2021/05/20 by Élie Bretin, Bretin, Elie, Roland Denis +7 · 1 citation
Engineering · Materials Science · #35A15 #35A35 #53E10 #53E40 #65M32 #74N20 #Block Copolymer Self-Assembly #FOS: Mathematics #Fluid Dynamics and Thin Films #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.2105.09627
openalex publication_date 2021/05/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/08/01
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.