Abstract

We have studied the nonequilibrium fluctuations that occur at the interface between two miscible phases of a near-critical binary mixture during a free-diffusion process. The small-angle static scattered intensity is the superposition of nonequilibrium contributions that are due to capillary waves and to bulk fluctuations. A linearized hydrodynamic description of the fluctuations allows us to isolate the two contributions and to determine an effective surface tension for the nonequilibrium interface. As the diffuse-interface thickness increases, we observe the crossover of the contribution from the capillary waves to the bulk fluctuations.

© 2001 Optical Society of America

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  1. A. Vailati, M. Giglio, “Giant fluctuations in a free diffusion process,” Nature 390, 262–265 (1997).
    [CrossRef]
  2. D. Brogioli, A. Vailati, M. Giglio, “Universal behavior of nonequilibrium fluctuations in free diffusion processes,” Phys. Rev. E 61, R1–R4 (2000).
    [CrossRef]
  3. P. Petitjeans, “Une tension de surface pour les fluids miscibles,” C. R. Acad. Sci. Paris 322, 673–679 (1996).
  4. S. E. May, J. V. Maher, “Capillary-wave relaxation for a meniscus between miscible liquids,” Phys. Rev. Lett. 67, 2013–2016 (1991).
    [CrossRef] [PubMed]
  5. D. H. Vlad, J. V. Maher, “Dissolving interfaces in the presence of gravity,” Phys. Rev. E 59, 476–478 (1999).
    [CrossRef]
  6. P. G. Smith, M. Van den Ven, S. G. Mason, “The transient interfacial tension between two miscible fluids,” J. Colloid Interface Sci. 80, 302–303 (1981).
    [CrossRef]
  7. D. D. Joseph, “Fluid dynamics of two miscible liquids with diffusion and gradient stresses,” Eur. J. Mech. B Fluids 9, 565–596 (1990).
  8. J. E. Mungall, “Interfacial tension in miscible two-fluid systems with linear viscoelastic rheology,” Phys. Rev. Lett. 73, 288–291 (1994).
    [CrossRef] [PubMed]
  9. P. Cicuta, A. Vailati, M. Giglio, “Equilibrium and nonequilibrium fluctuations at the interface between two fluid phases,” Phys. Rev. E 62, 4290–4296 (2000).
    [CrossRef]
  10. A. Vailati, M. Giglio, “q divergence of nonequilibrium fluctuations and its gravity-induced frustration in a temperature stressed liquid mixture,” Phys. Rev. Lett. 77, 1484–1487 (1996).
    [CrossRef] [PubMed]
  11. M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
    [CrossRef] [PubMed]
  12. A. Bassini, S. Musazzi, E. Paganini, U. Perini, F. Ferri, “Self-aligning optical particle sizer for the monitoring of particle growth processes in industrial plants,” Rev. Sci. Instrum. 69, 2484–2494 (1998).
    [CrossRef]
  13. L. I. Mandelstamm, “Uber die Rauhigkeit freier Flussigkeitsoberflachen,” Ann. Phys. (Leipzig) 41, 609–624 (1913).
    [CrossRef]
  14. L. D. Landau, E. M. Lifshifz, Fluid Mechanics (Pergamon, New York, 1959).
  15. A. Vailati, M. Giglio, “Nonequilibrium fluctuations in time-dependent diffusion processes,” Phys. Rev. E 58, 4361–4371 (1998).
    [CrossRef]
  16. T. R. Kirkpatrick, E. G. D. Cohen, J. R. Dorfman, “Fluctuations in a nonequilibrium steady state. I. Small gradients,” Phys. Rev. A 26, 995–972 (1982).
    [CrossRef]
  17. D. Ronis, I. Procaccia, “Nonlinear resonant coupling between shear and heat fluctuations in fluids far from equilibrium,” Phys. Rev. A 26, 1812–1815 (1982).
    [CrossRef]
  18. B. M. Law, J. C. Nieuwoudt, “Noncritical liquid mixtures far from equilibrium: the Rayleigh line,” Phys. Rev. A 40, 3880–3885 (1989).
    [CrossRef] [PubMed]
  19. R. Schmitz, E. G. D. Cohen, “Fluctuations in a fluid under a stationary heat flux II. Slow part of the correlation matrix,” J. Stat. Phys. 40, 431–482 (1985).
    [CrossRef]
  20. B. M. Law, J. V. Sengers, “Fluctuations in fluids out of thermal equilibrium,” J. Stat. Phys. 57, 531–547 (1989).
    [CrossRef]
  21. B. M. Law, R. W. Gammon, J. V. Sengers, “Light-scattering observations of long-range correlations in a nonequilibrium liquid,” Phys. Rev. Lett. 60, 1554–1557 (1988).
    [CrossRef] [PubMed]
  22. P. N. Segre, R. W. Gammon, J. V. Sengers, B. M. Law, “Rayleigh scattering in a liquid far from thermal equilibrium,” Phys. Rev. A 45, 714–724 (1992).
    [CrossRef] [PubMed]
  23. P. N. Segre, R. W. Gammon, J. V. Sengers, “Light-scattering measurements of nonequilibrium fluctuations in a liquid mixture,” Phys. Rev. E 47, 1026–1034 (1993).
    [CrossRef]
  24. W. B. Li, P. N. Segre, R. W. Gammon, J. V. Sengers, “Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures,” Physica A 204, 399–435 (1994).
    [CrossRef]
  25. G. P. Galdi, D. D. Joseph, L. Preziosi, S. Rionero, “Mathematical problems for miscible, incompressible fluids with Korteweg stresses,” Eur. J. Mech. B Fluids 10, 253–267 (1991).
  26. W. J. Ma, P. Keblinski, A. Maritan, J. Koplik, R. Banavar, “Dynamical relaxation of the surface tension of miscible phases,” Phys. Rev. Lett. 71, 3465–3468 (1993).
    [CrossRef] [PubMed]
  27. J. W. Cahn, J. E. Hilliard, “Free energy of a nonuniform system. Interfacial free energy,” J. Chem. Phys. 28, 258–267 (1958).
    [CrossRef]
  28. D. Atack, O. K. Rice, “The interfacial tension and other properties of the cyclohexane + anyline system near the critical solution temperature,” Discuss. Faraday Soc. 15, 210–218 (1953).
    [CrossRef]
  29. J. S. Huang, W. W. Webb, “Viscous damping of thermal excitations on the interface of critical fluid mixtures,” Phys. Rev. Lett. 23, 160–163 (1969).
    [CrossRef]
  30. H. J. V. Tyrrell, Diffusion and Heat Flow in Liquids (Butterworths, London, 1961).

2000 (2)

D. Brogioli, A. Vailati, M. Giglio, “Universal behavior of nonequilibrium fluctuations in free diffusion processes,” Phys. Rev. E 61, R1–R4 (2000).
[CrossRef]

P. Cicuta, A. Vailati, M. Giglio, “Equilibrium and nonequilibrium fluctuations at the interface between two fluid phases,” Phys. Rev. E 62, 4290–4296 (2000).
[CrossRef]

1999 (1)

D. H. Vlad, J. V. Maher, “Dissolving interfaces in the presence of gravity,” Phys. Rev. E 59, 476–478 (1999).
[CrossRef]

1998 (2)

A. Bassini, S. Musazzi, E. Paganini, U. Perini, F. Ferri, “Self-aligning optical particle sizer for the monitoring of particle growth processes in industrial plants,” Rev. Sci. Instrum. 69, 2484–2494 (1998).
[CrossRef]

A. Vailati, M. Giglio, “Nonequilibrium fluctuations in time-dependent diffusion processes,” Phys. Rev. E 58, 4361–4371 (1998).
[CrossRef]

1997 (1)

A. Vailati, M. Giglio, “Giant fluctuations in a free diffusion process,” Nature 390, 262–265 (1997).
[CrossRef]

1996 (2)

A. Vailati, M. Giglio, “q divergence of nonequilibrium fluctuations and its gravity-induced frustration in a temperature stressed liquid mixture,” Phys. Rev. Lett. 77, 1484–1487 (1996).
[CrossRef] [PubMed]

P. Petitjeans, “Une tension de surface pour les fluids miscibles,” C. R. Acad. Sci. Paris 322, 673–679 (1996).

1994 (2)

J. E. Mungall, “Interfacial tension in miscible two-fluid systems with linear viscoelastic rheology,” Phys. Rev. Lett. 73, 288–291 (1994).
[CrossRef] [PubMed]

W. B. Li, P. N. Segre, R. W. Gammon, J. V. Sengers, “Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures,” Physica A 204, 399–435 (1994).
[CrossRef]

1993 (2)

W. J. Ma, P. Keblinski, A. Maritan, J. Koplik, R. Banavar, “Dynamical relaxation of the surface tension of miscible phases,” Phys. Rev. Lett. 71, 3465–3468 (1993).
[CrossRef] [PubMed]

P. N. Segre, R. W. Gammon, J. V. Sengers, “Light-scattering measurements of nonequilibrium fluctuations in a liquid mixture,” Phys. Rev. E 47, 1026–1034 (1993).
[CrossRef]

1992 (1)

P. N. Segre, R. W. Gammon, J. V. Sengers, B. M. Law, “Rayleigh scattering in a liquid far from thermal equilibrium,” Phys. Rev. A 45, 714–724 (1992).
[CrossRef] [PubMed]

1991 (2)

G. P. Galdi, D. D. Joseph, L. Preziosi, S. Rionero, “Mathematical problems for miscible, incompressible fluids with Korteweg stresses,” Eur. J. Mech. B Fluids 10, 253–267 (1991).

S. E. May, J. V. Maher, “Capillary-wave relaxation for a meniscus between miscible liquids,” Phys. Rev. Lett. 67, 2013–2016 (1991).
[CrossRef] [PubMed]

1990 (2)

M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

D. D. Joseph, “Fluid dynamics of two miscible liquids with diffusion and gradient stresses,” Eur. J. Mech. B Fluids 9, 565–596 (1990).

1989 (2)

B. M. Law, J. C. Nieuwoudt, “Noncritical liquid mixtures far from equilibrium: the Rayleigh line,” Phys. Rev. A 40, 3880–3885 (1989).
[CrossRef] [PubMed]

B. M. Law, J. V. Sengers, “Fluctuations in fluids out of thermal equilibrium,” J. Stat. Phys. 57, 531–547 (1989).
[CrossRef]

1988 (1)

B. M. Law, R. W. Gammon, J. V. Sengers, “Light-scattering observations of long-range correlations in a nonequilibrium liquid,” Phys. Rev. Lett. 60, 1554–1557 (1988).
[CrossRef] [PubMed]

1985 (1)

R. Schmitz, E. G. D. Cohen, “Fluctuations in a fluid under a stationary heat flux II. Slow part of the correlation matrix,” J. Stat. Phys. 40, 431–482 (1985).
[CrossRef]

1982 (2)

T. R. Kirkpatrick, E. G. D. Cohen, J. R. Dorfman, “Fluctuations in a nonequilibrium steady state. I. Small gradients,” Phys. Rev. A 26, 995–972 (1982).
[CrossRef]

D. Ronis, I. Procaccia, “Nonlinear resonant coupling between shear and heat fluctuations in fluids far from equilibrium,” Phys. Rev. A 26, 1812–1815 (1982).
[CrossRef]

1981 (1)

P. G. Smith, M. Van den Ven, S. G. Mason, “The transient interfacial tension between two miscible fluids,” J. Colloid Interface Sci. 80, 302–303 (1981).
[CrossRef]

1969 (1)

J. S. Huang, W. W. Webb, “Viscous damping of thermal excitations on the interface of critical fluid mixtures,” Phys. Rev. Lett. 23, 160–163 (1969).
[CrossRef]

1958 (1)

J. W. Cahn, J. E. Hilliard, “Free energy of a nonuniform system. Interfacial free energy,” J. Chem. Phys. 28, 258–267 (1958).
[CrossRef]

1953 (1)

D. Atack, O. K. Rice, “The interfacial tension and other properties of the cyclohexane + anyline system near the critical solution temperature,” Discuss. Faraday Soc. 15, 210–218 (1953).
[CrossRef]

1913 (1)

L. I. Mandelstamm, “Uber die Rauhigkeit freier Flussigkeitsoberflachen,” Ann. Phys. (Leipzig) 41, 609–624 (1913).
[CrossRef]

Atack, D.

D. Atack, O. K. Rice, “The interfacial tension and other properties of the cyclohexane + anyline system near the critical solution temperature,” Discuss. Faraday Soc. 15, 210–218 (1953).
[CrossRef]

Banavar, R.

W. J. Ma, P. Keblinski, A. Maritan, J. Koplik, R. Banavar, “Dynamical relaxation of the surface tension of miscible phases,” Phys. Rev. Lett. 71, 3465–3468 (1993).
[CrossRef] [PubMed]

Bassini, A.

A. Bassini, S. Musazzi, E. Paganini, U. Perini, F. Ferri, “Self-aligning optical particle sizer for the monitoring of particle growth processes in industrial plants,” Rev. Sci. Instrum. 69, 2484–2494 (1998).
[CrossRef]

Brogioli, D.

D. Brogioli, A. Vailati, M. Giglio, “Universal behavior of nonequilibrium fluctuations in free diffusion processes,” Phys. Rev. E 61, R1–R4 (2000).
[CrossRef]

Cahn, J. W.

J. W. Cahn, J. E. Hilliard, “Free energy of a nonuniform system. Interfacial free energy,” J. Chem. Phys. 28, 258–267 (1958).
[CrossRef]

Carpineti, M.

M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

Cicuta, P.

P. Cicuta, A. Vailati, M. Giglio, “Equilibrium and nonequilibrium fluctuations at the interface between two fluid phases,” Phys. Rev. E 62, 4290–4296 (2000).
[CrossRef]

Cohen, E. G. D.

R. Schmitz, E. G. D. Cohen, “Fluctuations in a fluid under a stationary heat flux II. Slow part of the correlation matrix,” J. Stat. Phys. 40, 431–482 (1985).
[CrossRef]

T. R. Kirkpatrick, E. G. D. Cohen, J. R. Dorfman, “Fluctuations in a nonequilibrium steady state. I. Small gradients,” Phys. Rev. A 26, 995–972 (1982).
[CrossRef]

Dorfman, J. R.

T. R. Kirkpatrick, E. G. D. Cohen, J. R. Dorfman, “Fluctuations in a nonequilibrium steady state. I. Small gradients,” Phys. Rev. A 26, 995–972 (1982).
[CrossRef]

Ferri, F.

A. Bassini, S. Musazzi, E. Paganini, U. Perini, F. Ferri, “Self-aligning optical particle sizer for the monitoring of particle growth processes in industrial plants,” Rev. Sci. Instrum. 69, 2484–2494 (1998).
[CrossRef]

M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

Galdi, G. P.

G. P. Galdi, D. D. Joseph, L. Preziosi, S. Rionero, “Mathematical problems for miscible, incompressible fluids with Korteweg stresses,” Eur. J. Mech. B Fluids 10, 253–267 (1991).

Gammon, R. W.

W. B. Li, P. N. Segre, R. W. Gammon, J. V. Sengers, “Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures,” Physica A 204, 399–435 (1994).
[CrossRef]

P. N. Segre, R. W. Gammon, J. V. Sengers, “Light-scattering measurements of nonequilibrium fluctuations in a liquid mixture,” Phys. Rev. E 47, 1026–1034 (1993).
[CrossRef]

P. N. Segre, R. W. Gammon, J. V. Sengers, B. M. Law, “Rayleigh scattering in a liquid far from thermal equilibrium,” Phys. Rev. A 45, 714–724 (1992).
[CrossRef] [PubMed]

B. M. Law, R. W. Gammon, J. V. Sengers, “Light-scattering observations of long-range correlations in a nonequilibrium liquid,” Phys. Rev. Lett. 60, 1554–1557 (1988).
[CrossRef] [PubMed]

Giglio, M.

D. Brogioli, A. Vailati, M. Giglio, “Universal behavior of nonequilibrium fluctuations in free diffusion processes,” Phys. Rev. E 61, R1–R4 (2000).
[CrossRef]

P. Cicuta, A. Vailati, M. Giglio, “Equilibrium and nonequilibrium fluctuations at the interface between two fluid phases,” Phys. Rev. E 62, 4290–4296 (2000).
[CrossRef]

A. Vailati, M. Giglio, “Nonequilibrium fluctuations in time-dependent diffusion processes,” Phys. Rev. E 58, 4361–4371 (1998).
[CrossRef]

A. Vailati, M. Giglio, “Giant fluctuations in a free diffusion process,” Nature 390, 262–265 (1997).
[CrossRef]

A. Vailati, M. Giglio, “q divergence of nonequilibrium fluctuations and its gravity-induced frustration in a temperature stressed liquid mixture,” Phys. Rev. Lett. 77, 1484–1487 (1996).
[CrossRef] [PubMed]

M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

Hilliard, J. E.

J. W. Cahn, J. E. Hilliard, “Free energy of a nonuniform system. Interfacial free energy,” J. Chem. Phys. 28, 258–267 (1958).
[CrossRef]

Huang, J. S.

J. S. Huang, W. W. Webb, “Viscous damping of thermal excitations on the interface of critical fluid mixtures,” Phys. Rev. Lett. 23, 160–163 (1969).
[CrossRef]

Joseph, D. D.

G. P. Galdi, D. D. Joseph, L. Preziosi, S. Rionero, “Mathematical problems for miscible, incompressible fluids with Korteweg stresses,” Eur. J. Mech. B Fluids 10, 253–267 (1991).

D. D. Joseph, “Fluid dynamics of two miscible liquids with diffusion and gradient stresses,” Eur. J. Mech. B Fluids 9, 565–596 (1990).

Keblinski, P.

W. J. Ma, P. Keblinski, A. Maritan, J. Koplik, R. Banavar, “Dynamical relaxation of the surface tension of miscible phases,” Phys. Rev. Lett. 71, 3465–3468 (1993).
[CrossRef] [PubMed]

Kirkpatrick, T. R.

T. R. Kirkpatrick, E. G. D. Cohen, J. R. Dorfman, “Fluctuations in a nonequilibrium steady state. I. Small gradients,” Phys. Rev. A 26, 995–972 (1982).
[CrossRef]

Koplik, J.

W. J. Ma, P. Keblinski, A. Maritan, J. Koplik, R. Banavar, “Dynamical relaxation of the surface tension of miscible phases,” Phys. Rev. Lett. 71, 3465–3468 (1993).
[CrossRef] [PubMed]

Landau, L. D.

L. D. Landau, E. M. Lifshifz, Fluid Mechanics (Pergamon, New York, 1959).

Law, B. M.

P. N. Segre, R. W. Gammon, J. V. Sengers, B. M. Law, “Rayleigh scattering in a liquid far from thermal equilibrium,” Phys. Rev. A 45, 714–724 (1992).
[CrossRef] [PubMed]

B. M. Law, J. C. Nieuwoudt, “Noncritical liquid mixtures far from equilibrium: the Rayleigh line,” Phys. Rev. A 40, 3880–3885 (1989).
[CrossRef] [PubMed]

B. M. Law, J. V. Sengers, “Fluctuations in fluids out of thermal equilibrium,” J. Stat. Phys. 57, 531–547 (1989).
[CrossRef]

B. M. Law, R. W. Gammon, J. V. Sengers, “Light-scattering observations of long-range correlations in a nonequilibrium liquid,” Phys. Rev. Lett. 60, 1554–1557 (1988).
[CrossRef] [PubMed]

Li, W. B.

W. B. Li, P. N. Segre, R. W. Gammon, J. V. Sengers, “Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures,” Physica A 204, 399–435 (1994).
[CrossRef]

Lifshifz, E. M.

L. D. Landau, E. M. Lifshifz, Fluid Mechanics (Pergamon, New York, 1959).

Ma, W. J.

W. J. Ma, P. Keblinski, A. Maritan, J. Koplik, R. Banavar, “Dynamical relaxation of the surface tension of miscible phases,” Phys. Rev. Lett. 71, 3465–3468 (1993).
[CrossRef] [PubMed]

Maher, J. V.

D. H. Vlad, J. V. Maher, “Dissolving interfaces in the presence of gravity,” Phys. Rev. E 59, 476–478 (1999).
[CrossRef]

S. E. May, J. V. Maher, “Capillary-wave relaxation for a meniscus between miscible liquids,” Phys. Rev. Lett. 67, 2013–2016 (1991).
[CrossRef] [PubMed]

Mandelstamm, L. I.

L. I. Mandelstamm, “Uber die Rauhigkeit freier Flussigkeitsoberflachen,” Ann. Phys. (Leipzig) 41, 609–624 (1913).
[CrossRef]

Maritan, A.

W. J. Ma, P. Keblinski, A. Maritan, J. Koplik, R. Banavar, “Dynamical relaxation of the surface tension of miscible phases,” Phys. Rev. Lett. 71, 3465–3468 (1993).
[CrossRef] [PubMed]

Mason, S. G.

P. G. Smith, M. Van den Ven, S. G. Mason, “The transient interfacial tension between two miscible fluids,” J. Colloid Interface Sci. 80, 302–303 (1981).
[CrossRef]

May, S. E.

S. E. May, J. V. Maher, “Capillary-wave relaxation for a meniscus between miscible liquids,” Phys. Rev. Lett. 67, 2013–2016 (1991).
[CrossRef] [PubMed]

Mungall, J. E.

J. E. Mungall, “Interfacial tension in miscible two-fluid systems with linear viscoelastic rheology,” Phys. Rev. Lett. 73, 288–291 (1994).
[CrossRef] [PubMed]

Musazzi, S.

A. Bassini, S. Musazzi, E. Paganini, U. Perini, F. Ferri, “Self-aligning optical particle sizer for the monitoring of particle growth processes in industrial plants,” Rev. Sci. Instrum. 69, 2484–2494 (1998).
[CrossRef]

Nieuwoudt, J. C.

B. M. Law, J. C. Nieuwoudt, “Noncritical liquid mixtures far from equilibrium: the Rayleigh line,” Phys. Rev. A 40, 3880–3885 (1989).
[CrossRef] [PubMed]

Paganini, E.

A. Bassini, S. Musazzi, E. Paganini, U. Perini, F. Ferri, “Self-aligning optical particle sizer for the monitoring of particle growth processes in industrial plants,” Rev. Sci. Instrum. 69, 2484–2494 (1998).
[CrossRef]

M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

Perini, U.

A. Bassini, S. Musazzi, E. Paganini, U. Perini, F. Ferri, “Self-aligning optical particle sizer for the monitoring of particle growth processes in industrial plants,” Rev. Sci. Instrum. 69, 2484–2494 (1998).
[CrossRef]

M. Carpineti, F. Ferri, M. Giglio, E. Paganini, U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347–7354 (1990).
[CrossRef] [PubMed]

Petitjeans, P.

P. Petitjeans, “Une tension de surface pour les fluids miscibles,” C. R. Acad. Sci. Paris 322, 673–679 (1996).

Preziosi, L.

G. P. Galdi, D. D. Joseph, L. Preziosi, S. Rionero, “Mathematical problems for miscible, incompressible fluids with Korteweg stresses,” Eur. J. Mech. B Fluids 10, 253–267 (1991).

Procaccia, I.

D. Ronis, I. Procaccia, “Nonlinear resonant coupling between shear and heat fluctuations in fluids far from equilibrium,” Phys. Rev. A 26, 1812–1815 (1982).
[CrossRef]

Rice, O. K.

D. Atack, O. K. Rice, “The interfacial tension and other properties of the cyclohexane + anyline system near the critical solution temperature,” Discuss. Faraday Soc. 15, 210–218 (1953).
[CrossRef]

Rionero, S.

G. P. Galdi, D. D. Joseph, L. Preziosi, S. Rionero, “Mathematical problems for miscible, incompressible fluids with Korteweg stresses,” Eur. J. Mech. B Fluids 10, 253–267 (1991).

Ronis, D.

D. Ronis, I. Procaccia, “Nonlinear resonant coupling between shear and heat fluctuations in fluids far from equilibrium,” Phys. Rev. A 26, 1812–1815 (1982).
[CrossRef]

Schmitz, R.

R. Schmitz, E. G. D. Cohen, “Fluctuations in a fluid under a stationary heat flux II. Slow part of the correlation matrix,” J. Stat. Phys. 40, 431–482 (1985).
[CrossRef]

Segre, P. N.

W. B. Li, P. N. Segre, R. W. Gammon, J. V. Sengers, “Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures,” Physica A 204, 399–435 (1994).
[CrossRef]

P. N. Segre, R. W. Gammon, J. V. Sengers, “Light-scattering measurements of nonequilibrium fluctuations in a liquid mixture,” Phys. Rev. E 47, 1026–1034 (1993).
[CrossRef]

P. N. Segre, R. W. Gammon, J. V. Sengers, B. M. Law, “Rayleigh scattering in a liquid far from thermal equilibrium,” Phys. Rev. A 45, 714–724 (1992).
[CrossRef] [PubMed]

Sengers, J. V.

W. B. Li, P. N. Segre, R. W. Gammon, J. V. Sengers, “Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures,” Physica A 204, 399–435 (1994).
[CrossRef]

P. N. Segre, R. W. Gammon, J. V. Sengers, “Light-scattering measurements of nonequilibrium fluctuations in a liquid mixture,” Phys. Rev. E 47, 1026–1034 (1993).
[CrossRef]

P. N. Segre, R. W. Gammon, J. V. Sengers, B. M. Law, “Rayleigh scattering in a liquid far from thermal equilibrium,” Phys. Rev. A 45, 714–724 (1992).
[CrossRef] [PubMed]

B. M. Law, J. V. Sengers, “Fluctuations in fluids out of thermal equilibrium,” J. Stat. Phys. 57, 531–547 (1989).
[CrossRef]

B. M. Law, R. W. Gammon, J. V. Sengers, “Light-scattering observations of long-range correlations in a nonequilibrium liquid,” Phys. Rev. Lett. 60, 1554–1557 (1988).
[CrossRef] [PubMed]

Smith, P. G.

P. G. Smith, M. Van den Ven, S. G. Mason, “The transient interfacial tension between two miscible fluids,” J. Colloid Interface Sci. 80, 302–303 (1981).
[CrossRef]

Tyrrell, H. J. V.

H. J. V. Tyrrell, Diffusion and Heat Flow in Liquids (Butterworths, London, 1961).

Vailati, A.

P. Cicuta, A. Vailati, M. Giglio, “Equilibrium and nonequilibrium fluctuations at the interface between two fluid phases,” Phys. Rev. E 62, 4290–4296 (2000).
[CrossRef]

D. Brogioli, A. Vailati, M. Giglio, “Universal behavior of nonequilibrium fluctuations in free diffusion processes,” Phys. Rev. E 61, R1–R4 (2000).
[CrossRef]

A. Vailati, M. Giglio, “Nonequilibrium fluctuations in time-dependent diffusion processes,” Phys. Rev. E 58, 4361–4371 (1998).
[CrossRef]

A. Vailati, M. Giglio, “Giant fluctuations in a free diffusion process,” Nature 390, 262–265 (1997).
[CrossRef]

A. Vailati, M. Giglio, “q divergence of nonequilibrium fluctuations and its gravity-induced frustration in a temperature stressed liquid mixture,” Phys. Rev. Lett. 77, 1484–1487 (1996).
[CrossRef] [PubMed]

Van den Ven, M.

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Figures (2)

Fig. 1
Fig. 1

Scattered intensity I(q) plotted versus the scattered wave vector q for several different measurement times. The initial data set [denoted by the pluses (+)] was the intensity scattered by the initial equilibrium interface. Time is measured from the start of the remixing process. The graph shows the early stages of the remixing process when the scattered intensity is increasing with time. The solid curves represent the best fit of the experimental data to expressions (1)–(6).

Fig. 2
Fig. 2

Time evolution of (a) the concentration difference across the interface and (b) the interfacial surface tension.

Equations (9)

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Iintq  Δcint1+q/qcap2,
Ibulkq  Δcbulk1+q/qRO4,
qcap=ρβgΔcintσ1/2,
qRO=βgcνD1/4.
Iq, t=Iintq, t+Ibulkq, t.
Δct=Δcintt+Δcbulkt=Δct=0.
σ   dcdz2dz.
τcap=4ησq,
τbulk=1Dq211+qROq4.

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