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

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. Then, a scaling solution to the Enskog kinetic equation is proposed where the dependence of the scaled distributions φi of each species on the granular temperature occurs not only through the dimensionless velocity c = v/v0 (v0 being the thermal velocity) but also through the dimensionless driving force parameters. Approximate forms for φi are constructed by considering the leading order in a Sonine polynomial expansion. The ratio of kinetic temperatures T1/T2 and the fourth-degree velocity moments λ1 and λ2 (which measure non-Gaussian properties of φ1 and φ2, respectively) are explicitly determined as a function of the mass ratio, size ratio, composition, density, and coefficients of restitution. Second, 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 (α = 0.9 and 0.8) and three different solid volume fractions (ϕ = 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 λ1 and λ2, good agreement is found for the lower densities although significant discrepancies between theory and simulation are observed with increasing density.