Influence of density stratification on stability of a two-layer binary-fluid system with a diffuse interface

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A system of two layers separated by a diffuse interface which is created due to a phase separation in a binary liquid in the gravity field, is considered. The influence of the density stratification and the gravity on the stabilization of the solution is studied. The stability of two-layer base solutions with respect to long-wave disturbances in the framework of the linear stability analysis is investigated in the case of small density ratio and large Galileo number. It is found that the action of gravity can stabilize the equilibrium state.


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  1. 1.
    J.W. Cahn, J.E. Hilliard, J. Chem. Phys. 28, 258 (1958)ADSCrossRefGoogle Scholar
  2. 2.
    J.D. Van der Waals, J. Stat. Phys. 20, 197 (1979)MathSciNetADSCrossRefMATHGoogle Scholar
  3. 3.
    P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)ADSCrossRefGoogle Scholar
  4. 4.
    J. Lowengrub, L. Truskinovsky, Proc. R. Soc. London 454, 2617 (1998)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    D.M. Anderson, G.B. McFadden, A.A. Wheeler, Annu. Rev. Fluid Mech. 30, 139 (1998)MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    H. Abels, E. Feireisl, Preprint, MPI MIS Leipzig 74 (2007)Google Scholar
  7. 7.
    V.V. Khatavkar, P.D. Anderson, P.C. Duineveld, H.E.H. Meijer, J. Fluid Mech. 581, 97 (2007)MathSciNetADSCrossRefMATHGoogle Scholar
  8. 8.
    U. Thiele, S. Madruga, L. Frastia, Phys. Fluids 19, 122106 (2007)ADSCrossRefGoogle Scholar
  9. 9.
    O.A. Frolovskaya, A.A. Nepomnyashchy, A. Oron, A.A. Golovin, Phys. Fluids 20, 112105 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    S. Madruga, U. Thiele, Phys. Fluids 21, 062104 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    M. Verschueren, Ph.D. thesis Eindhoven University of Technology, 1999, p. 81Google Scholar
  12. 12.
    A. Oron, S.H. Davis, S.G. Bankoff, Rev. Mod. Phys. 69, 3433 (1996)Google Scholar

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© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Lavrentyev Institute of Hydrodynamics SB RASNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.Department of MathematicsTechnion — Israel Institute of TechnologyHaifaIsrael

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