Abstract

Rayleigh–Brillouin (RB) scattering profiles for air have been recorded for the temperature range from 255 to 340 K and the pressure range from 640 to 3300 mbar, covering the conditions relevant for the Earth’s atmosphere and for planned atmospheric light detection and ranging (LIDAR) missions. The measurements performed at a wavelength of λ=366.8nm detect spontaneous RB scattering at a 90° scattering angle from a sensitive intracavity setup, delivering scattering profiles at a 1% rms noise level or better. The experimental results have been compared to a kinetic line-shape model, the acclaimed Tenti S6 model, considered to be most appropriate for such conditions, under the assumption that air can be treated as an effective single-component gas with temperature-scaled values for the relevant macroscopic transport coefficients. The elusive transport coefficient, the bulk viscosity ηb, is effectively derived by a comparing the measurements to the model, yielding an increased trend from 1.0 to 2.5×105kg·m1·s1 for the temperature interval. The calculated (Tenti S6) line shapes are consistent with experimental data at the level of 2%, meeting the requirements for the future RB-scattering LIDAR missions in the Earth’s atmosphere. However, the systematic 2% deviation may imply that the model has a limit to describe the finest details of RB scattering in air. Finally, it is demonstrated that the RB scattering data in combination with the Tenti S6 model can be used to retrieve the actual gas temperatures.

© 2013 Optical Society of America

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    [CrossRef]
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  25. H. B. Zhang, Z. J. Yuan, J. Zhou, J. X. Dong, Y. R. Wei, and Q. H. Lou, “Laser-induced fluorescence of fused silica irradiated by ArF excimer laser,” J. Appl. Phys. 110, 013107 (2011).
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    [CrossRef]

2013

2012

B. M. Cornella, S. F. Gimelshein, M. N. Shneider, T. C. Lilly, and A. D. Ketsdever, “Experimental and numerical analysis of narrowband coherent Rayleigh–Brillouin scattering in atomic and molecular species,” Opt. Express 20, 12975–12986 (2012).
[CrossRef]

B. Witschas, C. Lemmerz, and O. Reitebuch, “Horizontal LIDAR measurements for the proof of spontaneous Rayleigh–Brillouin scattering in the atmosphere,” Appl. Opt. 51, 6207–6219 (2012).
[CrossRef]

Z. Y. Gu, M. O. Vieitez, E. J. van Duijn, and W. Ubachs, “A Rayleigh–Brillouin scattering spectrometer for ultraviolet wavelengths,” Rev. Sci. Instrum. 83, 053112 (2012).
[CrossRef]

K. Liang, Y. Ma, Y. Yu, J. Huang, and H. Li, “Research on simultaneous measurement of ocean temperature and salinity using Brillouin shift and linewidth,” Opt. Eng. 51, 066002 (2012).
[CrossRef]

2011

H. B. Zhang, Z. J. Yuan, J. Zhou, J. X. Dong, Y. R. Wei, and Q. H. Lou, “Laser-induced fluorescence of fused silica irradiated by ArF excimer laser,” J. Appl. Phys. 110, 013107 (2011).
[CrossRef]

2010

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, “Coherent and spontaneous Rayleigh–Brillouin scattering in atomic and molecular gases and gas mixtures,” 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, “Coherent Rayleigh–Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory,” J. Chem. Phys. 133, 164315 (2010).
[CrossRef]

B. Witschas, M. O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, and W. Ubachs, “Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air,” Appl. Opt. 49, 4217–4227 (2010).
[CrossRef]

2009

K. Schorstein, E. S. Fry, and T. Walther, “Depth-resolved temperature measurements of water using the Brillouin LIDAR technique,” Appl. Phys. B 97, 931–934 (2009).
[CrossRef]

2005

X. G. Pan, M. N. Shneider, and R. B. Miles, “Power spectrum of coherent Rayleigh–Brillouin scattering in carbon dioxide,” Phys. Rev. A 71, 045801 (2005).
[CrossRef]

M. Sneep and W. Ubachs, “Direct measurement of the Rayleigh scattering cross section in various gases,” J. Quant. Spectrosc. Radiat. Transfer 92, 293–310 (2005).
[CrossRef]

2004

X. G. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh–Brillouin scattering in molecular gases,” Phys. Rev. A 69, 033814 (2004).
[CrossRef]

2003

2002

X. G. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh–Brillouin scattering,” Phys. Rev. Lett. 89, 183001 (2002).
[CrossRef]

2000

1999

R. E. Graves and B. M. Argow, “Bulk viscosity: past to present,” J. Thermophys. Heat Transfer 13, 337–342 (1999).
[CrossRef]

1986

1983

1974

G. Tenti, C. D. Boley, and R. C. Desai, “On the kinetic model description of Rayleigh–Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

1973

G. J. Prangsma, A. H. Alberga, and J. J. M. Beenakker, “Ultrasonic determination of the volume viscosity of N2, CO, CH4, and CD4 between 77 and 300 K,” Physica 64, 278–288 (1973).
[CrossRef]

1972

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50, 2158–2173 (1972).
[CrossRef]

1942

L. Tisza, “Supersonic absorption and Stokes’ viscosity relation,” Phys. Rev. 61, 531–536 (1942).
[CrossRef]

1899

J. W. Strutt, “On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky,” Philos. Mag. 47, 375–384 (1899).

Alberga, A. H.

G. J. Prangsma, A. H. Alberga, and J. J. M. Beenakker, “Ultrasonic determination of the volume viscosity of N2, CO, CH4, and CD4 between 77 and 300 K,” Physica 64, 278–288 (1973).
[CrossRef]

Argow, B. M.

R. E. Graves and B. M. Argow, “Bulk viscosity: past to present,” J. Thermophys. Heat Transfer 13, 337–342 (1999).
[CrossRef]

Beenakker, J. J. M.

G. J. Prangsma, A. H. Alberga, and J. J. M. Beenakker, “Ultrasonic determination of the volume viscosity of N2, CO, CH4, and CD4 between 77 and 300 K,” Physica 64, 278–288 (1973).
[CrossRef]

Boley, C. D.

G. Tenti, C. D. Boley, and R. C. Desai, “On the kinetic model description of Rayleigh–Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50, 2158–2173 (1972).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2008).

Chapman, S.

S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases (Cambridge University, 1991).

Cornella, B. M.

Cowling, T. G.

S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases (Cambridge University, 1991).

Dai, R.

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, “Coherent and spontaneous Rayleigh–Brillouin scattering in atomic and molecular gases and gas mixtures,” 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, “Coherent Rayleigh–Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory,” J. Chem. Phys. 133, 164315 (2010).
[CrossRef]

de Boer, J.

C. S. Wang-Chang, G. E. Uhlenbeck, and J. de Boer, Studies in Statistical Mechaincs (North-Holland, 1964).

de Wijn, A. S.

A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, “Coherent Rayleigh–Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory,” 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, “Coherent and spontaneous Rayleigh–Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 043836 (2010).
[CrossRef]

Desai, R. C.

G. Tenti, C. D. Boley, and R. C. Desai, “On the kinetic model description of Rayleigh–Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50, 2158–2173 (1972).
[CrossRef]

Dong, J. X.

H. B. Zhang, Z. J. Yuan, J. Zhou, J. X. Dong, Y. R. Wei, and Q. H. Lou, “Laser-induced fluorescence of fused silica irradiated by ArF excimer laser,” J. Appl. Phys. 110, 013107 (2011).
[CrossRef]

Fry, E. S.

K. Schorstein, E. S. Fry, and T. Walther, “Depth-resolved temperature measurements of water using the Brillouin LIDAR technique,” Appl. Phys. B 97, 931–934 (2009).
[CrossRef]

Gimelshein, S. F.

Gong, W. P.

Graves, R. E.

R. E. Graves and B. M. Argow, “Bulk viscosity: past to present,” J. Thermophys. Heat Transfer 13, 337–342 (1999).
[CrossRef]

Gu, Z. Y.

Z. Y. Gu and W. Ubachs, “Temperature-dependent bulk viscosity of nitrogen gas determined from spontaneous Rayleigh–Brillouin scattering,” Opt. Lett. 38, 1110–1112 (2013).
[CrossRef]

Z. Y. Gu, M. O. Vieitez, E. J. van Duijn, and W. Ubachs, “A Rayleigh–Brillouin scattering spectrometer for ultraviolet wavelengths,” Rev. Sci. Instrum. 83, 053112 (2012).
[CrossRef]

Huang, J.

K. Liang, Y. Ma, Y. Yu, J. Huang, and H. Li, “Research on simultaneous measurement of ocean temperature and salinity using Brillouin shift and linewidth,” Opt. Eng. 51, 066002 (2012).
[CrossRef]

Kattawar, G. W.

Ketsdever, A. D.

Lemmerz, C.

Li, H.

K. Liang, Y. Ma, Y. Yu, J. Huang, and H. Li, “Research on simultaneous measurement of ocean temperature and salinity using Brillouin shift and linewidth,” Opt. Eng. 51, 066002 (2012).
[CrossRef]

Liang, K.

K. Liang, Y. Ma, Y. Yu, J. Huang, and H. Li, “Research on simultaneous measurement of ocean temperature and salinity using Brillouin shift and linewidth,” Opt. Eng. 51, 066002 (2012).
[CrossRef]

Lilly, T. C.

Liu, D. H.

Lou, Q. H.

H. B. Zhang, Z. J. Yuan, J. Zhou, J. X. Dong, Y. R. Wei, and Q. H. Lou, “Laser-induced fluorescence of fused silica irradiated by ArF excimer laser,” J. Appl. Phys. 110, 013107 (2011).
[CrossRef]

Ma, Y.

K. Liang, Y. Ma, Y. Yu, J. Huang, and H. Li, “Research on simultaneous measurement of ocean temperature and salinity using Brillouin shift and linewidth,” Opt. Eng. 51, 066002 (2012).
[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, “Coherent and spontaneous Rayleigh–Brillouin scattering in atomic and molecular gases and gas mixtures,” 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, “Coherent Rayleigh–Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory,” J. Chem. Phys. 133, 164315 (2010).
[CrossRef]

Miles, R. B.

X. G. Pan, M. N. Shneider, and R. B. Miles, “Power spectrum of coherent Rayleigh–Brillouin scattering in carbon dioxide,” Phys. Rev. A 71, 045801 (2005).
[CrossRef]

X. G. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh–Brillouin scattering in molecular gases,” Phys. Rev. A 69, 033814 (2004).
[CrossRef]

X. G. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh–Brillouin scattering,” Phys. Rev. Lett. 89, 183001 (2002).
[CrossRef]

Naus, H.

Noguchi, K.

Pan, X.

X. Pan, “Coherent Rayleigh–Brillouin scattering,” Ph.D. Thesis (Princeton University, 2003).

Pan, X. G.

X. G. Pan, M. N. Shneider, and R. B. Miles, “Power spectrum of coherent Rayleigh–Brillouin scattering in carbon dioxide,” Phys. Rev. A 71, 045801 (2005).
[CrossRef]

X. G. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh–Brillouin scattering in molecular gases,” Phys. Rev. A 69, 033814 (2004).
[CrossRef]

X. G. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh–Brillouin scattering,” Phys. Rev. Lett. 89, 183001 (2002).
[CrossRef]

Peters, M. F. E.

A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, “Coherent Rayleigh–Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory,” J. Chem. Phys. 133, 164315 (2010).
[CrossRef]

Prangsma, G. J.

G. J. Prangsma, A. H. Alberga, and J. J. M. Beenakker, “Ultrasonic determination of the volume viscosity of N2, CO, CH4, and CD4 between 77 and 300 K,” Physica 64, 278–288 (1973).
[CrossRef]

Reitebuch, O.

Ren, X. B.

Rossing, T. D.

T. D. Rossing, Springer Handbook of Acoustics (Springer, 2007).

Schorstein, K.

K. Schorstein, E. S. Fry, and T. Walther, “Depth-resolved temperature measurements of water using the Brillouin LIDAR technique,” Appl. Phys. B 97, 931–934 (2009).
[CrossRef]

She, C. Y.

Shimizu, H.

Shneider, M. N.

B. M. Cornella, S. F. Gimelshein, M. N. Shneider, T. C. Lilly, and A. D. Ketsdever, “Experimental and numerical analysis of narrowband coherent Rayleigh–Brillouin scattering in atomic and molecular species,” Opt. Express 20, 12975–12986 (2012).
[CrossRef]

X. G. Pan, M. N. Shneider, and R. B. Miles, “Power spectrum of coherent Rayleigh–Brillouin scattering in carbon dioxide,” Phys. Rev. A 71, 045801 (2005).
[CrossRef]

X. G. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh–Brillouin scattering in molecular gases,” Phys. Rev. A 69, 033814 (2004).
[CrossRef]

X. G. Pan, M. N. Shneider, and R. B. Miles, “Coherent Rayleigh–Brillouin scattering,” Phys. Rev. Lett. 89, 183001 (2002).
[CrossRef]

Sneep, M.

M. Sneep and W. Ubachs, “Direct measurement of the Rayleigh scattering cross section in various gases,” J. Quant. Spectrosc. Radiat. Transfer 92, 293–310 (2005).
[CrossRef]

Strutt, J. W.

J. W. Strutt, “On the transmission of light through an atmosphere containing small particles in suspension, and on the origin of the blue of the sky,” Philos. Mag. 47, 375–384 (1899).

Tenti, G.

G. Tenti, C. D. Boley, and R. C. Desai, “On the kinetic model description of Rayleigh–Brillouin scattering from molecular gases,” Can. J. Phys. 52, 285–290 (1974).

C. D. Boley, R. C. Desai, and G. Tenti, “Kinetic models and Brillouin scattering in a molecular gas,” Can. J. Phys. 50, 2158–2173 (1972).
[CrossRef]

Tisza, L.

L. Tisza, “Supersonic absorption and Stokes’ viscosity relation,” Phys. Rev. 61, 531–536 (1942).
[CrossRef]

Ubachs, W.

Z. Y. Gu and W. Ubachs, “Temperature-dependent bulk viscosity of nitrogen gas determined from spontaneous Rayleigh–Brillouin scattering,” Opt. Lett. 38, 1110–1112 (2013).
[CrossRef]

Z. Y. Gu, M. O. Vieitez, E. J. van Duijn, and W. Ubachs, “A Rayleigh–Brillouin scattering spectrometer for ultraviolet wavelengths,” 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, “Coherent and spontaneous Rayleigh–Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 043836 (2010).
[CrossRef]

B. Witschas, M. O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, and W. Ubachs, “Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air,” Appl. Opt. 49, 4217–4227 (2010).
[CrossRef]

M. Sneep and W. Ubachs, “Direct measurement of the Rayleigh scattering cross section in various gases,” J. Quant. Spectrosc. Radiat. Transfer 92, 293–310 (2005).
[CrossRef]

H. Naus and W. Ubachs, “Experimental verification of Rayleigh scattering cross sections,” Opt. Lett. 25, 347–349 (2000).
[CrossRef]

Uhlenbeck, G. E.

C. S. Wang-Chang, G. E. Uhlenbeck, and J. de Boer, Studies in Statistical Mechaincs (North-Holland, 1964).

van de Water, W.

B. Witschas, M. O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, and W. Ubachs, “Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air,” Appl. Opt. 49, 4217–4227 (2010).
[CrossRef]

A. S. Meijer, A. S. de Wijn, M. F. E. Peters, N. J. Dam, and W. van de Water, “Coherent Rayleigh–Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory,” 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, “Coherent and spontaneous Rayleigh–Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 043836 (2010).
[CrossRef]

van Duijn, E. J.

Z. Y. Gu, M. O. Vieitez, E. J. van Duijn, and W. Ubachs, “A Rayleigh–Brillouin scattering spectrometer for ultraviolet wavelengths,” 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, “Coherent and spontaneous Rayleigh–Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 043836 (2010).
[CrossRef]

B. Witschas, M. O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, and W. Ubachs, “Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air,” Appl. Opt. 49, 4217–4227 (2010).
[CrossRef]

Vieitez, M. O.

Z. Y. Gu, M. O. Vieitez, E. J. van Duijn, and W. Ubachs, “A Rayleigh–Brillouin scattering spectrometer for ultraviolet wavelengths,” 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, “Coherent and spontaneous Rayleigh–Brillouin scattering in atomic and molecular gases and gas mixtures,” Phys. Rev. A 82, 043836 (2010).
[CrossRef]

B. Witschas, M. O. Vieitez, E.-J. van Duijn, O. Reitebuch, W. van de Water, and W. Ubachs, “Spontaneous Rayleigh–Brillouin scattering of ultraviolet light in nitrogen, dry air, and moist air,” Appl. Opt. 49, 4217–4227 (2010).
[CrossRef]

Walther, T.

K. Schorstein, E. S. Fry, and T. Walther, “Depth-resolved temperature measurements of water using the Brillouin LIDAR technique,” Appl. Phys. B 97, 931–934 (2009).
[CrossRef]

Wang-Chang, C. S.

C. S. Wang-Chang, G. E. Uhlenbeck, and J. de Boer, Studies in Statistical Mechaincs (North-Holland, 1964).

Wei, Y. R.

H. B. Zhang, Z. J. Yuan, J. Zhou, J. X. Dong, Y. R. Wei, and Q. H. Lou, “Laser-induced fluorescence of fused silica irradiated by ArF excimer laser,” J. Appl. Phys. 110, 013107 (2011).
[CrossRef]

White, F. M.

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Figures (8)

Fig. 1.
Fig. 1.

Graphical representation of the procedure for verifying the scattering angle θ; (a) Residuals between the experimental RB-scattering profile, measured for 337.7 K and 3.30 bar, and the Tenti S6 calculations for three selected scattering angles: 89.2°, 89.8°, and 90.4°; note that a value of ηb=2.36×105kg·m1·s1, a result of the present study, was adopted to produce the theoretical curve. (b) Values of χ2, calculated according to the residuals, as a function of scattering angle used for Tenti S6 modeling. The green line is the parabolic fit to the χ2 values, giving a minimum at 89.8°. The estimated error (1σ) for this angle determination is less than 0.1°. (c) Optimized scattering angles together with their standard errors for all the measurements in data Set III.

Fig. 2.
Fig. 2.

Data Set I: normalized RB scattering profiles of air recorded at λ=366.8nm for pressures 725mbar and temperatures as indicated. The scattering angle for this data set was determined as θ=90.2° in the previous section. Experimental data (black dots) are compared with the convolved Tenti S6 model calculations (red line), with the input parameters listed in Table 1. Values of ηb at different temperatures are calculated from Eq. (9).

Fig. 3.
Fig. 3.

Data Set II: normalized RB scattering profiles of air recorded for pressures 1000mbar and temperatures as indicated. The scattering angle for this data set was determined as θ=90.4° in the previous section. Values of ηb at different temperatures are calculated from Eq. (9).

Fig. 4.
Fig. 4.

Measurement Set III: normalized RB scattering profiles of air recorded for pressures 3000mbar. The scattering angle for this data set was determined as θ=89.7° in the previous section. Values of ηb at different temperatures are directly obtained from the least-squared fit.

Fig. 5.
Fig. 5.

(a) Experimental RB scattering profile in air for 3.30 bar and 337.7 K (black dots), and convolved Tenti S6 calculations for bulk viscosity being 1.3×105 (green line), 2.4×105 (red line), and 3.5×105 (yellow line) kg·m1·s1, respectively. (b) Residuals between measured and theoretical scattering profiles for three values of the bulk viscosity. The vertical dotted lines indicate the frequency where the Brillouin side peaks occur. (c)  Plot of the χ2 as a function of bulk viscosity. The optimized value of bulk viscosity is found at the minimum of χ2=1.68. The statistical error for this fit is 0.6×106kg·m1·s1.

Fig. 6.
Fig. 6.

Bulk viscosities ηb for air plotted as a function of temperature (black rectangular symbols) as determined from RB-scattering measurements around 3 bar air pressure and at λ=366.8nm. The black straight line represents a linear fit to the experimental ηb values (see text). A comparison is made with values for the shear viscosity η (blue upper triangles) calculated by Eq. (5) in [19]. The blue dashed line is a linear fit to the η values. The (red) circular dots represent the values of derived bulk viscosity when stray light is taken into account. Note that the red dots are offset to the right by 2 K to circumvent overlap of data points.

Fig. 7.
Fig. 7.

Comparison of residuals for four selected sample measurements of RB scattering profiles in air for (p, T) conditions without and with stray light included.

Fig. 8.
Fig. 8.

Temperature retrieval from RB-scattering profiles in air. The derived temperatures for (a) data Set I and (b) data Set II, as function of measured temperatures. The dashed lines indicate where derived and measured values are equivalent.

Tables (1)

Tables Icon

Table 1. Conditions and Values of Transport Coefficients for the RB Scattering Measurementsa

Equations (9)

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y=pkv0η=NkBTkv0η,
fb=2nfvcsin(θ2),
Δρ=(ρs)p·Δs,
Δρ=(ρp)s·Δp,
η=η0·(TT0)3/2·T0+TηT+Tη,
κ=κ0·(TT0)3/2·T0+TA·eTB/T0T+TA·eTB/T,
χ2=1Ni=1N[Ie(fi)Im(fi)]2σ2(fi),
σηb=(N2d2χ2dηb2|η˜b)1/2,
ηb=a+b·T.

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