On anisotropic order parameter models for multi-phase systems and their sharp interface limits

Abstract

For a general class of diffuse anisotropic multi-phase order parameter (or phase-field) models we use formally matched asymptotic expansions to determine the asymptotic limit when a small parameter related to the thickness of the interface tends to zero. In the case of anisotropic Allen-Cahn systems we obtain in the limit that the interface moves by anisotropic mean curvature flow. At triple junctions a force balance holds which in the anisotropic case includes shear forces (Herring torque terms) acting normal to the interface. We further identify the singular limit of anisotropic Cahn-Hilliard systems.