Wetting and Prewetting of Anti-Phase Boundaries

A degenerate Allen-Cahn/Cahn-Hilliard system which was developed to describe simultaneous ordering and phase separation, can also be viewed as a diffuse interface approximation for various problems in materials science in which surface diffusion and motion by mean curvature are coupled. In the original context a low temperature coarsening limit, yielding geometric motion in the limit, was designed to describe small particles of a disordered phase whose shape evolves by surface diffusion which are embedded along grain boundaries which partition the system into two ordered variants. While an early analysis focused on systems in the proximity of the complete wetting limit 9], a later analysis extended these results also to the partial wetting setting 11]. We outline here some features which determine whether a given degenerate Allen-Cahn/Cahn-Hilliard system corresponds to complete or partial wetting in the limit, giving some explicit examples of both possibilities.