Measurement of Temperature-Dependent Bulk Viscosities of Nitrogen, Oxygen and Air From Spontaneous Rayleigh-Brillouin Scattering

Abstract

In this paper, the spontaneous Rayleigh-Brillouin scattering spectra of air are simulated to study the effect of uncertainties of pressure, temperature, scattering angle and the characteristic parameter uncertainty of the Fabry-Perot interferometer on the accurate measurement of the bulk viscosity. It is found that those uncertainties have an obvious impact on the bulk viscosity measurement deviation and the bulk viscosity can be measured accurately under higher pressures (≥3.0 bar). In order to obtain the accurate bulk viscosity of nitrogen, oxygen and air, the spontaneous Rayleigh-Brillouin scattering spectra are measured with the wavelength of 532 nm under pressure of 4.0-7.0 bar and at temperature from 289.0 K to 400.0 K. The linear relation between the measured bulk viscosity and temperature is established with R 2 being above 0.99 for nitrogen, oxygen and air respectively. By comparison, it is found that our measured bulk viscosities mostly agree with the reported values obtained by spontaneous Rayleigh-Brillouin scattering, coherent Rayleigh-Brillouin scattering, ultrasonic determination or theoretical calculation for nitrogen, oxygen and air within 3σ results at the same temperature. The factors arousing the differences between them are attributed to the obvious measurement error and the measured uncertainty of the bulk viscosity under low pressures and the defects in the theoretical model itself. The empirical formula for calculating the bulk viscosity for air from pure components is proposed and it can match our measured results well.INDEX TERMS Rayleigh-Brillouin scattering, bulk viscosity, empirical formula.

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

“…It needs to be stated that the relative intensity of Brillouin peak will decrease with the temperature increasing and this will induce a larger measured uncertainty of bulk viscosity for CO 2 . This result is similar to nitrogen, oxygen and air [9], [28] and is also proven in our following result.…”

“…For SRBS measurement, Wang stated that the value of η b /η s was not obviously dependent of temperature [18] but it is close to our results at the same temperature. According to the paper [28], the obvious measurement uncertainty under lower pressures (<4 bar) is the main factor that induces the difference between the paper [18] and our work. Meanwhile, the value of η b /η s of around 0.38 in our experiment is slightly larger than the value of 0.25 used in the paper [15] to describe the CRBS spectra of CO 2 under different pressures at 292 K, but close to the value of 0.39, 0.31 and 0.38 determined by Meijer et al [16], Lao et al [17] and Gu et al [11] at room temperatures.…”

“…For example, the measurement uncertainty of the bulk viscosity decreases from 1.4×10 −6 kgm −1 s −1 (17.5%) to 0.45×10 −6 kgm −1 s −1 (8.3%) with the pressure increasing from 1 bar to 4 bar in [11]. According to our preliminary work [28], the gaseous bulk viscosity can be determined accurately under higher pressures (4-7 bar). Therefore, in order to measure the bulk viscosity of CO 2 accurately and obtain the relation between it and the temperature, it is reasonable to measure η b under higher pressures due to the obvious Brillouin side features and the small measurement uncertainty.…”

“…The experimental setup developed to measure the SRBS spectra is similar to the papers [28], [31] and a brief introduction is made here. The laser with a wavelength of 532 nm and a power of 10 W is used to excite the gas SRBS.…”

“…According to [12], [28], the scattering angle θ mainly affects the total width of the Rayleigh-Brillouin scattering profile, while the bulk viscosity determines the pronounced occurrence of Brillouin side features; hence the two parameters are not strongly correlated. However, different values of the scattering angle will influence the place of minimal χ 2 , which determine the value of bulk viscosity.…”