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Swimming of microorganisms in quasi-two-dimensional membranes

Published online by Cambridge University Press:  29 January 2021

Carlos Alas Open the ORCID record for Carlos Alas [Opens in a new window] ,
Thomas R. Powers Open the ORCID record for Thomas R. Powers [Opens in a new window]  and
Tatiana Kuriabova Open the ORCID record for Tatiana Kuriabova [Opens in a new window]
Carlos Alas
Affiliation:
Department of Physics, California Polytechnic State University, San Luis Obispo, CA93407, USA
Thomas R. Powers
Affiliation:
Center for Fluid Mechanics, School of Engineering and Department of Physics, Brown University, Providence, RI02912, USA
Tatiana Kuriabova*
Affiliation:
Department of Physics, California Polytechnic State University, San Luis Obispo, CA93407, USA
*
†Email address for correspondence: [email protected]
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Abstract

Biological swimmers frequently navigate in geometrically restricted media. We study the prescribed-stroke problem of swimmers confined to a planar viscous membrane embedded in a bulk fluid of different viscosity. In their motion, microscopic swimmers disturb the fluid in both the membrane and the bulk. The flows that emerge have a combination of two-dimensional (2-D) and three-dimensional (3-D) hydrodynamic features, and such flows are referred to as quasi-two-dimensional. The cross-over from 2-D to 3-D hydrodynamics in a quasi-2-D fluid is controlled by the Saffman length, a length scale given by the ratio of the 2-D membrane viscosity to the 3-D viscosity of the embedding bulk fluid. We have developed a computational and theoretical approach based on the boundary element method and the Lorentz reciprocal theorem to study the swimming of microorganisms for a range of values of the Saffman length. We found that a flagellum propagating transverse sinusoidal waves in a quasi-2-D membrane can develop a swimming speed exceeding that in pure 2-D or 3-D fluids, while the propulsion of a 2-D squirmer is slowed down by the presence of the bulk fluid.

JFM classification

Biological Fluid Dynamics: Propulsion Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A35
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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