Skip to main content

Sedimentation and polar order of active bottom-heavy particles

Abstract

Self-propelled particles in an external gravitational field have been shown to display both an increased sedimentation length and polar order even without particle interactions. Here, we investigate self-propelled particles which additionally are bottom-heavy, that is they feel a torque aligning them to swim against the gravitational field. For bottom-heavy particles the gravitational field has the two opposite effects of i) sedimentation and ii) upward alignment of the particles’ swimming direction. We perform a multipole expansion of the one-particle distribution of non-interacting particles with respect to orientation and derive expressions for sedimentation length and mean particle orientation which we check against Brownian Dynamics simulations. For large strength of gravity or small particle speeds and aligning torque, we observe sedimentation with increased sedimentation length compared with passive colloids but also active colloids without bottom-heaviness. Increasing, for example, swimming speed the sedimentation profile is inverted and the particles swim towards the top wall of the enclosing box. We find maximal orientational order at intermediate swimming speeds for both cases of particles with bottom-heaviness and those without. Ordering unsurprisingly is increased for the bottom-heavy particles, but this difference disappears at higher levels of activity and for very high activities ordering goes to zero in both cases.

Graphical abstract

References

  1. 1.

    T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Phys. Rev. Lett. 75, 1226 (1995).

    ADS  Article  Google Scholar 

  2. 2.

    F. Ginelli, F. Peruani, M. Bär, H. Chaté, Phys. Rev. Lett. 104, 184502 (2010).

    ADS  Article  Google Scholar 

  3. 3.

    H.H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R.E. Goldstein, H. Löwen, J.M. Yeomans, Proc. Natl. Acad. Sci. U.S.A. 109, 14308 (2012).

    ADS  Article  Google Scholar 

  4. 4.

    R.A. Simha, S. Ramaswamy, Phys. Rev. Lett. 89, 058101 (2002).

    ADS  Article  Google Scholar 

  5. 5.

    D. Saintillan, M.J. Shelley, Phys. Rev. Lett. 100, 178103 (2008).

    ADS  Article  Google Scholar 

  6. 6.

    A. Baskaran, M.C. Marchetti, Proc. Natl. Acad. Sci. U.S.A. 106, 15567 (2009).

    ADS  Article  Google Scholar 

  7. 7.

    J. Tailleur, M.E. Cates, Phys. Rev. Lett. 100, 218103 (2008).

    ADS  Article  Google Scholar 

  8. 8.

    J. Bialké, T. Speck, H. Löwen, Phys. Rev. Lett. 108, 168301 (2012).

    ADS  Article  Google Scholar 

  9. 9.

    F.D.C. Farrell, M.C. Marchetti, D. Marenduzzo, J. Tailleur, Phys. Rev. Lett. 108, 248101 (2012).

    ADS  Article  Google Scholar 

  10. 10.

    Y. Fily, M.C. Marchetti, Phys. Rev. Lett. 108, 235702 (2012).

    ADS  Article  Google Scholar 

  11. 11.

    M.E. Cates, J. Tailleur, EPL 101, 20010 (2013).

    ADS  Article  Google Scholar 

  12. 12.

    G.S. Redner, M.F. Hagan, A. Baskaran, Phys. Rev. Lett. 110, 055701 (2013).

    ADS  Article  Google Scholar 

  13. 13.

    R. Golestanian, Phys. Rev. Lett. 108, 038303 (2012).

    ADS  Article  Google Scholar 

  14. 14.

    I. Theurkauff, C. Cottin-Bizonne, J. Palacci, C. Ybert, L. Bocquet, Phys. Rev. Lett. 108, 268303 (2012).

    ADS  Article  Google Scholar 

  15. 15.

    J. Tailleur, M.E. Cates, EPL 86, 60002 (2009).

    ADS  Article  Google Scholar 

  16. 16.

    J. Palacci, C. Cottin-Bizonne, C. Ybert, L. Bocquet, Phys. Rev. Lett. 105, 088304 (2010).

    ADS  Article  Google Scholar 

  17. 17.

    M. Enculescu, H. Stark, Phys. Rev. Lett. 107, 058301 (2011).

    ADS  Article  Google Scholar 

  18. 18.

    A. Pototsky, H. Stark, EPL 98, 50004 (2012).

    ADS  Article  Google Scholar 

  19. 19.

    H.C. Berg, Random Walks in Biology (Princeton University Press, 1993).

  20. 20.

    J.R. Howse, R.A.L. Jones, A.J. Ryan, T. Gough, R. Vafabakhsh, R. Golestanian, Phys. Rev. Lett. 99, 048102 (2007).

    ADS  Article  Google Scholar 

  21. 21.

    R. Golestanian, Phys. Rev. Lett. 102, 188305 (2009).

    ADS  Article  Google Scholar 

  22. 22.

    P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, L. Schimansky-Geier, Eur. Phys. J. ST 202, 1 (2012).

    Article  Google Scholar 

  23. 23.

    S. Childress, M. Levandowsky, E.A. Spiegel, J. Fluid Mech. 69, 591 (1975).

    ADS  Article  MATH  Google Scholar 

  24. 24.

    T.J. Pedley, J.O. Kessler, J. Fluid Mech. 212, 155 (1990).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  25. 25.

    M.A. Bees, N.A. Hill, Phys. Fluids 10, 1864 (1998).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  26. 26.

    K. Drescher, K.C. Leptos, I. Tuval, T. Ishikawa, T.J. Pedley, R.E. Goldstein, Phys. Rev. Lett. 102, 168101 (2009).

    ADS  Article  Google Scholar 

  27. 27.

    F. Ebert, P. Dillmann, G. Maret, P. Keim, Rev. Sci. Instrum. 80, 083902 (2009).

    ADS  Article  Google Scholar 

  28. 28.

    J. Yan, M. Bloom, S.C. Bae, E. Luijten, S. Granick, Nature 491, 578 (2012).

    ADS  Article  Google Scholar 

  29. 29.

    C.R. Williams, M.A. Bees, J. Exp. Biol. 214, 2398 (2011).

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Katrin Wolff.

Additional information

This article is published with open access at Springerlink.com

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Wolff, K., Hahn, A.M. & Stark, H. Sedimentation and polar order of active bottom-heavy particles. Eur. Phys. J. E 36, 43 (2013). https://doi.org/10.1140/epje/i2013-13043-x

Download citation

Keywords

  • Soft Matter: Colloids and Nanoparticles