Sedimentation of strongly and weakly charged colloidal particles: Prediction of fractional density dependence

TL;DR

This study models the sedimentation velocity of charged colloidal particles, revealing fractional power-law dependencies on particle concentration, with implications for understanding colloidal and biological suspensions.

Contribution

It introduces a fractional density dependence model for sedimentation velocity in charged colloids, extending understanding to both strongly and weakly charged systems.

Findings

Strongly charged spheres follow a $1 - p \, ext{phi}^{1/3}$ dependence.

Weakly charged spheres exhibit a $1 - p \, ext{phi}^{1/2}$ dependence.

Model applicability is limited to very dilute suspensions with low charge.

Abstract

We report on calculations of the reduced sedimentation velocity $U/U_{0}$ in homogenous suspensions of strongly and weakly charged colloidal spheres as a function of particle volume fraction $\phi$. For dilute suspensions of strongly charged spheres at low salinity, $U/U_{0}$ is well represented by the parametric form $1-p\phi^\alpha$ with a fractional exponent $\alpha=1/3$ and a parameter $p\simeq 1.8$, which is essentially independent from the macroion charge $Z$. This non-linear volume fraction dependence can be quantitatively understood in terms of a model of effective hard spheres with $\phi$-dependent diameter. For weakly charged spheres in a deionized solvent, we show that the exponent $\alpha$ can be equal to 1/2, if an expression for $U/U_0$ given by Petsev and Denkov [J. Colloid Interface Sci. 149, 329 (1992)] is employed. We further show that the range of validity of this expression is limited to very small values of $\phi$ and $Z$, which are probably not accessible in sedimentation experiments. The presented results might also hold for other systems like spherical proteins or ionic micelles.