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Article Dans Une Revue Physical Review E Année : 2021

Kinetic derivation of Cahn-Hilliard fluid models

Résumé

A compressible Cahn-Hilliard fluid model is derived from the kinetic theory of dense gas mixtures. The fluid model involves a van der Waals and Cahn-Hilliard gradient energy, a generalized Korteweg's tensor, a generalized Dunn and Serrin heat flux, and Cahn-Hilliard-type diffusive fluxes. Starting from the BBGKY hierarchy for gas mixtures, a Chapman-Enskog method is used-with a proper scaling of the generalized Boltzmann equations-as well as higher-order Taylor expansions of pair distribution functions. A Euler and van der Waals model is obtained at zeroth order, while the Cahn-Hilliard fluid model is obtained at first order, involving viscous, heat, and diffusive fluxes. The Cahn-Hilliard extra terms are associated with intermolecular forces and pair interaction potentials.
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Dates et versions

hal-04444776 , version 1 (22-08-2021)
hal-04444776 , version 2 (21-10-2021)
hal-04444776 , version 3 (08-11-2021)
hal-04444776 , version 4 (09-02-2024)

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Vincent Giovangigli. Kinetic derivation of Cahn-Hilliard fluid models. Physical Review E , 2021, 104, ⟨10.1103/physreve.104.054109⟩. ⟨hal-04444776v4⟩
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