Abstract
The spontaneous Rayleigh-Brillouin scattering spectra of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> are measured at different temperatures from 278 K to 369 K corresponding to the pressure range over 4-7 bar approximately and compared with the Tenti S6 model. The values of the bulk viscosity of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> at different pressures and temperatures are obtained by the principle of minimum value of χ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (normalized chi-square error) at the gigahertz frequency. It shows that the bulk viscosity of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> increases linearly with temperature, with a slope of (5.52±0.21)×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> kgm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . Meanwhile, the differences in the measured bulk viscosity of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and the ratio of bulk viscosity to shear viscosity between our work and the reported values by spontaneous or coherent Rayleigh-Brillouin scattering and theoretical calculation are analyzed. It is found that the changing of the ratio of bulk viscosity to shear viscosity with the temperature has the same tendency as the theoretical calculation, and the ratios agree with most reported values at the same temperatures, and the function between the ratio of bulk viscosity to shear viscosity and temperature is determined. In order to assess the accuracy of the obtained bulk viscosity in experiment, the bulk viscosity of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> predicted by the obtained relation is used as a known parameter for the theoretical model to retrieve the temperature of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> based on the measured SRBS spectrum under different pressures and temperatures. The absolute errors between the reference temperatures and the retrieved temperatures are less than 2.0 K. This result demonstrates that the obtained linear relationship between the temperature and the bulk viscosity of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> is credible not only under relative higher pressures (4 bar≤ p≤7 bar) but also under lower pressures (p<; 4 bar).
Highlights
Light scattering induced by particles smaller than the incident wavelength of light was studied by Rayleigh [1] more than a century ago
In order to assess the accuracy of the obtained linear relationship between the bulk viscosity of CO2 and the temperature, the measured spontaneous Rayleigh-Brillouin scattering (SRBS) spectra of CO2 at different temperatures under the pressures around 1-7 bar are used to retrieve temperatures based on the Tenti S6 model, which uses the predicted bulk viscosity of CO2 calculated from this linear relationship as a known parameter
In order to testify the accuracy of Equation (7) in experiment, the bulk viscosity of CO2 predicted by Equation (7) is used as a known parameter for the theoretical model to retrieve the temperature of CO2 based on the measured SRBS spectrum under the pressure approaching 1-3bar at the temperature of 282.2 K, 289.0 K, 293.8 K and 339.3 K, 5-6 bar at the temperature of 280.6 K, 286.3 K, 290.0 K, 293.0 K and 299.8 K, and 7 bar at the temperature of 360.0 K
Summary
Light scattering induced by particles smaller than the incident wavelength of light was studied by Rayleigh [1] more than a century ago. Published papers have shown that the measured bulk viscosities of CO2, which are obtained by comparing the measured CRBS or SRBS spectrum with the Tenti S6 model, are different. The SRBS spectra under higher pressures (around 4-7 bar) and at temperatures from 278 K to 369 K are measured and compared with the theoretically calculated spectra from the Tenti S6 model being convolved with instrument transmission function. In order to assess the accuracy of the obtained linear relationship between the bulk viscosity of CO2 and the temperature, the measured SRBS spectra of CO2 at different temperatures under the pressures around 1-7 bar are used to retrieve temperatures based on the Tenti S6 model, which uses the predicted bulk viscosity of CO2 calculated from this linear relationship as a known parameter.
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