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A freely suspended robotic swimmer propelled by viscoelastic normal stresses

Published online by Cambridge University Press:  28 June 2022

L.A. Kroo Open the ORCID record for L.A. Kroo [Opens in a new window] ,
Jeremy P. Binagia Open the ORCID record for Jeremy P. Binagia [Opens in a new window] ,
Noah Eckman ,
Manu Prakash Open the ORCID record for Manu Prakash [Opens in a new window]  and
Eric S.G. Shaqfeh Open the ORCID record for Eric S.G. Shaqfeh [Opens in a new window]
L.A. Kroo
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, United States
Jeremy P. Binagia
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, United States
Noah Eckman
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, United States
Manu Prakash
Affiliation:
Department of Bioengineering, Stanford University, Stanford, CA 94305, United States
Eric S.G. Shaqfeh*
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, United States Department of Chemical Engineering, Stanford University, Stanford, CA 94305, United States
*
†Email address for correspondence: esgs@stanford.edu
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Abstract

We present a self-propelled axisymmetric low-Reynolds-number swimmer (force- and torque-free) that, while unable to swim in a Newtonian fluid, propels itself in a non-Newtonian fluid as a result of fluid elasticity. The propulsion gait is pure ‘swirling’ and is demonstrated using a robotic swimmer, comprised of a ‘head’ sphere and a ‘tail’ sphere, whose swimming speed is shown to demonstrate good agreement with a microhydrodynamic asymptotic theory and numerical simulations. Schlieren imaging demonstrates that propulsion of the swimmer is driven by a strong viscoelastic jet at the tail, which develops due to the fore–aft asymmetry of the swimmer. Optimized cylindrical and conic tail geometries are shown to double the propulsive signal, relative to the optimal spherical tail. We show that we can use observations of this robot to infer rheological properties of the surrounding fluid. We measure the primary normal stress coefficient $\varPsi _1$ at shear rates ${<}1\,{\rm Hz}$, and show reasonable agreement with extrapolated bench-top measurements ($0.8\unicode{x2013}1.2\,{\rm Pa}\,{\rm s}^2$ difference). We also derive how the head rotation may be used to measure the second normal stress coefficient, $\varPsi _2$. The study demonstrates the exciting potential for a ‘swimming rheometer’, examining the intersection between swimming and sensing in complex fluids.

JFM classification

Biological Fluid Dynamics: Propulsion Non-Newtonian Flows: Rheology Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 944 , 10 August 2022 , A20
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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Kroo et al. supplementary movie 1

Schlieren imaging of a propelling swirler, demonstrating a non-inertial, viscoelastic jet coming off the tail (to the left). The counter-rotating head is on the right, and the robot propels to the right. 8x playback speed.

Download Kroo et al. supplementary movie 1(Video)
Video 8.3 MB

Kroo et al. supplementary movie 2

A torque-free, robotic swimmer self-propelling at low Re in the direction of the "head" sphere, in a viscoelastic polymeric fluid (0.1% polyacrylamide-based Boger fluid).

Download Kroo et al. supplementary movie 2(Video)
Video 7.4 MB

Kroo et al. supplementary movie 3

Swimmer does not propel in Newtonian fluids at low Re. This movie depicts the swimmer failing to propel in pure corn syrup (control experiment).

Download Kroo et al. supplementary movie 3(Video)
Video 8.9 MB