Kinetic derivation of Cahn-Hilliard fluid models.
basic_science · Level V
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- Record sourced from PubMed, PMID 34942763.
- Also identified by DOI 10.1103/PhysRevE.104.054109.
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Abstract
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.