The European Physical Journal Special Topics

, Volume 187, Issue 1, pp 135–144 | Cite as

Low Reynolds number hydrodynamics of asymmetric, oscillating dumbbell pairs



Active dumbbell suspensions constitute one of the simplest model systems for collective swimming at low Reynolds number. Generalizing recent work, we derive and analyze stroke-averaged equations of motion that capture the effective hydrodynamic far-field interaction between two oscillating, asymmetric dumbbells in three space dimensions. Time-averaged equations of motion, as those presented in this paper, not only yield a considerable speed-up in numerical simulations, but may also serve as a starting point when deriving continuum equations for the macroscopic dynamics of multi-swimmer suspensions. The specific model discussed here appears to be particularly useful in this context, since it allows one to investigate how the collective macroscopic behavior is affected by changes in the microscopic symmetry of individual swimmers.


European Physical Journal Special Topic Hydrodynamic Interaction Collective Motion Dumbbell Model Stroke Amplitude 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Toner, Y. Tu, S. Ramaswamy, Ann. Phys. 318, 170 (2005)MATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    W. Ebeling, L. Schimansky-Geier, Eur. Phys. J. Spec. Topics 157, 17 (2008)CrossRefADSGoogle Scholar
  3. 3.
    P.T. Underhill, J.P. Hernandez-Ortiz, M.D. Graham, Phys. Rev. Lett. 100, 248101 (2008)CrossRefADSGoogle Scholar
  4. 4.
    J. Strefler, W. Ebeling, E. Gudowska-Nowak, L. Schimansky-Geier, Eur. Phys. J. B 72, 597 (2009)MATHCrossRefADSGoogle Scholar
  5. 5.
    P. Romanczuk, I.D. Couzin, L. Schimansky-Geier, Phys. Rev. Lett. 102, 010602 (2009)CrossRefADSGoogle Scholar
  6. 6.
    A. Baskaran, M.C. Marchetti, Proc. Nat. Acad. Sci. USA 106, 15567 (2009)CrossRefADSGoogle Scholar
  7. 7.
    M.F. Copeland, D.B. Weibel, Soft Matter 5, 1174 (2009)CrossRefGoogle Scholar
  8. 8.
    A. Sokolov, I.S. Aranson, J.O. Kessler, R.E. Goldstein, Phys. Rev. Lett. 98, 158102 (2007)CrossRefADSGoogle Scholar
  9. 9.
    S. Ramaswamy, Phys. Rev. Lett. 89, 058101 (2002)CrossRefADSGoogle Scholar
  10. 10.
    A. Baskaran, M.C. Marchetti, Phys. Rev. E 77 (2008)Google Scholar
  11. 11.
    E. Lauga, D. Bartolo, Phys. Rev. E 78, 030901 (2008)CrossRefADSGoogle Scholar
  12. 12.
    G.P. Alexander, J.M. Yeomans, Europhys. Lett. 83, 34006 (2008)CrossRefADSGoogle Scholar
  13. 13.
    J. Dunkel, I.M. Zaid, Phys. Rev. E 80, 021903 (2009)CrossRefADSGoogle Scholar
  14. 14.
    V.B. Putz, J. Dunkel, J.M. Yeomans, Chem. Phys. (2010) doi: 10.1016/j.chemphys.2010.04.025Google Scholar
  15. 15.
    J. Dunkel, V.B. Putz, I.M. Zaid, J.M. Yeomans, Soft Matter 6, 4268 (2010)CrossRefGoogle Scholar
  16. 16.
    E.M. Purcell, Am. J. Phys. 45, 3 (1977)CrossRefADSGoogle Scholar
  17. 17.
    A. Shapere, F. Wilczek, Phys. Rev. Lett. 58, 2051 (1987)CrossRefADSGoogle Scholar
  18. 18.
    M. Polin, I. Tuval, K. Drescher, J.P. Gollub, R.E. Goldstein, Science 325, 487 (2009)CrossRefADSGoogle Scholar
  19. 19.
    J. Rotne, S. Prager, J. Chem. Phys. 50, 4831 (1969)CrossRefADSGoogle Scholar
  20. 20.
    H. Yamakawa, J. Chem. Phys. 53, 436 (1970)CrossRefADSGoogle Scholar
  21. 21.
    C.W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik (Akademischer Verlag, Leipzig, 1927)Google Scholar
  22. 22.
    J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics, International Series in the Physical and Chemical Engineering Sciences(Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965)Google Scholar
  23. 23.
    P. Mazur, Physica 110A, 128 (1982)MathSciNetADSGoogle Scholar
  24. 24.
    M. Leoni, J. Kotar, B. Bassetti, P. Cicuta, M.C. Lagomarsino, Soft Matter 5, 472 (2009)CrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2010

Authors and Affiliations

  1. 1.Rudolf Peierls Centre for Theoretical PhysicsUniversity of OxfordOxford, OX1 3NPUK

Personalised recommendations