Principles of hydrodynamic particle manipulation in internal Stokes flow

TL;DR

This paper models how force-free spherical particles are displaced in low Reynolds number vortical flows, revealing size-dependent behaviors useful for microfluidic particle sorting and manipulation.

Contribution

It provides a systematic hydrodynamic analysis of particle displacement in Stokes flows, highlighting mechanisms for particle deflection and capture in microfluidic devices.

Findings

Particles can be systematically deflected across streamlines.

Particles can approach channel walls exponentially closely.

Size-dependent behaviors enable sorting and filtering.

Abstract

Manipulation of small-scale particles across streamlines is the elementary task of microfluidic devices. Many such devices operate at very low Reynolds numbers and deflect particles using arrays of obstacles, but a systematic quantification of relevant hydrodynamic effects has been lacking. Here, we explore an alternate approach, rigorously modeling the displacement of force-free spherical particles in vortical Stokes flows under hydrodynamic particle-wall interaction. Certain Moffatt-like eddy geometries with broken symmetry allow for systematic deflection of particles across streamlines, leading to particle accumulation at either Faxen field fixed points or limit cycles. Moreover, particles can be forced onto trajectories approaching channel walls exponentially closely, making quantitative predictions of particle capture (sticking) by short-range forces possible. This rich, particle size-dependent behavior suggests the versatile use of inertial-less flow in devices with a long particle residence time for concentration, sorting, or filtering.