Journal
PHYSICAL REVIEW E
Volume 104, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.104.054109
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Funding
- ANR INSIDE project [ANR-19-CE05-0037-02]
- French Agence Nationale de la Recherche
- Agence Nationale de la Recherche (ANR) [ANR-19-CE05-0037] Funding Source: Agence Nationale de la Recherche (ANR)
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A compressible Cahn-Hilliard fluid model is derived from the kinetic theory of dense gas mixtures, involving various energy and flux terms. Chapman-Enskog method and Taylor expansion are used to obtain the Cahn-Hilliard fluid model, which includes viscous, heat, and diffusive fluxes.
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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