Abstract

We describe an experimental breadboard developed for the investigation of nonequilibrium fluctuations induced by macroscopic temperature and concentration gradients under microgravity conditions. Under these conditions the amplitude of the fluctuations diverges strongly for long wavelengths. The setup was developed at the University of Milan and at the University of California at Santa Barbara within the gradient-driven fluctuations experiment (GRADFLEX) project of the European Space Agency, in collaboration with the National Aeronautics and Space Administration. The apparatus uses a quantitative shadowgraph technique for characterization of the static power spectrum of the fluctuations S(q) and the measurement of their dynamics. We present preliminary experimental results for S(q) obtained in the presence of gravity for gradient-driven fluctuations for two cases, those induced in a liquid mixture with a concentration gradient produced by the Soret effect and those induced in a single-component fluid by a temperature gradient.

© 2006 Optical Society of America

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  1. See, for example, R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena (Wiley, 2001).
  2. See, for example, E. L. Cussler, Diffusion (Cambridge U. Press, 1997).
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    [CrossRef]
  4. D. Ronis and I. Procaccia, "Nonlinear resonant coupling between shear and heat fluctuations in fluids far from equilibrium," Phys. Rev. A 26, 1812-1815 (1982).
    [CrossRef]
  5. R. Schmitz and 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]
  6. B. M. Law, R. W. Gammon, and J. V. Sengers, "Light-scattering observations of long-range correlations in a nonequilibrium fluid," Phys. Rev. Lett. 60, 1554-1557 (1988).
    [CrossRef] [PubMed]
  7. P. N. Segrè, R. W. Gammon, J. V. Sengers, and B. M. Law, "Rayleigh scattering in a liquid far from thermal equilibrium," Phys. Rev. A 45, 714-724 (1992).
    [CrossRef] [PubMed]
  8. A. Vailati and M. Giglio, "Giant fluctuations in a free diffusion process," Nature 390, 262-265 (1997).
    [CrossRef]
  9. W. B. Li, P. N. Segrè, R. W. Gammon, and J. V. Sengers, "Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures," Physica A 204, 399-436 (1994).
    [CrossRef]
  10. D. A. Weitz, "Diffusion in a different direction," Nature 390, 233-235 (1997).
    [CrossRef]
  11. B. M. Law and J. V. Sengers, "Fluctuations in fluids out of thermal equilibrium," J. Stat. Phys. 57, 531-547 (1989).
    [CrossRef]
  12. B. M. Law and J. C. Nieuwoudt, "Noncritical liquid mixtures far from equibrium: the Rayleigh line," Phys. Rev. A 40, 3880-3885 (1989).
    [CrossRef] [PubMed]
  13. P. N. Segrè, R. W. Gammon, and J. V. Sengers, "Light scattering measurements of nonequilibrium fluctuations in a liquid mixture," Phys. Rev. E 47, 1026-1034 (1993).
    [CrossRef]
  14. A. Vailati and 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]
  15. P. N. Segrè, R. Schmitz, and J. V. Sengers, "Fluctuations in inhomogeneous and nonequilibrium fluids under the influence of gravity," Physica A 195, 31-52 (1993).
    [CrossRef]
  16. P. N. Segrè and J. V. Sengers, "Nonequilibrium fluctuations in liquid mixtures under the influence of gravity," Physica A 198, 46-77 (1993).
    [CrossRef]
  17. A. Vailati and M. Giglio, "Nonequilibrium fluctuations in time-dependent diffusion processes," Phys. Rev. E 58, 4361-4371 (1998).
    [CrossRef]
  18. J. M. Ortiz de Zárate and J. V. Sengers, "Boundary effects on the nonequilibrium structure factor of fluids below the Rayleigh-Bénard instability," Phys. Rev. E 66, 036305-1-17 (2002).
    [CrossRef]
  19. J. Oh, J. M. Ortiz de Zarate, J. V. Sengers, and G. Ahlers, "Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection," Phys. Rev. E 69, 021106-1-13 (2004).
    [CrossRef]
  20. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, 1959).
  21. J. M. Ortiz de Zárate and J. V. Sengers, "Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh-Bénard instability," Physica A 300, 25-52 (2001).
    [CrossRef]
  22. M. Wu, G. Ahlers, and D. S. Cannell, "Thermally induced fluctuations below the onset of Rayleigh-Bénard convection," Phys. Rev. Lett. 75, 1743-1746 (1995).
    [CrossRef] [PubMed]
  23. D. Brogioli, A. Vailati, and M. Giglio, "Universal behavior of nonequilibrium fluctuations in free diffusion processes," Phys. Rev. E 61, R1-R4 (2000).
    [CrossRef]
  24. G. Grinstein, "Generic scale invariance in classical nonequilibrium systems," J. Appl. Phys. 69, 5441-5446 (1991).
    [CrossRef]
  25. S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "The spatio-temporal structure of spiral-defect chaos," Physica D 97, 164-179 (1996).
    [CrossRef]
  26. F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell are preparing a manuscript to be called "Non-diffusive decay behavior of gradient driven fluctuations in a free-diffusion process."
  27. J. M. Ortiz de Zárate, F. Peluso, and J. V. Sengers, "Nonequilibrium fluctuations in the Rayleigh-Bénard problem for binary fluid mixtures," Eur. Phys. J. E 15319-333 (2004).
    [CrossRef] [PubMed]
  28. G. H. Wegdam, N. M. Keulen, and J. C. F. Michielsen, "Small angle Rayleigh scattering in CCl4 subjected to a temperature gradient," Phys. Rev. Lett. 55, 630-633 (1985).
    [CrossRef] [PubMed]
  29. M. Carpineti, F. Ferri, M. Giglio, E. Paganini, and U. Perini, "Salt-induced fast aggregation of polystyrene latex," Phys. Rev. A 42, 7347-7354 (1990).
    [CrossRef] [PubMed]
  30. F. Ferri, "Use of a charge coupled device camera for low-angle elastic light scattering," Rev. Sci. Instrum. 68, 2265-2274 (1997).
    [CrossRef]
  31. M. Van Dyke, An Album of Fluid Motion (Parabolic, 1982).
  32. S. P. Trainoff and D. S. Cannell, "Physical optics treatment of the shadowgraph," Phys. Fluids 14, 1340-1363 (2002).
    [CrossRef]
  33. J. R. de Bruyn, E. Bodenschatz, S. W. Morris, S. P. Trainoff, Y. Hu, D. S. Cannell, and G. Ahlers, "Apparatus for the study of Rayleigh-Benard convection in gases under pressure," Rev. Sci. Instrum. 67, 2043-2067 (1996).
    [CrossRef]

2004 (2)

J. Oh, J. M. Ortiz de Zarate, J. V. Sengers, and G. Ahlers, "Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection," Phys. Rev. E 69, 021106-1-13 (2004).
[CrossRef]

J. M. Ortiz de Zárate, F. Peluso, and J. V. Sengers, "Nonequilibrium fluctuations in the Rayleigh-Bénard problem for binary fluid mixtures," Eur. Phys. J. E 15319-333 (2004).
[CrossRef] [PubMed]

2002 (2)

S. P. Trainoff and D. S. Cannell, "Physical optics treatment of the shadowgraph," Phys. Fluids 14, 1340-1363 (2002).
[CrossRef]

J. M. Ortiz de Zárate and J. V. Sengers, "Boundary effects on the nonequilibrium structure factor of fluids below the Rayleigh-Bénard instability," Phys. Rev. E 66, 036305-1-17 (2002).
[CrossRef]

2001 (1)

J. M. Ortiz de Zárate and J. V. Sengers, "Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh-Bénard instability," Physica A 300, 25-52 (2001).
[CrossRef]

2000 (1)

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

1998 (1)

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

1997 (3)

A. Vailati and M. Giglio, "Giant fluctuations in a free diffusion process," Nature 390, 262-265 (1997).
[CrossRef]

D. A. Weitz, "Diffusion in a different direction," Nature 390, 233-235 (1997).
[CrossRef]

F. Ferri, "Use of a charge coupled device camera for low-angle elastic light scattering," Rev. Sci. Instrum. 68, 2265-2274 (1997).
[CrossRef]

1996 (3)

J. R. de Bruyn, E. Bodenschatz, S. W. Morris, S. P. Trainoff, Y. Hu, D. S. Cannell, and G. Ahlers, "Apparatus for the study of Rayleigh-Benard convection in gases under pressure," Rev. Sci. Instrum. 67, 2043-2067 (1996).
[CrossRef]

S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "The spatio-temporal structure of spiral-defect chaos," Physica D 97, 164-179 (1996).
[CrossRef]

A. Vailati and 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]

1995 (1)

M. Wu, G. Ahlers, and D. S. Cannell, "Thermally induced fluctuations below the onset of Rayleigh-Bénard convection," Phys. Rev. Lett. 75, 1743-1746 (1995).
[CrossRef] [PubMed]

1994 (1)

W. B. Li, P. N. Segrè, R. W. Gammon, and J. V. Sengers, "Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures," Physica A 204, 399-436 (1994).
[CrossRef]

1993 (3)

P. N. Segrè, R. Schmitz, and J. V. Sengers, "Fluctuations in inhomogeneous and nonequilibrium fluids under the influence of gravity," Physica A 195, 31-52 (1993).
[CrossRef]

P. N. Segrè and J. V. Sengers, "Nonequilibrium fluctuations in liquid mixtures under the influence of gravity," Physica A 198, 46-77 (1993).
[CrossRef]

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

1991 (1)

G. Grinstein, "Generic scale invariance in classical nonequilibrium systems," J. Appl. Phys. 69, 5441-5446 (1991).
[CrossRef]

1990 (1)

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

1989 (2)

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

B. M. Law and J. C. Nieuwoudt, "Noncritical liquid mixtures far from equibrium: the Rayleigh line," Phys. Rev. A 40, 3880-3885 (1989).
[CrossRef] [PubMed]

1988 (1)

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

1985 (2)

R. Schmitz and 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]

G. H. Wegdam, N. M. Keulen, and J. C. F. Michielsen, "Small angle Rayleigh scattering in CCl4 subjected to a temperature gradient," Phys. Rev. Lett. 55, 630-633 (1985).
[CrossRef] [PubMed]

1982 (2)

T. R. Kirkpatrick, E. G. D. Cohen, and J. R. Dorfman, "Light scattering by a fluid in a nonequilibrium steady state. II. Large gradients," Phys. Rev. A 26, 995-1014 (1982).
[CrossRef]

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

Ahlers, G.

J. Oh, J. M. Ortiz de Zarate, J. V. Sengers, and G. Ahlers, "Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection," Phys. Rev. E 69, 021106-1-13 (2004).
[CrossRef]

S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "The spatio-temporal structure of spiral-defect chaos," Physica D 97, 164-179 (1996).
[CrossRef]

J. R. de Bruyn, E. Bodenschatz, S. W. Morris, S. P. Trainoff, Y. Hu, D. S. Cannell, and G. Ahlers, "Apparatus for the study of Rayleigh-Benard convection in gases under pressure," Rev. Sci. Instrum. 67, 2043-2067 (1996).
[CrossRef]

M. Wu, G. Ahlers, and D. S. Cannell, "Thermally induced fluctuations below the onset of Rayleigh-Bénard convection," Phys. Rev. Lett. 75, 1743-1746 (1995).
[CrossRef] [PubMed]

Bodenschatz, E.

J. R. de Bruyn, E. Bodenschatz, S. W. Morris, S. P. Trainoff, Y. Hu, D. S. Cannell, and G. Ahlers, "Apparatus for the study of Rayleigh-Benard convection in gases under pressure," Rev. Sci. Instrum. 67, 2043-2067 (1996).
[CrossRef]

S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "The spatio-temporal structure of spiral-defect chaos," Physica D 97, 164-179 (1996).
[CrossRef]

Brogioli, D.

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

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell are preparing a manuscript to be called "Non-diffusive decay behavior of gradient driven fluctuations in a free-diffusion process."

Cannell, D. S.

S. P. Trainoff and D. S. Cannell, "Physical optics treatment of the shadowgraph," Phys. Fluids 14, 1340-1363 (2002).
[CrossRef]

S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "The spatio-temporal structure of spiral-defect chaos," Physica D 97, 164-179 (1996).
[CrossRef]

J. R. de Bruyn, E. Bodenschatz, S. W. Morris, S. P. Trainoff, Y. Hu, D. S. Cannell, and G. Ahlers, "Apparatus for the study of Rayleigh-Benard convection in gases under pressure," Rev. Sci. Instrum. 67, 2043-2067 (1996).
[CrossRef]

M. Wu, G. Ahlers, and D. S. Cannell, "Thermally induced fluctuations below the onset of Rayleigh-Bénard convection," Phys. Rev. Lett. 75, 1743-1746 (1995).
[CrossRef] [PubMed]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell are preparing a manuscript to be called "Non-diffusive decay behavior of gradient driven fluctuations in a free-diffusion process."

Carpineti, M.

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

Cohen, E. G. D.

R. Schmitz and 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, and J. R. Dorfman, "Light scattering by a fluid in a nonequilibrium steady state. II. Large gradients," Phys. Rev. A 26, 995-1014 (1982).
[CrossRef]

Croccolo, F.

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell are preparing a manuscript to be called "Non-diffusive decay behavior of gradient driven fluctuations in a free-diffusion process."

de Bruyn, J. R.

J. R. de Bruyn, E. Bodenschatz, S. W. Morris, S. P. Trainoff, Y. Hu, D. S. Cannell, and G. Ahlers, "Apparatus for the study of Rayleigh-Benard convection in gases under pressure," Rev. Sci. Instrum. 67, 2043-2067 (1996).
[CrossRef]

Dorfman, J. R.

T. R. Kirkpatrick, E. G. D. Cohen, and J. R. Dorfman, "Light scattering by a fluid in a nonequilibrium steady state. II. Large gradients," Phys. Rev. A 26, 995-1014 (1982).
[CrossRef]

Ferri, F.

F. Ferri, "Use of a charge coupled device camera for low-angle elastic light scattering," Rev. Sci. Instrum. 68, 2265-2274 (1997).
[CrossRef]

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

Gammon, R. W.

W. B. Li, P. N. Segrè, R. W. Gammon, and J. V. Sengers, "Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures," Physica A 204, 399-436 (1994).
[CrossRef]

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

P. N. Segrè, R. W. Gammon, J. V. Sengers, and 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, and J. V. Sengers, "Light-scattering observations of long-range correlations in a nonequilibrium fluid," Phys. Rev. Lett. 60, 1554-1557 (1988).
[CrossRef] [PubMed]

Giglio, M.

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

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

A. Vailati and M. Giglio, "Giant fluctuations in a free diffusion process," Nature 390, 262-265 (1997).
[CrossRef]

A. Vailati and 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, and U. Perini, "Salt-induced fast aggregation of polystyrene latex," Phys. Rev. A 42, 7347-7354 (1990).
[CrossRef] [PubMed]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell are preparing a manuscript to be called "Non-diffusive decay behavior of gradient driven fluctuations in a free-diffusion process."

Grinstein, G.

G. Grinstein, "Generic scale invariance in classical nonequilibrium systems," J. Appl. Phys. 69, 5441-5446 (1991).
[CrossRef]

Hu, Y.

J. R. de Bruyn, E. Bodenschatz, S. W. Morris, S. P. Trainoff, Y. Hu, D. S. Cannell, and G. Ahlers, "Apparatus for the study of Rayleigh-Benard convection in gases under pressure," Rev. Sci. Instrum. 67, 2043-2067 (1996).
[CrossRef]

Keulen, N. M.

G. H. Wegdam, N. M. Keulen, and J. C. F. Michielsen, "Small angle Rayleigh scattering in CCl4 subjected to a temperature gradient," Phys. Rev. Lett. 55, 630-633 (1985).
[CrossRef] [PubMed]

Kirkpatrick, T. R.

T. R. Kirkpatrick, E. G. D. Cohen, and J. R. Dorfman, "Light scattering by a fluid in a nonequilibrium steady state. II. Large gradients," Phys. Rev. A 26, 995-1014 (1982).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, 1959).

Law, B. M.

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

B. M. Law and J. C. Nieuwoudt, "Noncritical liquid mixtures far from equibrium: the Rayleigh line," Phys. Rev. A 40, 3880-3885 (1989).
[CrossRef] [PubMed]

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

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

Li, W. B.

W. B. Li, P. N. Segrè, R. W. Gammon, and J. V. Sengers, "Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures," Physica A 204, 399-436 (1994).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, 1959).

Michielsen, J. C. F.

G. H. Wegdam, N. M. Keulen, and J. C. F. Michielsen, "Small angle Rayleigh scattering in CCl4 subjected to a temperature gradient," Phys. Rev. Lett. 55, 630-633 (1985).
[CrossRef] [PubMed]

Morris, S. W.

S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "The spatio-temporal structure of spiral-defect chaos," Physica D 97, 164-179 (1996).
[CrossRef]

J. R. de Bruyn, E. Bodenschatz, S. W. Morris, S. P. Trainoff, Y. Hu, D. S. Cannell, and G. Ahlers, "Apparatus for the study of Rayleigh-Benard convection in gases under pressure," Rev. Sci. Instrum. 67, 2043-2067 (1996).
[CrossRef]

Nieuwoudt, J. C.

B. M. Law and J. C. Nieuwoudt, "Noncritical liquid mixtures far from equibrium: the Rayleigh line," Phys. Rev. A 40, 3880-3885 (1989).
[CrossRef] [PubMed]

Oh, J.

J. Oh, J. M. Ortiz de Zarate, J. V. Sengers, and G. Ahlers, "Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection," Phys. Rev. E 69, 021106-1-13 (2004).
[CrossRef]

Ortiz de Zarate, J. M.

J. Oh, J. M. Ortiz de Zarate, J. V. Sengers, and G. Ahlers, "Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection," Phys. Rev. E 69, 021106-1-13 (2004).
[CrossRef]

Ortiz de Zárate, J. M.

J. M. Ortiz de Zárate, F. Peluso, and J. V. Sengers, "Nonequilibrium fluctuations in the Rayleigh-Bénard problem for binary fluid mixtures," Eur. Phys. J. E 15319-333 (2004).
[CrossRef] [PubMed]

J. M. Ortiz de Zárate and J. V. Sengers, "Boundary effects on the nonequilibrium structure factor of fluids below the Rayleigh-Bénard instability," Phys. Rev. E 66, 036305-1-17 (2002).
[CrossRef]

J. M. Ortiz de Zárate and J. V. Sengers, "Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh-Bénard instability," Physica A 300, 25-52 (2001).
[CrossRef]

Paganini, E.

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

Peluso, F.

J. M. Ortiz de Zárate, F. Peluso, and J. V. Sengers, "Nonequilibrium fluctuations in the Rayleigh-Bénard problem for binary fluid mixtures," Eur. Phys. J. E 15319-333 (2004).
[CrossRef] [PubMed]

Perini, U.

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

Procaccia, I.

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

Ronis, D.

D. Ronis and 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.

P. N. Segrè, R. Schmitz, and J. V. Sengers, "Fluctuations in inhomogeneous and nonequilibrium fluids under the influence of gravity," Physica A 195, 31-52 (1993).
[CrossRef]

R. Schmitz and 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]

Segrè, P. N.

W. B. Li, P. N. Segrè, R. W. Gammon, and J. V. Sengers, "Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures," Physica A 204, 399-436 (1994).
[CrossRef]

P. N. Segrè, R. Schmitz, and J. V. Sengers, "Fluctuations in inhomogeneous and nonequilibrium fluids under the influence of gravity," Physica A 195, 31-52 (1993).
[CrossRef]

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

P. N. Segrè and J. V. Sengers, "Nonequilibrium fluctuations in liquid mixtures under the influence of gravity," Physica A 198, 46-77 (1993).
[CrossRef]

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

Sengers, J. V.

J. M. Ortiz de Zárate, F. Peluso, and J. V. Sengers, "Nonequilibrium fluctuations in the Rayleigh-Bénard problem for binary fluid mixtures," Eur. Phys. J. E 15319-333 (2004).
[CrossRef] [PubMed]

J. Oh, J. M. Ortiz de Zarate, J. V. Sengers, and G. Ahlers, "Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection," Phys. Rev. E 69, 021106-1-13 (2004).
[CrossRef]

J. M. Ortiz de Zárate and J. V. Sengers, "Boundary effects on the nonequilibrium structure factor of fluids below the Rayleigh-Bénard instability," Phys. Rev. E 66, 036305-1-17 (2002).
[CrossRef]

J. M. Ortiz de Zárate and J. V. Sengers, "Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh-Bénard instability," Physica A 300, 25-52 (2001).
[CrossRef]

W. B. Li, P. N. Segrè, R. W. Gammon, and J. V. Sengers, "Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures," Physica A 204, 399-436 (1994).
[CrossRef]

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

P. N. Segrè, R. Schmitz, and J. V. Sengers, "Fluctuations in inhomogeneous and nonequilibrium fluids under the influence of gravity," Physica A 195, 31-52 (1993).
[CrossRef]

P. N. Segrè and J. V. Sengers, "Nonequilibrium fluctuations in liquid mixtures under the influence of gravity," Physica A 198, 46-77 (1993).
[CrossRef]

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

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

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

Trainoff, S. P.

S. P. Trainoff and D. S. Cannell, "Physical optics treatment of the shadowgraph," Phys. Fluids 14, 1340-1363 (2002).
[CrossRef]

J. R. de Bruyn, E. Bodenschatz, S. W. Morris, S. P. Trainoff, Y. Hu, D. S. Cannell, and G. Ahlers, "Apparatus for the study of Rayleigh-Benard convection in gases under pressure," Rev. Sci. Instrum. 67, 2043-2067 (1996).
[CrossRef]

Vailati, A.

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

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

A. Vailati and M. Giglio, "Giant fluctuations in a free diffusion process," Nature 390, 262-265 (1997).
[CrossRef]

A. Vailati and 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]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell are preparing a manuscript to be called "Non-diffusive decay behavior of gradient driven fluctuations in a free-diffusion process."

Van Dyke, M.

M. Van Dyke, An Album of Fluid Motion (Parabolic, 1982).

Wegdam, G. H.

G. H. Wegdam, N. M. Keulen, and J. C. F. Michielsen, "Small angle Rayleigh scattering in CCl4 subjected to a temperature gradient," Phys. Rev. Lett. 55, 630-633 (1985).
[CrossRef] [PubMed]

Weitz, D. A.

D. A. Weitz, "Diffusion in a different direction," Nature 390, 233-235 (1997).
[CrossRef]

Wu, M.

M. Wu, G. Ahlers, and D. S. Cannell, "Thermally induced fluctuations below the onset of Rayleigh-Bénard convection," Phys. Rev. Lett. 75, 1743-1746 (1995).
[CrossRef] [PubMed]

Eur. Phys. J. E (1)

J. M. Ortiz de Zárate, F. Peluso, and J. V. Sengers, "Nonequilibrium fluctuations in the Rayleigh-Bénard problem for binary fluid mixtures," Eur. Phys. J. E 15319-333 (2004).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

G. Grinstein, "Generic scale invariance in classical nonequilibrium systems," J. Appl. Phys. 69, 5441-5446 (1991).
[CrossRef]

J. Stat. Phys. (2)

R. Schmitz and 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]

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

Nature (2)

A. Vailati and M. Giglio, "Giant fluctuations in a free diffusion process," Nature 390, 262-265 (1997).
[CrossRef]

D. A. Weitz, "Diffusion in a different direction," Nature 390, 233-235 (1997).
[CrossRef]

Phys. Fluids (1)

S. P. Trainoff and D. S. Cannell, "Physical optics treatment of the shadowgraph," Phys. Fluids 14, 1340-1363 (2002).
[CrossRef]

Phys. Rev. A (5)

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

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

T. R. Kirkpatrick, E. G. D. Cohen, and J. R. Dorfman, "Light scattering by a fluid in a nonequilibrium steady state. II. Large gradients," Phys. Rev. A 26, 995-1014 (1982).
[CrossRef]

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

B. M. Law and J. C. Nieuwoudt, "Noncritical liquid mixtures far from equibrium: the Rayleigh line," Phys. Rev. A 40, 3880-3885 (1989).
[CrossRef] [PubMed]

Phys. Rev. E (5)

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

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

J. M. Ortiz de Zárate and J. V. Sengers, "Boundary effects on the nonequilibrium structure factor of fluids below the Rayleigh-Bénard instability," Phys. Rev. E 66, 036305-1-17 (2002).
[CrossRef]

J. Oh, J. M. Ortiz de Zarate, J. V. Sengers, and G. Ahlers, "Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection," Phys. Rev. E 69, 021106-1-13 (2004).
[CrossRef]

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

Phys. Rev. Lett. (4)

M. Wu, G. Ahlers, and D. S. Cannell, "Thermally induced fluctuations below the onset of Rayleigh-Bénard convection," Phys. Rev. Lett. 75, 1743-1746 (1995).
[CrossRef] [PubMed]

G. H. Wegdam, N. M. Keulen, and J. C. F. Michielsen, "Small angle Rayleigh scattering in CCl4 subjected to a temperature gradient," Phys. Rev. Lett. 55, 630-633 (1985).
[CrossRef] [PubMed]

A. Vailati and 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]

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

Physica A (4)

W. B. Li, P. N. Segrè, R. W. Gammon, and J. V. Sengers, "Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures," Physica A 204, 399-436 (1994).
[CrossRef]

P. N. Segrè, R. Schmitz, and J. V. Sengers, "Fluctuations in inhomogeneous and nonequilibrium fluids under the influence of gravity," Physica A 195, 31-52 (1993).
[CrossRef]

P. N. Segrè and J. V. Sengers, "Nonequilibrium fluctuations in liquid mixtures under the influence of gravity," Physica A 198, 46-77 (1993).
[CrossRef]

J. M. Ortiz de Zárate and J. V. Sengers, "Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh-Bénard instability," Physica A 300, 25-52 (2001).
[CrossRef]

Physica D (1)

S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "The spatio-temporal structure of spiral-defect chaos," Physica D 97, 164-179 (1996).
[CrossRef]

Rev. Sci. Instrum. (2)

F. Ferri, "Use of a charge coupled device camera for low-angle elastic light scattering," Rev. Sci. Instrum. 68, 2265-2274 (1997).
[CrossRef]

J. R. de Bruyn, E. Bodenschatz, S. W. Morris, S. P. Trainoff, Y. Hu, D. S. Cannell, and G. Ahlers, "Apparatus for the study of Rayleigh-Benard convection in gases under pressure," Rev. Sci. Instrum. 67, 2043-2067 (1996).
[CrossRef]

Other (5)

M. Van Dyke, An Album of Fluid Motion (Parabolic, 1982).

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell are preparing a manuscript to be called "Non-diffusive decay behavior of gradient driven fluctuations in a free-diffusion process."

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, 1959).

See, for example, R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena (Wiley, 2001).

See, for example, E. L. Cussler, Diffusion (Cambridge U. Press, 1997).

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Figures (6)

Fig. 1
Fig. 1

Calculated static power spectrum for nonequilibrium fluctuations in the presence of a stabilizing gradient. The amplitude and wave vector were normalized by S 0 and q c , respectively. The dashed line corresponds to the q 4 divergence predicted for an unbounded sample in the absence of gravity.

Fig. 2
Fig. 2

Block diagram of the overall setup for the GRADFLEX flight experiment.

Fig. 3
Fig. 3

Schematic diagram of the prototype apparatus used to measure fluctuations in a single-component fluid heated from above. The upper surface of the sample is heated via the transparent ITO film, and the heat is removed from the lower surface of the silicon mirror by means of four Peltier modules. The optical path is evacuated to eliminate optical disturbances from air.

Fig. 4
Fig. 4

Log–log graph of the product of the shadowgraph transfer function T ( q ) and the structure factor S ( q ) of gradient-driven fluctuations in a 4.86   cm thick layer of CS 2 with a temperature difference of 20   K , heated from above. Open circles show the background noise spectrum, and the solid circles are the result of subtracting the background from the raw data. Individual data points are too dense to plot effectively for higher q, and solid curves connecting the points are shown instead.

Fig. 5
Fig. 5

Diagram of the experimental setup for the investigation of NEFs induced in a binary mixture by means of the Soret effect. The actual apparatus is oriented vertically so that the surfaces of the sapphire windows are horizontal.

Fig. 6
Fig. 6

Log–log graph of the product of the shadowgraph transfer function T ( q ) and the structure factor S ( q ) for gradient-driven concentration fluctuations in a 1.8   wt .% solution of 9100 molecular weight polystyrene in toluene. Open circles are raw data, and the dashed curve is the power spectrum of background noise acquired in the absence of fluctuations. Solid circles show the difference, which represents the actual power spectrum of NEFs modulated by the shadowgraph transfer function. The solid black curve represents a calculated estimate of the data expected under microgravity conditions.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

S ( q ) = S 0 1 + ( q / q c ) 4 ,
q c = { ( α g T ν κ ) 1 / 4 temperature   driven   NEFs ( β g c ν D ) 1 / 4 concentration   driven   NEFs .
q = [ 4 ν D T ( ν D T ) 2 ] 1 / 4 ,
= [ 4 P ( 1 P ) 2 ] 1 / 4 q c ,
q = [ 4 ν D ( ν D ) 2 ] 1 / 4 ,
= [ 4 S c ( 1 S c ) 2 ] 1 / 4 q c .
S Sh ( q ) = A T ( q ) S ( q ) ,
T ( q ) = sin 2 [ q 2 z / ( 2 k ) ] ,

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