Mean field theory for a driven granular gas of frictional particles

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 rn, a maximum tangential restitution coefficient rtm, and a Coulomb friction coefficient μ. The parameters can be tuned to explore a wide range of physical situations. In particular, the model contains the frequently used μ→∞ 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 (rn ≈ 1), we obtain a good agreement between mean field and simulations for μ=0.5 and rtm=0.4, but for much smaller values of rn the agreement is less good. We discuss the reasons of this discrepancy and possible refinements of our computational scheme.