I. CLASSICAL COLLOIDS THEORY OF SIZE DISTRIBUTION ; PAINTS, COALS, GREASES, ETC. ANOMALOUS VISCOSITY IN MODEL SUSPENSIONS BY G. I?. EVESON, STACEY G. WARD AND R. L. WHITMORE Received 6th April, 1951 An investigation has been made of the conditions in which the stress-strain relationship for stable suspensions of hard, discrete, non-interacting spherical particles in a Newtonian liquid is dependent upon the size distribution of the dispersed phase. Stable suspensions of spherical particles were found to behave as Newtonian fluids up to solid concentrations of a t least 20 yo by volume when the dispersed phase possessed a continuous size-distribution curve. In cir- cumstances where effects other than those due to physical interaction between particles were eliminated , stable suspensions of spherical material composed of varying proportions of two closely-sized fractions, the average diameters of which were widely different, behaved as anomalous fluids a t solid concentrations greater than 7.5 yo by volume over the range of shear rate investigated.At a given rate of shear they behaved similarly to suspensions of the large spherical particles in a liquid consisting of a suspension of the small particles. This non- Newtonian behaviour cannot at present be satisfactorily explained but i t ap- pears that the aggregate surface area and the degree of packing of the dispersed phase have no influence upon the relative viscosity. Detailed investigations of the rheological properties of suspensions have been made by’ a number of workers.Vand,l using glass spheres in an aqueous solution, and Ward and Whitmore, using methacrylate- polymer spheres in a different aqueous solution, found the viscosity to be independent of the rate of shear at all concentrations up to 45 yo by volume. Robinson, 3 however, found that with glass spheres suspended in certain dispersion media there was a tendency for the viscosity to decrease slightly with increasing shear rate. He attributed the variation to either the slow absorption of moisture by the liquid or an increase in its molecular weight due to mechanical stress at the high rates of shear employed (roo to 640 sec,-1). Broughton and Windebank * found that suspensions of glass spheres in organic liquids behaved as Newtonian liquids when the particle size exceeded about 30 microns. Below this value some anomalous behaviour was observed which they attributed to floccula- tion of the spheres in the suspending liquid.The general conclusion to be drawn from the work of these investigators and others 6,6 is that small par- ticles and organic liquids are most likely to produce anomalous effects, presumably due to flocculation effects. All workers have used spheres possessing a continuous size distribution and although it has been shown that the size ratio may affect the viscosity at a given concentrationJ2 size distribution has not been found to influence their stress-strain relationships. An investigation has now been made of conditions under which the relation- ship is dependent upon the size distribution of the suspended spheres.lVand, J . Physic. Chem., 1948, 52, 300. I&:ard and Whitmore, Brit. J , A+pl. Physics, 1950, I , 286, 326. Robinson, J . Physic. Chem., 1949, 53, 1042. Broughton and Windebank, Ind. Eng. Chem., 1938, 30, 407. Green and Weltman, Ind. Eng. Chem. (Anal.), 1943, 15, 201. Pryce-Jones, Proc. Phil. SOC. Durham, 1947, 10, 427. 11I 2 ANOMALOUS VISCOSITY Experimental Viscosities were measured in a modified Couette-type instrument designed to measure the rheological properties of fluids a t low rates oi shear. The visco- meter turntable was in the form of the frustum of a cone fitting into the base of a Perspex outer cylinder, 3-46 cm. int. diam. and 11-4 cm. deep. This material was selected in order to reduce heat transfer from the suspension to the visco- meter turntable and to facilitate the visual alignment of the inner cylinders.These were of Distrene and were hollow so that they could be loaded with suf- ficient mercury to give them a density slightly greater than that of the suspen- sion to be measured. This construction brought their centres of gravity near to their bases and simplified their vertical alignment in the viscometer. Their weights were sufficiently small for phosphor bronze galvanometer suspension wires to be used without exceeding the permissible tensile loads. Several cylinders were made to give three annular gaps and to enable the measurement of their end corrections. A full description of the viscometer, its characteristics and its calibration have been given elsewhere.' The instrument was set up in a room the air temperature of which could be controlled a t 25O f 1°C.Water from a thermostat was circulated through a jacket surrounding the outer cylinder at 25-2O C in order to maintain the sus- pension at 25' f 0-05OC. The viscometer was calibrated with each inner cylinder over a viscosity range of 1-4 to 18.6 centipoises and a shear-rate range within the limits of 0.04 and 1-2 sec.-l. The calibration liquids consisted of water-glycerol solutions the viscosities of which had been determined in N.P.L. calibrated B.S. Ostwald-tube viscometers. The suspensions consisted of methyl methacrylate polymer spheres in an aqueous lead nitrate + glycerol solution of density equal to that of the par- ticles and a viscosity of 8-5 centipoises, 0.01 yo of Dispersol OG being added to inhibit flocculation. The raw polymer powder (manufactured under the trade name of Kallodoc) was dry- and wet-sieved on B.S.screens and the finest sizes elutriated. Two closely-sized fractions, 72-100 mesh and finer than 300 mesh were then selected, the coarse fraction being also separated a t a definite density in order to remove all spheres likely to float or sink in the final suspensions. It possessed a flat-topped size-distribution curve with a ratio of largest to smallest sphere of 1.4/1 and an average sphere diameter of 182 microns. The fine sample had a similar size distribution with a ratio of largest to smallest sphere of 1.8/1 and an average sphere diameter of 38 microns. Viscosity determinations were first made on each of the samples a t intervaIs of 2-5 yo by volume up to a concentration of 20 yo.The rate of shear was varied by a t least 3/1 a t each concentration in three or four steps up to 1.0 sec.-1 at the surface of the inner cylinder. Only one inner cylinder, giving an annular gap of 2 mm. was used, since previous experimental work had shown that the measured viscosity was independent of the gap width. Six mixtures of the two samples, containing 10, 33&, 50, 66$, 90 and 95 yo by weight of the coarse material, were then prepared. Micrographs of the mix- tures containing 10 and 50 yo of coarse material are shown in Fig. I and z re- spectively. Viscosity determinations were then made on each mixture under the same conditions as for the two closely-sized samples. Results The measured viscosities were corrected for end effects in the viscometer, from the calibration curve for the particular inner cylinder used, giving the apparent viscosity, and the volume concentration adjusted to correct for the absence of sphere centres in a layer along the walls of the viscometer equal to the radius of the spheres by the method adopted by Vand.1 It was found that only the suspensions containing a single-sized fraction, and 95 % coarse fraction with 5 yo fine, behaved as Newtonian liquids over the whole range of concentration investigated.The remaining five suspensions exhibited anomalous effects, their apparent viscosities decreasing with increasing rate of shear a t all solid concentrations exceeding about 5 yo. Fig. 3 shows the variation, a t various volume concentrations, for a suspension of a mixture con- taining 10 yo of coarse and 90 yo of fine material.The rate of change of apparent viscosity with shear rate (which is a measure of the degree of anomaly present) Eveson, Ph.D. Thesis (University of Birmingham, 1950). Eveson, Whitmore and Ward, Nature, 1950, 166, 1074.FSG. I. E’lG. 2. [ T U fuce p a p 12.G. F. EVESON, S . G. WARD AND R. L. WHITMORE 13 a t any one rate of shear was almost constant, a t corresponding volume con- centrations, for mixtures containing from 35 t o 65 yo of the coarse material and rather higher for mixtures containing 10 yo and go yo of the coarse material. This is shown in Fig. 4 for a rate of shear of 0.5 sec.-l. The variation, a t one rate of shear, of the relative apparent viscosity of mixtures containing various proportions of the two closely-sized fractions is shown in Fig.5 a t various volume concentrations. FIG. 4. Discussion The experiments described above are of particular importance in that they illustrate the possibility of producing anomalies in a suspension of dispersed spheres solely through the physical interactions between the particles. By altering the size distribution of a mass of chemically identical spheres the magnitude of the viscosity anomaly can be changed at will or eliminated entirely, The properties of the suspending liquid are unimportant so long as they do not interact chemically with the spheres,I 4 ANOMALOUS VISCOSITY flocculate them, or permit electrostatic charges to develop on them (see ref.(2)). It is impossible at this stage to offer an adequate explanation of the phenomenon but the recognition that anomalous behaviour may, in some cases, be due solely to physical interactions between the suspended particles offers a new line of approach to the problem in which micro- scopic and cin6 techniques might play an important part. Fig. 5 indicates an appreciable and systematic variation in apparent viscosity with changes in the relative proportions cf coarse and fine spheres in the suspensions at a given rate of shear. This is unlikely to be due to the effect of packing amongst the spheres as the condition of closest packing (which is most likely to give a minimum viscosity) is obtained, FIG. 5. for the particular spheres employed, with I yo of fine and gg yo of coarse material. Fig. 5 shows that in fact the minimum was obtained with about equal proportions of the two sizes. There is also no doubt that the aggre- gate surface area is not a significant factor. It is possible, however, that they behaved as suspensions of the large particles in a liquid consisting of a suspension of the small particles. Calculated values based on this hypothesis are represented by the broken lines in Fig. 5 and show a marked similarity to the experimental curves. Further experiments designed to test this interesting possibility would be of considerable theoretical and practical value. The authors’ thanks are due to Mr. H. Stanley for assistance in the experimental work and to Imperial Chemical Industries (Plastics Division) for gifts of plastic materials. Department of Mining, The University, Edgbaston, Birmingham I 5.