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The European Physical Journal Special Topics

, Volume 223, Issue 9, pp 1895–1906 | Cite as

Competition between anisotropic viscous fingers

  • M. Pecelerowicz
  • A. Budek
  • P. SzymczakEmail author
Regular Article
Part of the following topical collections:
  1. Soft Matter in Confinement: Systems from Biology to Physics

Abstract

We consider viscous fingers created by injection of low viscosity fluid into the network of capillaries initially filled with a more viscous fluid (motor oil). Due to the anisotropy of the system and its geometry, such a setup promotes the formation of long-and-thin fingers which then grow and compete for the available flow, interacting through the pressure field. The interaction between the fingers is analyzed using the branched growth formalism of Halsey and Leibig (Phys. Rev. A 46, 7723, 1992) using a number of simple, analytically tractable models. It is shown that as soon as the fingers are allowed to capture the flow from one another, the fixed point appears in the phase space, corresponding to the asymptotic state in which the growth of one of the fingers in hindered by the other. The properties of phase space flows in such systems are shown to be remarkably insensitive to the details of the dynamics.

Keywords

Phase Space European Physical Journal Special Topic Viscosity Ratio Upstream Part Downstream Part 
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.

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References

  1. 1.
    R.A. Wooding, J. Fluid. Mech. 39, 477 (1969)CrossRefADSGoogle Scholar
  2. 2.
    G. Homsy, Annu. Rev. Fluid Mech. 19, 271 (1987)CrossRefADSGoogle Scholar
  3. 3.
    G. Menon, J. Non-Newton. Fluid Mech. 152, 113 (2008)CrossRefzbMATHGoogle Scholar
  4. 4.
    R. Booth, J. Fluid Mech. 655, 527 (2010)CrossRefADSMathSciNetzbMATHGoogle Scholar
  5. 5.
    G. Rousseaux, M. Martin, A. De Wit, J. Chromatogr. A 1218, 8353 (2011)CrossRefGoogle Scholar
  6. 6.
    A. Budek, P. Garstecki, A. Samborski, P. Szymczak, J. Fluid. Mech. (submitted) (2014)Google Scholar
  7. 7.
    J.D. Chen, D. Wilkinson, Phys. Rev. Lett. 55, 1892 (1985)CrossRefADSGoogle Scholar
  8. 8.
    E. Ben-Jacob, R. Godbey, N. Goldenfeld, J. Koplik, H. Levine, T. Mueller, L. Sander, Phys. Rev. Lett. 55, 1315 (1985)CrossRefADSGoogle Scholar
  9. 9.
    J.D. Chen, Exp. Fluids 5, 363 (1987)CrossRefGoogle Scholar
  10. 10.
    V. Horváth, T. Vicsek, J. Kertész, Phys. Rev. A 35, 2353 (1987)CrossRefADSGoogle Scholar
  11. 11.
    P. Kelemen, J. Whitehead, E. Aharonov, K. Jordahl, J. Geophys. Res. 100, B475 (1995)CrossRefADSGoogle Scholar
  12. 12.
    P. Szymczak, A.J.C. Ladd, J. Geophys. Res. 114, B06203 (2009)ADSGoogle Scholar
  13. 13.
    S. Curtis, J. Maher, Phys. Rev. Lett. 63, 2729 (1989)CrossRefADSGoogle Scholar
  14. 14.
    C.N. Baroud, S. Tsikata, M. Heil, J. Fluid Mech. 546, 285 (2006)CrossRefADSzbMATHGoogle Scholar
  15. 15.
    Y. Couder, F. Argoul, A. Arnéodo, J. Maurer, M. Rabaud, Phys. Rev. A 42, 3499 (1990)CrossRefADSGoogle Scholar
  16. 16.
    Y. Couder, J. Maurer, R. González-Cinca, A. Hernández-Machado, Phys. Rev. E 71, 31602 (2005)CrossRefADSGoogle Scholar
  17. 17.
    T.C. Halsey, M. Leibig, Phys. Rev. A 46, 7723 (1992)CrossRefADSGoogle Scholar
  18. 18.
    T.C. Halsey, Phys. Rev. Lett. 46, 1228 (1994)CrossRefADSGoogle Scholar
  19. 19.
    Y. Sawada, A. Dougherty, J. Gollub, Phys. Rev. Lett. 56, 1260 (1986)CrossRefADSGoogle Scholar
  20. 20.
    P. Szymczak, A.J.C. Ladd, Geophys. Res. Lett. 33, L05401 (2006)CrossRefADSGoogle Scholar
  21. 21.
    J. Krug, K. Kessner, P. Meakin, F. Family, Europhys. Lett. 24, 527 (1993)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Institute of Theoretical Physics, Faculty of PhysicsUniversity of WarsawWarsawPoland

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