Geometric evolution of bilayers under the degenerate functionalized cahn-hilliard equation

Using a multiscale analysis, we derive a sharp interface limit for the dynamics of bilayer structures of the functionalized Cahn-Hilliard equation with a cutoff diffusion mobility M(u) that is degenerate for u <= 0 and a continuously differentiable double-well potential W(u). We show that the bilayer interface does not move in the t = O(1) time scale. The interface motion occurs in the t = O(epsilon-1) time scale and is determined by porous medium diffusion processes in both phases with no jumps on the interface. In the longer O(epsilon-2) time scale, the interface motion is a complex combination of porous medium diffusion processes in both phases and the property of mass conservation.