Mean Field theory for a driven granular gas of frictional particles

Abstract

We propose a mean field (MF) theory for a homogeneously driven granular gas of inelastic particles with Coulomb friction. The model contains three parameters, a normal restitution coefficient $r_n$, a maximum tangential restitution coefficient $r_t^m$, and a Coulomb friction coefficient $\mu$. The parameters can be tuned to explore a wide range of physical situations. In particular, the model contains the frequently used $\mu \to \infty$ limit as a special case. The MF theory is compared with the numerical simulations of a randomly driven monolayer of spheres for a wide range of parameter values. If the system is far away from the clustering instability ($r_n \approx 1$), we obtain a good agreement between mean field and simulations for $\mu=0.5$ and $r_t^m=0.4$, but for much smaller values of $r_n$ the agreement is less good. We discuss the reasons of this discrepancy and possible refinements of our computational scheme.