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 θ = 55.7 • and an incident wavelength of λi = 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 η b are found to exhibit a linear dependence on temperature over the measurement interval in the range 1.0 − 2.0 × 10 −5 Pa•s. A temperature dependent value is deduced from a collection of experiments to yield: η b = (0.86 × 10 −5) + 1.29 × 10 −7 • (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 , λi, and θ), and for values for the gas transport coefficients. Spectral profiles for coherent RB-scattering in air are also computed, based on the Tenti-S6 formalism, and the predictions are compared with profiles of spontaneous RBS. Finally data on RB-scattering in air, obtained under a variety of pressure, temperature, wavelength and scattering angles, are analyzed in terms of universal scaling, involving the dimensionless uniformity parameter y and the dimensionless frequency x. Such scaling behaviour is shown to be well behaved for a wide parameter space and implies that RB-scattering spectra can be generated for a wide range of atmospheric applications of RB-scattering. The verification of this dimensionless scaling also shows that air can be treated as an ideal gas in the atmospheric regime, where y ≤ 1.

Grüneisen approach for universal scaling of the Brillouin shift in gases

“…The choice for an angle closer to forward scattering than the usual choice of perpendicular scattering (θ = 90 • ) provides conditions where the Brillouin side peaks are more pronounced. A similar reasoning holds for the use of green light (532 nm) resulting in more pronounced side peaks than for blue or ultraviolet light [23]. The gas scattering cell, equipped with Brewster windows, can be operated at elevated pressures up to 8 bar and a temperature control system is used to keep it at a constant temperature with uncertainty less than 0.1 • C. The RB-scattered light, collected under the fixed scattering angle, is constrained by a slit for a narrow opening angle of 0.5 • to accurately define the scattering geometry.…”

“…In the opposite case, the Knudsen regime with y 1, the Rayleigh peak and the Brillouin peaks in the RBS spectrum are completely overlapped and the Brillouin side peaks cannot be discriminated. For the intermediary or kinetic regime, y = O(1), the overlapping area between the Rayleigh and Brillouin side peaks becomes less [23].…”

Rayleigh-Brillouin scattering in binary mixtures of disparate-mass constituents: SF6−He,SF6−D2 , and Wang1, Ubachs2, Moraes3 et al. 2021Phys. Rev. ESelf Cite

“…For the present experiments a scattering angle θ = 55.7 ± 0.3 • is adopted, because at angles smaller than the usual setting of θ = 90 • the Brillouin side peaks become more pronounced [20,21]. The angle was determined by a homemade rotation goniometer stage, while the opening angle is less than 0.5 • , calculated from the geometry of a slit set behind the gas cell at a certain distance from the scattering center.…”

“…with k i and λ i the wave vector and wavelength of the incident light, n the refractive index, and θ the scattering angle [21]. This sets the dependence of the dynamic structure factor on the experimental conditions.…”

Rayleigh-Brillouin scattering in binary mixtures of disparate-mass constituents: SF$_6-$He, SF$_6-$D$_2$ and SF$_6-$H$_2$

“…For the present experiments a scattering angle θ = 55.7 ± 0.3 • is adopted, because at angles smaller than the usual setting of θ = 90 • C the Brillouin side peaks become more pronounced [20,21]. The angle was determined by a homemade rotation goniometer stage, while the opening angle is less than 0.5 • , calculated from the geometry of a slit set behind the gas cell at a certain distance from the scattering center.…”