Granular clustering self-consistent analysis for general coefficients of restitution

TL;DR

This paper analyzes the long-term behavior of granular clusters and gases with various velocity-dependent coefficients of restitution, revealing stability differences and the conditions under which clusters dissolve or persist.

Contribution

It introduces a self-consistent analysis method for granular clustering considering general velocity-dependent restitution coefficients, highlighting stability criteria.

Findings

Clusters with velocity-dependent r are unstable over long times

Clusters with velocity-independent r are stable and permanent

Velocity dependence of r influences cluster stability and dissolution

Abstract

We study the equilibrium behavior of one-dimensional granular clusters and one-particle granular gases for a variety of velocity dependent coefficients of restitution $r$. We obtain equations describing of the long time behavior for the cluster's pressure, r.m.s. velocity and granular inter-spacing. We show that for extremely long times, clusters with velocity dependent coefficients of restitution are unstable and dissolve into homogeneous, quasi-elastic gases, but clusters with velocity independent $r$ are permanent. This is in accordance with hydrodynamic studies pointing to the transient nature of density instabilities for granular gases with velocity dependent $r$.