Mathematical modeling of flocculation and dispersion of colloidal suspensions

Flocculation and dispersion of colloidal suspensions are important unit operations in many diverse industries. Inorganic salts, polymers/polyelectrolytes and surfactants are commonly used either to flocculate or to disperse a suspension. Several processes can take place simultaneously during flocculation: adsorption and desorption of polymer chains, relaxation of adsorbed chains, aggregation, floc fragmentation, reflocculation of broken flocs, and creaming or sedimentation of flocs. The process is highly nonlinear and complex as its behavior depends on many interfacial phenomena driven by the characteristics of solids, solvent and polymer, operating conditions, and equipment geometry.; A general and detailed mathematical framework for modeling flocculation and dispersion of colloidal suspensions in the presence of salts and polymers, under quiescent and shear flow conditions is presented in this thesis. The population balance framework for simultaneous aggregation and fragmentation is integrated with the theories of colloid stability. A novel feature of the present work is the computation of collision efficiency as a function of surface forces. The DLVO theory is used for computing the forces in the presence of salts while the forces due to the adsorbed polymer are computed using the scaling theory. The irregular and open structure of the flocs is taken into account by incorporating the fractal dimension and the permeability of flocs. Appropriate kernels are employed to model the fast diffusion-limited aggregation and the slow reaction-limited aggregation.; A step-by-step approach is followed to develop a reasonably comprehensive population balance model. The model is tested with relevant experimental data for flocculation of a variety of materials such as polystyrene latex, alumina and hematite. The model predictions are in reasonable agreement with experimental results, obtained with different flocculation devices such as the stirred tank and the Couette apparatus.; The mathematical framework presented here represents the first attempt towards developing a population balance model for polymer-induced flocculation. It is also an advancement over the existing models for flocculation in shear flow in the presence of salts as the collision efficiency is predicted as a function of surface forces.