A driven two-dimensional granular gas with Coulomb friction

TL;DR

This paper investigates the behavior of a homogeneously driven two-dimensional granular gas with Coulomb friction, analyzing how translational and rotational temperatures evolve and comparing theoretical models with numerical simulations.

Contribution

It introduces a mean field theory with four approximation levels for Coulomb friction and demonstrates that the full friction model accurately predicts simulation results.

Findings

Qualitative agreement with simple models

Quantitative accuracy with full Coulomb friction model

Identification of two relaxation times for temperature equilibration

Abstract

We study a homogeneously driven granular gas of inelastic hard particles with rough surfaces subject to Coulomb friction. The stationary state as well as the full dynamic evolution of the translational and rotational granular temperatures are investigated as a function of the three parameters of the friction model. Four levels of approximation to the (velocity-dependent) tangential restitution are introduced and used to calculate translational and rotational temperatures in a mean field theory. When comparing these theoretical results to numerical simulations of a randomly driven mono-layer of particles subject to Coulomb friction, we find that already the simplest model leads to qualitative agreement, but only the full Coulomb friction model is able to reproduce/predict the simulation results quantitatively for all magnitudes of friction. In addition, the theory predicts two relaxation times for the decay to the stationary state. One of them corresponds to the equilibration between the translational and rotational degrees of freedom. The other one, which is slower in most cases, is the inverse of the common relaxation rate of translational and rotational temperatures.