Homogeneous states in driven granular mixtures: Enskog kinetic theory versus molecular dynamics simulations

Abstract

The homogeneous state of a binary mixture of smooth inelastic hard disks or spheres is analyzed. The mixture is driven by a thermostat composed by two terms: a stochastic force and a drag force proportional to the particle velocity. The combined action of both forces attempts to model the interaction of the mixture with a bath or surrounding fluid. The problem is studied by means of two independent and complementary routes. First, the Enskog kinetic equation with a Fokker-Planck term describing interactions of particles with thermostat is derived. The ratio of kinetic temperatures $T_1/T_2$ and the fourth-degree velocity moments $\lambda_1$ and $\lambda_2$ (which measure non-Gaussian properties of $\varphi_i$) are explicitly determined as a function of the mass ratio, size ratio, composition, density and coefficients of restitution. Secondly, to assess the reliability of the theoretical results, molecular dynamics simulations of a binary granular mixture of spheres are performed for two values of the coefficient of restitution ($\alpha=0.9$ and 0.8) and three different solid volume fractions ($\phi=0.00785$, 0.1 and 0.2). Comparison between kinetic theory and computer simulations for the temperature ratio shows excellent agreement, even for moderate densities and strong dissipation. In the case of the cumulants $\lambda_1$ and $\lambda_2$, good agreement is found for the lower densities although significant discrepancies between theory and simulation are observed with increasing density.