Colloid Aggregation: Numerical Solution and Measurements

A model has been developed that describes the kinetics of particle aggregation by a numerical solution of the von Smoluchowski equation. While the complete model incorporates surface chemical phenomena, this paper discusses only the physical aggregation process, and focuses on long-term aggregation where aggregates composed of many primary particles (up to 2000) are formed. Model simulations were compared with laboratory experiments that were conducted with hematite spheres aggregating with no applied shear stress. Comparison was achieved by minimizing the sum of squared differences between the model and experimental data using two fitting parameters: the collision efficiency and the fractal dimension of the aggregates. The model was sensitive to the two parameters, which had a small degree of dependence on one another as evidenced by the orientation of the joint confidence regions. Estimates of the fractal dimension varied inversely with collision efficiency and were between 1.25 and 1.5; lower than many estimates by others for diffusion-controlled processes but consistent with cluster–cluster aggregation of aggregates comprised of very dense particles. The collision efficiency was estimated to be 1×10−4 for slow aggregation conditions, and 2×10−4 under rapid aggregation; these values reflect inclusion of hydrodynamic interactions and their significance in a system dominated by differential settling