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Temperature inversion in granular fluids under gravity

Rosa Ramirez·Rodrigo Soto
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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.

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Rosa Ramirez, Rodrigo Soto. 2002-10-21. Temperature inversion in granular fluids under gravity. https://doi.org/10.1016/s0378-4371(03)00028-1

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