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

The importance of the dynamic anomaly of the self-diffusion coefficient, which becomes zero at the colloidal glass transition volume fraction φg as DS∼(1−Φ(x,t)/φg)2, has recently been emphasized for understanding structural slowing down in concentrated hard-sphere colloidal suspensions, where Φ(x,t) is the average local volume fraction of colloids. This anomaly originates from the many-body correlations due to the long-range hydrodynamic interactions among colloidal particles. In order to reflect this anomaly in Brownian dynamics, we propose an effective diffusion model equation for the position vector Xi(t) of the particle i as dXi(t)/dt=u(Xi(t),t), where u(xi,t) is a Gaussian, Markov random velocity with zero mean and satisfies 〈u(xi,t)u(xj,t′)〉0=2δ(t−t′)DS(Φ(xi,t))δij1, where the brackets denote the average over an equilibrium ensemble of the fluid. This model is useful for studying not only the slow dynamics of the supercooled colloidal fluid but also the crystallization process in a hard-sphere suspension by Brownian-dynamics simulation.