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

TL;DR

This paper investigates the high-frequency behavior of the viscosity in neutral colloidal suspensions, revealing a square root singularity and providing a generalized formula applicable across all concentrations, aligning well with experimental data.

Contribution

It derives a universal asymptotic form for the viscosity at large frequencies for all volume fractions, extending previous low-concentration results to dense suspensions.

Findings

Viscosity exhibits a $( ext{frequency})^{-1/2}$ dependence at high frequencies.

The derived formula applies to both hard and soft potentials with similar asymptotic behavior.

Results agree with experiments when using the short-time self diffusion coefficient $D_s()$.

Abstract

The asymptotic frequency $\omega$, dependence of the dynamic viscosity of neutral hard sphere colloidal suspensions is shown to be of the form $\eta_0 A(\phi) (\omega \tau_P)^{-1/2}$, where $A(\phi)$ has been determined as a function of the volume fraction $\phi$, for all concentrations in the fluid range, $\eta_0$ is the solvent viscosity and $\tau_P$ the P\'{e}clet 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 $1/\omega \tau_P$ 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 $D_s(\phi)$ for non-dilute colloidal suspensions.