Sedimentation of Strongly and Weakly Charged Colloidal Particles: Prediction of Fractional Density Dependence

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 φ. For dilute suspensions of strongly charged spheres at low salinity, U/U 0 is well represented by the parametric form 1 − p φ α with a fractional exponent α = 1/3 and a parameter p ≃ 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 φ-dependent diameter. For weakly charged spheres in a deionized solvent, we show that the exponent α 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 φ 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.

Short-time transport properties in dense suspensions: From neutral to charge-stabilized colloidal spheres

“…Moreover, even for a nonadjusted effective charge, the position, q m , of the structure factor peak is very well described by the RMSA scheme. The position, r m , of the principal peak in the radial distribution function in these systems coincides within 5 % with the average geometric distance, r = n −1/3 , of two particles [87], which is here the only physically relevant static length scale. This feature has been used to derive the concentration-scaling predictions quoted in Eqs.…”

“…These data are in good agreement with Eq. (35) for a s = 1.8, whose validity is a consequence of the dominating far-field 2-body HI, and the scaling relation r ∼ φ −1/3 obeyed in low-salinity systems for φ ≤ 0.1 [87]. That charged spheres sediment more slowly than neutral ones can be rationalized as follows: For charged spheres at low salinity, near-contact configurations are very unlikely due to the strong electric repulsion.…”

“…Instead, for de-ionized systems, the following non-linear concentration dependencies have been predicted by theory [3,46,47,87]…”

“…The values of the exponents in the short-time expressions of Eqs. (33)(34)(35)(36) can be attributed essentially to the fact that, in de-ionized suspensions of strongly charge spheres, the location, r m = 2π/q m , characterizing the location of the principal peak in g(r) that characterizes the location of the next-neighbor shell coincides, within 5 % of accuracy (see [87] and Fig. 5), with the geometric mean distance r = n −1/3 = a(4π/3φ) 1/3 of two spheres.…”

Stochastic model for the dynamics of interacting Brownian particles

“…An analysis that makes use of a combination of stick and slip boundary conditions [40] helps to fit experimental data [4]. Moreover, for strongly charged spheres at low salinity based on an effective macroion fluid theoretical model, the mobility is well represented by the parametric form b 11 (Φ) = (6πηa) −1 (1 − pΦ α ) [41]. Using a model of effective hard spheres with Φ -dependent diameter, the values p ≃ 1.8 and α = 1 3 , can be explained.…”