Kinetic Theory of Granular Gases

Abstract

Granular fluids are many-body systems with very short range and strongly repulsive interactions that dissipate energy upon collision. The basic models are soft and hard inelastic spheres, which may or may not be driven by external deterministic or stochastic forces, as a means of maintaining a steady state. Starting from the Liouville equation and BBGKY hierarchy for such systems, we derive the Boltzmann and ring kinetic equations for the limiting case of instantaneous hard sphere interactions. The ring kinetic equation provides the basis from which fluctuating hydrodynamics and mode coupling theory can be derived. In the second part of this article non-Gaussian properties, such as cumulants and high energy tails, of the single-particle velocity distribution are studied for homogeneous granular fluids of inelastic hard spheres or disks, based on the Enskog-Boltzmann equation for the undriven and randomly driven case. The velocity distribution in the randomly driven steady state exhibits a high energy tail ~ exp(-Ac 3/2), where c is the velocity scaled by the thermal velocity and A ~ 1/√∈with ∈ the inelasticity. The results are compared with molecular dynamics simulations, as well as direct Monte Carlo simulations of the Boltzmann equation.