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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]

In estuaries and coastal waters, floc size and its statistical distributions of cohesive sediments are of primary importance, due to their effects on the settling velocity and thus deposition rates of cohesive aggregates. The development of a robust flocculation model that includes the predictions of floc size distributions (FSDs), however, is still in a research stage. In this study, a one-dimensional longitudinal (1-DL) flocculation model along a streamtube is developed. This model is based on solving the population balance equation to find the FSDs by using the quadrature method of moments. To validate this model, a laboratory experiment is carried out to produce an advection transport-dominant environment in a cylindrical tank. The flow field is generated by a marine pump mounted at the bottom center, with its outlet facing upward. This setup generates an axially symmetric flow which is measured by an acoustic Doppler velocimeter (ADV). The measurement results provide the hydrodynamic input data required for this 1-DL model. The other measurement results, the FSDs, are acquired by using an automatic underwater camera system and the resulting images are analyzed to validate the predicted FSDs. This study shows that the FSDs as well as their representative sizes can be efficiently and reasonably simulated by this 1-DL model. [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]

[Display omitted] The quasi-Monte Carlo (QMC) method was enhanced to solve the population balance model (PBM) including aggregation and fragmentation processes for simulating the temporal evolutions of characteristic sizes and floc size distributions (FSDs) of cohesive sediments. Ideal cases with analytical solutions were firstly adopted to validate this QMC model to illustrate selected pure aggregation, pure fragmentation, and combined aggregation and fragmentation systems. Two available laboratory data sets, one with suspended kaolinite and the other with a mixture of kaolinite and montmorillonite, were further used to monitor the FSDs of cohesive sediments in controlled shear conditions. The model results show reasonable agreements with both analytical solutions and laboratory experiments. Moreover, different QMC schemes were tested and compared with the standard Monte Carlo scheme and a Latin Hypercube Sampling scheme to optimize the model performance. It shows that all QMC schemes perform better in both accuracy and time consumption than standard Monte Carlo scheme. In particular, compared with other schemes, the QMC scheme using Halton sequence requires the least particle numbers in the simulated system to reach reasonable accuracy. In the sensitivity tests, we also show that the fractal dimension and the fragmentation distribution function have large impacts on the predicted FSDs. This study indicates a great advance in employing QMC schemes to solve PBM for simulating the flocculation of cohesive sediments. [ABSTRACT FROM AUTHOR]