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

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.