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

TL;DR

This paper extends the Enskog approximation to dense dissipative hard-sphere fluids with arbitrary energy loss models, deriving transport coefficients and solutions for the homogeneous cooling state in multiple dimensions.

Contribution

It introduces a generalized Enskog framework for energy-losing collisions, including velocity-dependent restitution, and develops solutions for transport properties in arbitrary dimensions.

Findings

Derived expressions for transport coefficients in dissipative hard-sphere fluids.

Provided a Chapman-Enskog based solution for the homogeneous cooling state.

Extended the model to arbitrary energy loss and dimensions.

Abstract

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.