A new flocculation dynamics model is established based on the proposed Taylor expansion moment method, for the fine particle aggregation and floc formation. Mechanisms of hydrodynamic shear and differential sedimentation dominated flocculation are studied in the framework of Smoluchowski mean field theory. The Taylor expansion technique is applied and the fractal dimension is introduced into the system of particle dynamics equations. The effects of particle diffusion and vertical transport have been included. The influence of collision efficiency and the combination with fractal dimension on the calculation results are studied. The formula for estimating the floc time accounting for the fractal dimension is derived. The proposed model is applicable to all the three types of floc mechanisms: Brownian motion, differential settlement and orthokinetic flocculation. Increase of fractal dimension number results in smaller critical floc size and reduced floc structure coefficient and smaller standard deviation of floc size distribution, which reflects the self-holding. Results of the present research show that particle flocculation and fragmentation can be balanced in a certain scope, to achieve the so-called self-retention.
Wan, Z., You, Z., Chen, J., & Wang, M. (2015). Modeling of aggregation kinetics by a new moment method. Applied Mathematical Modelling, 39(22), 6915–6924. https://doi.org/10.1016/j.apm.2015.02.041