Competitive Geometric Evolution of Amphiphilic Interfaces

We derive the curvature driven flow of closed-loop pore structures which arise a quasi-stationary states in the H−1 gradient flow of the Functionalized Cahn-Hilliard free energy which models amphiphilic mixtures. We extend this result to a sharp-interface reduction for the competitive evolution of disjoint collections of bilayer interfaces and closed-loop pores. In particular, for a mixture of spherical bilayers and circular, closed pores we explicitly identify two regimes: one in which spherical bilayers extinguish and the circular pores arrive at a common radius, and a complimentary regime in which spherical bilayers of differing radii stably coexist with commonradius, closed-loop, circular pores.