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Rayleigh-Brillouin scattering in binary mixtures of disparate-mass constituents: SF$_6-$He, SF$_6-$D$_2$ and SF$_6-$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 SF$_6-$He, SF$_6-$D$_2$ and SF$_6-$H$_2$. In these measurements, the pressure of the gases with heavy molecular mass (SF$_6$) is set at 1 bar, while the pressure of the lighter collision partner was varied. In view of the large polarizability of SF$_6$ and the very small polarizabilities of He, H$_2$ and 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 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 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.