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Acoustic propulsion of a small, bottom-heavy sphere

journal contribution
posted on 13.05.2020 by Francois Nadal, Sebastien Michelin
We present here a comprehensive derivation for the speed of a small bottom-heavy sphere forced by a transverse acoustic field and thereby establish how density inhomogeneities may play a critical role in acoustic propulsion. The sphere is trapped at the pressure node of a standing wave whose wavelength is much larger than the sphere diameter. Due to its inhomogeneous density, the sphere oscillates in translation and rotation relative to the surrounding fluid. The perturbative flows induced by the sphere’s rotation and translation are shown to generate a rectified inertial flow responsible for a net mean force on the sphere that is able to propel the particle within the zero-pressure plane. To avoid an explicit derivation of the streaming flow, the propulsion speed is computed exactly using a suitable version of the Lorentz reciprocal theorem. The propulsion speed is shown to scale as the inverse of the viscosity, the cube of the amplitude of the acoustic field and is a non trivial function of the acoustic frequency. Interestingly, for some combinations of the constitutive parameters (fluid to solid density ratio, moment of inertia and centroid to center of mass distance), the direction of propulsion is reversed as soon as the frequency of the forcing acoustic field becomes larger than a certain threshold. The results produced by the model are compatible with both the observed phenomenology and the orders of magnitude of the measured velocities.

Funding

European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under Grant Agreement 714027.

History

School

  • Mechanical, Electrical and Manufacturing Engineering

Published in

Journal of Fluid Mechanics

Volume

898

Publisher

Cambridge University Press (CUP)

Version

AM (Accepted Manuscript)

Rights holder

© The Authors

Publisher statement

This article has been published in a revised form in Journal of Fluid Mechanics https://doi.org/10.1017/jfm.2020.401. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © The Authors.

Acceptance date

17/05/2020

Publication date

2020-06-25

Copyright date

2020

ISSN

0022-1120

eISSN

1469-7645

Language

en

Depositor

Mr Francois Nadal. Deposit date: 12 May 2020

Article number

A10

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