Aggregation of colloidal particles plays a key role in a variety of applications. A very common situation is where colloidal particles aggregate in the presence of residual repulsive interaction, a situation commonly known as reaction-limited conditions. In the thirties, Fuchs extended Smoluchowski’s equation, developed for the rate of aggregation of colloidal particles under diffusion-limited conditions, to the case of reaction-limited conditions. Nevertheless, its use is limited to sufficiently dilute conditions. In this work we investigate by means of Brownian-Dynamic simulations the rate of aggregation of colloidal particles at high volume fractions, up to 30%. We have developed a correction to Smoluchowski’s equation for the rate of aggregation of colloidal particles under diffusion-limited conditions at high concentrations within the framework of trapping theory. This corrected aggregation kernel, accounting for concentration dependence effects, was implemented in a population-balance equations scheme and used to model the aggregation kinetics of colloidal particles undergoing diffusion-limited aggregation under concentrated conditions. It was found that classical Smoluchowski’s theory substantially underpredicts the rate of aggregation as well as the onset of gelation, with deviations becoming progressively more severe as the particle volume fraction increases. Similarly, we observed that even under reaction-limited conditions the rate of aggregation of particles under concentrated conditions is substantially higher than that expected from Fuchs-Smoluchowski’s theory. An attempt to develop a kernel that corrects for the effects of high concentrations has been made.
marco.lattuada@unifr.ch
