Inertia-driven flow symmetry breaking by oscillating plates

Abstract

While cilia are generally found in viscosity-dominated regimes, those of a comb jelly, the longest motile cilia in nature, are used for propulsion and feeding in inertia-dominated flows. Motivated by the effective fluid transport of cilia at relatively high Reynolds number, the characteristics of vortex formation and fluid transport are investigated numerically for a simple two-dimensional model of rigid plates in Re = O(10 − 102). The small plates oscillate symmetrically on both walls of a channel. Under some conditions, the vortical structures generated by the plates become asymmetric notably with respect to the channel midline. In relatively narrow channels, the interaction of counter-rotating vortices shed directly from the plates near the midline causes symmetry breaking, and thus the mixing of fluid particles across the midline is enhanced greatly. Meanwhile, in relatively wide channels, the diffused weak vortices that persist after previous strokes become asymmetric first. When the number of oscillating plates on each wall increases, the vortex generated by a plate is confined between two plates, and it is annihilated by the counter-rotating vortex generated by a neighbor plate during stroke reversal, thereby keeping them from propagating toward the midline. This collective motion of multiple plates hinders the vortices from undergoing symmetry breaking even at the relatively high Reynolds number of Re = 200, and mixing is suppressed accordingly.