Square root singularity in the viscosity of neutral colloidal suspensions at large frequencies

The asymptotic frequency, ω, dependence of the dynamic viscosity of neutral hard sphere colloidal suspensions is shown to be of the form η 0 A(φ)(ωτ P) −1/2 , where A(φ) has been determined as a function of the volume fraction φ, for all concentrations in the fluid range, η 0 is the solvent viscosity and τ P the Péclet time. For a soft potential it is shown that, to leading order in the steepness, the asymptotic behavior is the same as that for the hard sphere potential and a condition for the cross-over behavior to 1/ωτ P is given. Our result for the hard sphere potential generalizes a result of Cichocki and Felderhof obtained at low concentrations [1] and agrees well with the experiments of van der Werff et al [2] , if the usual Stokes-Einstein diffusion coefficient D 0 in the Smoluchowski operator is consistently replaced by the short-time self diffusion coefficient D s (φ) for non-dilute colloidal suspensions.