A Population Balance Model for Flocculation of Colloidal Suspensions Incorporating the Influence of Surface Forces

Flocculation is a key unit operation in domestic and industrial water treatment, beneficiation of minerals, dewatering of sludges and in many industrial solid-liquid separation processes. Coagulants and flocculants are commonly employed as additives to induce aggregation and improve subsequent filtration or dewatering operations. The characteristics of these additives have a strong influence on suspension stability and hence on rate of flocculation. When collisions between particles take place, the probability of aggregation depends mainly on the surface forces acting between colloidal particles. Population balance models for flocculation generally include kinetics of colloidal aggregation but mostly ignore surface and colloid chemistry of the suspension. Here, a population balance model is presented which incorporates fundamental theories of surface forces involved in flocculation and importantly in fragmentation. The collision efficiency is calculated as a function of total interaction energy between particles, which is estimated using the classical DLVO theory. The Hamaker constant of solids in solvent, an important model parameter, is computed by applying the approximate Lifshitz theory. The irregular and open structure of flocs is taken into account by estimating the collision frequency factor as a function of mass fractal dimension and permeability of aggregates. The model is tested and validated with published experimental data for flocculation of colloidal polystyrene latex and alumina suspensions in different devices. Simulation results on the effect of shear rate and solution pH are in close agreement with experimental data. Since the model incorporates the influence of variables such as pH and electrolyte concentration, it is more amenable for real-time optimization and control of industrial coagulation and flocculation units than existing flocculation models.