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The role of degenerate mobilities in Cahn‐Hilliard models
Author(s) -
Dziwnik Marion
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900396
Subject(s) - degenerate energy levels , degeneracy (biology) , quadratic equation , isotropy , physics , diffusion , work (physics) , anisotropy , statistical physics , condensed matter physics , mathematics , thermodynamics , quantum mechanics , geometry , bioinformatics , biology
The present work provides an insight into the role of degenerate mobilities in phase field models and in particular their influence on the evolution of the interface. The equation of interest is the Cahn‐Hilliard equation (in two space dimensions) with a polynomial double well free energy and different order‐parameter dependent, degenerate mobilities. According to the preliminary work [1], considering an anisotropic version of the equation, the asymptotic sharp interface limit subtly dependents on the degeneracy of the mobility. Whilst a quadratic degenerate mobility leads to a sharp interface model where bulk diffusion is present at the same asymptotic order as surface diffusion, a bi‐quadratic degenerate mobility leads to a sharp interface model where bulk diffusion is subdominant. The present study continues the preliminary work and shows that the type of the degeneracy has a qualitative impact on the evolution: Considering numerical simulations of the dewetting process of a thin solid film with four‐fold anisotropic surface energy, the evolution with bi‐quadratic degenerate mobility turns out to be more effective for film pinch‐off than with quadratic degenerate mobility. An extension to the isotropic Cahn‐Hilliard equation ensures that the characteristic difference in the pinch‐off behavior is in fact mobility‐dependent.