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

TL;DR

This study uses computer simulations to compare inelastic and elastic hard sphere gases under shear flow, showing that elastic models with adjustments can effectively replicate inelastic behavior at moderate dissipation levels.

Contribution

It demonstrates that elastic hard sphere models with an effective drag force and reduced collision rate can accurately mimic inelastic hard sphere transport properties in shear flow.

Findings

Elastic and inelastic gases show similar behavior for restitution coefficient $eta extgreater{} 0.7$.

High dissipation leads to observable differences such as anisotropy and overpopulation.

Simulation results support the exponential overpopulation of high-velocity tails.

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 dissipations