Slow Dynamics of Nonequilibrium Density Fluctuations in Concentrated Hard-Sphere Suspensions

The coupled diffusion equations recently proposed for concentrated hard-sphere suspensions of iInteracting Brownian particles, the nonlinear deterministic diffusion equation with the self-diffusion coefficient D S ( 0 ( x , t}) for the average local volume fraction 0(x, t), and the linear stochastic diffusion equation with Ds ( 0 ( x , t)) for the density fluctuations sn(x, t) are numerically solved under a spatially inhomogeneous, nonequilibrium initial state. Thus, in a supercooled region where 0B 0 < 0g, the slow evolution of the cluster-like glassy domains with 0 ( x , t) 0g and the slow relaxation of the nonequilibrium density fluctuations are shown to be caused by the dynamic singularity of the self-diffusion coefficient, Ds(0(x, t)) ~~ (1 — 0(x, t ) 0 g ) 2 , where 0 is a particle volume fraction, 0g = (4/3)3/(7 In 3 - 8 In 2 + 2) is the colloidal glass transition volume fraction, and 0B is the crossover volume fraction.