Megías A, Santos A. Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients.
Phys Rev E 2021;
104:034901. [PMID:
34654090 DOI:
10.1103/physreve.104.034901]
[Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Accepted: 08/17/2021] [Indexed: 11/07/2022]
Abstract
The transport coefficients for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal (α) and tangential (β) 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}→0. In addition, previous results [G. M. Kremer, A. Santos, and V. Garzó, Phys. Rev. E 90, 022205 (2014)10.1103/PhysRevE.90.022205] 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 (β→-1) and the conservative Pidduck's gas (α=β=1) are also obtained and discussed.
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