Effects of symmetry breaking in the viscous pumping of an oscillating plate in the intermediate Reynolds numbers.

Pumping fluid is essential to numerous applications across a wide range of scales from viscous dominated to inertia driven flows. Most traditional applications occur within a range where inertia is the dominating factor influencing the pump performance, and hence many practical designs are based on mechanisms that rely on this assumption. As one explores smaller devices, however, the increasing effect of viscosity renders these traditional mechanisms ineffective. In the current work, a bio-inspired pump is constructed from a two-dimensional oscillating solid and flexible plate to study the effect of diminishing inertia within a narrow channel. The goal is to quantify and better understand the role played by a shift from symmetric to asymmetric kinematics of an oscillating rigid or flexible plate in the transition regime between viscous and inertia dominated flows. This is done through both a temporal asymmetry using a rigid plate (e.g. scallop) and a geometric asymmetry using a passive one-way hinged articulation (e.g. jellyfish). One-way flexibility results in a rigid plate during the effective stroke while permitting a simple hinged articulation during the recovery stroke. The waveform used for the temporally asymmetric case consists of a basic triangle waveform which could generate faster effective strokes than recovery strokes. The results of the single-plate tests indicate that increased asymmetry introduced in the triangular wave actuation leads to increased pumping performance and energy consumption. In the case of flexible plates, the results show that a mass-specific pumping efficiency was higher for a higher actuation frequency at the same Reynolds numbers.