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Three-sphere low-Reynolds-number swimmer with a passive elastic arm

  • Alessandro Montino
  • Antonio DeSimoneEmail author
Open Access
Regular Article

Abstract.

One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer’s geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers.

Graphical abstract

Keywords

Living systems: Biomimetic Systems 

References

  1. 1.
    E.M. Purcell, Am. J. Phys. 45, 3 (1977)ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    E. Lauga, T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009)MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    M. Arroyo, L. Heltai, D. Millán, A. DeSimone, Proc. Natl. Acad. Sci. U.S.A. 109, 17874 (2012)ADSCrossRefGoogle Scholar
  4. 4.
    M. Arroyo, A. DeSimone, J. Mech. Phys. Solids 62, 99 (2014)MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    A. Najafi, R. Golestanian, Phys. Rev. E 69, 062901 (2004)ADSCrossRefGoogle Scholar
  6. 6.
    L.E. Becker, S.A. Koehler, H.A. Stone, J. Fluid Mech. 490, 15 (2003)MathSciNetADSCrossRefzbMATHGoogle Scholar
  7. 7.
    J.E. Avron, O. Kenneth, D.H. Oaknin, New J. Phys. 7, 234 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    J.E. Avron, O. Gat, O. Kenneth, Phys. Rev. Lett. 93, 186001 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    D. Tam, A.E. Hosoi, Phys. Rev. Lett. 98, 068105 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    F. Alouges, A. DeSimone, L. Giraldi, M. Zoppello, Int. J. Non-Linear Mech. 56, 132 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    F. Alouges, A. DeSimone, A. Lefebvre, J. Nonlinear Sci. 18, 277 (2008)MathSciNetADSCrossRefzbMATHGoogle Scholar
  12. 12.
    F. Alouges, A. DeSimone, A. Lefebvre, Eur. Phys. J. E 28, 279 (2009)CrossRefGoogle Scholar
  13. 13.
    F. Alouges, A. DeSimone, L. Heltai, Math. Models Meth. Appl. Sci. 21, 361 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    F. Alouges, A. DeSimone, L. Heltai, A. Lefebvre, B. Merlet, Discrete Contin. Dyn. Syst. Ser. B 18, 1189 (2013)MathSciNetCrossRefGoogle Scholar
  15. 15.
    A. DeSimone, F. Alouges, L. Heltai, A. Lefebvre, Natural Locomotion in Fluids and on Surfaces: Swimming, Flying and Sliding, chapt. ``Computing optimal strokes for low Reynolds number swimmers” (Springer, 2012) pp. 177--184Google Scholar
  16. 16.
    E. Passov, Y. Or, Eur. Phys. J. E 35, 78 (2012)CrossRefGoogle Scholar
  17. 17.
    R. Golestanian, A. Ajdari, Phys. Rev. E 77, 036308 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    M. Farkas, Periodic Motions, Applied Mathematical Sciences (Springer, New York, 1994)Google Scholar
  19. 19.
    S. Childress, Mechanics of Swimming and Flying (Cambridge University Press, 1981)Google Scholar
  20. 20.
    H.A. Stone, A.D.T. Samuel, Phys. Rev. Lett. 77, 4102 (1996)ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.GSSI - Gran Sasso Science InstituteL’AquilaItaly
  2. 2.SISSA - International School for Advanced StudiesTriesteItaly

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