Chapman-Enskog expansion about nonequilibrium states: the sheared granular fluid

TL;DR

This paper extends the Chapman-Enskog method to allow expansions around arbitrary, far-from-equilibrium states, enabling the derivation of hydrodynamic equations for complex systems like sheared granular gases.

Contribution

It introduces a generalized Chapman-Enskog approach that does not require near-equilibrium conditions, applicable to systems such as sheared granular fluids.

Findings

Derived hydrodynamic equations for far-from-equilibrium states

Applied method successfully to sheared granular gas

Extended the scope of Chapman-Enskog expansion beyond local equilibrium

Abstract

The Chapman-Enskog method of solution of kinetic equations, such as the Boltzmann equation, is based on an expansion in gradients of the deviations fo the hydrodynamic fields from a uniform reference state (e.g., local equilibrium). This paper presents an extension of the method so as to allow for expansions about \emph{arbitrary}, far-from equilibrium reference states. The primary result is a set of hydrodynamic equations for studying variations from the arbitrary reference state which, unlike the usual Navier-Stokes hydrodynamics, does not restrict the reference state in any way. The method is illustrated by application to a sheared granular gas which cannot be studied using the usual Navier-Stokes hydrodynamics.