Abstract
A geometrically discretized sectional population balance model for reaction‐limited aggregation of colloidal suspensions is presented. The two important model parameters are collision frequency factor and collision efficiency factor. The collision frequency factor is derived from physically realistic arguments proposed for collision of fractal aggregates. The collision efficiency factor is computed as a function of total interaction energy between particles, including short‐range structural repulsion forces. The irregular and open structure of aggregates is taken into account by incorporating their mass fractal dimension. The characteristic time constant of reaction‐limited aggregation, derived from dynamic scaling of mean aggregate size‐aggregation time data, is found to correlate with electrolyte concentration. The population balance model is tested with published experimental data for aggregation of γ‐alumina suspensions in the presence of different electrolytes. It is shown that the slow kinetics of aggregation under certain conditions of pH and electrolyte concentration require inclusion of short‐range structural repulsion forces along with van der Waals attraction and electrical double layer repulsion forces in an extended DLVO theory. The model predictions are in good agreement with experimental data for time evolution of mean aggregate diameter in the reaction‐limited aggregation regime. © 2005 American Institute of Chemical Engineers AIChE J, 2005