  We investigate the hydrodynamic effects on the dynamics of critical
concentration fluctuations in multicomponent fluid membranes. Two geometrical
cases are considered; (i) confined membrane case and (ii) supported membrane
case. We numerically calculate the wavenumber dependence of the effective
diffusion coefficient by changing the temperature and/or the thickness of the
bulk fluid. For some limiting cases, the result is compared with the previously
obtained analytical expression. An analogy of the multicomponent membrane to 2D
microemulsion is explored for the confined membrane geometry.
