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

The asymptotic frequency, , dependence of the dynamic viscosity of neutral hard-sphere colloidal suspensions is shown to be of the form₀A()(_p)^-1/2, whereA() has been determined as a function of the volume fraction , for all concentrations in the fluid range,₀ is the solvent viscosity, and_p is 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 crossover behavior to 1/_p, is given. Our result for the hardsphere potential generalizes a result of Cichocki and Felderhof obtained at low concentrations and agrees well with the experiments of van der Werffet al. if the usual Stokes-Einstein diffusion coefficientD₀ in the Smoluchowski operator is consistently replaced by the short-time self-diffusion coefficientD_s() for nondilute colloidal suspensions.