Temperature inversion in granular fluids under gravity

TL;DR

This paper investigates the temperature profile of granular fluids under gravity, revealing a temperature turn-up phenomenon explained by a modified heat flux law, with theoretical predictions validated by molecular dynamics simulations.

Contribution

It introduces a new understanding of heat flux in granular fluids, deriving a method to compute the transport coefficient $$ from the temperature profile.

Findings

Temperature increases linearly with height far from the base.

The positive temperature gradient is proportional to gravity and .

Theoretical predictions match molecular dynamics simulations.

Abstract

We study, via hydrodynamic equations, the granular temperature profile of a granular fluid under gravity and subjected to energy injection from a base. It is found that there exists a turn-up in the granular temperature and that, far from the base, it increases linearly with height. We show that this phenomenon, observed previously in experiments and computer simulations, is a direct consequence of the heat flux law, different form Fourier's, in granular fluids. The positive granular temperature gradient is proportional to gravity and a transport coefficient $\mu_0$, relating the heat flux to the density gradients, that is characteristic of granular systems. Our results provide a method to compute the value $\mu_0$ for different restitution coefficients. The theoretical predictions are verified by means of molecular dynamics simulations, and the value of $\mu_0$ is computed for the two dimensional inelastic hard sphere model. We provide, also, a boundary condition for the temperature field that is consistent with the modified Fourier's law.