(4a) 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. It essentially involves aggregation of particles and/or clusters in a liquid medium and fragmentation of resultant flocs, when shear is applied to improve rate of aggregation. Coagulants and flocculants are commonly employed as additives to induce flocculation and improve the subsequent filtration or dewatering operations. As such, 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. Many experimental studies have shown that aggregation does not occur, even at high shear rates, if the net interaction is repulsive in nature. These surface forces include van der Waals attraction, electrical double layer repulsion, steric repulsion or bridging attraction in presence of polymers and structural forces such as hydration repulsion. The nature and magnitude of these forces, in turn, depend on the surface chemistry of the suspension, usually represented in terms of variables like pH, type and concentration of electrolyte species, type and concentration of polymer used and its properties such as molecular weight distribution, charge density and functional groups present. The surface forces affect not only the probability of particle attachment but also floc fragmentation because rate of floc breakage depends on the forces holding the particles together.

Population balances are generally used to predict the evolution of floc size distribution with time. However, majority of the models do not take the effect of surface forces into account, which actually determine the efficiency of collisions between particles during flocculation. A detailed and general population balance model is presented for flocculation of colloidal suspensions incorporating fundamental theories of surface forces. The classical DLVO theory was used for flocculation in presence of simple inorganic electrolytes. It was suitably extended for situations in which non-DLVO forces such as hydration repulsion are active and affect rate of aggregation. The Hamaker theory was used for computing van der Waals attraction while an expression based on linear superposition approximation was employed for calculating electrical double layer repulsion. Since shear is usually applied in many industrial operations, kinetics of aggregation in shear flows as well as fragmentation of flocs due to applied shear are included in the population balance. Moreover, since flocs are highly irregular in structure and shape, they were represented as fractal aggregates in the present work. Model parameters such as the Hamaker constant of solids, particle surface potential and the floc fractal dimension were taken from literature sources. The floc breakage parameter was employed as an adjustable parameter and found to be a strong function of applied shear rate. The general population balance model incorporating surface force theories was tested with experimental data for flocculation of polystyrene latex and alumina suspensions in stirred tanks. The simulation results on the effect of important flocculation variables such as pH and shear rate were found to be in close agreement with experimental data for floc size distribution. It was assumed that shear rate was uniform throughout the suspension because the model was tested with data from small laboratory scale tanks. However, the model can be readily extended to include nonuniform shear rate by combining it with a suitable computational fluid dynamics model for fluid flow in large scale stirred tanks. Similarly, the present model can be made more general by incorporating a surface ionization or complexation model to predict particle surface potential as a function of pH and electrolyte concentration.