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In estuaries and coastal waters, the flocculation of cohesive sediments is significantly affected by extracellular polymeric substances secreted by microalgae. In this study, laboratory experiments are carried out to explore the role of two typical microalgae (Skeletonema costatum and Cyclotella meneghiniana) on suspended fine‐grained sediments under various turbulent shear and environmental conditions. The results show that the shear rate is a dominant factor in controlling the biomineral flocculation processes, and the existence of microalgae generally enhances the aggregation of mineral sediments with microalgae. It is also found that floc size distributions (FSDs) and mean sizes are clearly influenced by different algal species and concentrations, especially under intensive turbulent environments. Moreover, a quasi‐Monte Carlo (QMC) based bivariate population balance model is developed to simulate the FSDs of sediment‐algae flocs. This model is reasonably validated by two analytical solutions and laboratory observations, and indicates a potential extension for tracking the properties of microalgae‐associated fine sediment flocs due to the discrete nature of the QMC method. Plain Language Summary: The transportation of fine‐grained suspended sediments in estuaries and coastal environments is a factor in many engineering and environmental issues (e.g., siltation, dredging, bed morphology, and water quality). One important characteristic that affects the transport and fate of cohesive sediment particles is flocculation, which is the tendency of particles to aggregate and breakup sequentially to form clusters (flocs) of various sizes, densities, and settling velocities. Since they are abundant in the natural environment, microalgae and their sticky secretions play important roles in the flocculation of cohesive sediment as biological glues. However, few studies have been carried out to reveal the correlation between microalgae and sediment flocculation. Thus, this study aims to investigate the influences of microalgae on the flocculation of cohesive sediment particles in various turbulent environments. We find turbulent shear is dominant in the biomineral flocculation and that biomineral flocs are generally larger than pure sediment flocs. In addition, we develop a bivariate flocculation model to simulate the floc size distribution of biomineral flocs, which is well validated by theoretical solutions and laboratory results. This innovative model offers a preliminary application for multivariate models in biomineral flocculation, which promotes a prospect of future research to develop advanced transportation models. Key Points: The influence of microalgae on the flocculation of cohesive sediments is investigated by laboratory experiments and numerical modelsThe existence of microalgae and their secreted extracellular polymeric substances generally enhances the aggregation of biomineral flocsThe quasi‐Monte Carlo based bivariate population balance model can mimic the biomineral flocculation processes with reasonable accuracy [ABSTRACT FROM AUTHOR]

Abstract The Floc Size Distributions (FSDs) of suspended fine-grained sediment flocs play a prime role to estimate their own fate and the transport of contaminates attached to the flocs. However, developing an efficient flocculation model that is capable of simulating continuous and multimodal FSDs is still a challenge. Recently, the population balance equation solved by the Quadrature-Based Method of Moments (QBMM) with lognormal kernel density functions has been developed to investigate the aggregation and breakage processes. It coincides with some recent observations which describe a measured FSD in coastal waters with a set of constituted lognormal distributions. The newly developed lognormal QBMM was tested with several ideal flocculation kinetic kernels, none of which, however, was used for interpreting cohesive sediment dynamics. Therefore, it raised our interest to evaluate the model performance for fine-grained sediments in shear turbulence dominated environments. In this study, additional validations against two kaolinite laboratory experiments were tested in the framework of the extended QBMM. It is hypothesized that these subordinate lognormal distributions share the same value of standard deviation. Different from the previous methods, the common standard deviation is determined empirically to reduce the number of tracers and better represent the FSDs. With sediment flocculation kinetics, the predicted FSDs reasonably reproduce the FSDs observed in both the mixing chamber and the settling column experiments. Despite the lacking of explicit descriptions of microbial effects at the current stage, this model has the potential to be implemented into large-scale particle transport models and deserves a more in-depth study in the future. Highlights • The Floc Size Distributions (FSDs) of cohesive sediments were modeled. • The FSDs were represented as a superposition of several constituted lognormal distributions. • The subordinate lognormal FSDs shared the same value of standard deviation. • The model was firstly applied in a mixing jar experiment as a 0-D calibration. • The model was also applied in a settling column experiment as a 1-D validation. [ABSTRACT FROM AUTHOR]

The floc size distribution (FSD) is crucial to predict cohesive sediment dynamics in aquatic environments. Recently, increasing attention has been given to biofilm effects on the FSDs of suspended particles since the presence of biofilms on particle surfaces may lead to larger flocs and thus higher settling velocities. In this study, results from a settling column experiment conducted by Tang and Maggi (2018; https://doi.org/10.1002/2017JG004165) under nutrient‐free and biomass‐free, nutrient‐affected and biomass‐free, and nutrient‐affected and biomass‐affected conditions, with different suspended sediment concentrations, shear rates, and nutrient concentrations, have been used to validate modeled FSDs that is based on the population balance equation solved by the quadrature method of moments. In addition to the processes of aggregation and breakage, the effects of biofilm are expressed in the growth term of the population balance equation. The logistic growth pattern is used to account for an increase in biomass, which is primarily controlled by the specific growth rate and the carrying capacity. In this study, the biofilm growth rate is assumed nutrient dependent, and the carrying capacity of floc size is hypothesized to be proportional to the Kolmogorov microscale. With eight size classes to interpret a simulated FSD, the predicted and observed FSDs exhibit a reasonable match for all nutrient‐free and biomass‐free, nutrient‐affected and biomass‐free, and nutrient‐affected and biomass‐affected conditions. This simplified bioflocculation model fills the gap between the simulations of the FSDs of cohesive sediments without and with biofilms and has the potential to be included in large‐scale models in the future. Plain Language Summary: In estuaries or adjacent coastal regions, the transport of suspended sediment is responsible for many environmental and engineering issues, for example, siltation and dredging in navigation channels and harbors, water quality, water clarity, pollutants transport, and ecosystem responses. Suspended sediment particles can flocculate and thus can form aggregates with size, shape, density, and settling velocity largely different from the building particles. A challenge to predict the particle behaviors originates from a lack of flocculation models that are able to address the variations in floc size distributions. The aim of this study is to develop a flocculation model that includes besides the "classical" aggregation and breakage driven by turbulence also a biological process, which is biofilm growth. The biofilm growth and its impact on flocculation and thus floc size are simulated in a similar way as the growth of microbes but with different growth rates. The model is validated with laboratory experiments that have shown that the sizes of flocs made solely with sediment particles largely increase when incubated microbes are present. This model provides a sound basis to simulate the behavior of natural particles (minerals, organic, and biological particles) and particles from human origin (plastics) in future environmental risk assessment studies. Key Points: The quadrature‐based multiclass population balance model was used to model the floc size distributions of cohesive sedimentsThe effects of aggregation, breakage, and biofilm growth were included in the modelThe net increase in floc size due to biofilm effects is assumed to follow the logistic growth pattern [ABSTRACT FROM AUTHOR]

Abstract Estuarine and coastal regions are often characterized by a high variability of suspended sediment concentrations in their waters, which influences dredging projects, contaminant transport, aquaculture and fisheries. Although various three-dimensional open source software are available to model the hydrodynamics of coastal water with a sediment module, the prediction of the fate and transport of cohesive sediments is still far from satisfied due to the lack of an efficient and robust flocculation model to estimate the floc settling velocity and the deposition rate. Single-class and sometimes two-class flocculation models are oversimplified and fail to examine complicated floc size distributions, while quadrature-based or multi-class based flocculation models may be too complicated to be coupled with large scale estuarine or ocean models. Therefore, a three-class population balance model was developed to track the sizes and number concentrations of microflocs, macroflocs and megaflocs, respectively. With the assumption of a fixed size of microflocs and megaflocs, only four tracers are needed when coupled with the open-source TELEMAC system. It enables better settling flux estimates and better addresses the occurrence and concentration of larger megaflocs. This tri-modal flocculation model was validated with two experimental data sets: (1) 1-D settling column tests with the Ems mud and (2) in-situ measurements at the WZ Buoy station on the Belgian coast. Results show that the flocculation properties of cohesive sediments can be reasonably simulated in both environments. It is also found that the number of macroflocs created, when a larger macrofloc breaks up, is a statistical mean value and may not be an integer when applying the model in the field. Graphical abstract Image Highlights • The sizes of flocs are dynamically altered because of particle aggregation and breakage. • A three-class population balance flocculation model was developed. • This flocculation model has been successfully implemented in the open source TELEMAC. • Four tracer variables, representing the floc size distributions, were included in TELEMAC. • The model was validated with settling column tests and field measurements. [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]