文摘
The sedimentation half-times ts 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 cNaBr ranging from 50 to 1000 mM, where the particles may have formed clusters. In water and in ethanol, ts 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; ts 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 cNaBr, the ts values were the same as at no salt conditions, implying that there was no significant agglomeration before particles settled. In region II, ts decreased with increasing cNaBr, suggesting that the agglomeration and sedimentation half-times of medium-size clusters were comparable. In region III, the ts 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 tan for forming clusters of size 2Nm, where Nm = 1, 2, 3, ..., and the net predicted sedimentation half-time ts* for these clusters. The clusters were described by a fractal model with a fractal dimension df. Diffusion-limited clusters (df = 1.8) were compared to the coalescence-limit clusters (df = 3). The models provide some useful and accurate upper bounds of tan and ts*. Moreover, the effective sizes, density differences, and volume fractions of the clusters were obtained as a function of time. The predicted trend of ts* 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.