Non-normal tracer diffusion from stirring by swimming microorganisms

  • B. Eckhardt
  • S. ZammertEmail author
Regular Article
Part of the following topical collections:
  1. Active Matter


The experimentally observed non-Gaussian form of passive tracer distributions in media stirred by active swimmers (Leptos et al., Phys. Rev. Lett. 103, 198103 (2009)) are analyzed in terms of continuous time random walks. The walks are characterized by a trapping time distribution ψ(τ) with long time behaviour ψ(τ) ∝ τ −1−α and a step size distribution p(Δx) ∝ (Δx)−2−β . The experimentally observed behaviour that 〈x 2〉 ∝ t is obtained for a one-parameter family of exponents with β = 2α. However, the distribution function for this case is non-Gaussian and shows exponential tails. The shape of the distributions agrees rather well with the experimental observations from Leptos et al. and allows for the determination of the exponents.


Regular Article - Topical issue: Active Matter 


  1. 1.
    X.-L. Wu, A. Libchaber, Phys. Rev. Lett. 84, 3017 (2000).ADSCrossRefGoogle Scholar
  2. 2.
    C. Valeriani, M. Li, J. Novosel, J. Arlt, D. Marenduzzo, Soft Matter 7, 5228 (2011).ADSCrossRefGoogle Scholar
  3. 3.
    K.C. Leptos, J.S. Guasto, J.P. Gollub, A.I. Pesci, R.E. Goldstein, Phys. Rev. Lett. 103, 198103 (2009).ADSCrossRefGoogle Scholar
  4. 4.
    R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000).MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. 5.
    D. Brockmann, Eur. Phys. J. ST 157, 173 (2008).CrossRefGoogle Scholar
  6. 6.
    A. Visser, Marine Ecol. Progr. Ser. 222, 1 (2001).CrossRefGoogle Scholar
  7. 7.
    E. Lauga, T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009).MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    J.S. Guasto, R. Rusconi, R. Stocker, Annu. Rev. Fluid Mech. 44, 373 (2012).MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    H. Jiang, T.R. Osborn, C. Meneveau, J. Plankton Res. 24, 167 (2002).CrossRefGoogle Scholar
  10. 10.
    H. Jiang, C. Meneveau, T.R. Osborn, J. Plankton Res. 24, 191 (2002).CrossRefGoogle Scholar
  11. 11.
    E. Malkiel, J. Sheng, J. Katz, J.R. Strickler, J. Exp. Biol. 206, 3657 (2003).CrossRefGoogle Scholar
  12. 12.
    K. Drescher, R.E. Goldstein, N. Michel, M. Polin, I. Tuval, Phys. Rev. Lett. 105, 168101 (2010).ADSCrossRefGoogle Scholar
  13. 13.
    K. Drescher, J. Dunkel, L.H. Cisneros, S. Ganguly, R.E. Goldstein, Proc. Natl. Acad. Sci. U.S.A. 108, 10940 (2011).CrossRefGoogle Scholar
  14. 14.
    P.T. Underhill, J.P. Hernandez-Ortiz, M.D. Graham, Phys. Rev. Lett. 100, 248101 (2008).ADSCrossRefGoogle Scholar
  15. 15.
    H.C. Berg, Random Walks in Biology (Princeton University Press, 1993).Google Scholar
  16. 16.
    M. Polin, I. Tuval, K. Drescher, J.P. Gollub, R.E. Goldstein, Science 325, 487 (2009).ADSCrossRefGoogle Scholar
  17. 17.
    I.M. Zaid, J. Dunkel, J.M. Yeomans, J. R. Soc. Interface 8, 1314 (2011).CrossRefGoogle Scholar
  18. 18.
    Z. Lin, J.-L. Thiffeault, S. Childress, J. Fluid Mech. 669, 167 (2011).MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Fachbereich Physik and LOEWE Zentrum Synthetische MikrobiologiePhilipps-Universität MarburgMarburgGermany

Personalised recommendations