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Analytical study for swimmers in a channel

Published online by Cambridge University Press:  24 October 2019

A. Farutin ,
H. Wu ,
W.-F. Hu ,
S. Rafaï ,
P. Peyla ,
M.-C. Lai  and
C. Misbah Open the ORCID record for C. Misbah [Opens in a new window]
A. Farutin*
Affiliation:
Univ. Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
H. Wu
Affiliation:
Univ. Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
W.-F. Hu
Affiliation:
Department of Applied Mathematics, National Chung Hsing University, 145, Xingda Road, Taichung City 402, Taiwan
S. Rafaï
Affiliation:
Univ. Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
P. Peyla
Affiliation:
Univ. Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
M.-C. Lai
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu 300, Taiwan
C. Misbah
Affiliation:
Univ. Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
*
†Email address for correspondence: [email protected]
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Abstract

There is an overabundance of microswimmers in nature, including bacteria, algae, mammalian cells and so on. They use flagellum, cilia or global shape changes (amoeboid motion) to move forward. In the presence of confining channels, these swimmers exhibit often non-trivial behaviours, such as accumulation at the wall, navigation and so on, and their swimming speed may be strongly influenced by the geometric confinement. Several numerical studies have reported that the presence of walls either enhances or reduces the swimming speed depending on the nature of the swimmer, and also on the confinement. The purpose of this paper is to provide an analytical explanation of several previously obtained numerical results. We treat the case of amoeboid swimmers and the case of squirmers having either a tangential (the classical situation) or normal velocity prescribed at the swimmer surface (pumper). For amoeboid motion we consider a quasi-circular swimmer which allows us to tackle the problem analytically and to extract the equations of the motion of the swimmer, with several explicit analytical or semi-analytical solutions. It is found that the deformation of the amoeboid swimmer as well as a high enough order effect due to confinement are necessary in order to account for previous numerical results. The analytical theory accounts for several features obtained numerically also for non-deformable swimmers.

JFM classification

Biological Fluid Dynamics: Swimming/flying Biological Fluid Dynamics: Micro-organism dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 365 - 383
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Copyright
© 2019 Cambridge University Press 

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