# American Institute of Mathematical Sciences

September  2014, 19(7): 1889-1909. doi: 10.3934/dcdsb.2014.19.1889

## Mathematical modeling of phase transition and separation in fluids: A unified approach

 1 Facoltà di Ingegneria, Università e-Campus, 22060 Novedrate (CO) 2 DICATAM, Università di Brescia, Via Valotti, 9 - 25133 Brescia 3 DIBRIS, Università di Genova, Via Opera Pia 13, 16145 Genova

Received  April 2013 Revised  January 2014 Published  August 2014

A unified phase-field continuum theory is developed for transition and separation phenomena. A nonlocal formulation of the second law which involves an extra-entropy flux gives the basis of the thermodynamic approach. The phase-field is regarded as an additional variable related to some phase concentration, and its evolution is ruled by a balance equation, where flux and source terms are (unknown) constitutive functions. This evolution equation reduces to an equation of the rate-type when the flux is negligible, and it takes the form of a diffusion equation when the source term is disregarded. On this background, a general model for first-order transition and separation processes in a compressible fluid or fluid mixture is developed. Upon some simplifications, we apply it to the liquid-vapor phase change induced either by temperature or by pressure and we derive the expression of the vapor pressure curve. Taking into account the flux term, the sign of the diffusivity is discusssed.
Citation: Alessia Berti, Claudio Giorgi, Angelo Morro. Mathematical modeling of phase transition and separation in fluids: A unified approach. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 1889-1909. doi: 10.3934/dcdsb.2014.19.1889
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##### References:
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