On the derivation of a nonlinear stochastic diffusion equation for supercooled colloidal liquids and glasses

A formal theory of finding a nonlinear stochastic diffusion equation for density fluctuations in a suspension of colloidal hard spheres, which enables us to study the influence of solvent-mediated hydrodynamic interactions between particles as well as the direct interactions, is presented with the aid of the time-convolutionless projector method. The many-body correlations due to long-range hydrodynamic interactions are then shown to play an important role in the slow dynamics of density fluctuations near the colloidal glass transition. An effective nonlinear stochastic equation, which enables us to describe not only the dynamics of supercooled colloidal liquid but also that of colloidal glass consistently, is also proposed from a new standpoint obtained recently by the present author.