A new phase field model for inhomogeneous minimal partitions, and applications to droplets dynamics

Abstract

We propose and analyze in this paper a new derivation of a phase-field model to approximate inhomogeneous multiphase perimeters. It is based on suitable decompositions of perimeters under some embeddability condition which allows not only an explicit derivation of the model from the surface tensions, but also gives rise to a $\Gamma$-convergence result. Moreover, thanks to the nice form of the approximating energy, we can use a simple and robust scheme to simulate its gradient flow. We illustrate the efficiency of our approach with a series of numerical simulations in 2D and 3D, and we address in particular the dynamics of droplets evolving on a fixed solid.