Slow dynamics of equilibrium density fluctuations in suspensions of colloidal hard spheres near the glass transition

A mean-field theory for the dynamics of equilibrium suspensions of colloidal hard spheres near the glass transition is presented based on the standpoint recently proposed by the present author. It is shown that although the relative magnitude of the density fluctuations to the mean equilibrium density is small even near the glass transition, they are described by a nonlinear stochastic equation which originates from the long-range hydrodynamic interactions between particles. A nonlinear mean-field equation for the particle mean-square displacement is then derived. This equation is used to analyze the recent experimental data for equilibrium colloidal suspensions. Analyses show that no divergence of the alpha- and beta-relaxation times is found in the experimental data, although the dynamic properties of the colloidal liquid exhibit a drastic slowing down in the so-called supercooled region.