Steady state in a gas of inelastic rough spheres heated by a uniform stochastic force

TL;DR

This paper derives an analytical velocity distribution for a driven granular gas of inelastic rough spheres, revealing energy non-equipartition, kurtoses, and correlations, and compares it with numerical solutions to validate accuracy.

Contribution

It provides a new analytical solution for the steady state of a driven granular gas accounting for roughness and inelasticity, validated by numerical simulations.

Findings

Analytical velocity distribution matches numerical results in certain regimes.

Steady state exhibits near-Maxwellian velocity distributions.

Translational-rotational correlations favor perpendicular orientations.

Abstract

We study here the steady state attained in a granular gas of inelastic rough spheres that is subject to a spatially uniform random volume force. The stochastic force has the form of the so-called white noise and acts by adding impulse to the particle translational velocities. We work out an analytical solution of the corresponding velocity distribution function from a Sonine polynomial expansion that displays energy non-equipartition between the translational and rotational modes, translational and rotational kurtoses, and translational-rotational velocity correlations. By comparison with a numerical solution of the Boltzmann kinetic equation (by means of the Direct Simulation Monte Carlo method) we show that our analytical solution provides a good description that is quantitatively very accurate in certain ranges of inelasticity and roughness. We also find three important features that make the forced granular gas steady state very different from the homogeneous cooling state (attained by an unforced granular gas). First, the marginal velocity distributions are always close to a Maxwellian. Second, there is a continuous transition to the purely smooth limit (where the effects of particle rotations are ignored). And third, the angular translational-rotational velocity correlations show a preference for a quasiperpendicular mutual orientation (which is called "lifted-tennis-ball" behavior).