Modeling floc size distribution of suspended cohesive sediments using quadrature method of moments

• Quadrature Method Of Moments (QMOM) to solve the population balance equation
• Excellent computing efficiency to find the evolution of floc size distribution (FSD)
• A maximum of eight nodes & weights (i.e., sizes & number densities) in QMOM for FSD
• Collision efficiency could be larger than one due to the effects of organic matters.

An enhanced Quadrature Method Of Moments (QMOM) is employed to solve the population balance model (PBM) with a maximum of eight size classes for the purpose of describing the evolution of floc size distribution (FSD) of kaolinite suspension and colloidal montmorillonite. This approach can be used to estimate many representative sizes, e.g., d32 (Sauter mean size), d43 (De Broukere mean size), d60 (hydrodynamic mean size), and D50 (median size). The following three considerations are adopted to enhance the QMOM approach: (1) An adjustable factor, which is selected based on its ability to track up to eight size classes, is implemented; (2) moments higher than the third order are not necessarily simulated directly; (3) a restriction on the ratio between the minimum and maximum weights is used to exclude unreliable nodes. The above enhancements have been proposed by others, but are integrated for the first time in this study. Model results are verified by comparison with available experimental data. The results of this study suggest that the quadrature nodes and weights in the QMOM are the characteristic sizes and corresponding characteristic number densities to effectively predict the FSD of cohesive sediments. This study also demonstrates that the possible range of the correction factor (also sometimes referred to as “collision efficiency”) for the Euclidean collision frequency could be larger than one because of both the difference in floc structure represented by fractal dimension as well as the impacts of organic matter.