Open AccessMathematical modeling of phase transition and separation in fluids: A unified approach
Author(s) -
Alessia Berti,
Claudio Giorgi,
Angelo Morro
Publication year - 2014
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2014.19.1889
Subject(s) - compressibility , statistical physics , thermodynamics , physics , thermal diffusivity , mechanics , flux (metallurgy) , entropy (arrow of time) , unified field theory , phase transition , mixture theory , constitutive equation , classical mechanics , mathematics , theoretical physics , materials science , statistics , mixture model , finite element method , metallurgy
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