Phase-field models for fluid mixtures

• Published in: Mathematical and computer modelling Vol. 45; no. 9; pp. 1042 - 1052
• Main Author: Morro, A.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.05.2007; Elsevier Science
• Subjects: Exact sciences and technology; Fluid mixtures; Mathematical analysis; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; Partial differential equations; Phase fields; Phase transitions; Sciences and techniques of general use; Fluid mixtures; Phase transitions; Phase fields; Scientific computation; Multiphase flow; Continuity equation; Applied mathematics; Entropy; Mathematical model
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2006.08.011

The paper investigates the modelling of phase transitions in multiphase fluid mixtures. The order parameter is identified with the set of concentrations and is a phase field in that it varies smoothly in the space region. This in turn requires that the continuity equations be regarded as constraints on the pertinent fields. The phase field is viewed as an internal variable whose evolution is subject to thermodynamic requirements. The second law allows for an extra entropy flux which proves to be proportional to the time derivative of the order parameter. Previous papers on the subject are revisited. It follows that their recourse to external mass supplies or to ad-hoc entropy fluxes can be avoided. The analogy of the phase-field model, with that of mixtures with mass–density gradients and extra entropy flux, is emphasized.