Rheology of bidisperse granular mixtures via event driven simulations

The bulk rheology of bidisperse mixtures of granular materials is examined under homogeneous shear flow conditions using the event-driven simulation method. The granular material is modelled as a system of smooth inelastic disks, interacting via the hard-core potential. In order to understand the effect of sizeand mass-disparities, two cases were examined separately, namely, a mixture of different sized particles with particles having the same mass and the other with particles having the same material density. The relevant macroscopic quantities are the pressure, the shear viscosity, the granular energy (fluctuating kinetic energy) and the first normal stress difference. Numerical results on pressure, viscosity and granular energy are compared with a kinetictheory constitutive model with excellent agreement in the low dissipation limit even at large size-disparities. Systematic quantitative deviations occur for stronger dissipations. Mixtures with equal-mass particles show a stronger shear resistance as compared to an equivalent monodisperse system; in contrast, however, mixtures with equal-density particles show a reduced shear resistance. The granular energies of the two species are unequal, implying that the equipartition principle assumed in most of the constitutive models does not hold. Inelasticity is responsible for the onset of energy non-equipartion, but massdisparity significantly enhances its magnitude. This lack of energy equipartition can lead to interesting non-monotonic variation for the pressure, viscosity and granular energy with the mass-ratio if the size-ratio is held fixed, while the model predictions (with equipartition assumption) suggest a monotonic behaviour in the same limit. In general, the granular fluid is non-Newtonian with a measurable first normal stress difference (which is positive if the