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Phase-field evolution in Cahn–Hilliard–Korteweg fluids

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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.

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Authors and Affiliations

  1. Department of Mathematics, Computer Science and Economics, University of Basilicata, Campus Macchia Romana, 85100, Potenza, Italy

    V. A. Cimmelli & A. R. Pace

  2. Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale F. Stagno d’Alcontres 31, 98166, Messina, Italy

    F. Oliveri

Authors
  1. V. A. Cimmelli
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  2. F. Oliveri
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  3. A. R. Pace
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Correspondence to F. Oliveri.

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Cimmelli, V.A., Oliveri, F. & Pace, A.R. Phase-field evolution in Cahn–Hilliard–Korteweg fluids. Acta Mech 227, 2111–2124 (2016). https://doi.org/10.1007/s00707-016-1625-2

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  • DOI: https://doi.org/10.1007/s00707-016-1625-2

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