Fourier's Law for a Granular Fluid

TL;DR

This paper investigates Fourier's law in granular fluids, revealing a fundamental difference from normal fluids due to additional density gradient contributions, supported by microscopic explanations.

Contribution

It demonstrates the presence of density gradient terms in Fourier's law for granular fluids, contrasting with normal fluids, and provides a microscopic rationale for this difference.

Findings

Density gradient contributions in Fourier's law for granular fluids.

Microscopic explanation for the additional terms.

Validation of hydrodynamic description in granular systems.

Abstract

Newton' viscosity law for the momentum flux and Fourier's law for the heat flux define Navier-Stokes hydrodynamics for a simple, one component fluid. There is ample evidence that a hydrodynamic description applies as well to a mesoscopic granular fluid with the same form for Newton's viscosity law. However, theory predicts a qualitative difference for Fourier's law with an additional contribution from density gradients even at uniform temperature. The reasons for the absence of such terms for normal fluids are indicated, and a related microscopic explanation for their existence in granular fluids is presented.