Steady state of a fluidized granular medium between two walls at the same temperature

Abstract

The steady state of a low-density gas of inelastic hard spheres confined between two parallel walls at the same temperature is studied. Because of the dissipation in collisions, the state is not uniform but highly inhomogeneous with a nonlinear temperature profile. Direct Monte Carlo simulations show that in the nearly elastic limit the pressure is uniform, but the state exhibits anisotropy of the diagonal terms of the pressure tensor, contrary to the predictions of the Navier-Stokes equations. For larger inelasticity, the pressure becomes nonuniform. These rheological effects, peculiar to granular systems, are explained by means of a model kinetic equation based on the Boltzmann equation. The equation is solved by constructing a systematic perturbative expansion in the square root of the degree of inelasticity. The theoretical predictions compare well with the simulation results for small inelasticity, but they are in conflict for larger values of the degree of inelasticity. The analysis provides strong evidence that this is due to the asymptotic but divergent character of the expansion, similarly to what happens when the usual Chapman-Enskog expansion is applied to molecular fluids.