Failure and success of hydrodynamic interaction models

  • H. A. Knudsen
  • J. H. Werth
  • D. E. Wolf
Regular Article


In suspensions with charged particles, electrostatic forces and hydrodynamic interactions are both important to describe the system. We study different models of hydrodynamic interaction for monopolarly charged particles in a non-polar liquid. In this case, there is no screening of the Coulomb repulsion, so the repulsion between all pairs must be taken into account. The particles are expected to drift away from each other, however at a lower rate when hydrodynamic interaction between the particles is taken into account. Existing, frequently used models of hydrodynamic interactions tend to overestimate the slowing down of the charged particles, even to the extent that the particles effectively attract each other. This is demonstrated for some selected particle setups. We find that these anomalies even occur in dilute systems, if they contain sufficiently many particles. We explain why these anomalies can be avoided by an approach, in which the superposition of interactions is done in the friction tensor instead of the mobility tensor.


83.10.Mj Molecular dynamics, Brownian dynamics 82.70.Dd Colloids 83.10.Rs Computer simulation of molecular and particle dynamics 


  1. 1.
    S. McNamara, E.G. Flekkøy, K.J. Måløy, Phys. Rev. E 61, 4054 (2000).Google Scholar
  2. 2.
    J. Harting, A. Komnik, H.J. Herrmann, Lattice-Boltzmann Simulations of Transport Phenomena and Structuring in Suspensions, in Behavior of Granular Media, edited by P. Walzel, R. Grochowski, C.A. Krülle, S.J. Linz, Vol. 9 of Schriftenreihe Mechanische Verfahrenstechnik (Shaker Verlag, Aachen, 2006) p. 3.Google Scholar
  3. 3.
    A. Komnik, J. Harting, H.J. Herrmann, J. Stat. Mech.: Theor. Exp. 12003 (2004).Google Scholar
  4. 4.
    A.J.C. Ladd, R. Verberg, J. Stat. Phys. 104, 1191 (2001).Google Scholar
  5. 5.
    D. Hänel, Molekulare Gasdynamik (Springer, Berlin, 2004).Google Scholar
  6. 6.
    J.F. Brady, G. Bossis, Annu. Rev. Fluid Mech. 20, 111 (1988).Google Scholar
  7. 7.
    B. Cichocki, M.L. Ekiel-Jezewska, E. Wajnryb, J. Chem. Phys. 111, 3265 (1999).Google Scholar
  8. 8.
    B. Cichocki, R.B. Jones, R. Kutteh, E. Wajnryb, J. Chem. Phys. 112, 2548 (2000).Google Scholar
  9. 9.
    G. Bossis, J.F. Brady, J. Chem. Phys. 80, 5141 (1984).Google Scholar
  10. 10.
    D.J. Jeffrey, Y. Onishi, J. Fluid Mech. 139, 262 (1984).Google Scholar
  11. 11.
    M. Linsenbühler, J.H. Werth, S.M. Dammer, H.A. Knudsen, H. Hinrichsen, K.E. Wirth, D.E. Wolf, Powder Technol. 167, 124 (2006).Google Scholar
  12. 12.
    S. Kim, S.J. Karrila, MicrohydrodynamicsGoogle Scholar
  13. 13.
    J.G. Kirkwood, J. Riseman, J. Chem. Phys. 16, 565 (1948).Google Scholar
  14. 14.
    R.E.D. Wames, W.F. Holland, M.C. Shen, J. Chem. Phys. 46, 2782 (1967).Google Scholar
  15. 15.
    I.M. Janosi, T. Tel, D.E. Wolf, J.A.C. Gallas, Phys. Rev. E. 56, 2858 (1997).Google Scholar
  16. 16.
    R.B. Jones, R. Schmitz, Physica A 149, 373 (1988).Google Scholar
  17. 17.
    J. Rotne, S. Prager, J. Chem. Phys. 50, 4831 (1969).Google Scholar
  18. 18.
    E. Guazzelli, L. Oger (Editors), Interaction of Two Suspended Particles, NATO ASI Series (Kluwer Academic Publishers, 1995).Google Scholar
  19. 19.
    P. Mazur, W. van Saarloos, Physica A 115, 21 (1982).Google Scholar

Copyright information

© Springer 2008

Authors and Affiliations

  • H. A. Knudsen
    • 1
  • J. H. Werth
    • 2
  • D. E. Wolf
    • 2
  1. 1.Department of PhysicsUniversity of OsloOsloNorway
  2. 2.Department of Physics, and CeNIDEUniversity of Duisburg-EssenDuisburgGermany

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