Collision Rates in Charged Granular Gases

TL;DR

This paper derives how Coulomb repulsion affects collision rates and cooling in charged granular gases, showing a modified dissipation rate, a transition in temperature decay, and effects of charge redistribution, supported by simulations.

Contribution

It introduces a modified dissipation rate for charged granular gases accounting for Coulomb effects and analyzes the impact on cooling and charge distribution.

Findings

Dissipation rate is multiplied by a Boltzmann-like factor due to Coulomb repulsion.

Granular temperature decreases as t^-2 and then as 1/ln(t) after Coulomb barrier effects.

Charge redistribution can minimize collision rates by equalizing charges.

Abstract

The dissipation rate due to inelastic collisions between equally charged, insulating particles in a granular gas is calculated. It is equal to the known dissipation rate for uncharged granular media multiplied by a Boltzmann-like factor, that originates from Coulomb repulsion. Particle correlations lead to an effective potential that replaces the bare Coulomb potential in the Boltzmann factor. Collisional cooling in a granular gas proceeds with the known t^-2 -law, until the kinetic energy of the grains becomes smaller than the Coulomb barrier. Then the granular temperature approaches a time dependence proportional to 1/ln(t). If the particles have different charges of equal sign, the collision rate can always be lowered by redistributing the charge, until all particles carry the same charge. Finally granular flow through a vertical pipe is briefly discussed. All results are confirmed by computer simulations.