A Cahn-Hilliard multiphase system with mobilities for the simulation of wetting

This paper tackles the simulation of the wetting phenomenon using a phase field model. To this end, we extend to multiphase the Cahn-Hilliard model with doubly degenerate mobilities we introduced in [17] and we show that this extension still preserves the second order of approximation of the sharp limit. In a second part, we propose a simple and efficient numerical schemes that require only about 60 lines in Matlab. We then provide some numerical experiments illustrating the influence of mobility and surface tension coefficients. Finally, we explain how to apply our phase field model to approximate the wetting of a thin tube on different solid supports.