Generalized enskog theory for homogeneous systems |
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Authors: | J. Piasecki B. Cichocki |
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Affiliation: | (1) Institute of Theoretical Physics, Warsaw University, Warsaw, Poland |
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Abstract: | We propose a generalization of the Enskog equation for homogeneous dense systems including the complete three-particle dynamics. To this end the time derivative of the one-particle distribution is represented in the thermodynamic limit as the sum of three terms describing the effect of the initials-particle correlations, collisions withins-particle clusters, and coupling ofs-particle clusters to the surrounding gaseous medium, respectively. The analysis of casess=2 ands=3 is performed both for hard spheres and for a smooth, repulsive interaction. On assuming the equilibrium structure and spatial dependence of terms reflecting the effect of the medium, we obtain fors=2 the Enskog equation, and fors=3 a new equation, going beyond the Enskog theory. Apart from the Enskog collision term it contains additional contributions, and can be shown to reduce to the Choh-Uhlenbeck equation in the long-time, low-density limit. |
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Keywords: | Liouville equation kinetic theory thermodynamic limit hard spheres Enskog equation Choh-Uhlenbeck equation binary collision expansion reduced distributions thermal equilibrium |
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