Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients

TL;DR

This paper derives transport coefficients for dilute granular gases of inelastic and rough particles with various degrees of freedom, providing a unified framework that generalizes previous models and introduces new results for disks.

Contribution

It introduces a unified Chapman--Enskog approach to compute transport coefficients for inelastic, rough granular gases with arbitrary degrees of freedom, including new results for disk-shaped particles.

Findings

Derived transport coefficients as functions of degrees of freedom and restitution coefficients.

Recovered known results for smooth particles and hard spheres as special cases.

Presented new results for hard-disk gases with rotational degrees of freedom.

Abstract

The transport coefficients for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal ($\alpha$) and tangential ($\beta$) restitution are obtained in a unified framework as functions of the number of translational ($d_t$) and rotational ($d_r$) degrees of freedom. The derivation is carried out by means of the Chapman--Enskog method with a Sonine-like approximation in which, in contrast to previous approaches, the reference distribution function for angular velocities does not need to be specified. The well-known case of purely smooth $d$-dimensional particles is recovered by setting $d_t=d$ and formally taking the limit $d_r\to 0$. In addition, previous results [G. M. Kremer, A. Santos, and V. Garz\'o, Phys. Rev. E 90, 022205 (2014)] for hard spheres are reobtained by taking $d_t=d_r=3$, while novel results for hard-disk gases are derived with the choice $d_t=2$, $d_r=1$. The singular quasismooth limit ($\beta\to -1$) and the conservative Pidduck's gas ($\alpha=\beta=1$) are also obtained and discussed.