Velocity distribution in granular gases of viscoelastic particles

TL;DR

This paper investigates how the velocity distribution in a homogeneously cooling granular gas of viscoelastic particles deviates from Maxwellian behavior, revealing complex time-dependent dynamics and multiple relaxation regimes.

Contribution

It demonstrates that the simple scaling hypothesis fails for viscoelastic particles and identifies distinct evolution regimes of the velocity distribution function.

Findings

Deviation from Maxwellian distribution is non-monotonic over time.

Two relaxation regimes observed for small dissipation.

Analytical results agree with numerical simulations.

Abstract

The velocity distribution in a homogeneously cooling granular gas has been studied in the viscoelastic regime when the restitution coefficient of colliding particles depends on the impact velocity. We show that for viscoelastic particles the simple scaling hypothesis is violated, i.e., that the time dependence of the velocity distribution does not scale with the mean square velocity as in the case of particles interacting via a constant restitution coefficient. The deviation from the Maxwellian distribution does not depend on time monotonously. For the case of small dissipation we detected two regimes of evolution of the velocity distribution function: Starting from the initial Maxwellian distribution, the deviation first increases with time on a collision time-scale saturating at some maximal value; then it decays to zero on much larger time-scale which corresponds to the temperature relaxation. For larger values of the dissipation parameter there appears an additional intermediate relaxation regime. Analytical calculations for small dissipation agrees well with the results of a numerical analysis.