Transport properties of driven inelastic Maxwell mixtures

A granular binary mixture driven by a stochastic bath with friction is studied from the inelastic Boltzmann kinetic equation for inelastic Maxwell models. First, we focus on homogeneous steady state solutions, reached by the system due to the presence of the thermostat that compensates for the energy lost in collisions. At a macroscopic level, the homogeneous steady state is fully characterized by the partial granular temperatures of both species, which are determined and compared against molecular dynamics simulations of inelastic hard spheres. The comparison between theory and simulations shows an excellent agreement. Second, we solve the kinetic equation close to steady states by means of the Chapman–Enskog method adapted to dissipative dynamics. We consider the first-order approximation (Navier–Stokes hydrodynamic order) and compute explicitly the diffusion transport coefficients. The results obtained here for diffusion for inelastic Maxwell models agree with those derived for inelastic hard spheres when non-Gaussian corrections to the zeroth-order solution are neglected.