Volume 57, Number 3, May-June 2023
|Page(s)||1473 - 1509|
|Published online||18 May 2023|
A multiphase Cahn–Hilliard system with mobilities and the numerical simulation of dewetting
Univ Lyon, INSA de Lyon, CNRS UMR 5208, Institut Camille Jordan, 20 avenue Albert Einstein, F-69621 Villeurbanne, France
2 Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne, France
* Corresponding author: firstname.lastname@example.org.
Accepted: 6 March 2023
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.
Mathematics Subject Classification: 74N20 / 35A35 / 53E10 / 53E40 / 65M32 / 35A15
Key words: Phase field approximation / multiphase Cahn–Hilliard system / surface diffusion / degenerate mobilities / numerical approximation of dewetting
© The authors. Published by EDP Sciences, SMAI 2023
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