Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 365, Issue -, Pages 324-349Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2018.02.051
Keywords
Multiphase systems; Mean curvature flow; Mobilities; Phase field; Droplets wetting; Nanowires
Funding
- French National Research Agency (ANR) [ANR-12-BS01-0014-01, ANR-14-CE27-001]
- LABEX MILYON of Universite de Lyon within the program Investissements d'Avenir [ANR-10-LABX-0070, ANR-11-IDEX-0007]
- Mission pour l'interdisciplinarite within the program Defi Imag'In
- project COCA within the Programme Gaspard Monge of the Fondation Mathematique Jacques Hadamard
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The structure of many multiphase systems is governed by an energy that penalizes the area of interfaces between phases weighted by surface tension coefficients. However, interface evolution laws depend also on interface mobility coefficients. Having in mind some applications where highly contrasted or even degenerate mobilities are involved, for which classical phase field models are inapplicable, we propose a new effective phase field approach to approximate multiphase mean curvature flows with mobilities. The key aspect of our model is to incorporate the mobilities not in the phase field energy (which is conventionally the case) but in the metric which determines the gradient flow. We show the consistency of such an approach by a formal analysis of the sharp interface limit. We also propose an efficient numerical scheme which allows us to illustrate the advantages of the model on various examples, as the wetting of droplets on solid surfaces or the simulation of nanowires growth generated by the so-called vapor-liquid-solid method. (C) 2018 Elsevier Inc. All rights reserved.
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