Viscosity of Colloidal Suspensions

Abstract

Simple expressions are given for the Newtonian viscosity $η_N(ϕ)$ as well as the viscoelastic behavior of the viscosity $η(ϕ,ω)$ of neutral monodisperse hard sphere colloidal suspensions as a function of volume fraction $ϕ$ and frequency $ω$ over the entire fluid range, i.e., for volume fractions $0 < ϕ< 0.55$. These expressions are based on an approximate theory which considers the viscosity as composed as the sum of two relevant physical processes: $η(ϕ,ω) = η_{\infty}(ϕ) + η_{cd}(ϕ,ω)$, where $η_{\infty}(ϕ) = η_0 χ(ϕ)$ is the infinite frequency (or very short time) viscosity, with $η_0$ the solvent viscosity, $χ(ϕ)$ the equilibrium hard sphere radial distribution function at contact, and $η_{cd}(ϕ,ω)$ the contribution due to the diffusion of the colloidal particles out of cages formed by their neighbors, on the Péclet time scale $τ_P$, the dominant physical process in concentrated colloidal suspensions. The Newtonian viscosity $η_N(ϕ) = η(ϕ,ω= 0)$ agrees very well with the extensive experiments of Van der Werff et al and others. Also, the asymptotic behavior for large $ω$ is of the form $η_{\infty}(ϕ) + A(ϕ)(ωτ_P)^{-1/2}$, in agreement with these experiments, but the theoretical coefficient $A(ϕ)$ differs by a constant factor $2/χ(ϕ)$ from the exact coefficient, computed from the Green-Kubo formula for $η(ϕ,ω)$. This still enables us to predict for practical purposes the visco-elastic behavior of monodisperse spherical colloidal suspensions for all volume fractions by a simple time rescaling.