Rheology of dense granular mixtures: Particle-size distributions, boundary conditions, and collisional time scales

We computationally investigate the dependence of the rheology of dense sheared granular mixtures on their particle size distribution. We consider the simplest case of a binary mixture of two different sized particles where the fraction of large particles is varied from one simulation to the next while the total solid mass is kept constant. We find that the variation of the rheology with the particle size distribution depends on the boundary conditions. For example, under constant pressure conditions the effective friction coefficient μ^* (the ratio between shear and pressure stresses at the boundary) increases mildly with the average particle size. On the other hand, under constant volume conditions, μ^* has a nonmonotonic dependence on the average particle size that is related to the proximity of the system solid fraction to the maximum packing fraction. Somewhat surprisingly, then, μ^* scales with a dimensionless shear rate (a generalized inertial number) in the same way for either boundary condition. We show that, for our system of relatively hard spheres, these relationships are governed largely by the ratio between average collision times and mean-free-path times, also independent of boundary conditions.