1Laboratoire Jean Leray, Université de Nantes & CNRS UMR 6629, BP 92208, F-44322 Nantes Cedex 3, France 2Institut Denis Poisson, Université d'Orléans, Université de Tours, CNRS UMR 7013, BP 6759, F-45067 Orléans Cedex 2, France
ESAIM. Proceedings, Tome 66 (2019), pp. 22-41
Cet article a éte moissonné depuis la source EDP Sciences
The paper deals with the modelling of the relaxation processes towards thermodynamic equilibrium in a liquid-vapour isothermal mixture. Focusing on the van der Waals equation of state, we construct a constrained optimization problem using Gibbs' formalism and characterize all possible equilibria: coexistence states, pure phases and metastable states. Coupling with time evolution, we develop a dynamical system whose equilibria coincide with the minimizers of the optimization problem. Eventually we consider the coupling with hydrodynamics and use the dynamical system as a relaxation source terms in an Euler-type system. Numerical results illustrate the ability of the whole model to depict coexistence and metastable states as well.
1
Laboratoire Jean Leray, Université de Nantes & CNRS UMR 6629, BP 92208, F-44322 Nantes Cedex 3, France
2
Institut Denis Poisson, Université d'Orléans, Université de Tours, CNRS UMR 7013, BP 6759, F-45067 Orléans Cedex 2, France
@article{EP_2019_66_a2,
author = {Hala Ghazi and Francois James and H\'el\`ene Mathis},
title = {Vapour-liquid phase transition and metastability},
journal = {ESAIM. Proceedings},
pages = {22--41},
year = {2019},
volume = {66},
doi = {10.1051/proc/201966002},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201966002/}
}
TY - JOUR
AU - Hala Ghazi
AU - Francois James
AU - Hélène Mathis
TI - Vapour-liquid phase transition and metastability
JO - ESAIM. Proceedings
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SP - 22
EP - 41
VL - 66
UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/201966002/
DO - 10.1051/proc/201966002
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ID - EP_2019_66_a2
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%A Francois James
%A Hélène Mathis
%T Vapour-liquid phase transition and metastability
%J ESAIM. Proceedings
%D 2019
%P 22-41
%V 66
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201966002/
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Hala Ghazi; Francois James; Hélène Mathis. Vapour-liquid phase transition and metastability. ESAIM. Proceedings, Tome 66 (2019), pp. 22-41. doi: 10.1051/proc/201966002
