A multiphase Cahn-Hilliard system with mobilities and the numerical simulation of dewetting

TL;DR

This paper introduces a new multiphase Cahn-Hilliard model with degenerate mobilities, providing second order accuracy and effective numerical schemes for simulating complex surface diffusion and dewetting phenomena.

Contribution

It develops a novel multiphase Cahn-Hilliard model with doubly degenerate mobilities and demonstrates its accuracy and efficiency through numerical experiments.

Findings

Second order accuracy in approximating surface diffusion flow

Effective numerical scheme for complex dewetting simulations

Successful simulation of thin liquid tube dewetting on arbitrary supports

Abstract

We propose in this paper a new multiphase Cahn-Hilliard model with doubly degenerate mobilities. We prove by a formal asymptotic analysis that it approximates with second order accuracy the multiphase surface diffusion flow with mobility coefficients and surface tensions. To illustrate that it lends itself well to numerical approximation, we propose a simple and effective numerical scheme together with a very compact Matlab implementation. We provide the results of various numerical experiments to show the influence of mobility and surface tension coefficients. Thanks to its second order accuracy and its good suitability for numerical implementation, our model is very handy for tackling notably difficult surface diffusion problems. In particular, we show that it can be used very effectively to simulate numerically the dewetting of thin liquid tubes on arbitrary solid supports without requiring nonlinear boundary conditions.