  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.
