On the cooling law of a non-dilute granular gas

Abstract

The cooling law of a granular gas was investigated using a three-dimensional MD simulation code, which allowed us to include both inelasticity and frictional effects of the particle contacts. It was found that the kinetic energy decays in time as $E(t)\sim t^{-n}$; the exponent $n$ of the cooling law changes significantly with the solid fraction, $\alpha$, and the coefficient of restitution, $\epsilon$. For dilute gases, for times greater than $t_c$, we found that $n\approx 1$, in agreement with the results reported by Nie \etal~\cite{nie2002}. As $\alpha$ and/or $\epsilon$ increase, the cooling coefficient increases to an asymptotic value of $n\approx2.2$, which is slightly higher than the prediction made by Haff~\cite{haff}. We interpret this increase in the cooling exponent as a possible re-homogenization of the granular state.