Abstract

The spectral line shape of spontaneous Rayleigh–Brillouin scattering in CO2 is studied in a range of pressures. The spectrum is influenced by the bulk viscosity ηb, which is a relaxation phenomenon involving the internal degrees of freedom of the molecule. The associated relaxation rates can be compared to the frequency shift of the scattered light, which demands precise measurements of the spectral line shape. We find ηb=(5.7±0.6)×106kgm1s1 for the range of pressures p=24 bar and for room temperature conditions.

© 2014 Optical Society of America

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  1. X. G. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 71, 045801 (2005).
    [CrossRef]
  2. Z. Y. Gu, M. O. Vieitez, E. J. van Duijn, and W. Ubachs, Rev. Sci. Instrum. 83, 053112 (2012).
    [CrossRef]
  3. B. Witschas, C. Lemmerz, and O. Reitebuch, Opt. Lett. 39, 1972 (2014).
    [CrossRef]
  4. K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, Appl. Phys. B 105, 421 (2011).
    [CrossRef]
  5. “ADM-Aeolus: Science Report,” (ESA Communication Production Office, 2008).
  6. J. Lambert, Vibrational and Rotational Relaxation in Gases (Clarendon, 1977).
  7. Q. H. Lao, P. E. Schoen, and B. Chu, J. Chem. Phys. 64, 3547 (1976).
    [CrossRef]
  8. X. G. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 69, 033814 (2004).
    [CrossRef]
  9. A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, J. Chem. Phys. 133, 164315 (2010).
    [CrossRef]
  10. C. D. Boley, R. C. Desai, and G. Tenti, Can. J. Phys. 50, 2158 (1972).
    [CrossRef]
  11. G. Tenti, C. D. Boley, and R. C. Desai, Can. J. Phys. 52, 285 (1974).
  12. A. Chapman and T. G. Cowling, Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge Mathematical Library, 1970).
  13. W. E. Meador, G. A. Miner, and L. W. Townsend, Phys. Fluids 8, 258 (1996).
    [CrossRef]
  14. M. O. Vieitez, E.-J. van Duijn, W. Ubachs, B. Witschas, A. S. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, Phys. Rev. A 82, 043836 (2010).
    [CrossRef]
  15. Z. Y. Gu and W. Ubachs, Opt. Lett. 38, 1110 (2013).
    [CrossRef]

2014 (1)

2013 (1)

2012 (1)

Z. Y. Gu, M. O. Vieitez, E. J. van Duijn, and W. Ubachs, Rev. Sci. Instrum. 83, 053112 (2012).
[CrossRef]

2011 (1)

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, Appl. Phys. B 105, 421 (2011).
[CrossRef]

2010 (2)

A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, J. Chem. Phys. 133, 164315 (2010).
[CrossRef]

M. O. Vieitez, E.-J. van Duijn, W. Ubachs, B. Witschas, A. S. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, Phys. Rev. A 82, 043836 (2010).
[CrossRef]

2005 (1)

X. G. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 71, 045801 (2005).
[CrossRef]

2004 (1)

X. G. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 69, 033814 (2004).
[CrossRef]

1996 (1)

W. E. Meador, G. A. Miner, and L. W. Townsend, Phys. Fluids 8, 258 (1996).
[CrossRef]

1976 (1)

Q. H. Lao, P. E. Schoen, and B. Chu, J. Chem. Phys. 64, 3547 (1976).
[CrossRef]

1974 (1)

G. Tenti, C. D. Boley, and R. C. Desai, Can. J. Phys. 52, 285 (1974).

1972 (1)

C. D. Boley, R. C. Desai, and G. Tenti, Can. J. Phys. 50, 2158 (1972).
[CrossRef]

Boley, C. D.

G. Tenti, C. D. Boley, and R. C. Desai, Can. J. Phys. 52, 285 (1974).

C. D. Boley, R. C. Desai, and G. Tenti, Can. J. Phys. 50, 2158 (1972).
[CrossRef]

Chapman, A.

A. Chapman and T. G. Cowling, Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge Mathematical Library, 1970).

Chu, B.

Q. H. Lao, P. E. Schoen, and B. Chu, J. Chem. Phys. 64, 3547 (1976).
[CrossRef]

Cowling, T. G.

A. Chapman and T. G. Cowling, Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge Mathematical Library, 1970).

Dam, N. J.

M. O. Vieitez, E.-J. van Duijn, W. Ubachs, B. Witschas, A. S. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, Phys. Rev. A 82, 043836 (2010).
[CrossRef]

A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, J. Chem. Phys. 133, 164315 (2010).
[CrossRef]

de Wijn, A. S.

A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, J. Chem. Phys. 133, 164315 (2010).
[CrossRef]

M. O. Vieitez, E.-J. van Duijn, W. Ubachs, B. Witschas, A. S. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, Phys. Rev. A 82, 043836 (2010).
[CrossRef]

Desai, R. C.

G. Tenti, C. D. Boley, and R. C. Desai, Can. J. Phys. 52, 285 (1974).

C. D. Boley, R. C. Desai, and G. Tenti, Can. J. Phys. 50, 2158 (1972).
[CrossRef]

Gu, Z. Y.

Z. Y. Gu and W. Ubachs, Opt. Lett. 38, 1110 (2013).
[CrossRef]

Z. Y. Gu, M. O. Vieitez, E. J. van Duijn, and W. Ubachs, Rev. Sci. Instrum. 83, 053112 (2012).
[CrossRef]

Huang, J.

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, Appl. Phys. B 105, 421 (2011).
[CrossRef]

Lambert, J.

J. Lambert, Vibrational and Rotational Relaxation in Gases (Clarendon, 1977).

Lao, Q. H.

Q. H. Lao, P. E. Schoen, and B. Chu, J. Chem. Phys. 64, 3547 (1976).
[CrossRef]

Lemmerz, C.

Li, H.

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, Appl. Phys. B 105, 421 (2011).
[CrossRef]

Liang, K.

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, Appl. Phys. B 105, 421 (2011).
[CrossRef]

Ma, Y.

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, Appl. Phys. B 105, 421 (2011).
[CrossRef]

Meador, W. E.

W. E. Meador, G. A. Miner, and L. W. Townsend, Phys. Fluids 8, 258 (1996).
[CrossRef]

Meijer, A. S.

M. O. Vieitez, E.-J. van Duijn, W. Ubachs, B. Witschas, A. S. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, Phys. Rev. A 82, 043836 (2010).
[CrossRef]

A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, J. Chem. Phys. 133, 164315 (2010).
[CrossRef]

Miles, R. B.

X. G. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 71, 045801 (2005).
[CrossRef]

X. G. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 69, 033814 (2004).
[CrossRef]

Miner, G. A.

W. E. Meador, G. A. Miner, and L. W. Townsend, Phys. Fluids 8, 258 (1996).
[CrossRef]

Pan, X. G.

X. G. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 71, 045801 (2005).
[CrossRef]

X. G. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 69, 033814 (2004).
[CrossRef]

Peters, M. F. E.

A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, J. Chem. Phys. 133, 164315 (2010).
[CrossRef]

Reitebuch, O.

Schoen, P. E.

Q. H. Lao, P. E. Schoen, and B. Chu, J. Chem. Phys. 64, 3547 (1976).
[CrossRef]

Shneider, M. N.

X. G. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 71, 045801 (2005).
[CrossRef]

X. G. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 69, 033814 (2004).
[CrossRef]

Tenti, G.

G. Tenti, C. D. Boley, and R. C. Desai, Can. J. Phys. 52, 285 (1974).

C. D. Boley, R. C. Desai, and G. Tenti, Can. J. Phys. 50, 2158 (1972).
[CrossRef]

Townsend, L. W.

W. E. Meador, G. A. Miner, and L. W. Townsend, Phys. Fluids 8, 258 (1996).
[CrossRef]

Ubachs, W.

Z. Y. Gu and W. Ubachs, Opt. Lett. 38, 1110 (2013).
[CrossRef]

Z. Y. Gu, M. O. Vieitez, E. J. van Duijn, and W. Ubachs, Rev. Sci. Instrum. 83, 053112 (2012).
[CrossRef]

M. O. Vieitez, E.-J. van Duijn, W. Ubachs, B. Witschas, A. S. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, Phys. Rev. A 82, 043836 (2010).
[CrossRef]

van de Water, W.

M. O. Vieitez, E.-J. van Duijn, W. Ubachs, B. Witschas, A. S. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, Phys. Rev. A 82, 043836 (2010).
[CrossRef]

A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, J. Chem. Phys. 133, 164315 (2010).
[CrossRef]

van Duijn, E. J.

Z. Y. Gu, M. O. Vieitez, E. J. van Duijn, and W. Ubachs, Rev. Sci. Instrum. 83, 053112 (2012).
[CrossRef]

van Duijn, E.-J.

M. O. Vieitez, E.-J. van Duijn, W. Ubachs, B. Witschas, A. S. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, Phys. Rev. A 82, 043836 (2010).
[CrossRef]

Vieitez, M. O.

Z. Y. Gu, M. O. Vieitez, E. J. van Duijn, and W. Ubachs, Rev. Sci. Instrum. 83, 053112 (2012).
[CrossRef]

M. O. Vieitez, E.-J. van Duijn, W. Ubachs, B. Witschas, A. S. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, Phys. Rev. A 82, 043836 (2010).
[CrossRef]

Witschas, B.

B. Witschas, C. Lemmerz, and O. Reitebuch, Opt. Lett. 39, 1972 (2014).
[CrossRef]

M. O. Vieitez, E.-J. van Duijn, W. Ubachs, B. Witschas, A. S. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, Phys. Rev. A 82, 043836 (2010).
[CrossRef]

Yu, Y.

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, Appl. Phys. B 105, 421 (2011).
[CrossRef]

Appl. Phys. B (1)

K. Liang, Y. Ma, J. Huang, H. Li, and Y. Yu, Appl. Phys. B 105, 421 (2011).
[CrossRef]

Can. J. Phys. (2)

C. D. Boley, R. C. Desai, and G. Tenti, Can. J. Phys. 50, 2158 (1972).
[CrossRef]

G. Tenti, C. D. Boley, and R. C. Desai, Can. J. Phys. 52, 285 (1974).

J. Chem. Phys. (2)

Q. H. Lao, P. E. Schoen, and B. Chu, J. Chem. Phys. 64, 3547 (1976).
[CrossRef]

A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, J. Chem. Phys. 133, 164315 (2010).
[CrossRef]

Opt. Lett. (2)

Phys. Fluids (1)

W. E. Meador, G. A. Miner, and L. W. Townsend, Phys. Fluids 8, 258 (1996).
[CrossRef]

Phys. Rev. A (3)

M. O. Vieitez, E.-J. van Duijn, W. Ubachs, B. Witschas, A. S. Meijer, A. S. de Wijn, N. J. Dam, and W. van de Water, Phys. Rev. A 82, 043836 (2010).
[CrossRef]

X. G. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 69, 033814 (2004).
[CrossRef]

X. G. Pan, M. N. Shneider, and R. B. Miles, Phys. Rev. A 71, 045801 (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

Z. Y. Gu, M. O. Vieitez, E. J. van Duijn, and W. Ubachs, Rev. Sci. Instrum. 83, 053112 (2012).
[CrossRef]

Other (3)

“ADM-Aeolus: Science Report,” (ESA Communication Production Office, 2008).

J. Lambert, Vibrational and Rotational Relaxation in Gases (Clarendon, 1977).

A. Chapman and T. G. Cowling, Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge Mathematical Library, 1970).

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Figures (2)

Fig. 1.
Fig. 1.

Schematic diagram of the experimental setup for spontaneous Rayleigh–Brillouin scattering (not to scale). The UV laser beam (full black line) is reflected several times in the enhancement cavity to increase the scattering intensity. A reference beam (gray line), split off the main beam, is used for detector alignment. Scattered light is detected at 90° using a pinhole, a Fabry–Perot interferometer, and a photomultiplier (PMT).

Fig. 2.
Fig. 2.

(a)–(d) CO2 Rayleigh–Brillouin scattering spectra at pressures p=1,2,3, and 4 bar and for conditions of 296.5±0.5K. The spectra are shown together with the Tenti S7 model; the lower line indicates the difference between the model and experiment. The model calculations include a convolution with the instrument function of the FP-analyzer. The used bulk viscosities are indicated by the open symbols in frame (f). (e) Lines are χ2 differences between the experimental spectra and the Tenti S7 model as a function of ηb, the open balls indicate the minimum χ2. (f) Symbols indicate the bulk viscosity obtained by fitting the Tenti model to the experimental spectra. Dots are for the Tenti S6 model, open balls are for the Tenti S7 model. Full line: prediction using Eq. (1) with two rotational degrees of freedom and relaxation time τr=3.8×1010s. The dashed line represents the prediction of Eq. 28 in [13]. The points at p=1.5bar (indicated with filled squares for an analysis with Tenti S6 and open squares for Tenti S7) were measured using 403.0 nm laser light, and an FP-analyzer with fFSR=7553MHz, and fw=139MHz. To avoid congestion, only the error bars for the S6 model are shown, those of the S7 model are roughly the same.

Equations (3)

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ηb=2nkBT|jNjτj(1+iωτj)1N(3+jNj(1+iωτj)1)|,
ηb=2nkBTjNjτj/N2.
S(f)={1+[(2fFSR/πfw)sin(πf/fFSR)]2}1,

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