Nonequilibrium effects on slow dynamics in concentrated colloidal suspensions

An alternative stochastic diffusion equation is proposed to study the dynamics of nonequilibrium density fluctuations in concentrated hard-sphere suspensions of interacting Brownian particles with both hydrodynamic and direct interactions among particles. The singularity of the correlation effect of the many-body hydrodynamic interactions is shown to drastically influence the qualitative behavior of the relaxation of nonequilibrium density fluctuations, and thus to cause the two different slow relaxations whose time scales, $t_{\beta }$ and $t_{\alpha }$, diverge as the volume fraction of Brownian particles approaches the critical value ${\phi }_c=\frac{{\left(\frac{4}{3}\right)}^3}{(7\mathrm{}\ln 3-8\ln 2+2)}$; $t_{\beta }\sim {(1-\frac{\phi }{{\phi }_c})}^{-1\mathrm{}}$ and $t_{\alpha }\sim {(1-\frac{\phi }{{\phi }_c})}^{-2\mathrm{}}$.