Uniform shear flow in dissipative gases. Computer simulations of inelastic hard spheres and (frictional) elastic hard spheres

Abstract

In the preceding paper (cond-mat/0405252), we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHS) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHS), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor $(1+\alpha)/2$ (where $\alpha$ is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely the simple or uniform shear flow, by performing Monte Carlo computer simulations of the Boltzmann equation for both classes of dissipative gases with a dissipation range $0.5\leq \alpha\leq 0.95$ and two values of the imposed shear rate $a$. The distortion of the steady-state velocity distribution from the local equilibrium state is measured by the shear stress, the normal stress differences, the cooling rate, the fourth and sixth cumulants, and the shape of the distribution itself. In particular, the simulation results seem to be consistent with an exponential overpopulation of the high-velocity tail. The EHS results are in general hardly distinguishable from the IHS ones if $\alpha\gtrsim 0.7$, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high dissipationsComment: 23 pages; 18 figures; Figs. 2 and 9 include new simulations; two new figures added; few minor changes; accepted for publication in PR