Density-contrast induced inertial forces on particles in oscillatory flows

TL;DR

This paper develops a comprehensive analytical model for inertial forces on density-mismatched particles in oscillatory flows, applicable to microfluidic manipulation of cells and bacteria, supported by numerical simulations.

Contribution

It generalizes the Maxey--Riley equation to include arbitrary background flows and density differences, providing a unified framework for inertial effects in microfluidics.

Findings

Inertial forces are significant even for nearly density-matched particles.

The formalism accurately predicts particle displacement and separation in oscillatory flows.

Supports applications in microfluidic particle manipulation and separation.

Abstract

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 arbitrary 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 generalizes the Maxey--Riley equation, encompassing not only particle inertia, but consistently recovering, in the limit of large Stokes numbers, the Auton modification to added mass as well as the far-field acoustofluidic secondary radiation force.