Transport properties of dense dissipative hard-sphere fluids for arbitrary energy loss models

The revised Enskog approximation for a fluid of hard spheres which lose energy upon collision is discussed for the case that the energy is lost from the normal component of the velocity at collision but is otherwise arbitrary. Granular fluids with a velocity-dependent coefficient of restitution are an important special case covered by this model. A normal solution to the Enskog equation is developed using the Chapman-Enskog expansion. The lowest order solution describes the general homogeneous cooling state and a generating function formalism is introduced for the determination of the distribution function. The first order solution, evaluated in the lowest Sonine approximation, provides estimates for the transport coefficients for the Navier-Stokes hydrodynamic description. All calculations are performed in an arbitrary number of dimensions.

Figure 1

The four transport coefficients for a simple granular fluid in three dimensions at reduced density $n{\sigma }^3=0.5$. The transport coefficients are shown in dimensionless form as indicated by the labeling of each figure. The lines are the results of Ref. 6, the circles are the results of this paper and the broken line is the Gaussian approximation.