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.

翻译：本文提出了一种具有双重退化迁移率的新型多相Cahn-Hilliard模型。通过形式渐近分析证明，该模型能以二阶精度逼近具有迁移率系数和表面张力的多相表面扩散流。为展示该模型适用于数值逼近，我们提出了一种简单有效的数值方案及其紧凑的Matlab实现。通过多种数值实验的结果，我们展示了迁移率和表面张力系数的影响。凭借其二阶精度及对数值实现的良好适应性，本模型在处理极具挑战性的表面扩散问题时非常实用。特别地，我们证明该模型能有效模拟任意固体基底上薄液管去湿过程，且无需引入非线性边界条件。