Effective diffusion model on Brownian dynamics of hard-sphere colloidal suspensions

The importance of the dynamic anomaly of the self-diffusion coefficient, wh ich becomes zero at the colloidal glass transition volume fraction phi(g) a s D-S similar to (1 - Phi(x, t)/phi(g))(2), has recently been emphasized fo r understanding structural slowing down in concentrated hard-sphere colloid al suspensions, where Phi(x, t) is the average local volume fraction of col loids. This anomaly originates from the many-body correlations due to the l ong-range hydrodynamic interactions among colloidal particles. In order to reflect this anomaly in Brownian dynamics, we propose an effective diffusio n model equation for the position vector X-i(t) of the particle i as dX(i)( t)/dt = u(X-i(t), t), where rr(x(i), t) is a Gaussian, Markov random veloci ty with zero mean and satisfies [u(x(i), t)u(x(j), t')](0) = 2 delta(t - t' )D-S(Phi(x(i), t))delta(ij)1, where the brackets denote the average over an equilibrium ensemble of the fluid. This model is useful for studying not o nly the slow dynamics of the supercooled colloidal fluid but also the cryst allization process in a hard-sphere suspension by Brownian-dynamics simulat ion. (C) 1999 Elsevier Science B.V. All rights reserved.