Generalized Stokes-Einstein equation for spherical particle suspensions

The cooperative diffusion coefficient Dc for spherical particle suspensions is calculated using a ``mode-coupling'' method which extends previous calculations of Dc for critical fluids and semidilute polymer solutions. The renormalization of the viscosity in the velocity-velocity correlation function from the solvent to the suspension viscosity leads to a generalized Stokes-Einstein (SE) equation in which the suspension viscosity {η} replaces the solvent viscosity η₀ and the correlation length {ξ} (related to the osmotic compressibility) replaces the sphere radius R at nonvanishing suspension concentrations. Insertion of the leading order hard sphere virial expansions for {η} and the osmotic compressibility into our generalized SE equation gives a virial expansion for Dc which is consistent with theoretical estimates obtained by alternative methods. These leading order virial expansions are also consistent with experiments on model (``hard sphere'') suspensions. Results are given for the virial expansion of spherical liquid droplets interacting via a contact attractive interaction. Further experiments are required to test the generalized SE equation at higher suspension concentrations.