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.

Non-equilibrium memory effects: Granular fluids and beyond

“…The thermal and entropic approaches to the Mpemba effect have been scarcely compared [62,90]. In ref.…”

“…In ref. [90], it was shown that the thermal Mpemba effect may appear without its entropic counterpart -or vice versain a molecular fluid with non-linear drag. Therein, some situations appear in which the kinetic temperature overshoots the stationary value, which makes it necessary to revise the usual definition of the thermal Mpemba effect in this scenario.…”

“…The authors of ref. [90] propose a separation of the Kullback-Leibler divergence into a "kinetic" contribution plus a "local-equilibrium" distribution that allows for defining a non-equilibrium temperature, not necessarily associated with the average kinetic temperature, for any system relaxing to equilibrium. It seems worth exploring if this line of thought could lead to a unique framework for the thermal and entropic Mpemba effects.…”

Kinetic Theory-Based Methods in Fluid Dynamics

“…After a year-long preparation and a rigorous peer-review process, 12 articles were finally accepted for publication in this Special Issue. These articles report the latest developments in kinetic-theory-related numerical schemes [1,2] and typical applications in multiphase flows [3], thermal flows [4], micro/nano flows [5,6], flows in porous media [7], and compressible flows [8,9], as well as other areas of fluid dynamics [10][11][12]. Specifically, Song et al [1] proposed a simplified linearized Boltzmann method for the effective simulation of acoustic propagation with a lower cost of virtual memory.…”

“…Morozov and Titarev [10] utilized three numerical tools to study the dynamics of gas expansion due to intense nanosecond laser evaporation into vacuum, with specific attention paid to factors that are essential for experimental measurements. Megías and Santos [11] established a numerical model to interpret interactions between the dilute granular gases and a thermal bath made from smaller particles, and found that the Sonine approximation performs better than the Maxwellian approximation in revealing inelasticity, drag nonlinearity and memory effects. Qi et al [12] employed an immersed boundary-lattice Boltzmann method to simulate self-propelled particles in a simple shear flow, and studied the effects of multiple flow parameters (swimming Reynolds number, flow Reynolds number and blocking rate) on the kinematics and flow patterns.…”