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Abstract The time evolutions of local Particle Size Distributions (PSDs) of suspended kaolinite are explored under different hydrodynamic conditions. A setup that uses oscillating grids is adopted to generate a nearly isotropic turbulence in a settling column, and the results at the observation location show that the initial unimodal PSDs change to bimodal distributions due to flocculation processes. The first peak of the bimodal PSD, which represents primary particles (0.1–4 µm) and flocculi (4–20 µm), remains similar in size to the median size of the initial PSD. The second peak, which represents the flocs (> 50 µm), however, is size-varying under different experimental durations and shear rates. For low shear rates, the size of the second peak increases with time and reaches an equilibrium state; for high shear rates, it first increases and then decreases. Moreover, the two PSD peaks are reasonably simulated by a two-class population balance equation, with the experimental and predicted results comparing well. The results of this study also indicate that the optimum shear rate to boost flocculation is approximately 20 s−1. Highlights • Bimodal Particle Size Distributions (PSDs) were observed in a settling column with oscillating grids; • The first peak of the PSD, which represents the flocculi, remains close in size; • The second peak of the PSD, which represents the flocs, is size-varying under different environments; • The bimodal PSDs are reasonably predicted by the two-class population balance model; • The optimal shear rate to promote flocculation is around 20 s−1 in this experiment. [ABSTRACT FROM AUTHOR]

The population balance equation has been used to describe the evolution of particle populations caused by aggregation and breakup processes for several decades. Only recently has it been used to efficiently and directly predict the temporal variation of particle size distribution (PSD) for cohesive sediments by using the quadrature method of moments (QMOM). In this study, an extension of that effort carries out additional validations that compare with analytical solutions for pure coagulation systems, pure breakup systems, and combined coagulation and breakup systems. Besides, a laboratory experiment is conducted in a five liter mixing chamber to provide steady state PSD of suspended kaolinite with a chamber-averaged kaolinite concentration 0.52 g/L and shear rate 45 s − 1 . The model results match reasonably well with both of those from analytical solutions and kaolinite flocculation experiment results. Sensitivities regarding the selecting of different model input parameters (such as fractal dimensions, primary particle sizes, aggregation and breakage fitting parameters, and fragmentation distribution functions) are also checked. The results further confirm the capability of QMOM to predict PSD using its quadrature nodes and the corresponding weights. [ABSTRACT FROM AUTHOR]

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., d 32 (Sauter mean size), d 43 (De Broukere mean size), d 60 (hydrodynamic mean size), and D 50 (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. [ABSTRACT FROM AUTHOR]