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

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

2005-10-27

arxiv.org/abs/cond-mat/0510749v3

Phys. Rev. E 73, 021302 (2006)

Physics

Condensed Matter

Statistical Mechanics

23 pages, no figures. Submited to PRE Replaced to correct misc. errors Replaced to correct misc. errors, make notation more co

Scientific paper

10.1103/PhysRevE.73.021302

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.

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