Homogeneous cooling state for a granular mixture

The homogeneous cooling state for a binary mixture of inelastic hard spheres is studied using the Enskog kinetic theory. In the same way as for the one-component fluid, we propose a scaling solution in which the time dependence of the distribution functions occurs entirely through the temperature of the mixture. A surprising result is that the (partial) temperatures of each species are different, although their cooling rates are the same. Approximate forms for the distribution functions are constructed to leading order in a Sonine polynomial expansion showing a small deviation from Maxwellian, similar to that for the one-component case. The temperatures and overall cooling rate are calculated in terms of the restitution coefficients, the reduced density, and the ratios of mass, concentration, and sizes.