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Low-Reynolds-number swimming in a capillary tube

Published online by Cambridge University Press:  31 May 2013

L. Zhu ,
E. Lauga  and
L. Brandt
L. Zhu*
Affiliation:
Linné Flow Centre, KTH Mechanics, S-100 44 Stockholm, Sweden
E. Lauga
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla CA 92093-0411, USA
L. Brandt
Affiliation:
Linné Flow Centre, KTH Mechanics, S-100 44 Stockholm, Sweden
*
†Email address for correspondence: lailai@mech.kth.se
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Abstract

We use the boundary element method to study the low-Reynolds-number locomotion of a spherical model microorganism in a circular tube. The swimmer propels itself by tangential or normal surface motion in a tube whose radius is of the order of the swimmer size. Hydrodynamic interactions with the tube walls significantly affect the average swimming speed and power consumption of the model microorganism. In the case of swimming parallel to the tube axis, the locomotion speed is always reduced (respectively, increased) for swimmers with tangential (respectively, normal) deformation. In all cases, the rate of work necessary for swimming is increased by confinement. Swimmers with no force dipoles in the far field generally follow helical trajectories, solely induced by hydrodynamic interactions with the tube walls, and in qualitative agreement with recent experimental observations for Paramecium. Swimmers of the puller type always display stable locomotion at a location which depends on the strength of their force dipoles: swimmers with weak dipoles (small $\alpha $) swim in the centre of the tube while those with strong dipoles (large $\alpha $) swim near the walls. In contrast, pusher swimmers and those employing normal deformation are unstable and end up crashing into the walls of the tube. Similar dynamics is observed for swimming into a curved tube. These results could be relevant for the future design of artificial microswimmers in confined geometries.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Low-Reynolds-number flows: Boundary integral methods Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 726 , 10 July 2013 , pp. 285 - 311
Copyright
©2013 Cambridge University Press 

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Zhu et al. supplementary movie

'A neutral squirmer swimming in a curved pipe'.

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Zhu et al. supplementary movie

'A neutral squirmer following the helical trajectory in a straight pipe'

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Video 5.2 MB