Granular gas of viscoelastic particles in a homogeneous cooling state

TL;DR

This paper investigates the kinetic behavior of a granular gas of viscoelastic particles in a homogeneous cooling state, emphasizing the role of the third Sonine coefficient and high-energy tail dynamics, with analytical and numerical insights.

Contribution

It introduces a detailed analysis of the third Sonine coefficient in viscoelastic granular gases, challenging previous assumptions and providing new analytical and numerical results.

Findings

The third Sonine coefficient a3 is comparable to a2, contradicting previous smallness assumptions.

The high-energy tail of the velocity distribution evolves with time, affecting the system's kinetic properties.

Analytical predictions for a3, threshold velocity, and diffusion coefficient agree well with numerical simulations.

Abstract

Kinetic properties of a granular gas of viscoelastic particles in a homogeneous cooling state are studied analytically and numerically. We employ the most recent expression for the velocity-dependent restitution coefficient for colliding viscoelastic particles, which allows to describe systems with large inelasticity. In contrast to previous studies, the third coefficient a3 of the Sonine polynomials expansion of the velocity distribution function is taken into account. We observe a complicated evolution of this coefficient. Moreover, we find that a3 is always of the same order of magnitude as the leading second Sonine coefficient a2; this contradicts the existing hypothesis that the subsequent Sonine coefficients a2, a3 ..., are of an ascending order of a small parameter, characterizing particles inelasticity. We analyze evolution of the high-energy tail of the velocity distribution function. In particular, we study the time dependence of the tail amplitude and of the threshold velocity, which demarcates the main part of the velocity distribution and the high-energy part. We also study evolution of the self-diffusion coefficient D and explore the impact of the third Sonine coefficient on the self-diffusion. Our analytical predictions for the third Sonine coefficient, threshold velocity and the self-diffusion coefficient are in a good agreement with the numerical finding.