A lumped discrete population balance model for shear flocculation-model development

In the shear flocculation process, flocculation of ultrafine (size < 10 μm) hydrophobic particle occurs in the presence of a high shear field. Hence, it is necessary to consider both processes of coalescence and breakage, while modelling shear flocculation.In this paper, a lumped discrete population balance model is presented considering both processes of coalescence and breakage of flocs. A method is also proposed to convert discrete kernels to lumped discrete kernels by satisfying the constraints on them. The numerical solution of the model is compared with some special analytical solutions of the continuous population balance model, with which it is observed to be in agreement. The model equations are derived in such a way that it predicts correctly both the rate of change of number and the total volume of the flocs. The size distribution of a flocculating suspension can be predicted by this model.