Inhomogeneous Cooling of the Rough Granular Gas in Two Dimensions

TL;DR

This study investigates the decay of translational and rotational energies in a two-dimensional rough granular gas during inhomogeneous clustering, using simulations and scaling arguments to compare with ballistic aggregation models.

Contribution

It provides the first detailed numerical analysis of energy decay exponents in rough granular gases, highlighting differences from ballistic aggregation predictions.

Findings

Translational energy decays as t^{-1}

Rotational energy decays as t^{-1.6}

Decays are independent of restitution coefficients

Abstract

We study the inhomogeneous clustered regime of a freely cooling granular gas of rough particles in two dimensions using large-scale event driven simulations and scaling arguments. During collisions, rough particles dissipate energy in both the normal and tangential directions of collision. In the inhomogeneous regime, translational kinetic energy and the rotational energy decay with time $t$ as power-laws $t^{-\theta_T}$ and $t^{-\theta_R}$. We numerically determine $\theta_T \approx 1$ and $\theta_R \approx 1.6$, independent of the coefficients of restitution. The inhomogeneous regime of the granular gas has been argued to be describable by the ballistic aggregation problem, where particles coalesce on contact. Using scaling arguments, we predict $\theta_T=1$ and $\theta_R=1$ for ballistic aggregation, $\theta_R$ being different from that obtained for the rough granular gas. Simulations of ballistic aggregation with rotational degrees of freedom are consistent with these exponents.