Megías Alberto, Santos Andrés
Departamento de Física, Universidad de Extremadura, E-06006 Badajoz, Spain.
Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain.
Phys Rev E. 2021 Sep;104(3-1):034901. doi: 10.1103/PhysRevE.104.034901.
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.
对于具有恒定法向（α）和切向（β）恢复系数的非弹性粗糙硬磁盘或球体的稀薄颗粒气体，其输运系数在一个统一的框架内作为平动自由度（dₜ）和转动自由度（dᵣ）的函数得到。该推导通过采用类索宁近似的查普曼 - 恩斯科格方法进行，与先前的方法不同，在此方法中，角速度的参考分布函数无需指定。通过设定dₜ = d并形式上取dᵣ→0的极限，可得到纯光滑d维粒子的著名情形。此外，通过取dₜ = dᵣ = 3可重新得到先前关于硬球的结果[G.M. 克雷默、A. 桑托斯和V. 加尔佐，《物理评论E》90, 022205 (2014)10.1103/PhysRevE.90.022205]，而对于硬磁盘气体，通过选择dₜ = 2，dᵣ = 1可得到新的结果。还得到并讨论了奇异准光滑极限（β→ - 1）和保守的皮德克气体（α = β = 1）。
