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Velocity Distribution in a Viscous Granular Gas

Alexandre Rosas·Daniel ben-Avraham·Katja Lindenberg
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Abstract

We investigate the velocity relaxation of a viscous one-dimensional granular gas, that is, one in which neither energy nor momentum is conserved in a collision. Of interest is the distribution of velocities in the gas as it cools, and the time dependence of the relaxation behavior. A Boltzmann equation of instantaneous binary collisions leads to a two-peaked distribution with each peak relaxing to zero velocity as 1/t while each peak also narrows as 1/t. Numerical simulations of grains on a line also lead to a double-peaked distribution that narrows as 1/t. A Maxwell approximation leads to a single-peaked distribution about zero velocity with power-law wings. This distribution narrows exponentially. In either case, the relaxing distribution is not of Maxwell-Boltzmann form.

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Alexandre Rosas, Daniel ben-Avraham, Katja Lindenberg. 2004-04-20. Velocity Distribution in a Viscous Granular Gas. https://doi.org/10.1103/physreve.71.032301

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