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Suction in Darcy and Stokes interfacial flows: Maximum growth rate versus minimum dissipation

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Abstract

Two-dimensional flows with suction or mass loss are investigated within Darcy’s or Stokes’ framework. Examples include a Hele-Shaw cell with a lifted plate or extraction of lipids from a lipid bilayer. An initially circular patch ret-racts due to the suction and might undergo an instability whereby it becomes undulating. The selection of the wavelength of undulations is investigated with the help of an extremum principle, the minimization of the generalized dissipation, from which derive the flow equations.

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References

  • P. Manneville, Dissipative Structures and Weak Turbulence (Academic Press, New York, 1990)

  • P.-G. Saffman, G. Taylor, Proc. Roy. Soc. A 245, 312 (1958)

    Google Scholar 

  • J. Bataille, Rev. Inst. Pet. 23, 1349 (1968)

    Google Scholar 

  • L. Paterson, J. Fluid. Mech. 113, 513 (1981)

    Google Scholar 

  • G.I. Taylor, Proc. of Symposium at General Motors Research Laboratories, Warren Michigan, 1962, edited by R. Davies (Elsevier Publishing Company, New York, 1964)

  • M. Ben Amar, D. Bonn, Physica D 209, 1 (2005)

    Google Scholar 

  • M. Ben Amar, J.-M. Allain, N. Puff, M.I. Angelova, Phys. Rev. Lett. 99, 044503 (2007)

    Google Scholar 

  • M.J. Shelley, F.-R. Tian, K. Wlodarski, Nonlinearity 10, 1471 (1997)

    Google Scholar 

  • A. Lindner, D. Derks, M.J. Shelley, Phys. Fluids 17, 072107 (2005)

    Google Scholar 

  • K. Simons, E. Ikonen, Nature 387, 569 (1997)

    Google Scholar 

  • S. Munro, Cell 115, 377 (2003)

  • N. Puff, A. Lamaziere, M. Seigneuret, G. Trugnan, M.I. Angelova, Chem. Phys. Lip. 133, 195 (2005)

    Google Scholar 

  • P.-G. Saffman, J. Fluid Mech. 73, 593 (1976)

    Google Scholar 

  • Y. Pomeau, J. Phys. Lett. 42, L1 (1981)

  • F. Campelo, J.-M. Allain, M. Ben Amar, Europhys. Lett. 77, 38006 (2007)

  • C.-W. Park, G.M. Homsy, J. Fluid Mech. 139, 291 (1984)

    Google Scholar 

  • L.D. Landau, E.M. Lifshitz, Fluid Mech. Ellipses (1994)

  • D.G. Crowdy, S. Tanveer, J. Nonlinear Sci. 8, 261 (1998)

    Google Scholar 

  • L.J. Cummings, S.D. Howison, J. King, Eur. J. Appl. Math. 10, 635 (1999)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Laboratoire de Physique Statistique, École Normale Supérieure, 24 rue Lhomond, 75231, Paris Cedex 05, France

    M. Ben Amar & A. Boudaoud

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  1. M. Ben Amar
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  2. A. Boudaoud
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Correspondence to M. Ben Amar.

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Ben Amar, M., Boudaoud, A. Suction in Darcy and Stokes interfacial flows: Maximum growth rate versus minimum dissipation. Eur. Phys. J. Spec. Top. 166, 83–88 (2009). https://doi.org/10.1140/epjst/e2009-00883-1

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  • DOI: https://doi.org/10.1140/epjst/e2009-00883-1

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