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A Low-Reynolds-Number Treadmilling Swimmer Near a Semi-infinite Wall

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Natural Locomotion in Fluids and on Surfaces

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 155))

Abstract

We investigate the behavior of a treadmilling microswimmer in a two-dimensional unbounded domain with a semi-infinite no-slip wall. The wall can also be regarded as a probe or pipette inserted into the flow. We solve the governing evolution equations in an analytical form and numerically calculate trajectories of the swimmer for several different initial positions and orientations. We then compute the probability that the treadmilling organism can escape the vicinity of the wall. We find that many trajectories in a ‘wedge’ around the wall are likely to escape. This suggests that inserting a probe or pipette in a suspension of organism may push away treadmilling swimmers.

The work of the second author was supported in part by NSF grant DMS-0806821.

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Notes

  1. 1.

    See http://arXiv.org/abs/1104.0146 for color figures.

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Acknowledgments

The authors are grateful for the hospitality of the Geophysical Fluid Dynamics Program at the Woods Hole Oceanographic Institution (supported by NSF), and thank Matthew D. Finn for his helpful advice and suggestions. Some of the numerical calculations for this project were performed at the Institute for Information Management and Communication of Kyoto University.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Kiori Obuse

  2. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    Jean-Luc Thiffeault

Authors
  1. Kiori Obuse
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  2. Jean-Luc Thiffeault
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Corresponding author

Correspondence to Jean-Luc Thiffeault .

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Editors and Affiliations

  1. Courant Institute of Math Sciences, New York University, Mercer Street 251, New York City, 10012, New York, USA

    Stephen Childress

  2. Massachusetts Institute of Technology, Massachusetts Avenue 77, Cambridge, 02139, Massachusetts, USA

    Anette Hosoi

  3. , Department of Mechanical Engineering, The University of Michigan, Auto Lab 2027, Ann Arbor, 48109, Michigan, USA

    William W. Schultz

  4. , Mechanical and Aerospace Engineering, Cornell University, Ithaca, 14850, New York, USA

    Jane Wang

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Obuse, K., Thiffeault, JL. (2012). A Low-Reynolds-Number Treadmilling Swimmer Near a Semi-infinite Wall. In: Childress, S., Hosoi, A., Schultz, W., Wang, J. (eds) Natural Locomotion in Fluids and on Surfaces. The IMA Volumes in Mathematics and its Applications, vol 155. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3997-4_15

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