Abstract

The aim is to develop a rapid and direct method for measuring the bulk viscosity of a liquid as a function of temperature. Brillouin scattering of a laser beam in fresh water and salt water at different temperatures has been studied. The results show that there exists a close temperature-dependent relationship among the Brillouin frequency shift, the Brillouin linewidth, and the bulk viscosity of water. Thus the bulk viscosity of water can be determined directly from Brillouin-scattering measurements. The method has a high signal-to-noise ratio and high accuracy.

© 2003 Optical Society of America

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References

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  1. J. Lamb, “Thermal relaxation in liquids,” in Physical Acoustics, W. P. Mason, ed. (Academic, New York, 1965), pp. 203–209.
  2. J. Rouch, C. C. Lai, H. Chen, “Brillouin scattering studies of normal and supercooled water,” J. Chem. Phys. 65, 4016–4021 (1976).
    [CrossRef]
  3. J. Rouch, C. C. Lai, H. Chen, “High frequency sound velocity and sound absorption in supercooled water and the thermodynamic singularity at 228 °K,” J. Chem. Phys. 66, 5031–5034 (1977).
    [CrossRef]
  4. T. A. Litovitz, C. M. Davis, “Structural and shear relaxation in liquids,” in Physical Acoustics, W. P. Mason, ed. (Academic, New York, 1965), pp. 281–349.
  5. S. G. Brush, “Theory of liquid viscosity,” Chem. Rev. 62, 513–548 (1962).
    [CrossRef]
  6. G. D. Patterson, P. J. Carroll, “Light scattering spectroscopy of pure fluid,” J. Phys. Chem. 89, 1344–1354 (1985).
    [CrossRef]
  7. H. Z. Cummins, R. W. Gammon, “Rayleigh and Brillouin scattering in liquids: the Landau-Placzek ratio,” J. Chem. Phys. 44, 2785–2796 (1966).
    [CrossRef]
  8. S. M. Rytov, “Relaxation theory of Rayleigh scattering,” Sov. Phys. JETP 31, 1163–1171 (1970).
  9. D. H. Rank, “Brillouin effect in liquids in the prelaser era,” J. Acoust. Soc. Am. 49, 937–940 (1971).
    [CrossRef]
  10. R. D. Mountain, “Thermal relaxation and Brillouin scattering in liquids,” J. Res. Natl. Bur. Stand. Sect. A 70A, 207–220 (1966).
    [CrossRef]
  11. R. Y. Chiao, P. A. Fleury, “Brillouin scattering and the dispersion of hypersonic waves,” in Physics of Quantum Electronics, P. L. Kelly, P. E. Tannenwald, B. Laxs, eds. (McGraw-Hill, New York, 1965), pp. 241–252.
  12. I. L. Fabelinskii, “Spectra of molecular scattering of light,” Prog. Opt. 37, 97–110 (1997).
  13. I. L. Fabelinskii, Molecular Scattering of Light, translated from Russian by R. T. Beyer (Plenum, New York, 1968), Chaps. 2–4.
  14. D. J. Collins, J. A. Bell, R. Zanini, “Recent progress in the ocean measurement of temperature and salinity by optical scattering,” in Ocean Optics VII, M. A. Blizards, ed., Proc. SPIE489, 247–269 (1984).
    [CrossRef]
  15. J. G. Hirschberg, J. D. Byrne, A. W. Wouters, G. C. Boynton, “Speed of sound and temperature in the ocean by Brillouin scattering,” Appl. Opt. 23, 2624–2628 (1984).
    [CrossRef] [PubMed]
  16. G. D. Hickman, J. M. Harding, M. C. Garnes, A. Pressman, G. W. Kattwar, E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
    [CrossRef]
  17. Y. Emery, E. S. Fry, “Laboratory development of a LIDAR for measurement of sound velocity in the ocean using Brillouin scattering,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 210–215 (1997).
    [CrossRef]
  18. D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203, 335–340 (2002).
    [CrossRef]
  19. E. S. Fry, J. Katz, D. Liu, T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt. 49, 411–418 (2002).
    [CrossRef]
  20. X. Quan, E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. 34, 3477–3480 (1995).
    [CrossRef] [PubMed]
  21. R. C. Weast, ed., Handbook of Chemistry and Physics, 52nd ed. (The Chemical Rubber Co., Cleveland, Ohio, 1971–1972), p. F-36.

2002

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203, 335–340 (2002).
[CrossRef]

E. S. Fry, J. Katz, D. Liu, T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt. 49, 411–418 (2002).
[CrossRef]

1997

I. L. Fabelinskii, “Spectra of molecular scattering of light,” Prog. Opt. 37, 97–110 (1997).

1995

1991

G. D. Hickman, J. M. Harding, M. C. Garnes, A. Pressman, G. W. Kattwar, E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[CrossRef]

1985

G. D. Patterson, P. J. Carroll, “Light scattering spectroscopy of pure fluid,” J. Phys. Chem. 89, 1344–1354 (1985).
[CrossRef]

1984

1977

J. Rouch, C. C. Lai, H. Chen, “High frequency sound velocity and sound absorption in supercooled water and the thermodynamic singularity at 228 °K,” J. Chem. Phys. 66, 5031–5034 (1977).
[CrossRef]

1976

J. Rouch, C. C. Lai, H. Chen, “Brillouin scattering studies of normal and supercooled water,” J. Chem. Phys. 65, 4016–4021 (1976).
[CrossRef]

1971

D. H. Rank, “Brillouin effect in liquids in the prelaser era,” J. Acoust. Soc. Am. 49, 937–940 (1971).
[CrossRef]

1970

S. M. Rytov, “Relaxation theory of Rayleigh scattering,” Sov. Phys. JETP 31, 1163–1171 (1970).

1966

R. D. Mountain, “Thermal relaxation and Brillouin scattering in liquids,” J. Res. Natl. Bur. Stand. Sect. A 70A, 207–220 (1966).
[CrossRef]

H. Z. Cummins, R. W. Gammon, “Rayleigh and Brillouin scattering in liquids: the Landau-Placzek ratio,” J. Chem. Phys. 44, 2785–2796 (1966).
[CrossRef]

1962

S. G. Brush, “Theory of liquid viscosity,” Chem. Rev. 62, 513–548 (1962).
[CrossRef]

Bell, J. A.

D. J. Collins, J. A. Bell, R. Zanini, “Recent progress in the ocean measurement of temperature and salinity by optical scattering,” in Ocean Optics VII, M. A. Blizards, ed., Proc. SPIE489, 247–269 (1984).
[CrossRef]

Boynton, G. C.

Brush, S. G.

S. G. Brush, “Theory of liquid viscosity,” Chem. Rev. 62, 513–548 (1962).
[CrossRef]

Byrne, J. D.

Carroll, P. J.

G. D. Patterson, P. J. Carroll, “Light scattering spectroscopy of pure fluid,” J. Phys. Chem. 89, 1344–1354 (1985).
[CrossRef]

Chen, H.

J. Rouch, C. C. Lai, H. Chen, “High frequency sound velocity and sound absorption in supercooled water and the thermodynamic singularity at 228 °K,” J. Chem. Phys. 66, 5031–5034 (1977).
[CrossRef]

J. Rouch, C. C. Lai, H. Chen, “Brillouin scattering studies of normal and supercooled water,” J. Chem. Phys. 65, 4016–4021 (1976).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, P. A. Fleury, “Brillouin scattering and the dispersion of hypersonic waves,” in Physics of Quantum Electronics, P. L. Kelly, P. E. Tannenwald, B. Laxs, eds. (McGraw-Hill, New York, 1965), pp. 241–252.

Collins, D. J.

D. J. Collins, J. A. Bell, R. Zanini, “Recent progress in the ocean measurement of temperature and salinity by optical scattering,” in Ocean Optics VII, M. A. Blizards, ed., Proc. SPIE489, 247–269 (1984).
[CrossRef]

Cummins, H. Z.

H. Z. Cummins, R. W. Gammon, “Rayleigh and Brillouin scattering in liquids: the Landau-Placzek ratio,” J. Chem. Phys. 44, 2785–2796 (1966).
[CrossRef]

Dai, R.

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203, 335–340 (2002).
[CrossRef]

Davis, C. M.

T. A. Litovitz, C. M. Davis, “Structural and shear relaxation in liquids,” in Physical Acoustics, W. P. Mason, ed. (Academic, New York, 1965), pp. 281–349.

Emery, Y.

Y. Emery, E. S. Fry, “Laboratory development of a LIDAR for measurement of sound velocity in the ocean using Brillouin scattering,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 210–215 (1997).
[CrossRef]

Fabelinskii, I. L.

I. L. Fabelinskii, “Spectra of molecular scattering of light,” Prog. Opt. 37, 97–110 (1997).

I. L. Fabelinskii, Molecular Scattering of Light, translated from Russian by R. T. Beyer (Plenum, New York, 1968), Chaps. 2–4.

Fleury, P. A.

R. Y. Chiao, P. A. Fleury, “Brillouin scattering and the dispersion of hypersonic waves,” in Physics of Quantum Electronics, P. L. Kelly, P. E. Tannenwald, B. Laxs, eds. (McGraw-Hill, New York, 1965), pp. 241–252.

Fry, E. S.

E. S. Fry, J. Katz, D. Liu, T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt. 49, 411–418 (2002).
[CrossRef]

X. Quan, E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. 34, 3477–3480 (1995).
[CrossRef] [PubMed]

G. D. Hickman, J. M. Harding, M. C. Garnes, A. Pressman, G. W. Kattwar, E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[CrossRef]

Y. Emery, E. S. Fry, “Laboratory development of a LIDAR for measurement of sound velocity in the ocean using Brillouin scattering,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 210–215 (1997).
[CrossRef]

Gammon, R. W.

H. Z. Cummins, R. W. Gammon, “Rayleigh and Brillouin scattering in liquids: the Landau-Placzek ratio,” J. Chem. Phys. 44, 2785–2796 (1966).
[CrossRef]

Garnes, M. C.

G. D. Hickman, J. M. Harding, M. C. Garnes, A. Pressman, G. W. Kattwar, E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[CrossRef]

Gong, W.

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203, 335–340 (2002).
[CrossRef]

Harding, J. M.

G. D. Hickman, J. M. Harding, M. C. Garnes, A. Pressman, G. W. Kattwar, E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[CrossRef]

Hickman, G. D.

G. D. Hickman, J. M. Harding, M. C. Garnes, A. Pressman, G. W. Kattwar, E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[CrossRef]

Hirschberg, J. G.

Kattwar, G. W.

G. D. Hickman, J. M. Harding, M. C. Garnes, A. Pressman, G. W. Kattwar, E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[CrossRef]

Katz, J.

E. S. Fry, J. Katz, D. Liu, T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt. 49, 411–418 (2002).
[CrossRef]

Lai, C. C.

J. Rouch, C. C. Lai, H. Chen, “High frequency sound velocity and sound absorption in supercooled water and the thermodynamic singularity at 228 °K,” J. Chem. Phys. 66, 5031–5034 (1977).
[CrossRef]

J. Rouch, C. C. Lai, H. Chen, “Brillouin scattering studies of normal and supercooled water,” J. Chem. Phys. 65, 4016–4021 (1976).
[CrossRef]

Lamb, J.

J. Lamb, “Thermal relaxation in liquids,” in Physical Acoustics, W. P. Mason, ed. (Academic, New York, 1965), pp. 203–209.

Li, R.

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203, 335–340 (2002).
[CrossRef]

Litovitz, T. A.

T. A. Litovitz, C. M. Davis, “Structural and shear relaxation in liquids,” in Physical Acoustics, W. P. Mason, ed. (Academic, New York, 1965), pp. 281–349.

Liu, D.

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203, 335–340 (2002).
[CrossRef]

E. S. Fry, J. Katz, D. Liu, T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt. 49, 411–418 (2002).
[CrossRef]

Mountain, R. D.

R. D. Mountain, “Thermal relaxation and Brillouin scattering in liquids,” J. Res. Natl. Bur. Stand. Sect. A 70A, 207–220 (1966).
[CrossRef]

Patterson, G. D.

G. D. Patterson, P. J. Carroll, “Light scattering spectroscopy of pure fluid,” J. Phys. Chem. 89, 1344–1354 (1985).
[CrossRef]

Pressman, A.

G. D. Hickman, J. M. Harding, M. C. Garnes, A. Pressman, G. W. Kattwar, E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[CrossRef]

Quan, X.

Rank, D. H.

D. H. Rank, “Brillouin effect in liquids in the prelaser era,” J. Acoust. Soc. Am. 49, 937–940 (1971).
[CrossRef]

Rouch, J.

J. Rouch, C. C. Lai, H. Chen, “High frequency sound velocity and sound absorption in supercooled water and the thermodynamic singularity at 228 °K,” J. Chem. Phys. 66, 5031–5034 (1977).
[CrossRef]

J. Rouch, C. C. Lai, H. Chen, “Brillouin scattering studies of normal and supercooled water,” J. Chem. Phys. 65, 4016–4021 (1976).
[CrossRef]

Rytov, S. M.

S. M. Rytov, “Relaxation theory of Rayleigh scattering,” Sov. Phys. JETP 31, 1163–1171 (1970).

Walther, T.

E. S. Fry, J. Katz, D. Liu, T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt. 49, 411–418 (2002).
[CrossRef]

Wouters, A. W.

Xu, J.

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203, 335–340 (2002).
[CrossRef]

Zanini, R.

D. J. Collins, J. A. Bell, R. Zanini, “Recent progress in the ocean measurement of temperature and salinity by optical scattering,” in Ocean Optics VII, M. A. Blizards, ed., Proc. SPIE489, 247–269 (1984).
[CrossRef]

Appl. Opt.

Chem. Rev.

S. G. Brush, “Theory of liquid viscosity,” Chem. Rev. 62, 513–548 (1962).
[CrossRef]

J. Acoust. Soc. Am.

D. H. Rank, “Brillouin effect in liquids in the prelaser era,” J. Acoust. Soc. Am. 49, 937–940 (1971).
[CrossRef]

J. Chem. Phys.

H. Z. Cummins, R. W. Gammon, “Rayleigh and Brillouin scattering in liquids: the Landau-Placzek ratio,” J. Chem. Phys. 44, 2785–2796 (1966).
[CrossRef]

J. Rouch, C. C. Lai, H. Chen, “Brillouin scattering studies of normal and supercooled water,” J. Chem. Phys. 65, 4016–4021 (1976).
[CrossRef]

J. Rouch, C. C. Lai, H. Chen, “High frequency sound velocity and sound absorption in supercooled water and the thermodynamic singularity at 228 °K,” J. Chem. Phys. 66, 5031–5034 (1977).
[CrossRef]

J. Mod. Opt.

E. S. Fry, J. Katz, D. Liu, T. Walther, “Temperature dependence of the Brillouin linewidth in water,” J. Mod. Opt. 49, 411–418 (2002).
[CrossRef]

J. Phys. Chem.

G. D. Patterson, P. J. Carroll, “Light scattering spectroscopy of pure fluid,” J. Phys. Chem. 89, 1344–1354 (1985).
[CrossRef]

J. Res. Natl. Bur. Stand. Sect. A

R. D. Mountain, “Thermal relaxation and Brillouin scattering in liquids,” J. Res. Natl. Bur. Stand. Sect. A 70A, 207–220 (1966).
[CrossRef]

Opt. Commun.

D. Liu, J. Xu, R. Li, R. Dai, W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203, 335–340 (2002).
[CrossRef]

Prog. Opt.

I. L. Fabelinskii, “Spectra of molecular scattering of light,” Prog. Opt. 37, 97–110 (1997).

Remote Sens. Environ.

G. D. Hickman, J. M. Harding, M. C. Garnes, A. Pressman, G. W. Kattwar, E. S. Fry, “Aircraft laser sensing of sound velocity in water: Brillouin scattering,” Remote Sens. Environ. 36, 165–178 (1991).
[CrossRef]

Sov. Phys. JETP

S. M. Rytov, “Relaxation theory of Rayleigh scattering,” Sov. Phys. JETP 31, 1163–1171 (1970).

Other

R. Y. Chiao, P. A. Fleury, “Brillouin scattering and the dispersion of hypersonic waves,” in Physics of Quantum Electronics, P. L. Kelly, P. E. Tannenwald, B. Laxs, eds. (McGraw-Hill, New York, 1965), pp. 241–252.

T. A. Litovitz, C. M. Davis, “Structural and shear relaxation in liquids,” in Physical Acoustics, W. P. Mason, ed. (Academic, New York, 1965), pp. 281–349.

Y. Emery, E. S. Fry, “Laboratory development of a LIDAR for measurement of sound velocity in the ocean using Brillouin scattering,” in Ocean Optics XIII, S. G. Ackleson, R. Frouin, eds., Proc. SPIE2963, 210–215 (1997).
[CrossRef]

I. L. Fabelinskii, Molecular Scattering of Light, translated from Russian by R. T. Beyer (Plenum, New York, 1968), Chaps. 2–4.

D. J. Collins, J. A. Bell, R. Zanini, “Recent progress in the ocean measurement of temperature and salinity by optical scattering,” in Ocean Optics VII, M. A. Blizards, ed., Proc. SPIE489, 247–269 (1984).
[CrossRef]

J. Lamb, “Thermal relaxation in liquids,” in Physical Acoustics, W. P. Mason, ed. (Academic, New York, 1965), pp. 203–209.

R. C. Weast, ed., Handbook of Chemistry and Physics, 52nd ed. (The Chemical Rubber Co., Cleveland, Ohio, 1971–1972), p. F-36.

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Figures (9)

Fig. 1
Fig. 1

Setup geometry for the measurements of Brillouin scattering in water. M, mirror; L, lens; F-P, scanning Fabry-Perot interferometer; D, detector; BS, beam splitter; P, pinhole filter; and PMT, photomultiplier tube.

Fig. 2
Fig. 2

Measured spectrum of Brillouin scattering in water.

Fig. 3
Fig. 3

Measured spectra of Brillouin scattering. (a) Plots of six groups of measured data. (b) Averaged result of six groups’ data in (a).

Fig. 4
Fig. 4

Fitting result of averaged data. The result is obtained by a mixed function of Gaussians and Lorentzians, where FSR is the free spectral range of the Fabry-Perot interferometer used, ν B is the Brillouin shift, and Γ B is the Brillouin linewidth.

Fig. 5
Fig. 5

Measured spectra at different temperatures and salinities. (a) Measured spectra at different temperatures for fresh water (S = 0‰). (b) Measured spectra at different salinities of water (the temperature is T = 20 °C).

Fig. 6
Fig. 6

Measured results of the Brillouin shift and the Brillouin linewidth in water for different temperatures and salinities. (a) The measured Brillouin shift at different temperatures. (b) The measured Brillouin linewidth at different temperatures. Triangles, the results for fresh water (S = 0‰); squares, the results for water of salinity S = 35‰.

Fig. 7
Fig. 7

Measured results of the bulk viscosity of fresh water (S = 0‰). Triangles, the values of the bulk viscosity; squares, the values of the shear viscosity given by Eq. (7).

Fig. 8
Fig. 8

Plot of the ratio of bulk viscosity to shear viscosity of fresh water. As a comparison, three values found in Ref. 2 are given by squares.

Fig. 9
Fig. 9

Measured results of the bulk viscosity and the ratio of bulk viscosity to shear viscosity of salt water (S = 35‰). (a) Measured results of the bulk viscosity of salt water. In this figure, both the bulk viscosity and the shear viscosity are plotted. (b) Measured results of the ratio of bulk viscosity to shear viscosity. Triangles, the results that the shear viscosity of salt water is 3% greater than fresh water; squares, the results that the shear viscosity of salt water is 8% greater than fresh water.

Equations (12)

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

Iω=Iadδ/2πω-Ω02+δ2,
Γ=1ρ43 ηs+ηb+κCPγ-1,
ΓB=2δ=Γq2=1ρ43 ηs+ηb+κCPγ-1q2.
ΓB=1ρ43 ηs+ηbq2=1ρ43 ηs+ηb4π2νB2υ2.
ηb=ρυ2ΓB4π2νB2-43 ηs,
νB=±2nλ υ sinθ2.
ηb=ρλ2ΓB16π2n2 sin2θ2-43 ηs,
nS, T, λ=n0+Sn1+n2T+n3T2+n4T2+n5+n6S+n7Tλ+n8λ2+n9λ3.
ηs=1.008 exp2.4096T-20+0.0054T-20279.6531+T.
ηbηs=4.8840-0.2488t+7.3000×10-3t3-0.6125×10-5t3.
Δηb=δηbδΓB2ΔΓB2+δηbδνB2ΔνB21/2;
Δηb=ρυ24π2νB22ΔΓB2+ρυ22π2νB32ΔνB21/2.

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