Kinetic Theory and Memory Effects of Homogeneous Inelastic Granular Gases under Nonlinear Drag

TL;DR

This paper develops a kinetic theory for inelastic granular gases in a thermal bath with nonlinear drag, revealing how memory effects and temperature dynamics are influenced by inelasticity and drag nonlinearity.

Contribution

It introduces a first Sonine approximation that captures memory effects and improves predictions of temperature aging in granular gases under nonlinear drag.

Findings

Maxwellian approximation accurately predicts granular temperature at low inelasticity.

First Sonine approximation significantly improves temperature predictions with increasing inelasticity.

Memory effects like Mpemba and Kovacs are explained by the coupling of kurtosis and temperature.

Abstract

We study a dilute granular gas immersed in a thermal bath made of smaller particles with masses not much smaller than the granular ones in this work. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is modeled by a nonlinear drag force plus a white-noise stochastic force. The kinetic theory for this system is described by an Enskog--Fokker--Planck equation for the one-particle velocity distribution function. To get explicit results of the temperature aging and steady states, Maxwellian and first Sonine approximations are developed. The latter takes into account the coupling of the excess kurtosis with the temperature. Theoretical predictions are compared with direct simulation Monte Carlo and event-driven molecular dynamics simulations. While good results for the granular temperature are obtained from the Maxwellian approximation, a much better agreement, especially as inelasticity and drag nonlinearity increase, is found when using the first Sonine approximation. The latter approximation is, additionally, crucial to account for memory effects such as Mpemba and Kovacs-like ones.