Cluster-Growth in Freely Cooling Granular Media

TL;DR

This paper investigates the long-term cluster growth in freely cooling granular media by extending the inelastic hard sphere model to prevent collapse, introducing a new algorithm for cluster identification, and analyzing different growth regimes.

Contribution

It introduces an extended IHS model with contact energy to avoid inelastic collapse and proposes a continuous-space cluster identification algorithm, enabling long-time behavior analysis.

Findings

Identified three regimes: homogeneous cooling, cluster growth, and system-wide clustering.

Developed a burning-like algorithm for cluster detection based on particle distance.

Demonstrated mean-field theory applicability in the initial homogeneous regime.

Abstract

When dissipative particles are left alone, their fluctuation energy decays due to collisional interactions, clusters build up and grow with time until the system size is reached. When the effective dissipation is strong enough, this may lead to the `inelastic collapse', i.e. the divergence of the collision frequency of some particles. The cluster growth is an interesting physical phenomenon, whereas the inelastic collapse is an intrinsic effect of the inelastic hard sphere (IHS) model used to study the cluster growth - involving only a negligible number of particles in the system. Here, we extend the IHS model by introducing an elastic contact energy and the related contact duration t_c. This avoids the inelastic collapse and allows to examine the long-time behavior of the system. For a quantitative description of the cluster growth, we propose a burning - like algorithm in continuous space, that readily identifies all particles that belong to the same cluster. The criterion for this is here chosen to be only the particle distance. With this method we identify three regimes of behavior. First, for short times a homogeneous cooling state (HCS) exists, where a mean-field theory works nicely, and the clusters are tiny and grow very slowly. Second, at a certain time which depends on the system's properties, cluster growth starts and the clusters increase in size and mass until, in the third regime, the system size is reached and most of the particles are collected in one huge cluster.