Inhomogeneous cooling state of a strongly confined granular gas at low density

TL;DR

This paper investigates the inhomogeneous cooling behavior of a confined granular gas, revealing anisotropic velocity distributions, temperature differences, and energy transfer phenomena, supported by theoretical and simulation results.

Contribution

It introduces a scaling distribution for the inhomogeneous cooling state of a confined granular gas, accounting for anisotropy and temperature differences, extending previous homogeneous models.

Findings

Velocity distribution is anisotropic with two different granular temperatures.

Energy transfer occurs from lower to higher temperature degrees of freedom.

Theoretical predictions agree well with molecular dynamics simulations.

Abstract

The inhomogeneous cooling state describing the hydrodynamic behavior of a freely evolving granular gas strongly confined between two parallel plates is studied, using a Boltzmann kinetic equation derived recently. By extending the idea of the homogeneous cooling state, we propose a scaling distribution in which all the time dependence occurs through the granular temperature of the system, while there is a dependence on the distance to the confining walls through the density. It is obtained that the velocity distribution is not isotropic, and it has two different granular temperature parameters associated to the motion perpendicular and parallel to the confining plates, respectively, although their cooling rates are the same. Moreover, when approaching the inhomogeneous cooling state, energy is sometimes transferred from degrees of freedom with lower granular temperature to those with a higher one, contrary to what happens in molecular systems. The cooling rate and the two partial granular temperatures are calculated by means of a Gaussian approximation. The theoretical predictions are compared with molecular dynamics simulation results and a good agreement is found.