Inertial particle manipulation in microscale oscillatory flows

Recent work has shown that inertial effects in oscillating flows can be exploited for simultaneous transport and differential displacement of microparticles, enabling size sorting of such particles on extraordinarily short time scales. Generalizing previous theory efforts, we here derive a two-dimensional time-averaged version of the Maxey-Riley equation that includes the effect of an oscillating interface to model particle dynamics in such flows. Separating the steady transport time scale from the oscillatory time scale results in a simple and computationally efficient reduced model that preserves all slow-time features of the full unsteady Maxey-Riley simulations, including inertial particle displacement. Comparison is made not only to full simulations, but also to experiments using oscillating bubbles as the driving interfaces. In this case, the theory predicts either an attraction to or a repulsion from the bubble interface due to inertial effects, so that versatile particle manipulation is possible using differences in particle size, particle/fluid density contrast and streaming strength. We also demonstrate that these predictions are in agreement with experiments.