THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLTGE OF ENGINEERING RHEOLOGY OF PHARMACEUTICAL EMULSIONS Bhogilal Bo 'Sheth A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan 1960 August 1960 IP-450

Doctoral Committee" Professor Albert Mo Mattocks. Chairman Professor Frederick Fo Blicke Assistant Professor Jere E0 Goyan Professor Edgar F. Westrtnum Jr, Associate Professor Lee Fo Worrell ii

ACKNOWLEDGMENTS The author wishes to express his sincere appreciation: To Professor Albert M. Mattocks, for his suggestion of the problem, for advice and criticism during the course of the investigation, and especially for his assistance in the preparation of this manuscript. To the Horace H. Rackham School of Graduate Studies, The University of Michigan, for a fellowship for two years, and to the Horace H. Rackham School of Graduate Studies, the College of Pharmacy and the International Center, The University of Michigan, for financial assistance that permitted the author to complete his studies and pursue this research. To Dr. A. G. Paul, Assistant Professor of Pharmacognosy, The University of Michigan, for assistance in paxticle size measurements. To Mr. Bruce W. Arden, Lecturer in Mathematics and Research Associate at the Computing Center, The University of Michigan, for assistance in preparing programs for the IBM 704 computer. To Mr. J. A. Mannlein and Mr. N. G. Johnston, instrument makers at The University of Michigan, for their help in the development and maintenance of the viscometer used in this investigation. iii

TABLE OF CONTENTS Page ACKN1OWLEDGMENTS....... *......................o...........o iii LIST OF TABLES..o,,,ooo..,..o.....o......, vi LIST OF FIGURESo,....o,.oo..............oo........... o o............ xii INTRODUCTIONo.................................................. 1 LITERATURE REVIEW; RHEOLOGY OF EMULSIONS.S................... 3 Equations for Non-Newtonian Flow........... o.........o 3. The Williamson Equation.................................. 4 The Structure Equation................................ 6 The Ree-Eyring Equation................................... 8 Effect of Concentration of Dispersed Phase on Flow Properties of Emulsions................. o........................... 15 Fundamental Equations..........................o.... 15 Einstein's Equation.................................. 15 Hatschek's Equation.......o......................... 20 Taylor's Equation............................... 23 Richardson's Equation............................... 25 Mooney's Equation.................................... 26 Oldroyd's Equation........... o....o............... 28 Application of the Fundamental Equations.................. 31 Effect of Particle Size of Dispersed Phase on Flow Properties of Emulsions o.................o...................... 38 Effect of Viscosity of Dispersed Phase on Flow Properties of Emulsions o........ o....... o o................. o................... 43 Effect of Emulsifying Agent on Flow Properties of Emulsions... 45 Effect of Surface Charge of Dispersed Phase on Flow Properties of Emulsions.........o.........ooo.................. 48 Effect of Viscosity of the Continuous Phase on Flow Properties of Emulsions........................................ 52 STATEMETNT OF THE PROBLEM.o.... o............................o. 55 EXPERIMENTAL e....o....................................... 57 Apparatus and Materials..................................... 57 Description........................................ 57 Calibration........................................ 58 Strain gauges.................................. 58 Tachometer.....................o...... 58 Cup and bob dimensions and instrument constants... 59 iv

TABLE OF CONTENTS (CONT'D) Page Operating Procedure............................... 61 Materials Used......................................... 62 Selection of Materials............................... 62 Preparation of Solutions of Suspending Agents....... 63 Preparation of Emulsions............................ 65 Particle Size Measurement........................... 67 Flow Data................................................... 67 Series I.............................................. 67 Series II........................................... 72 Series III............................................. 74 Treatment of the Data.................................... 120 Selection of a Flow Equation............................ 120 Computational Method................................. 125 Relationships of Constants of the Structure Equation to the Variables Investigated.......................... 131 Series I Emulsions............... o...... 131 Series II Emulsions...................................... 143 Sedimentation of Series II Emulsions............ oo..... 165 Series IIT Emulsions,,o.......................... 168 DISCUSSION............................................ 186 LIST OF REFERENCES..,.,........................................ 189 v

LIST OF TABLES Table Page 1 Values of the Constant k for the Oliver-Ward Equation... 34 2 Calibration Constants for Strain Gauges............... 58 3 Cup and Bob Dimensions and Instrument Constants.....,.,. 60 4 Description of Materials Used.....,,,oo..........,...... 64 5 Corn Oil Emulsions Used in Investigation of Effect of Homogenizing Pressure and Concentration of Suspending Agent, Series II................................*...... 68 6 Corn Oil Emulsions Used in Investigation of Effect of Concentration of Oil and Suspending Agent, Series III... 69 7 Flow Data for Series I Emulsions; Cetyl Alcohol with Sodium Lauryl Sulfate Emulsifier; Equilibrium Flow Curves. 73 8 Flow Data for Series II Emulsions Without Suspending Agents.................................................. 75 9 Flow Data for Solutions of Suspending Agents Corresponding to Emulsions of Series II with Sodium Lauryl Sulfate Emulsifier.................. *.. e....... 76 10 Flow Data of Series II Emulsions with Sodium Lauryl Sulfate Emulsifier, Acacia Suspending Agent..,..,....... 78 11 Flow Data for Emulsions of Series II with Sodium Lauryl Sulfate Emulsifier, Sodium Carboxymethylcellulose Suspending Agent................................. 80 12 Flow Data for Emulsions of Series II with Sodium Lauryl Sulfate Emulsifier, Tragacanth Suspending Agent........ 82 13 Flow Data for Emulsions of Series II with Sodium Lauryl Sulfate Emulsifier, Sodium Alginate Suspending Agent.... 84 14 Flow Data for Solutions of Suspending Agents Corresponding to Emulsions of Series II with Span-Tween Emulsifier.... 86 vi

LIST OF TABLES (CONT'D) Table Page 15 Flow Data for Emulsions of Series II with Span-Tween Emulsifier, Sodium Alginate Suspending Agent............ 88 16 Flow Data for Emulsions of Series II with Span-Tween Emulsifier, Tragacanth Suspending Agent............... 90 17 Flow Data for Emulsions of Series II with Span-Tween Emulsifier, and Acacia Suspending Agent................ 92 18 Flow Data for Emulsions of Series II with Span-Tween Emulsifier, Sodium Carboxymethylcellulose Suspending Agent o o o o................o... o..................... 94 19 Flow Data for Emulsions of Series II with Span-Tween Emulsifier, Methylcellulose Suspending Agent........... 96 20 Flow Data for Emulsions of Series II with Span-Tween Emulsifier, Carbopol-934, Sodium Salt, Suspending Agent. 98 21 Flow Data for Methylcellulose Solutions Corresponding to Emulsions of Series III.....,................ o..... 100 22 Flow Data for Emulsions of Series III with 133557 Methylcellulose Suspending Agent.o.....o......... 101 23 Flow Data for Emulsions of Series III with 1.170o Methylcellulose Suspending Agent................ o... o 102 24 Flow Data for Emulsions of Series III with 1.002% Methylcellulose Suspending Agent......o..., o........o 103 25 Flow Data for Emulsions of Series III with 0.7800 Methylcellulose Suspending Agent.o..................... 104 26 Flow Data for Emulsions of Series III with 0.651% Methylcellulose Suspending Agent.........e............. 105 27 Flow Data for Emulsions of Series III with 0.5435 Methylcellulose Suspending Agent................0....... 106 28 Flow Data for Emulsions of Series III with 0.434% Methylcellulose Suspending Agent................,...... 107 vii

LIST OF TABLES (CONT'D) Table Page 29 Flow Data for Emulsions of Series III with 0.526o Methylcellulose Suspending Agent.o.,o.....oo............ 108 50 Flow Data for Sodium Carboxymethylcellulose Solutions Corresponding to Emulsions of Series III......o.o.... 109 31 Flow Data for Emulsions of Series III with 1.687% Sodium Carboxymethylcellulose Suspending Agent.......... 110 32 Flow Data for Emulsions of Series III with 1.476o Sodium Carboxymethylcellulose Suspending Agent..o....... 111 33 Flow Data for Emulsions of Series III with 1.265o Sodium Carboxymethylcellulose Suspending Agent.......... 112 34 Flow Data for Emulsions of Series III with 1.1535 Sodium Carboxymethylcellulose Suspending Agent.......... 113 35 Flow Data for Emulsions of Series III with 0.9840o Sodium Carboxymethylcellulose Suspending Agento.o...,... 114 36 Flow Data for Emulsions of Series III with 0.769% Sodium Carboxymethylcellulose Suspending Agent.......... 115 37 Flow Data for Emulsions of Series III with 0.562* Sodium Carboxymethylcellulose Suspending Agent.......... 116 38 Flow Data for Emulsions of Series III with 0.281*o Sodium Carboxymethylcellulose Suspending Agent.......... 117 39 Flow Data for Emulsions of Series III with 0.1870 Carbopol-934, Sodium Salt, Suspending Agent and the Corresponding Solution of Suspending Agent......... 118 40 Flow Data for Series III Emulsions with 0.125% Carbopol-934, Sodium Salt, Suspending Agent, and the Corresponding Suspending Agent Solution...o....o....... 119 41 Structure Equation Constants for Series I Emulsions: Cetyl Alcohol with Sodium Lauryl Sulfate Emulsifier; Equilibrium Flow Curves,.......... o........ o o..o o 132 viii

LIST OF TABLES (CONT'D) Table Page 42 Parameters of the Reciprocal Equation Relating Structure Equation Constants to Concentration, Series I Emulsions. 133 43 Limiting Viscosities, 0, for Series I Emulsions........ 142 44 Estimated Intrinsic Viscosities Based on Liquid Sheaths, Series I Emulsions o..................................... 142 45 Structure Equation Constants for Series II Emulsions Without Suspending Agents............................ 144 46 Structure Equation Constants for Solutions of Suspending Agents Corresponding to Emulsions of Series II with Sodium Lauryl Sufate Emulsifier...................... 147 47 Structure Equation Constants for Series II Emulsions with Sodium Lauryl Sulfate Emulsifier, Acacia Suspending Agent.. o.. O...................... o o. * o o o.. o 148 48 Structure Equation Constants for Series II Emulsions with Sodium Laryl Sulfate Emulsifier, Sodium Carboxymethylcellulose Suspending Agent................... 149 49 Structure Equation Constants for Series II Emulsions with Sodium Lauryl Sulfate Emulsifier, Tragacanth Suspending Agent.,............................ 0..... 150 50 Structure Equation Constants for Series II Emulsions with Sodium Lauryl Sulfate Emulsifier, Sodium Alginate Suspending Agent...... o............. o........... o *. 151 51 Structure Equation Constants for Solutions of Suspending Agents Corresponding to Emulsions of Series II with Span-Tween Emulsifier.............................. 152 52 Structure Equation Constants for Series II Emulsions with Span-Tween Emulsifier, Sodium Alginate Suspending Agent....... o o.......................................... 154 553 Structure Equation Constants for Series II Emulsions with Span-Tween Emulsifier, Tragacanth Suspending Agent. 155 ix

LIST OF TABLES (CONT'D) Table Page 54 Structure Equation Constants for Series II Emulsions with Span-Tween Emulsifier, Acacia Suspending Agent.......... 156 55 Structure Equation Constants for Series II Emulsions with Span-Tween Emulsifier, Sodium Carboxymethylcellulose Suspending Agent.........................o.. 157 56 Structure Equation Constants for Series II Emulsions with Span-Tween Emulsifier, Methylcellulose Suspending Agent.......oo.......o......O...........0**O..*........ 158 57 Structure Equation Constants for Series II Emulsions with Span-Tween Emulsifier, Carbopol-934, Sodium Salt, Suspending Agent.........,,....,....o...oo.,,,,.,.... o 159 58 Particle Size Distribution for Basic Emulsions of Series II...o o............ o......,..,..o......... 160 59 Parameters of the Equation C/f( ) = a + bC for Suspending Agent Solutions, Series IIo......o.............. 161 60 Parameters of the Equation? o(emul) = A + B o(solv) for Series II Emulsions......o.................o 164 61 Relative Settling Volumes, Limiting Viscosities and Yield Values of Emulsions and Solutions of Suspending Agents, Series II.........o oo.... o.......o.o.o.oo...o... 166 62 Structure Equation Constants for Suspending Agent Solutions Corresponding to Emulsions of Series IIIoo....... 169 65 Structure Equation Constants for Series III Emulsions with 1.337% and 1.170% Methylcellulose Suspending Agento 170 64 Structure Equation Constants for Series III Emulsions with 1.002% and 0.780% Methylcellulose Suspending Agent. 171 65 Structure Equation Constants for Series III Emulsions with 0o651%o and 0o0453 Methylcellulose Suspending Agent. 172 66 Structure Equation Constants for Series III Emulsions with 0o454%o and 0.5326 Methylcellulose Suspending Agent. 175 x

LIST OF TABLES (CONT'D) Table Page 67 Structure Equation Constants for Series III Emulsions with 1.687* and 1.476* Sodium Carboxymethylcellulose Suspending Agent.................................. o 174 68 Structure Equation Constants for Series III Emulsions with 1.265* and 1.1535 Sodium Carboxymethylcellulose Suspending Agent...o.................................. 175 69 Structure Equation Constants for Series III Emulsions with 0.984% and 0.769* Sodium Carboxymethylcellulose Suspending Agent...... o........ o............. o 176 70 Structure Equation Constants for Series III Emulsions with 0o562% and 0.281* Sodium Carboxymethylcellulose Suspending Agent.....o................................ 177 71 Structure Equation Constants for Series III Emulsions with,187% and 0.125o Carbopol-934, Sodium Salt, Suspending Agent.............. o..o...................o 178 72 Parameters of the Equation qo(emul) = A + B Xo(solv) for Series III Emulsions..... oooooo.ooo..o............ 180 73 Parameters of the Equation log bi = a + P log C Relating Constants of the Polynomial Equation to Concentration of Suspending Agent............................. 181 74 Parameters of the Equation lo(emul) = A + B to(solv) for Series III Emulsions......o.......o.......... 182 75 Intrinsic Viscosities of Series III Emulsions, Observed Values and Values Calculated with Taylor's Equation..... 184 xi

LIST OF FIGURES Figure Page 1 Potential-Energy Barrier for Flow, with and without Shear Gradient............... o.............. o *... 9 2 Diagram Illustrating the Hypothetical System of Oldroyd. 30 3 Down-Curves Showing Breakdown with Time for Cetyl Alcohol Emulsions of Series I.....o.e..........o...oo..o 71 4 Plot of \ Versus 1/S for the Ree-Eyring Equation, 1.17* Methylcellulose Solution of Series II...o........... 123 5 Computer Program for Evaluating Constants of the Structure Equation, Fortran Language........o....,....o..... 126 6 Flow Diagram of Program for Calculating Structure Equation Constants...,,.....o........o.oooooo.o.o.o oo o 128 7 Plot of Structure Equation Constants, JY. by and f Versus Concentration of Cetyl Alcohol forT-mulsions of Series I........ 0 0....... o *. o a 4.. e. 134 8 Plot of 1/7 Versus Concentration of Cetyl Alcohol for Emulsions of Series I........o,ooo,,Oo......,o..o...... 135 9 Plot of 1/bv Versus Concentration of Cetyl Alcohol for Emulsions of Series I..oo..ooo.,o.. o................OO*. 136 10 Plot of 1/f Versus Concentration of Cetyl Alcohol for Emulsions of Series I... o o ooooo,,,,,,,.oooooooo 137 11 Plot of 1/fo Versus Logarithm of Concentration of Cetyl Alcohol for Emulsions of Series I..,...,....,...ooo..oo 138 12 Plot of Log nV,,,Versus Concentration for Series I Emulsions............................ o.<.<.a..... 141 13 Plot of Structure Equation Constants f and by Versus Concentration of Suspending Agent for-Series II Emulsions with Sodium Alginate Suspending Agent, Sodium Lauryl Sulfate Emulsifier..........,,.,,,..... o o. o o 145 xii

LIST OF FIGURES (CONT'D) Figure Page. 14 Plot of Structure Equation Constant ao Versus Concentration of Suspending Agent for Series II Emulsions with Sodium Lauryl Sulfate Emulsifier, Sodium Alginate Suspending Agent....o.1.*................. 146 15 Plot of C/log Yk _ Versus C for Suspending Agent Solutions of Series II, Sodium Carboxymethylcellulose Suspending Agent....................................... 163 xii

INTRODUCTION Emulsions are an important class of pharmaceuticals. They represent a useful dosage form for drugs, especially those which are insoluble liquids. Being fluids, emulsions for oral administration are frequently more readily accepted by the patient who finds tablets or capsules difficult to swallow. Emulsified ointments are commonly preferred to those with petrolatum base because of more rapid release of medicament to the skin as well as greater ease of removal from the skin and clothing. Flavors are frequently prepared in emulsion form in order to have sufficient concentration of oil in the aqueous medium. Further, emulsions are used almost exclusively as the base for cosmetic lotions, shampoos and facial creams. The usefulness of an emulsion is strongly dependent upon its flow properties. Emulsions for internal use must have sufficient viscosity to prevent sedimentation and at the same time flow readily so as to be easily poured and swallowed. Those for parenteral use must be easily forced through a hypodermic needle. Emulsified lotions and ointments must behave as solids when undisturbed and yet be soft enough to be readily spread upon the skin. In spite of the importance of rheological properties of emulsions little knowledge of their flow properties is available. No correlation between rheological properties and ultimate applications of emulsions has been proposed. Thus, one who is preparing a new emulsion must depend upon the sense of touch to evaluate his efforts, and a laboratory marketing an emulsion must depend upon some arbitrary control procedure or simply hope that 1

2 variations in mixing, milling and other phases of the process will be so small as to furnish a uniform product. It appears, therefore, that the development of more logical approaches to formulation as well as the establishment of better control of product uniformity for emulsions will depend, to a large extent, upon the extension of knowledge of their flow properties.

LITERATURE REVIEW RHEOLOGY OF EMULSIONS Equations for Non-Newtonian Flow Emulsions have been found to exhibit both Newtonian and non-Newtonian flow, depending upon concentration of internal phase and composition of the suspending medium, but those of greatest interest to pharmacy, i.e., with concentration of dispersed phase above five percent, exhibit non-linear flow. In such case, the simple equation for viscosity: F/S =, where F is stress, S is shear and ( is coefficient of viscosity, no longer is applicable~ The equation of Bingham for plastic flow: (F-f)/S = pl' where f is yield value and ( pi is the coefficient of plastic viscosity, is equally inappropriate, since it demands linear flow beyond a fixed value of stress. Non-linear flow has been the subject of much investigationl,2,3,4,5, but only three equations have emerged which are generally useful in describing experimental data; these are the Williamson equation, the Structure equation and the Ree-Eyring equation. The three equations have in common the property of reducing to the Newtonian expression under suitable conditions, and the first two may reduce to the Bingham equation as well. Thus, these may be considered as generalized flow equations and not applicable exclusively to non-linear systems. 5

4 The Williamson Equation Williamson6 proposed that the total stress, F, consists of two components, F1, due to plastic resistance, and F2, due to ordinary viscous resistance. He found that the relationship of F1 to shear, S, could be described adequately by a simple hyperbola and thus obtained the following equation: F = F + F2 = fS +.o S, s +S where s and f are constants defining the curvature and qoo is a constant describing the ultimate viscosity approached by the system at high rates of shear. It is readily seen that F will become zero for linear flow so that the equation becomes the simple linear expression for Newtonian systems with ~.o equal to o Also, for plastic flow s is zero and the equation becomes that for a Bingham body. Williamson used the ratio, f/s, as an index to plasticity and the ratio, f/s Ri as a "false body constant" and was able with these terms to define the brushing qualities of paint in a useful manner7. He also noted that the viscosity at extremely low shear or limiting viscosity, Io, could be expressed as: 0 = f/ + v Shangraw8 noted that although the Williamson equation had been used successfully by Williamson and had been praised as the best equation available at that time for non-Newtonian flow curves9 it had not been used widely by others. On the basis of his own results, Shangraw presumed that

5 limited use had been made of this equation because of the large errors involved in estimation of the constants by Williamson's methods. The first of these methods was graphical and would be expected to result in large errors unless data were available for extremely high rates of shear. Williamsonts instrument was unusual in that it did furnish extremely high shear. The second method for estimation of the constants for the Williamson equation utilized three data points to estimate three constants, a procedure likely to involve large errorso To estimate the constants more accurately, Shangraw converted the equation to the linear form: F = f + BTs + BUS - (F/S)(s), which may be expressed as: F = bo + blS + b2F/S, where b = f + Yoo s, b1 = Yo and b = -s. This expression could be evaluated by least squares and thus could be fitted with any number of data points. By this means Shangraw obtained constants for the Williamson equation which gave predicted values generally within one percent of experimental when applied to methylcellulose solutions. Shangraw also found that plasticity constants, f/s, and false body constants, f/s-q, could be related to concentration of methylcellulose by log-lcg expressions. He utilized the values of limiting viscosity, to to calculate specific viscosity, s p which fitted the common form of plot used to obtain intrinsic viscosity, i.e., log Y sp/c vs. c, where c is concentration.

6 The Structure Equation Griml, using the method of Shangraw, applied the Williamson equation to data on suspensions of salicylamide in methylcellulose solution. He found the equation to fit flow curves in an acceptable manner but was unable to find any consistent relationship between constants of the equation and concentration of suspended material. Grim noted that the hyperbolic portion of the equation was arbitrarily selected as being suitable for describing flow data and that the portion of the flow curve most dependent on this function, that at low shear rate, showed the greatest deviation from the equation. Examining this part of the Williamson equation in detail, Grim isolated values for viscoelastic flow: F1 = F -he S = fS s +S Converting this to linear form, he obtained: 1/F1 = 1/f + (s/f)(l/), so that a plot of 1/F1 versus 1/S should be linear. Values plotted in this manner demonstrated a definite non-linearity at low and high values of S; thus Grim concluded that the simple hyperbolic function was not a correct representation of the viscoelastic resistance. Grim proposed that the total resistance to flow was composed of two components, as stated by Williamson, and that one of these is viscoelastic. The second component was said to be plastic, rather than Newtonian, since the flow curve at high rates of shear, though linear, has a positive intercept on the stress axis; thus: Fp = f + S,

7 where Fp is plastic resistance, f being the intercept on the stress axis obta.ined by extrapolation of the linear portion of the curve and Y( being the slope of the linear portion. Grim stated that 'the viscoelastic resistance decreases with rate of shear, becoming zero when the flow curve becomes.inear,,and that the decrease in viscoelastic resistance with shear is proportional to the resistance remaining: dFv/dS =- aF where Fv is viscoelastic resistance and a is a constant of proportionality0 Integration yielded: ln Fv = - aS + lnI, lnI being the constant of integrationo Grim expressed this i:. the form: F = b e-aS where bv, called the viscoelastic constant, is I from the previous expressionO Thus, the final equation, called the structure equation, is: F = f +I S -bve-aS Putting the expression for viscoelastic resistance inl the form.: -aS Fv f + o S -F = b e-a and plotting calculated values of Fv versus eS using the arbitrary value of Oo001 for a, Grim showed that this equation. fitted experimental data better than the Williamson equation. Further, he found the slope of the I.inear portion, ^, fitted experimental curves better than that calculated from the Williamson equation. Applying the structure equation to suspensionls Grim found the reciprocals of f, bv and o to be linear functions of the volume

8 concentration. Intercepts of these lines, representing infinite resistance, were judged to be a function of ultimate settling volume of the suspensions. The Ree-Eyring Equation Eyringl1 considered the flow of a liquid as a rate process and applied the theory of absolute reaction rates to the problem of viscosity. A liquid is considered to be made up of holes moving about in matter, these holes playing the same part in a liquid as molecules in the gas phase. Eyring considered two layers of molecules in a liquid, at a distance,1 apart, where one layer slides past the other under an applied force. If f is the force per square centimeter tending to displace one layer with respect to the other, and AU the difference in velocities between the two layers, then, by definition, Y = f X /AU where YI is the coefficient of viscosity. The motion is assumed to involve the passage of a molecule from one equilibrium position to another in the same layer. In order for this to occur, a suitable hole or site should be available and the production of such a site would require expenditure of energy, since work must be done in pushing back other molecules. Thus the motion of the molecule may be regarded as being equivalent to the passage of the system over a potential energy barrier (Fig. 1), Eyring defined the dimensions of the system as: = the distance between two successive equilibrium positions in the direction of motion, X3 = the distance between molecules in the direction of motion A = the mean distance between two adjacent molecules in the moving layer in the direction perpendicular to the direction of motion.

9 SHEAR GRADIENT (f) - 1 WITHOUT SHEAR s e/ >\ GRADIENT / / I \ \ WITH SHEAR Z-/ |I \ YGRADIENT w / \ - /2fX2X3X \ KSTIAT I/ /2 FINAL — 1/2 — STATE lL- ----------— _____ DIRECTION OF FLOW - " Fig. 1. Potential-Energy Barrier for Flow, with and without Shear Gradient

10 The potential energy barrier is considered to be symmetrical, so that the distance between the initial. equilibrium position and the activated state is 1/2 A o The applied force acting on a molecule in the direction of flow is f AA\ an.d, therefore, the energy acquired by a moving molecule when it has reached the top of the potential energy barrier is 1/2f X1 X, X. The force causing the flow thus reduces the height of the potential energy barrier in the forward direction by an amor..t l/2f h2X A, the height in the opposite direction being increased by the same amounto From the theory of absolute reaction rates, the number of times a molecule passes over the energy barrier, and hence moves in any direction, per second, is given by: k' = rT F - (/KT h F where o is the energy of activation per molecule at 0~ Kelvin, F and Ft are the partition functions of the initial and the activated states, respectively, K is the Boltzman constant, T is the absolute temperature, and h is Planck's constant~ Therefore, the specific rate of flow in the forward direction is given by: kf = kT Ft e -1/2fA 3 )/KT, h F or k k e 1/2 fAA3 /KT f 19 and the rate in backward direction is given by: kb = ke -1/2f A A /KT. The distance moved by the molecule per second, and hence the rate of motion, is given by kf X in one direction and kb k in the other, since the molecule

11 moves the distance A every time it passes over the potential energy barrier. The net rate of flow AU, is equal to (kf - kb)X. Therefore: u = k(e1/2 f A2 A /KT -1/2 f 3/\ /KT) -e or U = 2 A k sinh f x 3 A 2KT The expression for the viscosity of the liquid may then be written as: 2 >sk sinh(f A2 A3 A / 2KT) Ree and Eyring12 applied this equation to develop a generalized theory of non-Newtonian flow. According to this theory, a system is made up of different groups of flow units. The flow rate of the system is supposed to be a function of the relaxation times of the flow units which contribute to the flow process, the distribution of these relaxation times and, in the case of thixotropic flow, the deformation of the system with stress. The mechanical model of the system is as follows: 1i There are n groups of flow units differing in relaxation times and geometrical directions. 2. The fractional area on a shear surface of the nth unit is xn, and the shear stress per unit area acting on this area is fn. 3. All units on the same shear plane move with the same shear rate. From Eyring's viscosity equation, the rate of shear is given by: S = (A/A ) 2 k sinh <nfn where: n, = ( A2 \3 X )n / 2 KT.

12 The force acting on the units of the nth group is Xn fn and the stress, f, is given by: n f= - Xnfn Substituting from the equation for the rate of shear, we obtain.: n f = ~ xn sinh-1 gnS n=l where: n = /I(y/, / )n KKn J n is a constant proportional to the relaxation time of the nth kind. The equation for viscosity may be written as: n =\ X xn 3n sinh-1 n S. n.= n n. The function, (sinh-1 nS)/ n S, has the property that: lim pS O - 0 sinh-13S = 1, and: lim p S - oo sinh"l f S = Oo PS This is the generalized viscosity formula for non-Newtonian flow developed by Ree and Eyring. To illustrate, we may consider a system with three flow groups so that the equation may be written as: r = Xl1 + X2 2 sinh-1 2S + X3 3 sinh-l 3SO Q\ 2 ~P0 \3 ~3' The first term would represent the condition for Newtonian flow: Ss<< 1 and: (sinh-1 (31)/ (3S 1

13 The second term might be thought of as representing the case where: 2S_2 1, a condition for Newtonian flow at low rates of shear and non-Newtonian flow at high rates of shear. The third term might be thought of as representing the case where: 32S >> 1i, which is the condition for non-Newtonian flow. One or more components, with appropriate values for the constant an might be required to describe the flow properties of a given system. The equation was applied by Ree and Eyring to the data of Saunder and Treloar13 for masticated rubber at temperatures from 40~ to 140~, and to the data of Mooney on lightly milled crepe at temperatures from 69~ to 140~1 Agreement with experimental observations was found to be satisfactory. The constant c( was found to be independent of temperature because of the fact that the quantity, Aa /\ X increased linearly with temperature. The Ree-Eyring theory represents a theoretical approach to the problem of non-Newtonian viscosity. It is based on the fundamental properties of the constituents of a system and permits the calculation of the thermodynamic quantities related to the kinetics of the flow process. It also permits a theoretical study of the temperature dependence of viscosity. The equation could be applied to calculate flow curves of reduced shear rate versus shear stress, so that viscosity data at different temperatures could be directly compared. The expression for reduced rate of shear may be written as: Sr = S exp ( AH/RT), where LH is the enthalpy of activation, R is the gas constant and T is the absolute temperature. Ree and Eyring applied this method to the data of

14 14 15 16 Mooney4, Bestel and Belcher15 and Spencer and Dillon16. Satisfactory agreement between observed values and those calculated using the reported value for heat of activation was observed. Maron and Pierce17 applied the Ree-Eyring equation to the data of Maron and Fok18 on the flow behaviour of synthetic latex. The equation was found to be satisfactory with the assumption of one Newtonian and one nonNewtonian component, as follows: =X1 +il X2 2 ih-l P2S Q1 2s- P'2S or: = a + b sinh1 @2S, 2S where: a = x1 P1, a<1 and: b = x2 p2. Empirical relationships of the constants, a, b, and P2' with the volume fraction of the dispersed phase were described and the temperature dependence of the parameters was also determined. Ree and Eyringl9 extended their treatment to solutions of high polymers. They designated the solvent molecules as the zeroth group, so that: n = T Xn P3n sinh-1 PnS. n=o on pnS The contribution of the solvent is taken as Xo o, where Ylo is Equations are then derived for the relative viscosity, intrinsic viscosity,

15 limiting intrinsic viscosity and the inherent viscosity, using the basic definitions of these coefficients. The data of many workers, on polymer systems, is reviewed in light of these equations. Effect of Concentration of Dispersed Phase on Flow Properties of Emulsions Fundamental Equations Although many investigators have found empirical relationships between some function of viscosity and concentration of dispersed phase of emulsions, relatively few of these equations have theoretical foundation or promise of wide application to different types of emulsions. The first significant equation relating concentration of dispersed phase which was derived theoretically was that of Einstein, Although his equation was developed for dispersions of solid particles it served as the basis for theoretical expressions for emulsions as developed by Hatchek, Taylor, Richardson, Mooney and Oldroydo Einstein s Equation The derivation of Einstein20 is quite complex and several approaches have been used to arrive at the same result. Probably the most easily understood derivation is that presented by Sadron21 which utilizes the method of Burgers22 and Jeffrey23 in evaluating the components of flow. A resume of Sadron's presentation is summarized below. The assumptions are made that (1) the particles are rigid spheres, (2) there are no interactions between particles, and (3) all the particles in the suspension are identical and the suspension is homogeneous.

16 Considering a liquid in a system of laminar flow parallel to the x-z plane, the components of velocity may be stated as: u = u(y), v = 0, w = 0, the component u being a function of D, the position of the layer in the body of the liquid. The velocity gradient, or rate of shear, S, is expressed as: S = du/dyo When a particle is introduced into the liquid, flow is disturbed, resulting in additional components of flow, u', v, and w', due to the presence of the particle. The velocity of the liquid will have new components, ul, vl, and w1. These components must be evaluated by integration of the Stokes-Navier equations with the boundary conditions that there is no slip at the surface of the particle and that at infinite distance from the particle the initial flow is maintained; that is: U = u, v1 = = W = v = 0 = For the first condition it is necessary to know the motion assumed by the particle. For this purpose an arbitrary velocity is assumed.for the particle, and expressions for ul vl, and wl are evaluated for the specified boundary conditions. Next the force and torque produced by traction on the particle are calculated. Since these must vanish for the specified boundary conditions, the relations determining the actual velocity are obtained. In the case of an ellipsoid particle where a is the length of the semi-axis of revolution, b is the length of the equatorial radius, p is a/b and e is (p - i)/ (p2 + 1), Jeffrey23 has shown that, if the direction of the

17 axis of rotation is defined by the angles 0 and jt the corresponding angular * 0 velocities, e and would be given by: E = S e sins cos& sinf cos = S p2/(p2 + 1) - e sin2. For a spherical particle, a is equal to b and __ becomes zero, while T has the value of 1/2S. Thus, a sphere rotates around the z-axis with an angular velocity of (l/2)So A point on the surface of the sphere will have the velocity components: u (1/2) S y, v = (1/2) S x, w = 0, and the components of additional flow may be expressed as: u- = ul-u = -(l/2)Sy, vI = vl-v - -(1/2)Sx, w = w -w = 0. Inserting these values into the Stokes-Navier equations, the components of additional flow are calculated to be: u' = -(5/2) a3 S x2 y r-5 + (1/6) S a5 (3 y r-5 - 15 x2 y r-7), v' = -(5/2) a3 S x y2 r-5 + (1/6) S a5 (3 x r-5 - 15 x y2 r-7), w' = -(5/2) a3 S x y z r-5 + (1/6) S a5 15 x y z r-5, where r is the distance of the point from the origin and a is the radius of the particle. The second term is of the order of a5 r4, and may be neglected if a2 r-2 is small, a condition that is assumed to be fulfilled. Considering two planes with coordinates yl and -Y2, when there are no particles in the liquid, the undisturbed flow is given by: u = SO y, v = w = 0.

18 Next, in a suspension containing c particles per unit volume, a layer parallel to the x2 plane is considered, with ordinate y and thickness dy such that: Y2 < y (< Y and Xs. y and zs are the coordinates of the centre of a sphere in this layer. The additional flow due to the sphere at a point A (x=O, yl, z=0) on the surface of the sphere would be given by: uS = -(5/2) So a3 x2 (Y1-Y) rs5, as already indicated. A calculation is made of the x component of the additional flow due to all the particles contained in an element of volume around the point (xs, y, zs) and this is calculated to be (u'.c.dxs.dy.dzs) for (c.dxs.dy.dzs) particles. This component produces a retardation of the flow, and the retardation due to all the particles, 61 in the layer of thickness dy is: 61 = -(5/2) So a3 (y1-y) c dy ffx2 r-5 dx dz. -oo s s s This integral is evaluated to be: (2/3)TI (Y-y)1; therefore: 61 = -(5/3)~ So a3 c dy. Similarly, the retardation at the plane (y = -y2) is given by: S2 = +(5/3)J So a3 c dy. The relative horizontal velocity of flow in the planes (y = yl) and (y = -y2) is now decreased from So (Yl + Y2) by the amount 6,where: 6 = 1 +&2 = (10/3)t So a3 c dy.

19 Summing up the effect of all the layers from -Y2 to yl, the relative horizontal velocity of the two planes is calculated to be: So(Y1 + y2l-(lO/3)3>a3 c = SO (Y1 + Y2)(l-2.5 c V), where V is the volume of one particle. Now a calculation is made of the additional shearing stress, ', on the plane (y = Y1). This is given by: T' - fau' + u. 7 i Y __ Since u' and v' are independent of x, T' is given by: The additional shear rate produced by a single sphere (x,z is The additional shear rate, U', produced by a single sphere, (XsyYz)s is caculated to be: calculated to be: _U' = -(5/2)(x2 r-5 - 5 x2 y2 r-7). B) Y s s 1 On integrating over all spheres in one layer, and then over all layers, the resultant value vanishes. Therefore, the effect of the presence of the particles is a reduction in the relative horizontal velocity of the liquid in the planes (y=y1) and (y=y2). The total rate of shear and the total shearing stress at the planes are the same as before introduction of the particles. It is now assumed that the planes (y = yl) and (y = Y2) are the walls of a rotational viscometer. It should be noted that: d = Y1 + Y2 U = Relative velocity of the two walls. When the viscometer is filled with the dispersion medium and run with a relative velocity, U0, the shearing stress, To, is given by: To = o/d = S,

20 where Y o is the viscosity of the dispersion medium. When the particles are introduced in the dispersion medium, the planes move with a relative velocity U given by: U = d So (1-2.5 c V)o _, the shearing stress at the wall, is giver. by: r = (U/d =r uO (1-2.5 c V)/d, where A is the viscosity of the dispersionr Since -= To, oUd =Uo (1-2.5 c V)/d; therefore, r0 = 7(1-2-5 c V). As c is assumed very small, this may be written as: ( =ar1 (1 + 2.5 c V), and letting cV = ), the volume fraction of the dispersed phase, V =Yo (1 + 2.5 ). This is the well known Einstein equation for a dilute suspension of rigid noninteract-ing spheres Hatschek's Equation Hatschek24 derived an equation for the viscosity of an emulsion with a high co:acentration, 50% or more, of the dispersed phase, that would take into account the sharp increase in viscosity with increasing concentration of the dispersed phase. He considered a system containing uniform spheres. If the number or size of the spheres increases until each sphere touches twelve others, the particles would occupy 74.04% of the total volume.

21 The twelve points of contact would be the centres of the faces of a dodecahedron, and with any further increase in concentration, flattening of the particles must occur and the faces of the dodecahedron would be developed more and more. Two horizontal planes of the system are considered, one of which moves with a velocity v relative to the other; the velocity is considered to increase uniformly from one plane to the nexto Since the plane would be a cross section through the dodecahedron, the particles would have hexagonal shapes in the planes. If the system is sheared, the polyhedra must slide over one another, and Hatschek proposed that the movement cannot occur without distortion of the particle shape. As the movement continues, the hexagons would assume rectangular form, and on further displacement, the particles would revert to the hexagonal form. On the basis that the particle must occupy the same volume all the time, the dimensions of the rectangular parallelepiped formed at the point of maximum distortion are calculated to be: height = r 2 breadth = r 3/2 length = 3r, where r is half the distance between two parallel faces of the hexagon. These distances are measured from the middle points of successive layers of the continuous phase separating the particles. The factor tending to cause the return of the particle from the rectangular parallelepiped to the dodecahedron form is the interfacial tension between the two phases. The factor opposing this tendency is the viscosity of the two phases. Hatschek proposed that for every system there is a critical velocity beyond which the particles would not return to their original

22 dodecahedral form. Hatschek's equation treats only the case where this velocity is exceeded, since the treatment below the critical velocity is considered quite complex. Since the distortion of the particles results in an increase in the surface area, work must be done in the process. Hatschek considered an element of volume in the system having the form of a parallelepiped with a square base and height, 1, consisting of a particle of the dispersed phase of thickness d and the corresponding layer of the continuous phase around it. The work, A, required to cause displacement of the whole volume is given by: A = v 1 CL where v is the velocity and L_ is the viscosity of the system. The work, Al, required to cause displacement of the dispersed phase is given by: A1 = v dIt is proposed that, since both terms have the same form, the quantity l/d represents the ratio of the viscosity of the system to that of the continuous phase. That is: A-= 8o(l/d) The ratio, l/d, is represented by the ratio, f, of the total volume to the volume of the dispersed phase. That is: _=f 1/ 3 1 f 1/ d i 1/3-1 Therefore: If the total volume is taken as 1 fraction o the dispersed/3 f 1/3-1 If the total volume is taken as 1, and the volume fraction of the dispersed

23 phase as, we may write X =N /(1- 1/3), this being the conventional form of Hatschek's equation. Taylor's Equation Taylor25 extended Einstein's treatment to liquids containing droplets of a second liquid in suspension. Noting that the analysis would be extremely difficult-if one considered the deformation of the droplet caused by viscous forces, Taylor limited his analysis to conditions of low shear or small particle size so that the surface tension of the droplets would keep them spherical. Further, he assumed that there is no slippage at the particle surface and that any film on the surface merely transmits tangential stress from the outer fluid to the droplet. Using the analysis for slow motion of a viscous fluid presented by Lamb26, Taylor pointed out that the expression for each component of velocity contains three functions, one relating pressure distribution, the second representing an irrotational motion in a field of uniform pressure and the third representing vortex motion. Following Einstein, Taylor chose coordinate axes parallel to the principal axes of distortion, causing the function for vortex motion to disappear. Thus, the equation for one component of velocity becomes: u = r r2 bPu + A r2^3 D j P + A3x Z(i z(z+l) x +l ) ( d ( ax J where u is the component of velocity, k is the viscosity and r2 = x2 + y + z2. With unidimensional flow (u = A y~ v = 0), the irrotational flow at great distances from the droplet whose center is the origin of the coordinate axes can be represented by: 02 = 1/4 (x2 - y2).

24 Taylor defined the appropriate functions ( and Pn for outside the droplet as: 02 = 1/4-3i(x2 - y2), -3 = B-3 a5 x2 - y2, P3 = A3a x2 -y2 r5 r) and the functions for the liquid inside the droplet as: = B2(x2 - y2), P2 = A a-2 (x2 y2), where B_3, A_3, B2 and A2 are constants to be determined by the boundary conditions, -& and jA are the viscosities of the main body of the fluid and the droplet, respectively, r2 is x2 + 2 + z2 and a is the radius of the drop. Substituting these into the equation for velocity components the following expressions are obtained: Outside the drop: u = 1/2 A-3 a3 x x2 - y2 + B_3 a5 -5x(x2 - y2) +x+ /2x r5 r'( r;i v = 1/2 A_3 a3 y x2 y2 + B_3 a5 - (2 - 2) - l/4 y -y -3 yw = 1/2 A_3 a3 z x2 y2 + B_3 a5 -52(x2 y2) r7 Inside the drop: u' = A2 a-2 - 5_xr2 - _ x(x2 - y2 + zB2x zl zl v' = A2 a-2 5- 5 yr2 - z y(x2 y2) - zBy w' =A2 a-2 -2z(x2 - y2). Since continuity of velocity requires that u=u', v=v', ww_, and for the drop to remain spherical torques must be equal; i.e., ux + u_ + uz =0, it can be shown that the identities: 1/2 A_3 -5 B_3 = -z A2, zl 2 B3 + 1/2 = 5 A2 + zB2 zl and 1/2A.3 - 3B_3 + 1/2 = 0

25 must be satisfied. These identities furnish three equations with four unknowns, and Taylor derived a fourth equation to satisfy the demands for continuity of tangential stress on the droplet: A_3- 16 B_3 + = (16 A2 + 4 B2). The four equations in four unknowns were then solved to obtain: A3 = 5 ( A + 2/5))) B3 = - > _k_ t, A2 = zl ->3 z - ltt +r"L,T/ A3\ + A+ 4(-\A +k) z3 A B2 = - 3.. —" Einstein showed that the effect of the presence of solid spheres in suspension on the viscosity of a fluid depends only on p_3, and Taylor stated the same reasoning to be true in the case of liquid spheres. With solid spheres A = -5- and E instein's expression becomes: '~3. z T =i(1l + 2.5 ), where /,* is the viscosity of the suspension andE is the volume fraction of suspended spheres, while for liquid spheres the expression becomes: */ = l25I l + 2,.5 + 2/5.k), which may be called "Taylor's Equation," Richardson' s Equation Richardson27 proposed that there may be an increase in the space occupied by the dispersed phase by an amount c, so that the average separation of the discreet globules is decreased by a fraction 1/1, a being the distance between particles. He represented the ratio of this fraction. to the change in concentration by the symbol, x: x = - bl/<5c.1, where x may be looked upon as an interphasal compressibility, whose value dependsscnthe reative compressibility of the two phases. In simple terms, x

26 may be called the overcrowding of the dispersed phase which is resisted by the continuous phase. When flow takes place, it may be thought that the continuous medium has to move between obstacles of average separation 1, subject to viscous resistance denoted by j. If the overcrowding reduces the separation to (1- al), this resistance is supposed to increase to (L + At_ ), and: d & /q = -dl/l = x dc. Integrating, Richardson obtained: in xL = xc, or ' = Xexc Assuming x to be constant, Richardson's equation may be written in conventional form as: a = 'a ee k Mooney s Equation Mooney8 extended Einstein's equation to apply to a suspension of finite concentration. The analysis is limited to rigid spherical particles. Mooney's approach. is partly empirical in that the interaction between parameters are left for experimental determination. The analysis merely considers the space crowding effect of the suspended spheres on each other. There is no restriction imposed on the concentration or the particle size distribution. Mooney took into account the first-order interactions between particles. In a two-component system, spheres of size rl and partial volume concentration 1, crowd spheres of size r2 into the remaining free volume (1- \12C 1)l where X 12 is a crowding factor which may be different from unity.

27 Mooney first considered a monodisperse system of finite concentration where spheres, all of radius rl, are added to a suspension in two volume fractions, 1i and (2. The addition of the first fraction will increase the viscosity by a factor: H(~)1) = \ ll where H must reduce to Einstein's formula for small values of ( l. If the second fraction, d 2, is now added, there will be a further increase in the viscosity. Part of this increase may be considered to be caused by 0 2 in the viscosity of the remaining space not occupied by ). This increase will be H ( 12) such that: 1 12 =:2 1 -k 1 2 where k is a crowding factor different from unity. The crowding of (1 and 2 is mutual, and introducing 2 reduces the free volume accessible to 1 the effective concentration of.1 now being: t 21 = Ci,21 -k~2 H(~ ) is now replaced by H(t12). The product H(122).H(t 21) is the viscosity of a suspension of total concentration ($l + 1 2) and is equal to H(l1 + 2); thus: H(1 +< 2) = X = H(12).H(T2l) = H, H( 2 o II )2) 1 -k a), This functional equation is satisfied if H has the form: 2.5x H(x) = exp ( ), 1 - kx where x is the relative viscosity. The constant, 2,5, is chosen to agree with Einstein's equation when p approaches zero.

28 For a suspension of n groups of spheres, each group of a different diameter, we may write this as: n i In H() = 2,5 j=1 For a continuous distribution of diameters, we may write this as: in H(() = 2.5 fJ d(i '1 -' IX ji j If 6 is equal to (in r/r), we may write: ddp= P (6 ) d6-, and: ' P (6 ) d = l, where r is a mean radius, and 61 and 6 2 are the upper and lower limits of _ _o The equation can then be written as: in ~ = in H = 2.5 J64 Pi d6 Xo 1-,. d6i, which is called the Mooney equationo Oldroyd's Equation Oldroyd29 made a calculation of the elastic properties arising from the interfacial te.nsion between the two phases of a dilute emulsion. Following Einstein and Taylor, the individual drops and the concentration of the dispersed phase are assumed to be small, so that inertia effects and hydrodynamic interactions between drops can be ignored in calculating the behaviour of a typical macroscopic element of the emulsion. The interfacial tension is assumed to have a sufficiently large constant value to keep the suspended drops approximately spherical, although departure from the spherical shape

29 are taken into account. The boundary conditions of no slip and continuity of tangential stress at an interface are assumed. A homogeneous liquid, L*, is envisaged with the same macroscopic Theological properties as an emulsion consisting of drops of one Newtonian liquid L' of viscosity n' in another Newtonian liquid L of viscosity 1. The drop size is assumed uniform, each drop having diameter a. Two systems are considered, one in which a single drop of L' is surrounded by L filling the space: a r Lb where r< a is referred to spherical coordinates r_,, and ~. The rest of the space, r > b is filled with L*(Fig. 2). The radius b is chosen to give the correct volume concentration of the dispersed phase in the emulsion, so that: b3 = a3 /c, c being the concentration by volume of dispersed phase. The two systems are required to be indistinguishable to a given degree of accuracy, provided that observations are made at a distance r equal to R, sufficiently large compared to b. A perturbation method is used, following Frohlich and Sack30, who considered the rheological properties of a suspension of elastic particles in a viscous liquid, on the assumption that the suspended particles were solid spheres obeying Hooke's law. The following expression for the relative viscosity of the emulsion is derived: h= eor )Y +a( i+2s )(16 9 ) +3c(2+5 )-a( o d- (169+l/dr r is eq+u')y ti(o+2 ' dt16+19' -2c4(2>+5} Y-a(-a3(16+1 ) where A is equal to d/dt,

30 LL r< o \\\\ a < r< b //// r>b Fig. 2. Diagram Illustrating the Hypothetical System of Oldroyd

31 Oldroyd also made a calculation taking into account the slip due to the presence of a very thin film of the emulsifying agent at the interface and arrived at an expression similar to the one above. He concluded that the interfacial slip in a dilute emulsion should not affect the type of Theological behaviour, although it would affect the values of the rheological constants. Application of the Fundamental Equations Deviations from the theoretical Einstein factor of 2.5 have long been recognized for suspensoids31, and are usually attributed to causes such as flocculation, hydration of the particles, etc.32 Several modifications of Einstein's equation have been proposed, generally by adding terms to the power series form, and by varying the value of the constant k. An example is the equation by Guth and Simha33: sp = 2.5 + 4.94 2 + 8.78 3, where: a sp rel 1. The additional terms are introduced to take into account higher order hydrodynamic interactions than were considered in the original Einstein treatment. Bredee and deBooys34 discussed various modifications of the Einstein equation and proposed the following equation for nonsolvated spherical particles: rel - 62.5 ( 2 rel 6 (1 -)J Eilers35 found this equation suitable for values of ) from 0 to 0.65 for bitumen emulsions. For larger values of ( this and other equations were found

32 to give values too low. From a consideration of packing of non-plastic spheres of equal diameters, Eilers postulated that the curve relating viscosity to particle size must have an asymptote at ( = 0.74, since beyond this concentration flow of the dispersion can no longer take place. Further, the curve must fit the Einstein formula at extremely low concentrations, On this basis, Eilers proposed the following equation: trel = 1+ 2.'5 2 (21-a0P where a is 1.35. He found, however, that calculated viscosities were higher, and concluded that this must have been due to a deviation in the particle size of the emulsion. Maron, Madow and Krieger36 proposed an extension of the Einstein treatment, defining an apparent volume fractio: as: where )' is the apparent volume fraction and K is a constant. Then: Z= l '= o, and: In rel =bZ, b being a constant. The factor Z is included to obtain an analytic expression which would take into account the rapid increase of viscosity with increase in ~p. The authors found that with a suitable value of c_, the equation fit the data on latex emulsions up to a concentration of 60%. Rearrangement of the equation gives: d = 1 - (b ln( 7\/ ) cb

33 so that a graph of X versus ( should be linear, with a slope In(/r q o) of -b and an intercept of l/oXb, permitting the evaluation of both. and b. An interesting analysis has been presented by Oliver and Ward37 on the power series form of viscosity-concentration equations. They found that a plot of 1/rel versus c gave a linear plot for stable suspensions of spheres with volume concentrations up to 20%. The equation of the straight line may be written as: t rel 1 1 - kc, or, rel 1 + kc + k2c2 + k3c3.... where k is constant. For very low concentrations, this reduces to: rel = 1 + kc and if k is 2.5 the expression becomes identical with the Einstein equation. This equation was applied to the data of several workers with the results shown in Table 1. Leviton and Leighton45 extended Taylor's treatment by introducing a power series of. Emulsions of milk fat in skim milk and other continuous media were used and viscosity was measured in a capillary viscometer. Taylor's equation was modified to the following: In rel = 2.5lf + 2/5lo ( + 5/3 + ()11/3). For small values of p this reduces to the Taylor formula. The author points out that in the power series involving i, 5/ is included in conformity

34 TABLE 1 VALUES OF THE CONSTANT k FOR THE OLIVER -WARD EQUATION Worker Type of Size Ratio of k Range of Volume Viscometer Suspended Spheres Concno over which Equation Applies Eirich, Buzl & Capillary 2.0: 1 2.41 0-15 plus Margaretha38 Broughton & Rotating 1.8: 1 2.57 0-15 plus Windebank39 Cylinder 1 2 1 2.41 0-20 plus Whitmore40 Rising 1o4: 1 2.77 0-20 plus Sphere Eveson41 Rotating 1.4: 1 2.56 0-20 Cylinder Nandi42 Capillary 1.4: 1 2.42 0-35 Higginbotham43 Capillary 1.2: 1 2,38 0-25 Williams44 Capillary 5.0: 1 2,34 25-35 Oliver & Capillary 16: 1 2.45 0-30 Ward37;

35 with the suggestion of Smoluchowsky46. The term, Q l/3 has no theoretical significance but is included to obtain an agreement between observed and calculated values. Sibree47 applied Hatschek's equation to his data on emulsions of paraffins of various viscosities in water with sodium oleate as emulsifier. A concentric cylinder viscometer was used, and the viscosity was found to be independent of the rate of shear after a certain point. The Hatschek equation did not agree with experimental observations. Using observed values of _ and 'L O, viscosities of emulsion and continuous phase, respectively, Sibree calculated the theoretical volume percent of dispersed phase by rearranging the Hatschek equation: \3 Since, in every case, the calculated value of X was higher than the measured value, he calculated a volume factor, h, such that: h = Q calculated/ measured. For emulsions with more than 50% dispersed phase, h was found to have a value of 1.3. According to Sibree, this apparent increase in ~ may be due to the adsorbed film which increases the size of each drop. Sibree's modification of Hatschek's equation may be written as: in y rel = 1 1 = _____ 1. 48 1 Broughton and Squires measured the viscosity of emulsions of Nujol, benzene and olive oil in water with sodium oleate 1%, saponin 2% and triethanolamine oleate 5% as emulsifiers. A MacMichael viscometer was used, and limiting viscosities were calculated. They proposed a modification

36 of the Richardson equation: in r = a+ b2, which agreed with their data. Calculated values of the volume factor, h, in Sibree's modified equation, varied from much less than 1 to much more than the 1.3 proposed by Sibree. It was concluded that neither Hatschek's equation nor its modification as proposed by Sibree, agreed with experimental observations. The yield point was found to be a function of the limiting viscosity of the emulsion. Neogy and Ghosh49 measured the viscosity of three xylene-inwater emulsions with three cationic soaps as emulsifiers, and of a waterin-benzene emulsion with magnesium oleate as emulsifier. A Couette type instrument was used, and the average values of viscosity at minimum and maximum rates of shear were calculated. Good agreement for the oil-in-water emulsions and still better agreement for the water-in-oil emulsion was obtained with the modified form of Richardson's equation, as proposed by Broughton and Squires. In another study50 on xylene-in-water emulsions stabilized with sodium oleate, myristate, laurate, caproate, and saponin, where viscosities were measured in a similar manner, these workers found that only Richardson's equation fitted their data within 5%. Sibree's modification was not satisfactory. Toms51 studied the viscosities of various organic liquids with different univalent soaps as emulsifiers. Significant variations were found in the value of the volume factor, h, in Sibree's equation, due to the nature

37 of the emulsifying agent and the internal phase. However, a large number of values of h were found to be close to 1.3, indicating that Sibrees equation may give good agreement with experimental observations. Sherman32 investigated the effect on viscosity of varying the ratios of the two phases. Emulsions of mineral oil-in-water were prepared with sorbitan sesquioleate as emulsifier and a variable pressure capillary plastometer was used to measure viscosities. The results deviated considerably from values calculated with the Einstein equation and the modified equation of Guth and Simha. Hatschek's equation gave values lower than observed and the volume factor, h, from Sibree's equation was found to be 1.2 and independent of 4i. Richardson's equation was found to be applicable only to the emulsion with 3.5% emulsifier, all other results agreeing with the modified Richardson equation. Sherman also observed52 that Richardson's modified equation and Hatschek's equation as modified by Sibree agreed with experimental observations on water-in-oil emulsions where the viscosity of the dispersed phase was varied. Mooney28 applied his equation to the data of Eilers on emulsions of bituminous materials of high softening point, such that the droplets were essentially rigid at room temperature. The diameters varied from 1.6 to 4,7 microns so that the emulsions could be considered polydisperse. Since the function i was not known in detail, the equation was developed as a power series of, yielding: ln L = 2.5? + S A where ln 1 n An P1 h- i Pjd6 dn.

38 To the second degree in _ _, this equation becomes: ln = 2.5 X 'to 1 - 4l $ l From Eiler's data, \1 was found to have a value of 0.75. Effect of Particle Size of Dispersed Phase on Flow Properties of Emulsions Jellinek53 discussed a systematic treatment of distribution functions of emulsions and their average quantitiesb Expressions were presented for integral distributions with respect to diameter, surface area and volume. Other equations for the size distribution of emulsion particles have also been derived54,55o The measurement of particle size has been a considerable challenge because of the special conditions that prevail in an emulsion, e.go. Brownian motion and particle diameters generally below the level for easy microscopic measurement. Many methods have been reviewed by Nassenstein56. Perhaps the most widely used is the microscopic method, utilizing a camera lucida57 or microphotography58. For reducing the time involved in particle size measurement by photomicrographs, a rapid method has been developed59. Direct optical methods have also been used60,61. Various sedimentation techniques have been used as well, for measuring particle size in emulsions62 None of the basic relatonships derived for the viscosity of emulsions includes the particle size as a variable, with the exception of Oldroyd's equation, although there are many and conflicting reports on the effect of particle size and size distribution on the theological properties of an emulsion.

39 It has been reported that there are significant linear increases in the viscosity of whole milk upon homogenization63. Kremner and Soskin64 reported that low pressure homogenization of an emulsion of benzene-in-water with 5% sodium oleate as emulsifier caused an increase in the viscosity in the ratio of 2.5: 1. Since the major change upon homogenization would be greater dispersity and smaller particle size, it appears that changes observed can be attributed largely to decrease in particle size. Traxler65 considered the effect of size distribution on the flow of disperse systems. Two conditions may exist, one where the disperse phase is so large in amount that the particles are in some form of packing, another where the quantity is so small that the particles of the dispersed phase are not in contact with each other. Considering a disperse system having all spheres of the same size, the volume of the continuous phase is equal to the interstitial space of the disperse phase, The intestitial space varies with the packing arrangement and, as a consequence, the size of the individual interstice (identical with the dimension of the average film of continuous phase separating the dispersed particles) varies with the degree of packing. The loosest packing is obtained with four points of contact between any particle and those surrounding it. As the number of contact points increases, the percent of the interstitial space and the size of the average individual interstice decreases, until twelve points of contact are formed. The percentage of intersitial space for each of several packing arrangements for spheres of uniform size is shown below:

4o Points of Contact Percent Interstitial space 4 66.6 6 47.6 8 39.5 10 30.2 12 25.9 Considering two systems of the same volume concentration, one with particles of equal size, and the other containing particles of various sizes, the packing is looser in that containing various sizes. Therefore, this system is more fluid with fewer points of contact between particles and a thicker film of continuous phase separating them. Data was presented by Traxler to support this view. Two emulsions were prepared containing particles of quite uniform size. In one they were less than one micron in diameter (emulsion A), and in the other they were two to three microns (emulsion B). The viscosity of the emulsions and blends of the two were measured in a Saybolt-Furol instrlment. Results were as follows: Volume % Viscosity at 25~ Emulsion A Emulsion B Saybolt-Furol Units 0 100 36.0 10 90 23.0 20 80 21,5 30 70 20.0 40 6o 19.5 50 50 20.5 6o 40 21.5 7o 30 24.5 80 20 26.0 90 10 33.0 100 0 41.5 The authors concluded that, although some of the measurements were close to or slightly below the range of sensitivity of the instrument, it was shown that blends of the two emulsions were more fluid than either emulsion alone.

41 Traxler67 also made the point that the viscosity of an emulsion is a function of the condition of the surface of the particles as well as the size and size distribution of particles. Using a rising-sphere method, Ward and Whitmore68 measured the viscosity of suspensions of smooth spheres of methylmethacrylate polymer suspended in an aqueous solution of lead nitrate and glycerine. Various concentrations of spheres were measured with particle size ratios varying from 1.17 to 2.74 within the size range of 28 to 208 microns. It was concluded that the relative viscosity of a suspension of smooth hard noninteracting spheres is independent of the absolute size, decreasing with increasing size range to a constant value. Sibree69 reported that the viscosity of emulsions is independent of particle size and size distribution within wide limits for the same pair of liquids. Emulsions of several paraffins in water with sodium oleate as emulsifier were measured in a rotational viscometer. Leviton and Leighton45, working with emulsions of milk fat, found the viscosity to be independent of the particle size. No measurable increase in viscosity was found with a fourfold reduction in the diameter of the dispersed globules. In the study on the stability of emulsions using specific surface area measurements, Mullins and Becker70 measured the viscosities of emulsions of peanut oil, glyceryl ricinoleate, glyceryl trioleate and cod liver oil, made with two emulsifying agents and at four homogenization pressures An Ostwald viscometer was used. They reported that the change in specific surface

42 area, and consequently in particle size, did not influence the viscosity of the emulsions. A similar observation was made by Knoeckel and Wurster, who used the Drage rheometer in this study57. Richardson71 investigated the effect of particle size on the viscosity of emulsions, A falling sphere method was used to avoid continuous shearing action over a comparatively long time, as required for reading a capillary or a Couette type instrument, which might cause a breakdown of some globules in a concentrated emulsion. In the falling sphere instrument the droplets are sheared only when the solid sphere is in the vicinity of the particles. He found that as long as the emulsions were homodisperse the viscosity at high rates of shear varied inversely as the mean globule size. When a polydisperse distribution of particles was present, the system was less viscous than indicated by this relationship. It may be seen that the relationship of viscosity to particle size is not yet clear. There are several factors causing difficulty that need to be considered. Perhaps the major difficulty is isolation of the size and size distributioz effect from other factors affecting the rheological properties, It is hardly possible to avoid interaction between emulsifier and disperse phase which determines the nature of the particle surface, and this factor might make all other effects obscure. The use of several different diameters to describe the particle size creates further difficulty when comparison of results is attempted. It would appear that there are definite differences in viscosity between homogenized and non-homogenized emulsions. In this connection a

43 report by Axon72 may be mentioned. Axon developed a microscopic cell to examine semi-solid oil-in-water emulsions during flow. He observed two types of dispersions. In one, globules were associated in loose clusters in which each globule was free to move independently of its neighbours. In the other, a compact type of floccule occurred, where the globules were surrounded by a hydrated layer restricting their movement and presenting a mechanical barrier to deformation. It must be pointed out that the methods used for measuring viscosity were often inadequate for evaluating non-Newtonian flow. Since homogenization is generally one of the steps in the manufacture of industrial emulsion, practical systems may be of such narrow range of size distribution that this factor may have little significance. Effect of Viscosity of Dispersed Phase on Flow Properties of Emulsions Of the equations derived for the viscosity of an emulsion, only those of Taylor and Oldroyd include viscosity of the internal phase as one of the factors to be considered. Sibree47 prepared emulsions of two paraffins with a viscosity ratio of 38: 1 and found that the emulsions had a viscosity ratio of 1.4: 1. This, he concluded, was in agreement with Hatschek's equation which considers the viscosity of an emulsion to be independent of the viscosity of the dispersed phase. A similar observation was made by Sherman52 in his work with water-in-oil emulsions. The viscosity of the

44 internal phase was varied by addition of different alcoholic derivatives to the water phase, e.g., propylene glycol, sorbitol syrup (70%) and glycerineo The viscosities were measured in an Ostwald-type viscometer. Broughton and Squires8 stated that no generalization can be drawn as to the influence of the viscosity of the dispersed phase on that of the emulsion. They investigated emulsions of Nujol, benzene and olive oil with sodium oleate, saponin and triethanolamine as stabilizers, using a MacMichael viscometer for measurements. Toms51 carried out an extensive investigation of the effect of the internal phase and emulsifier on the viscosity of emulsions, It was found that for the same emulsifier, the viscosity of an emulsion varied widely with the nature of the internal phase. He stated that this may be explained by an alteration of the mutual solubilities of the three components of the emulsion, oil, water and emulsifier. Sherman also stated that the chemical nature of the dispersed phase may be of importance with particular reference to the emulsifier. From a consideration of the reports of these workers, it appears that the viscosity of the disperse phase does not have a significant effect in determining the viscosity of the emulsion. However, the chemical nature of the internal phase seems to be of importance, and the interaction between the internal phase and the emulsifier may be the most sigrificant factor affecting the viscosity of an emulsion.

45 Effect of Emulsifying Agent on Flow Properties of Emulsions In an extensive investigation, Toms51 prepared emulsions of eleven organic liquids using ten univalent soaps, sodium and potassium salts of lauric, myristic, palmitic, stearic and oleic acids. He found little change due to substitution of potassium for sodium in emulsions stabilized by laurate and oleate but significant changes with myristate, palmitate and stearate. On investigating the effect of the emulsifier on the value of the factor, h, in Sibree's modification of Hatschek's equation, he found the value to be altered only about 1% upon changing the cationic part of the molecule but about 20% by changing the fatty acid part of the molecule. Another observation was an increase in viscosity with greater concentration of emulsifier. Wilson and Parke73 investigated the viscosity of emulsions as a function of emulsifier concentration. The viscosity of a 70% benzenein-water emulsion passed through a minimum upon increase of emulsifier concentration at a concentration of 0.84% sodium oleate in the aqueous phaseo As a rule, however, it was found that viscosity increased continuously with increase in emulsifier concentrationo Sherman52, in his work on water-in-oil emulsions, found that addition of finely-divided carbon black to the emulsion as a stabilizer resulted in a pronounced increase in yield value and viscosity of the emulsion. He further observed that emulsions containing greater proportions of polyhydric alcohols in the dispersed aqueous phase exhibited

46 lower yield values and viscosities, This was explained on the basis of the specific absorption of the two phases on the carbon black surface, which is affected by the concentration of the polyhydric alcohols in the aqueous phase, leading to a decrease in the contribution towards viscosity and yield valueo Sherman74 also investigated the effect of the emulsifier on water-i.n-oil emulsions of high water contento Emulsions were prepared containing 605% glycerine and 65.5% water in the aqueous phase and 2.8% emulsifying agent and 25.2% mineral oil in the continuous phase. The composition was kept constant except that ten nan-ionic emulsifiers were used. Six of the emulsions were found to have relative viscosities cf the same order, bi't; marked. variatio:n.s were shown by the other four. On the basis of their resul.ts, Neogy and Ghosh50 also made the pcOiLt;'hat the viscosity of an emulsion depends on the emulsifier used. 48 Brought~on an:d Squires48 observed that for a given phase pair the relative limiti'.ng viscosi.ty varies widely with the type of emulsifier used. Mardles and DeWaele75 considered the rheological behaviour of suspensions and emulsions in, relation to properties of surface films adsorbed on the dispersed particleso They noted that small changes in composition of a disperse system lead to important variations in rheological properties du.e to changes in the character of the interfacial film. An increase in the friction. between particles results in larger sedimentation volumes and higher specific viscosities, In concentrated systems, this factor outweighs the usual hydrodylamic considerations~

47 A fact that has been brought up by several workers is that the globule size of an emulsion decreases with an increase in the concentration of the emulsifying agent, reaching a limiting value. This would seem reasonable in that at lower concentrations there may not be enough emulsifier available to cover a large area as would occur in a finer dispersion. Although most emulsifiers reduce the interfacial tension between the organic and the aqueous phases of the system, at lease one instance has been reported76 of an emulsifier increasing the interfacial tension. Alkali halides were found to stabilize emulsions of water in amyl alcohol. These salts are not surface-active but rather increase the interfacial tension of the system, Sherman77 recently reviewed the effect of the concentration of emulsifier on emulsion viscosity. A change in viscosity with varying concentrations of the emulsifier, for the same value of 2, has been observed by several workers. However, no attempt had been made to relate quantitatively the emulsifier concentration to the viscosity of the emulsion. From the experimental observations of several workers, Sherman concluded that a change in emulsifier concentration had a greater effect on emulsion viscosity in concentrated emulsions than in dilute systems. For his data on emulsions with varying concentrations of sorbitan sesquioleate the viscosity increased with concentration up to a value of of 0.5. This was explained as due to an increase in VLo. Beyond this value of _ much larger changes in viscosities were observed.

48 Sherman proposed an equation relating emulsion viscosity to the volume concentration of the oil as well as emulsifier concentration as follows: lnlrel = aC + G, where C is the emulsifier concentration and G is a constant. He pointed out that this equation is similar to the modified Richardson equation: ln \rel = k + A. Sherman suggested that the k in this equation is a function of emulsifier concentration C, The equation fitted the data of Broughton and Squires48, Sibree69, and Van der Waarden78. From the observations of these workers it appears difficult to describe the effect of the emulsifier on the rheological properties of emulsions. Sherman's equation is the only quantitative relationship proposed. However, the methods employed to measure viscosity by the workers whose data were used to prove this equation were not suitable for nonNewto:ziaan systems. It appears that much work is yet needed to define the effects of emulsifier on flow properties of emulsionso Effect of Surface Charge of Dispersed Phase on Flow Properties of Emulsions Smoluchowski46 proposed that for a charged particle in an electrolyte, the electrical double layer might be expected to increase the effective viscosity of a suspension of solid particles. This increase is called the electroviscous effect. For this condition, he obtained the relationship: r\%L' 2 Yf + 21 2 *5 L- ) 0 1 - -on, u

49 where - is the specific conductivity of the electrolyte, a is the radius of the solid particle, - is the dielctric constant of water and ~ is the electrokinetic potential of the particles with respect to the electrolyte. This formula assumed that the thickness of the double layer was small compared to the particle radius. A similar result was derived by Krasny-Ergen79. The increase in viscosity due to the presence of charges on the particles was qualitatively confirmed by Booth8~ in his experiments. Booth derived an expression for the viscosity of a suspension which involved all the assumptions made in the derivation of the Einstein equation. Further it was assumed that: 1. The thickness of the region containing the surface charge on the particle was small compared with the radius of the particle. 2o The ions in this region were immobile and could not move laterally over the surface. 3. The surface charge density at any point was fixed, and remained unchanged when the electrolyte was set in motion. 4. The potential across the region containing the surface charge was also unaffected by the motion of the electrolyte. 5o The double layer was small in thickness compared with the average distance between neighbouring particles. The equation derived by Booth was of the form: X =o 1 + 2.5 d a + an Qn | j 1 J where Qe denotes the charge on each particle and an is the coefficient of the Yth term in q The electroviscous effect was also observed by Tanford and Buzzel8l in a study of the viscosity of aqueous solutions of bovine serum albumin between the pH of 4.3 and 10.5, in which range the albuminr molecule behaved as a compact particle similar to a sphere. The

50o increase in the intrinsic viscosity was found to be in fairly good agreement with Booth's equation. Electroviscous effects were observed by the same workers in a study of the viscosity of ribonuclease between the pH values of 1 and 1182, The increase in viscosity, however, was larger than predicted by Booth's equation. van der Waarden78 investigated the viscosity of oil-in-water emulsions of varying particle size and concentration prepared with the same oil, and the same emulsifier. Viscosities were measured in a British Standard Institution viscometer and particle size was measured by a lightscattering method. Values of the constant K were calculated by the formula K= Il. The limiting values of K as _ approached zero were obtained by plotting:K versus _f The values were found to be higher than the value 2.5 of Einstein's equation for uncharged rigid spheres. It was found that the limiting value approached 2.5 as the emulsifier content approached zero. An apparent increase in volume was calculated, and from it, an increase inr the droplet radius by the equations: v = 4it (r + Ar)3/4 tre3/3 Ar = r (3 v-1 ) - The L r values were found to be independent of particle size, and it was concluded that oil droplets behaved as if they were enveloped.. by a rigid layer, which in this case was calculated to have a thickness of 30-35 A~o

51 This apparent increase in the radius of the spherical particle was ascribed to the charge on the oil droplet. The increase in viscosity, however, was much larger than predicted by the equation of Smoluchowski or Booth. In another investigation, van der Waarden, Harmsen and Schooten83 demonstrated that the influence of electrolytes on the viscosity of emulsions of moderate or high concentration increased with a decrease in the particle size. Emulsions were prepared with 10o of a medicinal oil in water stabilized by sodium naphtha sulfonates, and varying concentrations of sodium chloride were added. The results are presented below: Particle NaCl rel of Percentage Diameter Concn. Emulsion Decrease in. rel A0 (meq./L. ) 2050 0 1.42 2050 43 1. 41 585 0 lo65 about 10 '585 15 1 47 275 0 2.00 about 20 275 17 1.60 It was proposed that two types of electroviscous effect might be involved. First, the classical effect caused by an i.teraction between particle and

52 medium, causing an apparert voll.ume increase; second, the higher order effects caused 'by an i-nteraction betweern particles, which becomes more marked as the crncentration is increased. Oany the classical effect has been elaborated f~n.damentallyo The apparent increases in particle sizes *were still found to be constant 30-35 A0 for particles of all sizeso 84 Do-rnet and Reitzer4 studied the effects of particle charge on the viscosity cf a suspension u.sing spheres of carbon black carrying ionizable chemical groups as the charged particles It was found that the viscosity of the suspension did not depend on the charge per particle when the latter varied from 750 to 2260 elementary chargeso This conclusionr. was contrary to the theories of Smoluchowski and Booth. It would appear that considerably more work needs to be done in this field before any general co.c.lusio.i.s can be made. Effect of Viscosity of the Conti..nuous Phase on. Flow Properties of Emulsions Mocst of the relatiorships derived for the viscosity of an enmusion inc 1lde ro, the viscosity of the cont-in.uous phase It may be said that'' T| = T0 X.7 where x is the summation of' all other properties which may affect viscosityo The equation$ o.f Smoluchcwski,, for instan'ce, includes the dielectric constant of watero

553 It is important the viscosity of the continuous phase be that of the complete medium and not that of the basic solvent aloneo The difference may be quite significant if an agent such as methylcellulose or bentonite is present as an added stabilizer. It is reported that addition of bentonite to the con.tinuous phase stabilized an emul86 sion of benzene in water with sodium oleate emulsifier. Axon found that emulsions of liquid paraffin in water containing bentonite exhibited thixotropic flow. Knoeckel and Wurster7 studied the stability of emulsions with varying viscosities of the continuous phaseo The size frequency analysis technique was used to measure stability. and the viscosity of the continuous phase was varied by addition of methylcelluloseo Sodium lauryl sulfate was used as emulsifier. Since only one emulsifier and one viscous agent were used the effects of interactio:ns between these agents were not evaluated. Such an interactioun would often be the most significant factor affecting emulsion viscosity. and thus their results have limited applicationo Although the agents most cormnonly used. as stabilizers for emulsions cosfer non-Newtonian properties upon the continuous phase and the final emulsion, few studies have utilized methods of measurement which are suitable for non-Newtonian liquids. For any relationship

54 between viscosity, emulsion and. conti.nuous phase to be useful, the nonNe'wtoniian. properties must be considered.

STATEMENT OF THE PROBLEM The presently-available equations describing relationships of emulsion viscosity to various properties of dispersed and continuous phase have several features which limit their usefulness. First, they are based on data obtained by methods not suitable to non-Newtonian liquids, in spite of the fact that most practical emulsions are not of Newtonian character. Second, they assume Newtonian viscosity for the basic components of the emulsion as well as the emulsion, itself. Third, they are applicable, generally, to lower concentrations of dispersed phase than are commonly used. Fourth, these equations do not consider the interactions which commonly occur between emulsifier and dispersion medium or dispersed phase. Fifth, they have usually been developed from or tested with a small number of measurements on a limited type of emulsion. Development of the M-2 and M-3 viscometers made possible the automatic recording of all types of flow curves in a relatively short period of time. Development of the Structure Equation made it possible to describe flow properties of non-Newtonian liquids accurately with three constants which can be calculated from the data by means of an electronic computer. Thus, it has become practical to measure large numbers of samples and search for general relationships which might predict the flow properties of emulsions. 55

56 It was the purpose of this investigation to determine the flow properties of emulsions containing common non-Newtonian suspension media and to attempt a correlation of rheological behavior, as defined by the Structure Equation, with several pertinent factors, such as particle size, conceration of dispersed phase and concentration of suspending agent in the continuous phase.

EXPERIMENTAL Apparatus and Materials The M-3 Viscometer Description The suitability of a concentric cylinder rotational viscometer for measuring flow characteristics of pharmaceuticals and the development of an automatic recording viscometer for this purpose were described by Samyn87'88 in previous work at The University of Michigan. Shangraw89 designated this instrument the M-1 viscometer and described the development of the M-2 viscometer. The most important change in the M-2 viscometer was one of size, the overall dimensions being expanded to approximately four times those of the M-l. Grim91 used the M-2 viscometer with two modifications to study the rheology of pharmaceutical suspensions. The two modifications were that the point bearing of the bob was changed from stainless steel to Carboloy to reduce wear, and that a digital print-out recording system was added. The instrument used in this study, designated the M-3 viscometer, is similar to the M-2. It differs chiefly in having the cup drive consist of a spiral miter unit (VR 131, Boston Gear Works) and a horizontal motor, the two being connected by a double-belt pulley. It was felt that this would give better alignment of the cup and smoother operation. Another change from the M-2 viscometer is that a different make of x-y recorder is used (Model 2A, F. L. Mosely Co.). 57

58 Calibration Strain gauges. — Each of the strain gauges was calibrated by loading with weights and observing the corresponding deflection on the x-axis of the tracing. The curve of deflection versus weight was linear for all gauges. Readings of standard resistors were made at the same time, so that the calibration constants might be in terms of standard resistors and thus independent of the degree of amplification. Calibration results are shown in Table 2. TABLE 2 CALIBRATION CONSTANTS FOR STRAIN GAUGES Gauge Weight Equivalent to Standard Resistor oz. R1 - Gm. R2 - Gm. 4 28.61 57.38 8 81.06 162.94 16 156.48 313.72 32 297-78 597.05 80 701 75 1400.78 Tachometer. -- The tachometer was calibrated by measuring the deflection on the y-axis of the recorder using the 10 volt, fixed scale, and the speed of the motor in r.p.m., using a Hasler speed indicator, (Hasler-Tel Company), at each of several settings on the speed controller. These values were plotted and found to be linear, and the slope of the line was used as the calibration factor. All measurements were made using this scale so that the calibration factor remained constant.

59 Cup anld bob dimensions and instrument constants. -- Dimensions of the cup and bob are used for converting experimental data into units of shear and stress which represent the average values in the annulus between the cup and bob. Equations for the shear constant, Ks, for converting r.pom. to average rate of shear (in reciprocal seconds) are the Average equation91, the Fischer equation92 and the Andrade equation93. Selection of the proper equation is important if the gap between cup and bob is not small, but it was shown that all three give identical values, within experimental error, for the cup and bob used with the M-2 or M-3 viscometer94K Calculation of the shear constant may be illustrated with the Andrade equation, which is the one of choice: Ks s o 4i R In R c/Rb, ~C b) where Rc is the radius of the cup and Rb is the radius of the bobo The rate of shear is then calculated by: S = Ks (ropm.), where S is the average of shear in annullus Equations were presented by Samyn95 and Shangraw96 for the stress constant, Kf, for converting experimental measurements of force into average shearing stress. It was shown that both equations give the same value with. a small gap between cup and bob such as is found with the M-2 and M-3 viscometerso The Shangraw equation, which is the better of the two, is as follows: Kf = in Rc/Rb, -t h(R2 - Ri where h is the height of the bobo

60 A given value of stress, F, involves the stress constant, the weight equivalent recorded from the strain gauge, the gravity constant and the length of the lever arm connecting the bob to the strain gauge; thus: f = Kf. 980. Lever arm. Gm., where F is the stress in dyne/cm2. By using a wide range of gauges, it was possible to work with a constant lever arm and simplifying the conversion to multiplication by a single factor: F = T. Gm., where T is a new constant, is the product of Kf, lever arm and the gravity constant. Dimensions of the cup and bob and the instrument constants for the M-3 viscometer are presented in Table 3. TABLE 3 CUP AND BOB DIMENSIONS AND INSTRUMENT CONSTANTS Dimension or constant Value Inside radius of the cup, Rc 4.603 cm. Radius of the bob, Rb 4.523 cm. Height of the bob, h 19.431 cm. Lever arm 17.0 cm. Ks 5.9731* Kf 3.9333 x 10-4 cm.-3 -1 -2 T.. 6.5535 cm. sec. * Dimensionless

61 Operating Procedure A uniform procedure was followed in measuring rheological properties of all samples. Each sample was brought to temperature in an auxiliary water bath at 30~40 where it was kept for at least one hour. It was then transferred to the cup of the viscometer, care being taken to avoid incorporation of air. 'The sample was allowed to stand in the viscometer bath for at least ten minutes before measurement The viscometer bath was maintained at 30~ + 0.10 and the bath temperature was checked to insure that it was at bath temperature at the time of measurement. A strain gauge was generally selected so that the maximum stress to be recorded would fall within the upper half of the range of the gaugeo Both upcurve and downcurve were recorded, so that a failure to retrace would be noted. Differences in up- and downcurves would be encountered when the sample is thixotropic, air is entrapped in the sample or sedimentation occurs during measurement. Satisfactory retrace was obtained for all samples reported in this study. At least three successive flow curves were recorded for every sample. Either before or after the measurement, one of the calibrated resistors was switched into the circuit and its deflection on the stress axis marked. The recorded flow curves represented an infinite number of experimental points, but a finite number of values were required for

62 mathematical treatment of the data. For convenience, equally spaced intervals on the y-axis were chosen, the range of the values on this axis being constant for all curves. Materials Used Selection of Materials For initial experiments cetyl alcohol was chosen as the dispersed phase, since it could be emulsified in a liquid state and then allowed to cool to form solid particles which would not change in size. Most of the experimental work dealt with an oil as the dispersed phase and corn oil was selected for this purpose. Water was used as the solvent for the continuous phase. In the selection of the emulsifiers an effort was made to avoid those which cause extreme interactions. Two were selected: sodium lauryl sulfate and a mixture of 3 parts of sorbitan mono-oleate (Span-80) to 1 part polyoxyethylene mono-oleate (Tween-80). Flow properties of the continuous phase were varied by addition of various suspending agents. Methylcellulose, sodium carboxymethylcellulose, Carbopol-934 (sodium salt), sodium alginate, tragacanth and acacia were selected as suspending agents commonly used in pharmaceuticals. Concentrations of suspending agents to be used were determined by estimating the maximum concentration of solution that could be conveniently added to a prepared emulsion. This and graded levels of concentration below this were used.

65 A mixture of three parts methyl para-hydroxyberzoate to one part propylpara-hydroxybenzoate was added as a preservative 'to solutions of suspending agents and basic emulsc-ons, a concentration of 0.1% of the mixture being used. This was required to prevent microbial growth during storage of the samples. A description of materials used is shown in Table 4. Preparation of Solutions of Suspending Agents Methylcellulose solutions were prepared by adding, with stirring, the powdered material to about one-half the required amount of water previously heated to 70~. The preservative was dissolved in the water prior to incorporation of the methylcellulose. The mixture was made up to volume with cold water and stirred in an ice bath until its temperature reached approximately 0-5~. It was then stored in a refrigerator for at least two days and finally at room temperature for at least two days before use. Solutions of acacia, tragacanth, sodium alginate and sodium carboxymethylcellulose were prepared by mechanical dispersion of the powders in hot water containing the preservative. These were allowed to stand at room temperature for at least two days after solution was complete. The sodium salt of Carbopol-934 was prepared by dispersing Carbopol-934 in methanol and adding the calculated amount of sodium hydroxide dissolved in methanol so that an aqueous solution of the salt would have a poH of 7. The sodium salt precipitated and was filtered out and dried at 125~. Sufficient salt was prepared at one time for

64 TABLE 4 DESCRIPTION OF MATERIALS USED Material Manufacturer Control Noo Acacia, UOSoPo S B.Penick & Co. --- Methylcellulose, 1500 cps Dow Chemical Coo 6702 Sodium carboxymethyl- Hercules Powder Co. 1406 cellulose, type 7 MP Tragacanth, U.SoP, S.B. Penick & Co WSB337 Sodium alginate, UoSoPo Amend Drug and Chemical Co. C510569 Carbopol-934 BoFoGoodrich Chemical Co. 785 Corn oil, UoSoPo Corn Products Co. Sodium lauryl sulfate, E.I.Dupont De Nemour BWD-25671 UoSoPo & Coo Sorbitan mono-oleate Atlas Powder Co. 610 (Span 80) Polyoxyethylene mono-oleatel Atlas Powder Co. 502 (Tween 80) Methyl para-hydroxy benzoatel Heyden Chemical Coo CN3660 UoS.P Propyl para-hydroxy benzoate Heyden Chemical Co. CN360 UoS.P Cetyl alcohol, No.Fo Givaudan Delawanna Inc. --

65 the entier study. Solutions of this salt were made as needed by dispersirig it in an aqueous solution of the preservative. Solutions were stored at room temperature for at least two days before use. Solutions of suspending agents were assayed by drying at 80~ until most of the water had been removed, then drying at 105~ for two hours and weighing the residue. Preparation of Emulsions Three series of emulsions were made. The first series contained varying concentrations of cetyl alcohol. These were prepared by dissolving sodium lauryl sulfate and preservative in the required amount of hot water (70-800) and adding the melted cetyl alcohol with mechanical stirring. The emulsion was homogenized while hot with a Manton-Gaulin laboratory homogenizer (Model 15M8BA) at a pressure of 1000 lb/in2. The homogenizer was previously heated by passing hot water through it. The basic emulsion contai.ned 5.4% w/w of cetyl alcohol and 0.4% w/w of sodium lauryl sulfate. Emulsions of graded concentrations were prepared by dilution with water. The second series of emulsions had corn oil as the dispersed phase, two different emulsifiers and varying concentrations of several suspending agents. A basic emulsion was prepared containing 60% w/w of corn oil and 5% w/w of emulsifier, either sodium lauryl sulfate or the Span-Tween mixture. When sodium lauryl sulfate was used it was dissolved along with the preservative in the required amount of water prior to addition of oil. When Span and Tween were used, the Tween was dissolved in water and the Span in the oil. In both cases, the emulsion was formed

66 by mechanical stirring as the oil was added to the aqueous phaseo Homogenization was performed at several different pressures, and the basic emulsion was then mixed with the selected quantity of suspending agent solution and water to yield an emulsion containing 40% w/w of oil. The third series of emulsions contained corn oil and only one emulsifier, the Span-Tween mixture. Three suspending agents were used at different concentrationso The basic emulsion was prepared as previously described with 60o w/w oil and 5% w/w Span-Tween emulsifier. Only one homogenizing pressure, 3000 lb./in2, was used. Selected concentrations of suspending agent and oil were obtained by dilution with water and suspending agent solution. All emulsions were stirred carefully to avoid entrapping air and allowed to stand at room temperature for at least three days before measurement o Solutions of the suspending agents were made having the same concentration of the suspending agent and sodium lauryl sulfate or Tween-80 as the aqueous phase of the finished emulsions. Since Span-80 is not soluble in water it was not added to these solutions. In the experiments with emulsions containing varying proportions of oil, the amount of Tween-80 present in the aqueous phase varied with the concentration of the oil phase; therefore the effect of concentration of Tween-80 on flow properties of methylcellulose and sodium carboxymethylcellulose was examined. No effect was found, and solutions of suspending agents alone were used as blanks for this set of experimentso

67 The cetyl alcohol emulsions studied, series I, contained the following concentrations, % w/w, of cetyl alcohol: 5.4, 5.0, 4.5, 4.0, 3.5, 3.0, 2.5, 2.0, 1.5 and 1.0. The corn oil emulsions used for examination of effects of homogenizing pressures and concentration of suspending agent, series II, are shown in Table 5. The corn oil emulsions prepared for evaluation of the effects of concentration of oil and suspending agent, series II, are presented in Table 6. Particle Size Measurement Particle size analysis was carried out for all basic emulsions of the second series. The emulsion was mixed thoroughly and two drops were diluted to 100 ml. with a 50% solution of propylene glycol in water. A drop of this dilution was placed on a Petroff-Hauser bacteriateria coter (Arthur H. Thomas Co.). Measurement was performed using a microscope (Bausch and Lomb Co.) with a lOx eyepiece and a 47.4x objective. A grid in the eyepiece was calibrated with a stage micrometer, allowing direct measurement of particles. Fields from at least three slides were examined, at least 400 particles being measured. Flow Data Series I At the beginning of the experimental work it was thought that cetyl alcohol emulsions would be ideal for study. Since the emulsified

68 TABLE 5 CORN OIL EMULSIONS USED IN INVESTIGATION OF EFFECT OF HOMOGENIZING PRESSURE AND CONCENTRATION OF SUSPENDING AGENT SERIES II Emulsifier Suspending Concentration of Suspending Agent Agent in Aqueous Phase (% w/w) Sodium Sod. Carboxy- 0.84, 1.15, 1.46, 1.76, 2.07 Lauryl methylcellulo s Sulfate Sod. Alginate 0.42, 0.57, 0.72, 0.87, 1.02 Tragacanth 0.41, 0.56, 0.71, 0.85, 1.01 Acacia 8.16, 11.35, 14.81, 17.02, 19.95 Homogenizing Pressures, lb./in? -- 2000, 2500, 3000, 4000. Span 80- Sod. Carboxy- 0.92, 1.25, 1.59, 1.92, 2.26 Tween 80 methylcellulo se Sod. Alginate 0.42, 0.57, 0.73, 0.88, 1.03 Tragacanth 0.47, 0.65, 0.82, 0.99, 1.16 Acacia 7.83, 10.68, 13.54, 16.39, 19.24 Methylcellulose 0.68, 0.92, 1.17, 1.41. 1.66 Carbopol-934 0.14, 0.18, 0.23, 0.28, 0.33 Sodium Salt Homogenizing Pressures, lb./in? -- 1000, 2000, 3000, 4000, 5000.

69 TABLE 6 CORN OIL EMULSIONS USED IN THE INVESTIGATION OF EFFECT OF CONCENTRATION OF OIL AND SUSPENDING AGENT, SERIES III. '.. ' -- Suspending Agent Concn. of Suspending Concentration Oil agent % v/v _in Aqueous Phase % w/w_ Methylcellulose 0.326 11, 16, 22, 27, 38, 43, 49, 54 0.434 11, 22, 27, 32, 38, 43, 49, 54 0.543 11, 16, 22, 27, 32, 38, 43, 49, 54 0.651 11l, 16, 22, 27, 32, 38, 43, 49, 54 0.780 11, 16, 22, 27, 32, 38, 43, 49, 54 1.002 11, 16, 22, 27, 32, 38, 43, 49, 54 1.170 11, 26, 22, 27, 32, 38, 43, 49, 54 1.337 11, 16, 27, 32, 38, 43, 49, 54 Sodium 0281 11, 16, 22, 27, 32, 38, 43, 49, 54 Carboxymethyl - cellulose 0.562 11, 16, 22, 27, 32, 38, 43, 49, 54 0.769 11, 16, 22, 27, 32, 38, 43, 49, 54 0,984 11, 22, 27, 32, 38, 43, 49, 54 1.153 11, 16, 22, 27, 32, 38, 43, 49, 54 1.265 |ll, 16, 22, 27, 32, 38, 43, 49, 54 1.476 11, 16, 22, 27, 32, 38, 43, 49, 54 __________ 1.687!11, 16, 22, 27, 32, 38, 43, 49, 54 Carbopol-934 0.187 1, 16, 22, 27, 32, 3 8, 43, 49, 54 Sodium Salt 0.125 '11 16, 22, 27, 32, 38, 43, 49, 54 P B p z, } }.....

70 particles would be solid at room temperature no coalescence of particles sould occur and a stable system might be expected. Also, the emulsion would not require a suspending agent for stability and thus would be as simple an emulsion as might be prepared. When flow curves were recorded, however, hysteresis loops were obtained, and it was thought at first that the emulsions were thixotropic. Accordingly, down curves were recorded to represent breakdown with time. These were obtained by running first a complete upand downcurve, then setting the speed of the cup at the highest rate allowing shear to take place at this constant rate for a measured period of time before recording a downcurve. Shear at the top rate was thus allowed to take place for several fixed times until no further breakdown occurred and a downcurve corresponding to each time of shear was obtained. This procedure is the one proposed by Weltmann(9 for obtaining the coefficient of thixotropic breakdown with time. A typical set of these curves is shown in Fig. 3. It was found later that if one of these emulsions were allowed to stand in the viscometer for several hours after shearing, no build-up occurred and a flow curve would be identical to the equilibrium downcurve. Further, if a sample which had been previously measured and stored for periods up to one month were returned to the cup it would give the same curve as the equilibrium curve previously recorded. This made it appear that the original emulsions were not thixotropic but exhibited hysteresis loops due to occluded air or some permanent change taking place during measurement. In an effort to remove this effect several samples were subjected to reduced pressure for

7 65 43 2 i. 43 Sec. 2. 82 -- __ I 3. 146 I/ 4. 213 " 5. 60 1 7 1549 6. 1032 " / C.) B 7. Equilibrium _ F W 2: 1033 1 516 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 SHEARING STRESS,ARBITRARY UNITS Fig. 3. Down-Curves Showing Breakdown with Time for Cetyl Alcohol Emulsions of Series I

72 several hours with the aim of removing air. Other samples were centrifuged to remove air. In both cases hysteresis loops were still obtained when measurements were madeo Thus, the cause of hysteresis loops did not appear to be occluded air and were still unexplained. On the other hand, since the loops were not believed to represent thixotropy, only the equilibrium curves, representing a stable state of the emulsions, are presented. The equilibrium curves showed no hysteresis but were generally non-Newtonian. Equilibrium flow data are shown in Table 7. In the presentation of data, rate of shear is shown in units of reciprocal seconds. Shearing stress is given in arbitrary units as obtained from the tracing, and the appropriate factor for converting these to absolute units of stress, dyne-cm.2, is listed at the bottom of each data columno Series II This group of emulsions was prepared so as to contain a fixed quantity, 40% w/w, of corn oil as the dispersed phase. The variables examined were homogenization pressure at several levels, two types of emulsifying agent and six types of suspending agent at various concentrationso It was found that emulsions with or without suspending agent exhibited non-Newtonian flow without hysteresis loops. Acacia solution was Newtonian at all but the highest concentrations, and all other suspending agents showed non-Newtonian flow.

TABLE 7 FLOW DATA FOR SERIES I EMULSIONS CETYL ALCOHOL WITH SODIUM LAURYL SULFATE EMULSIFIER EQUILIBRIUM FLOW CURVES Shearing Stress Rate CONC. CETYL ALCOHOL (% w/w) of Shear Sec-1 5.4 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 129 2.70 2.28 1.80 1.45 0.86 0.90 0.90 1.15 0.77 0.68 258 3.10 2.65 2.16 1.76 1.15 1.16 1.25 1.68 1.10 1.06 387 3.60 3.00 2.50 2.02 1.40 1.40 1.50 2.12 1.39 1.42 516 3.93 3.32 2.79 2.27 1.62 1.62 1.77 2.55 1.70 1.75 775 4.70 3.95 3.34 2.77 2.04 2.01 2.26 3.35 2.25 2.45 904 5.02 4.24 3.60 3.00 2.24 2.21 2.49 3.73 2.52 2.75 - 1033 5.32 4.54 3.87 3.24 2.43 2.42 2.70 4.10 2.77 3.10 1162 5.70 4.84 4.13 3.47 2.64 2.63 2.92 4.45 3.05 3.42 1291 6.04 5.13 4.36 3.68 2.83 2.80 3.15 4.83 3.34 3.75 1420 6.37 5.40 4.62 3.90 3.00 2.96 3.36 5.19 3.60 4.10 1549 6.69 5.68 4.86 4.12 3.20 3.15 3.77 5.54 3.87 4.40 1679 7.00 5.95 5.10 4.32 3.37 3.32 3.98 5.90 4.13 4.75 1808 7.34 6.20 5.33 4.51 3.57 3.50 4.19 6.25 4.39 5.07 1937 7.66 6.48 5.57 4.75 3.75 3.67 4.39 6.62 4.64 5.45 2060 7.98 6.75 5.81 4.97 3.92 3.84 4.60 6.99 4.89 5.77 2195 8.30 7.00 6.05 5.18 4.14 4.00 4.80 7.32 5.15 6.12 Stress Conversion Factor -- Dyne - cm.2 123.8 129.1 128.0 130.1 128.0 102.2 76.0 54.4 134.0 49.7

74 Sodium lauryl sulfate had pronounced effect on methylcellulose, causing irregular flow curves, and on Carbopol, causing greatly reduced viscosity; hence this emulsifier was not used with these two suspending agents. Emulsions containing suspending agents appeared to have yield values in all cases. Solutions of suspending agents, with the exception of acacia, also had yield values. Flow data for emulsions without suspending agents are shown in Table 8, those for corresponding solutions of suspending agents are shown in Tables 9 and 14. Flow data for emulsions with sodium lauryl sulfate and the various suspending agents are presented in Tables 10-13 and data for emulsions with Span-Tween emulsifier and suspending agents are in Tables 15-20. Series III This series of emulsions was prepared and measured with the aim of learning more of the effects of concentration of dispersed phase and suspending agent. Thus, one basic system with one emulsifier, SpanTween, and with one homogenization pressure was utilized. The basic emulsion was diluted with water and suspending agent to obtain the concentration variations desired. All of the flow curves for this series were non-Newtonian, most of them appearing to have a yield value, and none showed hysteresis. Flow data for Series III emulsions are presented in Tables 22-29 and 31-40, and those for corresponding solutions of suspending agents are shown in Tables 2130.

TABLE 8 FLOW DATA SERIES II EMULSIONS WITHOUT SUSPENDING AGENT Shearing Stress Emulsifier Rate of Sodium Lauryl Sulfate Span-Tween Mixture Shear Sec 1 Homogenizing Pressure lb./in? 2000 2500 3000 4000 1000 2000 3000 4000 5000 129 0.27 0.57 0.56 0.29 0.15 0.17 0.22 0.220.2 258 0.38 0.77 0.80 0.40 0.26 0.33 0.33 0.35 0.36 387 O.48 0.94 0.99 0.50 0.38 0.43 O.49 0.47 0.48 516 0.55 1.07 1.15 0.60 0.50 0.56 0.62 0.62 0.62 646 0.64 1.22 1.30 0.70 0.62 0.69 0.75 0.75 0.76 -0 775 0.70 1.35 1.45 0.76 0.74 0.82 0.89 0.88 0.89 k 904 0.80 1.50 1.60 0.85 0.87 0.95 1.03 1.01 1.04 1033 0.85 1.62 1.75 0.93 0.99 1.o6 1.16 1.15 1.17 1162 0.94 1.75 1.90 1.00 1.10 1.19 1.29 1.27 1.28 1291 1.00 1.88 2.04 1.08 1.21 1.33 1.42 1.40 1.40 1420 1.07 2.00 2.19 1.17 1.34 1.43 1.57 1.55 1.55 1549 1.15 2.13 2.32 1.25 1.44 1.52 1.70 1.67 1.69 1679 1.22 2.25 2.45 1.33 1.56 1.68 1.84 1.80 1.83 1808 1.30 2.38 2.60 1.40 1.67 1.82 1.95 1.92 1.95 1937 1.36 2.50 2.74 1.50 1.77 1.94 2.08 2.07 2.07 2060 1.44 2.62 2.89 1.56 1.90 2.06 2.20 2.19 2.22 2195 1.50 2.72 3.03 1.65 2.01 2.17 2.34 2.32 2.32 2320 1.60 2.88 3.16 1.74 2.15 2.30 2.48 2.43 2.46 245 _ 1.67 1 3.00.0 1.81 1 2.25 1 2.42 1 2.60 2 2.55 2.58 Stress Conversion Factor -- Dyne - cm.2 _ 107.4 108.7 5 56.12 _ 108.1 11 58.94.7 57.67 I 57.23 57.23

TABLE 9 FLOW DATA FOR SOLUTIONS OF SUSPENDING AGENTS CORRESPONDING TO EMULSIONS OF SERIES II WITH SODIUM LAURYL SULFATE EMULSIFIER Flow Curves For Solutions Of Stabilizers, Series A Shearing Stress Suspending Agent Rate of Shear TRAGACANTH ACACIA Sec.1 Conc. Suspending Agent, (% w/w) _1.01 0.85 0.71 0.56 0.41 1 19.95 17.02 14.81 11.35 8.16 129 1.75 1.70 1.20 0.70 0.32 2.10 1.95 1.13 1.81 1.69 258 2.35 2.37 1.74 1.10 0.57 2.85 2.62 1.58 2.34 2.10 387 2.75 2.87 2.10 1.37 0.75 3.45 3.18 1.97 2.80 2.44 516 3.09 3.26 2.42 1.63 0.94 3.97 3.69 2.32 3.23 2.75 646 3.37 3.62 2.68 1.87 1.10 4.45 4.19 2.70 3.62 3.02 775 3.62 3.90 2.95 2.08 1.23 4.87 4.62 3.03 4.04 3.32 904 3.85 4.19 3.17 2.25 1.38 5.30 5.07 3.33 4.43 3.59 1033 4.07 4.45 3.39 2.44 1.51 5.70 5.48 3.67 4.81 3.85 1162 4.26 4.70 3.58 2.60 1.64 6.0 5.88 3.96 5.18 4.11 1291 4.45 4.92 3.77 2.75 1.75 6.42 6.26 4.25 5.53 4.35 1420 4.65 5.15 3.97 2.91 1.88 6.78 6.66 4.55 5.92 4.6 1549 4.78 5.35 4.14 3.05 2.00 7.12 7.02 4.84 6.27 4.84 1679 5.00 5.55 4.31 3.19 2.13 7.45 7.38 5.14 6.61 5.09 1808 5.15 5.75 4.50 3.28 2.25 7.75 7.73 5.41 6.95 5.33 1937 5.32 5.92 4.65 3.45 2.38 8.08 8.07 5.68 7.30 5.57 2060 5.48 6.13 4.82 3.61 2.50 8.40 8.41 5.95 7.66 5.82 2195 5.62 6.32 4.98 3.72 2.60 8.70 8.71 6.23 7.99 6.04 2324 5.77 6.50 5.13 3.85 2.75 8.99 9.08 6.51 8.36 6.31 2453 5.92 6.65 5.27 4.00 2.85 9.29 9.42 6.76 8.69 6.55 Stress Conversion Factor -- Dyne - cm.2 91.89 71.90 72.32 71.09 I 70.95 II 125.3 112.2 71.3 171.9 72.0

TABLE 9-Continued ____Shearing Stress Suspending Agent Rate of Shear SODIUM ALGINATE SODIUM CMC Sec.1 Cone. Suspending Agent, (% w/w) 1.02 0.87 0.72 0.57 0.42 2.07 1.76 1.46 1.15 0.84 129 1.55 1.02 1.40 0.80 0.38 0.77 1.01 0.55 0.5 0.28 258 2.50 1.75 2.40 1.40 0.68 1.35 1.82 1.05 0.93 0.51 387 3.25 2.30 3.30 1.95 0.98 1.87 2.60 1.50 1.32 0.75 516 3.85 2.76 4.05 2.43 1.28 2.32 3.25 1.90 1.70 0.98 646 4.37 3.20 4.82 2.90 1.56 2.74 3.90 2.30 2.07 1.19 - 775 4.89 3.58 5.42 3.32 1.80 3.16 4.50 2.64 2.45 1.40 904 5.32 3.92 6.00 3.73 2.12 3.50 5.04 3.02 2.74 1.62 1033 5.70 4.26 6.55 4.14 2.36 3.88 5.60 3.35 3.12 1.85 1162 6.07 4.56 7.05 4.50 2.59 4.20 6.10 3.70 3.45 2.04 1291 6.43 4.85 7.57 4.86 2.78 4.52 6.60 4.01 3.76 2.25 1420 6.75 5.12 8.05 5.20 3.05 4.82 7.08 4.34 4.10 2.45 1549 7.06 5.39 8.56 5.55 3.27 5.12 7.55 4.65 4.40 2.63 1679 7.35 5.64 8.92 5.88 3.49 5.40 8.00 4.97 4.70 2.85 1808 7.64 5.86 9.37 6.19 3.70 5.76 8.42 5.25 5.00 3.05 1937 7.90 6.10 9.76 6.50 3.90 5.92 8.85 5.53 5.30 3.25 2060 8.17 6.32 10.15 6.82 4.12 6.20 9.27 5.83 5.60 3.43 2195 8.44 6.55 10.54 7.13 4.32 6.45 9.70 6.1 5.90 3.64 2324 8.68 6.75 10.82 7.38 4.52 6.70 10.10 6.38 6.19 3.81 2453 8.93 6.95 11.23 7.66 4.72 6.95 10.50 6.65 6.46 4.00 Stress Conversion Factor -- Dyne - cmr2 130.0 129.1 60.9 1 61.6 60.7 254.0 120.2 119.5 79.5 | 79.7

TABLE 10 FLOW DATA FOR EMULSIONS OF SERIES II WITH SODIUM LAURYL SULFATE EMULSIFIER ACACIA SUSPENDING AGENT Shearing Stress Suspending Agent Homogenizing Pressure lb./in.2 Rate of 2000 2500 Shear Sec.1 Suspending Agent in Aqueous Phase (% w/w) 19.95 17.02 14.81 11.35 8.16 19.95 17.02 14.81 11.35 8.16 129 0.82 0.89 0.652 0.72 1.23 1.25 0.80 0.93 0.93 258 1.19 1.25 0.77 0.96 0.95 1.71 1.75 1.15 1.26 1.15 387 1.52 1.60 1.00 1.22 1.12 2.10 2.20 1.46 1.62 1.36 516 1.80 1.94 1.23 1.47 1.30 2.45 2.62 1.76 1.95 1.56 646 2.07 2.25 1.45 1.73 1.46 2.76 3.00 2.05 2.25 1.75 775 2.32 2.56 1.69 1.99 1.62 3.08 3.37 2.35 2.55 1.94 904 2.57 2.85 1.89 2.20 1.77 3.38 3.73 2.60 2.85 2.10 1033 2.80 3.14 2.10 2.42 1.93 3.65 4.10 2.86 3.14 2.27 1162 3.01 3.45 2.30 2.66 2.07 3.92 4.42 3.14 3.43 2.44 1291 3.25 3.75 2.50 2.90 2.25 4.19 4.76 3.39 3.70 2.60. 1420 3.49 4.01 2.70 3.15 2.40 4.45 5.12 3.65 4.00 2.77 1549 3.70 4.31 2.90 3.36 2.53 4.70 5.42 3.90 4.27 2.92 1679 3.92 4.57 3.10 3.58 2.72 4.95 5.76 4.15 4.56 3.10 1808 4.12 4.85 3.30 3.81 2.86 5.20 6.10 4.40 4.85 3~26 1937 4.33 5.10 3.50 4.05 3.00 5.42 6.40 4.65 5.11 3.44 2060 4.55 5.39 3.70 4.25 3.15 5.67 6.73 4.89 5.40 3.60 2195 4.75 5.67 3.90 4.50 3.30 5.90 7.04 5.14 5.68 3.75 2324 4.95 5.95 4.06 4.74 3.48 6.15 7.35 5.37 5.95 3.95 2453 5.16 6.20 4.28 4.98 3.62 11 6.37 7.65 5.60 6.23 4.102 Stress Conversion Factor -- Dyne - cm,2 798.5 403.1 407.1 212.7 1 181.9 || 803.4 | 402.3 409.5 213.6 156.

TABLE 10-Continued _ _____,_____Shearing Stress Homogenizing Pressure lb./in? Rate 3000 4000 of Shear Sec. Conc. Suspending Agent in Aqueous Phase (% w/w) _ 19.95 17.02 14.81 11.35 8.16 19.95 17.02 14.81 11.35 8.1 129 2.20 2.14 1.24 1.94 1.77 1.39 1.30 0.80 1.20 1.08 258 3.05 3.00 1.80 2.60 2.26 1.84 1.80 1.12 1.55 1.35 387 3.75 3.75 2.30 3.19 2.68 2.22 2.24 1.41 1.86 1.58 516 4.37 4.45 2.76 3.75 3.07 2.54 2.62 1.68 2.17 1.86 646 4.95 5.14 3.25 4.27 3.42 2.85 3.00 1.94 2.42 2.00 775 5.47 5.76 3.69 4.82 3.80 3.13 3.36 2.19 2.70 2.6 - 904 6.00 6.40 4.10 5.34 4.15 3.40 3.70 2.40 2.95 2.36 1033 6.50 7.00 4.55 5.85 4.49 3.68 4.04 2.65 3.19 2.51 1162 6.96 7.59 4.95 6.35 4.83 3.94 4.36 2.88 3.44 2.70 1291 7.42 8.16 5.35 6.83 5.15 4.19 4.68 3.10 3.70 2.86 1420 7.88 8.75 5.76 7-35 5.49 4.42 5.00 3.32 3.94 3.05 1549 8.32 9.30 6.16 7.83 5.80 4.68 5.31 3.55 4.17 3.20 1679 8.75 9.85 6.57 8.30 6.13 4.91 5.62 3.75 4.43 3.39 1808 9.15 10.39 6.95 8.77 6.45 5.15 5.90 3.97 4.68 3.55 1937 9.58 10.92 7.33 9.25 6.77 5.37 6.23 4.20 4.91 3.70 2060 10.00 11.45 7.71 9.74 7.10 5.60 6.52 4.40 5.15 3.88 2195 10.40 11.94 8.10 10.20 7.40 5.81 6.83 4.62 5.40 4.05 2320 10.79 12.50 8.49 10.70 7.75 6.05 7.12 4.83 5.62 4.22 2453 11.19 13.03 8.85 11.16 8.07 6.25 7.42 5.05 5.87 4.38 Stress Conversion Factor -- Dyne - cm.2 460.0 234.0 234.0 104.0 97.0 801.8 403.1 405.5 213.1 182.5 1 1 1~~~~~~~~~~~~~~~~~ 9705.

TABLE 11 FLOW DATA FOR EMULSIONS OF SERIES II WITH SODIUM LAURYL SULFATE EMULSIFIER SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT ___________________________________________________________Shearing Stress Homogenizing Pressure lb./in? of t 2000 [12500 of Sheaf See. Cone. Suspending Agent in Aqueous Phase ( W /w) 2.07 1.76 1.46 1.15 0.84 2.07 1.76 1.46 1.15 0.84 129 0.841.30 1.32 1.40 1.00 0.90 1.38 1.08 1.87 1.05 258 1.14 1.76 1.77 1.92 1.36 1.22 1.90 1.48 2.19 1.45 387 1.39 2.15 2.15 2.35 1.66 1.46 2.29 1.78 2.68 1.77 n 516 1.60 2.50 2.48 2.70 1.94 1.68 2.65 2.05 3.09 2.05 o 646 1.80 2.80 2.79 3.04 2.19 1.89 2.96 2.29 3.47 2.30 775 2.00 3.10 3.06 3.36 2.40 2.08 3.25 2.52 3.82 2.54 904 2.16 3.38 3.34 3.65 2.65 2.25 3.55 2.74 4. 16 2.76 1033 2.34 3.64 3.62 3.96 2.85 2.42 3.80 2.95 4.46 2.99 1162 2.50 3.90 3.88 4.27 3.10 2.59 4.05 3.15 4.80 3.20 1291 2.65 4.12 4.12 4.55 3.27 2.74 4.32 3.36 5.08 3.40 1420 2.82 4.39 4.35 4.83 3.50 2.90 4.55 3.55 5.39 3.62 1549 2.96 4.61 4.59 5.10 3.72 3.05 4.80 3.75 5.68 3.82 1679 3.12 4.85 4.84 5.37 3.91 3.19 5.02 3.90 5.97 4.00 1808 3.25 5.07 5.05 5.64 4.13 3.33 5.25 4.10 6.25 4.22 1937 3.40 5.30 5.25 5.90 4.34 3.45 5.50 4.30 6.53 4.40 2o6o 3.54 5.51 5.50 6.17 4.55 3.6o 5.70 4.48 6.82 4.60 2195 3.65 5.74 5.70 6.42 4.74 3.75 5.92 4.65 7.10 4.80 2320 3.80 5.95 5.90 6.69 4.94 3.87 6.15 4.82 7.35 5.00 2453 3.92 1 6.18 6.14 6.92 1 5.13 1[ 4.00 6.35 5.00 7.64 5.18 Stress Conversion Factor -- Dyne - cm:2 678.1 | 342.1 | 346.1 ) 164.3 | l.3 l 676.9 I 343.8 | 346.7 I 16.| 123

TABLE 11-Continued Shearing Stress Homogenizing Pressure lb./in? Rate of 3000 4000 Shear Sec.1 Cone. Suspending Agent in Aqueous Phase (% w/w) 2.07 1.76 1.46 1.15 0.84 2.07 1.761 1.46 1.15.84 129 1.34 2.27 1.93 2.00 1.42 1.07 1.72 1.25 1.95 1.30 258 1.82 3.05 2.63 2.74 1.90 1.42 2.35 1.65 2.55 1.75 387 2.19 3.69 3.17 3.30 2.30 1.70 2.77 2.00 3.07 2.12 516 2.51 4.23 3.64 3.81 2.65 1.95 3.16 2.26 3.52 2.40 646 2.80 4.72 4.05 4.25 2.97 2.16 3.50 2.52 3.90 2.69 o 775 3.05 5.16 4.42 4.66 3.26 2.36 3.85 2.75 4.27 2.95 H 904 3.32 5.60 4.80 5.07 3.55 2.55 4.15 2.97 4.62 3.20 1033 3.55 6.00 5.15 5.45 3.84 2.72 4.42 3.17 4.95 3.44 1162 3.79 6.40 5.50 5.82 4.10 2.90 4.70 3.38 5.26 3.67 1291 4.00 5.77 5.82 6.20 4.38 3.05 5.00 3.57 5.68 3.90 1420 4.21 7.15 6.13 6.55 4.62 3.20 5.24 3.75 5.90 4.12 1549 4.41 7.50 6.44 6.89 4.89 3.35 5.54 3.95 6.20 4.35 1679 4.62 7.85 6.75 7.24 5.14 3.50 5.74 4.15 6.50 4.55 1808 4.82 8.18 7.04 7.56 5.38 3.65 6.00 4.30 6.80 4.75 1937 5.00 8.52 7.33 7.90 5.63 3.80 6.23 4.44 7.06 4.97 2060 5.19 8.85 7.62 8.21 5.86 3.93 6.45 4.65 7.37 5.16 2195 5.38 9.18 7.91 8.55 6.10 4.07 6.66 4.32 7.62 5.39 2320 5.56 9.50 8.20 8.85 6.34 4.20 6.90 5.00 7.91 5.58 4253 5.74 9.83 8.49 9.19 6.59 4.35 7.12 5.15 8.20 5.80 Stress Conversion Factor -- Dyne - cm. 458.0 | 202.0 202.0 1 138.0 | 138.0 11 676.9 [ 342.7 346.7 163.7 16.8

TABLE 12 FLOW DATA FOR EMULSIONS OF SERIES II WITH SODIUM LAURYL SULFATE EMULSIFIER TRAGACANTH SUSPENDING AGENT Shearing Stress Homogenizing Pressure lb./in2 Rate 2000 2500 of Shear Sec 1 Conc. Suspending Agent in Aqueous Phase (% w/w) ~______ ~1.01 0.85 0.71 0.56 o. 41 1.01 0.85 0.71 0o.5~. 14 129 1.90 1.55 1.18 1.58 0.95 1.92 1.60 1.25 1.40 0.95 258 2.45 2.08 1.60 1.80 1.34 2.50 2.15 1.70 1.90 1.32 387 2.88 2.45 1.90 2.15 1.62 2.95 2.50 2.05 2.26 1.60 O 516 3.25 2.76 2.14 2.47 1.88 3.35 2.80 2.29 2.57 1.85 646 3.57 3.05 2.37 2.75 2.08 3.67 3.07 2.52 2.85 2.07 775 3.83 3.30 2.56 3.00 2.30 3.96 3.32 2.74 3.12 2.27 904 4.12 3.55 2.77 3.22 2.50 4.25 3.55 2.94 3.36 2.48 1033 4.46 3.79 2.95 3.47 2.70 4.50 3.78 3.12 3.58 2.67 1162 4.65 4.01 3.10 3.69 2.88 4.75 4.00 3.30 3.82 2.85 1291 4.90 4.25 3.30 3.90 3.06 5.00 4.20 3.47 4.00 3.00 1420 5.12 4.45 3.45 4.10 3.22 5.25 4.40 3.65 4.42 3.19 1549 5.37 4.65 3.65 4.31 3.40 5.50 4.60 3.80 4.40 3.35 1679 5.61 4.86 3.82 4.50 3.57 5.75 4.80 3.97 4.62 3.51 1808 5.86 5.08 3.98 4.73 3.75 5.95 5.00 4.14 4.82 3.8 1937 6.08 5.26 4.14 4.92 3.90 6.19 5.19 4.30 5.01 3.84 2060 6.32 5.49 4.30 5.13 4.07 6.41 5.37 4.46 5.22 4.00 2195 6.55 5.70 4.45 5.35 4.25 6.64 5.55 4.61 5.40 4.15 2320 6.77 5.90 4.63 5.55 4.41 6.85 5.75 4.77 5.60 4.31 2453 7.00 6.10 4.81 5.73 4.62 __ 7.10 5.94 4.95 5.77 4.49 Stress Conversion Factor -- Dyne - cm7.2 16o0.1 158.7 164.3 110.6 108.7 160.3 15.9 158.7 109.9 109.3

TABLE 12-Continued Shearing Stress Homogenizing Pressure lb./in? Rate 3000 4000 of Shear Sec. Cone. Suspending Agent in Aqueous Phase (% w/w) 1.01 0.85 0.71 0.56 0.41 1.01 0.85 0.71 0.56 1 0.4 129 2.07 1.62 1.68 1.97 1.45 1.80 1.45 1.12 1.23 0.85 258 2.83 2.23 2.68 2.75 2.05 2.40 1.95 1.52 1.67 1.19 387 3.40 2.67 3.47 3.35 2.52 2.80 2.29 1.83 2.00 1.46 516 3.87 3.08 4.15 3.86 2.95 ---- 2.62 2.09 2.32 1.69 646 4.32 3.42 4.75 4.37 3.32 3.50 2.88 2.32 2.60 1.91 C 775 4.70 3.74 5.32 4.82 3.67 3.76 3.13 2.54 2.85 2.12 U 904 5.10 4.05 5.88 5.23 4.03 4.08 3.39 2.74 3.10 2.33 1033 5.45 4.35 6.40 5.58 4.35 4.32 3.60 2.93 3.34 2.50 1162 5.80 4.64 6.88 6.02 4.67 4.58 3.84 3.12 3.56 2.69 1291 6.15 4.92 7.37 6.41 5.00 4.83 4.04 3.30 3.76 2.85 1420 6.45 5.20 7.85 6.81 5.30 5.07 4.25 3.48 4.00 3.05 1549 6.78 5.45 8.36 7.17 5.60 5.32 4.45 3.66 4.20 3.22 1679 7.10 5.72 8.80 7.55 5.90 5.55 4.64 3.83 4.41 3.40 1808 7.42 5.98 9.28 7.90 6.20 5-77 4.85 4.00 4.62 3.56 1937 7.72 5.24 9.73 8.28 6.48 6.00 5.05 4.16 4.83 3.72 2060 8.05 6.50 10.18 8.65 6.79 6.25 5.25 4.33 5.04 3.89 2195 8.35 6.75 10.62 9.00 7.08 6.47 5.43 4.50 5.25 4.06 2354 8.65 7.00 11.08 9.37 7.37 6.69 5.64 4.68 5.45 4.25 2453 8.96 7.25 11.50 9.74 7.68 U 6.95 5.85 4.85 5.64 4.38 Stress Conversion Factor -- Dyne - cm.2 122.3 111.0 55.7 56.0 5 160.1 158.9 158.4 109.9 109.3

TABLE 13 FLOW DATA FOR EMULSIONS OF SERIES II WITH SODIUM LAURYL SULFATE EMULSIFIER SODIUM ALGINATE SUSPENDING AGENT Shearing Stress Homogenizing Pressure Ib./in? Ra~e 2000 2500 Cone. Suspending Agent in Aqueous Phase (% W/w) _______ _ 1.02 "" 0.87 0.72 0.57 0.42 1.02 0.87 0.72 0.570.~2 ~1291.35 1.00 1.82 0.97 0.80 1.4o 1.12 1.661.18 0.82 2.85 1.42 2.53 1.38 1.10 1.92 1.52 2.37 1.66 2.23 1.74 3.10 1.70 1.38 2.32 1.85 2.89 2.05 1.44 5.54 2.00 3.57 2.00 1.60 2.63 2.13 3.32 2.39 p.8 2.81 2.22 4.00 2.25 1.82 2.90 2.38 3.72 2.69 1.90 775 3.06 2.43 4.40 -.50 2.02 3.15 2.59 4.07 2.95 2.12 3.30 2.64 4.75 2.72 2.22 3.40 2.80 4.40 3.20 2.32 — 33 3.52 2.80 5.12 2.98 2.40 3.60 2.99 4.70 3.44 2.48 1162 3.74 3.00 5.44 3.15 2.58 3.80 3.15 5.01 3.67 2.85 12^1 3.94 3.16 5.75 3.36 2.75 4.00 3.33 5.30 3.90 2.84 m 4.13 3.34 6.07 3.55 2.94 4.18 3.49 5.59 4.12 3.00 4P 1549 4.32 3.49 8.39 3.75 3.10 4.62 3.65 5.90 4.35 3.18 1679 4.50 3.65 6.88 3.95 3.25 4.54 3.80 6.15 4.55 3.34 -8c8 4.66 3.80 6.98 4.14 3.44 4.70 3.95 6.40 4.76 3.50 1937 4.84 3.95 7.25 4.33 3.61 4.88 4.10 6.65 4.97 3.66 2060 5.00 4.10 7.52 4.51 3.75 5.05 4.25 6.92 5.17 3.82 2195 5.17 4.25 7.82 4.70 3.95 5.20 4.39 7.17 5.38 3.97 2340 5.37 4.39 8.08 4.90 4.10 5.36 4.54 7.42 5.56 4.12 2453 5.50 4.53 8.35 5.07 4.25 5.52 4.67 7.65 5.75 4.55 Stress Conversion Factor -- Dyne - cn;2 ________ 345.0 339.8 161.3 159.1 156.8 346.1 339.8 1 i6o.6 160.6 158.9

TABLE 13 -Continued Shearing Stress Homogenizing Pressure lb./in. 3000 4000 Rate of Shear Cone. Suspending Agent in Aqueous Phase (%w/w) Sec.1 _ 1.02 0.87 0.72 0.57 0.42 _ 1.02 0.87 0.72 0.57 0.42 129 2.35 1.75 2.65 1.95 1.35 1.75 1.30 ---- 1.45 1.00 258 3.20 2.40 3.66 2.67 1.87 2.32 1.67 2.74 2.00 1.40 387 3.7 2. 4.45 3.4 30 2.72. 3.2 20 2.12 3.32 2.70 516 4.25 3.29 5.10 3.75 2.62 3.08 2.42 3.77 2.76 1.98 646 4.70 3.64 5.67 4.20 2.99 3.36 2.65 4.20 3.11 2.22 J 775 5.06 3.93 6.17 4.61 3.28 3.62 2.89 4.56 3.40 2.44 904 5.40 4.22 6.65 5.00 3.57 3.85 3.10 4.90 3.66 2.65 1033 5.70 4.49 7.12 5.38 3.85 4.10 3.26 5.25 3.95 2.85 1162 6.02 4.74 7.55 5.72 4.12 4.29 3.45 5.55 4.20 3.07 1291 6.30 4.95 7.93 6.05 4.39 4.48 3.64 5.84 4.42 3.24 1420 6.59 5.20 8.35 6.39 4.63 4.66 3.80 6.12 4.65 3.41 1549 6.84 5.43 8.70 6.70 4.88 4.85 3.95 6.39 4.88 3.58 1679 7.10 5.65 9.08 7.00 5.13 5.04 4.12 6.65 5.10 3.76 1808 7.35 5.87 9.45 7.32 5.35 5.20 4.25 6.92 5.30 3.92 1937 7.59 6.08 9.80 7.60 5.60 5.39 4.40 7.19 5.50 4.10 2060 7.82 6.28 10.21 7.88 5.83 5.55 4.55 7.43 5.72 4.25 2195 8.06 6.49 10.50 8.19 6.05 5.70 4.77 7.64 5.93 4.42 2320 8.26 6.70 10.83 8.45 6.26 5.89 4.85 7.92 6.14 4.58 2453 8.50 6.88 11.77 8.75 6.51 6.82 4.98 8.17 6.34 4.75 Stress Conversion Factor -- Dyne - cm2 240.0 236.0 113.0 113.0 113.0 1I 345.5 339.8 161.3 160.1 158.0

TABLE 14 FLOW DATA FOR SOLUTIONS OF SUSPENDING AGENTS CORRESPONDING TO EMULSIONS OF SERIES II WITH SPAN-TWEEN EMULSIFIER Suspending Agent Sod. CMC Tragacanth Methylcellulose Rate _Traat of Shear Cone. Suspending Agent in Aqueous Phase (% w/w) Sec.-1 2.26 1.92 1.59 1.25 0.92 ' 1.16 0.99 0.82 0.65 0.47 1.66 1.41 1.17 0.92 0.67 129 0.58 0.72 0.38 0.54 0.46 1.05 1.45 1.05 0.66 0.35 0.97 0.44 0.55 0.62 0.25 258 0.95 1.26 0.67 0.97 0.70 1.40 2.00 1.45 0.97 0.56 1.65 0.77 0.97 1.10 0.45 387 1.27 1.70 0.92 1.35 0.92 1.65 2.38 1.77 1.19 0.73 2.17 1.05 1.33 1.53 0.65 516 1.54 2.08 1.13 1.70 1.17 1.83 2.68 2.00 1.38 0.85 2.64 1.28 1.68 1.93 0.83 646 1.77 2.46 1.36 2.05 1.36 2.00 2.95 2.23 1.53 0.98 3.05 1.52 1.98 2.30 1.02 775 1.98 2.80 1.57 2.38 1.56 2.17 3.20 2.42 1.70 1.07 3.42 1.72 2.26 2.65 1.20 904 2.19 3.09 1.75 2.68 1.77 2.35 3.42 2.60 1.83 1.19 3.77 1.90 2.53 3.00 1.37 1033 2.37 3.37 1.92 3.00 1.95 2.43 3.63 2.77 2.07 1.27 4.07 2.07 2.77 3.33 1.53 1162 2.55 3.66 2.10 3.28 2.14 2.55 3.84 2.95 2.22 1.40 4.38 2.25 3.02 3.62 1.70 1291 2.70 3.91 2.27 3.55 2.32 2.67 4.02 3.10 2.32 1.49 4.65 2.40 3.25 3.92 1.85 1420 2.86 4.16 2.43 3.82 2.48.2.77 4.20 3.27 2.42 1.57 4.90 2.55 3.47 4.22 2.00 1549 3.00 4.40 2.58 4.07 2.64 2.90 4.40 3.42 2.54 1.68 5.15 2.70 3.68 4.50 2.17 1679 3.14 4.62 2.73 4.33 2.80 3.00 4.57 3.57 2.63 1.77 5.39 2.84 3.90 4.77 2.32 1808 3.27 4.85 2.88 4.60 2.97 3.12 4.73 3.70 2.75 1.84 5.62 2.99 4.10 5.03 2.45 1937 3.40 5.05 3.02 4.84 3.12 3.23 4.96 3.84 2.85 1.93 5.85 3.12 4.30 5.29 2.60 2060 3.52 5.26 3.16 5.10 3.28 3.31 5.05 3.98 2.95 2.00 6.07 3.24 4.49 5.55 2.75 2195 3.65 5.46 3.30 5.33 3.45 3.40 5.20 4.10 3.05 2.10 6.27 3.37 4.67 5.80 2.90 2324 3.77 5.67 3.44 5.57 3.61 3.50 5.35 4.23 3.15 2.18 6.47 3.48 4.85 6.04 3.04 2453 3.88 5.85 3.57 5.73 3.76 3.60 5.48 4.35 3.25. 2.28 6.68 3.60 5.04 1 6.27 3.18 Stress Conversion Factor -- Dyne - cm.2 1678.1 682.8 1344.9 356.3 199.6 1[348.5 16o.6 1|161.3 1161.8 |163.0 11443.1 1441.2 1357.6 215.7 15.7

TABLE 14-Continued Suspending Agent Rate I of. Acacia Sodium Alginate Carbopol 934 - Sod. Salt bec.1 Conc. Suspending Agent in Aqueous Phase (% w/W) 19.2 16T 13.5 10.7 78 1.03 0.88 0.73 0.57 0.42 0.33 0.28 0.23 0.18 0 0.23 o.4o 7.8 0.17 0.12 1.15 0.87 0.70 0.70 o.4o 1.00 0.35 0.33 0.30 0.17 0.45 0.74 0.50 0.32 0.20 1.80 1.35 1.12 1.15 0.67 1.39 0.85 0.85 0.48 0.25 387 0.65 1.08 0.72 0.45 0.29 2.27 1.74 1.45 1.52 0.89 1.69 1.05 1.07 o.64 0.33 5lC 0.87 1.4~ 0.93 o.6o 0.38 2.68 2.05 1.75 1.87 1.12 1.95 1.23 1.27 0.79 0.40 6D — r - 1.10 1.75 1.16 0.73 0.47 3.04 2.32 2.00 2.15 1.29 2.17 1.38 1.47 0.92 0.C8 775 1.33 2.10 1.39 0.87 0.57 3.36 2.57 2.23 2.42 1.47 2.37 1.54 1.66 1.06 0.55 -1 9C4 1.55 2.45 1.61 1.02 0.65 3.65 2.82 2.45 2.68 1.64 2.57 1.68 1.84 1.19 0.62 1.77 2.80 1.93 1.17 0.74 3.90 3.02 2.65 2.92 1.80 2.76 1.82 2.00 1.30 0.70 12 2.00 3.15 2.05 1.32 0.83 4.16 3.23 2.83 3.15 1.95 2.95 1.95 2.16 1.42 0.77 2.25 3.48 2.27 1.45 0.92 4.39 3.42 3.02 3.37 2.10 3.12 2.07 2.32 1.55 0.85 2.50 3.82 2.48 1.60 1.02 4.6o 3.60 3.19 3.57 2.25 3.28 2.22 2.47 1.67 0.92 159 2.74 4.l6 2.72 1.73 1.13 4.80 3.79 3.33 3.78 2.38 3.46 2.32 2.62 1.77 0.98 67o 2.95 4.50 2.94 1.87 1.22 5.00 3.94 3.50 3.97 2.51 3.62 2.43 2.75 1.89 1.05 3.16 4.83 3.15 2.03 1.33 5.19 4.10 3.65 4.17 2.64 3.77 2.55 2.90 1.99 1.12 1937 3.35 5.17 3.38 2.17 1.42 5.35 4.26 3.80 4.35 2.77 3.94 2.67 3.05 2.10 1.18 3.55 5.48 3.60 2.33 1.52 5.55 4.42 3.94 4.52 2.90 4.10 2.78 3.18 2.22 1.25 2195 3.74 5.83 3.82 2.48 1.62 5.70 4.57 4.07 4.70 3.02 4.24 2.90 3.32 2.32 1.32 232^ 3.94 6.15 4.05 2.62 1.72 5.87 4.70 4.22 4.86 3.15 4.38 3.00 3.45 2.42 1.39 2453 4.14 6.47 4.29 2.79 1.82 6.o4 4.85 4.35 5.03 3.26 4.53 3.12 3.60 2.50 1.46 Stress Conversion Factor -- Dyne - cm. 222.5 98.9 98.2 98.2 97.7 11233.6 1233.6 1196.3 12 3 20.5 1201.5 115.0 97.2 97.2

TABLE 15 FLOW DATA FOR EMULSIONS OF SERIES II WITH SPAN-TWEEN EMULSIFIER SODIUM ALGINATE SUSPENDING AGENT Shearing Stress Homogenizing Pressure lb./in? Rate of 1000 2000 3000 Shear Sec 1 Conc. Suspending Agent in Aqueous Phase (% w/w) 1.03 0.88 0.73 0.57 ' 0.42 1.03 0.88 0.73 0.57 0.42 1.03 0.88 0.73 0.57 0.42 129 1.18 0.9 1.52 1.00 0.69 1.30 1.00 0.74 1.20 0.80 1.3 1.003 0.80 1.20 082 258 1.77 1.39 2.88 1.56 1.09 1.90 1.49 1.12 1.77 1.18 1.89 1.50 1.17 1.76 1.23 387 2.29 1.78 3.09 2.00 1.42 2.40 1.90 1.42 2.28 1.54 2.38 1.88 1.47 2.24 1.56 516 2.73 2.12 3.74 2.45 1.75 2.85 2.23 1.70 2.75 1.86 2.77 2.24 1.75 2.78 1.88 646 3.12 2.45 4.35 2.86 2.05 3.25 2.55 1.94 317 2.16 3.16 2.55 2.01 3.08 2.18 775 3.48 2.75 4.86 3.24 2.34 3.62 2.85 2.20 3.59 2.47 3.51 2.83 2.24 3.49 2.45 904 3.81 3.01 5.37 3.59 2.61 3.95 3.12 2.41 3.99 2.75 3.85 3.11 2.47 3.85 2.74 1033 4.11 3.28 5.85 3.94 2.87 4.25 3.38 2.66 4.36 3.04 4.14 3.36 2.68 4.20 3.00 1162 4.40 3.52 6.32 4.26 3.12 4.56 3.64 2.84 4.72 3.29 4.44 3.62 2.89 4.55 3.25 1291 4.68 3.75 6.75 4.57 3.37 2.84 3.89 3.02 5.05 3.55 4.72 3.85 3.09 4.88 3.50 1420 4.95 3.98 7.18 4.88 3.60 5.12 4.11 3.20 5.38 3.80 5.00 4.07 3.27 5.20 3.74 1549 5.18 4.19 7.59 5.16 3.82 5.39 4.34 3.39 5.70 4.03 5.25 4.29 3.47 5.50 3.97 1679 5.45 4.40 8.00 5.45 4.04 5.64 4.55 3.57 6.01 4.27 5.50 4.49 3.65 5.82 4.20 1808 5.69 4.59 8.36 5.73 4.25 5.88 4.76 3.75 6.32 4.50 5.74 4.70 3.84 6.10 4.44 1937 5.92 4.78 8.74 6.00 4.45 6.12 4.97 3.92 6.64 4.72 5.98 4.90 4.00 6.40 4.60 2060 6.14 4.99 9.10 6.26 4.66 6.35 5.16 4.07 6.92 4.95 6.21 5.10 4.18 6.68 4.87 2195 6.38 5.15 9.45 6.52 4.87 6.57 5.36 4.25 7.19 5.16 6.42 5.28 4.35 6.95 5.10 2324 6.57 5.35 9.76 6.76 5.07 6.79 5.57 4.40 7.49 5.38 6.65 5.47 4.51 7.24 5.32 2453 6.78 5.52 10.12 7.02 5.28 7.00 5.75 4.52 7.75 5.60 6.88 5.65 4.68 7.50 5.52 Stress Conversion Factor -- Dyne - cm.2 375. 1373.6 1155.2 1173.3 173.6 11373.8 1373.8 1377.2 1173.3 1173.3 11373.8 1373.8 1374.5 172.2 173.1

TABLE 15-Continued Shearing Stress Homogenizing Pressure lb./in. Rate 4000 5000 of Shear Sec1 Conc. Suspending Agent in Aqueous Phase (% w/w) 1.03 0.88 0.73 0.57 0.42 r 1.03 0.88 0.73 0.57 0.42 129 1.27 0.99 0.75 1.17 0.75 1.33 1.00 0.76 1.15 0.79 258 1.87 1.45 1.07 1.72 1.12 1.92 1.72 1.12 1.72 1.15 387 2.35 1.82 1.37 2.15 1.45 2.39 1.87 1.42 2.20 1.51 516 2.77 2.16 1.63 2.60 1.74 2.80 2.20 1.70 2.62 1.82 646 3.12 2.45 1.89 3.00 2.00 3.19 2.52 1.94 3.00 2.10 775 3.49 2.73 2.11 3.37 2.29 3.54 2.83 2.17 3.40 2.38 o 904 3.80 3.00 2.31 3.75 2.55 3.87 3.08 2.38 3.77 2.64 1033 4.10 3.24 2.50 4.08 2.80 4.15 3.33 2.58 4.12 2.89 1162 4.39 3.49 2.69 4.42 3.03 4.45 3.58 2.79 4.43 3.15 1291 4.65 3.72 2.88 4.72 3.26 4.74 3.82 2.96 4.75 3.38 1420 4.91 3.93 3.05 5.04 3.40 5.00 4.04 3.15 5.07 3.62 1549 5.16 4.15 3.24 5.33 3.72 5.25 4.25 3.33 5.38 3.85 1679 5.42 4.36 3.40 5.64 3.93 5.50 4.45 3.51 5.68 4.07 1808 5.65 4.55 3.58 5.92 4.15 5.72 4.64 3.68 5.96 4.29 1937 5.87 4.75 3.74 6.19 4.36 5.96 4.83 3.85 6.25 4.49 2060 6.10 4.94 3.91 6.48 4.57 6.19 5.03 4 00 6.54 4.70 2195 6.32 5.12 4.07 6.75 4.76 6.41 5.22 4.17 6.83 4.90 2354 6.52 5.32 4.22 7.00 4.97 6.62 5.40 4.33 7.10 5.12 2453 6.74 5.49 4.37 7.27 5.18 6.84 5.58 4.49 7.36 5.33 Stress Conversion Factor -- Dyne - cm.2 373.8 I 375.2 376.5 172.8 | 173.1 373.8 373.8 324.5 1 172.5 173.6

TABLE 16 FLOW DATA FOR EMULSIONS OF SERIES II WITH SPAN-TWEEN EMULSIFIER TRAGACANTH SUSPENDING AGENT Shearing Stress Homogenizing Pressure Ib./in? Rate of 1000 2000 3000 Shea Sec. Conc. Suspending Agent in Aqueous Pnase (% w/w) ____ 1.163 0.991 0.818 0.646 o0.473 1.163 0.991 0.818 0.646 0.473 1.163 0.991 0.818 0.646 0.473 129 0.82 1.37 1.00 0.65 0.45 0.75 1.25 1.10 0.75 0.42 0.70 i.i4 0.92 0.60 0.37 258 1.17 2.00 1.52 1.00 0.72 1.08 1.82 1.59 1.14 0.64 0.99 1.63 1.35 0.88 0.55 387 1.48 2.55.1.92 1.32 0.94 1.33 2.26 2.01 1.45 0.84 1.22 2.02 1.70 1.14 0.72 516 1.72 3.00 2.80 1.60 i.16 1.56 2.66 2.40 1.74 1.03 1.43 2.37 2.02 1.37 0.87 0 646 1.95 3.42 2.65 1.85 1.38 1.76 3.05 2.74 2.01 1.22 1.61 2.70 2.32 1.58 1.04 775 2.15 3.82 2.98 2.12 1.57 1.95 3.38 3.05 2.29 1.39 1.79 3.01 2.58 1.80 1.20 904 2.35 4.18 3.27 2.37 1.75 2.12 3.73 3.36 2.54 1.52 1.95 3.30 2.84 2.00 1.35 1033 2.51 4.52 3.52 2.59 1.95 2.30 4.04 3.65 2.77 1.73 2.10 3.60 3.09 2.19 1.50 1162 2.70 4.87 3.85 2.77 2.12 2.46 4.34 3.92 3.00 1.89 2.24 3.89 3.33 2.38 1.64 1291 2.85 5.17 4.10 3.02 2.30 2.62 4.62 4.19 3.22 2.04 2.39 4.13 3.57 2.55 1.77 1420 3.01 5.49 4.37 3.20 2.47 2.75 4.90 4.45 3.44 2.19 2.52 4.39 3.82 2.72 1.92 1549 3.16 5.76 4.62 3.42 2.64 2.90 5.17 4.72 3.65 2.35 2.65 4.64 4.04 2.92 2.05 1679 3.32 6.05 4.88 3.64 2.80 3.05 5.44 4.96 3.87 2.48 2.79 4.89 4.25 3.07 2.19 1808 3.46 6.33 5.10 3.83 2.96 3.19 5.70 5.20 4.08 2.63 2.92 5.12 4.41 3.24 2.32 1937 3.61 6.62 5.32 4.01 3.12 3.32 5.95 5.44 4.27 2.78 3.05 5.35 4.68 3.40 2.43 2060 3.71 6.87 5.53 4.20 3.26 3.45 6.20 5.66 4.48 2.92 3.17 5.58 4.89 3.58 2.57 2195 3.87 7.12 5.78 4.40 3.42 3.65 6.45 5.90 4.68 3.06 3.28 5.28 5.10 3.75 2.70 2324 4.00oo 7.40 6.oo00 4.59 3.58 3.72 6.69 6.15 4.87 3.20 3.40 6.04 5.30 3.92 2.84 2453 4.14 7.65 6.24 4.75 3.72 3.84 6.93 6.36 5.07 3.25 3.52 6.25 5.50 4.08 2.98 Stress Conversion Factor -- Dyne - cmr2 349.6 1161.0 11.3 11.8 2.8 348.5 10. 1161.3 11.8 163.0 348.5 16o.1 161.3 116.8 12.3

TABLE i6- Continued ~~~~~~~~____~~~~________________________Shearing Stress Homogenizing Pressure Ib./in2 Rate 4000 5000 of Shear Sec-1 Cone. Suspending Agent in Aqueous Phase (% w/w) 1.163 0.991 0.818 0.646 0.473 1.163 0.991 0.818 0.64 0.473 129 1.42 1.12 0.80 0.50 0.3 0.69 1.15 0.75 0.54 0,32 258 2.00 1.58 1.18 0.75 0.54 0.92 1.74 1.10 0.81 050 387 2.49 1.98 1.30 0.95 0.71 1.13 2.20 1.40 1.04 0.65 516 2.91 2.32 1.79 1.15 0.87 1.32 2.57 1.69 1.25 0.82 646 3.29 2.65 2.05 1.34 1.02 1.51 2.95 1.95 1.45 0.96 2 775 3.65 2.95 2.32 1.54 1.17 1.67 3.30 2.20 1.67 1.10 904 3.99 3.24 2.57 1.72 1.32 1.82 3.60 2.45 1.85 1.23 1033 4.30 3.51 2.80 1.90 1.47 1.97 3.90 2.67 2.04 1.38 1162 4.61 3.80 3.04 2.07 1.62 2.12 4.19 2.89 2.22 1.52 1291 4.92 4.05 3.25 2.24 1.75 2.25 4.45 3.10 2.39 i.65 1420 5.20 4.30 3.47 2.40 1.89 2.38 4.73 3.31 2.57 1.78 1549 5.49 4.52 3.69 2.58 2.02 2.50 4.98 3.52 2.72 1.92 1679 5.75 4.77 3.89 2.74 2.15 2.63 5.22 3.72 2.88 2.05 1808 6.oo00 5.02 4.10 2.89 2.28 2.74 5.47 3.92 3.06 2.17 1937 6.26 5.24 4.30 3.05 2.40 2.87 5.70 4.12 3.22 2.30 2060 6.52 5.47 4.48 3.20 2.54 2.98 5.93 4.30 3.38 2.42 2195 6.77 5.70 4.67 3.37 2.65 3.09 6.16 4.48 3.54 2.55 2354 7.02 5-92 4.88 3.52 2.80 3.22 6.38 4.69 3.70 2.68 2453 7.26 1 6.12 5.07 3.67 2.92 3.32 6.60 4.87 3.86 2.80 Stress Conversion Factor -- Dyne cm72 161.1 1 0. 161.3 1 61.4 162.8 347.3 159.8 i6i.5 162.3 162.3

TABLE 17 FLOW DATA FOR EMULSIONS OF SERIES II WITH SPAN-TWEEN EMULSIFIER ACACIA SUSPENDING AGENT Shearing Stress Homogenizing Pressure Ib./in? Rate 1000 2000 3000 of Shear Sec.1 Conc. Suspending Agent in Aqueous Phase (% w/w) _____ 19.2 135 107 78 192 16.44 13.5 10.7 7.8 19.2 16.4 13.5 10.7 7.8 129 o.62 0.42 o.6o 0.39 0.26 0.8 0.55 0.37 0.52 0.36 0.95.60 o.44 0.59 0.3 258 1.18 0.81 1.14 0.75 0.50 1.50 1.01 0.70 0.95 o.66 1.52 1.00oo 0.73 1.00 0.62 387 1.69 1.18 1.66 1.10 0.73 2.14 1.45 1.02 1.40 0.95 2.08 1.37 1.00 1.37 0.90 516 2.20 1.55 2.17 1.45 0.96 2.75 1.88 1.33 1.85 1.24 2.60 1.75 1.26 1.76 1.16 646 2.65 1.90 2.69 1.79 1.18 3.33 2.31 1.62 2.27 1.53 3.10 2.10 1.54 2.15 1.41 775 3.10 2.24 3.20 2.13 1.42 3.90 2.70 1.91 2.68 1.82 3.59 2.43 1.80 2.48 1.66 904 3.55 2.56 3.62 2.47 1.65 4.45 3.12 2.20 3.10 2.09 4.05 2.75 2.05 2.85 1.92 1033 3.95 2.87 4.13 2.80 1.85 4.97 3.50 2.50 3.51 2.36 4.48 3.07 2.31 3.19 2.17 1162 4.35 3.20 4.50 3.12 2.06 5.50 3.87 2.77 3.92 2.64 4.92 3.36.56 355 2.6440 1291 4.74 3.50 5.07 3.41 2.29 5.97 4.27 3.07 4.28 2.96 5.32 3.65 2.80 3.90 2.65 1420 5.11 3.80 5.52 3.75 2.50 6.47 4.64 3.29 4.71 3.19 5.70 3.95 3.04 4.25 2.89 1549 5.49 4.09 5.99 4.06 2.70 6.94 5.00 3.60 5.12 3.45 6.08 4.23 3.28 4.62 3.12 1679 5.84 4.38 6.41 4.37 2.92 7.41 5.37 3.88 5.50 3.74 6.45 4.50 3.51 4.97 3.38 1808 6.19 4.65 6.87 4.66 3.13 7.86 5.74 4.14 5.90 4.00 6.80 4.78 3.75 5.32 3.62 1937 6.55 4.94 7.32 4.99 3.33 8.32 6.07 4.40 6.30 4.25 7.15 5.05 3.95 5.65 3.85 2060 6.87 5.20 7.75 5.27 3.55 8.72 6.44 4.68 6.68 4.52 7.50 5.29 4.21 6.00 4.10 2195 7.20 5.49 8.17 5.58 3.75 9.17 6.76 4.94 7.09 4.78 7.83 5.52 4.44 6.35 4.34 2324 7.50 5.75 8.60 5.90 3.96 9.58 7.10 5.20 7.45 5.06 8.15 5.82 4.66 6.70 4.58 2453 7.82 6.03 9.05 6.20 4.16 10.00; 7.45 5.45 7.85 5.32 8.48 6.07 4.90 7.05 4.84 Stress Conversion Factor -- Dyne - cm.2 347.3.161.1 611l.3 161.8 1162.8 11347.3 L347.3 1341.5 | 161.3 1159.4 346.1 1346.1 340.9 1.3 158.

TABLE 17-Continued __ _________________________________________________________ Shearing Stress Homogenizing Pressure Ib./in? Rate of 4000 5000 Shear Sec. -1 Cone. Suspending Agent in Aqueous Phase (% w/w) _ 19.2 l6.4 T 13.5 10.7 7.8 19.2 16.4 13.5 10.7 7.8 129 0.71 0.53 0.30 0.49 0.50 0.72 0.47 0.28 0o.5 45 258 1.20 0.97 0.52 0.80 0.72 1.22 0.69 0.58 0.87 0.68 387 1.68 1.39 0.74 1.10 0.93 1.67 1.08 0.82 1.22 0.89 516 2.12 1.81 0.93 1.40o 1.12 2.10 1.38 1.05 1.57 1.09 646 2.54 2.19 1.14 1.70 1.31 2.51 1.64 1.26 1.92 1.28 775 2.94 2.56 1.33 1.98 1.52 2.90 1.90 1.49 2.24 1.50 Li 904 3.34 2.95 1.52 2.27 1.72 3.26 2.15 1.69 2.58 1.70 1033 3.70 3.30 1.70 2.4 1.91 3.61 2.40 1.89 2.89 1.90 l162 4.06 3.64 1.87 2.82 2.10 3.95 2.63 2.08 3-93 2.10 1291 4.40o 4.00 2.05 3.07 2.29 4.27 2.85 2.27 3.50 2.30 1420 4.74 4.32 2.20 3.35 2.48 4.57 3.08 2.47 3.79 2.50 1549 5.06 4.62 2.36 3.63 2.67 -4.88 3.29 2.65 4.07 2.68 1679 5.39 4.97 2.51 3.90 2.87 5.18 3.50 2.84 4.38 2.88 1808 5.70 5.27 2.67 4.i6 3.07 5.45 3.70 3.01 4.65 3.07 1937 6.00oo 5.80 2.82 4.41 3.25 5.72 3.91 3.19 4.92 3.27 2060 6.30 5.90 2.97 4.68 3.45 5.97 4.10 3.37 5.20 3.08 2195 6.59 6.22 3.12 4.94 3.65 6.23 4.29 3.54 5.47 3.68 2320 6.88 6.52 3.26 5.21 3.87 6.50 4.49 3.70 5.74 3.87 2453 7.16 6.83 3.42 5.47 4.05 6.75.68 3.87 6.02 4.07 Stress Conversion Factor -- Dyne - cmn2 347.3 9344.9 341.5 161.1 153.2 J| 344.9 |1 346.1 |6o. 343.2 | l l 153.9

TABLE 18 FLOW DATA FOR EMULSIONS OF SERIES II WITH SPAN-TWEEN EMULSIFIER SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT Homogenizing Pressure Ib./in? Rate 1000 2000 3000 Sear Sec-> Cone. Suspending Agent in Aqueous Phase (% w/w) _____ 2.26 1.92 1.59 1.25 0.92 2.26 1.92 1.59 1.25 0.92 2.26 1.92 1.59 0.92 129 0.85 0.70 0.80 0.60 0.40 0.99 0.79 0.98 0.69 0.82 1.00 0.77.4 0.83 258 1.33 1.07 1.25 0.94 0.60 1.49 1.20 1.48 1.02 1.20 1.52 1.13 1.66 1.21 387 1.74 i.4o 1.62 1.25 0.78 1.92 1.55 1.92 1.32 1.54 1.95 1.45 2.12 1.55 o 516 2.10 1.70 1.99 1.52 0.95 2.29 1.80 2.33 1.58 1.85.32 1.75 2.55 1.85 646 2.40 1.98 2.30 1.80 1.12 2.61 2.14 2.70 1.84 2.16 2.66 2.01 2.92 2.13 775 2.70 2.24 2.61 2.05 1.30 2.94 2.40 3.05 2.09 2.47 2.97 2.25 3.30 2.42 904 2.97 2.45 2.90 2.30 1.47 3.21 2.63 3.40 2.32 2.77 3.23 2.47 3.65 2.70 1033 3.22 2.67 3.14 2.54 1.62 3.48 2.86 3.71 2.55 3.06 3.50 2.68 3.98 2.97 1162 3.45 2.89 3.40 2.77 1.76 3.75 3.09 4.04 2.78 3.34 3.77 2.88 4.31 3.25 1291 3.69 3.07 3.65 3.00 1.92 3.98 3.29 4.34 2.99 3.61 4.02 3.07 4.62 3.50 1420 3.90 3.26 3.88 3.20 2.o6 4.22 3.48 4.62 3.20 3.89 4.25 3.25 4.92 3.77 1549 4.10 3.45 4.10 3.40 2.20 4.43 3.68 4.92 3.42 4.15 4.48 3.45 5.19 4.00 1679 4.30 3.62 4.30 3.62 2.35 4.65 3.87 5.19 3.63 4.40 4.69 3.62 5.48 4.25 1808 4.50 3.80 4.51 3.82 2.49 4.86 4.05 5.45 3.83 4.66 4.90 3.80 5.75 4.55 1937 4.68 3.95 4.71 4.00 2.61 5.05 4.22 5.70 4.o01 4.92 5.10 3.95 6.00 4.74 2060 4.85 4.12 4.90 4.20 2.75 5.25 4.40 5.96 4.20 5.17 5.30 4.13 6.26 4.99 2195 5.02 4.26 5.10 4.38 2.87 5.44 4.52 6.21 4.37 5.47 5.48 4.29 6.53 5.20 2324 5.20 4.42 5.30 4.56 3.00 5.62 4.72 6.45 4.58 5.75 5.67 4.45 6.76 5.45 2453 5.35 4.56 5.48 4.75 3.15 5.76 4.88 6.68 4.75 5.90 5.85 4.57 7.00 5.68 Stress Conversion Factor -- Dyne -.cm? 681.7 1684.0 o 531.6 1356.3 1377.2 |1678.1 1682.8 1344.9 [356.3 199.6 11674.6 682.5 343.8 |9-96

TABLE 18-Continued Shearing Stress Homogenizing Pressure Ib./in? Rate 4000 5000 of Shear Sec 71 Cone. Suspending Agent in Aqueous Phase (% w/w) 2.26 1.92 1.59 1.25 0.92 2.26 1.92 1.59 1.25 0.92 129 1.03 0.77 1.00 1.12 0.77 0.90 0.69 0.95 1.15 0.75 258 1.52 1.14 1.47 1.66 1.12 1.36 1.05 1.43 1.70 1.10 387 1.94 1.44 1.88 2.12 1.42 1.75 1.33 1.84 2.16 1.40 516 2.30 1.72 2.24 2.54 1.72 2.07 1.62 2.22 2.60 1.70 646 2.62 1.99 2.60 2.93 1.98 2.34 1.92 2.55 3.00 1.98 775 2.94 2.23 2.45 3.34 2.24 2.66 2.09 2.87 3.42 2.24 904 3.22 2.45 3.25 3.71 2.50 2.92 2.31 3.19 3.83 2.50 1033 3.50 2.65 3.66 4.08 2.75 3.15 2.52 3.49 4.20 2.75 1162 3.74 2.85 3.87 4.44 2.99 3.40 2.71 3.80 4.56 3.01 1291 3.98 3.05 4.15 4.80 3.23 3.62 2.90 4.o6 4.93 3.25 1420 4.21 3.23 4.42 5.14 3.48 3.83 3.09 4.32 5.27 3.50 1549 4.42 3.42 4.70 5.46 3.73 4.05 3.26 4.60 5.62 3.75 1679 4.64 3.60 4.95 5.79 3.95 4.24 3.44 4.85 5.95 3.98 1808 4.85 3.77 5.22 6.10 4.17 4.43 3.60 5.10 6.28 4.22 1937 5.04 3.93 5.47 6.42 4.4o 4.62 3.76 5.35 6.60 4.40 2060 5.24 4.10 5.70 6.73 4.64 4.82 3.92 5.60 6.91 4.68 2195 5.93 4.26 5.95 7.04 4.85 4.99 4.07 5.83 7.22 4.92 2320 5.62 4.42 6.18 7.33 5.07 5.16 4.22 6.05 7.51 5.14 2453 5.79 4.57 6.42 7.64 5.30 5.33 4.38 6.28. 7.82 5.37 Stress Conversion Factor —Dyne - cm72 678.1 682.8 340.9 198.8 200.0 679.3 679.3 1 344.4 199.6 200.0

TABLE 19 FLOW CURVES FOR EMULSIONS OF SERIES OF II WITH SPAN-TWEEN EMULSIFIER,METHYLCELLULOSE SUSPENDING AGENT Shearing Stress Homogenizing Pressure lb./in2 Rate 1000 2000 3000 of Shear Sec. Cone. Suspending Agent in Aqueous Phase (% w/w) 1.661 1.415 1.168 0.922 0.676 1.661 1.415 1.168 0.922 0.676 1.661 1.415 1.168 0.922 0.67 129 0.50 0.62 0.70 0.65 0.541 1.23 0.85 0.70 0.70 0.54 1.19 0.82.6 0.70 0.50 258 0. 0.0.98 1.14 1.12 0.'92 1.85 1.30 1.10 1.14 0.90 1.80 1.28 1.03 1.12 0.82 387 1.00 1.25 1.50 1.50 1.28 2.35 1.42 1.50 1.20 2.28 1.65 1.35 1.48 1.1 516 1.20 1.50 1.82 1.85 1.62 2.75 1.99 1.71 1.85 1.50 2.67 1.98 1.62 1.82 646 1.37 1.70 2.11 2.21 1.93 3.11 2.27 1.99 2.16 1.78 3.05 2.25 1.88 2.10 1.70 775 1.52 1.90 2.38 2.52 2.24 3.45 2.54 2.22 2.45 2.06 3.39 2.52 2.13 2.395 904 1.67 2.07 2.64 2.85 2.51 3.75 2.79 2.45 2.75 2.33 3.68 2.75 2.33 2.67 2.20 1033 1.80 2.25 2.76 3.12 2.80 4.04 3.01 2.66 3.02 2.58 3.95 2.99 2.52 2.92 2.42 1162 1.92 2.40 3.10 3.38 3.06 4.32 3.23 2.88 3.22 2.84 4.22 3.0.74 3.17.65 1291 2.05 2.55 3.31 3.68 3.31 4.57 3.44 3.08 3.54 3.05 4.45 3.40 2.92 3.42 2.88 1420 2.16 2.70 3.52 3.93 3.57 4.82 3.63 3.26 3.76 3.28 4.69 3.60 3.10 3.65 3.10 1549 2.27 2.84 3.72 4.18 3.82 5.04 3.82 3.45 4.00 3.50 4.90 3.78 3.27 3.90 3.30 1679 2.38 2.98 3.92 4.40 4.05 5.25 4.00 3.65 4.20 3.74 5.12 3.96 3.45 4.12 3.50 1808 2.49 3.10 4.10 4.65 4.29 5.48 4.19 3.81 4.45 3.95 5.33 4.15 3.63 4.34 3.73 1937 2.57 3.22 4.30 4.88 4.50 5.68 4.36 3.98 4.67 4.17 5.55 4.32 3.80 4.55 3.93 2060 2.67 3.33 4.46 5.10 4.73 5.89 4.52 4.15 4.89 4.38 5.74 4.49 3.95 4.77 2195 2.78 3.45 4.69 5.32 4.99 6.08 4.69 4.32 5.10 4.60 5.93 4.65 4.12 4.98 4.33 2324 2.86 3.56 4.8o 5.55 5.19 6.27 4.85 4.48 5.30 4.80 6.12 4.81.4.27 5.18 4.52 2453 2.95 3.66 4.98 5.75 5.40 6.47 5.01 4.65 5.52 5.00 6.33 4.97 4.42 5.40 4.72 Stress Conversion Factor -- Dyne - cm72 905.7 679.3 357.5 216.4 155.2 443. 441.2 357.6 215.7 154.7 440.2 441.2 1357.6 214. 153.6

TABLE 19-Continued Shearing Stress Homogenizing Pressure lb./in2 RATE 4000 5000 OF SHEAR SEC-.1 Cone. Suspending Agent in Aqueous Phase (% W/w) 1.661 1.415 1.168 0.922 0.676 1 i.661 1.415 1.168 0.922 0.676 129 1.32 0.90 0.70 0.70 0.58 1.20 0.87 0.68 0.74 0.55 258 2.02 1.40 1.14 1.14 0.97 1.82 1.35 1.10 1.22 0.93 387 2.55 1.80 1.50 1.54 1.30 2.34 1.75 1.45 1.64 1.25 516 3.00 2.12 1.82 1.89 1.62 2.75 2.06 1.76 1.98 1.63 646 3.37 2.44 2.10 2.22 1.92 3.11 2.35 2.03 2.33 1.86 775 3.72 2.70 2.33 2.52 2.20 3.45 2.62 2.27 2.63 2.15 904 4.05 2.98 2.57 2.80 2.48 3.75 2.85 2.50 2.96 2.40 1033 4.33 3.17 2.82 3.05 2.72 4.05 3.09 2.70 3.17 2.65 1162 4.62 3.42 3.00 3.32 2.97 4.31 3.30 2.92 3.44 2.90 1291 4.87 3.63 3.20 3.57 3.21 4.57 3.50 3.12 3.70 3.12 1420 5.12 3.83 3.41 3.83 3.44 4.82 3.72 3.32 3.94 3.35 1549 5.38 4.01 3.60 4.05 3.68 5.03 3.89 3.49 4.19 3.59 1679 5.60 4.20 3.79 4.28 3.92 5.26 4.08 3.67 4.43 3.82 1808 5.82 4.39 3.97 4.52 4.13 5.48 4.26 3.85 4.65 4.03 1937 6.03 4.57 4.14 4.73 4.35 5.69 4.43 4.o0 4.87 4.25 2o6o 6.25 4.75 4.32 4.95 4.57 5.89 4.60 4.17 5.09 4.46 2195 6.43 4.92 4.49 5.i6 4.79 6.08 4.76 4.34 5.32 4.68 2320 6.64 5.07 4.65 5.38 5.00 6.28 4.93 4.50 5.50 4.88 2453 6.84 5.25 4.81 5.58 5.22 6.47 5.08 4.67 5.73 5.09 Stress Conversion Factor -- Dyne - cmn2 ~439.3 437.4 356.9 213.7 153. 443.1 444.0 357 213.7 153.9

TABLE 20 FLOW CURVES FOR EMULSIONS OF SERIES II WITH SPAN-TWEEN EMULSIFIER, CARBOPOL-934, SODIUM SALT SUSPENDING AGENT Shearing Stress Homogenizing Pressure lb./in2 Rate of 1000 2000 3000 Shear Sec. Cone. Suspending Agent in Aqueous Phase (% w/w) 0.334 0.285 0.235 0.185 0.136 0.334 0.285 0.235 0.185 0.136 0.334 0.285 0.235 0.185 0.136 129 1.00 6 0.9 0.52 0.32 1.17 0.82 0.69 0.70 0.42 1.10 0.77 0.75 0.68 0.43 258 1.50 1.07 1.52 0.87 0.55 1.68 1.20 1.07 1.09 0.69 1.62 1.17 1.17 1.07 0.72 387 1.92 1.41 2.00 1.20 0.77 2.08 1.55 1.40 1.42 0.93 2.05 1.47 1'55 1.43 O.Q6 516 2.28 1.70 2.50 1.51 1.00 2.48 1.84 1.70 1.75 1.15 2.42 1.77 1.87 1.77 1.20 C 646 2.64 1.98 2.92 1.81 1.21 2.82 2.12 2.00 2.06 1.35 2.75 2.02 2.17 2.07 1.42 775 2.98 2.25 3.36 2.10 1.43 3.15 2.39 2.26 2.35 1.52 3.09 2.29 2.45 2.36 1.64 904 3.30 2.51 3.75 2.38 1.61 3.46 2.64 2.52 2.62 1.76 3.39 2.52 2.73 2.63 1.86 1033 3.58 2.75 4.15 2.65 1.82 3.76 2.89 2.79 2.90 1.99 3.68 2.75 2.98 2.90 2.07 1162 3.87 2.99 4.50 2.90 2.00 4.05 3.12 3.04 3.16 2.18 3.96 2.98 3.24 3.17 2.27 1291 4.16 3.22 4.78 3.16 2.20 4.34 3.35 3.26 3.41 2.36 4.24 3.18 3.48 3.43 2.45 1420 4.44 3.45 5.19 3.40 2.38 4.62 3.52 3.50 3.69 2.55 4.52 3.41 3.72 3.69 2.64 1549 4.71 3.66 5.53 3.66 2.57 4.88 3.86 3.74 3.94 2.74 4.77 3.62 3.98 3.94 2.83 1679 4.97 3.88 5.90 3.90 2.75 5.16 4.00 3.95 4.19 2.92 5.04 3.84 4.23 4.19 3.02 1808 5.22 4.11 6.20 4.15 2.92 5.42 4.22 4.19 4.44 3.11 5.30 4.04 4.45 4.45 3.20 1937 5.48 4.30 6.55 4.37 3.11 5.67 4.44 4.40 4.69 3.28 5.53 4.25 4.68 4.68 3.40 2060 5.72 4.50 6.88 4.62 3.30 5.93 4.64 4.62 4.92 3.46 5.78 4.45 4.92 4.93 3.58 2195 5.99 4.70 7.20 4.84 3.45 6.19 4.85 4.84 5.16 3.64 6.02 4.63 5.14 5.15 3.79 2324 6.22 4.90 7.50 5.07 3.65 6.42 5.06 5.04 5.40 3.82 6.25 4.83 5.37 5.39 3.95 2453 6.47 5.12 7.82 5.30 3.82 6.88 5.25 5.25 5.65 4.00! 6.50 5.03 5.58 5.62 4.17 Stress Conversion Factor -- Dyne - cm:2 159.3 159.3 1 89.1 1 89.3 1 89.9 1158.2 159.4 118.1 189.7 1 90.4 1158.7 1158.9 118.2 I 89.5 90.2

TABLE 20-Continued Shearing Stress Homogenizing Pressure lb./in? Rate of Shear 4000 5000 Sec. 1 Conc. Suspending Agent in Aqueous Phase (7 w/w) ]O0.334 0.285 0.235 0.185 0.136 0.334 0.285 1 0.235 0.185 0.136 129 1.23 0.88 0.92 0.77 0.50 1.37 0.94 0.88 0.73 0.48 258 1.75 1.30 1.38 1.20 0.80 1.92 1.37 1.30 1.15 0.77 387 2.17 1.65 1.75 1.62 1.05 2.36 1.72 1.70 1.52 1.05 516 2.55 1.97 2.10 1.95 1.33 2.75 2.04 2.05 1.85 1.29 646 2.92 2.23 2.42 2.28 1.57 3.10 2.34 2.35 2.18 1.51 775 3.24 2.50 2.73 2.60 1.80 3.45 2.62 2.64 2.45 1.76 o 904 3.57 2.77 3.02 2.88 2.02 3.77 2.87 2.92 2.75 1.98 kO 1033 3.87 3.00 3.35 3.17 2.25 4.09 3.12 3.19 3.03 2.20 1162 4.18 3.25 3.58 3.46 2.46 4.40 3.38 3.47 3.30 2.39 1291 4.45 3.50 3.85 3.73 2.65 4.68 3.60 3.72 3.57 2.60 1420 4.73 3.73 4.10 4.00 2.87 4.95 3.84 3.98 3.83 2.80 1549 5.00 3.95 4.35 4.27 3.07 5.24 4.02 4.24 4.09 3.00 1679 5.26 4.17 4.62 4.55 3/26 5.50 4.27 4.47 4.34 3.17 1808 5.53 4.38 4.85 4.80 3.47 5.77 4.50 4.72 4.59 3.38 1937 5.79 4.60 5.10 5.05 3.67 6.02 4.70 4.95 4.84 3.57 2060 6.04 4.80 5.35 5.32 3.86 6.29 4.92 5.18 5.08 3.78 2195 6.27 5.02 5.58 5.57 4.07 6.55 5.12 5.42 5.33 3.96 2324 6.53 5.22 5.82 5.82 4.25 6.78 5.33 5.65 5.57 4.15 2453 6.77 5.43 6.05 6.05 4.45 _ 7.08 5.55 5.88 5.80 4.35 Stress Conversion Factor -- Dyne - cm72 1583.2 158.7 I 118.2 88.7 I 89.5 II 159. 158.9 | 118.2 89.9 90.2

TABLE 21 FLOW DATA FOR METHYLCELLULOSE SOLUTIONS CORRESPONDING TO EMULSIONS OF SERIES III Shearing Stress Rate of Conc. Methylcellulose (% w/w) Shear Sec: 1 1. 337 1.170 1.002 0.780 0.65 0.543 0.134 0.326 129 0.83 0.85 0.77 0.49 0.43 0.42 0.18 0.17 '55 1.45 1.50 1.39 0.89 0.79 0.62 0.30 0.28 357 1.95 2.05 1.94 1.27 1.14 0.82 O. 0.42 0.38 516 2.37 2.55 2.46 1.62 1.48 1.02 0.54 0.48 646 2.76 3.00 2.92 1.95 1.80 1.20 0.05 0.57 775 3.12 3.40 3.33 2.28 2.10 1.38 0.7568 0 90UL 3.43 3.80 3.75 2.57 2.40 1.57 0.88 0.80 0C33 3.72 4.17 4.12 2.88 2.72 1.75 1.00 0.90 1162 4.01 4.50 4.49 3.17 2.98 1.92 1.10 0.99 1291 4.27 4.82 4.82 3.42 3.24 2.09 1.21 1.10 1420 4.52 5.13 5.17 3.73 3.52 2.25 1.32 1.20 1549 4.75 5.42 5.56 3.97 3.81 2.42 1.42 1.30 1679 5.00 5.72 5.80 4.21 4.05 2.57 1.53 1.40 1S08 5.20 5.98 6.12 4.48 4.30 2.74 1.64 1.50 1937 5.42 6.25 6.41 4.70 4.52 2.88 1.73 1.60 2060 5.63 6.51 6.70 4.94 4.79 3.05 1.85 1.70 2195 5.83 6.77 7.00 5.19 5.02 3.22 1.95 1.80 2324 6.01 7.02 7.26 5.42 5.25 3.39 2.05 1.90 2_-53 __6.22 7.27 7.54 6.14 5.46 3.57 2.17 2.00 Stress Conversion Factor -- Dyne - cm.2 | 233.6 | 146.9 | 104.4 1 82.3 67.4 77.2 | 2.5 55.9

TABLE 22 FLOW DATA FOR EMULSIONS OF SERIES III WITH 1.337% METHYLCELLULOSE SUSPENDING AGENT Shearing Stress Rate Conc. Oil (% v/v) f Shear 5+.2 48.7 43.3 37.9 32.4 27.0 16.2 10.8 Sec 1 _ 129 1.85 1.62 1.42 1.24 1.11 1.01 0.70 O.68 258 2.7 22.50 2.25 2.01 1.80 1.72 1.17 1.15 387 3.40 3.16 2.87 2.59 2.40 2.25 1.57 1.52 516 4.00 3.70 3.40 3.08 2.85 2.64 1.92 1.87 646 4.48 4.21 3.90 3.54 3.29 3.10 2.20 2.17 775 4.92 4.63 4.31 3.95 3.80 3.50 2.50 2.45,0' 5.33 5.02 4.69 4.33 4.05 3.85 2.75 2.70 1033 5.72 5.42 5.07 4.66 4.38 4.17 3.00 2.94 1162 6.12 5.79 5.40 5.00 4.69 4.46 3.23 3.17 1291 6.46 6.14 5.75 5.31 5.00 4.72 3.45 3.37 1420 6.80 6.47 6.05 5.60 5.27 5.01 3.67 3.57 1549 7.13 6.77 6.35 5.88 5.55 5.27 3.85 3.77 1679 7.43 7.07 6.65 6.16 5.82 5.52 4.05 3.95 1808 7.74 7.36 6.92 6.42 6.06 5.77 4.18 4.12 1937 8.04 7.64 7.21 6.68 6.31 6.00 4.40 4.30 2060 8.32 7.90 7.48 6.92 6.55 6.23 4.57 4.45 2195 8.60 8.19 7.74 7.16 6.78 6.45 4.72 4.61 2324 8.88 8.55 7.99 7.40 7.00 6.67 4.90 4.77 2453 9.15 l 8.72 1 8.24 7.63 1 7.24 6.89 5.06 4.93 Stress Conversion Factor -- Dyne - cm72 273.4 1 273.4 I 273.4 I 273.4 273.4 1 277.1 | 323.8 322.7

TABLE 23 FLOW DATA FOR EMULSIONS OF SERIES III WITH 1.170% METHYLCELLULOSE SUSFENDING AGENT Shearing Stress Rate. Cone. Oil (% v/v) Shear -ec.- 54.2 48.7 43.3 37.9 3.4 27.0 21.6 L6.2 1 1.50 1.19 1.17 1.00 0.85 0.76 1.11.03.7 25; 2.20 1.85 1.85 1.63 1.47 1.32 1.96 1.75 1 3 7 2.75 2.37 2.45 2.13 1.92 1.77 2.65 2.39 2.3 516 3.24 2.83 2.94 2.60 2.38 2.16 3.28 2.95 2.85. ^.6 3.68 3.24 3.39 3.00 2.76 2.52 3.85 3.47 3.6 775 4.07 3.60 3.80 3.37 3.11 2.87 4.35 3.95 3.8 90^' | 4.45 3.95 4.16 3.74 3.44 3.16 4.80 4.38 4.25 1C33 -.77 4.27 4.50 4.07 3.75 3.45 5.25 4.79 4.64 -62 5.08 4.57 4.84 4.37 4.05 3.75 5.68 5.18 5.00 1291 5.38 4.85 5.15 4.65 4.32 4.00 6.07 5.57 5.37 a'2- 5.68 5.12 5.45 4.93 4.57 4.25 6.48 5.92 5.74 15-9 5.97 5.38 5.74 5.20 4.82 4.48 6.85 6.27 6.06 679 6.25 5.65 6.01 5.47 5.08 4.71 7.226.6 6.62 c 6.51 5.90 6.30 5.73 5.32 4.93 7.57 6.92 6.70 1-37 6.79 6.15 6.57 5.97 5.55 5.15 7.89 7.25 7.0 nrC2 7.05 6.38 6.82 6.20 5.78 5.36 8.23 7.55 7.30 2195 7.31 6.62 7.07 6.45 6.00 5.58 8.55 7.85 758:32a 7.55 6.84 7.34 6.69 6.23 5.79 8.87 8.15 7.85 -253 7.80 7.07 7.58 6.92 6.44 5.98 9.17 8.45 8.14 Stress Conversion Factor - Dyne - cm.2 ___ 274.9 ] 274.1 237.1 242.4 I 243.0 [ 240.7 1.9 1 147.3 1 147.3

TABLE 24 FLOW DATA FOR EMULSIONS OF SERIES III WITH 1.002% METHYLCELLULOSE SUSPENDING AGENT Shearing Stress Rate of Conc. Oil (% v/v) Shear Sec:. 54.2 48.7 43.3 37.9 32.4 27.0 21.6 16.2 10.8 129 1.87 1.41 1.18 1.18 1.00 1.07 1.01 0.82 0.77 258 2.77 2.27 2.35 2.07 1.71 1.92 1.72 1.49 1.36 387 3.55 2.92 3.10 2.75 2.32 2.60 2.39 2.00 1.89 516 4.22 3.51 3.75 3.40 2.85 3.25 2.95 2.52 2.40 6+6 4.81 4.03 4.38 3.95 3.35 3.82 3.50 3.00 2.80 775 5.38 4.52 4.92 4.49 3.83 4.38 4.00 3.45 3.25 904 5.89 5.00 5.42 4.97 4.25 4.88 4.45 3.87 3.6 1033 6.36 5.42 5.92 5.42 4.65 5.35 4.89 4.29 4.00 1162 6.82 5.85 6.38 5.89 5.05 5.80 5.29 4.64 4.38 1291 7.27 6.24 6.85 6.30 5.42 6.25 5.70 5.00 4.71 1420 7.69 6.64 7.27 6.70 5.79 6.68 6.10 5.35 5.02 1549 8.08 7.00 7.70 7.10 6.13 7.07 6.47 5.70 5.34 1679 8.50 7.35 8.10 7.49 6.48 7.47 6.83 6.02 5.67 1808 8.88 7.71 8.50 7.85 6.82 7.83 7.18 6.37 5.97 1937 9.25 8.04 8.87 8.20 7.13 8.20 7.52 6.67 6.25 2060 9.65 8.38 9.25 8.57 7.49 8.55 7.85 6.98 6.55 2195 9.98 8.70 9.62 8.90 7.75 8.92 8.19 7.30 6.82 2324 10.34 9.02 9.97 9.24 8.05 9.27 8.51 7.57 7.10 2453 10.68 _ 9.34 10.34 1 9.60 8.36 9.62 1 8.82 1 7.87 7.38 Stress Conversion Factor -- Dyne - cm.2 169.2 _ 170.8 1 137.8 137.4 142.7 117.7 117.7 117.7 118.

TABLE 25 FLOW DATA FOR EMULSIONS OF SERIES III WITH 0.780% METHYLCELLULOSE SUSPENDING AGENT Shearing Stress Rate of Conc. Oil (% v/v) Shear Sec1 54.2 48.7 43.3 37.9 32.4 27.0 21.6 16. 10.8 129 1.24 1.05 0.82 1.07 0.75 0.63 80.47.8 258 1.90 1.70 1.34 1.82 1.32 1.17 0.87 1.23 1.10 387 2.46 2.27 1.82 2.50 1.84 1.62 1.27 1.71 1.56 516 2.93 2.80 2.27 3.10 2.29 2.01 1.62 2.17 1.98 646 3.38 3.25 2.67 3.62 2.74 2.40 1.95 2.62 2.40 775 3.83 3.70 3.05 4.15 3.16 2.76 2.26 3.02 2.77 904 4.23 4.08 3.43 4.65 3.55 3.12 2.56 3.44 3.15 e 1033 4.57 4.45 3.77 5.10 3.93 3.49 2.85 3.82 3.49 o 1162 4.94 4.85 4.10 5.57 4.30 3.82 3.18 4.17 3.80 1291 5.27 5.20 4.42 6.oo 4.67 4.15 3.45 4.52 4.12 1420 5.62 5.55 4.72 6.42 5.02 4.45 3.70 4.87 4.44 1549 5.95 5.89 5.00 6.83 5.35 4.75 3.98 5.19 4.76 1679 6.27 6.22 5.31 7.18 5.68 5.07 4.22 5.53 5.07 1808 6.60 6.54 6.69 7.60 5.98 5.33 4.47 5.85 5.38 1937 6.90 6.85 5.87 7.98 6.30 5.62 4.70 6.20 5.65 2060 7.19 7.16 6.14 8.35 6.62 5.89 4.95 6.49 5.92 2195 7.50 7.49 6.41 8.70 6.92 6.17 5.19 6.80 6.22 2324 7.77 7.77 6.66 9.07 7.21 6.43 5.42 7.09 6.50 2453 8.07 8.05 6.94 9.40 7.51 6.70 5.65 1 7.87 6.73 Stress Conversion Factor -- Dyne - cm.2 169.5 | 149.5 148.7 108.7 109.3 1o9. 109.3 83.9 84.5

TABLE 26 FLOW DATA FOR EMULSIONS OF SERIES III WITH 0.651% METHYLCELLULOSE SUSPENDING AGENT Shearing Stress Rate of Conc. Oil (q v/v) Shear Sec.1 54.2 48.7 43.3 37.9 32.4 27.0 21.6 16.2 10.8 129 1.35 1.03 0.75 0.60 0.50 0.43 0.38 0.34 0.54 258 2.10 1.70 1.30 1.07 0.90 0.78 0.70 0.64 0.99 387 2.77 2.25 1.77 1.45 1.25 1.10 0.98 0.89 1.40 516 3.18 2.75 2.22 1.83 1.58 1.39 1.25 1.15 1.81 646 3.87 3.23 2.60 2.19 1.88 1.67 1.50 1.38 2.1 775 4.35 3.68 3.00 2.54 2.17 1.94 1.74 1.61 2.54 ~0 4 4.80 4.10 3.39 2.85 2.45 2.20 1.99 1.84 2.92 1033 5.23 4.50 3.74 3.17 2.73 2.45 2.20 2.05 3.27 0 1162 5.67 4.86 4.07 3.46 3.00 2.69 2.43 2.27 3.62 1291 6.07 5.21 4.39 3.75 3.24 2.92 2.64 2.47 3.94 1420 6.47 5.57 4.70 4.04 3.52 3.15 2.84 2.67 4.25 1549 6.88 5.92 5.00 4.32 3.78 3.37 3.05 2.87 4.57 1679 7.23 6.25 5.28 4.57 4.00 3.60 3.25 3.05 4.87 1808 7.59 6.59 5.60 4.82 4.24 3.82 3.44 3.24 5.16 1937 7.95 6.91 5.88 5.07 4.47 4.02 3.65 3.42 5.47 2060 8.32 7.24 6.17 5.32 4.68 4.23 3.84 3.60 5.75 2195 8.65 7.53 6.44 5.57 4.92 4.42 4.02 3.79 6.04 2324 9.00 7.83 6.72 5.84 5.13 4.63 4.23 3.96 6.33 2453 9.35 8.14 1 7.00 6.07 5.35 4.84 1 4.40 4.4 Stress Conversion Factor -- Dyne - cm.2 121.7 121.7 121.1 121.1 121.1 119.7 119.0 119.67.

TABLE 27 FLOW DATA FOR EMULSIONS OF SERIES III WITH 0.543% METHYLCELLULOSE SUSPENDING AGENT Shearing Stress Rate of Cone. Oil (% v/v) Shear _______________ Sec1 54.2 48.7 33 37.9 32. 427.0 21.6 1.210.8 129 1.23 0.84 0.62 0.68 0.54 0.46 0.39 0.32 0.23 258 1.90 1.40 1.06 1.16 0.97 0.82 0.70 0.58 0.53 387 2.48 1.87 1.47 1.62 1.34 1.16 1.00 0.84 0.76 516 3.02 2.30 1.84 2.02 1.71 1.46 1.30 1.10 0.98 646 3.50 2.75 2.19 2.45 2.08 1.80 1.57 1.34 1.20 775 3.96 3.11 2.52 2.84 2.42 2.08 1.85 1.57 142 904 4.40 3.50 2.85 3.22 2.75 2.38 2.12 1.82 163 0 1033 4.82 3.87 3.17 3.58 3.07 2.67 2.38 2.04 1.83 1162 5.20 4.21 3.47 3.95 3.38 2.96 2.62 2.25 2.04 1291 5.62 4.56 3.78 4.30 3.72 3.23 2.87 2.48 2.23 1420 6.00 4.88 4.07 4.62 4.01 3.50 3.12 2.68 2.43 1549 6.38 5.19 4.34 4.97 4.31 3.76 3.35 2.88 2.63 1679 6.75 5.52 4.62 5.29 4.60 4.02 3.60 3.10 282 1808 7.10 5.83 4.88 5.62 4.87 4.27 3.82 3.32 3.00 1937 7.45 6.13 5.15 5.92 5.16 4.51 4.05 3.52 3.18 2060 7.80 6.45 5.42 6.25 5.45 4.77 4.28 3.71 3.37 2195 8.13 6.74 5.69 6.57 5.75 5.01 4.50 3.92 3.56 2324 8.47 7.03 5.95 6.87 6.02 5.25 4.73 4.10 3.74 2453 8.82 7.35 6.22 7.18 6.30 5.50 4.95 4.32 3.94 Stress Conversion Factor -- Dyne - cm72 ~_______ 103.5 I 1103.0 103.0 76. 76.1 77.2 77.1 77.2 7.4

TABLE 28 FLOW DATA FOR EMULSIONS OF SERIES III WITH 0.434%o METHYLCELLULOSE SUSPENDING AGENT Shearing Stress Rate of Conc. Oil (% v/v) Shear Sec. 54.2 48.7 43.3 37.9 32.4 27.0 21.6 16.2 10.8 129 0.75 0.62 0.45 0.47 0.43 0.37 0.25 0.22 0.22 258 1.19 1.00 0.77 0.82 0.77 0.65 0.46 0.39 0.37 387 1 31 1.39 1.08 1.15 1.09 0.90 0.65 0.57 0.52 516 1.88 1.44 1.35 1.44 1.40 1.16 0.84 0.74 0.67 646 2.23 2.02 1.60 1.75 1.70 1.42 1.04 0.89 0.82 775 2.50 2.32 1.85 2.03 2.00 1.67 1.22 1.06 0.95 90C 2.77 2.60 2.10 2.32 2.28 1.92 1.40 1.24 1.10 10C33 3.07 2.88 2.34 2.58 2.56 2.14 1.57 1.38 1.24 0 -112 3.34 3.15 2.57 2.85 2.84 2.37 1.75 1.54 1.37 129 1 3.59 3.43 2.80 3.12 3.12 2.62 1.92 1.68 1.51 i1a^20 3.84 3.68 3.02 3.36 3.38 2.85 2.08 1.83 1.65 1549 4.08 3.94 3.23 3.62 3.64 3.07 2.25 1.98 1.77 i-'679 1 4.32 4.18 3.45 3.87 3.92 3.30 2.40 2.12 1.92 1PC8O ~4.55 4.44 3.68 4.13 4.17 3.52 2.55 2.25 2.03 1937 4.77 4.67 3.88 4.36 4.40 3.73 2.73 2.37 2.17 2060 5.01 4.92 4.09 4.60 4.66 3.97 2.91 2.50 2.30 2195 5.24 5.17 4.30 4.84 4.92 4.18 3.10 2.62 2.43 23 4 5.48 5.40 4.50 5.07 5.14 4.40 3.24 2.75 2.57 o453 5.70 | 5.63 | 4.70 1 5.30 1 5.39 | 4.62 | 3.42 2.92 2.68 Stress Conversion Factor -- Dyne - cm_2 136.5 111.2 | 110.4 83.4 | 69.9 | 69.5 82.8 82.5 82.5

TABLE 29 FLOW DATA FOR EMULSIONS OF SERIES III WITH 0.326% METHYLCELLULOSE SUSPENDING AGENT Shearing Stress Rate of Conc. Oil (% v/v) Shear ______________ Sec-1 54.2 48.7 43.3 37.9 32.4 27.0 21.6 16.2 10.8 129 0.73 0.63 0.42 0.35 0.27 0.28 0.23 0.20 0.20 258 1.16 1.05 o.68 0.59 o.46 o.48 0.38 0.34 o.35 387 1.52 1.42 0.98 0.82 o.64 o.66 0.52 0.48 0.49 516 1.87 1.80;.24 1.04 0.82 o.85 0.70 0.62 o.62 646 2.20 2.15 1.47 1.26 0.99 1.o4 0.85 0.74 0.75 775 2.51 2.47 1.70 1.48 1.17 1.21 1.00 0.87 0.88 904 2.80 2.80 1.95 1.69 1.34 1.4o 1.15 1.03 1.02 1033 3.10 3.12 2.18 1.89 1.51 1.57 1.32 1.16 1.15 0 1162 3.38 3.42 2.38 2.09 1.68 1.77 1.47 1.28 1.28 1291 3.67 3.73 2.62 2.30 1.87 1.93 1.6 1 1.42 1.41 1420 3.92 4.03 2.85 2.50 2.03 2.10 1.75 1.54 1.54 1549 4.18 4.33 3.07 2.68 2.20 2.27 1.92 1.68 1.68 1679 4.45 4.61 3.31 2.88 2.37 2.45 2.05 1.82 1.80 1808 4.70 4.89 3-52 3.08 2.53 2.62 2.20 1.95 1.93 1937 4.95 5.17 3.75 3.28 2.70 2.77 2.35 2.07 2.06 2060 5.19 5.46 3.95 3.48 2.87 2.96 2.50 2.19 2.18 2195 5.45 5.75 4.17 3.68 3.05 3.13 2.65 2.33 2.32 2324 5.69 6.00 4.37 3.86 3.21 3.30 2.78 2.45 2.44 2453 5.93 6.30 4.58 4.05 3.37 3.48 2.93 2.57 2.57 Stress Conversion Factor -- Dyne - cm.2 104.3 I 78.0o 78.3 | 78.8 I 70.0o 64.8 o 64.2 I 63.7 I 55.9 1

TABLE 30 FLOW DATA FOR SODIUM CARBOXYMETHYLCELLULOSE SOLUTIONS CORRESPONDING TO EMULSIONS OF SERIES III Shearing Stress Rate of Conc. Sodium Carboxymethyl Cellulose (% w/W) Shear Sec. 1.687 1.476 1.265 1.153 0.984 0.769 0.562 0.281 129 0.62 0.70 -5747 0.52 0.35 0.52 0.22 0.18 258 1.07 1.25 0.84 0.94 0.66 0.85 0.39 0.30 387 1.45 1.75 1.17 1.32 0.95 1.13 0.57 0.42 516 1.80 2.13 1.46 1.65 1.21 1.45 0.73 0.54 646 2.12 2.52 1.76 1.98 1.46 1.70 0.89 0.65 775 2.40 2.88 2.04 2.27 1.73 1.95 1.05 0.76 904 2.67 3.25 2.28 2.56 1.95 2.20 1.20 0.87 H 1033 2.94 3.57 2.50 2.83 2.17 2.43 1.35 0.98 ~ 1162 3.19 3.90 2.75 3.12 2.42 2.65 1.49 1.09 1291 3.43 4.22 2.97 3.37 2.62 2.88 1.62 1.20 1420 3.64 4.48 3.19 3.62 2.84 3.11 1.77 1.30 1549 3.85 4.75 3.40 3.87 3.03 3.32 1.90 1.41 1679 4.05 5.02 3.60 4.1o 3.23 3.53 2.05 1.51 18o8 4.25 5.27 3.77 4.37 3.42 3.75 2.19 1.62 1937 4.44 5.52 3.99 4.52 3.61 3.94 2.32 1.71 2060 4.63 5.77 4.18 4.75 3.80 4.15 2.44 1.82 2195 4.82 6.o0 4.36 4.95 3.98 4.34 2.57 1.92 2324 5.00 6.25 4.53 5.17 4.15 4.55 2.70 2.02 2453 5.17 6.49 4.72 5.38 1 4.32 1 4.75 2.84 2.12 Stress Conversion Factor -- Dyne - cm72 235.8 142.0 6.7 124.9 113.9 80.3 88.1 5.7

TABLE 31 FLOW DATA FOR EMULSIONS OF SERIES III WITH 1.687% SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT ~~~~~~_____ ~~~~___________________Shearing Stress Rate of Cone. Oil (% v/v) Shear Sec. 54.2 48.7 43.3 37.9 32.4 27.0 21.6 16.2 10.8 129 1.30 1.23 1.45 1.50 1.32 1.13 1.00 0.89 0.73 258 2.32 1.82 2.20 2.30 2.00 1.75 1.57 1.42 1.20 387 2.93 2.33 2.78 3.00 2.66 2.27 2.08 1.85 1.62 516 3.48 2.80 3.37 3.55 3.15 2.75 2.52 2.26 1.98 646 3.96 3.23 3.86 4.12 3.67 3.21 2.95 2.65 2.32 775 4.44 3.60 4.33 4.63 4.12 3.65 3.35 3.00 2.65 904 4.84 3.98 4.75 5.14 4.58 4.03 3.72 3.35 2.95 1033 5.26 4.32 5.18 5.60 4.98 4.41 4.06 3.67 3.24 1162 5.66 4.65 5.59 6.05 5.39 4.75 4.40 3.98 3.52 1291 6.03 4.97 5.98 6.49 5.76 5.10 4.70 4.26 3.75 1420 6.40 5.28 6.35 6.90 6.15 5.42 5.00 4.52 4.02 1549 6.75 5.58 6.71 7.30 6.50 5.75 5.28 4.80 4.27 1679 7.10 5.89 7.05 7.68 6.85 6.05 5.57 5.06 4.48 1808 7.43 6.15 7.39 8.05 7.17 6.35 5.84 5.29 4.71 1937 7.74 6.42 7.71 8.40 7.50 6.64 6.11 5.54 4.92 2060 8.07 6.70 8.04 8.75 7.82 6.92 6.37 5.77 5.14 2195 8.37 6.97 8.35 9.07 8.10 7.20 6.62 6.00 5.34 2324 8.66 7.21 8.64 9.40 8.40 7.47 6.88 6.24 5.57 2453 8.97 7.47 8.95 9.72 8.69 7.74 7.12 6.48 575 Stress Conversion Factor -- Dyne - cm. 378.4 388.9 298.8 227.7 230.2 232.3 234.2 235.2 232.

TABLE 32 FLOW DATA FOR EMULSIONS OF SERIES III WITH 1.476% SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT SHEARING STRESS Rate of Cone. Oil (% v/v) Shear Sec:1_ 54.2 48.7 37.9 32.4 27.0 21.6 16.2 10.8 129 1.83 1.50 1.27 0.98 0.76 1.23 1.04 0.90 258 2.76 2.22 1.88 1.49 1.18 1.93 1.67 1.52 387 3.50 2.78 2.44 1.87 1.52 2.50 2.20 2.02 516 4.16 3.40 2.91 2.26 1.88 3.00 2.69 2.50 646 4.82 3.92 3.40 2.65 2.20 3.55 3.15 2.94 775 5.37 4.40 3.82 3.00 2.48 4.04 3.60 3.5 go904 5.97 4.87 4.23 3.32 2.75 4.49 4.o01 3.75 1033 6.47 5.31 4.60 3.66 3.02 4.93 4.40 4.12 1162 6.98 5.70 4.98 3.96 3.27 5.33 4.78 4.47 1291 7.48 6.12 5.32 4.25 3.54 5.75 5.14 4.81 1420 7.93 6.50 5.69 4.53 3.78 6.13 5.49 5.14 1549 8.39 6.90 6.oo00 4.81 4.01 6.50 5.84 5.46 1679 8.84 7.26 6.34 5.07 4.24 6.87 6.16 5.77 1808 9.24 7.62 6.66 5.33 4.44 7.21 6.47 6.08 1937 9.69 7.97 6.97 5.60 4.65 7.55 6.79 6.37 2060 10.08 8.30 7.27 5.85 4.86 7.89 7.10 6.66 2195 10.49 8.62 7.57 6.10 5.07 8.23 7.41 6.94 2324 10.87 8.96 7.87 6.34 5.27 8.55 7.70 7.23 2453 11.25 1 9.27 1 8.16 6.58 5.48 8.88 8.00oo 7.50 Stress Conversion Factor -- Dyne - cm72 22.1 22.1 262.1 262.9 262.9 4l6.5 142.7 144.9

TABLE 33 FLOW DATA FOR EMULSIONS OF SERIES III WITH 1.265% SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT Shearing Stress Rate of Conc. Oil (% v/v) Shear Sec.1 54.2 48.7 43.3 37.9 32.4 27.0 21.6 16.2 - 10.8 129 1.45 1.20 0.98 1.77 1.37 1.15 1.00 1.00 0.82 258 2.11 1.75 1.44 1.19 2.07 1.77 1.62 1.61 1.38 387 2.70 2.24 1.85 1.54 2.73 2.35 2.13 2.13 1.85 516 3.25 2.69 2.24 1.85 3.33 2.87 2.62 2.62 2.29 646 3.74 3.12 2.62 2.16 3.90 3.40 3.07 3.15 2.70 775 4.22 3.53 2.95 2.45 4.48 3.87 3.51 3.57 3.12 904 4.63 3.90 3.29 2.72 4.97 4.32 3.95 4.00 3.53 e 1033 5.07 4.27 3.60 3.00 5.47 4.74 4.35 4.42 3.88 1162 5.46 4.63 3.91 3.25 5.95 5.14 4.72 4.78 4.26 1291 5.88 4.95 4.22 3.50 6.42 5.56 5.12 5.17 4.60 1420 6.26 5.29 4.49 3.74 6.87 5.96 5.47 5.55 4.94 1549 6.63 5.62 4.77 3.97 7.29 6.35 5.82 5.95 5.24 1679 6.98 5.92 5.04 4.21 7.73 6.73 6.18 6.26 5-5 1808 7.33 6.24 5.30 4.44 8.16 7.12 6.51 6.60 5.91 1937 7.68 6.53 5-57 4.66 8.56 7.47 6.85 6.94 6.20 2060 8.01 6.84 5.83 4.89 8.96 7.82 7.17 7.27 6.50 2195 8.33 7.12 6.07 5.10 9.37 8.16 7.49 7.60 6.81 2324 8.67 7.41 6.32 5.31 9.75 8.52 7.79 7.92 7.11 2453 8.98 7.68 6.58 1 5.52 10.12 8.87 8.12 8.23 7.43 Stress Conversion Factor -- Dyne - cm.-2 262.2 264.6 ] 266.3 | 267.7 [ 125.0 [ 126.4 [ 123.9 [ 114.0 1 4.0

TABLE 34 FLOW DATA FOR EMULSIONS OF SERIES III WITH 1.153% SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT Shearing Stress Rate of Conc. Oil (% v/v) Shear Sec:1 |54.2 48.7 43.3 37.9 32.4 27.0 21.6 16.2 10.8 129 1.38 1.10 0.88 1.50 1.28 1.02 0.8 0.72 0.63 258 1.95 1.57 1.28 2.20 1.94 1.59 1.36 1.19 1.07 387 2.45 2.98 1.62 2.80 2.45 2.05 1.79 1.58 1.48 516 2.92 2.36 1.93 3.40 2.97 2.50 2.17 1.94 1.81 646 3.37 2.72 2.25 3.95 3.45 2.95 2.55 2.39 2.13 775 3.80 3.07 2.54 4.48 3.92 3.34 2.92 2.64 2.46 904 4.19 3.40 2.82 5.00 4.38 3.74 3.27 2.96 2.77 1033 4.56 3.73 3.10 5.46 4.81 4.15 3.62 3.28 3.7 1162 4.93 4.05 3.36 5.95 5.22 4.50 3.95 3.58 3.35 1291 5.30 4.34 3.62 6.43 5.65 4.85 4.28 3.89 3.6 1420 5.65 4.64 3.87 6.88 6.07 5.20 4.59 4.20 3.89 1549 6.00 4.93 4.12 7.34 6.46 5.57 4.88 4.45 4.17 1679 6.33 5.21 4.35 7.77 6.85 5.91 5.19 4.74 4.44 1808 6.66 5.49 4.59 8.20 7.2.2 6.25 5.49 5.00 4.70 1937 6.98 5.76 4.82 8.62 7.59 6.57 5.78 5.25 4.95 2060 7.29 6.03 5.05 9.02 7.96 6.89 6.07 5.52 5.18 2195 7.60 6.32 5.27 9.43 8.33 7.20 6.35 5.79 5.4 2324 7.96 6.57 5.50 9.85 8.68 7.50 6.63 6.05 5.68 2453 8.22 6.83 5.72 10.25 9.02 7.83 6.90 6.29 5.90 Stress Conversion Factor -- Dyne - cm.2 259.5 259.6 261.2 124.1 124.8 124.5 124.9 125.4 124.9

TABLE 35 FLOW DATA FOR EMULSIONS OF SERIES III WITH 0.984% SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT Shearing Stress Rate of Cone. Oil (% v/v) Shear Seca 54.2 48.7 43.3 37.9 32.4 27.0 21.6 10.8 129 0.83 1.43 1.41 1.27 1.03 0.89 0.70 0.52 258 1.23 2.08 2.05 1.93 1.60 1.36 1.14 0.88 387 1.55 2.68 2.68 2.52 2.07 1.80 1.52 1.22 516 1.87 3.24 3.20 3.04 2.52 2.20 1.87 1.51 646 2.17 3.77 3.70 3.58 2.98 2.62 2.23 1.80 775 2.45 4.28 4.27 4.09 3.43 2.99 2.56 2.07 904 2.72 4.77 4.77 4.58 3.82 3.36 2.88 2.38 1033 2.98 5.24 5.25 5.03 4.24 3.72 3.19 2.66 H 1162 3.24 5.71 5.72 5.49 4.60 4.07 3.50 2.92 1291 3.48 6.16 6.17 5.95 4.97 4.40 3.81 3.18 1420 3.73 6.60 6.61 6.38 5.34 4.74 4.10 3.42 1549 3.97 7.00 7.03 6.81 5.70 5.06 4.38 3.68 1679 4.19 7.42 7.46 7.21 6.06 5.37 4.65 3.92 1808 4.41 7.83 7.88 7.63 6.41 5.68 4.90 4.13 1937 4.62 8.24 8.30 8.02 6.75 5.97 5.17 4.38 2060 4.83 8.63 8.70 8.43 7.10 6.27 5.45 4.57 2195 5.05 9.01 9.08 8.81 7.41 6.57 5.70 4.81 2324 5.26 9.39 9.49 9.39 7.74 6.87 5.95 5.04 2453 5.47 9.76 9.88 9.57 8.07 1 7.17 6.22 5.24 Stress Conversion Factor -- Dyne - cm72 328.4 155.4 133.0 114.6 114. 11.0 113.3 11.3

TABLE 36 FLOW DATA FOR EMULSIONS OF SERIES III WITH 0.769% SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT Shearing Stress Rate of Cone. Oil (o v/v) Shear Sece1> 54.2 48.7.3 37.9 32.4 27.0 21.6 16.2 10.8 129 1.57 1.27 1.27 1.03 0.85.~8 0.58 0.45 0.38 258 2.24 1.77 1.79 1.49 1.26 1.04 0.90 0.76 0.85 387 2.80 2.24 2.28 1.89 1.60 1.35 1.20 1.03 1.13 516 3.34 2.68 2.73 2.26 1.93 1.64 1.47 1.25 1.45 646 3.83 3.06 3.18 2.68 2.25 1.92 1.72 1.50 1.70 775 4.32 3.49 3.62 3.03 2.57 2.20 1.96 1.72 1.95 904 4.79 3.88 4.02 3.38 2.90 2.46 2.21 1.92 2.20 1033 5.25 4.26 4.43 3.74 3.20 2.74 2.45 2.14 2.43 1162 5.70 4.63 4.82 4.07 3.50 3.00 2.68 2.35 2.65 1291 6.16 4.98 5.22 4.42 3.82 3.25 2.93 2.57 2.88 1420 6.58 5.36 5.61 4.74 4.10 3.52 3.17 2.77 3.11 1549 7.00 5.73 6.00 5.05 4.38 3.77 3.39 2.98 3.32 1679 7.41 6.07 6.38 5.38 4.67 4.02 3.62 3.18 3.53 1808 7.83 6.42 6.75 5.72 4.93 4.27 3.84 3.37 3.75 1937 8.20 6.72 7.12 6.02 5.20 4.48 4.05 3.57 3.94 2060 8.60 7.09 7.47 6.34 5.48 4.73 4.27 3.78 4.15 2195 9.00 7.43 7.84 6.64 5.75 4.97 4.48 3.97 4.34 2324 9.38 7.75 8.18 6.95 6.02 5.18 4.68 4.15 4.55 2453 9.75 8.07 8.54 7.27 6.28 5.43 1 4.90 4.33 4.75 Stress Conversion Factor -- Dyne - cm. 139.9 139.9 109.3 109.2 109.2 108.1 10.6 106.480.3

TABLE 37 FLOW DATA FOR EMULSIONS OF SERIES III WITH 0.562% SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT ________________________ _ Shearing Stress Rate of Cone. Oil (% v/v) Shear Sec1- 54.2 48.7 43.3 37.9 32.4 27.0 21.6 16.210.8 129 0.95 0.72 0.70 0.88 0.72 0.58 0.45 0.39 0.31 258 1.39 1.07 1.15 1.29 1.05 0.89 0.75 0.64 0.52 387 1.75 1.36 1.48 1.68 1.38 1.15 0.99 0.86 0.73 516 2.12 1.66 1.80 2.05 1.72 1.43 1.22 1.o6 o.9o 646 2.48 1.95 2.12 2.42 2.03 1.70 1.46 1.27 1.07 775 2.82 2.22 2.42 2.80 2.34 1.97 1.69 1.48 1.25 go904 3.16 2.50 2.75 3.15 2.65 2.22 1.92 1.68 1.42 1033 3.48 2.77 3.04 3.50 2.95 2.50 2.15 1.88 1.59 1162 3.82 3.03 3.33 3.84 3.25 2.75 2.39 2.08 1.76 1291 4.12 3.29 3.65 4.17 3.52 3.00 2.62 2.27 1.93 1420 4.42 3.55 3.92 4.50 3.79 3.25 2.83 2.48 2.10 1549 4.71 3.79 4.23 4.82 4.08 3.48 3.06 2.67 2.26 1679 5.00 4.04 4.48 5.17 4.37 3.72 3.27 2.86 2.42 1808 5.30 4.28 4.77 5.49 4.64 3.97 3.47 3.04 2.58 oN 1937 5.58 4.50 5.03 5.80 4.92 4.20 3.68 3.22 2.74 2060 5.88 4.74 5.30 6.11 5.19 4.44 3.89 3.40 2.90 2195 6.16 4.98 5.58 6.41 5.45 4.68 4.08 3.57 3.06 2324 6.42 5.22 5.84 6.71 5.75 4.92 4.29 3.76 3.21 2453 6.70 5.55 6.12 7.00 5.98 5-14 4.50 1 3.94 3.38 Stress Conversion Factor -- Dyne - cm.2 _________ 155.2 155.9 111.6 87.4 I 87.4 87.6 88.1 87. 88.1

TABLE 38 FLOW DATA FOR EMULSIONS OF SERIES III WITH 0.281% SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT Shearing Stress Rate of Cone. Oil (% v/v) Shear Sec.1 54.2 48.7 43.3 37.9 32.4 27.0 21.6. 210.8 29.6 0.57 0.61 0.50.42 0.40 0.33 0.32 0.26: 258 0.97 0.82 0.89 0.74 0.60 0.60 0.52 0.48 0.40 387 1.25 1.07 1.14 0.96 0.78 0.80 0.68 0.64 0.55 516 1.52 1.32 1.40 1.19 0.98 0.97 0.83 0.78 0.68 646 1.79 1.55 1.66 1.42 1.17 1.17 1.00 0.93 0.80 775 2.05 1.80 1.93 1.63 1.36 1.38 1.16 1.07 0.95 904 2.29 2.02 2.18 1.85 1.56 1.57 1.33 1.22 1.07 1033 2.54 2.25 2.43 2.07 1.74 1.75 1.50 1.39 1.20 e 1162 2.79 2.48 2.69 2.28 1.92 1.94 1.65 1.53 1.34 1291 3.03 2.64 2.92 2.50 2.10 2.12 1.82 1.68 1.48 1420 3.27 2.92 3.18 2.71 2.27 2.32 1.97 1.83 1.60 1549 3.50 3.13 3.42 2.92 2.47 2.49 2.121.98 1.72 1679 3.74 3.35 3.67 3.12 2.65 2.68 2.29 2 1.85 1808 3.96 3.57 3.91 3.34 2.82 2.86 2.43 2.27 1.98 1937 4.18 3.77 4.15 3.54 3.00 3.05 2.60 2.422.10 2060 4.40 3.97 4.37 3.74 3.18 3.22 2.75 2.57 2.2 2195 4.62 4.19 4.60 3.96 3.36 3.40 2.90 2.70 2.35 2324 4.85 4.39 4.82 4.15 3.52 3.57 3.03 2.83 2.4 2453 5.07 4.60 5.07 4.35 3.69 3.75 3.19 2.97 2.57 Stress Conversion Factor -- Dyne - cm72 121.6 08.7 77.5 80.3 | 80.9 I 69.4 69.6 657 65.7

TABLE 39 FLOW DATA FOR EMULSIONS OF SERIES III WITH 0.187% CARBOPOL-934,SODIUM SALT SUSPENDING AGENT AND THE CORRESPONDING SUSPENDING AGENT SOLUTION ~~~~~~~ ~~~~~~_____________ ___ _________Shearing Stress Rate of Conc. Oil (% v/v) Shear Sec. 6t 4.2 48.7 43.3 37.9 32.4 27.0 21.6 16.2 10.8 0.0 129 1.49 1.40 0.86 0.57 0.46 o.41 0.37 0.33 0.35 0.38 258 2.06 2.00 1.29 0.93 0.76 0.64 0.57 0.52 0.54 0.58 387 2.52 2.52 1.68 1.23 0.99 0.86 0.78 0.72 0.74 0.36 516 2.92 3.00 2.02 1.51 1.26 1.07 0.98 0.87 0.88 0.92 646 3.30 3.43 2.37 1.80 1.47 1.26 1.15 1.05 1.05 1.06 775 3.66 3.84 2.70 2.05 1.70 1.47 1.32 1.22 1.20 1.22 904 4.00 4.24 3.00 2.30 1.90 1.65 1.49 1.38 1.37 1.36 1033 4.33 4.60 3.32 2.56 2.13 1.83 1.65 1.52 1.50 1.50 1162 4.63 4.97 3.60 2.82 2.33 2.00 1.82 1.67 1.65 1.62 1291 4.92 5.33 3.88 3.03 2.54 2.19 1.98 1.83 1.80 1.75 1-20 5.21 5.67 4.17 3.26 2.75 2.35 2.15 1.97 1.93 1.87 1549 5.52 6.00 4.43 3.49 2.95 2.53 2.30 2.12 2.07 2.0 1679 5.80 6.34 4.70 3.73 3.15 2.70 2.45 2.25 2.20 2.12 1808 6.07 6.67 4.97 3.93 3.34 2.88 2.62 2.39 2.33 2.24 1937 6.36 6.98 5.24 4.16 3.52 3.04 2.75 2.53 2.46 2.37 2060 6.64 7.30 5.48 4.37 3.71 3.20 2.92 2.67 2.57 2.49 2195 6.91 7.60 5.75 4.57 3.92 3.38 3.07 2.80 2.73 2.61 2324 7.17 7.88 6.00 4.80 4.08 3.52 3.18 2.93 2.84 2.74 2453 7.43 8.16 6.25 4.98 4.27 3.69 3.35 3.07 2.99 2.83 Stress Conversion Factor -- Dyne - cm72 109.8 82.3 82.3 82.3 82.3 81.4 81.2 80.5 80.3 79.3

TABLE 40 FLOW DATA FOR EMULSIONS OF SERIES III WITH 0.125% CARBOPOL-934, SODIUM SALT, SUSPENDING AGENT AND THE CORRESPONDING SUSPENDING AGENT SOLUTION Shearing Stress Rate of Conc. Oil (% v/v) Shear Sec. __ 4.2 48.7 43.3 37.9 32.4 27.0 21.6 16.2 10.8 0 129 1.o8 0.89 0.53 0.37 0.28 0.26 0.22 0.24 0.19 0.19 258 1.57 1.36 0.87 0.60 0.47 0.39 0.33 0.36 0.31 0.33 387 1.97 1.75 1.16 0.82 0.65 0.53 0.45 0.48 0.42 0.44 516 2.32 2.11 1.43 1.04 0.82 0.66 0.57 0.59 0.54 0.55 646 2.65 2.46 1.70 1.25 0.99 0.78 0.69 0.70 0.64 0.66 775 2.95 2.80 1.98 1.45 i.i6 0.92 0.78 0.82 0.74 0.76 H )04 3.24 3.10 2.23 1.65 1.31 1.04 0.90 0.92 0.83 0.87 1033 3.53 3.42 2.47 1.84 1.45 1.17 1.01 1.04 0.94 1.00 1162 3.81 3.72 2.70 2.03 1.60 1.30 1.10 1.14 1.03 1.07 1291 4.07 4.00 2.93 2.22 1.75 1.44 1.21 1.25 1.13 1.17 1420 4.34 4.29 3.15 2.38 1.90 1.57 1.31 1.34 1.22 1.27 1549 4.58 4.57 3.39 2.54 2.05 1.69 1.42 1.45 1.31 1.37 1679 4.83 4.83 3.60 2.70 2.20 1.81 1.53 1.57 1.41 1.48 1808 5.07 5.10 3.83 2.94 2.35 1.92 1.63 1.67 1.51 1.57 1937 5.32 5.38 4.04 3.11 2.50 2.05 1.75 1.77 1.58 1.67 2060 5.57 5.62 4.27 3.30 2.64 2.16 1.84 1.87 1.69 1.76 2195 5.80 5.90 4.48 3.46 2.80 2.28 1.94 1.99 1.78 1.86 2324 6.03 6.17 4.68 3.62 2.94 2.39 2.04 2.09 1.87 1.94 2453 6.28 6.42 4.89 3.81 3.10 2.52 2.14 2.18 1.97 2.06 Stress Conversion Factor -- Dyne - cm72 _98.4 71.9 72.2 72.6 72.6 70.4 70.8 60.8 60.4 53.9

120 Treatment of the Data Selection of a Flow Equation Since the Ree-Eyring equation represents a theoretical approach to non-Newtonian flow, it was decided to test it on flow data for emulsions. The equation may be written: V'L = JXn,3n sinh-1 nS l ~'n - nS v Because of the occurrence of one of the constants, g, in the inverse n hyperbolic sine function this equation is difficult to apply. The methods which have been used have involved assumptions regarding the shape of flow curves, extrapolations of curves well beyond the range of measurement and insertion of approximate values for certain of the constants. Ree and Eyring12 proposed graphical methods for evaluating n for systems requiring up to three components to describe the flow. The simplest case was that of a Newtonian system where J 1 1 and is equal to xl n1/< 1. For a system with a Newtonian and one non-Newtonian component the equation becomes: = x1 -+ x2 2 sinh- S. < 1 < 2 2S Since the last portion of the right side of the equation approaches zero at high rates of shear, it was reasoned that only the Newtonian component, called j, is measured under these conditions. Accbrdingly, Ree and Eyring obtained the value of _ by extrapolation of the curve relating

121 X and 1/S to zero value of 1/S. The flow equation was then expressed as: \ -a\- xe2p2 sinh-1 2 S )< (?t2S Following this L - was plotted vs.S to yield x2 2/ o< as the intercept on the S axis, the hyperbolic function going to 1 as S approaches zero: lim- v= x2+ 2. Having thus described the evaluation of xl /1L and x2 2/< 2, Ree and Eyring did not present a method for determining the value of P2, but it is assumed that they utilized the approximation, sinh-1 2 S _- 2n 2S2S, for high values of S. If the parameters determined in this manner reproduced the curve satisfactorily they concluded that the system had flow units belonging to these two groups only. For a system requiring three groups to describe its flow, one of the groups being Newtonian, the curve of v vs. S would rise sharply in the low range of S. The part of the experimental curve corresponding to high values of S was extrapolated to zero value of S, and the parameters for the first two components were evaluated as in the previous case. The parameters for the third component were calculated from the equation: _- x - 2 sinh-1 2S) = 3 3 sih-1 PS For a system of two non-Newtonian and no Newtonian components an approximate equation was written in terms of shearing stress: F = x1 S + x? In 2S + x2 In F2,~.. oK

122 The first right hand term was evaluated from data representing low rates of shear, and the other two terms approximated from high shear data. From these values approximate viscosities,, were calculated. 1 was then obtained from the following relationship using high values of S only: Y\1 - X xl ( 1- s1inh- l iS ) This method gave approximate values for the parameters which were judged by the fit of the equation to experimental data. Other methods for evaluation of parameters of the Ree-Eyring equation were described by Maron and Pierce17 and Maron and Sisko98o For a system requiring one Newtonian and one non-Newtonian component, the equation was written in the form: \ = a + b sinh-2S, f 2s where a is (xl1 1/< 1) and b is (x2 2/c 2)' Values of V 2 were arbitrarily selected and plots of t versus (sinh-1 2S/ S) were made. Values of 92 were adjusted until a linear graph was obtained. A similar method was used for a system with one Newtonian and two nonNewtonian components. In attempting to apply the Ree-Eyring equation to emulsions and solutions of suspending agents it was found that curves relating VL and 1/S were continuously curved throughout and that extrapolation was not reasonable. A curve of this type is illustrated in Fig. 4 -

123 1.4.. 2.... 1.0 0.8 77 7 0.6 0.4 0.2 0 1.0 2.0 3.0 4.0 5.0 I/S x 103 Fig. 4. Plot of i Versus 1/S for the Ree-Eyring Equation; 1.17* Methylcellulose Solution of Series II

124 Further, when a value of F_; was taken from the graph and t - plotted vso S, this curve was also non-linear throughout, making extrapolation difficult. Attempting the graphical method for a three-component system showed, again, that one would need to extrapolate a curved line well beyond the range of its measurement. When the method of Maron and co-workers was attempted it was found that little change in curves of _ vs. sinh-1 2S/ /2S occurred with large change in arbitrarily-selected values of 2. Thus, a wide range of 2, as much as ten- or twenty-fold, gave essentially the same slopes, and there was little basis for acceptance of any one value. From these results it was concluded that, however desirable it may be to utilize the equation of Ree and Eyring, there is yet no satisfactory method for determination of its parameters. A similar comment was made by Maron and Krieger99 who stated that although the Ree-Eyring theory looks very promising as a general flow law, the equations yielded by this theory are difficult and tedious to handle and the parameters of the equation are not always easily interpretable. Although Williamson's equation, when applied by means of least squares, fitted flow curves for methylcellulose8 and for various suspensionsl quite well, certain weaknesses of this equation were noted by Grim10. The assumption of the simple hyperbolic form for the lower portion of the flow curve, the poor fit of the assymptote, j, to the curve and the failure of the constants to change in regular fashion with increase in concentration

125 were pointed out as objectionable features. Thus, the Williamson equation was not considered the best to use for flow curves of emulsions. The Structure equation, presented by GrimO0, was evaluated by converting it to linear form: F = bo + blx1 + b2x2 where bo, b1 and b2 are f, f o, and-bvy respectively, xl is and x2 is eaS. The constant a was assigned a value of 0.001 by Grim who evaluated the other constants by least squares utilizing the square root method of Dwyer0O1, The equation was found to fit the flow data on suspensions and the constants were found to bear a simple relationship to concentration of suspended solid. Thus, the Structure equation appears to be the best equation available for the description of non-Newtonian flow curves, at least for aqueous solutions and dispersions. Accordingly, it was selected for use with the aim of correlating flow constants with the variables investigated. Computational Method With the extensive data obtained in this study, it was desirable to evaluate the constants of the Structure equation by means of an automatic computer. The IBM 704 data processing system (International Business Machines Corp.) was used for this purpose. The program, written in Fortran language, is presented in Figo 5.

126 Statement Statement No. DIMENSION A(3,4), X(50,5), B(4), AO(12), Y(50), C(50) 1 EQUIVALENCE (A,AO) 2 READ INPUT TAPE 7,3, NRUN, NDATA, PT, T 3 FORMAT (213, F4.1, F7.3) 4 DO 5 I = 112 5 AO(I) = 0. 6 DO 12 K = 1, NDATA 7 READ INPUT TAPE 7,8 (X(K,I), I = 2,4) 8 FORMAT (2F4.3, F4.2) 9 X(K,I) = 1.0 10 DO 12 I = 1,3 11 DO 12 J = 1,4 12 A(I,J) = A(I,J) + X(K,I)* X(K,J) 13 DO 19 K = 1,3 14 DO 19 I = 1,3 15 IF (I-K) 16,19,16 16 D = A(I,K) 17 DO 18 J = 1,4 18 A(I,J) = A(K,K)* A(I,J) - D* A(K,J) 19 CONTINUE 20 DO 21 I = 1,3 21 B(I) = (A(I,4)/A(I,I))* T 22 B(2) = B(2)* 0.001 23 WRITE OUTPUT TAPE 6,24, NRUN, NDATA, (B(I), I = 1,3) 24 FORMAT (1HOI3, I10, 3F15.8) 25 S = 0. 26 DO 32 K = 1, NDATA 27 Y(K) = B(1) + (B(2) (X(K,2)* 1000.)) + B(3)* X(K,3) 127 X(K,5) = X(K,4)* T 28 C(K) = (ABSF(X(K,5)-Y(K)))/X(K,5) 29 S = S + C(K) 30 WRITE OUTPUT TAPE 6, 31, K, X(K,5), Y(K), C(K) 31 FORMAT (1H, 13, 3F15.8) 32 CONTINUE 33 DEV = S/PT 34 WRITE OUTPUT TAPE 6,35, NRUN, DEV 35 FORMAT (1H, 13, F15.8) 36 GO TO 2 Figo 5. Computer Program for Evaluating Constants of the Structure Equation, Fortran Language

127 The symbols used in this program are explained below: NRUN - Identifying number of the run. NDATA - Number of data points used in the calculation. PT - NDATA written as a floating point number. T - Factor for converting stress to absolute units. X(K,2) -.00. S. X(K,3) - e-aS X(K,4) - Shearing stress in arbitrary recorded units. B(l) - The constant f. B(2) - The constant -T - * 1000. B(3) - The constant bv. X(K,5) - Observed valu- of stress, in absolute units. Y(K) - Calculated value of stress, corresponding to X(K,5). C(K) - Deviation of Y(K) from X(K,5), expressed as a fraction of X(K,5). S - Summation of C(K). DEV - Average deviation. The flow diagram of the program is shown in Fig. 6. The program writes the three simultaneous equations for the three unknowns, resulting from application of the method of least squares, in the form of matrix. Statement 5 sets all elements initially at zero. In statements 6 through 12, elements of the matrix are calculated for each set of data points, X(K,I), values of the elements being accumulated as the data are read ino Statements 13 through 19 calculate new values for the diagonal elements and those in the fourth column, while all other elements are eliminated. In Statement 21, the value of the constant is calculated from the diagonal and the corresponding element in the fourth column. The computation of the coefficients is illustrated by a simple example in which the constants B(l), B(2) and B(3) are assigned values of 0, 1 and -1 respectively:

128 START PUTCH '1 _> 2 NRUN, NDATA, P', T 1 - AOi —0 k-i YES ' V e /^\ ^ ^k N ATA NO IPUNClH k ^k+ l\ Xk 'X 2 X,,3 Xkk 2 =,YES i — 1 __ i> 3 NO / _ - {j.~_ + A *-AAij+kiXk Xkj 4 Iis <IS /> NDATA1>3 kk-k+1 NO I 1 YES J + ^ NO Aij0-Akk *Ai-D*kj "/^YS E^B^ NR, NDHATA. Bl,BB3 i NO Xk, 5-(AXk i/A T 5-/X 5 k L DEV-oP/T PUNCH R, DE, L k,X 5 Yk C k -SS+Ck Fig. 6. Flow Diagram of Program for Calculating Structure Equation Constants

129 Three simultaneous equations relating these constants may now be written in the form of a matrix, to be called the a matrix, as follows: 1 2 3 -1 3 1 0 1 2 3 0 Following the program, elements of a new matrix, to be called the c matrix, are calculated setting K at 1, I at 2 and 3, and J at 1,2,3,4. It must be noted that K cannot have the same value as I by the specification in Statement 15. According to Statement 18, the new values for the elements of the c matrix are: c21 = 1 x 3 - 3 x 1 = 0 c22 = 1 x 1 3 x 2 = -5 c23 =1 x -3 x 3 = -9 c24 = 1 x - 3 x -1 = 4 c31 =1 - 2x1 = 0 c32 = 1 x 3 - 2 x 2 = -1 c33 = 1 x 3 - x 3 = 0 c34 = 1 x - 2 x -1 = 2. Since K is not equal to I, the elements of the first row are not changed. The c matrix may then be written as: 1 2 3 -1 0 -5 -9 4 0 -1 -3 2.

130 Elements of another matrix, to be called the d matrix, are now calculated by setting K at 2, I at 1,3 and J at 1,2,3,4, as done previously. The elements of the d matrix are as follows: dll = -5 x 1 - 2 x 0 = -5 d2 = -5 x 2 - 2 x -5 = 0 d13 = -5 x 3 - 2 x -9 = 3 d14 = -5 x -1 - 2 x 4 = -3 d31 = -5 x 0 -(-1) x 0 = 0 d32 = -5 x -1 -(-1) x -5 = 0 d33 = -5 x -3 -(-1) x -9 = 6 d34 = -5 x 2 -(-1) x 4 = -6 The elements of the second row are not changed. The d matrix may then be written as follows: -5 0 3 -3 0 -5 -9 4 0 0 6 -6 Finally, elements of another matrix, to be called the e matrix, are calculated setting K at 3, I at 1,2 and J at 1,2,3-4. The elements of the e matrix are as follows: e = 6 x -5 - 3 x 0 = -30 el2 = 6 x 0 - 3 x 0 = 0 e13 =6 x 3 -3 x 6 0 e4 = 6 x -3 - x -6= 0 e21 =6 x0 - (-9) x 0 = 0 e22 =6 x -5 - (-9) x 0 = -30 e23 = 6 x -9 - (-9) x 6 = 0 e24 = 6 x 4 - (-9) x 6 = -30 ~

131 The e matrix may then be written as follows: -30 0 0 0 0 -30 0 -30 0 0 6 -6 It may be seen that the e matrix above gives the values assigned to the constants in this calculation. Multiplication of the coefficients by the conversion factor to give the constant in absolute units is carried out in Statement 21. B(2) must be decoded by a factor of 0.001, this being dohe in Statement 22. Statement 27 is used to obtain calculated values of stress and Statement 127 to obtain the corresponding observed values in absolute units. In Statement 28, the deviation from observed value is calculated as a fraction of observed value. The deviation is cumulated over all the data points, and the average deviation is obtained in Statement 33. The information obtained from the three output Statements 23, 30 and 34 includes the constants of the Structure equation, observed values of stress in absolute units and the corresponding calculated values, deviation of the calculated values from the observed expressed as fraction of the observed value, and the average deviation. Relationships of Constants of the Structure Equation to the Variables Investigated Series I Emulsions The constants of the Structure equation computed for Series I emulsions are presented in Table 41.

152 TABLE 41 STRUCTURE EQUATION CONSTANTS FOR SERIES I EMULSIONS: CETYL ALCOHOL WITH SODIUM LAURYL SULFATE EMULSIFIER; EQUILIBRIUM FLOW CURVES. Conc. Cetyl f f Alcohol I Dyne/cmr2 Poise Dyne/cm.2 Dyne/cm? % w/w_______ 5. 4 425.6 0.2803 141.9 283.7 5.0 402.9 0.2346 159.3 243.6 4.5 22.4 0.2076 142.1 82.3 4.0 257.0 0.1939 103.4 153.6 3.5 180.0 0.1622 98.3 81.3 3.0 155.2 0.1186 85.8 69.4 2.5 84.9 0.1304 33.7 51.2 2.0 106.1 0.1346 66.4 39.7 1.5 136.3 0.2560 72.6 63.7 1.0 20.9 0.1294 0 20.9

133 The only variable investigated in this group of emulsions was concentration of the dispersed phase, cetyl alcohol. A plot of the corstants, rT, bv and f versus concentration is shown in Fi.g 7o The constants did not follow concentration.n as regular marnner as might, be desired; nevertheless, it was thought worthwhile to determine whether the 102 reciprocal relationship to concentration, as found by Grim0 with suspensions, might be applicable. Reciprocal plots are shown in Figso 8-10, where it is seen that fair agreement with the reciprocal equation was obtained. The yield values, fo, for this series die not fit in terms of concentration but did in terms of log concentration, as is shown in Fig. 11. The reciprocal equation is generally expressed as follows, l/Flow Constant = k/SI - kC, where k is a constant, S' is the reciprocal of the intercept on the abscissa and C is the concentration of dispersed phaseo The values of k, k/S' and S' obtained for series I constants are shown in Table 42. TAB.LE 42 PARAMETERS OF THE RECIPROCAL EQUATION RELATING STRUCTURE EQUATION CONSTANTS TO CONCENTRATION SERIES I EMULSIONS Flow k/ Constant k/ST SI k qT^ 9.60 ol.1 1.065 bv 0.023 14.1 o324 f 0 012 15.9 0.195

134 500 e f DYNE-Cm.2 0 bvDYNE-Cm;2 400 POIS 7coXI0O, POISE cf) 1100 O 1.0 2.0 3. 4.0 5.0 6.0 ~ % W/0W I-0 0 0 1.0 2.0 3.0 4.0 5.0 6.0 CONCENTRATION OF CETYL ALCOHOL, %W/W Fig. 7. Plot of Structure Equation Constants, LO, by and f Versus Concentration of Cetyl Alcohol for EmuTsions of Series I

10 8 H 0 0 I 2 3 4 5 6 7 CONCENTRATION OF CETYL ALCOHOL, % W/W Fig. 8. Plot of l/qo Versus Concentration of Cetyl Alcohol for Emulsions of Series I

0 1 2 -18 - < 1 2G5670 0 2 3 4 57 8 CONCENTRATION OF CETYL ALCOHOL, % W/ W Fig. 9. Plot of I/bv Versus Concentration of Cetyl Alcohol for Emulsions of Series I

12.4__ _ _ _ __ _ _ _ 12.0 9.6 ^^ ~~~~~~~~~~~H if) 7.2 44 -2.4 0___________________________________ 0 I2 3 4 5 67 CONCENTRATION OF CETYL ALCOHOL, /% W/W Fig. 10. Plot of l/f Versus Concentration of Cetyl Alcohol for Emulsions of Series I

40 30 20 __-_oTo~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C I0 0 ____ ____ I0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 LOG. CONCENTRATION Fig. 11. Plot of 1/fo Versus Logarithm of Concentration of Cetyl Alcohol for Emulsions of Series I

139 Values of k/S' obtained in this or a similar manner have been proposed as the value of the reciprocal for the dispersion medium alone, but this has been questioned103. If these values were so-interpreted for series I emulsions the suspending medium, which is water, would be non-Newtonian. Thus, this interpretation of k/S' does not appear acceptable. Values of S' have been regarded as the reciprocal of the ultimate settling volume, although this has not been proven. The predicted value of sedimentation constant, 1/S', is different for each constant, although they may agree within error for this series. All of them indicate, as would be noted from the flow data, that the ultimate settling volume for cetyl alcohol particles is quite high, ranging from 11 to 16% by volume of cetyl alcohol. Considering that for rhombohedral packing the volume of solid in the sediment would be about 74%, this indicates that the cetyl alcohol particles might have an effective volume several times their actual volume. This is not unexpected for cetyl alcohol, since it has been noted that emulsions with concentrations of 10% are creams which do not flow when subjected to gravitational force. The effective-volume concept can be used for further speculation. One can calculate the limiting viscosity, Y\, representing the viscosity as S approaches zero, from the Structure equation as follows: F = f + E S - bve-aS, dF/dS = \ + abve-S, lim dF/dS = = + ab S-+O

140 These can then be used to calculate specific viscosities, sp' by the formula: Sp=!o(emul.)/ o(solv.) -1. Calculated values of L and sp for series I emulsions are shown in Table 43. A plot of InYs vs. C is commonly used to obtain intrinsic viscosity, L rl, as the slope of the line, and this type of graph is shown in Fig. 12. An intrinsic viscosity of 29.4 was obtained in this manner. The Einstein equation predicts an intrinsic viscosity of 2.5 and experimental determinations have produced values in the range of 2.0 to 2.84. The high value of 29.4 can be explained on the basis of electroviscous effect or formation of liquid sheaths about the particles. It is a common concept that emulsion particles may bear surface charges such that they repel one another and thus behave as though they were of much larger volume. The presence of immobilized liquid envelopes about the particles has also been frequently proposed27,47, and this, too, gives the particles a large effective volume. With series I emulsions the emulsifier, sodium lauryl sulfate, may be expected to be attached to the cetyl alcohol through the hydrocarbon chain and have the hydrophilic sulfate radicals extended outward into the aqueous phase. The sulfate groups would thus constitute charged hydrated layers on the particle surfaces causing large electroviscous effects. The ratio of effective to actual concentration might be estimated by dividing the volume corresponding to rhombohedral packing, 74%, by the volume concentration predicted by

141 1.8..... 0 1.7 1. 1_ 1.25 I. 0 L 1.4 1.0 I --- — -- 0 1.0 2.0 3.0 4.0 5.0 6.0 CONCENTRATION OF CETYL ALCOHOL, % W/W Fig. 12. Plot of Log gsp Versus Concentration for Series I Emulsions

142 the reciprocal plots, Fig. 8-10, to be the ultimate settling volume. The ratios obtained might then be divided into the intrinsic viscosity, 29.4, to obtain values corrected for the effective volume. Results of this treatment, shown in Table 44, show these values for intrinsic viscosity to be grouped about the Einstein constant. TABLE 43 LIMITING VISCOSITIES, Xo, FOR SERIES I EMULSIONS Conc. Cetyl 0 Sp Alcohol 0 s _%w/w _______ 0.0 0.008 0.0 1.0 0.129 15.2 1.5 0.329 40.0 2.0 0.201 24.1 2.5 0.164 19.5 3.0 0.204 24.5 3.5 0.261 31.5 4.0 0.297 36.1 4.5 0~350 42.7 5.0 0.394 48.2 5.4 0.422 51.7 TABLE 44 ESTIMATED INTRINSIC VISCOSITIES BASED ON LIQUID SHEATHS Constant Ratio Estimated Used To Effect. Intrinsic Estimate:Actual Viscosity S' Vol. 8.2 3.6 b 10.4 2.8 f 11.8 2.5

143 Series II Emulsions The constants of the Structure equation for series II emulsions are presented in Tables 45-57D Emulsions of this series contained one concentration of corn oil, 40% w/w, as the dispersed phase. Two emulsifiers were utilized, and several suspending agents in varying concentration were investigated. Different homogenization pressures were used, It was expected that variation in homogenization pressures would yield different particle size distributions and that this effect on flow properties of emulsions might be investigated. Size-measurements were made on the basic emulsions and data are presented in Table 58~ From these measurements it may be seen that no significant differences in particle size resulted from verying homogenization pressures or the use of two different emulsifiers. Further, on inspection of the: flow constants, Tables 45-57, it was concluded that no consistent changes in flow properties accompanied the change in homogenization pressure. Thus, the effect of homogenization pressure within the range of study was concluded to be negligible and subsequent treatment of flow constants utilized averages of those obtained at different homogenization pressures. A typical set of curves showing the change in constants of the Structure equation with variation of concentration of suspending agent is shown in Figures 13 and 14. Although the Structure equation constants of emulsions and solutions of suspending agents increased with increased concentration of suspending agent, no simple relationship of flow constants to concentration could

TABLE 45 STRUCTURE EQUATION CONSTANTS FOR SERIES II EMULSIONS WITHOUT SUSPENDING AGENTS. Homogenizing Pressure f Bc b f lb./in2 Dyne/cm2 Poise Dyne/cm2 Dyne/cm. Sodium Lauryl.ilfate Emulsifier 2000 39.8 0.568 17.9 21.9 2500 95.6 0.0947 42.2 47.4 3000 50.4 0.0391 26.7 23.7 4000 42.2 0.0629 19.2 23.0 Span-Tween Emulsifier 1000 6.0 0.0517 4.9 1.1 2000 6.2 0.0546 3.0 3.1 3000 9.9 0.0574 6.2 3.7 4000 9.5 0.562 5.3 4.2 5000 10.0 0.0565 5.4 4.6

145 1500..... 1300 1100 / / z / %W / z / zI/ / 0 ) / U~~/ u/ 500 / r / I 00 300 I 00 0 0.2 0.4 0.6 0.8 1.0 CONCENTRATION OF SUSPENDING AGENT IN AQUEOUS PHASE %W/W Fig. 13. Plot of Structure Equation Constants f and bv Versus Concentration of Suspending Agent for Series II Emulsions with Sodium Alginate Suspending Agent, Sodium Lauryl Sulfate Emulsifier

146 0.6 0.5 w.. M 0.2 0.1 0 0.2 0.4 0.6 0.8 1.0 1.2 CONCENTRATION OF SODIUM ALGINATE IN AQUEOUS PHASE,%W/W Fig. 14. Plot of Structure Equation Constant iq Versus Concentration of Suspending Agent for Series II EmuTsions with Sodium Lauryl Sulfate Emulsifier, Sodium Alginate Suspending Agent

147 TABLE 46 STRUCTURE EQUATION CONSTANTS FOR SOLUTIONS OF SUSPENDING AGENTS CORRESPONDING TO EMULSIONS OF SERIES II WITH SODIUM LAURYL SULFATE EMULSIFIER. Cone. Suspending f by fo Agent % w/w Dyne/cmy Poise D yne/cm. Sodiumi Alginate 1.02 853,4 0.1471 737.8 115.6 0.87 593.3 0.1403 528.9 64.5 0.72 425.9 0.1173 400.0 25.9 0.57 201.6 0.1166 188.8 12.8 0.42 80.5 0.0869 79.3 1.2 Tragacanth 1.01 402.7 0.0650 268.3 134.4 0.85 348.9 0.0601 253.7 95.2 0.71 249.5.0591 1183.6 65.9 0.56 171.2.0494 139.2 32.0 0.41 71.0.0450 58.9 12.2 Sodium Carboxymethyl Cellulose Type 7MP 2.07 866.2 0.3935 811.2 55.1 1.76 515.5 0.3196 489.8 25.7 1.46 246.5 0.2304 2 36.0 10.5 1.14 112.7 0.1675 107.0 5.6 0.84 42.2 0.1144 39.8 2,4 Acacia 19.95 71.5 0.3191 67.4 4.1 17.02 - - 0.3478 14.81 -- 0.2074 11.35 ---- 0.1156 8.16 _ 0.0698

148 TABLE 47 STRUCTURE EQUATION CONSTANTS FOR SERIES II EMULSIONS WITH SODIUM LAURYL SULFATE EMULSIFIER, ACACIA SUSPENDING AGENT. Cone. Suspending Agent in Aqueous f bv 2 o 2 Phase % w/w Pse Dynec/cm/ Dyne/m. Hom. Press. 2000 1b./in2 19.95 1442.8 1.1205 1015.7 427.2 17.02 579.7 0.7945 361.1 218.5 14.81 343.6 0.5760 233.6 110.0 11.35 172.2 0.3619 79.4 92.9 8.16 160.3 0.2041 55.8 104.5 Horn. Press 2500 lb./in? 19.95 2182.1 1.2409 1479.5 702.5 17.02 806.3 0.4456 410.1 396.2 14.81 568.1 0.7168 369.3 198.8 11.35 270.4 0.4359 141.8 128.6 8.16, 186.3 0.1867 69.6 11 6.7 Hor. Press. 3000 lb./in? 19.95 2316.5 1.2022 1599.9 716.6 17,02 985.8 0.8605 661.3 324.5 14,81 522.0 0.6430 349.0 173.1 11.35 301.3 0.3773 151.4 149.9 8.16 _ i 245.6 0.2213 109.7 135.9_ Horn. Press. 4000 ib./in? 19.95 2223.3 1.1805 1376.7 846.6 17.02 986.5 0.8343 621.1 365.4 14.81 564.1 0.6135 347.5 216.5 11.35 362.2 0.3663 164.0 198.2 8.16 284.6 0.2427 120.9 163.6

149 TABLE 48 STRUCTURE EQUATION CONSTANTS FOR SERIES II EMULSIONS WITH SODIUM LAURYL SULFATE EMULSIFIER, SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT. Conc. Suspending 1 Agent in Aqueous f b f Phase % w/w Dyne/cm? poise i Dyne/cm. Dyne/cm? Hom. Press. 2000 lb./in2 2.07 1306.6 Oo5807 893.6 413.i 1.76 990.0 0.4759 663.7 326.3 1.15 464.1 0.2834 291.5 172 6 0.84 292.6 0.2231 170 8 121.8 Hom. Press. 2500 lb./in2 2.07 1395.0 0.5636 940.5 454.5 1.76 1079.6 0.4713 721.2 358.5 1.46 796.7 0.3961 509.4 287.3 1.15 519.4 0.3087 292.6 226.8 0.84 353.3 0.2046 223.8 130.1 Homr..ress. 3000 lb./in2 2.07 1455.9 0.5078 989,6 466.3 1.76 1049. 9 0.4010 700.7 349.2 1.46 883.3 0.3543 581.8 301.5 1.15 601.8 0.2820 390.4 211.4 0.84 391.8 0.2173 1 242.5 149o2 Hom. Press. 4000 lb./in? 2.07 1677.1 0.5460 1116.1 561.0 1.76 1474.7 0.4516 1064.4 410.3 1.46 3 1035.0 0.3111 705.9 329.0 1. 15 658.8 1 0O2894 409.7 249.1 0_84 434.3 1 0.2120 269.8 164,5

150 TABLE 49 STRUCTURE EQUATION CONSTANTS FOR SERIES II EMULSIONS WITH SODIUM LAURYL SULFATE EMULSIFIER, TRAGACANTH SUSPENDING AGENT. Cone. Suspending \\ Agent in Aqueous f bv f Phase w/w Dyne/cm. | Poise Dynecm Dye/cm Horn. Press. 2000 lb./in. 1.01 596.1 0.2246 339.3 256.7 0.85 508.8 0.1942 303.436 205.403 0.71 399-7 0.1637 237.1 162.6 0.56 278.4 O.1491 142.5 135.9 0.41 224.6 0.1152 143.8 80.9 Horn. Press. 2500 Ib./in? 1,01 646.1 0.2095 390.1 256.0 0.85 535.3 0.1741 319.2 216.0 0,71 449.9 0.1425 284.3 165.6 o. 56 342.8 0.1247 218.9 123.9 0.41 236.2 0.1071 157.0 79.2 Horn. Press. 3000 lb./in? 1.01 560.9 0.2270 359.5 201.3 0.85 393.6 0.1742 252.2 141.1 0.71 267.8 0.1578 208.7 59.1 0.56 233.6 0.1308 148.9 84.7 0.41 170.4 0.1045 111.8 58.7 Hom. Press. 4000 lb./in2 1.01 589.8 Oo2202 348.3 241.5 0.85 486.9 0.1867 298.9 188.0 0.71 383.5 0.1622 241.7 141.8 0.56 240.1 0.1596 116.6 123.6 0.41 196.9 0.1188 128.1 68.8

151 TABLE 50 STRUCTURE EQUATION CONSTANTS FOR SERIES II EMULSIONS WITH SODIUM LAURYL SULFATE EMULSIFIER, SODIUM ALGINATE SUSPENDING AGENT Conc. Suspending T Agent in Aqueous f f Phase % w/w Dyne/cm2 Poise Dyne/c Dyne/cm2 Hon. Press. 2000 lb./in? 1.02 1188.6 0.3313 827.3 361.3 0.87 901.4 0o2780 643~2 258.2 0.72 740.5 0.2621 522.2 218.3 0.57 329.3 0.2020 209.2 120.1 0.42 265.6 oo1716 174.6 91.0 Hom. Press. 2500 lb./in? 1.02 1310.7 0.2710 939.2 371.5 0.87 994.3 0.2615 706.6 28707 0.72 695.3 0.2316 493.0 202.3 0.57 473.9 0.1930 334.5 139.3 0.42 269.9 0.1769 169.1 100.8 Horn. Press. 3000 lb./in2 1.02 1458.0 0.2647 999.6 458.4 0.87 1070.2 0.2459 740.6 329.6 0.72 785.6 0.2099 556.2 229.4 0.57 547.8 0.1905 385.4 162,3 o 042 356.6 0.1611 244.6 112.0 Hom. Press. 4000 lb./in? 1.02 1202.8 o4100o 65 54 547o4 0.87 1165.8 0.2367 828.5 337~3 0.72 834.6 0.2122 584.2 250.4 0,57 581.7 0.1875 407o1 174.6 0o42 389.5 o,1541 273 0 116 5

152 TABLE 51 STRUCTURE EQUATION CONSTANTS FOR SUSPENDING AGENT SOLUTIONS CORRESPONDING TO EMULSIONS OF SERIES II WITH SPAN-TWEEN EMULSIFIER. Conc. Suspending f 2 f Agent % w/w Dyne/cm2 oise Dyne/cm. Dyne/cm. Methylcellulose 1500 CPS 1.661 1496.8 0.3573 1341.3 155.6 1.415 868.3 0.3117 797.6 70.7 1.168 475.9 0.2342 442.5 33.4 0.922 274.4 0.1851 257.8 16.6 0.676 79.7 0.1165 75.9 3.8 Sodium Carboxymethylcellulose Type 7MP 2.259 1408.5 0.3394 1258.1 150.3 1.924 828.5 0.2935 761.6 66.9 1.589 387.0 0.2267 357.2 29.7 1.254 208.9 0.1662 197.0 11.8 0.919 143.8 0.1382 119.1 24.7 Carbopol-934, Sodium Salt 0.334 488.2 0.1829 334.9 153.3 0.285 351.5 0.1197 298.1 53.4 0.235 200.2 0.0913 177.5 22.7 0.185 77.8 0.0701 64.2 13.6 0.136 21.8 0.0493 813.3 8.4

153 TABLE 51-Continued Conc. Suspending f bv fo Agent %o w/w, EDyne/cm.,|oise Dyne/cm2 yne/c Agent./W c M..lr-? Dyne/cm. Acacia 19.245 42.2 0.3645 49.4 16.391 ---- 0.2536 - 13.537 —. 0.1672 - 10.683 --- 0.1138 7.828 ---- 0.0769 _____ Sodium Alginate 1.034 859.9 1 0.2499 603.1 256.8 O.881 750,2 i 0.1748 625.1 12542 0.727 535,7 1 0.1435 459.8 75o9 0.574 3390 0.1267 297.4 41,6 0.421 179. 4 0.0959 I 158.2 21.1 Tragacanth 1.163 566.8 0.1052 371.6 195.2 0.991 462.1 0.0951 319.3 142.8 0.818 326.9 0.0861 229.5 97. 4 O.646 229.8 o.o0656 170.9 58.9 0.473 127.7 0* 0635 99~ 4 28.3

154 TABLE 52 STRUCTURE EQUATION CONSTANTS FOR SERIES II EMULSIONS WITH SPAN-TWEEN EMULSIFIER, SODIUM ALGINATE SUSPENDING AGENT. Conc. Suspending T Agent in Aqueous f b Phase % w/w Dyne/cm Poise Dy e/cm Hom. Press. 1000 lb./in2 1.034 1523.6 0.4558 1263.7 259.9 0.881 1155.5 0.4004 966.9 188.6 0.727 773.3 0.3462 616.8 156.4 0.574 553.2 0.2860 467.4 85.8 0.421 371.8 ' 0.2319 317.0 54.9 Hom. Press. 2000 lb./in? 1.034 1550.3 0.4749 1250.8 299.5 0.881 1123.0! 0.4448 893.8 233.1 0.727 855.8 0.3722 693.8 161.9 0.574 590.6 0.3235 476.8 113.8 0.421 362.4 0.2576 290.7 71.7 Hom. Press. 3000 lb./in. 1.034 1446.7 0.4927 1132.0 314.7 0.881 1144.9 0.4233 903.4 240.9 0.727 810.0 0.4035 622.0 188.0 0.574 554.9 0.3142 431.3 123.6 0.421 394.2 0.2560 266.1 83.1 Horn. Press. 4000 lb./in? 1.034 1469.2 1 0.4636 1161.5 i 307.7 0.881 1080.9 0.4260 845.2 235.7 0.727 759.8 0.3797 584.8 1 75.1 0.574 539.0 0.3063 421.0 118.0 0.421 325.1 0.2406 251.8 73.3 Hom. Press. 5000 lb./in? 1.034 1480.5 0.4744 1156.3 324.1 0.881 i165.8 0.4040 937.3 228.5 0.727 i 795 8 0.3757 618.4 177.4 0.574 516.1 0.3204 394.9 121.2 0.421 _ 351.1 0.2425 275.0 _ 76.1

155 TABLE 53 STRUCTURE EQUATION CONSTANTS FOR SERIES II EMULSIONS WITH SPAN-TWEEN EMiLSIFIER, TRAGACANTH SUSPENDING AGENT. Conc. Suspending f.f "V Agpnt in Aqueous Dyne/cm2 Poise Dyne/cm? Dyne/cm2 Phase % w/w__ Hom. Press. 1000 lb./in2 1.163 831.8 0.2688 636.8 195.0 0.991 652.5 0.2517 513.2 139.3 0.818 466.7 0.2304 368.4 98,2 0.646 293.7 0.2018 i 338.3 54.4 0.473 497.8 0.1719 i 164.4 33,5 Hom. Press. 2000 lb./in2 1.163 691.2 0.2810 508.442 182,8 0.991 538.8 0.2464 407.4 131.5 0.818 472.2 0.2367 359*2 113.0 O.646 313.3 0.2140 242.1 71.2 0.473 1 154.8 0.1630 120.4 34.4 Horn. Press. 3000 lb./in2 1.163 632.2 0.2561 461.6 170.6 0.991 457.2 0.2322 336.0 121.2 0.818 374.6 0.2177 278.8 95.8 0.646 224.1 0.1823 166.1 57.9 0.473 115.5 0.1519 85.2 L 30.3 Horn. Press. 4000 lb./in2 1.163 596.9 0.2467 44o.6 156.2 0.991 443.3 0.2331 322.9 120.3 0.818 301.1 0.2045 229.7 71.4 o.646 163.6 01793 1 17.7 45.9 0.473 L 115.3 0.1494 85.9 29.4 Hom. Press. 5000 lb,/in. 1.163 562.0 02497 4099 152.1 0.991 i 5599 0.2152 442.8 117.1 0.818 326.3 0.2084 247.9 78.4 0.646 198.0 0.1789 147.8 50.2 0,473 94.9 0.1488 68.8 26.1

TABLE 54 STRUCTURE EQUATION CONSTANTS FOR SERIES II EMULSIONS WITH SPAN-TWEEN EMULSIFIER, ACACIA SUSPENDING AGENT. Conc. Suspending b Agent in Aqueous f bv Phase % w/w Dyne/cm2 Poise Dyne/cm? Homo Press. 1000 lb./in? 19.24 869.3 0.7854 860.8 16o39 462.6 o 0.6806 462.2 13.54 455.1 0.7149 337.3 10.68 109.7 0.3656 107.8 7.83 558.8 0.2488 56.3 Horn. Press. 2000 lb./in? 19.24 990.5 1.0475 964.1 16.39 457.4 0.8852 435.2 13.54 232.6 0.6727 216.6 10o68 112.0 0.4738 101.9 7.83 72.8L 0.3179 64.8 Hom. Press. 3000 lb./in? 19.24 1099.8 0.7844 1003.0 16.39 609.8 0.6259 550.8 13.54 263.3 0.5801 215.1 10.68 1 104.1 0.4228 68.2 7.83 60o9 O 0.2880 46.2 Hom. Press. 4000 1b./in2 19.24 843.6 0.6982 783.6 16.39 523.8 0.7598 509.4 13.54 316.4 0.3565 298.2 10.68 113.2 0.3155 84.9 7.83 60.7 0.2361 10.4 Horn. Press. 5000 lb./in? 19.24 949.8 0.5933 886.8 16.39 532.3 0.4604 502.3 13.54 332.7 0.4172 320.2 10.68 198.7 0. 3181 184.0 7.83 62.1 i 0.2384 17.9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 4 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

157 TABLE 55 STR'E-TC 'RE EQUATION CONSTANTS FOR SERIES II EMULSIONS WITH SPA-N v I WEE EMULSIFIER, SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT. Cone. S tspen.ding' f b fo Agent in Aquieous Dyne/cm? Poise y Dye/cm. Dye/cm i, Phase % w/w, Horn. Press. 1000 lb./in? 22,29 2200.2 0.6527 1898.4 301.9 1.924 j 1714.0 0.6226 1478.1 235.9 1.589 1496.5 i 0.6189 1291.1 205.3 1.254 629.9 i 0.4518 535.8 94.1 _ 0.919 _ 338.6 0.3542. 266.8 70.7 Hom. Press. 2000 lb,/in2 2.259 2317.7 0.7178 1939.9 377~8 1.924 1793.6 0.6742 1499.2 294.4 1.589 i 998.2 0.561.8 823.3 174.8 1.254 594.9 o 0.4647 458.2 136.6 0.919 315.2 0.3615 221.6 93.6 Horn. Press. 3000 lb./in2 2.259, 2289.1 0.7370 1.893.6 395~ 4 1,924 1616.9; 0.6596 | 1312.3 304.6 1.589 1 1111.6 0.5590 1 890.9 220.7 0 o 919 _331.2 0.3352 231.3 99.8 Hom. Press. 4000 lb./in2 2.259 2260.6 0.7391 1846.2 414.4 1.924 1556.9 0.6776 1243.2 313.7 1.589 906.0 0.5469 712.9 193.2 1.254 512.5 0.4232 383.4 129.1 0. 9i9 287.9 0.3205 192.3 95.6 Horn. Press. 5000 lb./in2 2.259 1963.4 0o7137 1604.0 359 4 1.924 1481.3 0.6462 1218.2 263.0 1o 589 909.2 0.5357 724,4 184.9 1,254 539.8 0.4312 410.7 129.1 0.919 i 276.0 0.3306 185.2 90.8

158 TABLE 56 STRUCTURE EQUATION CONSTANTS FOR SERIES II EMULSIONS WITH SPAN-TWEEN EMULSIFIER, METHYLCELLULOSE SUSPENDING AGENT Cone. Suspending Agent in Aqueous f ~ b, f Phase % w/ww Dyne/cm?, Poise Dyne/cmn Dyne/cm2 Homo Press. 1000 lb./in. 1.661 1646o0 O 4610 1373.7 272.3 lo415 1574.0 0.4161 1331.0 243,0 1.168 899.2 0.3859 771.4 127.7 Oo922 I 527.5 0.3086 478.5 49.0 0.o676 _ 281 9 0.2356 258.0 23 9 Horn. Press, 2000 lbo/in2 1o661 1868o~ 4 0:4520 1519.8 348o6 1.415; 1309o5 0.4021 | 1120.8 188.7 1o 168 826 1 0.3613 1 686.8 139.4 0.922 488.9 0.2992 418.3 70.6 0o676 1 241.8 0.2241 210.4 31.4 Homo Press. 3000 lb./in? I1.661 1818. 3 0.4354 1483.6 334 7 141i5 1282.0 i 0.4035 1069.8 212.2 1.168 789.5 | 0.3430 664.2 125o3 0.922 456.3! 0.2980 o 381.2 752031 o0.676 228.7 0.2362 200.1 28.5 Homo P-ress. 4000 lb./in? lo 661 2050.2 o 4378 i 1668.3 381.9 1.415 13947 0.4008 1154.8 239.9 1.168 917.0 0.3499 780.6 189 4 0.922 512.6 0.2913 445.0 67.6 0.676 270.0 0.2238 234.4 35.5 Hom. Press 5000 lb /in2 1"661 1887.9 i 0.4453 1554.2 333.7 1,415 1.362 o7 j 0.3985 j 1127.0 235.7 1.168 899.2 i 0.3357 i 769.2 130.0 0o922 572.8 i 0.2800 502.5 70.2 O o 676 265. 1 i 0.2182 i 230 7 38 4

159 TABLE 57 STRUCTURE EQUATION CONSTANTS FOR SERIES II EMULSIONS WITH SPAN-TWEEN EMULSIFIER, CARBOPOL-934, SODIUM SALT, SUSPENDING AGENTo Conc. Suspending Agent in Aqueous f bv PLase % w/ PoiseDyne/cmcm Poise e/cne/cm Homo Press. 1i000 l.bo/in2 0.334 420.8 0.2584 324.7 96.0 0.285 304e7 0o2153 247.6 57.1 0.235 236.2 o1940 195.8 40o4 0.185 123.7 0 O1.461 108a3 15.4 0.136 63.1 0.1161 56ol. 7.0 Homr Press. 2000 lbo/in2 0.334 436.5 0.2620 312.6 12309 0.285 315.0 0.2199 233.3 81.7 0.235 2104 0.1725 167.8 42o7 0.185 1 422 0 518 109.2 32o9 0.136 80o1 0.1167 63.2 16.9 Horn. Press. 3000 lb./in? 0.334 450.0 0.2467 335.6 11404 0O285 299.8 0.2101 222.2 1 77.6 0.235 231.9 i 0 1801 181.4 50o6 0.185 1,52.0 Oo 1471 121.5 30 4 0.136 88.1 i 0.1184 70. 5 17.5 Homr Press. 4000 lb /in' 0.334 470.5 i 02553 340o0 130,4 0.285 343 0 I 0o2188 252.7 90.3 0.235 271.3 0.1872 12053 66.0 0.185 172. 3 i 0.1530 135.5 36.8 0.1,36 _ 102o8 0 1228 81 9 20.8 Homo Press, 5000 ib./in2 0~334 510,8 0.2597 356.7 154o0 0.285 I 371.5 I o 2153 273.4 98 1 0.235 259.5 0o1834 1 i96.9 62.6 0 o 185 164o 0 O 1499 129.1 34,8 0.136! 101.4 0.1206 i 81,.2 20.1

16o TABLE 58 PARTICLE SIZE DISTRIBUTION FOR SERIES III, BASIC EMULSIONS Particle Counted Particles, Stated Size Diameter Homogenizing Pressure lb/ir? Microns Sodium Lauryl Sulfate Emulsifier 2000 2500 3000 4ooo < 1.5 111 75 140 250 1.5-3 179 216 192 106 3-4.5 69 61 81 38 7.5-6 32 19 23 28 6-7.5 15 7 2 4 Span-Tween Emulsifier 1000 2000 3000 4000 5000 < 1.5 233 288 306 266 336 1.5-3 205 165 165 175 172 3-4.5 22 9 6 7 2 7.5-6 8 3 2 1 1 6-7.5 - - - 3 2

161 be found. Reciprocal plots, semi-logarithmic and logarithmic plots were generally non-linearo Certain qualitative comparisons can be made, howeve.' from an examination of the tables of flow constants. The constants, b and rT, were larger with sodium lauryl sulfate emulsifier in all cases V except when carboxymethylcellulose was the suspending agent. Acacia solution alone was Newtonian, except for the highest concentration, but emulsions containing acacia were non-linear. Those with Span-Tween emulsifier showed no yield value, but those with sodium lauryl sulfate did exhibit yield values. Emulsions without suspending agents were nonlinear with rather high yield values, the yield value for the emulsion with sodium lauryl sulfate being higher than that with Span-Tween. Since the Structure equation constants could not be directly related to concentration of suspending agent, limiting viscosities, o __ were calculated as for series I. These values were then examined for quantitative relationships to concentration. The equation of Robinson(04 for suspensions of spherical particles was found to fit the data for suspending agents. This equation may be expressed as: C/f(T) = a - bC, where f(r) may be In re' 'sp or rell/ -1. An important difference was noted, however, in that the slope of the curves, when f(r) was In Trel' was positive instead of negative as generally is found with suspensions, A typical curve is shown in Figure 15. This is not surprising, since there is no reason to believe that suspending agents in solution would have effects equivalent to solid spheres. Thus, the constants of this equation cannot be interpreted in the manner used for dispersions of

162 spherical particles, and the equation must be considered. as simply a — empirical description of the data. As such it enables one to compa're the flow properties of one suspending agent with. another. The eqation. C/ln irel = a + bC, was used for sodium alginate, sodium carboxymethylc.llulos. tragacanth, and methylcellulose solutions. For acacia, the equation C/rT a - bC, was used, and none of the three functions fitted the data fo.r Carbopol-934. Values of the constants obtained are shownm in Table 59. TABLE 59 PARAMETERS OF THE EQTATION C/f(q') = a + bC FOR STSPENDING AGENTS Suspending Emulsifier Agent. Sodium Lauryl Sulfate Span-'ween a b a b Acacia 0.72 0.07 0.59 0.05 Sodium Alginate 0.08 0.51 O.06 0.55 Sodium Carboxymethylcellulose 0.20 0.24 0.20 0.24 Tragacanth 0.06 o.48 0.06 O.48 Methylcellulose.- 14 0.21 The constants, a and b, determined in this manner, can be used to compare relative viscosities of solutions of suspending agents or might be used to determine the concentration required to furnish a solution with a given relative viscosity. Relative viscosity in this case refers only to limitirg

163 1.0 O SODIUM LAURYL SULFATE EMULSIFIER * SPAN-TWEEN EMULSIFIER 0.9 0. 0.3 0.4 - 0.3 ------------------------------- 0 0.4 0.8 1.2 1.6 2.0 2.4 CONCENTRATION %/ W/W Fig. 15. Plot of C/log Trel Versus C for Suspending Agent Solutionsof Series II, Sodium Carboxymethylcellulose Suspending Agent

164 viscosities and not to flow properties at high rates of shear. The limiting viscosities of the emulsions of series II did not yield specific viscosities which followed the equations commonly used to calculate intrinsic viscosity. Values of To for the emulsion were linearly related to those for the solvent (solution of suspending agent) by the equation: %o(emul.) = A + B %o(solv.) where A and B are constants. Values of these constants are shown in Table 60. From them it can be seen that the addition of oil to the emulsifiersuspending agent solution caused a greater increase in limiting viscosity in some cases than in others. The change was greatest for acacia as the suspending agent and, in most cases, for Span-Tween as the emulsifier. TABLE 60 PARAMETERS OF THE EQUATION no(emul) = A + Bno(solv) FOR SERIES II EMULSIONS.~Suspending,Emulsifier Suspending _ Agent Sodium Lauryl Sulfate Span-Tween Mixture A B A B Tragacanth 0.13 1.12 0.25 o.96 Acacia 0.11 3.73 0.02 4.35 Sodium Algimate 0.19 1.23 0.15 1.45 Sodium Carbomethylcellulose 0.33 0.93 0.19 1.79 Methylcellulose 0.25 1.20 Carbopol-934 Sodium Salt 01- 4 0.78

165 Sedimentation of Series II Emulsions It was decided to measure ultimate settling volumes of the emulsions of series II in order to see if flow constants might be related to degree of sedimentation. Samples of each emulsion were placed in 100l-ml graduated cylinders with glass stoppers and allowed to stand at room temperatureo The volume of the sedimented disperse phase was measured at intervals of about one week until no further sedimentation was noted. These observations were continued over a period of six months, at which time all samples showing sedimentation had reached equilibriumn Some of the samples exhibited no separation during this period. Average values of relative settling volume, S', limiting viscosities, rlo and yield values, fo, are shown in Table 61l Plots of SI vs. constants of the Structure equation, vs, To and vs fo were non-linear in every case, and comparisons of the curves indicated no clear relationship of sediment volume to these constantso On the otther hand, sediment volume appeared to be a linear function of concentration of suspending agent. This indicates that the factors contributed by the suspending agent are not simply flow properties and that these unknown factors influencing sedimentation have a greater effect than viscosity or yield valueo By means of the linear plots of S' vSo concentration of suspending agent it is possible to make some comparisons as to effectiveness of d.ifferent suspending agents within the ranges of concentration studied. Acacia was quite inferior to the other suspending agents, regardless of which of the two emulsifiers was used, and it had the peculiar property of increasing

166 TABLE 61 RELATIVE SETTLING VOLUMES, LIMITING VISCOSITIES AND YIELD VALUES OF EMULSIONS AND SOLUTIONS OF SUSPENDING AGENTS, SERIES II Sodium Lauryl Sulfate Emulsifier Conc. Suspending Relative Settling f f Agent in Aqueous Volume o(emul) o(solv) (emul) (solv) Phase, % w/w S' Poise Poise Dyne-cm' Dyne-cm Tragacanth 1.01 1 0.580 0.333 171 134 0.85 2.25 0.476 0.314 126 95 0.71 2.07 0.399 0.243 91 66 0.56 2.01 0.300 0.189 36 32 0.41 1.84 0.246 0.104 31 12 Acacia 19.95 1.64 2.554 0.386 673 4 17.02 1.71 1.372 0.348 326 0 14.81 1.74 0.962 0.207 175 1 0 11 31 1.80 0.519 0.116 152 0 8.16 1.83 0.303 0.070 150 0 Sodium Alginate 1.02 2.17 1 1.170 0.885 301 116 0.87 2.16 0.985 0.669 225 64 0.72 2.10 0.768 0.517 172 26 0.57 1.93 0.527 0.305 113 13 0.42 1.82 0.381 0.166 65 1 Sodium Carboxymethylcellulose 2.07 1.534 1.205 j 370 55 1.76 - 1.223 0.809 282 26 1.46 - 0.953 0.466 196 10 1.15 2.23 0.637 0.274 i 88 6 0.84 2.06 o.441 0.154 90 2 No Suspending Agent 1 1.76 0.090 0.008 31 i 0

167 TABLE 61 (Cont'd) RELATIVE SETTLING VOLUMES, LIMITING VISCOSITIES AND YIELD VALUES OF EMULSIONS AND SOLUTIONS OF SUSPENDING AGENTS, SERIES II Span-Tween Emulsifier Conc. Suspending Relative Settling f f Agent in Aqueous Volume o(emul) o(solv) (emud) (sov)2 Phase, % w/w S' Dyne-cm Dyne-cm Tragacanth 1.16 2.20 0.'752 0.477 239 195 0.99 2.11 0.642 0.141 188 143 0.82 2.16 0.516 0.316 132 97 0.65 2.04 0.374 0.237 117 59 0.47 1.87 0.262 0.163 72 98 Acacia 19.24 1.34 1.682 0.414 0 0 16.39 1.41 1.1(4 0.273 0 0 13.54 1.53 0.826 0.171 0 0 10.68 1.56 0.489 0.114 0 0 Sodium Alginate 1.03 2.28 1.665 0.853 434 257 0.88 2.25 1.329 0.800 303 125 0.73 2.24 1.003 0.603 225 76 0.57 2.24 0.748 0.424 149 42 0.42 2.23 0.526 0.254 105 21 Sodium Carboxymethylcellulose 2.26 2.20 2.549 1.598 474 150 1.92 2.16 2.006 1.055 339 77 1.59 2.06 1.453 o.584 306 30 1.25 1.87 0.890 0.363 215 12 0.92 1.85 0.560 0.257 263 25 Methylcellulose 1.66, 2.18 1.966 1.699 334 156 1.41 2.19 1.565 1.109 224 71 1.17 2.20 1.090 0.676 132 33 0.92 2.12 0.741 o.443 67 17 0.68 2.11 0.454 0.192 31 4 Carbopol-934, Sodium Salt 0.33 - 0.591 0.518 124 153 0.28 - 0.462 0.418 81 53 0.23 2.28 0.534i-6 0.269 53 23 0.18 2.24 0.270 0.134 30 14 0.14 2.06 0.190 0.063 16 8 No Suspendinjg Agent 2.10 0.060 o 0.008 3 0

168 the degree of sedimentation with increasing concentration. All other suspending agents decreased the degree of sedimentation with increasing concentration. Tragacanth and carboxymethylcellulose gave lower values of S' with Span-Theen than with sodium lauryl sulfate emulsifier; sodium alginate gave lower values with sodium lauryl sulfate. With Span-Tween emulsifier the suspending agents may be ranked as follows: Carbopol > Sodium alginate > tragacanth = methylcellulose > carboxymethylcellulose > acacia. With sodium. lauryl sulfate emulsifier the ranking is: tragacanth > sodium alginate > carboxymethylcellulose > acacia. With no suspending agent Span-Tween gave higher values of S' than sodium lauryl sulfate. Series III Emulsions Emulsions of series III were prepared and measured with the aim of obtaining more detail as to effects of concentration of suspending agent and disperse phase on flow properties of emulsions. For this purpose eight levels of sodium carboxymethylcellulose, eight of methylcellulose and two of Carbopol were used with seven to nine different concentrations of oil at each level of suspending agent. Only one emulsifier, Span-Tween, was usedo Structure equation constants for series III emulsions are presented in Tables 63-71. Constants for the solutions of suspending agents are in Table 62. Structure equation constants for suspending agents did not follow the reciprocal relationship found by Grim(l0) for suspensions, but the values of 7i-el computed from b, and r did fit the equation used for the

169 TABLE 62 STRUCTURE EQUATION CONSTANTS FOR SUSPENDING AGENT SOLUTIONS CORRESPONDING TO EMULSIONS OF SERIES III. Suspending Agent % w/w Dyne/cm Poise Dyne/cm2 Dyne/cm2 Methylcellulose 1500 CPS 1.3367 918.5 0.2433 837o1 81.4 1.1696 580.4 0.2156 540.1 133.2 1.0025 361.5 0.1846 341.9 19 6 0.7797 111.7 0.1526 98.8 12.8 0.651 100.7 0.1131 99.2 1.46 0.543 36.6 0.0904 30.9 5.8 0.434 19.5 0.0652 14.9 4o5 0.326 I 6.6 0.0392 3.2 3.4 Sodium Carboxymethylcellulose Type 7MP 1.687 638.6 0.2559 588.4 280 4 1.476 433.2 0.2120 404.1 29.1 1.265 1 282.7 0.1757 266.1 16.6 1.153 267.8 0.1752 253.8 14,0 0.984 155.2 0.1433 152.2 3o0 0.769 114.6 0.1119 97.7 16.9 0.562 47.7 i 0.0838 44.7 3.0 0.281 18.1 0.0500 14.6 3.6 Carbopol-934, Sodium Salt 0.181 70.0 0.0649 52.9 17.1 0.125 17.8 0.0344 13.6 4,3

170 TABLE 65 STRUCTURE EQUATION CONSTANTS FOR SERIES III EMULSIONS WITH 1.337% AND 1.170O METHYLCELLULOSE SUSPENDING AGENT. Conc. Oil f b fo v/v De/ Poise Dne/cm? Dyne/cm Poise 1.337 % w/w Suspending Agent in Aqueous Phase 54.2 1602.4 0.4056 1253.8 348.5 48.7 1517.2 0.3914 1224.6 292.5 43.3 1422.2 0.3737 1182.6 239.6 37.9 1328.0 0.3434 1135.6 192.4 32.4 1255.0 0.3269 1096.8 158.2 27.0 1187.8 0.3253 1045.4 142.4 16.2 983.1 0.2942 883.3 99.8 10,8 979.4 0.2768 886.2 93.2 1,170 % w/w Suspending Agent in Aqueous Phase 54.2 1257.1 0.3892 981.2 275.9 48.7 1145.1 0.3513 949.9 195.2 43.3 1041.3 0.3347 840.3 151.1 37.9 936.1 0.3266 814.9 121.2 32.4 872.2 0.3066 778.5 93.8 27,0 793.3 002859 717.3 76.1 21.6 718.9 0.2771 651.1 67.8 16.2 644.6 602629 588.7 56.0 10.8 637.691 0.2471 540.153 48.6

171 TABLE 64 STRUCTURE EQUATION CONSTANTS FOR SERIES III EMULSIONS WITH 1.002% AND 0.780% METHYLCELLULOSE SUSPENDING AGENTo Conc. Oil f j. b. f % v/v Dyne/cm2 Poise Dyne/cm2 Dyne/cm2 1.002 % w/w Suspending Agent in Aqueous Phase 54.2 9999 0.3539 806o7 193 2 48.7 836.3 03314 701o5 134,8 43 3 767.9 0.2878 691o2 7~ 6 37.9 669.6 0.2826 599.9 69.6 32,4 56602 0.2721 510.3 56 0 27~0 550.4 0.2532 509.3 41,l 21o6 490o2 0.2382 450,4 39~8 16.2 400.4 0.2269 372o4 27o9 10.8 387.5 0.2097 362.9 24,6 Oo780 % w/w Suspending Agent in Aqueous Phase 54.2 635 599 0.3142 514.040 121.559 48.7 540o6 0.2857 466.2 74o4 43.3 433.6 0O2561 388.1 45 5 32.4 301.9 0.2209 278,8 23o0 27.0 258.8 0o2004 241 1 17o7 21.6 202.5 0.1760 197.0 5,4 16.2 169.7 0.1940 150 o1 196

172 TABLE 65 STRUCTURE EQUATION CONSTANTS FOR SERIES III EMULSIONS WITH 0.651% AND 0.543% METHYLCELLULOSE SUSPENDING AGENT. Conc. Oil f b f o v 2. ___c___ V ______ Dyne/cm2 Poise Dyne/cm. Dyne/cm? 0.651 g w/w Suspending Agent in Aqueous Phase 54.2 513.4 0.2678 426.6, 86.8 48.7 431.6 0.2398 374.2 57.4 43.3 326.6 0,2213 292.8 33.8 37.9 262.4 0.2004 242.3 20.2 32.4 206.7 0.1864 190o6 i6.l 27.0 178.1 0.1690 166.8 11.2 21.6 149.6 0.1573 139.4 10.2 16.2 137.3 0.1503 131.3 6.0 10.8 119.8 0.1369 115.1 4.7 0O543 % w/w Suspending Agent in Aqueous Phase 54.2 363.9 0.2326 295.6 68.3 48.7 264.5 0.2072 227.1 37.3 43.3 195o7 0.1865 174.6 21.2 37~9 148.0 0.1678 132.9 15.0 32.4 112.7 0.1528 102.7 10.0 27.0 98.5 0.1361 91.7 6.8 21.6 80.6 0.1253 76.1 4.4 16.2 56.9 0.1128 54.8 2.1 10.8 45.3 0.1016 462 ___

173 TABLE 66 STRUCTURE EQUATION CONSTANTS FOR SERIES III EMULSIONS WITH 0.434% AND 0.326% METHYLCELLULOSE SUSPENDING AGENT. Cone, Oil f b f o i / o - - r - - ' P / Po2s D ne/cm o n% v/vO Dyne/cm. Poise Dyn e /cm? 0.434 % w/w Suspending Agent in Aqueous Phase 54,2 295.9 0.2041 251.8 44.1 48.7 182.3 0o1866 1580 24.3 43.3 132.7 o.1614 11,54 17.3 37.9 100o.4 0.1425 89.6 10.8 32.4 i 731 0.1264 677 5.4 27.0 46.5 0.1133 40o2 6.3 21.6 37.1 0.1008 1 32.5 46 10.8 27.4. 0800 22.5 4_9 0.326 % w/w Suspending Agent in Aqueous Phase 54.2 198.9 0.1761 161.7 37.3 48.7 119.4 0.1546 100.9 18.6 43.3 59.5 0.1239 47.5 12.0 37.9 44.5 0.1132 35~2 9.3 27.0 21.6 0.0834 16.0 5.6 21.6 14.o 0.067 10.6 3-4 16.2 12.4 0.586 9.1 3.3 _ 10.8 __ 10.2 0.0508 66.7 3.6 10o8 1012 0~0508 6~7 3.6

174 TABLE 67 STRUCTURE EQUATION CONSTANTS FOR SERIES III EMULSIONS WITH 1.687% AND 1.476% SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT. Conc. Oil f b f Cc% v/v | Dyne/cm.2 Poise Dyne/cm2 Dyne/cm? 1.687 % w/w Suspending Agent in Aqueous Phase 54.2 1863.4 0.6670 1557.2 306.2 48.7 1445.0 006331 1168.5 276.5 43.3 1350.4 0.5759 1102.1 247.7 37.9 1119.0 0o4790 39806 180.4 32.4 1001.9 0.4370 849.0 152.8 27.0 872.7 0.4016 742.5 130.1 21.6 832.6 0.3637 724.5 108. 1 16.2 744.1 0.3380 65001 94.0 10.8 652.9 0.2988 585o5 67.4 1.476 % w/w Suspending Agent in Aqueous Phase 54.2 1431.5 006571 1151.1 280.4 48c7 1149.1 0.5537 928.1 220.9 43.3 1145.0 0.5198 94006 204.8 37.9 967.5 0.5027 782.3 185.3 32.4 721.8 0.4307 583.1 13808 27.0 616.8 0.3527 519.7 97.1 21.6 566.9 0.3145 479.8 87o0 16,2 491o2 0.2791 42402 67.0 10o8! 475.5 0.2630 422.8 52o9

175 TABLE 68 STRUCTURE EQUATION CONSTANTS FOR SERIES III EMULSIONS WITH 1.265% AND 1.153% SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENTo Conc, Oil f bf bv f % v/v Dyne/cm2 Poise Dyne/cm2 Dyne/cm 1.265. w/w Suspending Agent in Aqueous Phase 54.2 1045.4 0o5614 825.7 219.7 48.7 839.5 0.5091 659 1 180o4 43.3 691.5 0O4500 550.9 140.6 37.9 557.0 0.3902 444.9 112.0 32.4 483.7 0.3329 402,0 81.7 27.0 411.2 0.3004 342.5 68 7 21.6 378.0 0,2667 323.0 54.9 16o2 25600 0.2475 308.9 47.6 10.8 293o0 0.2330 258.0 35o9 1.153 % w/w Suspending Agent in Aqueous Phase 54.2 837.3 0.5496 615 2 222.1 48.7 640.8 0.4772 465o4 175.5 43.3 530.6 04058 394.9 13507 37.9 432.1 0.3532 327.1 105o0 32.4 379 5 0.3148 290ol 89.4 27.0 322,2 0,2749 257~2 64o7 21.6 280o0 0.2453 227.8 52.2 16.2 261o6 0.2226 223.5 38.0 10.8 245.3 0.2082 215.3 30.1

176 TABLE 69 STRUCTURE EQUATION CONSTANTS FOR SERIES III EMULSIONS WITH 0.984% AND 0.769% SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT. Cone. Oil f 1 bv fo % V/v Dyne/cm2 Poise Dyne/cm2 Dyne/cm2 0.984 % w/w Suspending Agent in Aqueous Phase 54.2 680.1 0.4723 523.9 156,2 48.7 533.6 0o4157 412.5 121.1 43.3 434.7 0.3697 332.9 102.7 37.9 340.7 0.3199 263.8 77.7 32.4 291.1 0.2641 233.0 58.1 27.0 253.5 0.2364 207.1 46.3 21.6 216.5 0.2052 184.0 32.4 10.8 174.1 0.1793 156.6 17.5 0.769 % w/w Suspending Agent in Aqueous Phase 54.2 455.0 0.3820 316.3 138.8 48.7 327.8 0.3347 216.3 111.5 43.3 250.6 0.2842 166.7 83.9 37.9 203.5 0.2448 136.7 66.8 32.4 171.8 0.2138 119.3 52.4 27.0 142.7 0.1846 103.2 39.4 21.6 125.1 0.1652 93.6 31.5 16.2 105.7. 01478 83.2 22.5 10.O8, 96. 7 0.1337 8200 14.7

177 TABLE 70 STRUCTURE EQUATION CONSTANTS FOR SERIES III EMULSIONS WITH 0.562% AND 0.281% SODIUM CARBOXYMETHYLCELLULOSE SUSPENDING AGENT. Cone. Oil f b bv! f % v/v Dyne/cm2 Poise Dyne/cm. Dyne/cm2 0.562 % w/w Suspending Agent in Aqueous Phase 54.2 294.5 0.3113 210.5 | 83.9 48.7 195.8 0.2729 131.6 64.1 43.3 154.9 0.2187 113.6 41.3 37.9 134.6 0.1988 95.6 39.0 32,4 104,6 0.1733 o 73.8 30.9 27.0 78.9 0.1536 i 54.3 24,6 21.6 70.3 0.1348 1 53.5 16.8 16.2 59.5 0.1182 i 45.5 14.0 10.8 45.9 0.1035 34.8 11.1 0.281 9 w/w Suspending Agent in Aqueous Phase 54.2 1 139.8 0.1975 95.5 44.3 48.7 88.4 0.1699 55.3 33o1 43.3 58.9 0.1376 34.2 24.7 37.9 47.2 0.1244 26.2 20.9 32.4 34.8 0.1085 18.4 16.4 27.0 29.6 0.0948 16.5 13.1 21.6 26.4 0.080.61506 10.8 16.2 18.5 0.0728 7,9 10.6 10.8 21.3 0.0612 14.0 703

178 TABLE 71 STRUCTURE EQUATION CONSTANTS FOR SERIES III EMULSIONS WITH 0.187% AND 0.125% CARBOPOL-934, SODIUM SALT, SUSPENDING AGENT. Conc. Oil f b f~ Conc. v/vi Dyne/cm2 Poise Dyne/cmo2 Dyne/cm2 0.187 % w/w Suspending Agent in Aqueous Phase 54.2 36301 0.1920 244.1 119.0 48,7 284.9 0.1651 212,1 72,8 43.3 168.7 0,1450 130.4 38.3 37-9 120.4 0.1217 99.1 21.2 32.4 85o7 0.1107 68.8 16o9 27.0 68.3 0o0964 53.0 15.3 21.6 62.5 0.0871 49.2 13.3 16.2 59.9 0.0779 49.1 10o9 10.8 62.4 0.0736 49.6 13.5 0.125 b w/w Suspending Agent in Aqueous Phase 54.2 252.3 0.1544 180.1 72.1 48.7 155.4 0.1284 119.1 36,3 4303 93.2 0o1085 76.8 16.4 37-9 51.9 0o0930 41,3 10.6 32.4 33.2 0.0747 24.8 8.4 27,0 22.6 0.0637 j 14.9 706 21.6 18.6 0.0547 11.4 7~1 16,2 16.9 0.0477 9.4 7o5 10o8 19.4 0.0408 14.4 5.0

179 suspending agents of series II; i.e., C/ln rel- = a + bC, and the constants obtained are shown below: Suspending Agent a b Methylcellulose 0o14.21 Carboxymethylcellulose.123 0.29 These values agree reasonably well with those from series II. The Structure equation constants for the emulsions of series III did not follow a simple relationship to concentration of oil, but a polynomial with three terms adequately described the change in reciprocals of the flow constants with change in oil concentration for all but the emulsion containing Carbopol. l/Constant = bo + b10 + b22. Coefficients of this equation were evaluated by least squares using the IBM 704 computer and a program quite similar to the one previously described. Values obtained for the coefficients are given in Table 72~ These coefficients were found to be related logarithmically to concentration of suspending agent: log bi = a + P log c, where i is 0, 1, or 2, c is the concentration by weight of suspending agent in the aqueous phase, a and P are constants. Thus, with the two equations the flow constants for emulsions with any oil concentration and any suspending agent concentration can be calculated. Values of a and P are in Table 735 Emulsions with Carbopol exhibited a peculiar property; these with Low concentrations of oil were less viscous than the suspending agent alone. This was though to be due to concentration of the salf at the interface,

TABLE 72 PARAMETERS OF THE EQUATION 1/Constant = bo + b0 + b202 FOR EMIULSIONS OF SERIES III Suspending Agent Methylcellulose Sodium Carboxymethylcellulose Cone. Suspending Structure Cone. Suspending Structure Agent in Aqueous Equation Polynomial Constant Agent in Aqueous Equation Polynomial Constant Phase, % w/w Constant Phase, % w/w Constant f bcx105 -b1x1O5 b2x103 f bcx105 -blxlO0 b2x105 1.33557 1.189 1.415 0.676 1.687 1.787 2.716 0.819 1.170 2.206 5.520 19.57 1.476 2.654 4.585 1.445 1.002 5.193 5.588 29.45 1.265 3.979 6.450 1.574 0.780 12.49 6.700 49.74 1.153 4.850 6.18 -1.100 0.651 10.48 20.26 77.77 0.984 7.081 1.5- 5.890 0.543 31.18 99.59 88.66 0.769 13.04 2 8 9.010 0.454 55.43 149.5 107.3 0.562 28.81 78.6 59.29 0.556 143.3 48.4 334.1 0.281 6.60 111.4 9.-78 1.557 bv 1.514 1.588 1.106 1.687 b 1.925 2.262 -0.084 1.170 1.943 2.209 0.859 1.476 2.845 5.555 -0.260 1.002 5.427 6.1o6 5.872 1.265 4.361 5.634 -0.541 0.780 9.760 6.655 6.970 1.153 5.075 2.444 -7.4oo00 0.651 10.80 19.98 7.500 0.984 7.555 8.400 -5.280 0.543 50.16 89.17 74.43 0.769 15.95 11.75 -15.17 0.454 65.12 200.5 161.4 0.562 36.56 90.27 60.20 0.526 222.3 765.5 678.6 0.281 112.1 155.4 75.50 00 bo -bl b2 bo -bl b2 1.33557 5.894 2.93355 0.495 1.687 3.954 6.259 5.001 1.170 4.670 5.225 2.747 1.476 4.896 9.767 6.589 1.002 5.219 4.857 0.950 1.265 5.160 7.558 1.787 0.780 7.499 8.905 2.854 1.153 5.766 8.555 2.210 0.651 8.245 9.4o4 2.018 0.984 6.765 10.26 2.748 0.543 11.759 19.567 o10.458 1 0.769 9.179 16.159 7.287 0.454 15.585 28.806 17.526 0.562 11.968 25.722 4.11ii5 0.526 25.922 62.711 47.144 0.281 20.479 44.110 29.577

181 TABLE 73 PARAMETERS OF THE EQUATION log bi = a + P log C RELATING CONSTANTS OF THE POLYNOMIAL EQUATIOT TO CONCENTRATION OF SUSPENDING AGENT Structure Suspending Polynomial Equation. Agent Constant Constant Methyl- f bo -2.485 -.3877 cellulose -b1 -2.485 -53343 1b2 -1.750 -2.567 To1 bo 0.743 -1.213 b2 0.095 -3.190 bv bo -2.578 -~3870 -bl -2.278 -4.577 b2 -2.431 -4.592 Sodium f bo -2129 -0.340 Carboxy- -b1 -1.847 -0.345 methyl- b2 -2.641 -0 119 cellulose T00 bo o.838 -0o101 -bl 1.025 -0.139 b2 0.535 -0.242 bv bo -2.112 -0.267 -bi -2.050 -0225 b2 -2.590 -o.640

182 though other explanations might be proposed. Carbopol is more sensitive to added substances than most other suspending agents, being a linear polymer thought to be kept extended through charged groups along the chain, The flow constants for the emulsions containing Carbopol did not fit the same equations as did the constants for the other emulsions, and no satisfactory relationship of flow properties to concentration of Carbopol was found. Limiting viscosities were calculated for this series, and the equation previously used for series II, relating To of emulsion and solvent was found to apply to most of the emulsions. The equation, which is as follows: Qo(emul) A + B o(solv) ' fitted all of the carboxymethylcellulose data and the methylcellulose data where the concentration of oil was 27% or less. Constants of the equation are given in Table 74. TABLE 74 PARAMETERS OF THE EQUATION To(emul) = A + B o(solv) FOR SERIES III EMULSIONS Conc. Oil Suspending Agent % v/v |Sodium Carboxymethylcellulose Methylcellulose A B A B 54.2 0.17 3043 48.7 0.12 2.02 43.3 0.05 1.95 37.9 0.05 1o64 32.4 0.04 1.76 27.0 0.03 1.66 0.06 1.26 21.6 Oo02 13.0.o04 1,10 16.0 0,01 1.07 0.05 1,10 10.8 0.00 1,08 0,01 1.06

183 Limiting viscosities were used to calculate specific viscosities for series III emulsions, and from these values intrinsic viscosities were obtained by plotting log vsp/ vs. c. There are two theoretical equations for intrinsic viscosity, Einstein's, which predicts a value of 2.5 for rigid spheres, and. Taylor's, which predicts a value less than 2o5 for liquid, spheres, Taylor's equation may be expressed as follows: trel 1 + 2.5 i + 2/5lo(solv) i + 0o(solv) or, rel = 1 + 2.5 K0 where ni is the viscosity of the dispersed. phase and K is equal to (li + 2/5lo(solv))(li + lo(solv)~ Since Taylor's derivation is based on low concentrations of dispersed. phase it is commonly evaluated. in the form: Tsp = rrel - 1 2 o 5 K, [r]= lim sp/0 = 2.5 K Values of intrinsic viscosities found and calculated by Taylor's equation are presented in Table 75. From Table 75 it is seen that the observed intrinsic viscosities increased with decreased no(solv) as predicted by Taylor's equation but the observed values were, in all cases but one, smaller than predicted. Deviations from Taylor's equation have been noted before(45'105) and Oldroyd developed a mod.ified equation to account for the rigidity of the oil particle occurring due to the absorbed film of emulsifying agent. Oldroydis equation predicts a higher value than expected. from Taylor's equation, Likewise, doublet formation by the particles or othe forms of agglomeration are said to increase the value of intrinsic viscosity(l05) The two factors

184 which might explain the lowering of intrinsic viscosity are slippage at the surface of the particles and distortion of the particles TABLE 75 INTRINSIC VISCOSITIES OF SERIES III EMULSIONS OBSERVED VALUES AND VALUES CALCULATED WITH TAYLOR'S EQUATION Conc. Suspending [r] [r] Agent in Aqueous Observed Calculated Phase, % w/w Methylcellulose 1.34 0.673 1.429 1.17 0.245 1.558 1.00 0.608 1.687 0.78 0.794 1.958 0.65 1.153 2.015 0.54 1.439 2.177 0.43 1.713 2.318 0533 2.495 2.369 Sodium Carboxymethylcellulose 1.69 0.713 1 517 1.48 0.718 1.629 1.26 0 837 1.713 1.15 0.322 1.763 0.98 0.209 1o901 0.77 0o455 2.019 0.56 1.432 2.164 0.28 1.820 2.314 Carbopol-934, Sodium Salt o019 0.159 1.230 0.12 0.504 2.350 Slippage at the surface of dispersed particles might occur through shear of a thick layer of absorbed emulsifier. If such shearing took place a velocity gradient would exist between the continuous medium and the dispersed particle

185 which would have the same effect as decreasing the viscosity of the liquid. in the particle, causing the intrinsic viscosity to decrease. Deformation of the dispersed particle may occur as the size of the particle is larger and as the rate of shear is greater. Since the lowest value of shear used for numerical evaluation of flow constants was 129 sect l it seems possible that the emulsion particles might have been deformed to some extent throughout the portion of the curves used for measurement, An estimate of the distortion at 129 sec.-1 by the equation presented by Nawab and Mason 106 L-B = Garn (1 + 19p/l6) L B 2r 1 + p where L and B are the length and width of the prolate spheroid, a is the diameter of the undeformed sphere, r is the interfacial tension, G is the velocity gradient and p is o(oil)/o(solv), indicated about 2% distortion, This does not make it seem that distortion is the cause for low values of intrinsic viscosity in series III emulsions,

DISCUSSION Perhaps the most significant result of this work is the demonstration that the Structure equation can be applied to emulsions. Previously, this equation had been found to describe accurately the flow curves of about two hundred systems representing solutions of several suspending agents and suspensions of several different solids. The fact that the equation was equally applicable to about six hundred flow curves representing solutions of suspending agents and emulsions used in this study indicates its broad usefulness. Because of the lack of suitable equations for non-Newtonian flow, workers studying emulsions have carefully avoided non-Newtonian systems or have assumed linear flow at low rates of shear and used lowshear instruments for measurement. At the same time, the complexities of non-Newtonian flow have been avoided in theoretical developments so that the fundamental equations of Einstein, Taylor and Oldroyd assume Newtonian properties for the media and are limited to suspensions so dilute that no interaction between particles occurso One of the pitfalls of using low shear measurements and assuming Newtonian flow is that a material which has a yield value may not be in laminar flow at such shear rates, making the measurements erroneous. Also, it is generally found with non-Newtonian materials that no linear portion exists in the lower part of the flow curve but that instruments are frequently used which cover so narrow a range of shear that the curve appears linear in the region of measurement. As was shown in this work, use of the Structure equation enables one to describe non-Newtonian flow over a wide range of shear and, 186

187 from the flow constants, to obtain limiting viscosities which might be used to test theoretical equations and conceptsO There is yet some question as to the validity of limiting viscosities obtained from flow constants, especially in view of the:fact that yield values are commonly found in disperse systems but do not contribute to the limiting viscosity as calculated. To justify the soundness of this use of limiting viscosity it appears necessary that simplified systems be studied which will satisfy the assumptions of the theoretical equations. For example, the dispersed particles should be uniformly sized and not agglomerated, the emulsifying agent should either be one known to have no effect or one with known surface properties, and electroviscous effects should be eliminatedo Once simplified systems of this sort are shown to be predictable by theory, the effects of added factors can be evaluated systematically. Some evidence to support the use of limiting viscosities from the Structure equation was obtained in this work. Values for series I emulsions yielded estimates of intrinsic viscosity agreeing with. the Einstein factor of 2.5 when corrected for ultimate settling volumeo Similar applications of samples of Grim's data on suspensions of solids yielded intrinsic viscosities quite close to Einstein's constant except where the concentration of suspending agent was high. Test of Taylor's equation indicated agreement with the equation at low concentration of suspending agent but poor agreement at high concentration~ The reciprocal relationship of flow constants to concentration of dispersed phase was not applicable to the data on emulsions obtained

188 in this work. This is believed to be due to the effect of flow in the dispersed droplets, and some modification of the equation, similar to that used by Taylor, appears to be needed in order to predict ultimate settling volume. Also, the actual measurement of sedimentation is so crude as to make difficult any test of an equation. Refinement of laboratory methods for sedimentation is greatly needed for this purpose. The status of the rheology of emulsions was aptly described by Oldroyd(106) in a recent paper: "Naturally, the cases which the mathematician finds easiest to make detailed calculations about are so idealized... that they must always remain the most difficult on which to carry out observations. But one must admit that real emulsions and suspensions cannot be expected to have Theological properties any simpler than the idealized infinitely dilute ones amenable to theoretical analysiso"

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