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The asymptotic frequency $\omega$, dependence of the dynamic viscosity ofneutral hard sphere colloidal suspensions is shown to be of the form $\eta_0A(\phi) (\omega \tau_P)^{-1/2}$, where $A(\phi)$ has been determined as afunction of the volume fraction $\phi$, for all concentrations in the fluidrange, $\eta_0$ is the solvent viscosity and $\tau_P$ the P\'{e}clet time. Fora soft potential it is shown that, to leading order steepness, the asymptoticbehavior is the same as that for the hard sphere potential and a condition forthe cross-over behavior to $1/\omega \tau_P$ is given. Our result for the hardsphere potential generalizes a result of Cichocki and Felderhof obtained at lowconcentrations and agrees well with the experiments of van der Werff et al, ifthe usual Stokes-Einstein diffusion coefficient $D_0$ in the Smoluchowskioperator is consistently replaced by the short-time self diffusion coefficient$D_s(\phi)$ for non-dilute colloidal suspensions.Comment: 18 pages LaTeX, 1 postscript figur

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