Chapman-Enskog expansion about nonequilibrium states: the sheared granular fluid
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.
Keywords
Cite
@article{arxiv.cond-mat/0510749,
title = {Chapman-Enskog expansion about nonequilibrium states: the sheared granular fluid},
author = {James F. Lutsko},
journal= {arXiv preprint arXiv:cond-mat/0510749},
year = {2007}
}
Comments
23 pages, no figures. Submited to PRE Replaced to correct misc. errors Replaced to correct misc. errors, make notation more consistant, extend discussion