Inertial focusing of small particles in oscillatory channel flows

Abstract

This study leverages the immersed boundary-lattice Boltzmann method to investigate the inertial focusing dynamics of a small neutrally buoyant particle in oscillatory channel flows driven by two distinct pressure gradient (PG) waveforms. Through an in-depth analysis of particle behavior, this research delineates the effects of PG waveforms, particle Reynolds number (Rep), and Womersley number (Wo) on the inertial focusing processes, and contrasts these findings with conventional Poiseuille flow-induced inertial focusing. Our results reveal that oscillatory flows induce more intricate focusing patterns than those observed in Poiseuille flow. The streamwise PG oscillation alters the particle focusing positions and introduces minor lateral oscillations in the post-focusing phase. The square PG waveform positions particles closer to the channel wall compared to Poiseuille flow, whereas the sine PG waveform positions particles closer to the channel center. Moreover, an increase in Rep nudges the focusing positions towards the channel center, while a higher Wo pushes them towards the walls. Notably, at Wo ≥ 5, the flow's oscillatory effect dominates over its inertial effect (i.e. Rep) on particle focusing. The study also underscores the capability of oscillatory flows to reduce the required channel length for particle focusing, albeit at the cost of increased focusing time. Contrary to Poiseuille flow, where the focusing length shortens with an increased Rep, oscillatory flow demonstrates an inverse correlation, with an increase in Rep extending the focusing length. Furthermore, while a higher Rep is beneficial in Poiseuille flow, it adversely affects the focusing effect in oscillatory flow. The focusing efficiency peaks at Wo = 3.5 for both waveforms, with the sine PG waveform offering superior efficiency due to the lower lift forces generated. Consequently, for optimal focusing in similar conditions, it is recommended to set Rep and Wo to 0.075 and 3.5, respectively.