Transport of ellipsoidal microplastic particles in a 3D lid-driven cavity under size and aspect ratio variation

The primary goal of this paper is to model and study the behavior of ellipsoidal microplastic particles in a 3D lid-driven cavity. An Eulerian equation for the hydrodynamics is solved toward stationarity under the Reynolds number 1000 and coupled with a Lagrangian system governing the particle dynamics. The key points of departure in the modeling are laminar flow and small particle Reynolds number under which the drag force has extensively been studied. We then address the question, what would be the behavior of prolate and oblate particles under extreme conditions, where the aspect ratio tends to either ∞ (thin needle) or 0 (thin disk). The corresponding tool, Singular Perturbation Theory, not only settles the analysis of the critical manifold but also underlies a quasi-steady state approximation (QSSA) of the particle velocity around the manifold. We show that in a certain range of particle aspect ratio, the QSSA gives quite good approximations of the particle positions yet more computational efficiency. Sedimentation is shown to highly be dependent on the particle’s initial position, aspect ratio, and size. Meanwhile initial position determines to which direction the fluid stream drifts the particles, larger size and aspect ratio closer to 1 increase the likelihood of sedimenting. We also show that neutrally buoyant particles prefer to deposit on the cavity base as well as on vorticity-dominating regions. Generally, buoyant particles with aspect ratios between 1/20 and 20 spin faster than tumble, and they spin even faster as the aspect ratio gets smaller.