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An ultrasonic-wave system was developed to measure the rheological properties of non-Newtonian materials based on their responses to shear and pressure waves. This system was composed of a commercial shear wave transducer and various homemade devices, including a signal generator, a signal conditioner, and a transmission/receiving switch. The shear wave reflections at the interface between the delay line and the unknown test materials can be interpreted by the signals measured with calibration materials (e.g. air, water, olive oil and honey) that have well-known rheological properties. If the Voigt viscoelastic model is used to describe the dynamic behaviour of these test materials, the interpreted data can be used to determine the acoustic impedances, and thus solve for their shear moduli (G), kinematic viscosities (ν) and bulk densities (ρ). After the calibration procedures, the proposed system was used to test a consolidating kaolinite slurry with zero salinity and an initial suspended sediment concentration of 420 g l–1. The measurements showed that the shear modulus G is developed until consolidation for approximately 100 h. Afterward, the G gradually approached a value on the order of 500 N m–2 after approximately 200 h. This corresponded to an initial viscosity of approximately 7 × 10−5 m2 s–1, which decreased slowly over time to approximately 4 × 10−6 m2 s–1 after 300 h. With minor modification to capture pressure waves from the shear wave transducer, the bulk density can also be measured. The integrated system offers a non-invasive and efficient method for characterizing non-Newtonian fluids, providing valuable insights into their rheological properties, which are crucial for a wide range of industrial and scientific applications. [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]

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]

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]

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]

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]

A strong maximum ebb current (>3 m/s) in the upper water column was observed at Station CS3 in the middle of the North Passage of the Yangtze River Estuary during the wet season, which was higher than either its upstream or downstream counterparts. To better understand the mechanisms and factors causing the strong ebb current, a vertical one-dimensional (1-D) model was used to conduct a diagnostic study. The model used time series of observed tidal amplitudes, vertical salinity, and suspended sediment concentration (SSC) profiles to compute the density and turbulence. Two tunable parameters, the tidal amplitude attenuation coefficient (i.e., the phase lag) and the background surface pressure gradient that represents the net pressure gradient induced by the freshwater discharge and baroclinic effect, were used to determine the best match with the observed high velocity amplitudes in addition to the bottom roughness height. Three hypotheses of possible causes are tested: (1) the large freshwater discharge, (2) the bottom stratification effects (which were caused by a possible high near-bed suspended sediment gradient), and (3) the unique location of the CS3 station that was influenced by local geometry. The findings show that neither of the first two factors has much influence on the pronounced ebb velocities. Instead, the energy loss caused by the change of channel geometry and a maximum convex bathymetry in the North Passage of the Yangtze River Estuary are the main reasons behind the extremely high observed ebb current velocity profiles. The high near-bottom SSC and gradient located within 0.5 m above the bed only slightly alters the velocity profiles. This 1-D model is convenient for testing a different hypothesis and for coupling with other selected variables to account for the floc size distributions in future studies. [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]

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]

The observation of floc size distribution (FSD) for quantitative description of its properties over a sufficient size range, from a few microns to a few millimeters, is still a challenge in most marine environments. In this study, an inexpensive image acquisition and processing system is developed for achieving this objective. Images are acquired by using a Sony Alpha NEX-5R camera body with a CMOS sensor, a Sony E-mount to Nikon F-mount adaptor, extension tubes, a Nikon macro lens, and a close-up lens that can identify flocs with a minimum size of 5 μm. The light source and camera trigger are controlled by a micro-controller that was assembled for this project. These images are analyzed by using MATLAB Image Processing Toolbox. The processed floc size and their statistical distributions are confirmed with two available sample sets. The validated process is then applied to measure the steady state FSDs of kaolinite suspensions for different shear rates, suspended sediment concentrations, salinities, and a selected organic matter, guar gum. Although the presence of salt promotes flocculation of suspended kaolinite, only a small amount of salt, around 0.5 ppt, is needed to reach the saturation status. Thus for the test salinities (0.5, 1, 2, 3, 5, and 9 ppt), the measured FSDs show little difference among each other. On the other hand, guar gum affects kaolinite flocculation significantly and the maximum effect happens at a guar gum concentration around 15 mg/L when the kaolinite concentration is around 0.52 g/L. At this dosage the characteristic floc size is the largest. [ABSTRACT FROM AUTHOR]

Shear rates play a critical role in the coagulation-flocculation-sedimentation processes of colloidal particles. Under high shear environments, it is widely accepted that the median floc size at equilibrium (D) decreases with an increase in shear rates (G). For low shear conditions, however, conflicting D - G relationships were measured in previous laboratory experiments, without a clear explanation of the reasons and a reasonable reproduction of the physical processes. In this study, the direct numerical simulation technique was used to mimic the flocculation of two typical colloidal particles (i.e., latex and silica) with different densities but under similar hydrodynamic conditions. Our results show that the previous different observations at low shear are mainly caused by particle gravity, which influences the particle residence time in a device system. They also confirm previous arguments about limited residence time due to gravitational settling being the reason for the observed peak, in accordance with Winterwerp (1998) [J. Hydraul. Res. Vol 36, pp. 309–326]. This study implies that to better investigate the shear-dominated flocculation of high-density particles such as sediments, settling processes should be addressed unless particles are always in suspension under specific conditions. • Previous studies show conflicting observations of D (floc size) vs. G (shear rate). • The Lattice Boltzmann Method was used to mimic the flocculation of latex and silica. • The gravity and shear that influence the particle residence time play a primary role. [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]

To manage coastal and estuarine waters, it is critical to accurately predict the movements of cohesive and non-cohesive sediments. There are well-established methods to estimate the behavior of non-cohesive sediments; however, without extensive knowledge on flocculation processes it remains difficult to predict the behavior of cohesive sediments. Flocculation is one of the main processes (e.g., erosion, deposition, settling, consolidation and flocculation) in cohesive sediment dynamics. The study of flocculation is an interdisciplinary work since it relates to various physical (e.g., transport, settling and deposition), chemical (e.g., contaminant uptake and transformation) and biological (e.g., community structure activities and metabolism) activities. Nevertheless, a widely-accepted flocculation model that can quantitative simulating the Floc Size Distributions (FSDs) for a relatively large study domain has not yet been fully developed. In this study, a multi-class population balance flocculation model was developed to address the occurrence of suspended microflocs, macroflocs and megaflocs in Belgian coastal waters (southern North Sea). The floc size distributions were represented by the size and mass fraction of each particle group. 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. Specifically, the growth of an aggregate because of biofilm attachment and extracellular polymeric substance glue is averaged to each elementary particle, with its growth rate response to various bio-activities. 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. It was validated by observation data at the station MOW1 close to Zeebrugge harbor during both peak algae bloom and low biomass periods. It shows that when the biomass is abundant the predictions of the mean settling velocities are largely underestimated when the biological effect is neglected. This model will enhance our knowledge of the dynamics of suspended particulate matters, especially the biophysical influences on the fate and transport of estuarine aggregates. [ABSTRACT FROM AUTHOR]