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Elastohydrodynamic propulsion of a magnetically actuated filament

Sohum Kapadia1,*, Julien Chopin2,†, and Arshad Kudrolli1,‡

  • *Contact author: skapadia@clarku.edu
  • †Contact author: chopin.phys@protonmail.com
  • ‡Contact author: akudrolli@clarku.edu
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Phys. Rev. Research 8, 043032 – Published 9 October, 2026

DOI: https://doi.org/10.1103/gd8c-4t3q

Abstract

We investigate the low-Reynolds-number propulsion of a slender elastic filament with a dipolar magnetic head actuated by an oscillating magnetic field in a viscous fluid by studying its strokes and net forward motion. To capture these dynamics, we employ an elastohydrodynamic (EH) framework that couples Euler-Bernoulli beam mechanics with resistive force theory. Unlike prescribed-kinematics models, filament shapes here emerge self-consistently from the actuation and the force and torque boundary conditions (BCs). We demonstrate that viscous boundary contributions are crucial for quantitative agreement and show that the swimming dynamics are governed by the EH length and a magneto-viscous-elastic stroke amplitude introduced here. The swimming speed is nonmonotonic with increasing ratio of the swimmer length to the EH length and is shown to reach a maximum when the swimmer length is on the order of the EH length. We further discuss the analytical limit in which the tail BCs can be described as free, and the limitations that arise when viscous contributions to the BCs are ignored.

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References (24)

  1. J. Gray, The movement of sea-urchin spermatozoa, J. Exp. Biol. 32, 775 (1955).
  2. S. J. Lighthill, Mathematical Biofluiddynamics (SIAM, Philadelphia, PH, 1975).
  3. C. H. Wiggins, D. Riveline, A. Ott, and R. E. Goldstein, Trapping and wiggling: Elastohydrodynamics of driven microfilaments, Biophys. J. 74, 1043 (1998).
  4. C. H. Wiggins and R. E. Goldstein, Flexive and propulsive dynamics of elastica at low Reynolds number, Phys. Rev. Lett. 80, 3879 (1998).
  5. J. Gray and G. J. Hancock, The propulsion of sea-urchin spermatozoa, J. Exp. Biol. 32, 802 (1955).
  6. R. E. Johnson, An improved slender-body theory for Stokes flow, J. Fluid Mech. 99, 411 (1980).
  7. E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Prog. Phys. 72, 096601 (2009).
  8. E. Lauga, The Fluid Dynamics of Cell Motility (Cambridge University Press, Cambridge, UK, 2020), Vol. 62.
  9. O. S. Pak, W. Gao, J. Wang, and E. Lauga, High-speed propulsion of flexible nanowire motors: Theory and experiments, Soft Matter 7, 8169 (2011).
  10. T. S. Yu, E. Lauga, and A. Hosoi, Experimental investigations of elastic tail propulsion at low Reynolds number, Phys. Fluids 18, 091701 (2006).
  11. B. Rodenborn, C.-H. Chen, H. L. Swinney, B. Liu, and H. Zhang, Propulsion of microorganisms by a helical flagellum, Proc. Natl. Acad. Sci. USA 110, E338 (2013).
  12. B. Liu, L. Chen, and J. Zhang, Effective and efficient modeling of the hydrodynamics for bacterial flagella, Phys. Fluids 37, 011903 (2025).
  13. P. H. Htet and E. Lauga, Load-dependent resistive-force theory for helical filaments, Philos. Trans. R. Soc. A 383, 20240260 (2025).
  14. H. Gadêlha, On the optimal shape of magnetic swimmers, Regular Chaotic Dyn. 18, 75 (2013).
  15. M. Dasgupta, B. Liu, H. C. Fu, M. Berhanu, K. S. Breuer, T. R. Powers, and A. Kudrolli, Speed of a swimming sheet in Newtonian and viscoelastic fluids, Phys. Rev. E 87, 013015 (2013).
  16. R. E. Johnson and C. J. Brokaw, Flagellar hydrodynamics. A comparison between resistive-force theory and slender-body theory, Biophys. J. 25, 113 (1979).
  17. B. M. Friedrich, I. H. Riedel-Kruse, J. Howard, and F. Jülicher, High-precision tracking of sperm swimming trajectories with nanometer scale resolution, J. Exp. Biol. 213, 1226 (2010).
  18. V. Kantsler and R. E. Goldstein, Fluctuations, dynamics, and the solitary wave of a swimming microorganism, Phys. Rev. Lett. 108, 038103 (2012).
  19. E. E. Keaveny, S. W. Walker, and M. J. Shelley, Optimization of chiral structures for microscale propulsion, Nano Lett. 13, 531 (2013).
  20. S. Ramananarivo, R. Godoy-Diana, and B. Thiria, Passive elastic mechanism to mimic fish-muscle action in anguilliform swimming, J. R. Soc. Interface 10, 20130667 (2013).
  21. A. Biswas, T. Huynh, B. Desai, M. Moss, and A. Kudrolli, Dynamics of magnetoelastic robots in water-saturated granular beds, Phys. Rev. Fluids 8, 094304 (2023).
  22. See Supplemental Material at https://link.aps.org/supplemental/10.1103/gd8c-4t3q for characterization data, drag coefficients, analytical solution to EH model with minimal BC, EH model shape comparisons, RFT propulsion calculations, and the list of videos.
  23. K. Yang, C. Lu, X. Zhao, and R. Kawamura, From bead to rod: Comparison of theories by measuring translational drag coefficients of micron-sized magnetic bead-chains in Stokes flow, PLoS ONE 12, e0188015 (2017).
  24. E. Lauga, Floppy swimming: Viscous locomotion of actuated elastica, Phys. Rev. E 75, 041916 (2007).

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Phys. Rev. Research 8, 043032– Published 9 October, 2026
  • Received 10 June 2026
  • Accepted 19 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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