Hydrodynamic effect on concentration fluctuation in a two-component fluid membrane with a spherical shape

To the Gaussian model of a two-component fluid membrane with a spherical shape, we apply the mode coupling theory to study the hydrodynamic effect on the relaxation coefficient of concentration fluctuation in the homogeneous phase close to the critical point. In particular, when the viscosities of the three-dimensional fluids are the same inside and outside the vesicle, we obtain a concise analytical expression representing the hydrodynamic effect on the smallest wave-number mode. We derive its approximate expressions in various parameter regions to discuss the size effect of the vesicle. Much larger wave-number modes are studied numerically by means of our theoretical result. It is suggested that the hydrodynamic effect be diffusion-like, irrespective of the vesicle size, as long as the wavelength is much longer than the correlation length.