Geodesic
Vapour-liquid phase transition and metastability
Hala Ghazi1 ; Francois James2 ; Hélène Mathis1
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
ESAIM. Proceedings, Tome 66 (2019), pp. 22-41 Cet article a éte moissonné depuis la source EDP Sciences

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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.
DOI : 10.1051/proc/201966002

Hala Ghazi 1 ; Francois James 2 ; Hélène Mathis 1

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/}
}
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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

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