Measurement of Bulk Viscosity of CO₂ Based on Spontaneous Rayleigh-Brillouin Scattering

The spontaneous Rayleigh-Brillouin scattering spectra of CO ₂ 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 ₂ at different pressures and temperatures are obtained by the principle of minimum value of χ ² (normalized chi-square error) at the gigahertz frequency. It shows that the bulk viscosity of CO ₂ increases linearly with temperature, with a slope of (5.52±0.21)×10 ^-8 kgm ^-1 s ^-1 k ^-1 . Meanwhile, the differences in the measured bulk viscosity of CO ₂ 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 ₂ predicted by the obtained relation is used as a known parameter for the theoretical model to retrieve the temperature of CO ₂ 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 ₂ is credible not only under relative higher pressures (4 bar≤ p≤7 bar) but also under lower pressures (p<; 4 bar).