Fourier state of a fluidized granular gas

Abstract

It is shown that the Boltzmann equation for smooth inelastic hard disks or spheres admits a solution describing a steady state characterized by uniform pressure and linear temperature profile. Such a state has been observed previously both in numerical solutions of the Boltzmann equation and in molecular dynamics simulations. Quite peculiarly, pressure and temperature gradient are not independent but their ratio is a function of the coefficient of restitution. Several properties of the solution are discussed. In particular, it is shown that a linear Fourier-like law is verified for arbitrary temperature gradient.