Dependence of Cluster Growth on Coefficient of Restitution in a Cooling Granular Fluid

TL;DR

This study investigates how the coefficient of restitution affects cluster growth in a cooling granular fluid, revealing that the asymptotic growth rate is largely independent of inelasticity despite delayed crossover times.

Contribution

It provides detailed simulation results showing that cluster growth dynamics are weakly sensitive to restitution coefficient, challenging previous assumptions about energy decay influence.

Findings

Crossover time increases as restitution approaches elastic limit.

Asymptotic cluster growth is independent of restitution coefficient.

Power-law growth amplitude is weakly affected by inelasticity.

Abstract

Starting from configurations having homogeneous spatial density, we study kinetics in a two-dimensional system of inelastically colliding hard particles, a popular model for cooling granular matter. Following an initial time period, the system exhibits a crossover to an inhomogeneous regime that is characterized by the formation and growth of particle-rich clusters. We present results on the time dependence of average mass of the clusters and that of average kinetic energy, obtained via event driven molecular dynamics simulations, for a wide range of values for the coefficient of restitution ($e$), by fixing the overall density of particles in the system to a constant number. The time of onset of crossover from homogeneous to the inhomogeneous regime, as is well known, strongly increases as one moves towards the elastic limit. Nevertheless, our presented results suggest that the asymptotic growth is independent of $e$, for uniform definition of cluster, onset of which has a different $e$-dependence than the onset of above mentioned crossover. In other words, not only the exponent but also the amplitude of the power-law growth, which is widely believed to be the form of the evolution, is at the most very weakly sensitive to the choice of $e$. While it is tempting to attribute this fact to the similar feature in the decay of energy, we caution that our current understanding is not matured enough to draw such a connection between cluster growth and energy decay in a meaningful manner.