Sedimentation of flexible fibers through an ordered array of pillars

In this study, we extend our previous work [Makanga et al., Physical Review Fluids 8, 044303 (2023)] to investigate the effects of a periodic array of pillars on the settling dynamics of a flexible fiber in a viscous fluid. By means of numerical simulations, we show that the fiber trajectory falls at long times into one of two migration modes, ``zigzag" and ``displacement", which are determined by the short-time scattering dynamics induced by fiber-pillar interactions. In the zigzag mode, there is no average displacement relative to the direction of gravity; the center of mass of the fiber follows a quasi-straight line. Conversely, in the displacement mode, there is a net displacement relative to the direction of gravity; the fiber center of mass follows a cyclical skew-bumping path. We show how this long-time behavior can be predicted using a theoretical model with minimal ingredients. These findings, together with the long-time transport properties of the fiber, provide insights into future experiments, as well as the design of gravity-based deterministic lateral displacement (DLD) devices to sort elongated particles based on their geometric and/or mechanical properties.