Free Cooling Phase-Diagram of Hard-Spheres with Short- and Long-Range Interactions

TL;DR

This study investigates the phase behavior and clustering of granular gases with short- and long-range interactions, revealing how non-contact forces influence cooling dynamics and structure formation.

Contribution

It introduces a mean field theory that accurately predicts the effects of non-contact interactions on granular cooling and clustering, validated by molecular dynamics simulations.

Findings

Attractive potentials promote clustering and faster cooling.

Repulsive potentials inhibit clustering and slow down cooling.

A universal cooling behavior is observed in the homogeneous regime.

Abstract

We study the stability, the clustering and the phase-diagram of free cooling granular gases. The systems consist of mono-disperse particles with additional non-contact (long-range) interactions, and are simulated here by the event-driven molecular dynamics algorithm with discrete (short-range shoulders or wells) potentials (in both 2D and 3D). Astonishingly good agreement is found with a mean field theory, where only the energy dissipation term is modified to account for both repulsive or attractive non-contact interactions. Attractive potentials enhance cooling and structure formation (clustering), whereas repulsive potentials reduce it, as intuition suggests. The system evolution is controlled by a single parameter: the non-contact potential strength scaled by the fluctuation kinetic energy (granular temperature). When this is small, as expected, the classical homogeneous cooling state is found. However, if the effective dissipation is strong enough, structure formation proceeds, before (in the repulsive case) non-contact forces get strong enough to undo the clustering (due to the ongoing dissipation of granular temperature). For both repulsive and attractive potentials, in the homogeneous regime, the cooling shows a universal behaviour when the (inverse) control parameter is used as evolution variable instead of time. The transition to a non-homogeneous regime, as predicted by stability analysis, is affected by both dissipation and potential strength. This can be cast into a phase diagram where the system changes with time, which leaves open many challenges for future research.