Kinetic derivation of Cahn-Hilliard fluid models

Vincent Giovangigli (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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.

Domaines: Physique mathématique [math-ph]

Vincent Giovangigli. Kinetic derivation of Cahn-Hilliard fluid models. 2021. ⟨hal-03323739v1⟩