(18b) Predicting the Critical Length Scale for Clustering Instabilities in the Homogenous Cooling of Inelastic Particles

Experiments and molecular dynamics (MD) simulations have demonstrated the existence of clustering instabilities in systems of solid, inelastic particles. Previous work has also qualitatively shown clustering in these systems through stability analyses of the continuum balances for granular materials. However, the quantitative ability of continuum models to predict clustering instabilities has not been assessed. In this work, hard-sphere, event-driven MD simulations of the homogenous cooling system (HCS) are used to study clustering instabilities in granular systems. Detection of instabilities in a given simulation is determined via Haff's law. The specific aim is to determine the critical system size at which clustering appears over a wide range of parameter space. By comparing the critical length scale found in simulations with the predictions of stability analysis performed by Garzó (2005), this work aims to validate the quantitative ability of continuum models to predict instabilities for monodisperse granular flows.