The Effect of Diameter Ratio and Volume Ratio on the Viscosity of Bimodal Suspensions of Polymer Latices

Previously, the rheological properties of different sized monodisperse polymer latices of polystyrene and polymethyl methacrylate (PMMA) were determined. This paper describes procedures in which carefully prepared blends of the same monodisperse latices were mixed together to examine the effect of the differences in size between the latices (diameter ratio) on the rheology of the blend. The relative viscosities of these blends were then measured as a function of the total volume fraction and compared with those of the constituent parts. In a bimodal suspension, theory predicts that a maximum packing fraction and hence a minimum viscosity is achieved with 27% small particles by volume. The experiments revealed that a minimum viscosity was obtained with 25% small particles by volume and with a diameter ratio of 7.83. At this diameter ratio, the small particles are able to pass through the triangular pore between the large particles and this essentially leads to an increased maximum packing fraction of the suspension. Hence the suspension will have a lower viscosity. Other diameter ratios at 25% small particles by volume that led to suspensions with lower viscosities were 4.03, 6.37, and 11.15. On the other hand the suspensions with diameter ratios of 2.81 and 5.67 led to increases in viscosity. This is a result of the small particles being too big to fit in the gaps between the large particles. All the other diameter ratios at all the other compositions (i.e., 50 and 75% small particles by volume) resulted in viscosities higher than that obtained for the monodisperse polystyrene latex. These effects may be explained by changes in the value of the maximum packing fraction. An increased maximum packing fraction of the system leads to lower viscosities and vice versa. The results challenge the conventional view that simply increasing the diameter ratio at a fixed composition leads to reduced viscosities and increased maximum packing fractions. This simple picture does not appear to hold for binary suspensions of colloidal particles at every particle size ratios.