# [063] Chapman-Enskog expansion about nonequilibrium states with application to the sheared granular fluid

The Chapman-Enskog method of solution of kinetic equations, such as the Boltzmann equation, is based on an expansion in gradients of the deviations of 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 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.

Recommended citation: James F. Lutsko, "Chapman-Enskog expansion about nonequilibrium states with application to the sheared granular fluid", *Phys. Rev. E*, **73**, 21302 (2006)

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