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

Abstract

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 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 and agrees well with the experiments of van der Werff et al, 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.