PhysRevFluids.6.053102.pdf (1.64 MB)
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Direct measurement of unsteady microscale Stokes flow using optically driven microspheres

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posted on 14.06.2021, 15:16 authored by Nicolas Bruot, Pietro Cicuta, Hermes Bloomfield-Gadêlha, Raymond Goldstein, Jurij Kotar, Eric Lauga, Francois NadalFrancois Nadal
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.


Geometric, Topological, and Statistical Dynamics in Soft Matter and Mathematical Biology

Engineering and Physical Sciences Research Council

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ERC Consolidator grant 682754

ERC PoC grant CellsBox

Wellcome Trust Investigator Award 207510/Z/17/Z

Marine Microbiology Initiative of the Gordon and Betty Moore Foundation, Grant 7523



  • Mechanical, Electrical and Manufacturing Engineering

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Physical Review Fluids






American Physical Society


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This is an Open Access Article. It is published by the American Physical Society under the Creative Commons Attribution 4.0 International Licence (CC BY 4.0). Full details of this licence are available at:

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Mr Francois Nadal. Deposit date: 15 May 2021

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