Inertial Forces on Microparticles in Oscillatory Flows

Particle manipulation is a core task of microfluidic devices. Understanding in detail how and when a particle’s trajectory deviates from streamlines of the flow informs the control necessary for concentration, separation, and sorting of microscale objects in applications. Recently, it has been recognized that inertial forces can be a powerful tool for accomplishing such tasks, even in low-Reynolds-number microfluidics. Our work focuses on oscillatory flows, where inertia can be brought to bear on smaller length and time scales than in steady-flow scenarios. Revisiting the classical theory of particle trajectories by Maxey and Riley, we derive a rigorous generalization of their equation of motion, which, for neutrally buoyant particles, gives rise to a universal inertial force expression based on gradients and curvature of the background flow field [1]. A similar analysis for particles with density contrast [2] reveals additional force terms and incorporates earlier theoretical descriptions such as Auton’s correction and the secondary radiation force of acoustofluidics as limiting cases. This body of work shows that time-averaged inertial forces in microscale oscillatory flows are strong compared to other effects and that their sign and spatial dependence can be altered by controlling the flow field. The theory spans the entire range of Stokes numbers, dovetails with acoustofluidics in the inviscid limit, and has been rigorously checked against direct numerical simulations. For many experiments such as bubble microfluidics relying on oscillatory flow this formalism provides a quantitative guide for device design.

[1] Agarwal, S., Chan, F.K., Rallabandi, B., Gazzola, M. and Hilgenfeldt, S., 2021. An unrecognized inertial force induced by flow curvature in microfluidics. PNAS 118, p.e2103822118.

[2] Agarwal, S., Bhosale, Y., Upadhyay, G., Gazzola, M. and Hilgenfeldt, S., 2022. Density-contrast induced inertial forces on particles in oscillatory flows, preprint.