Relaxation dynamics of two-component fluid bilayer membranes

We theoretically investigate the relaxation dynamics of a nearly-flat binary lipid bilayer membrane by taking into account the membrane tension, hydrodynamics of the surrounding fluid, inter-monolayer friction and mutual diffusion in each monolayer. We find that two relaxation modes associated with the mutual diffusion appear in addition to the three previously discussed relaxation modes reflecting the bending and compression of the membrane. Because of the symmetry, only one of the two diffusive mode is coupled to the bending mode. The two diffusive modes are much slower than the bending and compression modes in the entire realistic wave number range. This means that the long time relaxation behavior is dominated by the mutual diffusion in binary membranes. The two diffusive modes become even slower in the vicinity of the unstable region towards phase separation, while the other modes are almost unchanged. In short time scales, on the other hand, the lipid composition heterogeneity induces in-plane compression and bending of the bilayer.