Rayleigh-Brillouin light scattering spectroscopy of air; experiment, predictive model and dimensionless scaling

Abstract

Spontaneous Rayleigh-Brillouin scattering (RBS) experiments have been performed in air for pressures in the range 0.25 - 3 bar and temperatures in the range 273 - 333 K. The functional behaviour of the RB-spectral profile as a function of experimental parameters, such as the incident wavelength, scattering angle, pressure and temperature is analyzed, as well as the dependence on thermodynamic properties of the gas, as the shear viscosity, the thermal conductivity, the internal heat capacity and the bulk viscosity. Measurements are performed in a scattering geometry detecting at a scattering angle $\theta=55.7^\circ$ and an incident wavelength of $\lambda_i=532.22$ nm, at which the Brillouin features become more pronounced than in a right angles geometry and for ultraviolet light. For pressure conditions of 1 - 3 bar the RB-spectra, measured at high signal-to-noise ratio, are compared to Tenti-S6 model calculations and values for the bulk viscosity of air are extracted. Values of $\eta_b$ are found to exhibit a linear dependence on temperature over the measurement interval in the range $1.0 - 2.0 \times 10^{-5}$ Pa$\cdot$s. A temperature dependent value is deduced from a collection of experiments to yield: $\eta_{\rm b} = (0.86 \times 10^{-5}) + 1.29 \times 10^{-7} \cdot (T - 250)$. These results are implemented in model calculations that were verified for the low pressure conditions ($p < 1$ bar) relevant for the Earth's atmosphere. As a result we demonstrate that the RB-scattering spectral profiles for air under sub-atmospheric conditions can be generated via the Tenti-S6 model, for given gas-phase and detection conditions ($p$, $T$, $\lambda_i$, and $\theta$), and for values for the gas transport coefficients.