Skip to main content
Log in

Twisting and buckling: A new undulation mechanism for artificial swimmers

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract

Among the various locomotion strategies of the animal kingdom, the undulation locomotion is of particular interest for biomimetic applications. In this paper, we present an artificial swimmer set into motion by a new and non-trivial undulation mechanism, based on the twisting and buckling of its body. The swimmer consists of a long cylinder of ferrogel which is polarized transversely and in opposite directions at each extremity. When it is placed on a water film and submitted to a transverse oscillating magnetic field, the worm-like swimmer undulates and swims. Whereas symmetry breaking is due to the field gradient, the undulations of the worm result from a torsional buckling instability as the polarized ends tend to align with the applied magnetic field. The critical magnetic field above which buckling and subsequent swimming is observed may be predicted using elasticity equations including the effect of the magnetic torque. As the length of the worm is varied, several undulation modes are observed which are in good agreement with the bending modes of an elastic rod with free ends.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. Guo, Q. Pan, M.B. Khamesee, Microsyst. Technol. 14, 307 (2008)

    Article  Google Scholar 

  2. J.J. Abbott, K.E. Peyer, M.C. Lagomarsino et al., Int. J. Robotic Res. 28, 1434 (2009)

    Article  Google Scholar 

  3. D.L. Hu, J. Nirodya, T. Scotta et al., Proc. Natl. Acad. Sci. U.S.A. 106, 10081 (2009)

    Article  ADS  Google Scholar 

  4. G.B. Gillis, J. Exp. Biol. 201, 3245 (1998)

    Google Scholar 

  5. R.M. Alexander, in The Biology of Nematodes, Chapt. 13, edited by D.L. Lee (Taylor and Francis Inc., 2002)

  6. J. Korta, D.A. Clark, C.V. Gabel, L. Mahadevan, A.D.T. Samuel, J. Exp. Biol. 210, 2383 (2007)

    Article  Google Scholar 

  7. A. Crespi, A. Badertscher, A. Guignard et al., Rob. Autom. Syst. 50, 163 (2005)

    Article  Google Scholar 

  8. R. Dreyfus, J. Baudry, M.L. Roper, M. Fermigier, H.A. Stone, J. Bibette, Nature (London) 437, 862 (2005)

    Article  ADS  Google Scholar 

  9. A. Snezhko, M. Belkin, I.S. Aranson, W.K. Kwok, Phys. Rev. Lett. 102, 118103 (2009)

    Article  ADS  Google Scholar 

  10. E.M. Purcell, Am. J. Phys. 45, 3 (1977)

    Article  ADS  Google Scholar 

  11. C.H. Wiggins, R.E. Goldstein, Phys. Rev. Lett 80, 3879 (1998)

    Article  ADS  Google Scholar 

  12. L.E. Becker, S.A. Koehler, H.A. Stone, J. Fluid Mech. 490, 15 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. J.E. Avron, O. Gat, O. Kenneth, Phys. Rev. Lett. 93, 186001 (2004)

    Article  ADS  Google Scholar 

  14. D. Tam, A.E. Hosoi, Phys. Rev. Lett. 98, 068105 (2007)

    Article  ADS  Google Scholar 

  15. N. Coq, O. du Roure, J. Marthelot, D. Bartolo, M. Fermigier, Phys. Fluids. 20, 051703 (2008)

    Article  ADS  Google Scholar 

  16. E. Lauga, T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  17. S. Sudo, S. Segawa, T. Honda, J. Intell. Mater. Syst. Struct. 17, 729 (2006)

    Article  Google Scholar 

  18. S. Foner, E.J. McNiff, Rev. Sci. Instrum. 39, 171 (1968)

    Article  ADS  Google Scholar 

  19. A.G. Greenhill, Proc. Inst. Mech. Engrs. 1.10, 182 (1883)

    Article  Google Scholar 

  20. L.D. Landau, E.M. Lifshitz, Theory of Elasticity, 3rd ed. (Pergamon Press, Oxford, 1986)

  21. T.R. Powers, Rev. Mod. Phys. 82, 1607 (2010)

    Article  ADS  Google Scholar 

  22. J.B. Keller, Phys. Fluids. 10, 3009 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. M. Lalanne, P. Berthier, J. der Hagopian, Mechanical Vibrations for Engineers (Wiley-Interscience, 1983)

  24. M.C. Lagomarsino, F. Capuania, C.P. Lowe, J. Theor. Biol. 224, 215 (2003)

    Article  Google Scholar 

  25. M. Roper, R. Dreyfus, J. Baudry, M. Fermigier, J. Bibette, H.A. Stone, J. Fluid Mech. 554, 167 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. J. Gray, G.J. Hancock, J. Exp. Biol. 32, 802 (1955)

    Google Scholar 

  27. J. Lighthill, SIAM Rev. 18, 161 (1976)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Oukhaled, G., Cebers, A., Bacri, JC. et al. Twisting and buckling: A new undulation mechanism for artificial swimmers. Eur. Phys. J. E 35, 121 (2012). https://doi.org/10.1140/epje/i2012-12121-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2012-12121-y

Keywords

Navigation