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

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. Garzó, 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.

14 pages, 7 figures; v2: Minor changes

References in corpus (7)

• Velocity distribution of a homogeneously driven two-dimensional granular gas
• Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas
• Velocity Distribution of a Homogeneously Cooling Granular Gas
• Transport coefficients of a granular gas of inelastic rough hard spheres
• Sonine approximation for collisional moments of granular gases of inelastic rough spheres
• Orientational correlation and velocity distributions in uniform shear flow of a dilute granular gas
• Driven and undriven states of multicomponent granular gases of inelastic and rough hard disks or spheres

Cited by in corpus (1)

• Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. II. Stability analysis