Hierarchy of consistent n-component Cahn-Hilliard systems

Franck Boyer (1) , Sebastian Minjeaud (2, 3)

1 I2M - Institut de Mathématiques de Marseille
2 JAD - Laboratoire Jean Alexandre Dieudonné
3 CASTOR - Control, Analysis and Simulations for TOkamak Research

In this paper, we propose a new generalization of the well-known Cahn-Hilliard two-phase model for the modelling of n-phase mixtures. The model is derived using the consistency principle: we require that our n-phase model exactly coincide with the classical two-phase model when only two phases are present in the system. We give conditions for the model to be well-posed. We also present numerical results (including simulations obtained when coupling the Cahn-Hilliard system with the Navier-Stokes so as to obtain a phase-field model for multiphase flows) to illustre the capability of such modelling.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Franck Boyer, Sebastian Minjeaud. Hierarchy of consistent n-component Cahn-Hilliard systems. Mathematical Models and Methods in Applied Sciences, 2014, 24 (14), pp.2885-2928. ⟨10.1142/S0218202514500407⟩. ⟨hal-00933674⟩