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

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.

17 pages, 7 figures; v2: one new appendix, minor changes in the main text. Published in the special issue of Entropy "Kinetic Theory-Based Methods in Fluid Dynamics"

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Cited by in corpus (4)

• Mpemba meets Newton: Exploring the Mpemba and Kovacs effects in the time-delayed cooling law
• Non-equilibrium memory effects: granular fluids and beyond
• The Mpemba effect in the Descartes protocol: A time-delayed Newton's law of cooling approach
• Time-delayed Newton's law of cooling with a finite-rate thermal quench: Impact on the Mpemba and Kovacs effects