TY - JOUR

T1 - Self-diffusion in granular gases

T2 - Green-Kubo versus Chapman-Enskog

AU - Brilliantov, Nikolai V.

AU - Pöschel, Thorsten

PY - 2005/6

Y1 - 2005/6

N2 - 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 ε which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, ε=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of ε on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for ε=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.

AB - 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 ε which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, ε=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of ε on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for ε=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.

UR - http://www.scopus.com/inward/record.url?scp=31144448217&partnerID=8YFLogxK

U2 - 10.1063/1.1889266

DO - 10.1063/1.1889266

M3 - Article

AN - SCOPUS:31144448217

VL - 15

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 2

M1 - 026108

ER -