Temperature inversion in granular fluids under gravity

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 μ 0, relating the heat flux to the density gradients, that is characteristic of granular systems. Our results provide a method to compute the value μ 0 for different restitution coefficients. The theoretical predictions are verified by means of molecular dynamics simulations, and the value of μ 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.