Brilliantov Nikolai V, Pöschel Thorsten
Institute of Physics, University Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany.
Chaos. 2005 Jun;15(2):26108. doi: 10.1063/1.1889266.
We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution epsilon which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, epsilon=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of epsilon on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for epsilon=const both methods lead to the same result for the self-diffusion coefficient. For the case of impact-velocity dependent coefficients of restitution, the Green-Kubo method is, however, either restrictive or too complicated for practical application, therefore we compute the diffusion coefficient using the Chapman-Enskog method. We conclude that in application to granular gases, the Chapman-Enskog approach is preferable for deriving kinetic coefficients.
我们使用格林 - 久保关系和查普曼 - 恩斯科格方法，研究示踪剂在均匀冷却的耗散粒子气体中的扩散（自扩散）。耗散粒子碰撞由恢复系数ε描述，对于实际材料特性，该系数取决于碰撞速度。首先，我们像通常为简化分析那样，使用恒定恢复系数ε = const来考虑自扩散。其次，研究了ε对碰撞速度的简化（分段）依赖关系下的自扩散。最后，考虑了实际粘弹性粒子气体的扩散。我们发现，对于ε = const，两种方法得出的自扩散系数结果相同。然而，对于恢复系数依赖于碰撞速度的情况，格林 - 久保方法要么具有局限性，要么在实际应用中过于复杂，因此我们使用查普曼 - 恩斯科格方法计算扩散系数。我们得出结论，在应用于颗粒气体时，推导动力学系数时查普曼 - 恩斯科格方法更可取。
