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 de nsity fluctuations in a suspension of colloidal hard spheres, which enables us to study the influence of solvent-mediated hydrodynamic interactions be tween particles as well as the direct interactions, is presented with the a id of the time-convolutionless projector method. The many-body correlations due to long-range hydrodynamic interactions are then shown to play an impo rtant 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 a lso that of colloidal glass consistently, is also proposed from a new stand point obtained recently by the present author. (C) 2001 Elsevier Science B. V. All rights reserved.