A limiting model for a low Reynolds number swimmer with $ N $ passive elastic arms

François Alouges; Aline Lefebvre-Lepot; Jessie Levillain; François Alouges; Aline Lefebvre-Lepot; Jessie Levillain

doi:10.3934/mine.2023087

Mathematics in Engineering

2023, Volume 5, Issue 5: 1-20. doi: 10.3934/mine.2023087

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Research article

A limiting model for a low Reynolds number swimmer with $ N $ passive elastic arms

1.
Centre Borelli, ENS Paris-Saclay, CNRS, Université Paris-Saclay, 91190 Gif-sur-Yvette, France
2.
CMAP, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France

Received: 02 March 2023 Revised: 18 April 2023 Accepted: 18 April 2023 Published: 11 May 2023

We consider a low Reynolds number artificial swimmer that consists of an active arm followed by $ N $ passive springs separated by spheres. This setup generalizes an approach proposed in Montino and DeSimone, Eur. Phys. J. E, vol. 38, 2015. We further study the limit as the number of springs tends to infinity and the parameters are scaled conveniently, and provide a rigorous proof of the convergence of the discrete model to the continuous one. Several numerical experiments show the performances of the displacement in terms of the frequency or the amplitude of the oscillation of the active arm.
- low Reynolds number swimmers,
- partial differential equations,
- ordinary differential equations,
- discrete model,
- continuous model,
- convergence
Citation: François Alouges, Aline Lefebvre-Lepot, Jessie Levillain. A limiting model for a low Reynolds number swimmer with $ N $ passive elastic arms[J]. Mathematics in Engineering, 2023, 5(5): 1-20. doi: 10.3934/mine.2023087

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Abstract

We consider a low Reynolds number artificial swimmer that consists of an active arm followed by $ N $ passive springs separated by spheres. This setup generalizes an approach proposed in Montino and DeSimone, Eur. Phys. J. E, vol. 38, 2015. We further study the limit as the number of springs tends to infinity and the parameters are scaled conveniently, and provide a rigorous proof of the convergence of the discrete model to the continuous one. Several numerical experiments show the performances of the displacement in terms of the frequency or the amplitude of the oscillation of the active arm.

References

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