A mathematical model governing the short-range transport of microplastic particles in a lid-driven cavity with an obstacle

Microplastic in freshwater has been known to absorb, adsorb, and later desorb persistent organic pollutants as well as in its tiny size acts as an infiltrator to vital tissues; it may therefore corrupt physiological processes of organic lives. The fate of microplastic particles can be understood by revealing to what extent certain material properties (e.g., size and density) determine local behavior such as sedimentation and interaction with biofilm. This work seeks to gain an understanding of the short-range transport of microplastic particles in freshwater through devising a lid–driven cavity with a biofilm-covering obstacle as the medium. A stationary Navier–Stokes equation for an incompressible fluid at a moderate Reynolds number provides the background flow field. Microbeads are injected into the flow field, where their motion is governed by a Lagrangian system of equations. Advanced features such as dry particle–particle and particle–wall collisions as well as adhesion between particles and biofilm portraying particle entrapment are presented. Various simulations and parameterization studies are carried out to determine the impact of material properties, obstacle geometry, and adhesion force on the deposition profiles. In most cases, particles are trapped in the biofilm and in regions around the cavity with negative Okubo–Weiss numbers whereby the relative vorticity is dominating against the local strains.