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Swimming sheet in a viscosity-stratified fluid

Published online by Cambridge University Press:  20 May 2020

Rajat Dandekar  and
Arezoo M. Ardekani Open the ORCID record for Arezoo M. Ardekani [Opens in a new window]
Rajat Dandekar
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 49707, USA
Arezoo M. Ardekani*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 49707, USA
*
†Email address for correspondence: [email protected]
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Abstract

In this work, we theoretically investigate the motion of a Taylor swimming sheet immersed in a viscosity-stratified fluid. The propulsion of the swimmer disturbs the surrounding fluid, which influences the transport of the stratifying agent described by the advection–diffusion equation. We employ a regular perturbation scheme to solve the coupled differential equations of motion up to the second order with the small parameter given by the ratio of the wave amplitude and the wavelength. The expression for the swimming velocity is linear in the magnitude of the viscosity gradient, while depending on the Péclet number in a non-monotonic way. Interestingly, we find that the Péclet number governs the propensity of the sheet to propel towards regions of favourable viscosities. In particular, for small Péclet numbers ($0<Pe<3$), the swimmer prefers regions of low viscosity, while for high Péclet numbers ($Pe>3$), the swimmer prefers regions of high viscosity. Our analysis shows that purely hydrodynamic effects might be responsible for the experimentally observed accumulation of swimmers near favourable viscosity regions. We find that viscosity gradients influence other motility characteristics of the swimmer, such as power expenditure and hydrodynamic efficiency, and provide analytical expressions for both.

JFM classification

Biological Fluid Dynamics: Swimming/flying
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 895 , 25 July 2020 , R2
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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