Fluid-dynamic equations for granular particles in a host medium

A kinetic model for a granular gas interacting with a given background by binary dissipative collisions is analyzed, with particular reference to the derivation of macroscopic equations for the fundamental observables. Particles are modelled as inelastic hard spheres under the assumption of collision dominated regime (small mean free path). Closure of the relevant moment equations is achieved by resorting to a maximum entropy principle, and two specific entropy functionals have been worked out in detail, in the class of the admissible ones for the relevant linearextended Boltzmann equation. Considered macroscopic fields include density, mass velocity, and granular temperature. In the hydrodynamic limit when the mean free path tends to zero, a single drift-diffusion equation of Navier-Stokes type is recovered for the only hydrodynamic variable of the physical problem.