Advertisement

A circle swimmer at low Reynolds number

  • R. Ledesma-AguilarEmail author
  • H. Löwen
  • J. M. Yeomans
Regular Article
Part of the following topical collections:
  1. Active Matter

Abstract

Swimming in circles occurs in a variety of situations at low Reynolds number. Here we propose a simple model for a swimmer that undergoes circular motion, generalising the model of a linear swimmer proposed by Najafi and Golestanian (Phys. Rev. E 69, 062901 (2004)). Our model consists of three solid spheres arranged in a triangular configuration, joined by two links of time-dependent length. For small strokes, we discuss the motion of the swimmer as a function of the separation angle between its links. We find that swimmers describe either clockwise or anticlockwise circular motion depending on the tilting angle in a non-trivial manner. The symmetry of the swimmer leads to a quadrupolar decay of the far flow field. We discuss the potential extensions and experimental realisation of our model.

Keywords

Topical contribution 

References

  1. 1.
    J. Toner, Y.H. Tu, S. Ramaswamy, Ann. Phys. 318, 170 (2005).MathSciNetADSCrossRefzbMATHGoogle Scholar
  2. 2.
    P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009).ADSCrossRefGoogle Scholar
  3. 3.
    M.E. Cates, Rep. Prog. Phys. 75, 042601 (2012).ADSCrossRefGoogle Scholar
  4. 4.
    P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, L. Schimansky-Geier, Eur. Phys. J. ST 202, 1 (2012).CrossRefGoogle Scholar
  5. 5.
    A. Najafi, R. Golestanian, Phys. Rev. E 69, 062901 (2004).ADSCrossRefGoogle Scholar
  6. 6.
    J.E. Avron et al., New J. Phys. 7, 234 (2005).ADSCrossRefGoogle Scholar
  7. 7.
    R. Dreyfus, J. Baudry, H.A. Stone, Eur. Phys. J. B 47, 161 (2005).ADSCrossRefGoogle Scholar
  8. 8.
    D.J. Earl, C.M. Pooley, J.F. Ryder, I. Bredberg, J.M. Yeomans, J. Chem. Phys. 126, 064703 (2007).ADSCrossRefGoogle Scholar
  9. 9.
    R. Golestanian, A. Ajdari, Phys. Rev. E 77, 036308 (2008).ADSCrossRefGoogle Scholar
  10. 10.
    R. Golestanian, Eur. Phys. J. E 25, 1 (2008).CrossRefGoogle Scholar
  11. 11.
    G.P. Alexander, J.M. Yeomans, Europhys. Lett. 83, 34006 (2008).ADSCrossRefGoogle Scholar
  12. 12.
    E. Lauga, D. Bartolo, Phys. Rev. E 78, 030901 (2008).ADSCrossRefGoogle Scholar
  13. 13.
    A.M. Leshansky et al., New J. Phys. 9, 145 (2009).CrossRefGoogle Scholar
  14. 14.
    G.J. Elfring, E. Lauga, Phys. Rev. Lett. 103, 088101 (2009).ADSCrossRefGoogle Scholar
  15. 15.
    H.C. Berg, L. Turner, Biophys. J. 58, 919 (1990).ADSCrossRefGoogle Scholar
  16. 16.
    W.R. DiLuzio, L. Turner, M. Mayer, P. Garstecki, D.B. Weibel, H.C. Berg, G.M. Whitesides, Nature 435, 1271 (2005).ADSCrossRefGoogle Scholar
  17. 17.
    E. Lauga, W.R. DiLuzio, G.M. Whitesides, H.A. Stone, Biophys. J. 90, 400 (2006).ADSCrossRefGoogle Scholar
  18. 18.
    J. Hill, O. Kalkanci, J.L. McMurry, H. Koser, Phys. Rev. Lett. 98, 068101 (2007).ADSCrossRefGoogle Scholar
  19. 19.
    V.B. Shenoy, D.T. Tambe, A. Prasad, J.A. Theriot, Proc. Natl. Acad. Sci. U.S.A. 104, 8229 (2007).ADSCrossRefGoogle Scholar
  20. 20.
    S. Schmidt, J. van der Gucht, P.M. Biesheuvel, R. Weinkamer, E. Helfer, A. Fery, Eur. Biophys. J. 37, 1361 (2008).CrossRefGoogle Scholar
  21. 21.
    I.H. Riedel, K. Kruse, J. Howard, Science 309, 300 (2005).ADSCrossRefGoogle Scholar
  22. 22.
    D.M. Woolley, Reproduction 126, 259 (2003).CrossRefGoogle Scholar
  23. 23.
    B.M. Friedrich, F. Jülicher, New J. Phys. 10, 123025 (2008).ADSCrossRefGoogle Scholar
  24. 24.
    S. Nakata, Y. Iguchi, S. Ose, M. Kuboyama, T. Ishii, K. Yoshikawa, Langmuir 13, 4454 (1997).CrossRefGoogle Scholar
  25. 25.
    G. Volpe, I. Buttinoni, D. Vogt, H.J. Kümmerer, C. Bechinger, Soft Matter 7, 8810 (2011).ADSCrossRefGoogle Scholar
  26. 26.
    B. ten Hagen, Bachelor thesis, University of Düsseldorf (2011).Google Scholar
  27. 27.
    H.C. Crenshaw, Amer. Zool. 36, 608 (1996).Google Scholar
  28. 28.
    E.M. Purcell, Am. J. Phys. 45, 3 (1977).ADSCrossRefGoogle Scholar
  29. 29.
    J. Dunstan, G. Mino, E. Clement, R. Soto, Phys. Fluids 24, 011901 (2012).ADSCrossRefGoogle Scholar
  30. 30.
    H. Shum, E.A. Gaffney, D.J. Smith, Proc. R. Soc. London, Ser. A 466, 1725 (2010).MathSciNetADSCrossRefzbMATHGoogle Scholar
  31. 31.
    M. Leoni, T.B. Liverpool, EPL 92, 64004 (2010).ADSCrossRefGoogle Scholar
  32. 32.
    Y. Fily, A. Baskaran, M.C. Marchetti, Soft Matter 8, 3002 (2012).ADSCrossRefGoogle Scholar
  33. 33.
    S. van Teeffelen, H. Löwen, Phys. Rev. E 78, 020101 (2008).CrossRefGoogle Scholar
  34. 34.
    S. van Teeffelen, U. Zimmermann, H. Löwen, Soft Matter 5, 4510 (2009).ADSCrossRefGoogle Scholar
  35. 35.
    B. ten Hagen, S. van Teeffelen, H. Löwen, J. Phys.: Condens. Matter 23, 194119 (2011).ADSCrossRefGoogle Scholar
  36. 36.
    C.M. Pooley, G.P. Alexander, J.M. Yeomans, Phys. Rev. Lett. 99, 228103 (2007).ADSCrossRefGoogle Scholar
  37. 37.
    G.P. Alexander, C.M. Pooley, J.M. Yeomans, Phys. Rev. E 78, 045302 (2008).ADSCrossRefGoogle Scholar
  38. 38.
    B. ten Hagen, R. Wittkowski, H. Löwen, Phys. Rev. E 84, 031105 (2011).ADSCrossRefGoogle Scholar
  39. 39.
    J. Dunkel, V.B. Putz, I.M. Zaid, J.M. Yeomans, Soft Matter 6, 4268 (2010).ADSCrossRefGoogle Scholar
  40. 40.
    V.B. Putz, J.M. Yeomans, J. Stat. Phys. 137, 1001 (2009).MathSciNetADSCrossRefzbMATHGoogle Scholar
  41. 41.
    G.J. Elfring, E. Lauga, Phys. Fluids 23, 011902 (2011).ADSCrossRefGoogle Scholar
  42. 42.
    R. Golestanian, J.M. Yeomans, N. Uchida, Soft Matter 7, 3074 (2011).ADSCrossRefGoogle Scholar
  43. 43.
    F. Alouges, A. Desimone, L. Heltai, A. Lefebvre-Lepot, B. Merlet, arxiv:1007.4920v2.Google Scholar
  44. 44.
    H. Löwen, J. Phys.: Condens. Matter 13, R415 (2001).CrossRefGoogle Scholar
  45. 45.
    M. Leoni, J. Kotar, B. Bassetti, P. Cicuta, M. Cosentino Lagomarsino, Soft Matter 5, 472 (2008).ADSCrossRefGoogle Scholar
  46. 46.
    R. Wittkowski, H. Löwen, Phys. Rev. E 85, 021406 (2012).ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.The Rudolf Peierls Centre for Theoretical PhysicsUniversity of OxfordOxfordUK
  2. 2.Institut für Theoretische Physik II: Weiche MaterieHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

Personalised recommendations