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Pré-Publication, Document De Travail 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/Cahn-Hilliard gradient energy, a generalized Korteweg's tensor, a generalized Dunn and Serrin heat flux, and Cahn-Hilliard diffusive fluxes. Starting form 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. An Euler/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)

Identifiants

  • HAL Id : hal-04444776 , version 3

Citer

Vincent Giovangigli. Kinetic derivation of Cahn-Hilliard fluid models. 2021. ⟨hal-04444776v3⟩
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