Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

Abstract

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.

15 pages, 1 figure

References in corpus (6)

• Dynamics of Freely Cooling Granular Gases
• The Inelastic Maxwell Model
• Hydrodynamics and transport coefficients for Granular Gases
• Diffusion of impurities in a granular gas
• Long-time behavior of Granular Gases with impact-velocity dependent coefficient of restitution
• Velocity Distribution of Inelastic Granular Gas in Homogeneous Cooling State

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• Long-time tails in freely cooling granular gases
• Event-driven Molecular Dynamics of Soft Particles
• Dispersal and organization of polarized cells: non-linear diffusion and cluster formation without adhesion