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Hydrodynamics of micro-swimmers in films

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journal contribution
posted on 10.12.2018 by Arnold J.T.M. Mathijssen, Amin Doostmohammadi, Julia M. Yeomans, Tyler Shendruk
One of the principal mechanisms by which surfaces and interfaces affect microbial life is by perturbing the hydrodynamic flows generated by swimming. By summing a recursive series of image systems, we derive a numerically tractable approximation to the three-dimensional flow fields of a stokeslet (point force) within a viscous film between a parallel no-slip surface and a no-shear interface and, from this Green’s function, we compute the flows produced by a force- and torque-free micro-swimmer. We also extend the exact solution of Liron & Mochon (J. Engng Maths, vol. 10 (4), 1976, pp. 287–303) to the film geometry, which demonstrates that the image series gives a satisfactory approximation to the swimmer flow fields if the film is sufficiently thick compared to the swimmer size, and we derive the swimmer flows in the thin-film limit. Concentrating on the thick-film case, we find that the dipole moment induces a bias towards swimmer accumulation at the no-slip wall rather than the water–air interface, but that higher-order multipole moments can oppose this. Based on the analytic predictions, we propose an experimental method to find the multipole coefficient that induces circular swimming trajectories, allowing one to analytically determine the swimmer’s three-dimensional position under a microscope.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Fluid Mechanics

Volume

806

Pages

35 - 70

Citation

MATHIJSSEN, A.J.T.M. ... et al., 2016. Hydrodynamics of micro-swimmers in films. Journal of Fluid Mechanics, 806, pp. 35-70.

Publisher

© Cambridge University Press

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

01/09/2016

Publication date

2016-09-29

Notes

This paper was submitted for publication to the journal Journal of Fluid Mechanics and the definitive published version is available at https://doi.org/10.1017/jfm.2016.479

ISSN

0022-1120

eISSN

1469-7645

Language

en

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