An anisotropic phase-field model for solid-state dewetting and its sharp-interface limit. (24th February 2017)

• Record Type: Journal Article
• Authors: Dziwnik, Marion; Münch, Andreas; Wagner, Barbara
• Is Part Of: Nonlinearity. Volume 30:Number 4(2017:Apr.)
• Page Start: 1465
• Page End: 1496
• Publication Date: 2017-02-24
• Subjects: phase-field model -- matched asymptotic expansions -- exponential asymptotics -- sharp interface model -- free boundary problems -- dewetting solid films; 76Dxx -- 76Txx -- 35B40 -- 35C20 -- 49Jxx; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa5e5d
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We propose a two-dimensional phase field model for solid state dewetting where the surface energy is weakly anisotropic. The evolution is described by the Cahn–Hilliard equation with a bi-quadratic degenerate mobility together with a bulk free energy based on a double-well potential and a free boundary condition at the film-substrate contact line. We derive the corresponding sharp interface limit via matched asymptotic analysis involving multiple inner layers. We show that in contrast to the frequently used quadratic degenerate mobility, the resulting sharp interface model for the bi-quatratic mobility is consistent with the pure surface diffusion model. In addition, we show that natural boundary conditions at the substrate obtained from the first variation of the total free energy including contributions at the substrate imply a contact angle condition in the sharp-interface limit which recovers the Young–Herring equation in the anisotropic and Young's equation in the isotropic case, as well as a balance of fluxes at the contact line (or contact point).