Direct Measurement of Unsteady Microscale Stokes Flow Using Optically Driven Microspheres

TL;DR

This study provides the first direct experimental measurement of unsteady microscale Stokes flow around oscillating particles, revealing phase lag and flow orbits that inform understanding of microscale fluid dynamics and synchronization.

Contribution

It introduces a novel optical trapping method to measure unsteady flow fields at the microscale, validating theoretical predictions of phase lag and flow orbits in unsteady Stokes flow.

Findings

Tracer particles exhibit elliptical Lissajous figures consistent with low-frequency flow models.

Measured phase shifts scale with distance and angle as predicted by theory.

Results have implications for understanding microscale synchronization phenomena.

Abstract

A growing body of work on the dynamics of eukaryotic flagella has noted that their oscillation frequencies are sufficiently high that the viscous penetration depth of unsteady Stokes flow is comparable to the scales over which flagella synchronize. Incorporating these effects into theories of synchronization requires an understanding of the global unsteady flows around oscillating bodies. Yet, there has been no precise experimental test on the microscale of the most basic aspects of such unsteady Stokes flow: the orbits of passive tracers and the position-dependent phase lag between the oscillating response of the fluid at a distant point and that of the driving particle. Here, we report the first such direct Lagrangian measurement of this unsteady flow. The method uses an array of $30$ submicron tracer particles positioned by a time-shared optical trap at a range of distances and angular positions with respect to a larger, central particle, which is then driven by an oscillating optical trap at frequencies up to $400$ Hz. In this microscale regime, the tracer dynamics is considerably simplified by the smallness of both inertial effects on particle motion and finite-frequency corrections to the Stokes drag law. The tracers are found to display elliptical Lissajous figures whose orientation and geometry are in agreement with a low-frequency expansion of the underlying dynamics, and the experimental phase shift between motion parallel and orthogonal to the oscillation axis exhibits a predicted scaling form in distance and angle. Possible implications of these results for synchronization dynamics are discussed.