Phase Separation of Liquid Mixtures

  • A. G. Lamorgese
  • R. Mauri


We simulate the phase segregation of a deeply quenched binary mixture using a pseudo-spectral method. Our theoretical approach follows the standard model H, where convection and diffusion are coupled via a body force, expressing the tendency of the demixing system to minimize its free energy. This driving force induces a material flux which, for liquid mixtures, is much larger than that due to pure molecular diffusion, as in a typical case the Peclet number N Pe , expressing here the ratio of thermal to viscous forces, is of order 104. Using a pseudo-spectral method, we integrate the equations of motion in 2D, showing that the behavior of the system as it phase segregates depends on the values of the Peclet number. When N Pe < 102, the formation of sharp interfaces and the growth of the single- phase domains are two successive stages of the phase segregation process, while for N Pe > 103 the two events occur simultaneously, showing that the system is never at quasi-equilibrium during the segregation process. In addition, we show that, when N Pe > 103, the microscale Reynolds number increases dramatically.


Phase Separation Liquid Mixture Peclet Number Spinodal Decomposition Sharp Interface 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chou Y.C., Goldburg W.I. (1979) Phase Separation and Coalescence in Critically Quenched Isobutyric-Acid-Water and 2-6-Lutidine-Water Mixtures. Phys. Rev. A 20, 2105–2113, and references therein 150 A.G. Lamorgese, R. MauriGoogle Scholar
  2. 2.
    Wong N.C., Knobler C. (1981) Light-Scattering Studies of Phase Separation in Isobutyric Acid -I- Water Mixtures: Hydrodynamic Effects. Phys. Rev. A 24, 3205–3211, and references thereinCrossRefGoogle Scholar
  3. 3.
    Cumming A., Wiltzius P., Bates F.S., Rosedale J.H. (1992) Light-scattering experiments on phase-separation dynamics in binary fluid mixtures. Phys. Rev. A 45, 885–896, and references thereinCrossRefGoogle Scholar
  4. 4.
    Guenoun P., Gastaud R., Perrot F., Beysens D. (1987) Spinodal Decomposition Patterns in an Isodensity Critical Binary Fluid: Direct-Visualization and Light-Scattering Analyses. Phys. Rev. A 36, 4876–4890CrossRefGoogle Scholar
  5. 5.
    White W.R., Wiltzius P. (1995) Real space measurement of structure in phase separating binary fluid mixtures. Phys. Rev. Lett. 75, 3012–3015CrossRefGoogle Scholar
  6. 6.
    Siggia E. (1979) Late Stages of Spinodal Decomposition in Binary Mixtures. Phys. Rev. A 20, 595–601CrossRefGoogle Scholar
  7. 7.
    Lifehitz E.M., Pitaevskii L.P. (1984). Physical Kinetics (Ch. 12 ). Pergamon Press, New YorkGoogle Scholar
  8. 8.
    Hohenberg P.C., Halperin B.I. (1977) Theory of Dynamic Critical Phenomena, Rev. Mod. Phys. 49, 435–480CrossRefGoogle Scholar
  9. 9.
    Jasnow D., Vinals J. (1996) Coarse-grained description of thermo-capillary flow. Phys. Fluids 8, 660–669CrossRefGoogle Scholar
  10. 10.
    Vails O.T., Farrell J.E. (1993) Spinodal decomposition in a three-dimensional fluid model. Phys. Rev. E 47, R36–R39, and references thereinCrossRefGoogle Scholar
  11. 11.
    Tanaka H., Araki T. (1998) Spontaneous Double Phase Separation Induced by Rapid Hydrodynamic Coarsening in Two-Dimensional Fluid Mixtures. Phys. Rev. Lett. 81, 389–392CrossRefGoogle Scholar
  12. 12.
    Vladimirova N., Malagoli A., Mauri R. (1999a) Diffusio-phoresis of two- dimensional liquid droplets in a phase-separating system. Phys. Rev. E 60, 2037–2044CrossRefGoogle Scholar
  13. 13.
    Vladimirova N., Malagoli A., Mauri R. (1999b) Two-Dimensional Model of Phase Segregation in Liquid Binary Mixtures. Phys. Rev. E 60, 6968–6977CrossRefGoogle Scholar
  14. 14.
    Gupta R. (1999) Phase Segregation of Deeply Quenched Liquid Mixtures. Ph.D. Thesis, The City College of CUNY, New YorkGoogle Scholar
  15. 15.
    Gupta R., Mauri R., Shinnar R. (1999) Phase separation of liquid mixtures in the presence of surfactants. Ind. Eng. Chem. Res. 38, 2418–2424CrossRefGoogle Scholar
  16. 16.
    Gupta R., Mauri R., Shinnar R. (2001) Phase Segregation of Deeply Quenched Liquid Mixtures. J. Chem. Phys., submittedGoogle Scholar
  17. 17.
    Califano F., Mauri R., Shinnar R. (2001) Private CommunicationsGoogle Scholar
  18. 18.
    Landau L., Lifehitz E.M. (1953) Fluid Mechanics (Ch. 6 ). Pergamon Press, New YorkGoogle Scholar
  19. 19.
    Mauri R., Shinnar R., Triantafyllou G. (1996) Spinodal decomposition in binary mixtures. Phys. Rev. E 53, 2613–2623CrossRefGoogle Scholar
  20. 20.
    Vladimirova N., Malagoli A., Mauri R. (1998) Diffusion-driven phase separation of deeply quenched mixtures. Phys. Rev. E 58, 7691–7699CrossRefGoogle Scholar
  21. 21.
    Cahn J.W., Hilliard J.E. (1959) Free energy of a nonuniform system. III. Nucleation in a two-component incompressible fluid. J. Chem. Phys. 31, 688–699CrossRefGoogle Scholar
  22. 22.
    Van der Waals J.D. (1979) The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. Reprinted in J. Stat. Phys. 20, 200–244CrossRefGoogle Scholar
  23. 23.
    Tanaka H. (1996) Coarsening mechanisms of droplet spinodal decomposition in binary fluid mixtures. J. Chem. Phys. 105, 10099–10114CrossRefGoogle Scholar
  24. 24.
    Gupta R., Mauri R., Shinnar R. (1996) Phase separation of liquid mixtures in the presence of surfactants. Ind. Eng. Chem. Res. 35, 2360–2372CrossRefGoogle Scholar
  25. 25.
    San Miguel M., Grant M., Gunton J.D. (1985) Phys. Rev. A 31, 1001–1011CrossRefGoogle Scholar
  26. 26.
    Vladimirova N., Malagoli A., Mauri R. (2000) Two-dimensional model of phase segregation in liquid binary mixtures with an initial concentration gradient. Chem. Eng. Sci. 55, 6109–6118CrossRefGoogle Scholar
  27. 27.
    Tannehill J.C., Anderson D.A., Pletcher R.H. (1997) Computational Fluid Mechanics and Heat Transfer. Taylor & Francis, LondonGoogle Scholar

Copyright information

© Springer-Verlag Italia, Milan 2002

Authors and Affiliations

  • A. G. Lamorgese
    • 1
  • R. Mauri
    • 1
  1. 1.Dipartimento di Ingegneria Chimica, Chimica Industriale e Scienza dei MaterialiUniversità di PisaPisaItaly

Personalised recommendations