JOURNAL OF COLLOID AND INTERFACE SCIENCE 191, 11–21 (1997) ARTICLE NO. CS974915 The Effect of Diameter Ratio and Volume Ratio on the Viscosity of Bimodal Suspensions of Polymer Latices R. Greenwood, * ,1 P. F. Luckham, * ,2 and T. Gregory² * Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology, and Medicine, Prince Consort Road, London SW7 2BY, United Kingdom; and ² 129 Orchard Road, Anerley, London SE20 8DW, United Kingdom Received November 13, 1995; accepted April 3, 1997 1. INTRODUCTION Previously, the rheological properties of different sized monodis- perse polymer latices of polystyrene and polymethyl methacrylate Many industrial concentrated dispersions, e.g., inks and (PMMA) were determined. This paper describes procedures in paints, are not monodisperse, but have a wide particle size which carefully prepared blends of the same monodisperse latices distribution. It is commonly known that increasing the vol- were mixed together to examine the effect of the differences in ume fraction of a particulate suspension increases the viscos- size between the latices (diameter ratio) on the rheology of the ity and that the viscosity increases markedly as the maximum blend. The relative viscosities of these blends were then measured packing fraction of the particles is reached. Furthermore, it as a function of the total volume fraction and compared with those is widely recognized that the maximum packing fraction of of the constituent parts. In a bimodal suspension, theory predicts a monodisperse system can be increased by broadening the that a maximum packing fraction and hence a minimum viscosity particle size distribution. Thus, polydispersity can give a is achieved with 27%small particles by volume. The experiments lower viscosity at the same volume fraction or permit a revealed that a minimum viscosity was obtained with 25% small higher volume loading of particles at the equivalent viscos- particles by volume and with a diameter ratio of 7.83. At this ity. Despite this practical significance, relatively few experi- diameter ratio, the small particles are able to pass through the mental and theoretical studies have been made. triangular pore between the large particles and this essentially A systematic study of the effect of polydispersity can be leads to an increased maximum packing fraction of the suspension. Hence the suspension will have a lower viscosity. Other diameter achieved by investigating systems in which it is well defined, ratios at 25% small particles by volume that led to suspensions such as a bimodal suspension. By introducing smaller parti- with lower viscosities were 4.03, 6.37, and 11.15. On the other cles, such that they fit in between the larger particles, it is hand the suspensions with diameter ratios of 2.81 and 5.67 led to conceptually possible to achieve higher volume fractions. increases in viscosity. This is a result of the small particles being Optimization of the size difference (or diameter ratio) and too big to fit in the gaps between the large particles. All the other the volume ratio (composition) could lead to bimodal sys- diameter ratios at all the other compositions (i.e., 50 and 75% tems having greater volume fractions for the same viscosity small particles by volume) resulted in viscosities higher than that compared to monomodal systems. Conversely, the viscosity obtained for the monodisperse polystyrene latex. These effects may may be greatly reduced by switching from a monomodal to be explained by changes in the value of the maximum packing a bimodal system at the same volume fraction. This could fraction. An increased maximum packing fraction of the system produce a more environmentally sensitive product due to leads to lower viscosities and vice versa. The results challenge the less polluting solvent. In other systems a lower viscosity conventional view that simply increasing the diameter ratio at a would minimize pumping costs. This is exemplified by re- fixed composition leads to reduced viscosities and increased maxi- search into high solids loading coal/water mixtures that can mum packing fractions. This simple picture does not appear to be easily pumped over long distances (1–3). In addition to hold forbinary suspensions of colloidal particles at every particle the reductions in viscosity, other rheological improvements size ratios.  1997 Academic Press in bimodal systems have been observed. Wagstaff and Chaf- Key Words: rheology; bimodal dispersions; polymer latices; di- ameter ratios; superlattices. fey (4) reported that the volume fraction at which shear thickening occurs is increased and that dilatant behavior (5, 6) can be avoided by broadening the size distribution. It is well known that concentrated monodisperse systems exhibit both elastic and viscous properties ( 7 – 9 ) . However, 1 Current address: Dept. of Chemistry, University of Keele, United there have been very few studies of the effect of diameter Kingdom. 2 To whom correspondence should be addressed. ratio and composition on the viscoelastic properties of bi- 11 0021-9797/97 $25.00 Copyright  1997 by Academic Press All rights of reproduction in any form reserved.