A Phase-field Model for Solid-state Dewetting and Its Sharp-interface Limit
نویسندگان
چکیده
We propose a phase field model for solid state dewetting where the surface energy is weakly anisotropic. The evolution is based on the Cahn-Hilliard equation with degenerate mobility 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. The resulting sharp interface model is consistent with the pure surface diffusion model. In addition, we show that the natural boundary conditions, as indicated from the first variation of the total free energy, imply a contact angle condition for the dewetting front, which, in the isotropic case, is consistent with the well-known Young’s equation.
منابع مشابه
Numerical determination of the surface and composition profiles for a film of binary mixture on a solid substrate
We numerically study the static structures resulting from the coupled demixing and dewetting of a film of binary liquid on a solid substrate. The model corresponds to the static limit of the diffuse interface model describing the phase separation process for a binary liquid (model-H), when supplemented by boundary conditions at the evolving free surface. The resulting variational problem is dis...
متن کاملPhase field approach for simulating solid-state dewetting problems
We propose a phase field model for simulating solid-state dewetting and the morphological evolution of patterned islands on a substrate. The evolution is governed by the Cahn–Hilliard equation with isotropic surface tension and variable scalar mobility. The proposed approach easily deals with the complex boundary conditions arising in the solid-state dewetting problem. Since the method does not...
متن کاملA preconditioned solver for sharp resolution of multiphase flows at all Mach numbers
A preconditioned five-equation two-phase model coupled with an interface sharpening technique is introduced for simulation of a wide range of multiphase flows with both high and low Mach regimes. Harten-Lax-van Leer-Contact (HLLC) Riemann solver is implemented for solving the discretized equations while tangent of hyperbola for interface capturing (THINC) interface sharpening method is applied ...
متن کاملPhase-field modelling of solute trapping during rapid solidification of a Si–As alloy
The effect of nonequilibrium solute trapping by a growing solid under rapid solidification conditions is studied using a phase-field model. Considering a continuous steady-state concentration profile across the diffuse solid-liquid interface, a new definition of the nonequilibrium partition coefficient in the phase-field context is introduced. This definition leads, in particular for high growt...
متن کاملSharp Interface Limit of a Homogenized Phase Field Model for Phase Transitions in Porous Media
A homogenized phase field model for phase transitions in porous media is considered. By making use of the method of formal asymptotic expansion with respect to the interface thickness, a sharp interface limit problem is derived. This limit problem turns out to be similar to the classical Stefan problem with surface tension and kinetic undercooling.
متن کامل