Local heat flux and energy loss in a 2D vibrated granular gas

TL;DR

This study uses simulations to measure local heat flux and energy loss in a 2D vibrated granular gas, testing a generalized Fourier's law and comparing results with hydrodynamic theories.

Contribution

It introduces a generalized Fourier's law including density gradients for granular gases and determines transport coefficients across various inelasticities.

Findings

Transport coefficients kappa and mu are identified for different parameters.

Agreement with hydrodynamic theory is limited to very small inelasticities.

kappa and mu show non-monotonic behavior beyond small inelasticities.

Abstract

We performed event-driven simulations of a two-dimensional granular gas between two vibrating walls and directly measured the local heat flux and energy dissipation rate in the stationary state. Describing the local heat flux as a function of the coordinate x in the direction perpendicular to the driving walls, we use a generalization of Fourier's law, q_x(x) = kappa d_x T(x) + mu d_x rho(x), to relate the local heat flux to the local gradients of the temperature and density. This ansatz accounts for the fact that density gradients also generate heat flux, not only temperature gradients. The transport coefficients kappa and mu are assumed to be independent of x, and we check the validity of this assumption in the simulations. Both kappa and mu are determined for different system parameters, in particular, for a wide range of coefficients of restitution. We also compare our numerical results to existing hydrodynamic theories. Agreement is found for kappa for very small inelasticities only. Beyond this region, kappa and mu exhibit a striking non-monotonic behavior.