Viscosity minimum in bimodal concentrated suspensions under shear

We study a model of concentrated suspensions under shear in two dimensions. Interactions between suspended particles are dominated by direct-contact viscoelastic forces and the particles are neutrally bouyant. The bimodal suspensions consist of a variable proportion between large and small droplets, with a fixed global suspended fraction. Going beyond the assumptions of the classical theory of Farris (R.J. Farris, Trans. Soc. Rheol. 12, 281 (1968)), we discuss a shear viscosity minimum, as a function of the small-to-large-particle ratio, in shear geometries imposed by external body forces and boundaries. Within a linear-response scheme, we find the dependence of the viscosity minimum on the imposed shear and the microscopic drop friction parameters. We also discuss the viscosity minimum under dynamically imposed shear applied by boundaries. We find a reduction of macroscopic viscosity with the increase of the microscopic friction parameters that is understood using a simple two-drop model. Our simulation results are qualitatively consistent with recent experiments in concentrated bimodal emulsions with a highly viscous or rigid suspended component.