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Highlights • The biomineral flocs in the Belgian coast were investigated during two contrasting periods. • The observed floc size distributions were decomposed to represent microflocs, macroflocs and megaflocs. • A simple flocculation model that can describe the biofilm growth of flocs was developed. • This model was successfully implemented in the open TELEMAC with five passive tracers. Abstract The Floc Size Distributions (FSDs) of biomineral suspended particles are of great importance to understand the dynamics of bio-mediated Suspended Particulate Matters (SPMs). Field observations were investigated at Station MOW1 in Belgian coastal waters (southern North Sea) during two typical periods with abundant and reduced biomass. In addition, the Shen et al. (2018) [Water Res. Vol 145, pp 473–486] multi-class population balance flocculation model was extended to address the occurrence of suspended microflocs, macroflocs and megaflocs during these contrasting periods. The microflocs are treated as elementary particles that constitute macroflocs or megaflocs. The FSD is represented by the size and mass fraction of each particle group, which corresponds to a temporal and spatial varying mass weighted settling velocity. The representative sizes of macroflocs and megaflocs are unfixed and migrated between classes mainly due to the effects of turbulent shear, differential settling and biofilm growth. The growth of an aggregate because of bio-activities is allotted to each elementary particle. It is further hypothesized that the growth kinetics of biomineral particles due to biofilm coating follows the logistic equation. This simple bio-flocculation model has been successfully coupled in the open source TELEMAC modeling system with five passive tracers in a quasi-1D vertical case. Within an intra-tide scale, the settling velocity (w s) is large during slack tides while it is small during maximum current velocities because of variations in turbulence intensities. Nonetheless, the w s may be largely underestimated when the biological effect is neglected. For a seasonal pattern, the w s is higher in biomass-rich periods in May than in biomass-poor periods in October. While the mean sizes of megaflocs are close during the two periods, the macroflocs during algae bloom periods are more abundant with a larger mean size. This study enhances our knowledge on the dynamics of SPMs, especially the biophysical influences on the fate and transport of estuarine aggregates. [ABSTRACT FROM AUTHOR]

• The effects of anionic, cationic and neutral organic matters on the aggregation of microplastics are investigated. • All of the organic matters show positive effects on the growth of biofilm-coated microplastic aggregates. • The two-class population balance model is used to track the small and large microplastic subgroups under turbulence. Biofilm-coated microplastics are omnipresent in aquatic environments, carrying different organic matter (OM) that in turn influences the flocculation and settling of microplastic aggregates. In this study, the effects of chitosan, guar gum, humic acid, and xanthan gum on the flocculation of anthropogenic microplastics are examined under controlled shear through the mixing chamber experiments. The results show that all of the selected OMs have positive effects on biofilm culturing and thus enhance the growth of microplastic flocs, with more evident promoting effects for cationic and neutral OMs (i.e., chitosan and guar gum) than anionic OMs (i.e., humic acid and xanthan). No critical shear rate is observed in the size vs. shear relationship based on our measurements. In addition, the quadrature-based two-class population balance model is employed to track the development of bimodal floc size distributions (FSDs) composed of small and large microplastic flocs. The model predictions show reasonable agreement with the observed FSDs. The largest error of settling flux from the two-class model is 7.8% in contrast with the reference value measured by the camera-based FSDs with 30 bins. This study highlights the role of different OMs on microplastic flocculation and indicates that a two-class model may be sufficient to describe microplastic transport processes in estuaries. [Display omitted] [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]