Density-contrast induced inertial forces on particles in oscillatory flows

Oscillatory flows have become an indispensable tool in microfluidics, inducing inertial effects for displacing and manipulating fluid-borne objects in a reliable, controllable and label-free fashion. However, the quantitative description of such effects has been confined to limit cases and specialized scenarios. Here we develop an analytical formalism yielding the equation of motion of density-mismatched spherical particles in oscillatory background flows, generalizing previous work. Inertial force terms are systematically derived from the geometry of the flow field together with analytically known Stokes number dependences. Supported by independent, first-principles direct numerical simulations, we find that these forces are important even for nearly density-matched objects such as cells or bacteria, enabling their fast displacement and separation. Our formalism thus consistently incorporates particle inertia into the Maxey-Riley equation, and in doing so provides a generalization of Auton's modification to added mass, as well as recovering the description of acoustic radiation forces on particles as a limiting case.