On a phase field model for solid-liquid phase transitions

Sylvie Benzoni-Gavage (1) , Laurent Chupin (2) , Didier Jamet (3) , Julien Vovelle (1)

1 ICJ - Institut Camille Jordan
2 LMBP - Laboratoire de Mathématiques Blaise Pascal
3 CEA (DEN/DTP/SMTH)

A new phase field model is introduced, which can be viewed as nontrivial generalisation of what is known as the Caginalp model. It involves in particular nonlinear diffusion terms. By formal asymptotic analysis, it is shown that in the sharp interface limit it still yields a Stefan-like model with: 1) a (generalized) Gibbs-Thomson relation telling how much the interface temperature differs from the equilibrium temperature when the interface is moving or/and is curved with surface tension; 2) a jump condition for the heat flux, which turns out to depend on the latent heat and on the velocity of the interface with a new, nonlinear term compared to standard models. From the PDE analysis point of view, the initial-boundary value problem is proved to be locally well-posed in time (for smooth data).

Keywords: Phase field; Caginalp model; Sharp interface; Nonlinear diffusion

Domains: Analysis of PDEs [math.AP]

Sylvie Benzoni-Gavage, Laurent Chupin, Didier Jamet, Julien Vovelle. On a phase field model for solid-liquid phase transitions. Discrete and Continuous Dynamical Systems - Series S, 2012, 32 (6), pp.1997-2025. ⟨hal-00549828v2⟩