The modified Enskog equation

Abstract

Arguments are presented for a modified form of the nonlinear Enskog equation, which describes the time dependence of the single-particle distribution function in a dense gas of hard spheres. Unlike the usual Enskog equation it is not restricted to small spatial non-uniformities, and may thus be used to derive Burnett and higher-order hydrodynamic equations. In a single-component system both equations are equivalent at the level of the Navier-Stokes equations. The main importance of the modified Enskog equation becomes manifest when it is extended to mixtures of hard spheres. It is shown that the existing versions of Enskog's theory for mixtures lead to results which are in conflict with irreversible thermodynamics (more specifically, the Onsager symmetry relations do not hold), whereas the present modified Enskog theory gives results in complete agreement with irreversible thermodynamics.