Density-contrast induced inertial forces on particles in oscillatory flows: quantifying an efficient tool in microfluidics and acoustofluidics.

Oscillatory flows have become an indispensable tool in inertial microfluidics, exerting significant and consistent forces on fluid-borne objects. The use of localized oscillating objects to precisely manipulate particles is now pushing the envelope of existing theories, which are unable to account for experimental observations. While earlier work formalized an unrecognized attractive contribution towards oscillating interfaces acting even on neutrally buoyant particles, here we quantify additional inertial forces on particles due to a finite density contrast. Through a rigorous analytical modeling approach we find that these forces emerge from an interplay between particle inertia, slip velocity and flow gradients, and are important, in particular, for nearly density matched cell-sized particles in biomicrofluidics, where they can be used for fast displacement and separation. We further show that the Auton modification to the added mass term in the Maxey-Riley equation naturally emerges from our theory as a limiting case. Our formalism also generalizes the far-field acoustofluidic secondary radiation force on particles in inviscid flows to include viscous effects, thus bridging the two fields. These predictions are confirmed against independent direct numerical simulations.