Instabilities in a free granular fluid described by the Enskog equation

TL;DR

This paper performs a linear stability analysis of a granular fluid using the Enskog equation, revealing how dissipation influences stability and transport coefficients, with results differing from previous models that ignored dissipation effects.

Contribution

It introduces a stability analysis based on the Enskog equation accounting for dissipation-dependent transport coefficients, improving upon previous models.

Findings

Transversal shear modes are unstable at long wavelengths.

Longitudinal heat mode instability depends on dissipation levels.

Quantitative differences from prior models increase with dissipation.

Abstract

A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability as functions of the wave vector, the dissipation, and the density. In contrast to previous studies, this description is based on the results derived from the Enskog equation for inelastic hard spheres [V. Garz\'o and J. W. Dufty, Phys. Rev. E {\bf 59}, 5895 (1999)], which takes into account the dependence of the transport coefficients on dissipation. As expected, linear stability shows two transversal (shear) modes and a longitudinal (``heat'') mode to be unstable with respect to long enough wavelength excitations. Comparison with previous results (which neglect the influence of dissipation on transport) shows quantitative discrepancies for strong dissipation.