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No net motion for oscillating near-spheres at low Reynolds numbers

Published online by Cambridge University Press:  04 March 2019

K. Lippera
Affiliation:
LadHyX, UMR CNRS 7646, Ecole polytechnique, 91128 Palaiseau, France
O. Dauchot
Affiliation:
EC2M, UMR CNRS 7083 Gulliver, ESPCI ParisTech, 10 rue Vauquelin, 75005 Paris, France
S. Michelin
Affiliation:
LadHyX, UMR CNRS 7646, Ecole polytechnique, 91128 Palaiseau, France
M. Benzaquen
Affiliation:
LadHyX, UMR CNRS 7646, Ecole polytechnique, 91128 Palaiseau, France
Corresponding

Abstract

We investigate the flow around an oscillating nearly spherical particle at low, yet non-vanishing, Reynolds numbers ( $Re$ ), and the potential resulting locomotion. We analytically demonstrate that no net motion can arise up to order one in $Re$ and order one in the asphericity parameter, regardless of the particle’s shape. Therefore, geometry-induced acoustic streaming propulsion, if any, must arise at higher order.

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JFM Rapids
Copyright
© 2019 Cambridge University Press 

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