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- Title
Phase-field evolution in Cahn-Hilliard-Korteweg fluids.
- Authors
Cimmelli, V.; Oliveri, F.; Pace, A.
- Abstract
In this paper, the diffusion of different phases in a third-grade Korteweg fluid is modeled by introducing a phase-field as a new independent thermodynamic variable. The constitutive equations are supposed to depend on the mass density and its spatial derivatives up to the second order, as well as on specific internal energy, barycentric velocity and phase-field, together with their first-order spatial derivatives. The compatibility of the model with the second law of thermodynamics is exploited by applying a generalized Liu procedure. For isothermal and isochoric phases, a general evolution equation for the phase-field, which generalizes the classical Cahn-Hilliard equation, is derived. Specific entropy and free energy are proved to depend on the basic unknown fields as well as on their gradients. A general constitutive equation for the Cauchy stress, which encompasses the classical one postulated by Korteweg in 1901, is obtained.
- Subjects
FLUID mechanics; PARTIAL differential equations; KORTEWEG-de Vries equation; INCOMPRESSIBLE flow; BARYCENTRIC dynamical time
- Publication
Acta Mechanica, 2016, Vol 227, Issue 8, p2111
- ISSN
0001-5970
- Publication type
Article
- DOI
10.1007/s00707-016-1625-2