must therefore be performed; i n other words, there w i l l be a repulsion between the p a r t i c l e s . The amount of work required to bring the p a r t i c l e s from i n f i n i t e separation to a given distance i s the repulsive energy or the • repulsive p o t e n t i a l at the given distance. The repulsive p o t e n t i a l de-creases roughly exponentially with increasing p a r t i c l e separation. With increasing e l e c t r o l y t e concentration, the range of the repulsion i s considerably reduced because of the greater compression of the double layer. In Figure 2, three p o t e n t i a l curves are shown which are v a l i d f or the same p a r t i c l e s but for d i f f e r e n t e l e c t r o l y t e concentrations i n -dicated, by "low", "intermediate", and "high". In the lower part of the same f i g u r e , the energy i s plotted as a function of the distance. As pointed out before, the a t t r a c t i o n remains p r a c t i c a l l y the same when the e l e c t r o l y t e concentration of the medium i s varied. 4. The summation of Repulsion and A t t r a c t i o n The summation of repulsive and a t t r a c t i v e energy i s car r i e d out as follows:- The net p o t e n t i a l curve of p a r t i c l e i n t e r a c t i o n , i s constructed simply by adding the a t t r a c t i v e and the repulsive p o t e n t i a l at each p a r t i c l e distance, considering the a t t r a c t i v e p o t e n t i a l negative and the repulsive p o t e n t i a l p o s i t i v e . Figure 3 shows the r e s u l t s of these additions for three e l e c t r o l y t e concentrations indicated as "low", "intermediate", and "high" r e s p e c t i v e l y . In constructing these three net curves of i n t e r a c t i o n , another e a r l i e r mentioned short range repulsion force - contributed from both Born and so l v a t i o n repulsions - were taken i n t o account. (34) Van .Olphen gave a very d e t a i l e d discussion about the i n t e r p r e t a t i o n of s t a b i l i t y and f l o c c u l a t i o n i n terms of the shapes of the n e t J p o t e n t i a l curves of p a r t i c l e i n t e r a c t i o n . The net i n t e r a c t i o n curves for a low and a medium s a l t con-centration show a minimum with predominant a t t r a c t i o n at close approach Figure 2. Repulsive and a t t r a c t i v e energy as a function of p a r t i c l e separation of three e l e c t r o l y t e concen-t r a t i o n s . A f t e r van Olphen^- ' . Figure 3(c) vRt \ • j P A R TICLE i J / SEPARATION w Figure 3(b) Figure 3. Net interaction energy as a function of particle separation. (a) Low electrolyte concentration, (b) Intermediate electrolyte concentration. (c) High electrolyte con-centration. After van Olphen^^)^ 56 and a maximum with predominant repulsion at greater distances. No such maximum i s displayed by the curve for a high electrolyte concentration. Owing to their Brownian motion, two particles may approach each other in a relative position at which the deep minimum in...the poten-t i a l energy occurs and become associated because of the prevailing attraction. If repulsion dominates, part of the way during the mutual -approach of the particles (curves for medium and low electrolyte concen-tration) , the diffusion w i l l be counteracted by the extraneous repulsive force f i e l d , and the. rate of agglomeration w i l l decrease. At a high electrolyte concentration at which the .potential curve shows no repulsion at any distance (Figure 3(c)), particle agglo-meration occurs at a maximum rate (rapid coagulation). At intermediate electrolyte concentrations (Figure 3(b)), the coagulation isfslowed down; by the long-range repulsion (slow coagulation). At very low electrolyte concentration (Figure 3(a)), the coagulation process is so much retarded by the appreciable long-range repulsion that i t may take weeks or months before flocculation becomes perceptible in the sol. Under these con-.;: ditions, the sol i s , for a l l practical purposes, considered "stable". Figure 3 i s a concise representation of s t a b i l i t y . A large section of the potential curve above the distance coordinate,, or a large energy barrier, reduces the rate at which the sol particles associate by "jumping over the barrier", when the barrier becomes smaller, the rate of coagulation increases, and in the absence of a barrier, the rate is maximal. -The addition of electrolytes causes a compression of the double-layer and therefore a reduction of the range of repulsion and a 57 r e d u c t i o n of the magnitude of the energy b a r r i e r i n the i n t e r a c t i o n curve. 5. Secondary Minimum As discussed i n the o r i g i n of y i e l d s t r e s s , there are two schools of thought which can be used to e x p l a i n the g e l s t r u c t u r e . The f i r s t group are i n favor of a long range e l e c t r i c a l forces which permit the i n d i v i d u a l p a r t i c l e s to i n t e r a c t over distances of the order of 1000A. This i s u s e f u l f o r e x p l a i n i n g the e x i s t e n c e of p l a s t i c i t y i n a 0.05% m o n t m o r i l l o n i t e as w e l l as i n the formation of t a c t o i d s . These phenomena can be explained now by c o n s i d e r i n g double-l a y e r r e p u l s i o n and van der Waals a t t r a c t i o n as the two opposing f o r c e s . The double-layer r e p u l s i o n decays more r a p i d l y w i t h d i s t a n c e than does the van der Waals f o r c e s . Hence, beyond the p a r t i c l e separations which have been considered p r e v i o u s l y i n the d i s c u s s i o n of the s t a b i l i t y t heory, there w i l l be a d i s t a n ce where the van der Waals a t t r a c t i o n once more p r e -dominates, and a long-range minimum w i l l occur i n the i n t e r a c t i o n curve. Under fa v o r a b l e c o n d i t i o n s , t h i s secondary minimum (which was omitted i n Figure 3) may become deep enough to " t r a p " the p a r t i c l e s i n t h i s p o s i t i o n , which i s of the r i g h t order of s e p a r a t i o n to i n t e r p r e t ; the t a c t o i d f o r -mation. However, s i n c e some u n c e r t a i n t y s t i l l e x i s t s concerning the (34) magnitude of the van der Waals forces at l a r g e separations , no d e f i n i t e proof has been given that t h i s e x p l a n a t i o n i s the r i g h t one. D. O r i g i n of Cross-rlinked Gel S t r u c t u r e i n Clay Suspension A l l the i n t e r a c t i o n s between p a r t i c l e s of suspensions which have been discussed so f a r are those between the e l e c t r i c double l a y e r s of the same s i g n . The question of the behavior between the e l e c t r i c double layer w i l l be discussed in the following sections on the formation of a cross-linked gel structure i n clay suspensions. The negative double layer on the f l a t unit-layer surfaces and positive double layer on the edge surfaces w i l l be introduced f i r s t , then the modes of particle association and the construction of cross-linked structure w i l l be _ mentioned. 1. Negative Double Layer on the Flat Unit-layer Surfaces In 3.2 i t has been shown that^the clay la t t i c e carries a net negative charge as a result of isomorphous substitutions of certain electropositive elements of lower valence. The net negative lattice charge is compensated by cations which are located on the unit-layer sur-faces. In the presence of water, the adsorbed compensating cations spontaneously form a diffuse counter-ion atmosphere, which, together with the la t t i c e charge, constitutes a negative double layer. There are i n -dications that this double layer is more adequately described by the (34) Stern model than by the Gouy model 2. Positive Double Layer on the Edge Surfaces of Clay Plates At the edges of the plates, the tetrahedral s i l i c a sheets and the octahedral alumina sheets are disrupted, and "broken bonds" occur as mentioned in 3.2. This situation at the edge surfaces is therefore analogous to that of the surface of s i l i c a and alumina sol particles. On such surfaces a double layer is created by the adsorption of potential-. determining ions. An alumina particle i s either positively or negatively charged, depending onithepH of the solution. A s i l i c a particle is usually negatively charged, but i n the presence of small amounts of Al ions in solution, reversal of charge takes place. Since such small con-centrations of aluminum ions w i l l occur i n the equilibrium l i q u i d of a clay suspension owing to the s l i g h t s o l u b i l i t y of the c l a y , . i t i s quite possible to have a p o s i t i v e double layer on the. broken s i l i c a surface of the edge. Moreover, i t i s possible that the s i l i c a sheets are pre-f e r e n t i a l l y broken at the places where aluminum ions have substituted s i l i c o n , so that a surface i s exposed which i s comparable with an alumina rather than with a s i l i c a surface. Hence under appropriate conditions (34) the e n t i r e edge surface area may w e l l carry a p o s i t i v e double layer Several observations support the concept of a p o s i t i v e edge charge. One i n t e r e s t i n g , relevant experiment i n t h i s respect has been (34 40) performed by Thiessen ' . He mixed a k a o l i n i t e s o l and a negative gold s o l and prepared an electron micrograph of the mixture. I t appeared that the small negative gold p a r t i c l e s were exclu s i v e l y adsorbed at the edge surfaces of the large k a o l i n i t e plates. Rather obviously.the pre-ferred edge attachment of the gold p a r t i c l e s i s a r e s u l t of mutual f l o c c u l a t i o n of the negative gold p a r t i c l e s and the p o s i t i v e k a o l i n t e edges. Also supporting the concept of the p o s i t i v e charge i s .the fa c t that clays show a c e r t a i n anion adsorption capacity as discussed i n 3.2. I t seems l i k e l y that a p o s i t i v e edge double layer i s responsible for the adsorption of anions acting as counter-ions. 3. Modes of P a r t i c l e A s s o c i a t i o n and Cross-linked Gel Structure In suspensions of p l a t e - l i k e p a r t i c l e s , three d i f f e r e n t modes of p a r t i c l e association must be considered i n the f l o c c u l a t i n g system:- . edge-to-edge (EE), edge-to-face (EF) , and face-to-face (FF). In clay 60 suspensions, these associations w i l l be governed by different potential curves, since three different combinations of the two double iayers are involved, and hence the total van der Waals attraction energies are (34) different for the three modes of association EF .and EE association w i l l lead to voluminous card-house struct-ures and, therefore, at moderate clay concentrations, to gelation. This is the origin of the cross-linked gel structure. FF association on the other hand, merely leads to thicker and possibly larger particles, which appear as "floes" or cause gelation of the system. EE and EF. association and dissociation are sometimes described as flocculation. and deflocculation processes, whereas FF association and dissociation are called aggregation and dispersion, although the latter are just different kinds of flocculation and deflocculation (Figure 4). E. Cross-linked Gel Structure (34) Van.Olphen presented arguments against the alternatives to the ppstulation of opposite charges on faces and edges and the de-velopment of a yield stress as a result of positive-edge-to-negative face linking. One possible alternative is that the edge surfaces carry a weak negative double layer or none at a l l because of a low concentration or absence of potential-determining anions for these surfaces. Another alternative i s that a ribbon-like network is created by the association of particle faces in such a way that only part of their faces become attached. It would appear from these arguments that the best hypothesis is that of an association of negative faces and positive edges, leading 61 (c) (d) (e) (f) (g) F i g u r e 4, Modes of p a r t i c l e a s s o c i a t i o n i n c l a y s u s p e n s i o n s , and t e r m i n o l o g y . (a) " D i s p e r s e d " and " d e f l o c c u l a t e d " . (b) "Aggregated" b u t " d e f l o c c u l a t e d " ( f a c e - t o - f a c e a s s o c i -a t i o n , or p a r a l l e l o r o r i e n t e d a g g r e g a t i o n ) . (c) E d g e - t o -f a c e f l o c c u l a t e d but " d i s p e r s e d " , (d) Edge^to-edge f l o c c u l a t e d but " d i s p e r s e d " . (e) E d g e - t o - f a c e f l o c c u l a t e d and " a g g r e -g a t e d " , ( f ) Edge-to-edge f l o c c u l a t e d and " a ggregated", (g) E d g e - t o - f a c e and edge-to-edge f l o c c u l a t e d and " a g g r e g a t e d " . A f t e r van O l p h e n ^ ^ ) ^ to a voluminous cubic card house structure. The concept of a p o s i t i v e (87 88) double layer was f i r s t introduced by van Olphen ' i n the i n t e r -p r e t a t i o n of the complex s t a b i l i t y behavior of montmorillonite suspensions. Later, S c h o l f i e l d and Samson^ 9^ adopted the same hypothesis i n the . explanation of f l o c c u l a t i o n and anion adsorption i n k a o l i n i t e s o l s . The card house may be v i s u a l i z e d as a system of p a r a l l e l plates which are held together by cross-linked p a r t i c l e s perpendicular to the p a r a l l e l p l a t e s . The c r o s s - l i n k i n g force in;the double-T-shaped units of the card house i s supplied by the e l e c t r o s t a t i c a t t r a c t i o n between the oppositely charged edges and faces. This c r o s s - l i n k i n g force has to be higher than the repulsive force between the negatively charged p a r a l l e l plates i n thedouble-T u n i t . The breakdown of the cubic card-house structure upon the. addition of small amounts of s a l t may be seem as a reduction of the cross-l i n k i n g force. This reduction may be a r e s u l t of a decrease i n the e f f e c t i v e a t t r a c t i v e charges on edge and face surfaces owing to a s h i f t of counter-ions toward the surfaces. Since i n the double-T structure a balance of repulsive and a t t r a c t i v e forces e x i s t s which i s possibly only s l i g h t l y in,[favor of the a t t r a c t i o n , a small reduction of i t due to the e f f e c t pf a small concentration of s a l t on.the compression of the double layer would lead to the breakdown of the card house. Upon the addition of more s a l t to the system, the double layers on both edge and face surfaces are compressed further. Many p o s s i b i l i t i e s f o r p a r t i c l e a ssociation are now opened: EE a s s o c i a t i o n by van der Waals a t t r a c t i o n may no longer be 63 prevented by the double-layer repulsion between the two positive edge double layers. Although such association probably occurs in the salt-floccula-tion process, i t cannot be a dominating event, since salt flocculation is governed by the valence of the cations. Therefore, salt flocculation is governed by the changes in the negative-face double layer according to the Schulze-Hardy rule. The compression of the double layer in the presence of flocculating amounts of salt may have the following two consequences:-1. The degree of FF association-may be increased by van der Waals attraction. 2. The FF repulsion may be reduced only to such an extent that the cross-linking EF, forces (electrostatic as well as van der Waals) becomes once more larger than the repulsion between the parallel plates in the -double-T unit. The yield stress w i l l rise i f 2. predominates, but not i f 1. prevails. At very high concentrations of salt., FF association becomes more and more important, and hence the yield stress begins to decrease. Because different clays may be expected to have different, double-layer properties, they do not•necessarily react in the same way to the addition of electrolytes. The flow behavior at different salt concentrations depends Dn. which of the three types of association pre-vails at a certian salt concentration, and the relative degrees of such association are dependent on the double-layer properties. 64 3.4. Clay Sample Preparation A. Ideal Clay Sample (34) 1. For Scientific Investigation  An ideal clay sample should f i l l the following requirements:-a) No organic substance. b) No soluble salt. c) No mineral impurities. In converting the suspension into the described ion form, d) 100 per cent of the exchange position should be occupied by a single cation species. e) No. structure decomposition due to the conversion. (44) 2. For Industrial Purpose  Natural clay after wetting, -grinding^and dispersing is used for test. B. Disadvantages of. Conversion Methods G e d r o i t s ^ ^ commented that a l l the displacing (by salt, al k a l i or acid) methods for the determination of the amount of adsorbed* cations in the s o i l , and of the direct determination of i t s adsorptive capacity, suffer from certain disadvantages such as the decomposition action of the displacing agents and coagulation action of the salt solutions. He recommended the use of the weakest electrolyte, viz. * In his days, the adsorption mechanism was the prevailing concept for what is known as the ion exchange process of clay. Therefore, adsorbed cations and adsorptive capacity respectively mean exchangeable cations and exchange capacity. 65 pure water and the method of electrodialysis of which the dialysis rate is much accelerated owing to the electric current passing through the solution. Hence, the trend in the conversion methods was changed some-what from the displacing method to the electrodialysis method, since . the conversion mechanism is exactly the same as that of the direct determination of exchange capacity. In addition to the above mentioned two techniques another, once very popular, preparation method w i l l be discussed, in which various ion forms of a clay are prepared via the hydrogen form followed by the addition of an equivalent amount of the base of.the desired metal to the hydrogen form. By this way numerous studies have been made of the physical properties of supposedly monoionic clays . 1. Disadvantages of the Displacing Method The.literature contains a large amount of information on acid solubility, because of the general economic importance of the acid-clay reaction, but relatively l i t t l e data on solubility in alkalies (91) Nutting , who studied the solubility of the clay minerals in great detail, arrived at the.general conclusion that above certain minimum concentrations, acids remove al k a l i metals, alkaline earths, iron, and aluminum from the clay minerals, and alkalis dissolve the s i l i c a . Therefore, acids_,alkalis, acidic salts or alkaline salts have definite solution or decomposition effect on clay. (34) Though neutral salts w i l l have very l i t t l e solution effect and have no or very minor decomposition effect, they, as well as acids 66 and non-neutral salts, do cause coagulation (flocculation and aggregation) of clay particles and reduce the exchange sites. This and the occupation +2 +3 of exchange positions by Mg or Al even due to very small solution or decomposition action often make i t impossible to prepare a clay in which 100 per cent of the exchange positions are occupied by a single cation species. 2. Disadvantages of electrodialysis Various investigators have indicated that electrodialysis of certain of the clay minerals may cause their decomposition. Thus, (92) + Kelly indicated that, as the cations are replaced by H ,aluminum moves from octahedral positions to exchange positions, and Hofmann and Giese^ 4^ showed that, in general, unexchangeable cations are lost from within the lattice before a l l the exchangeable cations are replaced by H+. Electrodialysis has frequently been used to prepare H clays for cation-exchange studies or for use as the starting point for ex-aminations of the physical properties of clay carrying specific ex-changeable cations. Because of the likelihood of significant amounts of disintegration of the clay minerals, the procedure must be used with caution. Many of the investigations which have used, this procedure are of l i t t l e value, since the clay minerals were altered, and the cation composition was not what i t was thought to be, because of the very difficultlyreplaceable aluminum moving from the lattice to exchange . . (48) positions (93) Paver and Marshall treat electrodialyzed clays with 67 n e u t r a l s a l t s , and l i b e r a t e d aluminum. The amount freed increased w i t h the concentration of the s a l t to a maximum which was approximately equiva-l e n t to the exchange ca p a c i t y of the clay.. 3. Hydrogen Clays ( 9 3 ) (94 ) I t was- shown by Paver and M a r s h a l l , C h a t t e r j e e and P a u l , ( 9 5 ) Mukherjee.et a l , that hydrogen mont m o r i l l o n i t e and hydrogen k a o l i n i t e are i n r e a l i t y hydrogen-aluminum systems. I t i s impossible to prepare a c l a y + 3+ i n which a l l the exchange p o s i t i o n s are occupied by H , s i n c e A l moves from the l a t t i c e to exchange p o s i t i o n s before s a t u r a t i o n w i t h H + becomes complete. The f a c t that hydrogen clays are i n r e a l i t y hydrogen-aluminum systems i s of great importance i n c l a y and s o i l i n v e s t i g a t i o n s . The f a i l u r e to recognize t h i s f a c t has caused many erroneous conclusions to be reported and much confusion i n i n t e r p r e t i n g r e s u l t s . C. P r e p a r a t i o n of Clay Sample i n t h i s Work (see a l s o 5 . 5 . ) For the purpose of i n v e s t i g a t i n g the e f f e c t of s a l t concentra-t i o n and c a t i o n valence on maximum and maximum developable y i e l d s t r e s s , the c l a y was simply prepared by washing out the s o l u b l e s a l t according to the f o l l o w i n g c o n s i d e r a t i o n s : -1. With regard to. the foregoing d i s c u s s i o n about the d i s -advantages of the conversion methods i n v o l v e d i n preparing the s c i e n t i f i c sample, the n e u t r a l s a l t d i s p l a c i n g method seemed to be the best. By. t h i s method,, the c l a y can be converted to s p e c i f i c i o n form f o r the measure-, ment of maximum developable y i e l d s t r e s s . But c l a y samples of d i f f e r e n t ion form w i l l have d i f f e r e n t cation exchange capacity (96, for example), hence i t i s d i f f i c u l t to explain the cation valence e f f e c t on the maxi- . mum developable y i e l d s t r e s s . 2. In.the sample preparation f o r an i n d u s t r i a l t e s t , o r i g i n a l clay i s used, which includes the soluble s a l t s that w i l l disturb the behavior of the clay to the added s a l t concentration and to cation valence e f f e c t s . 69 Chapter 4  PRESENT WORK 4.1. Variables Studied A. Dependent Variable Maximum (including maximum developable) y i e l d stress (see also 3.1, 5.5, 6.5 and 6.8). Maximum y i e l d stress of a clay suspension at a given concentration of a s a l t i s the y i e l d stress of the mass as developed a f t e r a s p e c i f i c aging time. Maximum developable y i e l d stress of a clay suspension i s the maximum y i e l d stress as developed at the p a r t i c l e saturation concentration of a given s a l t . B. Independent Variables 1. Changed a) Cation Valence Two mono-, two d i - and one t r i - y a l e n t cations were used (see also the next secti o n ) . b) Salt NaCl, CuCl, CaC^, MnC^ and CeCl^ were used. CuCl may sur-vive i n the presence of water i f strong o x i d i z i n g agents are not also present. MnC^, a f a m i l i a r laboratory reagent, i s more d i f f i c u l t l y (97) oxidized than F e C ^ c) Salt Concentration Varied from zero to the f l o c c u l a t i o n concentration. 2. Kept Constant In consideration of a l l the factors discussed i n 2.1 and 3.2, the following variables were kept constant:-a) Clay System The c l a y samples were always prepared from the. same sample of Bentonite clay and by same procedure (see also 5.1 and 5.5). There-fore, p a r t i c l e s i z e , s i z e d i s t r i b u t i o n , chemical c o n s t i t u t i o n and l a t t i c e structure etc. of the dispersed phase of the suspension were maintained constant throughout the experiments. b) Concentration of Clay i n the Paste* The concentration was set at 19.06 per cent by weight of clay, since t h i s gave a good reading of y i e l d stress on the recorder and also since i t f a l l s into the range which, as mentioned i n 2.7, has not been w e l l investigated. * According to Seale and Grimshaw , paste i s an a r t i f i c i a l prepared suspension (a mixture of s o l i d and l i q u i d i n which t h e . l i q u i d pre-dominates) which w i l l not flow, but only changes i t s shape when sub-jected to pressure. 71 c) Dispersion Medium Was d i s t i l l e d water before the addition of s a l t . d) pH Value of Clay Paste . As neutral (pH = 7) as possible by adding a ne u t r a l s a l t to avoid any p o t e n t i a l decomposition e f f e c t on clay sample (see 3.4). e) Size of Cation (not s i z e of the hydrated ion, see 3.3) The cations were so selected that t h e i r i o n i c r a d i i were very close to each other. Values are shown i n Table I. TABLE I - Ionic R a d i i of Cations Used i n the Experiment Cations Na + Cu + C a 2 + Mn 2 + Ce 3* Ionic radius 0.98 0.95 0.94 0.80 1.02 , f) Anion Chloride s a l t s were employed i n t h i s work. As shown i n 3.3, Chloride ion. should not be involved i n exchange reactions. g) Surface Active Agent Not. used at a l l . _.. h) Temperature of Measured Systems Always held at 20°C. 72 4.2. Special Features of This Work A. A Feasible Method to Measure Y i e l d Stress By using a very low speed and a grooved bob (3 1) and cylinder r o t a t i o n a l viscometer, a non-flow y i e l d stress can be measured within a reasonable time (see 3.1). B. -Simple Paddle Randomly Destroys Gel Structure A few strokes of a very simple paddle shown i n Figure 6 i n 5.2 was used to randomly destroy the gel structure of the.clay suspension. This makes a good s t a r t i n g point for)the measurement of the y i e l d stress of the clay system and solves the p a r t i c l e o r i e n t a t i o n or "shear harden" problem (see 3.1). Tests were made to check the r e p r o d u c i b i l i t y of the measurements with t h i s pretreatment. Chapter 5 EXPERIMENTAL 5.1. Materials A. Bentonite Clay The, Bentonite clay examined i n t h i s work was Beaver-Bond Western -Bentonite manufactured by Magnet Cove Barium Corporation L t d . , Rosalin, A l b e r t a . A t y p i c a l analysis of Beaver-Bond Bentonite as supplied by the company i s shown i n Table I I . As for the exchangeable cations, zeta p o t e n t i a l and p a r t i c l e s i z e and shape, see 6.2, 6.4,J, and 6.3, r e s p e c t i v e l y . TABLE II - Chemical Composition of Beaver-Bond Western Bentonite sio 2 A 1 2 0 3 F e 2 0 3 CaO MgO Na 20 K 20 Moisture Com-bined H 20 (% by weight) 61.37 20.64 2.96 0.63 1.96 2.34 0.39 6-9 6-8 74 B. Chemicals A l l the chemicals used were of reagent grade. 5.2. Main Apparatus A. Haake Rotovisco Viscometer - a r o t a t i n g bob type visometer (39) This equipment i s described i n d e t a i l by van Wazer et a l The Rotovisco as i l l u s t r a t e d i n Figure 5 made, by Gebruder-Haake i n B e r l i n ^ West Germany, i s undoubtedly the most v e r s a t i l e viscometer now a v a i l a b l e commercially. .The Rotovisco w i l l measure apparent v i s c o s i t i e s i n the range -3 7 of 5 x 10 to 4 x 10 poises. The range of apparent rates of shear i s 10 2 to 10 4 sec. ^ and the range of shear stress i s 10 to 10^ dynes/cm 2. A l l of t h i s i s accomplished with an accuracy of about 1 to 2%. The measuring head and the co n t r o l panel are connected by a f l e x i b l e metal cable. The c o n t r o l panel houses the e l e c t r i c components and a sychronous motor operating at 3000 r.p.m.. The power i s transmitted to the measuring head through a 10-position geared transmission. The lever on top of; the control panel, may be movedfrom one p o s i t i o n to another through a neutral p o s i t i o n while the motor i s turning, thus per-mitting rapid s h i f t s i n speed during the measurement. The 10 b a s i c speeds are from 3.6 to 582 r.p.m., a l l of which can be reduced by a speed reducer (see next s e c t i o n ) . The f l e x i b l e drive cable i s contained wit h i n the metal cable. This same cable transmits to the control panel e l e c t r i c a l signals from the stress-measuring device. Shear stress i s measured by a p r e c i s i o n t o r s i o n spring which i s interposed between the rotor i n the sample f l u i d and the transmission cable. Thus the viscous Figure 5. Haaks Rotovisco Visocometer drag on the rotor i s measured by the d e f l e c t i o n or twisting of the t o r s i o n spring. This twisting i s measured by means of a potentiometer. The s i g n a l i s recorded continuously as a function of time by a Mosley 710 B s t r i p chart recorder. For temperature control the cup i s held i n an insulated jacket through which water from a constant temperature bath was c i r c u l a t e d . B. A l t e r a t i o n Made to^ Basic Viscometer 1. Speed Reducer A ZG10 ten to one speed reducer was used to produce such a low bob speed that the y i e l d stress value could be assessed, w i t h i n experimental error, without using the extrapolation technique (see also 3.1 and 6.9). With the speed reducer the lowest speed of r o t a t i o n was 0.432 r.p.m..: 2. Grooved Bob SVP II and Cylinder SVP In the experimental work, the torque sensing device, de-signated head 500, was used i n conjunction with the cup and bob, de-signated SVP and SVP I I . Table I I I and Figure 6 show the dimensions of the cup and bob set and the stress conversion f a c t o r r e l a t e d to them. The dimensions of the grooves and teeth were measured with the Vernier Micromaster M-150 microscope with help from the author's classmate, V.R. P h i l l i p s . "The conversion f a c t o r was obtained by c a l i b r a t i n g the Rotovisco with standard v i s c o s i t y o i l S-2000 (see Appendix IV), as supplied by the Cannon Instrument Company. 77 Figure 6. Schematic drawing of bottom view of the SVPII bob (after gold plating). TABLE I I I - Dimensions and Stress Conversion Factor for The Cup and Bob Set SVP and SVP II Cup diameter (mm.) 23.1 Bob diameter (mm.) 20.2 Bob length (mm.) 2 Shear stress (dynes/cm ) 518 S 19.6 for Measuring Head 500 where: S = reading on Rotovisco meter scale i n normal range. From Figure 6, i t can.be seen that the smooth area of the outer extreme of the bob i s : A s = 0.19 x n x h while the grooved surface area 3. Gold P l a t i n g The grooved bob SVP II wasjoriginally n i c k e l plated but was found to be corroded by some of the s a l t s . This was corrected by having the bob gold plated. x [(10.1 - 0.25)/10.1] x n x h where: Hence 3 A /A = 1.50/(0.19 .+ 1.50) = 0.888. n = number, of teeth or grooves on the surface of bob. 79 41 Gum Sealing In order to reduce the amount of sample used for each t e s t , the c y l i n d r i c a l s t a i n l e s s s t e e l block supplied by the manufacturer was used at the bottom of the c y l i n d e r . However, t h i s created a leak between the cylinder and the block. De-sugared ordinary chewing gum was used to s e a l the leak, and i t worked p e r f e c t l y . 5. Cap to prevent evaporation Shown i n Figure 7 i s a p l e x i g l a s s cap containing a water r e s e r v o i r which was placed around the stem of the bob and over the cylinder to minimize the loss of water from the sample during the aging period and the t e s t i n g time. 6. Mixing Paddle This was used to randomly destroy the gel structure (see Figure 8 and 4.2). C. Centrifuge An International;Universal model UV centrifuge was used i n washing out the soluble s a l t s (see also 5.5). 5.3 Experimental Accuracy A l l the experimental data w i l l be expressed i n two forms. One i s i n s i g n i f i c a n t f i g u r e s , the other i s with 95 per cent confidence l i m i t s . 1 80 Figure 7. Schematic drawing of the plexiglass cap (key-dimensions are included). ' Figure 8. Schematic drawing of the plexiglass mixing paddle (key dimensions are included). 5.4. C a l i b r a t i o n Procedures A. Thermometer The A.S.T.M. 90°C thermometer was put i n a constant tempera-ture bath and cal i b r a t e d against a model 2801 A Hewlett Packard quartz thermometer. I t was found that the l a t t e r reading was 19.97 ± 0.02°C corresponding to 20°C of the A.S.T.M. thermometer. B. Bob Speed While Rotovisco Using Reducer ZG10 The bob was c a l i b r a t e d by timing with a Cave and Company stop watch. The r a t i o of the bob speed was found to be inversely pro-p o r t i o n a l to the value of the machine term U. v The^ ..uiFactor i s 1.206 ± 0 (see Appendix IV). where: U = no. of gear p o s i t i o n on top of con t r o l unit of Rotovisco viscometer, assumed to be sec. i n dimension. ^Factor = Ratio of bob speed measured without speed reducer to that 486 stated i n (39) ( — — x 1.2 r.p.m.), dimensionless. C. Chart Speed of Recorder Within the accuracy of the stop watch, i t was the same as stated i n the manual. D. Stress Conversion Factor I t was c a l i b r a t e d against standard o i l manufactured by Cannon Instrument Company. D e t a i l s see Appendix IV. 83 5.5. Experimental Procedures A. Procedures for Washing. Out Soluble Salts in Clay Since the washing is a repeated process, a flow chart is constructed in Figure 9 to i l l u s t r a t e the procedures. The schematic meaning of the block is similar to that of the computer flow chart. The numbers in the blocks correspond to those i n the descriptions be-low:-1. Weight in each of eight 50 ml plastic centrifuge tubes about 5 gm of clay and enough d i s t i l l e d water to produce a suspension of about 15 per cent by weight of clay. 2. Mix the clay suspension with glass rod and shake i t with Deluxe mixer for 1 minute at a rate scale of 6. 3. Balance the weight of the centrifuge tube set (clay sus-pension plus plastic tube plus stainless steel container), such that among each of the four pairs, the sets are within 0.1 gm. of each other, by adding d i s t i l l e d water to the gap between the plastic and steel tubes. Then.put the sets in pairs into the centrifuge opposite to each other. 4. Centrifuge the clay suspension at the speed scale = 3/4 for 30 minutes. Stop the centrifuge without using brake. 5. Add d i s t i l l e d water to the centrifuge solids to the "same value" in 1. 6. F i l t e r the supernatant suspension by(:mixing i t with Hyflo Super-cel (suspension:.eel = 100:1 by weight) and by running the mixture through a number 50 Whatmann f i l t e r paper in a 15 cm if1 Buchner Funnel Figure 9. Flow chart of procedures to wash out soluble salt in clay. which was precoated with 500 ml of 10 per cent by weight Hyflo Super-c e l s l u r r y to 250 ml. 7. D i l u t e 10 ml of the f i l t r a t e to 200 ml with d i s t i l l e d water.and measure the ppm as NaCl of t o t a l ion i n the f i l t r a t e by the conductance c e l l i n a Banton Demineralizer of Barnstead S t i l l and S t e r i l i z e r Company. 8. Store the centrifuged s o l i d s i n a b o t t l e as washed clay sample. B. Determination of (Hygroscopic) Moisture Content of Clay by  Weighing Method 1. D e f i n i t i o n of Hygroscopic Moisture S o i l , l i k e any f i n e l y comminuted material, i s hygroscopic, that i s , i t i s capable of adsorbing water vapor from the a i r with which i t i s i n contact. The amount of water iri the s o i l which i s i n e q u i l i -brium with the water vapor i n the a i r , i s c a l l e d the hygroscopic moisture of the s o i l . 2. Determination of Hygroscopic M o i s t u r e ^ ^ About 5 gm. of s o i l accurately weighed, i n a weighing b o t t l e , are dried for 5 hours at 105-110°C i n a drying oven with b o t t l e l i d open. The time of drying i s counted from the moment the temperature of the oven has attained 105°C. At the end of that time the weighing b o t t l e i s removed from the oven, closed with the l i d , cooled i n a desiccator and weighed. The loss i n weight, calculated on 100 gm of s o i l , i s the percentage hygroscopic moisture. 3. Determination of Moisture Content The'method used was exactly the same as that f o r the deter-mination of hygroscopic moisture except that the sample was smaller and because of i t s nature was pasted i n a t h i n layer on to the i n s i d e sur-face of the weighing b o t t l e . C. Sample.'Preparation for y i e l d Stress Measurement 1. Without Salt The moisture content of washed clay was adjusted to 80.94. per cent, corresponding to a.maximum y i e l d stress of 3.08 x 10^'dynes/ 2 cm (see 6.7). 2. With Salt Put i n the soluble s a l t free sample the amount of s a l t r e -required to make a paste of the desired concentration, mix and l e t i t (33) agei-for at least 3 days before, t e s t i n g . D. Y i e l d Stress Measurement 1. Mix the sample to be measured about 12 hours before the test s t a r t s to s t i r up the s e t t l e d coarser p a r t i c l e s and to l e t the 87 sample have enough time to get r i d of the a i r bubbles* introduced by the a g i t a t i o n . 2. Check Water i n constant temperature bath, set the regulator to desired temperature, open cooling water valve, s t a r t the s t i r r e r pump, the Rotovisco and the recorder. 3. Set the thermometer. 4. Check that the cup and bob are clean. 5. A f t e r 10 minutes or longer warm up of the machines, adjust the zero points and the readings on both Rotovisco meter and recorder. 6. Place the cap and bob, then the cup i n the Rotovisco. 7. Check the temperature on thermometer so that temperature i s correct. 8. Measure the shear stress with the bob turning i n the a i r . 9. Take out the cup, put i n the sample and mix the sample with the paddle. The sample should be s u f f i c i e n t to r i s e to the same l e v e l on the upper r i n g of the bob when the cup with the sample i s pushed into the Rotovisco. * A i r incorporated i n a clay paste has an adverse e f f e c t on i t s p l a s t i c i t y , so that such a clay appears to be "short", but recovers i t s p l a s t i c i t y when the a i r has been removed. : The amount of a i r worked into clay during the preparation of a paste i s much larger than gener-a l l y r e a l i z e d , and i t s adverse influence i s often very serious(33). 88 10. Check the reading on the recorder to make sure that the spring i s completely relaxed and the bob does not s t i c k to the cap. 11. A f t e r a c e r t a i n time or aging time (about 12 ho.urs) , warm up the Rotovisco and recorder and measure the (maximum) y i e l d stress of the sample. E. Aging Test for Maximum Y i e l d Stress Used to locate the minimum aging time needed to develop the maximum y i e l d s t r e s s . .This i s done by making y i e l d stress measurements a f t e r d i f f e r e n t time periods of re s t before shearing. The time i s counted from the end of procedure 9 i n the l a s t s ection. F, . Determination of Exchangeable Cations 1.Procedures for Unwashed C l a y ^ * ^ a) 15 gm. sample i s extracted with 40 per cent aqueous ethanol* to remove soluble s a l t s . b) Extract with absolute ethanol to remove water and to make clay dry quickly. c) A i r dry the clay. * E t h y l alcohol u.s.p. 95% tested f o r a c i d i t y (reason see 3.4) as follows:-Mix 50 ml of alcohol with*" 35 ml of C02~free water, add a few drops of phenolphalein, and t i t r a t e with 0.1 N NaOH to a s l i g h t pink colour. Not more than 0.1 ml of NaOH s o l u t i o n should be r e q u i r e d ^ D . Aqueous alcohol s o l u t i o n i s used to eliminate the hydrolysis e f f e c t on clay (see also 6.2). I f the s o l u t i o n i s a c i d i c , i t can be neutralized by - NH OH to pH 7. 89 d) 10 gm. a i r dried sample i s dispersed i n 50 ml of N. NH^Cl (adjusted by NH^ OH. exactly to pH 7), digest over a water bath at 70°C for 1 hour, shake in t e r m i t t e n l y during t h i s period and then set aside overnight at room temperature. e) The mixture i s f i l t e r e d . f) The residue i s washed with small portions of N., NH^Cl u n t i l the t o t a l v o l . of combined f i l t r a t e and washings i s 200 ml. I_ | *4"2 ~r* 2 g) Amount of Na , K , Ca or Mg was analysed i n ppm, with a Perkin-Elmer atomic absorption spectroscope i n B.C. Research Council, by the author's classmate M.S.Liu. ; Involved i n t h i s are the d i l u t i o n of the sample to a readable concentration and the c a l i b r a t i o n by a standard s o l u t i o n . L a C ^ i s added both i n the standard s o l u t i o n and +2 the sample for determination of Ca to exclude the combined i n t e r -ference from (phosphate), s i l i c a t e and aluminum. 2. Procedures for Washed Clay Exactly the same as that for unwashed clay except s t a r t i n g d i r e c t l y from step c ) . G. Determination of Soluble Salt 100 gm. sample i s extracted with 300 ml of d i s t i l l e d water^~*^ Then the extract i s analysed r i g h t away^ 9^ with an atomic absorption spectroscope. H.;iZeta P o t e n t i a l A c t u a l l y no attempt was made to measure an exact value of 90 t he z e t a p o t e n t i a l . No e f f o r t was made t o get a c o r r e l a t i o n between the z e t a ' p o t e n t i a l and the maximum y i e l d s t r e s s , b u t o n l y a c o n f i r m a t i o n o f t he s i g n o f the s u r f a c e cha rge o f t he B e n t o n i t e c l a y p a r t i c l e was o f i n t e r e s t t o a s s i s t i n the t h e o r e t i c a l e x p l a n a t i o n o f the phenomena n o t e d i n the maximum y x e l d s t r e s s r e s u l t s . T h e r e f o r e , o n l y t he e l e c t r o p h o r e t i c v e l o c i t y ( i n c l u d i n g d i r e c t i o n ) o f b o t h washed and unwashed c l a y p a r t i c l e s i n wa te r s u s -p e n s i o n a t the s t a t i o n a r y l e v e l s * i n the c y l i n d r i c a l c e l l o f a Rank B r o t h e r s p a r t i c l e m i c r o e l e c t r o p h o r e s i s appa r a tu s Mark I I was o b s e r v e d . T h i s work was done w i t h the a s s i s t a n c e o f t he a u t h o r ' s c l a s s m a t e , B . C . Bowen. I. Pho tog raphs 1. E l e c t r o n M i c r o s c o p e Pho tog raphs Bo th the washed and unwashed c l a y p a r t i c l e s d i s p e r s e d i n e i t h e r wa te r o r wa te r p l u s d e t e r g e n t were p h o t o g r a p h e d , ( see F i g u r e 11 i n 6.3) by M r . N .N . Wa lker w i t h the H i t a c h i HU I IA e l e c t r o n m i c r o s c o p e i n the Depar tment o f M e t a l l u r g y a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a . * The w a l l s o f the e l e c t r o p h o r e s i s c e l l w i l l i n g e n e r a l be cha rged i n the p r e s e n c e o f s o l v e n t ( u s u a l l y n e g a t i v e l y i n wa te r ) and t h i s w i l l l e a d to a s t r e a m i n g o f t he o p p o s i t e l y cha rged s o l v e n t nea r t he w a l l s toward the a p p r o p r i a t e e l e c t r o d e . T h i s e l e c t r o - o s m o t i c s t r e a m i n g v e l o c i t y wou ld be u n i f o r m a c r o s s t he c e l l were i t no t f o r the r e -v e r s e f l o w a t h y d r o s t a t i c e q u i l i b r i u m wh i ch i t s e l f obeys P o i s u i l l e ' s f l o w . - The c o m b i n a t i o n o f t h e s e opposed f l ows l e a d s t o a s i t u a t i o n where the s o l v e n t i t s e l f i s o n l y s t a t i o n a r y a t w e l l d e f i n e d l e v e l s i n the c e l l . C l e a r l y t he o b s e r v e d v e l o c i t y o f a p a r t i c l e i s o n l y e q u a l to i t s own e l e c t r o p h o r e t i c v e l o c i t y when measured a t t h e s e " s t a t i o n a r y l e v e l s " . A Wild microscope was used to take photographs of washed clay suspension without s a l t and with s a l t s ; NaCl, C a C ^ and McC^. For some of those with s a l t s , p a r t i c l e modes corresponding to before, at and beyond maximum y i e l d stress were photographed by the author's supervisor, Dr. K.L. Pinder (see Figure 20 to 25 i n 6.11). Chapter 6 RESULTS AND DISCUSSION 6.1. Preliminary Experiment for Washing Out Soluble Salt (see also 5.5). A preliminary experiment had been done on the total ion con-centration of the f i l t r a t e vs. the number of washings (Table 4 and Figure 10), showing that four washing cycles were needed and that the 2 equilibrium ion concentration is about 1.6 x 10 ppm after step 7 in 5.5. In the experiment, a l l the steps stated in the descriptions corresponding to Figure 9 were exactly followed. TABLE IV- Total Ion Concentration of Clay F i l t r a t e in Washing Out Soluble Salt 1st Number of 2nd 3rd Washing Cycle 4th 5th 6 th Total ion concen-tration of clay f i l t r a t e from step 7 in 5.5. (10~ 2 ppm as NaCl) 3.5 2.4 2.2 1.7 1.5 1.7 Meq. as NaCl/100 gm clay 7.5 5.1 4.7 3.6 3.2 3.6 93 2 3 4 5 6 NUMBER OF WASHING CYCLE Figure 10. T o t a l ion concentration of clay f i l t r a t e i n washing out soluble s a l t . 94 6.2. Exchangeable Cations of Beaver-Bond,.Western Bentonite^ A. Chemical Composition and Exchangeable Cation of Unwashed Clay Shown in Table 5 are the.analysis results of exchangeable cations and soluble salt of washed and unwashed clays. TABLE V - Exchangeable Cations and Soluble Salt (meg/100 gm clay) of Washed and Unwashed Clays Cations Na + K + C a 2 + Mg Soluble Na:•. unwashed clay 31.96 2.28 26.57 3.33 0.301 washed clay 20.18 2.40 29.30 2.72 A comparison between the chemical composition given in Table II and that of exchangeable cations of unwashed clay in Table V is given below (basis: 100 gm clay):-for Na: Ca Mg in chemical composition 2.34 x = 1.74 gm Na20 0.32 0.45 1.18 as exchangeable cations 31.96 x Na x 10~3 = 0.7348 gm 0.0892 0.05325 0.0405 Because the values i n Table II are only typical analytical data, i t i s not possible to say that there i s any significant difference for Ca in the chemical composition or as exchangeable cations. This means i t i s highly possible that a l l Ca exists in the clay as exchangeable cations. For Na, K and Mg, the amount i n the chemical composition i s d e f i n i t e l y higher than that as exchangeable cations. Most potassium i s supposed to be f i x e d i n c l a y . The f i x a t i o n of K i s a popular phenomenon (40 48 99) and a tremendous amount of work has been done on the subject ' ' Mg i s used as construction blocks i n the clay minerals, hence the small amount of exchangeable magnesium i s to be expected. I t appears that about ha l f of the Na i n the clay might belong to some unsoluble and un-exchangeable impurities, since there i s j u s t a trace amount of soluble Na + as shown i n Table V. B. Exchangeable Cations i n Washed and Unwashed Clay + 2+ As shown i n Table V, the amount of exchangeable K , Ca 2+ + and Mg does not change markedly f or the two cla y s , but that of Na shows a hig h l y s i g n i f i c a n t reduction because of the washing process. The amount i s quite comparable to that of the sum of t o t a l change i n ion concentration as NaCl of the f i r s t to the fourth wash c y c l e . This could be due to the hydrolysis of Na + i n d i s t i l l e d w a t e r ^ ^ ' ^ ' ^ ' . Therefore, washing out the soluble s a l t by alcohol i s recommended to avoid t h i s e f f e c t . 6.3.. Size and Shape-of P a r t i c l e s and P a r t i c l e Agglomerates What i s meant by the s i z e and shape of the p a r t i c l e s i s r e a l l y the value of those c h a r a c t e r i s t i c s f o r p a r t i c l e s or agglomerates of p a r t i c l e s when dispersed i n water. The s i z e and shape i s highly dependent on the dispersing medium. As i l l u s t r a t e d i n Figure 11, a l i t t l e soap as 96 Washed; dispersed i n water. Washed; dispersed i n water with detergent. Figure 11. Electron microscopic photos of Beaver-Bond Western Bentonite P a r t i c l e s (2,500X). w e l l as alcohols or other organic solvents w i l l coagulate the p a r t i c l e s . This i s possibly' due to the adsorption of the surfactant on the p a r t i c l e surface and the lowering of d i e l e c t r i c constant of the water such that the e l e c t r i c double layer i s compressed, and the range of p a r t i c l e r e p u l sion i s reduced and the s i z e of the energy b a r r i e r becomes smaller. However, i n both dispersions the washed cla y p a r t i c l e i s s i g n i f i c a n t l y l a rger i n s i z e than the unwashed one. This could be due to discarding the supernatant suspension, which contains the f i n e p a r t i c l e s , i n step 4 of the procedures f o r washing out the soluble s a l t (see 5.5). 6.4. E l e c t r o p h o r e t i c V e l o c i t y of the Clay P a r t i c l e (see also 5.5). The p a r t i c l e was examined at the lower stationary l e v e l by focusing the ultramicroscope at 0.2555 mm over the bottom inner surface of the c y l i n d r i c a l c e l l of the Rank Brothers p a r t i c l e micro electrophoresis apparatus. A. Speed of the P a r t i c l e During electrophoretic v e l o c i t y measurements, the p a r t i c l e s appear to change d i r e c t i o n sometimes due to the Brownian motion of the p a r t i c l e s . Owing to the Brownian motion, the p a r t i c l e s c o l l i d e f r e -quently, but a f t e r the c o l l i s i o n they separate again. Hence, the speed of the p a r t i c l e , measured as the time to pass one graphic d i v i s i o n i n the microscope, v a r i e s .quite a b i t from 98 one particle to another as shown i n Table VI. The speed of the unwashed particles ns on the average a l i t t l e faster than that of the washed particles when a potential of 30 volts i s applied to the electrodes. It seems that the main reason for this would be the larger size of the washed particle (see Figure 11 and 6.3). The surface charge and zeta potential should be very small in light of the slow speed of the particles. TABLE VI,- Electrophoretic Speed of Beaver-Bond Western Bentonite Particles (measured as the time in seconds to pass one graphic division in the ultramicroscope when 30 volts is applied to the electrodes) Washed Clay Particle. Unwashed Clay Particle 18.26 16.02 15.74 18.58 22.18 13.44 14.46 15.04 20.52 12.12 21.64 14.52 19.50 Ave. 18.35 ± 2.61 15.04 ± 3.08 B. Charge Sign of the Clay Particle Both the washed and unwashed particles move.. - from cathode to anode. This means that the particles are negatively charged. 99 6.5. A T y p i c a l Y i e l d Stress Result In Figure 12 i s a t y p i c a l shear stress recording of a y i e l d s t r e s s measurement. Section ab i s the stress of the bob when turning i n a i r . be expresses a trace stress remained a f t e r the sample i s set i n the Rotovisco. cd i l l u s t r a t e s e l a s t i c i t y of clay g e l which follows exactly Hook's law. At point d ( y i e l d p o i n t ) , the gel structure breaks down and the stress decays r a p i d l y at f i r s t and then slowly to an equilibrium value. Because of the slow speed of the bob (see 3.1,and 6.9), the grooves of the bob (6.10), and- the hard spring, the y i e l d stess can be d i r e c t l y read from the recording as the d i f f e r e n c e between d and ab, m u l t i p l i e d by the scale and stress conversion f a c t o r s . The scale conversion f a c t o r f o r the recorder scale of 2 m.v./lO in. i s 0.2; that i s 10 recorder scale d i v i s i o n s at 2 m.v./lO in. are equivalent to a scale reading of 2 on the meter of the Rotovisco. 6.6. -Reproducibility of y i e l d Stress Measurement According to the measurements on a washed clay (19.01% by weight of clay) without added s a l t , the per cent error at 95 per cent confidence i s ± 1.86. The maximum y i e l d stresses (after 12 hour aging) 3 3 3 2 were 5.73 x 10 , 5.67 x.10 and ,5.75.x 10 dynes/cm . Another seri e s of measurements of a washed clay (18.97% by weight of clay) gave a better r e p r o d u c i b i l i t y . The per cent error at . 3 95% confidence i s ± 0.663. The maximum y i e l d stresses were 5.33 x 10 , 3 - 3 2 5.35 x 10 and 5.35 x 10 dynes/cm . 100 d e e b a o o o o o o o o o o o o < Figure 12. A typical shear stress recording. 101 The good r e p r o d u c i b i l i t y of y i e l d stress indicates that the technique used f o r destroying the clay p a r t i c l e o r i e n t a t i o n p r i o r to a te s t by the paddle was very e f f e c t i v e . 6.7. Moisture Content Based on Maximum Y i e l d Stress Starting from a washed clay of 19.66 wt. % clay, a se r i e s of measurements of y i e l d stress were made at d i f f e r e n t wt. % of clay, each sample being prepared from the s t a r t i n g one. The r e s u l t s are given i n Table VII and shown i n Figure 13. The s e n s i t i v i t y of the maximum y i e l d stress to the clay content ( or moisture content) i s so high that one scale reading, on the recorder at 2 mv when spring 500 i s used, i s equivalent to 0.01 wt. % change of clay concentration. For example, f o r the f i r s t s e r i e s of y i e l d stress measurements d i s -3 cussed i n the l a s t section, the average value i s (5.72 ± ,0.11) x 10 2 2 dynes/cm . The error of ± 110 dynes/cm i s equivalent to about ± 0.01 wt. % clay. This means when a clay sample has a maximum y i e l d stress 3 2 of 5.72 x 10 dynes/cm , the clay content of the sample i s (19.01 ± 0.01) wt. %. TABLE VII - Moisture Content on Maximum Y i e l d Stress Recorder Reading at Head 500 and 5. mv Y i e l d Stress2 (dynes/cm ) wt.% of Clay wt.% of Water. 119 1.24 x 10 4 19.66 80.34 9 1 - 4 > 90 5 89.6 9 0 ' 3 9.41 x 103 19.37 80.63 63.4 6.59 x 10 3 19.10 80.90 50.7 5.27 x 10 3 18.97 81.03 102 WT% OF WATER IN CLAY PASTE 81 80-5 80 19 19-5 20 WT% OF CLAY IN CLAY PASTE Figure 13. Moisture content effect on maximum yield stress. 103 One thing which must be mentioned here i s that van Olphen (80,101) plotted the Bingham y i e l d stress against (C-Cm), using double logarithmic 2 sc a l e s , and obtained a s t r a i g h t l i n e corresponding to T .= k (C-Cm) at B high Bentonite concentrations. where: C = clay concentration k,Cm = constant Therefore, the r e l a t i o n s h i p got i n t h i s work i s good i n the observed range, but the question of how wide a range t h i s can be extended should be answered by further study. 6.8. Aging Test of Clay Paste (Without Salt) (see also 3.1. and 5.5). The y i e l d stress of a washed clay (19.06 wt. % clay) was measured a f t e r various aging periods. In view of Figure 14 and Table VIII, the minimum aging time required f o r the clay paste to develop i t s f u l l g e l strength was chosen as 12 hours. If 11 hours i s considered to be the minimum aging time, the average maximum y i e l d stress of the 19.06 wt. % 3 2 clay i s (6.19 ± 0.18) x 10 dynes/cm , the per cent error i s ± 2.84%. TABLE VIII - Aging Test of Clay Paste (19.06 wt. % clay, without s a l t ) Aging Period (hr) Recorder Reading at 2 mv and Head 500 Y i e l d Stress dynes/cm z 0 41.5 4.32 x 10 3 1 46.6 4.85 2 53.5 5.56 4 55.3 5.75 8 57.5 5.98 11 60.2 6.26 13 hr. 47 min. 58.8 6.12 20 hr. 45 min. 59.5 6.19 YIELD STRESS X 10 , dynes/ cm2 Oi (Ti OQ c rt > 00 . H-3 OQ ro cn o H i tf CO si r t O c CO ft) vo o ON o ft) 2 m * 0 T Since the l o c a t i o n of the minimum aging time was the only purpose of th i s t e s t , no attempt has been made to curve f i t the data. An assumed dotted l i n e was therefore drawn through the data. The l i n e i s s i m i l a r to those found f o r 6, 8 and 10 wt. % Aquagel B e n t o n i t e ^ 1 2 ^ . 6.9. E f f e c t of Rototional Speed of Bob, on.Yield S t r e s s ( see also 3.1) A set of measurements of the y i e l d stress of a washed clay paste (19.39 wt. % clay) were made at d i f f e r e n t r o t a t i o n a l speeds of the bob. The data are shown i n Table IX. Shear rate was calculated from Equation (3) i n 3.1. From the log-log p l o t of verse i n Figure 15, i t can be seen that the flow equation of the investigated clay system ; follows a simple power law. TABLE.IX - Rotating Speed of Bob on Y i e l d Stress U W* rad/sec. dynes/cm 2 Shear rate rad./sec. 2 3.684 1.14 x 10 4 140 3 2.455 1.13 x 10 4 93.1 6 1.228 1.02 x 10 4 46.6 9 0.81.84 9.88 x 10 3 31.0 18 0.4093 9.60 x 10 3 15.5 162 0.04530 9.55 x 10 3 1.72 * Calibrated bob speed (see also 5.4). 106 5 1 • • / sec • / sec — ian • rad i • S L O P E = 1 3 - 8 / 0 - 6 5 0 = 21-2 3* TY o o _ l UJ . > 10 ANGULAR • • 2xl0"2 i f i i i i i l 1 l l 1 i 1 I 1 2xl03 IO4 SHEAR STRESS r b, dynes / cm2 Figure 15. Log-log plot of to versus x 107 Figure 16 clearly illustrates that the extrapolation of the flow curve of the clay system to zero shear rate w i l l not be necessary, because the yield stress measured at U = 162 with speed re-ducer ZG10 i s , within experimental error, equivalent to that of zero shear rate. 6.10. Grooved Bob and Yield Stress (see also 5.2) (37) Vocadlo and Charles did a series of very interesting ex-periments of the (3 effect on yield stress. The results are reproduced in Figure 17. If the extrapolation to the range B = 0.742 to B = 1 i s valid, the M' at B = 1 can be considered as the true value of Mi of the ' o - o examined system. As calculated in 5.2, the B of the bob employed in this work is 0.888, hence the per cent error of My assessed by the bob w i l l y.be - ± 3.4% , ± 3.6% and ± 5.7% respectively for MgO, kaolin and T i 0 2 systems based on the "Pseudo-true" value of My. It should be emphasized again that the extrapolation into the B = 0.742 to 8 = 1 range by only three data points is doubtful and hence the name "Pseudo-true" value of Mq.. Even i f the extrapolation is correct, the measurement of yield stress by the bob in this work is ju s t i f i e d by the time saved, as mentioned in 3.1, at the sacrifice of a l i t t l e accuracy; as low as ± 3.5% for most systems. 6.11. Salination and Cation Valence on Maximum Yield Stress A. Molality of Salt As mentioned in 2.4, N i c h o l s o n f o u n d that the degree of 50 SHEAR RATE, 100 radians / sec 150 Figure 16. Extrapolation of flow curve to zero shear rate of a 19.39 wt. % clay paste without s a l t . Figure 17. Torque versus the geometric f a c t o r s g f o r suspensions of TiCL, k a o l i n and MgO i n water. Aft e r Vocadlo and Charles(37). 110 raggedness of the decay curve increased with' increased cation strength. In order to check i f there i s some r e l a t i o n s h i p between maximum y i e l d s tress and i o n i c strength, a p l o t of y i e l d stress versus m o l a l i t y of s a l t was made i n Figure 18. Since i n c a l c u l a t i n g the i o n i c strength i t i s necessary to use the m o l a l i t y , Figure 19 i s a sort of an amplified p l o t of the lower concentration part of Figure 18. No curve f i t t i n g has been attempted i i view of the shape v a r i a t i o n s from one system to another. The range f o r m o l a l i t i e s below Q^W2M.was not observed because of the l i m i t of the s e n s i t i v i t y of the spring used i n these tests f o r the low shear stresses on the one hand, and because the maximum developable y i e l d s t r e s s occurs beyond these concentrations anyway(CaG^ i s the only exception). Due to the very f l a t maximum, the determination of the mo l a l i t y corresponding to the maximum developable y i e l d s t r e s s of CuCl and NaCl i s not accurate. An estimate of the uncertainty of these values was made. I t should be remembered that the r e p r o d u c i b i l i t y discussed i n 6.6 i s that f o r the system of washed cla y without s a l t . What we have now are systems with d i f f e r e n t s a l t s . Therefore, i t seems to be reasonable to estimate the accuracy of the maximum developable y i e l d s tress by the three points nearest to the maximum. By t h i s means, the maximum developable y i e l d stresses and the corresponding m o l a l i t i e s were estimated and are shown with a l l the other maximum y i e l d stress data ; i n Table X - XIV. The per cent errors i n the maximum developable y i e l d stress are quite comparable with those given i n 6.6. The average maxi-mum y i e l d stress f o r CuCl, MnCl 2 and CeCl^, systems i n which the Cu +, 2+ 3+ Mn and Ce are found i n only trace amount,, i n natural clay, i s pro-TTT MAXIMUM v-3 YIELD STRESS x 10 , dynes/cm' cn O H -< O CO g > o / / / • / I* I » I \ \ \ \ \ \ • < N I 4 / / < o 5 s O l CO H m o • o r o • < • > < O 2 O Z O <9 3 O O C — 2. 2. 2. 2. b l N N I < / o 6 ro cn 00 w H m TABLE X - Maximum Yield Stress of CaCl 2 System at Different Concentration of CaCl 0 Molality , Meq/100 gm Clay 2 Yield Stress (dynes/cm ) 0.003 2.618 5.46 x 10 3 0.004 3.401 4.62 0.008 6.982 3.96 0.01 8.72.7 3.38 0.016 13.96 3.17*| f 3.14 x 10 3.11 J 0.024 20.95 3.87 0.032 27.93 2.50 0.040 34.91 2.51 0.048 41.89 3.13 TABLE XI - Maximum Y i e l d Stress of NaCl System at Di f f e r e n t Concentration of NaCl M o l a l i t y meg/lOO gm clay Y i e l d Stress (dynes/cm ) 0.002 0.008 0.01 0.015 0.025 0.03 0.04 0.07 0.08 0.09 0.11 -0.13 0.20 0.0820±0.014 0.8488 3.398 4.247 6.371 10.62 12174 16.99 29.73 33.98 38.22 46.72 55.21 84.94 34.8+6.0 6.19, x 10" 6.59 x 10" 7.13 x 10-7.59 x 10" 9.27 x 10" 1.04 x 10 1.17 x 10 1.36 x 10 1.38 x 10 saturation point 1.37 x 10 1.33 x 10 4 1.33 x 10 4 4 1.26 x 10 estimated , ave. satur-(1.37+0.0258) x 10 atio n point per cent error=17 per cent error=1.88 115 TABLE XII - Maximum Yield Stress of CuCl System at Different Concentration of CuCl Molality Meq./lOO gm Clay 2-Yield Stress (dynes/cm ) 0.003 1.274 0.005 2.123 0.01. 4.247 . \ 0.015 6.370 0.0175 7.431 0.02 8.492 0.025 10.62 0.03 12.74 0.016310.0038 6.92+1.6 per cent error=23 7.29 x 10" 9.10 x 10" 1.07 x 10^ 1.10 x 10* 1.11 x 10* saturation point 1.10 x 10 9.70 x 10 3 8.84 x 10 3 (1.1110.0149) x.lO estimated 4 ave.satu-ration point per cent error=1.35 TABLE XIII - Maximum Yield Stress of MnCl 2 System at Different Concentration of MnCl 2 Molality.. Meq./lOO gm Clay 2 Yield Stress (dynes/cm ) 0.004 3.398 7.08 x 10 3 0,006 5.098 7.90 0.007 5.948 8.27 0.007.5 6.3/3 8.32 x 10 3 saturation point 0.008 6.780 8.23 0.012 10.20 6.63 0.016 13.60 5.28 0.024 20.42 5.11 0.032 27.24 5.25 estimated 0.00742+0.00068 6.3110,58 (8.2710.116) x , „3 10 ave.satu-ration per cent error=9.2 per cent error= point =1.40 116 TABLE XIV - Maximum Y i e l d Stress of CeCl^ System at D i f f e r e n t Concentration of CeCl„ M o l a l i t y Meq./100 gm Clay Y i e l d Stress (dynes/cm 2) 0.002 2.549 5.93 x 10 3 0.003 3.823 6.48 0.004 5.098 7.06 0.005 6.373 7.69 0.0055 7.011 7.72. saturation point 0.006 7.649 7.62 0.007 8.925 7.42 0.008 10.20 6.73"! 6.65) 6.69 x 10 3 0.01 12.76 5.13 0.012 15.31 3.73 0.016 20.42 3.79 0.020 25.54 3.93 0.030 3i8.36 3.42 estimated 0.00554±0.00073 7.06±0.93 (7. 68±0.117) ^ ave. satur-x 10 a t i o n point per cent error=13 per cent error=1.53 117 portional to the molality of the salt i n the clay paste. In other words, the a b i l i t y of the salt to build up the gel strength is inversely pro-portional to the valence of the cation in the salt. This can be qualitatively explained by the compression effect of the electric double layer. The higher the valence of the cation, the stronger the compressive power, the easier i t is to cause coagulation and thus the .weaker a b i l i t y to build up gel strength. + +2 For NaCl and CaC^, systems in which Na and Ca are in large amounts in the object clay (see Table V), the behavior i n the maximum yield stress i s very different from the other three systems. The NaCl system has the highest maximum developable yield stress and the slowest decaying speed of the maximum yield stress after saturation point. The CaCl2 system coagulates immediately when the salt concentration is beyond 0,002M. 2. Milliequivalents (meq.) per 100 gm clay at Maximum Yield Stress From Table X-XIX,. the effect of the meq. of salt per 100 gm clay can be analysed as follows:-a) For NaCl and CaClv, systems, the amount of the salt at satu-ration point is very different from the other three systems. The object clay can tolerate the largest meq. of NaCl; as high as 34 meq., but cannot tolerate even 2.6 meq. CaC^. This could be interpreted by assuming that the structure of the object clay is such that i t prefers + +2 + to adsorb Na and Ca . For. Na , because of i t s low exchange power in general, i t takes a higher concentration to cause ion exchange by the 118 mass action law (see 3.2) and thus takes multiple amounts of "Na to +2 exchange with those ions of higher valence. For Ca , the much stronger a b i l i t y to compress the electric double layer, coagulates the clay immediately before i t has too much chance to make ion exchange. b) For CuCl, MnCl 2 and CeCl 3, the washed clay (19.06 wt. %) almost equally exchanged with them. That is why they can be compared and have a certain relationship between the maximum developable yield stress and the valence of cation as mentioned in the last section. 3. Microphotographs In order to check the coagulation state near the saturation point, microphotographs were taken and are shown in Figure 20 to 25. The calibration photo is included to show the scale as well as the "noise" in the background by d i r t . That for the washed clay suspension, a significant coagulation takes place may be due to the incomplete dis-persion of the particles. In the CaCl 2 system, clear agglomerates can be seen. They are most lik e l y caused by flocculation since they look more transparent than those i n the NaCl and MnCl 2 systems, i n which dense floes are shown which could be caused mainly by aggregation (see 3.2). Figure 20 to 25 illustrates the tendency of stronger co-agulation at higher salt concentrations, a good demonstration of the salt concentration effect on coagulation. According to the photos, i t seems that the coagulation does not happen exactly when the yield stress is at i t s maximum developable value. Therefore, the point at which the maximum developable yield stress occurs is called the saturation point, 119 Ca Iteration (scale- one dark d i v i s K f Washed clay + water, 500X f i g u r e 20. KicropHotos o £ washed clay suspension and c a l i b r a t i o n 120 121 f it a) a) aafore sat rt at s a t u r a t e « 122 f w f il f i g u r e 23. Hicrop Yiotos o £ H n C l 2 system betor e s a t u r a t i o n D i f f e r e n t A g S l o m e r 500X. f gure 2 4 . Micropnotos o £ ttnCl2 system at sa turation P oint. Different a g glomer s . 500X. 124 f f i g u r e 25. 1! 1 • • • \ • • • * • % 9 I • 1 „ o f A vration o: H i c r o p n o t o s ,f ^ C l 2 system f aeelc-mers. D i f f e r e n t ags 500X. 125 i n the sense that at that point the a b i l i t y of a salt to build up the gel strength is saturated. > 126 Chapter 7,  CONCLUSIONS The conclusions reached after this study are li s t e d below:-1. By using a low rotational speed (0.432 r.p.m.) and a grooved bob (3 = 0.888), a non-flow yield stress can be assessed within a reason-able time with a small experimental error. 2. A few strokes of a very simple paddle can serve to destroy randomly the gel structure of clay. This produces a good starting con-dition for the measurement of the yield stress of the clay system and solves the particle orientation or "shear harden" problem. 3. As to the cation effect on maximum yield stress; among the five salts tested, NaCl and CaC^ behave very differently from the other three salts. This is probably because of the large amount of Na + and +2 Ca in the investigated clay. The clay can tolerate the largest amount of NaCl, and can be build up to the strongest gel by NaCl but the clay is coagulated immediately by CaC^ and no gel can be observed within the concentration range examined. CuCl, MnC^ and CeCl^ exchange approximately equally with the clay and a definite relationship exists \ -between the maximum"developable yield stress and the molality of the salt added. The former is proportional to the latter. In other words, among the salts with cations that are contained in trace amount in natural clay and the chloride ion or other non-adsorbable anions, the a b i l i t y of the salt to build up the gel strength is inversely proportional to the valence of the cation in the salt. 4. Maximum yield stress is a very accurate parameter for measuring moisture content of clay pastes. The accuracy i s as high as 0.01% by weight. 5. The maximum yield stress can be accurately measured but the molality of the salt at the saturation point can only roughly be e s t i -mated because of the f l a t maximum of yield stress. 6. The clay particles examined i n this work are negatively charged. The surface charge is very small due to the small excess of nagative charge on the f l a t surface over the positive charge on the edge of the particle.. 7. Aging time for this clay to develop i t s maximum gel structure was a minimum of about 12 hours. 128 Chapter. 8v RECOMMENDATIONS As a r e s u l t of t h i s study, several recommedations can be made:-1. ' In washing out the soluble s a l t s i n the clay, 40% aqueous (98") ethanol should be used to eliminate the hydrolysis e f f e c t . 2. A ./radioactive tracer t e c h n i q u e ^ 4 ^ might be used to follow the degree of cation exchange between the added s a l t and the clay (see Appendix I I ) . 3. D i f f e r e n t concentrations of clay could be prepared to ob^r serve the clay concentration e f f e c t at the same s a l t concentration on the maximum y i e l d s t r e s s . 4. To check the p r o p o r t i o n a l i t y of the maximum y i e l d stress to mo l a l i t y of the s a l t , other s a l t s which o r i g i n a l l y are found i n only trace q u a n t i t i e s i n clay such as ThCl^ and (Hexol) C1^^J can be used. Though the i o n i c radius of T h + 4 or Hexol +^ might.be d i f f e r e n t from Cu +, +2 +3 Mn or Ce , t h i s e f f e c t would be shielded by the large m o l a l i t y e f f e c t . A l C l ^ , as with NaCl and CaC^, i s expected to have a s p e c i a l e f f e c t on the c l a y . This could be checked too. (9 3 D 5. A r t i f i c i a l c e l l u l o s e p a r t i c l e s ' of very small p l a t e -129 -iq.J.1,: - ~ . . . . . — l i k e or lath-like shape : /can be employed to observe, the shape and size effect of the particles on the maximum yield stress. However, the surface of the cellulose particle should be examined f i r s t to determine which kind of electric double layer is formed in salt solutions. 130 LITERATURE CITED 1. Doherty, D. J . , Kurd, R.^J.-Oil and Colour Chemists Assn., 41:42 (1958). 2. Dahlgren, S.E., J . C o l l o i d Science, 13:151 (1958). 3. Osborne, D.G., Thornton, S., Br. J . Appl. Phys., 10:214 (1959). 4. Kerr, P.F., S c i e n t i f i c American 209:132 (1963). 5. Pinder, K.L., Can. J . Chem. Eng. 42:132 (1964). 6. Alves, G.E., Boucher, D.F., Pi g f o r d , R.L., Chem. Eng. Progr. 48:385 (1952). 7. Bernstein, H.B., Barr, M., J . Am. Pharm. Assn. 44:375 (1955). 8. McKay, W.N., Boucher, W.W., M i l i n e , J . , Presented at C.I.C. Meeting Montreal, Oct. (1963). 9. 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Weltmann, R.N. , J . App l . Phys . , 14:343 (1943). 23. Green, H. Weltmann, R ??N., Ind. Eng. Chem.^lS^Ol (1943). 24. Pryce-Jones, J . Chemistry and Ind . , 233 (1948). 25. K i s t l e r , S .S . , J . Phys. Chem., 36:2948 (1932). 26. Hofmann, U. , K o l l o i d Z e i t s c h r i f t , 125:86 (1952). 27. Abduragimova, L .A . , Rebinder, P .A. , Serb-Serbina, N .N. , Inst , of Phys. Chem., Academy of Science U.S.S.R. , March 20 (1955).. 28. S co t t -B l a i r , G.W. J . S c i e n t i f i c Instruments, 17:169 (1940). 29. M'Eween, H.B., P r a t t , M.I., Trans. Far . Soc. 53:535 (1957). 30. Sparnsasy, M.J . , Jochems, P.W., V o l . I I, Sec. B, 3rd Intern . Congr. of Surface A c t i v i t y , Cologne (1960). 31. Brown,,J.P., Pinder,>K%L., Can. J. Chem. Eng., 49:38 (1971). 32. Moore, F., "Rheology of Ceramic Systems", Inst, of Ceram. Text book Series (1965). 33. Searle, A.B., Grimshaw, R.W., "The Chemistry and Physics .of. Clays and Other Ceramic Materials", 3rd ed. Ernest Benn Limited (1959). 34. H. van Olphen, "An Introduction to Clay Colloid Chemistry", Interscience (1963). 35. Freundlish,H. von,Schmidt, 0., Lindau, G., Kolloid Beihfte, 36:43 (1932). 36. Neumann, B.S. Sanson, K.G., Clay Minerals, 9:231 (1971). 37. Vocadlo, J.J., Charles, M.E., Can. J, Chem. Eng. 49:576 (1971). 38. Bulletin of the British Soc. of Rheology, 3:7 (1966). 39. Van Wazer et a l . , "Viscosity and Flow Measurement", Interscience Publishers (1963). 40. Marshall, C.E., "The Physical Chemistry and Mineralogy of Soils", Vol. I: Soil Materials, John Wiley (1964). 41. Weyl, W.A. and Ormsby, W.C., "Atomic Approach to the Rheology of Sand-Water and Clay-Water Mixtures", in "Rheology", Vol.3, edited: by Eirich, 1960. 132 42. H. van Olphen,.. J.- Inst. P e t r o l . , 36:223 (1950). 43. Morrison, S.R., Harper, J.C., Ind. Eng. Chem. Fundementals 4:178 (1965). 44. Rebinder, e d i t o r , "Physicochemical Mechanics of Clay-Mineral Dis-persions ",(1967). 45. Finke, A., Heinz, W. , Rheologica Acta 1, #4/6, 530 (19.61). 46. Boardman, G., Whitmore, R.L., Laboratory P r a c t i c e , p.782 (1961). 47. H a l l , E.O.,"Yield Point Phenomena i n Metals and All o y s " , M c M i l l i a n (1970). 48. Grim, R.E., "Clay Mineralogy",2nd ed., McGraw-Hill (1968). 49. Mattson, S., S o i l S c i . , 32:343 (1931). 50. K e l l y , W.P., "Cation Exchange in. Soils",Reinhold (1948). 51. I b i d . , Proc. 1st Intern. Congr. S o i l S c i . , 4:483 (1927). 52. Jenny, H., Overstreet, R., S o i l S c i . , 47:257 (1939). 53. I b i d . , Ayers, A.D., S o i l S c i . , 48:9 (1939). 54. Jenny, H., J . Phys. Chem., 40:501 (1936). 55. Buswell, A.M., Dudenbostel, B.F. ,• J . Am. Chem. S o c , 63:2554 (1941) 56. Magistad, O.C., Burgess, P.S., A r i z . Univ. A g r i . Expt. Sta., Tech. B u l l . 20 (1928). 57. Low, P.F., P r o c 9th N a t l . Clay Conf. p.219 (1962). 58. Wilklander, L., Chap. IV,- p.163, Am. Chem. Soc. Monograph (1964). 59. Jenny, H., Ayers, A.D., S o i l S c i . , 48:443 (1939). 60. Wilklander, L., :Ann. Roy. Agr. C o l l . Sweden, 14 (1946). 61. Marshall, C E . , "The C o l l o i d Chemistry of the S i l i c a t e Minerals", Academic, New York (1949). 62. Baver, L.D., Witerkorn, H.F., S o i l S c i . , 40:403 (1935). 63. Winterkon, H.F., Baver, L.D., S o i l S c i . , 38:291 (1934). 64. Ravikovitch, S., S o i l S c i . , 38:219;279 (1934). 65. Scarseth, G.D. , J . Am. Soc. Agron. , 27F:596 (1935). 133 66. Toth, S.J., S o i l S c i . , 44:299 (1937). 67. McAuliffe, CD.,, H a l l , M.S., Dean, L.A., Hendricks, S.B., S o i l S c i . Soc. Am. P r o c , 12:119 (1947). 68. Dickman, S.R., Bray, R:H., S o i l S c i . , 52:263 (1941). 69. S c h o f i e l d , R.K. . Trans. B r i t . Ceram. S o c , 39:147 (1940). 70. I b i d . , Trans. B r i t . Ceram. S o c , 48:207 (1949). 71. Peech, M. S o i l S c i . , 59:25 (1945). 72. Peech, M., Alexander, L.T.,Dean, L.A.,- U.S'. Dept. Agr. C i r c . 757 (1947). 73. Mattson, S., S o i l S c i . , 31:311 (1931). 74. Oka, S./'Theory and A p p l i c a t i o n s " i n "Rheology" Vol.3, edited by E i r i c h (I960). 75. Macey, H.H., Trans. B r i t . Ceram. S o c , 41:73 (1942). 76. McBain, J.W., J . Phys. Chem., 30:239 (1926). . 77. Grim, R.E. , Cuthbert, F.L.,- J . Am. Ceram. S o c , 28:90 (1945). 78. McDowell, CM.,Usher, F.L., Proc. Roy. S o c , A131:564 (1931). 79. Hofmann, U.,Fahn, R. , Weiss, A., Clay Min. B u l l . , 2:7,0 (1953). 80. . H. van olphen, .-Clays and Clay Min., 4th N a t l . Conf., p.273 (1956). 81. Hauser, E.A., Reed, C.E., J . Phys. Chem., 40:1169 (1936)., 41:911 (1937). 82. Quincke, G., Ann. Physik [2] 113, 531 (1861). 83. H. von Helmholtz, Ann. Physik [3] 7, 337 (1879). 84. Gouy, C , J . Phys.,. 9:457 (1910). 85. Mackor, E.L., Rec. Trav. Chim., 70:841 (1951). 86. B o l t , G.H., J . C o l l o i d S c i . , 10:206 (1955). 87. H. van Olphen, Rec. Trav. Chim., 69:1308 ( I ) , 1313:^1322 ( I I ) , (1950). 88. I b i d . , Discussions Faraday S o c , 11, (The Size and Shape Factor i n C o l l o i d a l Systems), 82 (1951). 134 89. Sc h o f i e l d , R.K., Samson, H.R., Discussions Faraday Soc., 18 (Coagulation and F l o c c u l a t i o n ) , 135; 220 (1954). 90. Gedroits, K.K., "Chemical Analysis of Soils",Translated from Russian, (1963). 91. Nutting, P.G., U.S. Geol. Surv., Profess. Paper 197F; p.219 (1943). 92. K e l l y , W.P., S o i l S c i . , 40:103 (1935). 93. Paver, H., Marshall, C.E., J . Soc. Chem. Ind. (London), 53:750 (1934). 94. Chatterjee, B., Paul, M. , Indian J . Agr. S c i . , 12:113 (1942). 95. Mukherjee, J.N., Chatterjee, B., Goswai, P.C., J . Indian Chem. S o c , 19:40 (1942). 96. Hofmann, U., Klemen, R., Z. Anorg. Chem., 262:95 (1950) ref e r r e d by Grim (48) p.206. 97. Gould, E.S., "Inorganic Reactions and Structure",1962. 98. David, D.J., Analyst^, 85:495 (1960). 99. Jackson, M.L.,Truog, E., Proc. S o i l S c i . Am., 4:136 (1939). 100. Bar-on, P.,Shainberg, I., S o i l S c i . , 4:241 (1970). 101. H. van Olphen, Proc. 6th N a t l . Conf., Clays and Clay Minerals, Pergamon Press, New York, 196 (1959). 102. Clem, A.G., Doehler, R.W., Clay and Clay Min. Proc. 10:272 (1963), 103. Borland, J.W., Reitmeiter, R.F.,Soil S c i . , 69:261 (1950). 135 NOMENCLATURE AC b C C m h k m M c n P. . V R T : . u - l T y p i c a l Units 2 Equal to A]•: plus A cm B S Area of grooves per u n i t height, calculated ^ at R^ cm Surface area of r i b s per u n i t height as calc u l a t e d by summing i n d i v i d u a l arc length ^ at R, • cm D Depth of groove cm Clay concentration wt'. % Constant Rate of s t r a i n tensor sec Height of bob immersed i n f l u i d d cm b' 2 Constant or equal to 1 + ^ (R^*/R^) Equal to dlnto/dlnx^. Moment on grooved c y l i n d e r dyne-cm Number of teeth or grooves on the surface of bob 2 I s o t r o p i c pressure dyne/cm 2 Stress tensor ^ dyne/cm Distance from center of bob to r i b surface cm Distance from center of bob to bottom of groove cm Radius of cyl i n d e r cm Reading on Rotovisco meter scale i n normal range 2 Stress deviator dyne/cm Number of gear p o s i t i o n on top of cont r o l unit of Rotovisco viscometer, assumed to be sec. i n dimension sec. Greek Letters Typical Units g Equal to A'-/A 6.. Kronecker delta e Equal to 5 Addition parameters K. 2 x. Shear stress at the surface of bob dyne/cm b 2 T Bingham yield stress dyne/cm B 2 x Yield stress dyne/cm o 2 Shear stres at surface of smooth cylinder dyne/cm $ E l e c t r i c a l potential at the surface of particle in Stern's electric double layer volt Stern potential volt to Angular velocity of bob radian/sec (bFactor Ratio of bob speed measured without speed reducer to that stated in^ ' (486/U x 1.2 r.p.m.) 137 APPENDIX I  BENTONITE CLAY I - l , D e f i n i t i o n Various d e f i n i t i o n s of Bentonite have been given i n the l i t e r a t u r e , but generally a l l agree that Bentonite i s a g e o l o g i c a l term used to designate a n a t u r a l l y occurring, very f i n e grained material l a r g e l y composed of the clay mineral, m o n t m o r i l l o n i t e . Accordingly;,a d e s c r i p t i o n and discussion of montmorillonite i s applicable to Bentonite as w e l l . Bentonite, i n a d d i t i o n to montmorillonite, con-tains a small portion of other mineral matter, usually a combination of quartz, f e l d s p a r , v o l c a n i c g l a s s , organic matter, gypsum, or p y r i t e . With respect to i t s g e o l o g i c a l c l a s s i f i c a t i o n ^ 4 ^ montmorilld-n i t e i s a species of the dioctaKedral smectities or montmorillonites sub-group of smectite or montiiiorillonite-saponite group. Vermiculite i s of the same type as smectite and mica. Muscotive i s a species of the mica group. K a o l i n i t e i s a species of the k a o l i n i t e s sub-group of the k a o l i n i t e - s e r p e n t i n e group. I t i s of a d i f f e r e n t type from that of smectite. 1-2. Structure of Montmorillonite Chemically, montmorillonite i s described as a hydrous aluminum s i l i c a t e containing small amounts of a l k a l i and a l k a l i n e - e a r t h 138 metals. Structurally, montmorillonite Is made of two basic building blocks, the aluminum octahedra sheet and the s i l i c a tetrahedral sheet. A single montmorillonite unit c e l l consists of two s i l i c a tetrahedral sheets, between which is an aluminum octahedral sheet. Lengths and widths of montmorillonite flakes are from 10 to 100 times the thickness. The montmorillonite la t t i c e is negative in charge, owing primarily to isomorphous replacements of ions within the structure. This negative character is balanced by cations which are held on the surface of the flakes. Cations held in this fashion by the clay can be readily ex-changed, the most commonly.found in nature are sodium and calcium. The exchange cations, both by type and amount, that are associated with montmorillonite are of great importance since they largely control i t s physical properties. Montmorillonite adsorbs water whenever i t is available. Water adsorption occurs to the greatest extent on the basal surfaces of the clay and in this fashion pries adjacent flakes apart, resulting in an overall volume increase of the clay. A diagrammatic edge view of montmorillonite is shown in Figure 26. Na I (exchangeable) b 6. Diagrammatic edge view of montmorillonite a f t e r M a r s h a l l ^ 0 ) . 140 APPENDIX II RADIOACTIVE TRACER TECHNIQUE TO. FOLLOW EXCHANGE STATE.OF SALT WITH EXCHANGEABLE CATION OF CLAY As mentioned in 3.2. the classical method of leaching, washing, and subsequent analysis in the determination of the cation exchange capacity and nature of the exchangeable cations always i n -volves at least two cations, each of which may impose special characteristics. Hence, methods,,which involve single radioactive tracers and which determine the labile pool of ions of a given kind are l i k e l y to yield a better approach. The method was f i r s t used by Borland and Reitemeier^"'"^"^ for calcium, and has been extended to other cations by Fisher and Grahen/ 4^. A small known amount of a radioactive tracer in solution is equilibrated against the exchanger. For calcium at equilibrium (Ca*/Ca) E x c h_ = ( C a V C a ) ^ ^ But ( C a * ) E x c h > i s given by the loss of the radioisotope from the original solution. Once ( ^ a ) g 0 i n is determined by atomic spectroscope and ( ^ a * ) g 0 i n ky counting, then ( C a ) ^ ^ can be calculated by the foregoing equilibrium relation. 141 APPENDIX III COMPUTER PROGRAMS* I I I - l . Main Programs A. Main Program PKL - calculating mean value, i t s 95, 99 or 99.5 confidence limit and per cent error of a set of data. $RUN P K L 5 = K L ( 9 4 ) < - * S O U R C E * SPRI N T = * D U M M Y * I , 2 9 ) + * S I N K * OR $RUN PKL 5 = K L ( 9 4 ) + * S O U R C E * 6= * S I N K * ._RE-AD „.,N,, . B A.S.E.; . . .Z. I . I , ) .M, P.C NK N F.. M» M...I N..I 2_AND__THE REST IN F 1 C . 0 . M= + l , R E P E A T C A L C U L A T I O N OF THE CURRENT DATA WITH D I F F E R E N T P E R C E N T A G E C O N F I N D E N C E ; M=Oi S T C P A F T E R THE CURRENT C A L C U L A T I O N ; M = - l , READ NEW D A T A . B. Main Program KL - specially written for PKL. R E A L MNZ, L C Z D IMENS ION Z ( 1 0 0 ) COMMON T 9 5 O 0 ) , T 9 9 ( 8 0 ) , T 9 9 5 ( 0 0 ) C A L L T V A L U ( T T 9 5 . T T 9 9 , T T 9 9 5 ) _ K R I J E J 6 , . 1 9 J ; ; F O R M A T ( 1 8 H * * * * E N T E R D A T A * * * * ) R E A D ( 5 , 2 ) N, BASE F O R M A T ( 1 2 , F 1 C . 0 ) R E A D ( 5 , 3 ) ( Z ( I ) , I = 1, N) F 0 R M A T ( 5 F 1 C . 0 ) _ G 0 _ T 0 _ 1 1 W R I T E ( 6 , 1 9 ) RE AD (5 t 2) M, PCNKNF C A L L M N V B L U I N , B A S E , Z , P C N K N F , "MNZ, H I Z , 1 L O Z , E R Z , PRSNER ) W R I T E I 6 , 8 ) MN Z, E R Z , PRSNER , H I Z , LOZ . FOR M A T ( / 5 X , 5HM NI = , F 1 0 . 5 , 5 X , "i l 'FR Z= , .... 1 F l O . ' i / 1 C X , 8HPRSNER = , F 1 0 . 5/5X , 1 5HH IZ = , F 1 0 . 5 , 5X, 5HL0Z = , F 1 0 . 5 / / / ) I F ( M ) 9 , 9 9 , 12 STOP END _9__ 19 10 2 12 11 99 * see III-4 for Nomenclature. 142 C. Main Program XK - ca l cu l a t i ng v i s c o s i t y conversion f a c to r K from standard o i l v i s c o s i t y and s t ress record ings . REAL MNX ,. MNK, M N Z» LOX, LOK, LOZ DIMENSION X(LOG), I(100) COMMON T95I80), T99(80), T995(80) CALL TVALUITT95, TT99, TT995) 10 'READ ("5, 2") N O , NU, "N, DAS'E 2 FORMAT (2115, 15, F10.0) WRITE (6, 4 )__ NO . 4 FORMAT (10X, 9F***CALI 15, 3H***/) IF (NO .EQ. 0) STOP IF (NU .GT. 0) RO TO 20 READ (5, 3) (Z (I ), I = 1, N) CALL MNVALU(NC, NU, N, BASE, Z, 95., MNZ, HIZ, LOZ, ERZ, PRSNER) WR I.TE_<6,..6.) _NU.,_N : 6 FORMAT (IX, 3HU = , 13, 5X, 3HN =, 13) WRITE (6, 8) MNZ, ERZ, PRSNER 8 FORMAT (/5X.5HMNZ =, F10.5, 5X, 5HG*Z = , F10.5, 1 5X, 8HPRSNER =, F10.5/////) GO TO 10 _2_0 READ (5, 3)__(_X_( I_)„,__I____.1J_J1) 3 FORMAT (10F8.0) CALL MNVALUINO, NU, N, BASE, X, -9 5., -MNX, Hi-X, LOX, ERX, PRSNER) WRITE (6,66) NU, N 66 FORMAT (IX, 3HU =, 13, 5X, 3FW =, 13) WRITE (6, 9) MNX, ERX, PRSNER J2 FORMAT. (/!3X, 5HMNX =. F1C.5. 5X, 5HERX =, F10.5// • '•' 1 5X, 8HPRSNER =, F10.5//) IF (NO .LT. 6000) GO TO 30 IF (NO .LT. 2CC00) GO TO AO GO TO 50 30 STNVSC = 146.4 SF AC TR_ =_ 0. 5 ; GO TO 6 0 40 STNVSC = 146.4 SFACTR = 1.0 GO TO 60 50 STNVSC = 7856. . SJLACJ_____4.. *  60 CALL XMNU-, KNX, MNZ, MNK, ERX, ERZ, ERK, HIK, LOK, STNVSC, 1 SFACTR, PRSNER, ACEPSN) WRITE (6, 5) MNK, HIK, LCK, ERK 5 FORMAT (30X, 5HMNK =, F12.5//20X, 5HHIK =, F12.5, 5X, 1 5HL0K =, F12.5//30X, 5HERK =, F12.5/) WR ITF ( 6, 7) PRSNER, ACE P SN , 7 FORMAT (30X, 8HPRSNER =, F7.3.5X, 8HACEPSN =, F7.3/////) GO TO 10 END D. Main Program VS.CO - c a l c u l a t i n g v i s c o s i t y from stress recordings. REAL MNX, MNZ, K, MNVSCO, LOVSCO, LOX, LOZ DIKE NSI 0N_ X (1.00J , _Z_( 1 00J COMMON T95(8 0)» T99(80), T995180), CHI10180), CHI50I80 ),CHI95(80> CALL TVALU(TT95, TT99, TT995) 10 READ (5, 2) NO, NU, N, BASE, SFACTR 2 FORMAT (2115, I5.2F10.0) IF (NO .GT. 10000) GO TO 99 K = 7.57 . . GO TO 999 99 K=6.11 599 HRITE(6,4) NO 4 FORMAT (1CX, 9H***CALI - 115, 3H***/) IF (NO .EQ. 0) STOP IF ( NU .GT. 0) GO "TO 20 : READ (5, 3) ( Z ( I ) , I = 1, N) CALL MNVALU(NO, NU, N, BASE, Z, 95., MNZ, HIZ, LOZ, ERZ, PRSNER) WRITE (6, 6) NU, '.' 6 FORMAT (IX, 3HU =, 13, 5X, 3HN =, 13) . , V: WRITE (6, 8) MNZ, ERZ, PRSNER 8 FORMAT... t/5X, 5HMNZ =, F10.5, 5X, 5HERZ F10.5, "" 1 5X, 8H PRSNER = , F10.5/////) GO TO 10 20 READ (5, 3) (XII), I = 1, N) 3 FORMAT (10F8.0) CALL MNVALU(NO, NU, N, BASE, X, 95., MNX, HIX, LOX, ERX, PRSNER) WR I TE ( 6, 66) NU, N 66 FORMAT (IX, 3HU =, 13, 5X, 3HN =, 13) WRITE (6, 9) MNX, ERX, PRSNER 9 FORMAT (/5X, 5HMNX =, F10.5, 5X, 5HERX =, F10.5// 1 5X, 8HPRSNER =, F10.5//) CALL VSCOINU, MNX, MNZ, K, ERX, ERZ, PSNERK, MNVSCO, HIVSCO, 1_LO.V SC.0,_ERV SC0 , UF ACTR , _SFAC.TR ,...P.RSNER,_.ACEPSN) WRITE (6, 5) MNVSCO 5 FORMAT (30X, 8HMNVSC0 =, F12.5/////) GO TO 10 END 144 E..Main Program SEARCH - linear interpretation of data (of viscosity and density of dispersing medium). DIMENSION AI10, 10), B(10), C(10), X(2C, 20), Y(20), DI10), V(10) COMMON A, B 9 CALL LSQMCO(3,2) CALL SOLUTNtA, B, 3, OET» D) D.Q_9.Q.JL_^_l.i_3 90 WRITE16, 4 ) It D ( I ) 4 FORMAT (20X, 2HD(, 12, 3H) =,, E20.9) CALL LSQMCO(3, 2) CALL SOLUTNtA, B, 3, DET, V) "DO 100 1 = 1,3 100 WRITE.6, 11) I, V(I) . 11 FORMAT (20X, 2HV(, 12, 3H) = ,.E20.9) IF (N .EQ. 2) GO TO 200 CALL SEARCH11., 0.1, 30, 75., 0.2, 25, 1 0( 1 ) , D(2), 0(3), V ( l ) , V(2), V<3)> N = N + 1 GQ_J_CL_9 — — 2CC CALL SEARCH( 1., 0.1, 30, 73., 0.3, 25, 1 0(1), D(2), D(3), V ( l ) , V(2), V(3)) GO TO 9 END I I I - 2 . Subroutines A. -Subroutine TVALU - for generating T values for 95, 99 and 99.5 per cent confidence limit calculations. SUBROUTINE TVALU(TT95 , TT99, TT995) _C_SUBRD.U1JNE_XVALJUI :  C COMMON T95(80), T99(80), T995180), CHI10180), CHI50(80),CHI95(80) READ (5, 1) (T95(I), I = 1, 80) READ (5, 1) (T99(I), I = 1, 80) READ (5, 1) (T995(I), I = 1, 80) J F ORM AJ__(_1 OF 8 ...O.L_ WRITE (6, 11) 11 FORMAT (60X, 12HT1DF - T79DF/) WRITE (6, 20) 20 FORMAT (10X, 5H*T95*) WRITE (6, 2) ( T 9 5 U ) , 1 = 1, 80) WR IT E_ ( 6 ,_3a) • ' 30 FORMAT (10X, 5H<=T99*=) WRITE (6, 2) (T99II), I = 1, 80) WRITE (6, 40) AO FORMAT (10X, 6H*T995*) WRITE (6, 2) (T995(I)f I = 1, 80) 2 FORMAT _(2QX,_J.0F8.4) • RETURN END 145 B. Subroutine MNVBLU - specially written for main program KL. 2_. 70 10 600 30 JL99_5.(8.0.)_ SUBROUTINE MNVBLUtN » BASE, 1HIK, LOK, ERK, PRSNER) .C_MEAN VALUE ( WI TH .95 OR 99 CR .99.5 C 'CON'FTDE N'C'E LIMIT ) OF 'K 'DATA C MEAN VALUE LIMIT = MNK + OR - ERK C REAL K, LOK, MNKK, MNK DIMENSION K(N) , T(80) C.OMM.QN_J.9.5.(.0.0.)..,_.T_9i»_L8.0Jj. M = N - 1 WRITEI6, 1) BASE 1 FORMAT(10 X, 6H-DATA-/5X, 1 F10.5, IH)) WRITE(6, 2) ( K ( I ) , JF OR MAT L5F.I. C ._5_.)__ SMK = 0.0 SMSQK = C O DO 10 I = 1, N SMK = SMK *• Ki I ) KII.) = K.M ) + .BASE _SK5 QK = SMSGK + K(I) XN K, PCNKNF, MNK, .P-E£_CENT_ 7H(BASE = , I = 1, N) 2 N MNK = SMK / SMK = SMK + SQS = (XN * IFISQS .GE. WRITE(6,4 ) XN + BASE XiM * BASE SMSQK - SMK ** CO) GO TO 6C0 2) / (XN * (XN- 1.0>> FORMAT(2 CX, 34HSCS VALUE IS LESS ERK = 0.0 GO TO 90 IF (PCNKNF - 99.) 30, AO, 50 T(M) = T95(M) GO T0_2_Q : THAN ZERO// ) AO T(M) = T 99(M) GO TO 20 50 T(M) = T995IM) 20 ERK = T(M) * SORT(SQS/XM) 90 IF (MNK .NE. 0.0) GO TO 900 WRITE (6, 5.2 5 F0RMAT(2CX, 15HMNK EQUALS ZERO//) MNK = 1 . 9CC PRSNER = ERK / MNK * 100.0 IF(MNK .NE. 1.) GO TO 1CC0 MNK = 0 . JJC C 0. H.I K = MNK ERK Continued. 146 Subroutine MNVBLU - Continued, LOK = MNK - ERK RETURN END $DATA $STOP 12.706 __4.3027 . 3. 1825 .2. 7764 .2. 5706 2.4*69 . 2.3646 2 .3060 2.2622 2.2281 2.1C98 2.093 2.0518 9.9248 4.0321 3.3554 3.2498 2.8609 14-089 4.7733 3.8325 3.6897 3.1737 C. Subroutine XK - calculating K from standard o i l viscosity and recordings, SUBROUTINE XKINU, BARX, EARZ, MNK , ERRORX, ERRORZ, 1 ERK, HIK, LOK, STNVSC, SFACTR, PRSNER, ACEPSN) C SUBROUTINE XK J C REAL K, MNK, LQK U = NU SME = BARX - 8ARZ ERROR = ERRCSX • ERRORZ SHI = SME • ERROR SLO ._=... SME_-. ERROR UFACTR =10 FAC TR = U * SFACTR *UF ACTR K = STNVSC / F ACTR MNK = K / SME HIK = K / SLC _LCK_.=„ K / SHI ERK = HIK - MNK PRSNER = ERK / MNK * 1C0.0 ACEPSN = 0.5 / SME * 100.0 WRITE (6, 2) SHE FORMAT (35X, 5HSME =, F12.5//I RETURN ; _ END D. Subroutine MNVALU - c a l c u l a t i n g mean v a l u e , i t s 95,99 or 99.5 per cent confidence l i m i t and per cent e r r o r of a set of data. SUBROUTINE MNVALU(NO, NU, N, BASE, K, PCNKNF, MNK, HIK, LOK, 1 ERK, PRSNER) C.MEAN VALUE (WITH 95 OR. 99 OR 99.5 PER CENT CONf IOENCE LIMIT.) C MEAN VALUE ?WITH 95 OR 99 CR 99.5 PER CENT CCNFIOENCE LIMIT< C OF K 0ATA C MEAN VALUE LIMIT = MNK + OR - ERK C REAL K, MNK, LCK, MNKK DIM EM SI-Q N -K (N-) ,_„T:( -8 0) : COMMON T95180), T99I80), T995I80) M = N - 1 WRITE (6, 1) BASE 1 FORMAT (60X, 6H-DATA-/55X, 7H(3 ASE = , F5.1, IH) ) IF (N.GE. 10) GO TC 60 WRITE (6, 2) (K( I) . I = 1, N) 2 FORMAT (40X, 3F10.5) GO TO 70 60 WRITE (6, 3) (Kt I) , I = 1, N) 3 FORMAT (-VOX, 1CF5.1) 70 SMK = 0.0 SMSQK = Q.O  DO 10 I = 1, N SMK = SMK + K(I) K(I) = K(I) + BASE 10 SMSQK = SMSQK + K ( l ) ** .2 XN = N MNK = SMK / XN » BASE . '_ • SMK = SMK + XN * BASE SQS = UN * SMSCK - SMK ** 2) / (XN * (XN- 1.0)) IFISQS .GE. 0.0) GO TO 6C0 WRITE(6,4 ) 4 F0RMAT(20X, 34HSQS VALUE IS LESS THAN ZERO//) ERK = 0.0 . :  GO TO 90 600 IF (PCNKNF - 99.) 30, 40, 50 30 T(M) = T95(M) GO TO 20 40 T(M) = T99(M) GO TO 20 50 TIM) = T995(M) 20 ERK = T(M) * SORTISQS/XN) 9C IF (MNK .NE. 0.0) GO TC 900 WRITE(6,5) 5 FORMAT(20X, 15HMNK EQUALS ZERO//) MNK = 1. . r  9C0 PRSNER = ERK / MNK * 100.0 IF(MNK .NE. 1.) GO TO 1000 MNK = 0. 10C0 HIK = MNK + ERK LOK = MNK - ERK RETURN END 148 E. S u b r o u t i n e VSCO - c a l c u l a t i n g v i s c o s i t y f o r R o t o v i s c o . SUBROUTINE VSCOINU, MNX, MNZ, K, ERX, ERZ , PSNERK, MNVSCO, 1.HIVSC0, LOVSCO, ER.VSCC, U F A C T R» SFACTR,.. PRSNER,. ACEPSN) C SUBROUTINE VSCO C VSCC =U * (S *SFACTR) * K C REAL MNX, MNZ, K, MNVSCC, LOVSCO U = NU SMN = MNX - MNZ •  ERROR = ERX + ERZ FACTR = U * SFACTR * K MNVSCO = SMN * FACTR WRITE ( 6 , 2) SMN, ERROR 2 FORMAT (35X, 5HSNN =, F12.5, 10X, 7HERROR '=, F10.5//) RETURN! END F. S u b r o u t i n e SEARCH - . l i n e a r l y i n t e r p r e t i n g ( v i s c o s i t y and d e n s i t y ) d a t a . SUBROUTINE SEARCH(SRPFST, SRPINC, NX 3, SOTFST, SOTINC, NX2, 1 D l , D2, C3, VI, V2, V3) X2 = SOTFST X3 = SRPFST WRITEI6, 3) J3 _JL0.RM.AT l/Z5_X_»_9-iASE ARCH I_NG.Z_13Xf_2±U(2,_.l. 2 X, _2FX 3 ,._ 1 13X, 1HD, 1CX, 4HVSC0/) DO 200 I = 1, NX3 X3 = X3 + SRPINC * 2. 00 200 J = 1, NX2 X2 = X2 + SOTINC D_=_D.l _+__D.2_*_X 2_+. _ D 3_ 3 : '. VSCO = VI + V2 * X2 + V3 * X3 WRITE.6, 4) X2, X3, D, VSCO A FORMAT (2X, AF14.5) IF ( J .EQ. NX2) X2 = SCTFST 200 CONTINUE RETURN _ _ END 149 G. Subroutine LSQMCO - setting least square equations from data. SUBROUTINE LSQMCO(N, L) DJ.MENSI.ON_A_Un„._LO.)^ COMMON A, B .r^-<ii READ (5, 210) (IX(K, IU), K = 1, M ) f 1U = 1,LJ,(Y(I), I = 1, L) 21C FORMAT T8FT0.0') IF ( X l l , 1> .EQ. 0.0) STOP IF (N. EC. 3) GO TO 1000 IF__l N_.EG.__4)_G.O TO 2P.0.0 _ J : 10C0 WRITE (6, 230) 23C FORMAT 1/////40X, 2HX1, 13X, 2HX2, 13X, 2HX3, 13X, 1HY/) DO 220 I = 1, L 22C WRITE 16, 240) (X(K, I ) , K = 1, N) , Y d ) 24C FORMAT (30X, 4F15.5) _G.Q_._T.0 290 • '. WRITE (6, 260) FORMAT 1/////35X, 2HX1, 13X, 2HX2, 13X, 2HX3, 13X.2HX4, 13X, 1HY/) DO 280 I = 1, L WRITE (6, 270) (X(K, I ) , K = 1, H), Y(I) FORMAT (25X, 5F15.5) _DJL_25JQ_L_=;__..1.,__N : 1_ ~Bl I) =0.0 * DO 250 J = 1, N 250 At I, J ) = 0.0 NP = 0 DO 400 I = 1, N NP = NP +.. 1 : : IF (NP .GT. N) GO TO 500 DO 400 IU = It L B ( I ) = B ( I ) + X ( l , l U ) * Y ( I U ) DO 400 J = 1, NP A l l , J) = A ( I , J) + X(I, IU) * X(J , IU) IF (I . E G ^ _ J) GO TO 400 '  A { J , I ) = A ( I , J ) 4 0 0 CONTINUE WRITE (6, 2) 2 F0RMAT(//5X,43H ORIGINAL MATRIX AND RIGHT HAND SIDE VECTOR/) DO 501 I = 1, N IF (N .EC. 3) GO TO 30C0 [ [ IF (N .EC. 4) GO TO 40C0 30C0 WRITE (6, 3) ( A U , J ) , J = I, N), BID 3 FORMAT (IX, 4F30.9J GO TO 501 40C0 WRITE (6, 4) ( A l l , J ) , J = 1 , N), 8(1) 4 FOR MAT. _ (1 X , 5F2 0.9) '. 501 CONTINUE 5CC RETURN END 150 H. Subroutine SOLUTN - solving matrix by "Jordon Elimination"method. SUBROUTINE S0LUTN(A, B, N, DET, C) C A, 8 = MATRIX NAME I_J____NJjMB5.R_0f ^ C DIMENSION A(10, 10), B(1C), C(10), X(20, 20), Y(20), D(10), V(10) C THE PIVOTAL CONDENSATION NM1 = N — 1 DET = 1.0 D_Q_60_ K_=_1.,._NM1 _ KP1 = K + 1 L = K DO 20 I = KP1, N 20 IF (ABS(A(I t K)) .GT. ABS(AIL, K)) ) L = I IF (L .EC. K) GO TO 40 DO 3 Q_.J _= _K ,_N TEMP = A(K, J) A(K, J) = A(L, J) 30 A(L, J) = TEMP TEMP = B(K) BI.KJ = B(L) B.(.L.)__= T.EM. P , C ELIMINATION 40 DO 60 I = KP l , N FACTOR = A ( I , K) / A(K, K) DO 50 J - Ki N 50 A ( I , J) = A(I, J) - FACTOR * A(K, J) DET.DET A M ,..„•_) _ : , : : 60 B(I) = B(I) - FACTOR * B(K) DET = DET * A ( I , 1) K = N 17C KM1 = K - 1 DO 200 I = 1, KMl FACTOR = A{ I_, K_) /_.AIK, K) A(I, K) = A U , K) - A(K, K) * FACTOR 2CC B(I) = Bd) - B(K) * FACTOR K = K — 1 IF (K .GT. 1) GO TO 170 C SOLUTIONS DO_l 80 I = 1, N : 180 C(I ) = B(I) / A( I , I ) WRITEI6, 2) 2 F0RMAT(//5X,27HTHE JCRCAN ELIMINATION FORM/) DO 501 I = 1, N IF (N .EC. 3) GO TO 30C0 "'v.v _^ I_F_ ( N_ . E C .__4 ) G0_J0__4Q.C 0 3CC0 WRITE (6, 3) ( A l l , J ) , J = 1, N), B d ) 3 FORMAT {IX, 4F30.9) GO TO 501 4CCC WRITE (6, 4) ( A l l , J ) , J = 1, N)t BID 4 FORMAT (IX, 5F20.9) .501 CONT I NUE . . 5CC WRITE (6, 6) DET 6 FORMAT (2CX, 5HDET =, 1PE2C.9) WRITE (6, 5) 5 F0RMAT(//5X,20HTHE SOLUTICN /) RETURN END . .•: . I III-3. Usage of Combinations of Main Program arid Subprogram (see Table XV) TABLE XV - Usage of Combinations of Main Program and Subprogram Usage Calculate mean value, i t s 95,99 or 99.5 confidence l i m i t and per cent error of a set of data. Combination $RUN PKL 5=KL(94)+*SOURCE* SPRINT=*DUMMY*(,29)+*SINK*. Entering data see the r e s t of the main program PKL. PKL i s disk form of (main pro-gram KL + subroutine TVALU + subroutine MNUALU). Calculate v i s c o s i t y conversion f a c t o r K from standard o i l v i s -c o s i t y , and stress recordings. Main program XK + subroutine TVALU + subroutine MNVLUA + subroutine XK. Calculate v i s c o s i t y from stress Main program VSCO + subroutine recordings. TVALU + subroutine MNVLUA + subroutine VSCO. L i n e a r l y i n t e r p r e t data (of v i s -c o s i t y and density of dispersing medium). Main program SEARCH + subroutine LSQMCO + subroutine SOLUTN + subroutine_SEARCH._ III-4. Nomenclature f o r Computer Programs (see also NOMENCLATURE) Ty p i c a l Units N Number of data NO Number assigned to the K c a l i b r a t i o n experiment NU F i x point form of U sec. PCNKNF Percentage confidence PRSNER Per cent error, i . e . , (error/mean value) x 100 S r Reading pn recorder corresponding to S SFACTR Ratio o f S to S * 152 Ty p i c a l Units SHI SLO SME.SMN SMK SMSQK SOTFST SRPFST SRPINC STNVSG TIDF,T79DF T95,T9?,T9'95 TEMP UFACTR ACEPSN BARX,BARZ BASE D DET ERRORX,ERRORZ High l i m i t of S Low l i m i t of S Mean value of S Sum of K data Sum of K squares St a r t i n g point f o r searching f o r s a l t composition wt. % Star t i n g point f o r searching f o r syrup composition wt. % Increasement amount f o r searching f o r syrup composition wt. % V i s c o s i t y of standard o i l c p . T value of one, seventy-nine degree(s) of freedom f or a s p e c i f i c per cent con-fidence T value of 95,99,99.5 per cent c o n f i -dence Temporary storage p o s i t i o n Factor of speed reduction. For ZG10, UFACTR=10. Acceptable per cent e r r o r , which i s assumed to be the maximum recorder reading error Mean value X,Z data Base value of each datum Density datum g m / c c M u l t i p l i c a t i o n value of main diagonal terms of matrix Error of X,Z from BARX,BARZ f o r a s p e c i f i c per cent confidence 153 T y p i c a l Units ERK,ERX,ERZ ERVSCO HIK,HIXYHIZ HIVSCO K LOK,LOX,LOZ LOVSCO M MNK,MNKK,MNX, MNZ MNVSCO V VSCO XN X,Y,Z Error of K,X,Z from MNK,MNX,MNZ f o r a s p e c i f i c per cent confidence Error of v i s c o s i t y value from MNUSCO fo r a s p e c i f i c per cent confidence High l i m i t of K,X,Z High l i m i t of v i s c o s i t y value V i s c o s i t y conversion factor Low l i m i t of K,X,Z Low l i m i t of v i s c o s i t y value Flag v a r i a b l e Mean value of K,KK,X,Z Mean value of v i s c o s i t y Viscosity, datum V i s c o s i t y Floating-point form of N Datum c p . c p . dyne/cm^ c p . c p , c p . c p , 154 APPENDIX IV CALIBRATION OF CONVERSION FACTORS OF HAAKE. ROTOVISCO VISCOMETER IV-1. T h e o r e t i c a l For the Haake Rotovisco viscometer the equations f o r the determination of the stress at the bob surface contain a c a l i b r a t i o n f a c t o r A. To assess the stress conversion factor A, the v i s c o s i t y con-version factor K must be f i r s t determined using a standard o i l . ' Then the spring moment at the f u l l scale reading of the meter M.-J.QQ a n c * t n u s A can be evaluated. A. C a l i b r a t i o n of V i s c o s i t y Conversion Factor K For Newtonion f l u i d y = U x "UFactor x S x K (8) S = S' x SFactor (9) where: u = v i s c o s i t y of f l u i d between bob and cy l i n d e r . 2 c p . = 0.01 dyne sec/cm -UFactor = Factor of speed reduction. 1 For ZG10, • 'UFactor = 10, dimensionless K = v i s c o s i t y conversion f a c t o r , c p . S'= reading on recorder corresponding to S, dimensionless ..SFactor = r a t i o of S to S d i m e n s i o n l e s s Substituting f o r S from Equation (9) i n Equation (8), we get K (U\x UFactor x SFactor 5 ( S' } ( 1 0 ) B. Spring Moment at F u l l Scale Reading of Meter "M^Q^ The viscometer f l u i d flow system i s i l l u s t r a t e d i n Figure 27. where: v^ = l o c a l tangential v e l o c i t y , a function of radius, cm/sec. r.G.Z. = c y l i n d r i c a l coordinates. r[=] cm; 9[=] radium (rad.); Z[=] cm. [=] = has unit of. Assumptxons : 1. The l i q u i d i s incompressible; 2. The motion of the l i q u i d i s not turbulent; 3. The streamlines are c i r c l e s on the h o r i z o n t a l planes perpendicular to the axes of r o t a t i o n - neglecting the e f f e c t of c e n t r i f u g a l forces 4. The motion i s stationary; 5. There i s no r e l a t i v e motion between the cylinders and the material i n immediate contact with the cylinder; 6. The motion of the l i q u i d i s the same on^each plane perpendicular to the axis of r o t a t i o n ; that i s the motion i s two-dimensional - neg-l e c t i n g the end e f f e c t . Figure 27. Bob rotating in cup of Rotovisco Viscometer. 157 According to Newton's Law of Viscosity, dv_ 100 d r where: x n = s h e a r s t r e s s e x e r t e d i n 9' d i r e c t i o n on f l u i d r o s u r f a c e s o f c o n s t a n t r by f l u i d i n r e g i o n o f l e s s e r r , dyne/cm^. at s t e a d y s t a t e : M = c o n s t a n t w i t h r a d i u s = 2 ™ 2 h T r 0 (12) where: M = moment t r a n s f e r r e d from bob t o c y l i n d e r i n r d i r e c t i o n , dyne-cm. s i n c e v = r„ o t dVg = r d _ + codr and i t has been shown t h a t (Mr = 0 f o r deformable f l u i d s (27,p.232) and d v6 du (13) - r — dr dr combining Equations (11), (12) and (13), we get 50M , dr . , ( — j ) = - dco Trhy r Integrated with the boundary conditions: a t r = Rc, co = 0, at r = R^ , OJ = _ , The equation becomes y = 2 5 M 2 ( e2 _ i ) ( 1 4 ) TTh-jR c where: E = R c M = — x M i 0 0 ( 1 5 ) 100 i U U where: ^100 = m o m e n t exerted by viscometer on h e l i c a l spring corresponding to maximum meter reading of 100, dyne-rcm. 25 toFactor = Uu. x UFactor (16) 486 Substituting f o r M from Equation (15), f o r „ from Equation (16) and for S from Equation (9), we get: 2 2 77.76hT7 R ..Factor Mioo = ( ~ TJ L— > K ( 1 7 ) e - 1 C. Stress Conversion Factor A At the outer surface of bob, Equation (12) becomes: •"b • 2VhTb M. and T. = ^ (18) b 2 ^ where: = shear stress exerted by bob on the f l u i d surface adjacent to i t , dyne/cm2. 159 Combining Equations (15) and (18), we get T. b = A S M. 100 and A 2 (19) IV-2. Procedure to Measure Viscosity-by Haake Rotovisco Viscometer Steps 1 to 7 are exactly the same as those in 5.5, Pro-cedure to measure yield stress. 8. Pour sample liquid into cup to the level so that the liquid w i l l just overflow a l i t t l e b i t into the upper part of the bob after the cup is set in the Rotovisco. keep st i r r i n g sample at the highest speed u n t i l the temperature is equal to the set value,say 20°C. 11. Measure the shear stress at various rotating speeds of bob. IV-3. Sample Calculation for K, ^^QQ a n <^ A A set of sample calibration data as shown in the.computer output on the next page were got from the calibration of K with standard O i l . The MNZ in CALI-10601 was mean S' value when the bob rotated in 9. Set the cup into the Rotovisco. 10. Shift the gear slowly from low speed tp high speed and I o o o o O O o o o o O o o o a o o o o o o o o o o o r> o o o o o o o o o o o o o o o o p o o o o o o o p o o o o o o o p o o o o o o o o o o o o o o o j o o o o o o o o o o o o r> o o o i o o o o o o 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O O O O O O O O O O O O O O O O O O O O O O O C D O O O O o O O s O O O O O O O O O o o p o o o o o 00000 W o * O O o O O i o O f N J o o o o o p o o O O O O O O O O -O O O O O to O O O O O O O O O '-U 00 to O O O O O o o o o o o o r - j O O O O O O O - J O O O O O O O O OOOOOOOO 00'000000 OOOOOOOO 00 . O O O O O O o o 00000W00 O O O O O ' 0 0 0 O O O O O O O O O O O O O O O O 00:000000 o o ,0 o o o o o O O O O O O O O 00 |o O O O O O O O O O O O O O O O O O O O O . O O O O O O o o p o o o o o o o p o o o o o o o p o o o o o o o p o o o o o 00 jo O O O O O -O O O O O O O O 00000'000 O O O O O O O O O O O O O O O O o o o o o p o o o o o o c c o o o c 000000. O O O O O O O O O O O O O O O O O O O O O O O N J OOOOOOO-J OOpOOOO-J OOOOOOCU) o o p o o o o w o o p o o o o o o o o o o p o o OOOOOOO'oJ OOOCOOON) OOOOOOOf-O O O O O O O O l O O O O O O O - * J 00 Jo O O O O O o o c c o o o o O O O O O O O O O O o O O O O O o o p o o o o o o o p o o o o o o o p o o o o o o o p o o o o o o o p o o o o o O O O O O O O O o o o o o p o o o o o o o p o o o o o o o p o o . o o o o o p o o O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O ' O O O O O O o o p o o o o o o o p o o o o o o o p o o o o o o o p o o o o o 00 O O O O O U J o o o o o p o o o o o o o p o o 00000,000 o o o o o p o o OOOOO iOO_ o o o o o o o o o o o o o o 000000 o o o o o o o o o o o o 1 O O O O O t\j o o p o o o o c o o o o o o o o w OOOOOOOro o o p o o o o u i 00 o o o o w ^ O O O O O pOv*) O O O O O . O O U l O O O O O . O O o o o o o p o o . O O O O O O M * l O O O O O O O u . O O O O O O O O O O O O O O O O O O O O O O O O o o o o o o r s i i N j o o o o o o o o O O O 3* O O O O -J CD O O O O '-*> -O o o o O -J ~J o o p o o o o o OOOOO PCDIM OOOOOOCr-F-O OOO 00 o ^ OOOOO pvOCD ' o p O O OOOOOOOro 000000*0" OO;0 00owrsj o o o o o o o r v 0000000 ,© o o p o o o o o 00 O O O O O O o o p o o o o o O O O O O O O O o o o o o p o o o o o o o p o o O O O O O O O O O O O O O O O O O O O O O O O O O O ' o o o o o o o o p o o o o o o o io o 00 o o 161 a i r , which was treated as a zero point f o r shearing stress or v i s c o s i t y measurement. . The MNX i n CALI - 10601 was mean S' value when the bob rotated i n standard o i l , which was the net value above the previous mentioned zero point. The ERX included ERZ. T y p i c a l K data are shown i n Tables-XVI"* and XVII. In Table XVII, the average K i s 82.7. Therefore, using the data i n Tables I I I and XVIII, M^QQ can be calculated from Equation (17): M. 77.76 x 1.96 x (3.1416)2 x (1.155) 2 x 1.206 x 82.7 100 = 6.50 x 10 . dynes-cm; And thus A can be evaluated with Equation (19): 6.50 x 10 5 A = = 518 dynes/cm , as 200 x 3.1416 x 1.96 x (1.01) Stated i n Tables I I I and XVII. IV-4. Calibration Data (see Tables XVI and XVII) TABLE XVI - Calibration. Data of.K, M 1 Q Q and. A of. SVP II in S VP Cup" (with clutch, brake ring, speed reducer, head 50 and nickle plated SVPII) Standard O i l Sensitivity of Recorder U K Data Average K % Error S-200 1 mv , 1 7.94 • 7.93 . 7.92 . (635.4 c p . 7.86 7.89 7.81 7.89 ± 0.049 0.62 at 19.97°.C) 2 7.(61 7.70 7.95 7.75 ± 0.43 5 T 6 ~ ' 3 8.12 1,2,3 7.89 + 0.10 1.3 S-600 10 mv 1 8.05 8.04 8.04 (1,986 c p . 7.57 7.59 7.62 at 19.9 n c ) 7.65 7.63 7.64 7.7'6 ± 0.17 2.1 2 8.04 8.02 7.96 7.51 7.53 7.57 7.79 7.84 7.83 7.83 ± 0.14 1.8 1,2 7.77 ± 0.10 1.3 S-200JD 50 mv 1 7.69 7.72 - 7.72 (7,856 c p . 7.53 7.53 7.53 . at 19.97°C) 7.57 7.57 7.58 7.60 ± 0.063 0.83 2 7.70 7.70 7.70 7.47 7.47 7.47 7.51 7.57 7.61 7.57 ±0.080 1.1 1.2 7.57 ± 0.038 0.50 for S-200 and. S-600 1,2,3 • 7.81 ± 0.073 0.935 l^ihh = 6.14 x 10: dynes-cm; A = 48.9 dynes/cm' OA ro TABLE XVII - Calibration Data of K, M and A of SVPIIin SVP, Cup (without clutch, brake ring; with speed reducer, head 500 and gold plated SVPII) S tandard O i l Sensitivity of Recorder U K Data " Average K % Error S-2000 (7,839 c p . at 20°C) 5 mv 2 mv 1 1 82.1 83.2 82.7 ± 6.97 8.43 M100 " 6 ' 5 0 x IO"' dynes-cn ; A = 2 518 dynes/cm TABLE XVIII - Calibration Data of ..Factor (see also Table $IV and Equation (16)) U 162 81 54 27 18 9 6 3 2 - 1 ..Factor 1:202 1.205 1 .206 1.206 . 1.206 1.206 1.206 1.206 1.206 1.206 Average ..Factor = 1.206 ± 0 - -164 APPENDIX V DENSITY AND VISCOSITY- MATCH V- l . The Ambition of i n i t i a l Work (see also 2.5) It was i n i t i a l l y proposed to study the.effect of the i n -dividual particle parameters such as particle size and shape, and the nature of the dispersing medium on the yield value of a r t i f i c i a l slurries of cellulose acetate particles in a Newtonian liquid. This would allow the determination of a complete mathematical model for the thixotropic behavior of such slurries as illustrated i n Figure 28. The main problem i n such a study i s the prevention of the settling or floating of the particles during the long aging periods prior to the yield value measurements. Hence an exact density match between the particles and dispersing mediums with a wide range of viscosities and salt concentrations was necessary. V-2. Match Requirements and Some Data of Prepared Dispersing Mediiim Thixotropic dispersions are depicted as a large network structure of loosely bonded macromolecules, filaments or particles (9) suspended in a Newtonian solvent or solution ". . The a r t i f i c i a l cellulose acetate particle suspension was prepared by putting the particles into a Newtonian dispersion medium composed of corn syrup and water, or polyethylene glycol (PEG),water and dextrose adjusted 165 this gel this shearing stress decay part was found was found to be of to follow 2nd order — zero order Hooks law reversible reaction type (27) by kinetic approach(5) TIME Figure 28. Stress behavior during shearing of a Thixotropic System. 166 for viscosity and density by varying amounts of CMC and fructose. The density of the dispersing medium w i l l be required to be the same as that of the particle and the viscosity of the medium is required to be at two different levels according to the factorial design used in the study. With respect to the t r i a l s , as shown in Tables^XIX and XX, i t seems that fructose can increase the density but affects the viscosity very l i t t l e , however, CMC can increase viscosity but affect the density only a very small amount. TABLE XIX - Density and Viscosity Data,of CMC in CaCl 2 (0.02M) - Corn Syrup (82.7 wt. %) Solution wt. % Density by Weighing Viscosity by of CMC Bottle Method Rotovisco (gm/c.c.) (cp.) 0 1.304 1761 0.25 1.303 186 0.50 1.304 232 0.75 1.304 362 1.00 1.303 712 1.25 1.306 1.50 1.310 Newtonian (see below) J Non-Newtonians (see below) wt. % Viscosity or apparent viscosity (cp.) U = of CMC . 162 81 54 27 18 9_ 6 0.25 0.50 0.75 1.00 719 661 685 1.25 2,160 2,170 2,030 1,940 1,760 1,650 1.50 7,450 7,270 6,650 6,080 5,310 4,290 3,850 3 2 1 178 175 174 186 186 186 229 , 230 237 360 363 769 741 696 TABLE XX - Density and Viscosity Data of Fructose, Dextrose and Salts in 35 wt. % PEG Solution Molality of Density (9/c.c.) by Westfal Balance Viscosity (c.p.) by Cannon--Fenske Viscometer Salt Original plus plus 2R Dextrose Original plus plus 2R Dextrose 2R Dextrose and 2R Fructose 2R Dextrose and 2R Fructose 0(35 wt.% PEG) 1.062 1.121 1.176 119.3 162.4 227.3 0.4M CaCl- 1.083 1.140 1.194 131.4 183.3 271.2 0.8 1.106 1.160 1.212 144.7 205.1 317.2 1.2 1.124 1.180 1.234 158.9 235.1 384.5 1.5 1.141 1.193 1.241 171.3 257.7 438.6 0.4M NaCl 1.069 1.128 1.184 117.2 160.6 231.1 1.5 1.097 1.151 1.204 112.6 158.6 238.0 0.4M CeCl- 1.121 1.174 1.227 134.4 186.9 287.9 where: R = weight ratio of Dextrose or Fructose to salt i n the same system. 

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