Transport Coefficients for Granular Media from Molecular Dynamics Simulations

TL;DR

This study uses molecular dynamics simulations to evaluate transport coefficients like thermal conductivity and shear viscosity in granular media, confirming some theoretical predictions while highlighting discrepancies at high inelasticity.

Contribution

It provides a detailed comparison of simulation results with kinetic theory predictions for granular flow transport properties.

Findings

Shear viscosity closely matches kinetic theory predictions.

Thermal conductivity is overestimated by kinetic theory, especially at high inelasticity.

Transport coefficients decrease with increasing inelasticity.

Abstract

Under many conditions, macroscopic grains flow like a fluid; kinetic theory pred icts continuum equations of motion for this granular fluid. In order to test the theory, we perform event driven molecular simulations of a two-dimensional gas of inelastic hard disks, driven by contact with a heat bath. Even for strong dissipation, high densities, and small numbers of particles, we find that continuum theory describes the system well. With a bath that heats the gas homogeneously, strong velocity correlations produce a slightly smaller energy loss due to inelastic collisions than that predicted by kinetic theory. With an inhomogeneous heat bath, thermal or velocity gradients are induced. Determination of the resulting fluxes allows calculation of the thermal conductivity and shear viscosity, which are compared to the predictions of granular kinetic theory, and which can be used in continuum modeling of granular flows. The shear viscosity is close to the prediction of kinetic theory, while the thermal conductivity can be overestimated by a factor of 2; in each case, transport is lowered with increasing inelasticity.