A systematic theory for the dynamics of concentrated hard-sphere suspensions of interacting Brownian particles with both hydrodynamic and direct interactions is presented. An alternative equation for the number density of particles is derived. The volume-fraction dependence of the shortand long-time self-diffusion coefficients is thus explored from a new point of view. Both the short-range and the long-range hydrodynamic interactions are shown to play an important role in both coefficients, while the direct interactions are reduced drastically by the hydrodynamic interactions.

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We study concentrated binary colloidal suspensions, a model system which has a glass transition as the volume fraction φ of particles is increased. We use confocal microscopy to directly observe particle motion within dense samples with φ ranging from 0.4 to 0.7. Our binary mixtures have a particle diameter ratio d S /d L = 1/1.3 and particle number ratio N S /N L = 1.56, which are chosen to inhibit crystallization and enable long-time observations. Near the glass transition we find that particle dynamics are heterogeneous in both space and time. The most mobile particles occur in spatially localized groups. The length scales characterizing these mobile regions grow slightly as the glass transition is approached, with the largest length scales seen being ∼ 4 small particle diameters. We also study temporal fluctuations using the dynamic susceptibility χ 4 , and find that the fluctuations grow as the glass transition is approached. Analysis of both spatial and temporal dynamical heterogeneity show that the smaller species play an important role in facilitating particle rearrangements. The glass transition in our sample occurs at φ g ≈ 0.58, with characteristic signs of aging observed for all samples with φ > φ g .

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