Brownian dynamics (BD) simulations have been performed on the aggregation dynamics of colloidal particles within the context of a ball-and-string model. Particles are treated as hard spheres that can bind irreversibly through a string attached to their surface. The model is set up to mimic some aspects of the aggregation of casein micelles in renneted milk. In this study we test the model of Smoluchowski by comparing it with our BD simulation model. Aggregation kinetics was studied by models in a range of volume fractions from =4x10-6 to 0.20. We found aggregation rates close to the Smoluchowski rates at low volume fractions, increasing sharply at higher concentrations. Simulations for simpler models also give rates slightly above theoretical values, but only at very high dilution. We show that only when a large fraction of the particles have already clustered is the quasi-stationary solution used in Smoluchowski theory attained. This partially explains the increase in rate with volume fraction. The steep increase in rate with volume fraction also explains why fractal aggregation, in which the effective volume fraction of the clusters increases with cluster size, leads to gelation.
Rzepiela, A. A., van Opheusden, J., & van Vliet, T. (2001). Brownian dynamics of aggregation kinetics of hard spheres with flexibele bounds. Journal of Colloid and Interface Science, 244, 43-50. https://doi.org/10.1006/jcis.2001.7917