Vapour-liquid phase transition and metastability

• Main Authors: Ghazi Hala, James Francois, Mathis Hélène
• Format: Article
• Language: English
• Published: EDP Sciences 2019-01-01
• Series: ESAIM: Proceedings and Surveys
• Online Access: https://www.esaim-proc.org/articles/proc/pdf/2019/02/proc196602.pdf

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.