Abstract

We used a form of schlieren interferometry to measure the mean-squared amplitude and temporal autocorrelation function of concentration fluctuations driven by the presence of a gradient during the free diffusion of a urea solution into water. By taking and processing sequences of images separated in time by less than the shortest correlation time of interest, we were able to simultaneously measure dynamics at a number of different wave vectors. The technique is conceptually similar to the shadowgraph method, which has been used to make similar measurements, but the schlieren method has the advantage that the transfer function is wave-vector independent rather than oscillatory.

© 2006 Optical Society of America

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  1. See, for example, B. J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics (Wiley, 1976), and references therein.
  2. A. P. Y. Wong and P. Wiltzius, "Dynamic light scattering with a CCD camera," Rev. Sci. Instrum. 64, 2547-2549 (1993).
    [CrossRef]
  3. L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlators," Rev. Sci. Instrum. 70, 3214-3221 (1999).
    [CrossRef]
  4. F. Ferri, "Use of a charge coupled device camera for low-angle elastic light scattering," Rev. Sci. Instrum. 68, 2265-2274 (1997).
    [CrossRef]
  5. I. Rehberg, S. Rasenat, M. de la Torre Juárez, W. Schöpf, F. Hörner, G. Ahlers, and H. R. Brand, "Thermally induced hydrodynamic fluctuations below the onset of electroconvection," Phys. Rev. Lett. 67, 596-599 (1994).
    [CrossRef]
  6. 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]
  7. M. Giglio, M. Carpineti, and A. Vailati, "Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r)," Phys. Rev. Lett. 85, 1416-1419 (2000).
    [CrossRef] [PubMed]
  8. M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, "Near-field intensity correlations of scattered light," Appl. Opt. 40, 4036-4040 (2001).
    [CrossRef]
  9. D. Brogioli, A. Vailati, and M. Giglio, "Heterodyne near-field scattering," Appl. Phys. Lett. 81, 4109-4111 (2002).
    [CrossRef]
  10. D. Brogioli, A. Vailati, and M. Giglio, "A schlieren method for ultra-low-angle light scattering measurements," Europhys. Lett. 63, 220-225 (2003).
    [CrossRef]
  11. D. Brogioli, A. Vailati, and M. Giglio, "Universal behavior of nonequilibrium fluctuations in free diffusion processes," Phys. Rev. E 61, R1-R4 (2000).
    [CrossRef]
  12. S. P. Trainoff and D. S. Cannell, "Physical optics treatment of the shadowgraph," Phys. Fluids 14, 1340-1363 (2002).
    [CrossRef]
  13. S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "Spiral defect chaos in large aspect ratio Rayleigh-Benard convection," Phys. Rev. Lett. 71, 2026-2029 (1993).
    [CrossRef] [PubMed]
  14. 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]
  15. M. Denin, G. Ahlers, and D. S. Cannell, "Spatiotemporal chaos in electroconvection," Science 272, 388-390 (1996).
    [CrossRef]
  16. Y. Galerne, I. Poinsot, and D. Schaegis, "Direct absolute measurements of the two-dimensional elastic constants in smectic C* liquid crystal films," Appl. Phys. Lett. 71, 222-224 (1997).
    [CrossRef]
  17. A. Yethiraj, R. Mukhopadhyay, and J. Bechoefer, "Two experimental tests of a fluctuation-induced first-order phase transition: intensity fluctuation microscopy at the nematic-smectic-A transition," Phys. Rev. E 65, 021702-1-021702-16 (2002).
    [CrossRef]
  18. See, for example, M. V. Berry, The Diffraction of Light by Ultrasound (Academic, 1966).
  19. H. F. Talbot, "Facts relating to optical science," Philos. Mag. 9, 401 (1836).
  20. A. Vailati and M. Giglio, "Giant fluctuations in a free diffusion process," Nature 390, 262-265 (1977).
  21. D. A. Weitz, "Diffusion in a different direction," Nature 390, 233-235 (1997).
    [CrossRef]
  22. A. Vailati and M. Giglio, "Nonequilibrium fluctuations in time-dependent diffusion processes," Phys. Rev. E 58, 4361-4371 (1998).
    [CrossRef]
  23. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, 1959).
  24. 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]
  25. P. N. Segrè and J. V. Sengers, "Nonequilibrium fluctuations in liquid mixtures under the influence of gravity," Physica A 198, 46-77 (1993).
    [CrossRef]
  26. E. O. Schulz-DuBois and I. Rehberg, "Structure function in lieu of correlation function," Appl. Phys. 24, 323-329 (1981).
    [CrossRef]
  27. A. V. Wolf, M. G. Brown, and P. G. Prentiss, "Concentrative properties of aqueous solution: conversion tables," in Handbook of Chemistry and Physics, 69th ed. (CRC Press, 1988), pp. D264-D265.

2003 (1)

D. Brogioli, A. Vailati, and M. Giglio, "A schlieren method for ultra-low-angle light scattering measurements," Europhys. Lett. 63, 220-225 (2003).
[CrossRef]

2002 (3)

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

D. Brogioli, A. Vailati, and M. Giglio, "Heterodyne near-field scattering," Appl. Phys. Lett. 81, 4109-4111 (2002).
[CrossRef]

A. Yethiraj, R. Mukhopadhyay, and J. Bechoefer, "Two experimental tests of a fluctuation-induced first-order phase transition: intensity fluctuation microscopy at the nematic-smectic-A transition," Phys. Rev. E 65, 021702-1-021702-16 (2002).
[CrossRef]

2001 (1)

2000 (2)

M. Giglio, M. Carpineti, and A. Vailati, "Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r)," Phys. Rev. Lett. 85, 1416-1419 (2000).
[CrossRef] [PubMed]

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

1999 (1)

L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlators," Rev. Sci. Instrum. 70, 3214-3221 (1999).
[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)

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]

Y. Galerne, I. Poinsot, and D. Schaegis, "Direct absolute measurements of the two-dimensional elastic constants in smectic C* liquid crystal films," Appl. Phys. Lett. 71, 222-224 (1997).
[CrossRef]

1996 (2)

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]

M. Denin, G. Ahlers, and D. S. Cannell, "Spatiotemporal chaos in electroconvection," Science 272, 388-390 (1996).
[CrossRef]

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)

I. Rehberg, S. Rasenat, M. de la Torre Juárez, W. Schöpf, F. Hörner, G. Ahlers, and H. R. Brand, "Thermally induced hydrodynamic fluctuations below the onset of electroconvection," Phys. Rev. Lett. 67, 596-599 (1994).
[CrossRef]

1993 (4)

A. P. Y. Wong and P. Wiltzius, "Dynamic light scattering with a CCD camera," Rev. Sci. Instrum. 64, 2547-2549 (1993).
[CrossRef]

S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "Spiral defect chaos in large aspect ratio Rayleigh-Benard convection," Phys. Rev. Lett. 71, 2026-2029 (1993).
[CrossRef] [PubMed]

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]

1981 (1)

E. O. Schulz-DuBois and I. Rehberg, "Structure function in lieu of correlation function," Appl. Phys. 24, 323-329 (1981).
[CrossRef]

1977 (1)

A. Vailati and M. Giglio, "Giant fluctuations in a free diffusion process," Nature 390, 262-265 (1977).

1836 (1)

H. F. Talbot, "Facts relating to optical science," Philos. Mag. 9, 401 (1836).

Ahlers, G.

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]

M. Denin, G. Ahlers, and D. S. Cannell, "Spatiotemporal chaos in electroconvection," Science 272, 388-390 (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]

I. Rehberg, S. Rasenat, M. de la Torre Juárez, W. Schöpf, F. Hörner, G. Ahlers, and H. R. Brand, "Thermally induced hydrodynamic fluctuations below the onset of electroconvection," Phys. Rev. Lett. 67, 596-599 (1994).
[CrossRef]

S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "Spiral defect chaos in large aspect ratio Rayleigh-Benard convection," Phys. Rev. Lett. 71, 2026-2029 (1993).
[CrossRef] [PubMed]

Bechoefer, J.

A. Yethiraj, R. Mukhopadhyay, and J. Bechoefer, "Two experimental tests of a fluctuation-induced first-order phase transition: intensity fluctuation microscopy at the nematic-smectic-A transition," Phys. Rev. E 65, 021702-1-021702-16 (2002).
[CrossRef]

Bodenschatz, E.

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]

S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "Spiral defect chaos in large aspect ratio Rayleigh-Benard convection," Phys. Rev. Lett. 71, 2026-2029 (1993).
[CrossRef] [PubMed]

Brand, H. R.

I. Rehberg, S. Rasenat, M. de la Torre Juárez, W. Schöpf, F. Hörner, G. Ahlers, and H. R. Brand, "Thermally induced hydrodynamic fluctuations below the onset of electroconvection," Phys. Rev. Lett. 67, 596-599 (1994).
[CrossRef]

Brogioli, D.

D. Brogioli, A. Vailati, and M. Giglio, "A schlieren method for ultra-low-angle light scattering measurements," Europhys. Lett. 63, 220-225 (2003).
[CrossRef]

D. Brogioli, A. Vailati, and M. Giglio, "Heterodyne near-field scattering," Appl. Phys. Lett. 81, 4109-4111 (2002).
[CrossRef]

M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, "Near-field intensity correlations of scattered light," Appl. Opt. 40, 4036-4040 (2001).
[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]

Brown, M. G.

A. V. Wolf, M. G. Brown, and P. G. Prentiss, "Concentrative properties of aqueous solution: conversion tables," in Handbook of Chemistry and Physics, 69th ed. (CRC Press, 1988), pp. D264-D265.

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]

M. Denin, G. Ahlers, and D. S. Cannell, "Spatiotemporal chaos in electroconvection," Science 272, 388-390 (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]

S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "Spiral defect chaos in large aspect ratio Rayleigh-Benard convection," Phys. Rev. Lett. 71, 2026-2029 (1993).
[CrossRef] [PubMed]

Carpineti, M.

M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, "Near-field intensity correlations of scattered light," Appl. Opt. 40, 4036-4040 (2001).
[CrossRef]

M. Giglio, M. Carpineti, and A. Vailati, "Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r)," Phys. Rev. Lett. 85, 1416-1419 (2000).
[CrossRef] [PubMed]

Cipelletti, L.

L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlators," Rev. Sci. Instrum. 70, 3214-3221 (1999).
[CrossRef]

Denin, M.

M. Denin, G. Ahlers, and D. S. Cannell, "Spatiotemporal chaos in electroconvection," Science 272, 388-390 (1996).
[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]

Galerne, Y.

Y. Galerne, I. Poinsot, and D. Schaegis, "Direct absolute measurements of the two-dimensional elastic constants in smectic C* liquid crystal films," Appl. Phys. Lett. 71, 222-224 (1997).
[CrossRef]

Giglio, M.

D. Brogioli, A. Vailati, and M. Giglio, "A schlieren method for ultra-low-angle light scattering measurements," Europhys. Lett. 63, 220-225 (2003).
[CrossRef]

D. Brogioli, A. Vailati, and M. Giglio, "Heterodyne near-field scattering," Appl. Phys. Lett. 81, 4109-4111 (2002).
[CrossRef]

M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, "Near-field intensity correlations of scattered light," Appl. Opt. 40, 4036-4040 (2001).
[CrossRef]

M. Giglio, M. Carpineti, and A. Vailati, "Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r)," Phys. Rev. Lett. 85, 1416-1419 (2000).
[CrossRef] [PubMed]

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 (1977).

Hörner, F.

I. Rehberg, S. Rasenat, M. de la Torre Juárez, W. Schöpf, F. Hörner, G. Ahlers, and H. R. Brand, "Thermally induced hydrodynamic fluctuations below the onset of electroconvection," Phys. Rev. Lett. 67, 596-599 (1994).
[CrossRef]

Juárez, M. de la Torre

I. Rehberg, S. Rasenat, M. de la Torre Juárez, W. Schöpf, F. Hörner, G. Ahlers, and H. R. Brand, "Thermally induced hydrodynamic fluctuations below the onset of electroconvection," Phys. Rev. Lett. 67, 596-599 (1994).
[CrossRef]

Landau, L. D.

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

Lifshitz, E. M.

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

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]

S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "Spiral defect chaos in large aspect ratio Rayleigh-Benard convection," Phys. Rev. Lett. 71, 2026-2029 (1993).
[CrossRef] [PubMed]

Mukhopadhyay, R.

A. Yethiraj, R. Mukhopadhyay, and J. Bechoefer, "Two experimental tests of a fluctuation-induced first-order phase transition: intensity fluctuation microscopy at the nematic-smectic-A transition," Phys. Rev. E 65, 021702-1-021702-16 (2002).
[CrossRef]

Poinsot, I.

Y. Galerne, I. Poinsot, and D. Schaegis, "Direct absolute measurements of the two-dimensional elastic constants in smectic C* liquid crystal films," Appl. Phys. Lett. 71, 222-224 (1997).
[CrossRef]

Prentiss, P. G.

A. V. Wolf, M. G. Brown, and P. G. Prentiss, "Concentrative properties of aqueous solution: conversion tables," in Handbook of Chemistry and Physics, 69th ed. (CRC Press, 1988), pp. D264-D265.

Rasenat, S.

I. Rehberg, S. Rasenat, M. de la Torre Juárez, W. Schöpf, F. Hörner, G. Ahlers, and H. R. Brand, "Thermally induced hydrodynamic fluctuations below the onset of electroconvection," Phys. Rev. Lett. 67, 596-599 (1994).
[CrossRef]

Rehberg, I.

I. Rehberg, S. Rasenat, M. de la Torre Juárez, W. Schöpf, F. Hörner, G. Ahlers, and H. R. Brand, "Thermally induced hydrodynamic fluctuations below the onset of electroconvection," Phys. Rev. Lett. 67, 596-599 (1994).
[CrossRef]

E. O. Schulz-DuBois and I. Rehberg, "Structure function in lieu of correlation function," Appl. Phys. 24, 323-329 (1981).
[CrossRef]

Schaegis, D.

Y. Galerne, I. Poinsot, and D. Schaegis, "Direct absolute measurements of the two-dimensional elastic constants in smectic C* liquid crystal films," Appl. Phys. Lett. 71, 222-224 (1997).
[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]

Schöpf, W.

I. Rehberg, S. Rasenat, M. de la Torre Juárez, W. Schöpf, F. Hörner, G. Ahlers, and H. R. Brand, "Thermally induced hydrodynamic fluctuations below the onset of electroconvection," Phys. Rev. Lett. 67, 596-599 (1994).
[CrossRef]

Schulz-DuBois, E. O.

E. O. Schulz-DuBois and I. Rehberg, "Structure function in lieu of correlation function," Appl. Phys. 24, 323-329 (1981).
[CrossRef]

Segrè, P. N.

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

Sengers, J. V.

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

Talbot, H. F.

H. F. Talbot, "Facts relating to optical science," Philos. Mag. 9, 401 (1836).

Trainoff, S. P.

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

Vailati, A.

D. Brogioli, A. Vailati, and M. Giglio, "A schlieren method for ultra-low-angle light scattering measurements," Europhys. Lett. 63, 220-225 (2003).
[CrossRef]

D. Brogioli, A. Vailati, and M. Giglio, "Heterodyne near-field scattering," Appl. Phys. Lett. 81, 4109-4111 (2002).
[CrossRef]

M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, "Near-field intensity correlations of scattered light," Appl. Opt. 40, 4036-4040 (2001).
[CrossRef]

M. Giglio, M. Carpineti, and A. Vailati, "Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r)," Phys. Rev. Lett. 85, 1416-1419 (2000).
[CrossRef] [PubMed]

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 (1977).

Weitz, D. A.

L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlators," Rev. Sci. Instrum. 70, 3214-3221 (1999).
[CrossRef]

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

Wiltzius, P.

A. P. Y. Wong and P. Wiltzius, "Dynamic light scattering with a CCD camera," Rev. Sci. Instrum. 64, 2547-2549 (1993).
[CrossRef]

Wolf, A. V.

A. V. Wolf, M. G. Brown, and P. G. Prentiss, "Concentrative properties of aqueous solution: conversion tables," in Handbook of Chemistry and Physics, 69th ed. (CRC Press, 1988), pp. D264-D265.

Wong, A. P. Y.

A. P. Y. Wong and P. Wiltzius, "Dynamic light scattering with a CCD camera," Rev. Sci. Instrum. 64, 2547-2549 (1993).
[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]

Yethiraj, A.

A. Yethiraj, R. Mukhopadhyay, and J. Bechoefer, "Two experimental tests of a fluctuation-induced first-order phase transition: intensity fluctuation microscopy at the nematic-smectic-A transition," Phys. Rev. E 65, 021702-1-021702-16 (2002).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

E. O. Schulz-DuBois and I. Rehberg, "Structure function in lieu of correlation function," Appl. Phys. 24, 323-329 (1981).
[CrossRef]

Appl. Phys. Lett. (2)

D. Brogioli, A. Vailati, and M. Giglio, "Heterodyne near-field scattering," Appl. Phys. Lett. 81, 4109-4111 (2002).
[CrossRef]

Y. Galerne, I. Poinsot, and D. Schaegis, "Direct absolute measurements of the two-dimensional elastic constants in smectic C* liquid crystal films," Appl. Phys. Lett. 71, 222-224 (1997).
[CrossRef]

Europhys. Lett. (1)

D. Brogioli, A. Vailati, and M. Giglio, "A schlieren method for ultra-low-angle light scattering measurements," Europhys. Lett. 63, 220-225 (2003).
[CrossRef]

Nature (2)

A. Vailati and M. Giglio, "Giant fluctuations in a free diffusion process," Nature 390, 262-265 (1977).

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

Philos. Mag. (1)

H. F. Talbot, "Facts relating to optical science," Philos. Mag. 9, 401 (1836).

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. E (3)

A. Yethiraj, R. Mukhopadhyay, and J. Bechoefer, "Two experimental tests of a fluctuation-induced first-order phase transition: intensity fluctuation microscopy at the nematic-smectic-A transition," Phys. Rev. E 65, 021702-1-021702-16 (2002).
[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]

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

Phys. Rev. Lett. (4)

I. Rehberg, S. Rasenat, M. de la Torre Juárez, W. Schöpf, F. Hörner, G. Ahlers, and H. R. Brand, "Thermally induced hydrodynamic fluctuations below the onset of electroconvection," Phys. Rev. Lett. 67, 596-599 (1994).
[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]

M. Giglio, M. Carpineti, and A. Vailati, "Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r)," Phys. Rev. Lett. 85, 1416-1419 (2000).
[CrossRef] [PubMed]

S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, "Spiral defect chaos in large aspect ratio Rayleigh-Benard convection," Phys. Rev. Lett. 71, 2026-2029 (1993).
[CrossRef] [PubMed]

Physica A (2)

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]

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. (3)

A. P. Y. Wong and P. Wiltzius, "Dynamic light scattering with a CCD camera," Rev. Sci. Instrum. 64, 2547-2549 (1993).
[CrossRef]

L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlators," Rev. Sci. Instrum. 70, 3214-3221 (1999).
[CrossRef]

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

Science (1)

M. Denin, G. Ahlers, and D. S. Cannell, "Spatiotemporal chaos in electroconvection," Science 272, 388-390 (1996).
[CrossRef]

Other (4)

See, for example, M. V. Berry, The Diffraction of Light by Ultrasound (Academic, 1966).

See, for example, B. J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics (Wiley, 1976), and references therein.

A. V. Wolf, M. G. Brown, and P. G. Prentiss, "Concentrative properties of aqueous solution: conversion tables," in Handbook of Chemistry and Physics, 69th ed. (CRC Press, 1988), pp. D264-D265.

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

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the schlieren apparatus.

Fig. 2
Fig. 2

Difference images showing fluctuations for two different liquids undergoing free diffusion. (a) Schlieren image of a 4.5   mm square area showing fluctuations in a urea–water sample. (b) Shadowgraph image of a 4.5   mm square area showing fluctuations in a glycerol–water sample.

Fig. 3
Fig. 3

Structure function C m ( q , d t ) measured at t = 4200   s as a function of time delay d t . The open squares are experimental data for q = 277 cm - 1 , and the solid curve is the result of fitting Eq. (10) to the data. The dashed horizontal line is the fitted limit of C m ( q , d t ) for a long time delay.

Fig. 4
Fig. 4

Static structure factor S ( q , t ) as a function of wave vector q as measured 600   s (open circles) and 4200   s (open squares) after establishing the interface. The solid curves fits of Eq. (3) to the data. The results of analyzing the same set of data images by using the static method are shown as solid symbols for comparison. For this analysis the background was determined separately, as described in the text.

Fig. 5
Fig. 5

Time constant τ ( q , t ) as a function of wave vector q for data taken 600   s (open circles) and 4200   s (open squares) after forming the interface. The solid curves are the results of fitting Eq. (4) to the data. As time increases, the crossover wave vector corresponding to the maximum value for τ decreases slowly, and the maximum time constant increases.

Equations (10)

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q c ( t ) = [ β g c ( t ) ν D ] 1 / 4 ,
S ( q , t ) = S 0 ( t ) 1 + [ q / q c ( t ) ] 4 .
S 0 ( t ) = 1 ( 2 π ) 2 k B T ( n c ) 2 Δ c ( t ) ρ β g ,
τ ( q , t ) = 1 D q 2 { 1 + [ q c ( t ) / q ] 4 } .
C m ( q , d t ) | δ ˜ i ( q , t , d t ) | 2 t = 2 | i ( q , t ) | 2 t 2 Re i ( q , t ) × i * ( q , t + d t ) t ,
| i ( q , t ) i 0 ( q ) | 2 t = A S ( q ) + B ( q ) = | i ( q , t ) | 2 t | i 0 ( q ) | 2 .
Re [ i ( q , t ) i 0 ( q ) ] [ i * ( q , t + d t ) i 0 * ( q ) ] t = A S ( q ) G ( q , d t ) = Re i ( q , t ) i * ( q , t + d t ) t | i 0 ( q ) | 2 .
C m ( q , d t ) = 2 { A S ( q ) [ 1 G ( q , d t ) ] + B ( q ) } .
G ( q , d t ) = exp [ d t τ ( q ) ] ,
C m ( q , d t ) = 2 ( A S ( q ) { 1 exp [ - d t τ ( q ) ] } + B ( q ) ) .

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