Effect of Interparticle Interactions on Agglomeration and Sedimentation Rates of Colloidal Silica Microspheres

The sedimentation half-times t s of initially monodisperse dispersions of 750, 505, and 350 nm silica microspheres were measured in water, in ethanol, and in aqueous NaBr solutions of concentration c NaBr ranging from 50 to 1000 mM, where the particles may have formed clusters. In water and in ethanol, t s was about 8, 18, and 33 h for the 750, 505, and 350 nm particles, respectively. These values were the same as the ones predicted by Stokes’ law, suggesting that the particles were monodisperse and remained so during sedimentation; t s values remained the same with increasing particle weight fraction up to 0.03, indicating no hydrodynamic interactions. Three regions of NaBr concentrations with different settling behavior were found for each size. In region I or at lower c NaBr, the t s values were the same as at no salt conditions, implying that there was no significant agglomeration before particles settled. In region II, t s decreased with increasing c NaBr, suggesting that the agglomeration and sedimentation half-times of medium-size clusters were comparable. In region III, the t s values were quite similar for all particles, and independent of the NaBr concentration, indicating that at short times the particles formed large clusters which settled rapidly. The zeta potentials of the particles in water or in NaBr solutions were measured and used to predict the corresponding Fuchs–Smoluchowski stability ratios, which were sensitive to the chosen Hamaker constant values and the NaBr concentrations. Two models, based on the Smoluchowski steady-state and the more general unsteady-state agglomeration rates, were developed for obtaining the agglomeration times t an for forming clusters of size 2 N m , where N m = 1, 2, 3, ..., and the net predicted sedimentation half-time t s * for these clusters. The clusters were described by a fractal model with a fractal dimension d f. Diffusion-limited clusters (d f = 1.8) were compared to the coalescence-limit clusters (d f = 3). The models provide some useful and accurate upper bounds of t an and t s *. Moreover, the effective sizes, density differences, and volume fractions of the clusters were obtained as a function of time. The predicted trend of t s * was consistent with the experimental data. The predictions supported the inferences that the particles were unagglomerated in region I, formed medium size clusters in region II, and rapidly formed large clusters in region III.