Dynamics of phase separation in confined two-component fluid membranes

We investigate the dynamics of phase separation in two-component fluid membranes confined between parallel and rigid bounding plates. Through numerical simulation, we find dramatic slow coarsening of the order parameter field within the simulation time. In particular, a microphase separation is obtained as an equilibrium phase for sufficiently large values of the elastic coupling, being consistent with the previous mean-field analysis. We also provide the physical interpretation of such slow kinetics in terms of the elastic effects arising from the Helfrich interactions, together with theoretical analysis on the average domain size in the strong segregation regimes.