Modeling particle-size distribution dynamics in a flocculation system

Flocculation dynamics accounting for both particle coagulation and aggregate breakage was simulated mathematically by using modified sectional modeling techniques. The methodological improvement included the use of a continuous-size density function, instead of a characteristic size for each size section, the applications of a comprehensive curvilinear model for the coagulation kinetics, and the fractal scaling relationship for particle aggregates. Simulation results demonstrated that a flocculation system could arrive at a dynamic steady state after a period of flocculation when coagulation and breakage counterbalanced each other, resulting in a stationary size distribution with a unique peak mass concentration. Three distinct breakage distribution functions—binary, ternary, and normal distribution—did not differ considerably based on the simulation results of the steady-state size distributions. A lower shear rate, breakage rate constant, a higher collision efficiency, and initial particle concentration would result in larger aggregates in a flocculation system. The numerical simulations compared well with the results of the jar-test flocculation experiments using latex microspheres, suggesting the applicability of the curvilinear–fractal–breakage modeling system for the process simulation of the flocculation units used in water and wastewater treatment.