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Taylor’s swimming sheet in a yield-stress fluid

Published online by Cambridge University Press:  30 August 2017

D. R. Hewitt Open the ORCID record for D. R. Hewitt [Opens in a new window]  and
N. J. Balmforth Open the ORCID record for N. J. Balmforth [Opens in a new window]
D. R. Hewitt*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
N. J. Balmforth
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada
*
†Email address for correspondence: drh39@cam.ac.uk
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Abstract

A yield stress is added to Taylor’s (Proc. R. Soc. Lond. A, vol. 209, 1951, pp. 447–461) model of a two-dimensional flexible sheet swimming through a viscous fluid. Both transverse waves along the sheet, as in Taylor’s original model, and longitudinal waves are considered as means of locomotion. In each case, numerical solutions are provided over a range of the two key parameters of the problem: the wave amplitude relative to the wavelength and a Bingham number which describes the strength of the yield stress. The numerical solutions are supplemented with discussions of various limits of the problem in which analytical progress is possible. When the yield stress is large, the swimming speed for low wave amplitude is exactly double that for a Newtonian fluid, for either type of wave.

JFM classification

Non-Newtonian Flows: Non-Newtonian Flows Non-Newtonian Flows: Plastic materials Biological Fluid Dynamics: Propulsion

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Papers
Information
Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 33 - 56
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© 2017 Cambridge University Press 

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