A crucial role of long-range hydrodynamic interactions near the colloidal glass transition based on time-convolutionless mode-coupling theory

The time-convolutionless mode-coupling theory (TMCT) recently proposed for molecular systems is employed to derive a TMCT equation for the collective-intermediate scattering function in suspensions of hard-sphere colloids from the nonlinear Langevin equations with the hydrodynamic interactions between colloids. The nonlinear memory function contained in the TMCT equation consists of two types of interactions between colloids; a mechanical interaction and a hydrodynamic interaction. It is predicted from the TMCT equation how the hydrodynamic interactions can affect the ergodic to non-ergodic transition at a critical point. Then, such a hydrodynamic effect is tested by the experimental data for suspensions of hard-sphere colloids with size polydispersities. Thus, it is emphasized that the long-range hydrodynamic interactions are indispensable to explain the polydispersity dependence of the experimental critical points which is quite different from that of simulations where only the mechanical interactions are taken into.