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Updated: Aug 9, 2026

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Published on: December 4, 2017
Chapman-Enskog expansion about nonequilibrium states with application to the sheared granular fluid
1Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Boulevard du Triomphe, 1050 Brussels, Belgium.
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 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.
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