Slow dynamics of nonequilibrium density fluctuations in hard-sphere suspensions

The coupled diffusion equations recently proposed for concentrated hard-sphere suspensions are numerically solved to investigate the dynamics of density fluctuations around time-dependent nonequilibrium (spatially inhomogeneous) states. As the volume fraction of spheres φ approaches the critical value ${\mathrm{\phi }}_{\mathrm{g}}$ from below, the self-intermediate scattering function ${\mathrm{F}}_{\mathrm{S}}$(k,t) is shown to obey two different slow relaxations whose time scales ${\mathrm{t}}_{\mathrm{{\rm B}}}$ and ${\mathrm{t}}_{\mathrm{\alpha }}$ diverge as the separation parameter σ=(φ-${\mathrm{\phi }}_{\mathrm{g}}$)/${\mathrm{\phi }}_{\mathrm{g}}$ approaches zero: ${\mathrm{t}}_{\mathrm{{\rm B}}}$∼|σ${\mathrm{|}}^{\mathrm{-}\mathrm{{\rm B}}}$ and ${\mathrm{t}}_{\mathrm{\alpha }}$∼|σ${\mathrm{|}}^{\mathrm{-}\mathrm{\alpha }}$, where ${\mathrm{\phi }}_{\mathrm{g}}$=(4/3${)}^3$/(7ln3-8ln2+2). Thus, the importance of nonequilibrium effects on slow dynamics is stressed from a unifying viewpoint.