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. In addition to the advection-diffusion terms, the PBE transport equation involves a deposition sink term. Seven size classes of MPs are modeled in the DC method, which is compared to the PBE method. The evolution of particle size distribution is compared between the two methods using a simplified test case of a schematized estuary with tidal forcing and river discharge. This work successfully demonstrates the applicability and appropriateness of the PBE model in modeling the transport of MPs to track the dynamic and complete size distribution at a reduced computational cost in comparison to the DC model. With the PBE method, it is possible to address other diversities of the MPs such as the shape and density.