Numerical calculation of coagulation kinetics incorporating fractal theory

Based on the Smoluchowski equation, a kinetic model was formulated by introducing the fractal dimension. In the kinetic model, fractal dimension at different time is calculated by considering of the void and primary particles contained in the floes. Using the kinetic model, the coagulation kinetics was calculated by the method of finite difference. The calculation results showed that the characteristics of the structure and collision efficiency play an important role in particle size distribution. The higher of the fractal dimension and the collision efficiency, the broader of the particle size distribution will be obtained, which indicated the floes with large size were formed. The results also revealed a tendency of decrease in the fractal dimension with the increase of floe size, which is resulted from the unproportionate growth between the floe size and the number of the primary particles contained in the floes. The validity of the calculation was proved by a series of experiments using aluminum sulfate as coagulant for the flocculation of humic substances.