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Dynamics of a circular array of liquid columns

Dynamics of an array of liquid columns

  • Physics of Fluids
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Abstract.

We report on an experimental study of an array of liquid columns, hanging below an overflowing circular dish fed at a constant flow-rate. This one-dimensional pattern exhibits spatio-temporal chaos as well as a host of ordered dynamical regimes, depending on flow-rate, initial positions, number of columns, and liquid properties. In this paper, we present stability diagrams obtained with liquids of different properties and an extensive quantitative study of the ordered, predictable dynamical states. Some destabilization mechanisms of these regimes are also presented.

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References

  • M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993)

    Article  ADS  Google Scholar 

  • M.I. Rabinovich, A.B. Ezersky, P.D. Weidman, The dynamics of patterns (World Scientific Publishing, 1998)

  • A. Prigent et al., Phys. Rev. Lett. 89 014501 (2002)

  • D. Barkley, L.S. Tukerman, Phys. Rev. Lett. 94, 014502 (2005)

    Article  ADS  Google Scholar 

  • R. Kerswell, Nonlinearity 18, R17R44 (2005)

  • M. Rabaud, S. Michalland, Y. Couder, Phys. Rev. Lett. 64, 184 (1990)

    Article  ADS  Google Scholar 

  • S. Michalland, M. Rabaud, Physica D 61, 197 (1992)

    Article  MATH  ADS  Google Scholar 

  • H. Cummins, L. Fourtune, M. Rabaud, Phys. Rev. E 47, 1727 (1993)

    Article  ADS  Google Scholar 

  • L. Fourtune, W.J. Rappel, M. Rabaud, Phys. Rev. E 49, R3576 (1994)

  • L. Pan, J.R. de Bruyn, Phys. Rev. Lett. 70, 1791 (1993)

    Article  ADS  Google Scholar 

  • L. Pan, J.R. de Bruyn, Phys. Rev. E 49, 483 (1994)

    Article  ADS  Google Scholar 

  • A.J. Simon, J. Bechhoefer, A. Libchaber, Phys. Rev. Lett. 61, 2574 (1988)

    Article  ADS  Google Scholar 

  • J.-M. Flesselles, A.J. Simon, A.J. Libchaber, Adv. Phys. 40, 1 (1991)

    Article  ADS  Google Scholar 

  • G. Faivre, J. Mergy, Phys. Rev. A 46 963 (1992)

    Google Scholar 

  • M. Ginibre, S. Akamatsu, G. Faivre, Phys. Rev. E 56 780 (1997)

    Google Scholar 

  • P. Rupp, R. Richter, I. Rehberg, Phys. Rev. E 67, 036209 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  • J. Burguete, D. Maza, H.L. Mancini, Physica D 174, 56 (2003)

    Article  MATH  ADS  Google Scholar 

  • Y. Kuramoto, Chemical oscillations, waves and turbulence (Springer-Verlag, 1978)

  • A. Pumir, P. Manneville, Y. Pomeau, J. Fluid Mech. 135 27 (1983)

    Google Scholar 

  • P. Manneville, The Kuramoto-Sivashinsky equation: a progress report, in Propagation in systems far from equilibrium (Springer Verlag, 1991)

  • C. Misbah, A. Valance, Phys. Rev. E 49, 166 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  • C. Counillon, L. Daudet, T. Podgorski, M.C. Jullien, S. Akamatsu, L. Limat, Europhys. Lett. 40, 37 (1997)

    Article  ADS  Google Scholar 

  • C. Counillon, L. Daudet, T. Podgorski, L. Limat, Phys. Rev. Lett. 80, 2117 (1998)

    Article  ADS  Google Scholar 

  • P. Brunet, J.-M. Flesselles, L. Limat, Europhys. Lett. 56, 221 (2001)

    Article  ADS  Google Scholar 

  • P. Brunet, J.-M. Flesselles, L. Limat, Eur. Phys. J. B 35, 525 (2003)

    Article  ADS  Google Scholar 

  • P. Brunet, L. Limat, Phys. Rev. E 70, 046207 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  • Lord Rayleigh, Scientific papers (Cambridge University Press, Oxford, 1900), Vol. II

  • G.I. Taylor, Proc. R. Soc. London Ser. A 201, 192 (1950)

    Article  MATH  ADS  Google Scholar 

  • M. Fermigier, L. Limat, J.E. Wesfreid, P. Boudinet, C. Quillet, J. Fluid Mech. 236, 349 (1992)

    Article  MATH  ADS  Google Scholar 

  • G.M. Carlomagno, in Proceedings of the Second AIMETA Congress (1974), p. 253

  • W.G. Pritchard, J. Fluid Mech. 165, 433 (1986)

    Article  Google Scholar 

  • F. Giorgiutti, A. Bleton, L. Limat, J.E. Wesfreid, Phys. Rev. Lett. 74, 538 (1995)

    Article  ADS  Google Scholar 

  • F. Giorgiutti, L. Limat, Physica D 103, 590 (1997)

    Article  ADS  Google Scholar 

  • F. Giorgiutti, L. Limat, J.E. Wesfreid, Phys. Rev. E 57, 2843 (1998)

    Article  ADS  Google Scholar 

  • P. Coullet, G. Iooss, Phys. Rev. Lett. 64, 866 (1990)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • R.E. Goldstein, G.H. Gunaratne, L. Gil, P. Coullet, Phys. Rev. A 43, 6700 (1991)

    Article  ADS  Google Scholar 

  • S. Fauve, S. Douady, O. Thual, J. Phys. II France 1, 311 (1991)

    Article  Google Scholar 

  • B. Caroli, C. Caroli, S. Fauve, J. Phys. I France 2, 281 (1992)

    Article  Google Scholar 

  • H. Riecke, H.G. Paap, Phys. Rev. A 45, 8605 (1992)

    Article  ADS  Google Scholar 

  • L. Gil, Europhys. Lett. 48, 156 (1999)

    Article  ADS  Google Scholar 

  • L. Gil, Physica D 147, 300 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • F. Daviaud, M. Bonetti, M. Dubois, Phys. Rev. A 42, 3388 (1990)

    Article  ADS  Google Scholar 

  • I. Mutabazi, C.D. Andereck, Phys. Rev. Lett. 70, 1429 (1993)

    Article  ADS  Google Scholar 

  • P. Brunet, G. Gauthier, L. Limat, D. Vallet, Exp. Fluids 37, 645 (2004)

    Article  Google Scholar 

  • C. Pirat, C. Mathis, P. Maissa, L. Gil, Phys. Rev. Lett. 92, 104501 (2004)

    Article  ADS  Google Scholar 

  • C. Pirat, A. Naso, J.-L. Meunier, P. Maissa, C. Mathis, Phys. Rev. Lett. 94 134502 (2005)

  • I. Aranson, L. Kramer, Rev. Mod. Phys., 74 99 (2002)

    Google Scholar 

  • P. Brunet, Ph.D. Thesis, Paris 6 University (2002), available online at: http://tel.ccsd.cnrs.fr/documents/archives0/00/00/22/42/index_fr.html

  • E.M. Nicola, M. Or-Guil, W. Wolf, M. Bar, Phys. Rev. E 65 055101(R) (2002)

  • M. Howard, M. van Hecke, Phys. Rev. E 68 026213 (2003)

    Google Scholar 

  • R. Mikkelsen, M. van Hecke, T. Bohr, Phys. Rev. E 67 046207 (2003)

  • P. Brunet, C. Clanet, L. Limat, Phys. Fluids 16 2688 (2004)

  • V.G. Levich, Physicochemical Hydrodynamics (Prentice Hall, 1962)

  • B.A. Malomed, M.I. Tribelsky, Physica D 14 67 (1984)

  • M.R.E. Proctor, C.A. Jones, J. Fluid Mech. 188 301 (1988)

    Google Scholar 

  • H. Levine, W.J. Rappel, H. Riecke, Phys. Rev. A 43 1122 (1991)

    Google Scholar 

  • F. Giorgiutti, Ph.D. thesis, Paris 6 University (1995)

  • P. Brunet, Phys. Rev. E (2006), submitted

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Authors and Affiliations

  1. Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH) UMR 7636 of CNRS, ESPCI, 10 rue Vauquelin, 75005, Paris, France

    P. Brunet & L. Limat

  2. Saint-Gobain Recherche, 39 quai Lucien Lefranc., 93303, Aubervilliers Cedex, France

    P. Brunet & J.-M. Flesselles

  3. Laboratoire Matière et Systèmes Complexes, UMR of CNRS, University Paris 7, 2 Place Jussieu, 75005, Paris, France

    L. Limat

Authors
  1. P. Brunet
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  2. J.-M. Flesselles
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  3. L. Limat
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Correspondence to P. Brunet.

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Brunet, P., Flesselles, JM. & Limat, L. Dynamics of a circular array of liquid columns. Eur. Phys. J. B 55, 297–322 (2007). https://doi.org/10.1140/epjb/e2007-00057-y

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  • DOI: https://doi.org/10.1140/epjb/e2007-00057-y

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