Analytical Modeling of Microplastic Transport in Rivers: Incorporating Sinking, Removal, and Multi-Phase Dynamics

Microplastics (MP) are transported through rivers, acting as major conduits to oceans, yet standard transport models often fail to capture polymer-specific dynamics like settling and removal. This study proposes two novel analytical frameworks to address this: a modified Advection–Dispersion Equation (ADE) incorporating first-order sinking and removal, and a multi-phase model accounting for hydrodynamic–particle coupling. We derived exact closed-form solutions for a finite pulse input and validated the baseline model against established results. Our results demonstrate that the conventional ADE significantly overestimates peak MP concentrations, while the modified ADE reveals a “stretching” effect that extends the duration of ecosystem exposure. Our analysis indicates that sinking is the primary driver of mass loss to sediments, with higher sinking rates reducing aqueous concentrations by approximately 50% compared to non-settling scenarios. However, removal employs negligible influence during the initial pulse phase but shows cumulative impact over long transport distances. The study highlights the critical need to incorporate sediment accumulation terms into risk assessments, as ignoring sinking leads to underestimating benthic pollution and overestimating marine flux. Additionally, the multi-phase formulation provides a theoretical basis for modeling dense plastic spills where particles alter flow momentum.