Assimilating Size Diversity: Population Balance Equations Applied to the Modeling of Microplastic Transport.

Modeling of microplastic (MP) transport in the aquatic environment is complicated by the diverse properties of the plastic particles. Traditional modeling methods such as Lagrangian particle tracking and Eulerian discrete class (DC) methods have limitations as they are not best placed to account for the diverse characteristics of individual particles, namely, size, density, and shape, which are crucial for determining the transport of MPs. In this work, we address the issue of particle size diversity by using the population balance equations (PBE) method.

Weathering Plastics as a Planetary Boundary Threat: Exposure, Fate, and Hazards.

We described in 2017 how weathering plastic litter in the marine environment fulfils two of three criteria to impose a planetary boundary threat related to "chemical pollution and the release of novel entities": (1) planetary-scale exposure, which (2) is not readily reversible. Whether marine plastics meet the third criterion, (3) eliciting a disruptive impact on vital earth system processes, was uncertain. Since then, several important discoveries have been made to motivate a re-evaluation.

A quasi-Monte Carlo based flocculation model for fine-grained cohesive sediments in aquatic environments.

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.

A tri-modal flocculation model coupled with TELEMAC for estuarine muds both in the laboratory and in the field.

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.

Competition between kaolinite flocculation and stabilization in divalent cation solutions dosed with anionic polyacrylamides.

Divalent cations have been reported to develop bridges between anionic polyelectrolytes and negatively-charged colloidal particles, thereby enhancing particle flocculation. However, results from this study of kaolinite suspensions dosed with various anionic polyacrylamides (PAMs) reveal that Ca(2+) and Mg(2+) can lead to colloid stabilization under some conditions. To explain the opposite but coexisting processes of flocculation and stabilization with divalent cations, a conceptual flocculation model with (1) particle-binding divalent cationic bridges between PAM molecules and kaolinite particles and (2) polymer-binding divalent cationic bridges between PAM molecules is proposed.

A two-class population balance equation yielding bimodal flocculation of marine or estuarine sediments.

Bimodal flocculation of marine and estuarine sediments describes the aggregation and breakage process in which dense microflocs and floppy macroflocs change their relative mass fraction and develop a bimodal floc size distribution. To simulate bimodal flocculation of such sediments, a Two-Class Population Balance Equation (TCPBE), which includes both size-fixed microflocs and size-varying macroflocs, was developed. The new TCPBE was tested by a model-data fitting analysis with experimental data from 1-D column tests, in comparison with the simple Single-Class PBE (SCPBE) and the elaborate Multi-Class PBE (MCPBE).