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A squirmer across Reynolds numbers

Published online by Cambridge University Press:  29 April 2016

Nicholas G. Chisholm ,
Dominique Legendre ,
Eric Lauga  and
Aditya S. Khair
Nicholas G. Chisholm
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Dominique Legendre
Affiliation:
IMFT (Institut de Mécanique des Fluides de Toulouse), Université de Toulouse, INPT-UPS, Allée Camille Soula, F-31400 Toulouse, France
Eric Lauga
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Aditya S. Khair*
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
*
†Email address for correspondence: akhair@andrew.cmu.edu
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Abstract

The self-propulsion of a spherical squirmer – a model swimming organism that achieves locomotion via steady tangential movement of its surface – is quantified across the transition from viscously to inertially dominated flow. Specifically, the flow around a squirmer is computed for Reynolds numbers ($Re$) between 0.01 and 1000 by numerical solution of the Navier–Stokes equations. A squirmer with a fixed swimming stroke and fixed swimming direction is considered. We find that fluid inertia leads to profound differences in the locomotion of pusher (propelled from the rear) versus puller (propelled from the front) squirmers. Specifically, pushers have a swimming speed that increases monotonically with $Re$, and efficient convection of vorticity past their surface leads to steady axisymmetric flow that remains stable up to at least $Re=1000$. In contrast, pullers have a swimming speed that is non-monotonic with $Re$. Moreover, they trap vorticity within their wake, which leads to flow instabilities that cause a decrease in the time-averaged swimming speed at large $Re$. The power expenditure and swimming efficiency are also computed. We show that pushers are more efficient at large $Re$, mainly because the flow around them can remain stable to much greater $Re$ than is the case for pullers. Interestingly, if unstable axisymmetric flows at large $Re$ are considered, pullers are more efficient due to the development of a Hill’s vortex-like wake structure.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 796 , 10 June 2016 , pp. 233 - 256
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Copyright
© 2016 Cambridge University Press 

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