Rayleigh-Brillouin scattering in binary mixtures of disparate-mass constituents: ${\mathrm{SF}}_6\text{−}\mathrm{He},{\mathrm{SF}}_6\text{−}{\mathrm{D}}_2$, and ${\mathrm{SF}}_6\text{−}{\mathrm{H}}_2$

The spectral distribution of light scattered by microscopic thermal fluctuations in binary mixture gases was investigated experimentally and theoretically. Measurements of Rayleigh-Brillouin spectral profiles were performed at a wavelength of 532 nm and at room temperature, for mixtures of ${\mathrm{SF}}_6\text{−}\mathrm{He},{\mathrm{SF}}_6\text{−}{\mathrm{D}}_2$, and ${\mathrm{SF}}_6\text{−}{\mathrm{H}}_2$. In these measurements, the pressure of the gases with heavy molecular mass $\left({\mathrm{SF}}_6\right)$ is set at 1 bar, while the pressure of the lighter collision partner was varied. In view of the large polarizability of ${\mathrm{SF}}_6$ and the very small polarizabilities of He, ${\mathrm{H}}_2$, and ${\mathrm{D}}_2$, under the chosen pressure conditions these low mass species act as spectators and do not contribute to the light scattering spectrum, while they influence the motion and relaxation of the heavy ${\mathrm{SF}}_6$ molecules. A generalized hydrodynamic model was developed that should be applicable for the particular case of molecules with heavy and light disparate masses, as is the case for the heavy ${\mathrm{SF}}_6$ molecule, and the lighter collision partners. Based on the kinetic theory of gases, our model replaces the classical Navier-Stokes-Fourier relations with constitutive equations having an exponential memory kernel. The energy exchange between translational and internal modes of motion is included and quantified with a single parameter $z$ that characterizes the ratio between the mean elastic and inelastic molecular collision frequencies. The model is compared with the experimental Rayleigh-Brillouin scattering data, where the value of the parameter $z$ is determined in a least-squares procedure. Where very good agreement is found between experiment and the generalized hydrodynamic model, the computations in the framework of classical hydrodynamics strongly deviate. Only in the hydrodynamic regime both models are shown to converge.

Figure 1

Comparison of computations of the RB-scattering profiles between generalized macroscopic theory vs classical hydrodynamics approach for mixtures with internal relaxation number $z=10$ for varying scattering angles $\theta$ and the case of $p=1$ bar ${\mathrm{SF}}_6$ in a mixture with $p=1$ bar of helium.

Figure 2

Schematic diagram of the experimental setup for spontaneous Rayleigh-Brillouin scattering at 532 nm. A Verdi-V5 laser provides continuous wave light at 532.22 nm, at a power of 5 Watt and bandwidth less than 5 MHz. The laser light is split into two beams. The pump beam crosses the RB-scattering gas cell producing scattered light that is captured under an angle $\theta ={(55.7\pm 0.3)}^{\circ }$. A small fraction of the power, retained in a reference beam transmitted through ${\mathrm{M}}_4$, is used to align the beam path after the gas cell towards the detector. The scattered light after a bandpass filter (${\mathrm{F}}_{\mathrm{BW}}$) is analyzed in a Fabry-Perot interferometer (FPI), with free spectral range of 2.9964 GHz and an instrument linewidth of ($58\pm 3$) MHz, and is collected on a photo-multiplier tube (PMT). Mirrors, lenses, and diaphragm pinholes are indicated as ${\mathrm{M}}_i,{\mathrm{L}}_i$, and ${\mathrm{D}}_i$. A slit of 500 $\mu \mathrm{m}$ is inserted to limit the opening angle for collecting scattering light, therewith optimizing the resolution.

Figure 3

Measured Rayleigh-Brillouin scattering profiles (black) of binary mixtures of ${\mathrm{SF}}_6$-He as measured for the various conditions as indicated, and a comparison with the binary the mixture model (red). Also an RBS spectrum of pure ${\mathrm{SF}}_6$, at 1 bar, is shown for comparison. Bottom graphs display the corresponding residuals. The experimental data were measured at wavelength of ${\lambda }_i$ = 532.22 nm and scattering angle of $\theta =55.7^{\circ }$, and these spectra are on a scale of normalized integrated intensity over one FSR.

Figure 4

Same as Fig. 3 now for ${\mathrm{SF}}_6$/${\mathrm{D}}_2$ mixtures.

Figure 5

Same as Fig. 3 now for ${\mathrm{SF}}_6$/${\mathrm{H}}_2$ mixtures.

Figure 6

The value of $z$ derived from the comparison between experimental spectra and computed spectra for generalized hydrodynamics, for all pressure combinations, and for the three mixtures of ${\mathrm{SF}}_6\text{−}\mathrm{He},{\mathrm{SF}}_6\text{−}{\mathrm{D}}_2$, and ${\mathrm{SF}}_6\text{−}{\mathrm{H}}_2$. The derived uncertainties are also indicated.

Figure 7

Direct comparison of experimental Rayleigh-Brillouin scattering profiles for 1 bar ${\mathrm{SF}}_6$, admixed with 1 bar of the three light collision partners He, ${\mathrm{H}}_2$, and ${\mathrm{D}}_2$.

Figure 8

Comparisons between the measured Rayleigh-Brillouin scattering profiles of binary mixtures of ${\mathrm{SF}}_6$-He and generalized relaxation hydrodynamics theory as well as for the classical hydrodynamics approach for mixtures. The experimental data were measured with 1 bar ${\mathrm{SF}}_6$ and 1 bar He at wavelength of ${\lambda }_i$ = 532.22 nm and scattering angle of $\theta =55.7^{\circ }$. The theoretical spectra are, for the purpose of comparison with experiment, convolved with the instrumental width of 58 MHz. The spectra are plotted on a scale of normalized integrated intensity over one FSR.