The rheology of bimodal hard-sphere dispersions

The viscosity of a monolayer of a suspension of bimodally distributed hard spheres is determined for area fractions, φa, from 0.15 to 0.74 with different particle size ratios, λ (diameter of large sphere/diameter of small spheres=1, 2, and 4), and different fractions of small spheres of total solids, ξ (0.07, 0.27, 0.49, 0.64, and 0.83). Particle distributions are generated by a Monte Carlo technique and the hydrodynamic interactions are calculated by Stokesian dynamics. These results, which correspond to the high-frequency dynamic viscosities, are compared with those from the dynamic simulation of hydrodynamically interacting spherical particles [Chang and Powell, J. Fluid Mech. 253, 1 (1993)]. Dynamic simulation is found to yield higher relative viscosities, ηr, as compared with the results of Monte Carlo simulation at high concentrations. This results from the absence of long clusters that completely cross a periodic cell in the Monte Carlo simulations that are present in the dynamic simulations. When φa is normalized by the maximum packing fraction, φm2-D, all the viscosity data fall onto a master curve. This is the same trend as that found in dynamic simulations, except that the Monte Carlo simulation gives lower relative viscosities for φa/φm2-D > 0.3. When λ and φa are fixed, ηr decreases as ξ increases from zero, reaches a minimum, and then increases as ξ→1, similar to the trend found in the dynamic simulations. Good agreement is found among the results of two-dimensional simulations, experiments, and three-dimensional simulations for monodispersed suspensions