Molecular simulation of Rayleigh-Brillouin scattering in binary gas mixtures and extraction of the rotational relaxation numbers

Rayleigh-Brillouin scattering (RBS) in gases has received considerable attention due to its applications in LIDAR (light detection and ranging) remote sensing and gas property measurements. In most cases, the RBS spectra in the kinetic regime are calculated based on kinetic model equations, which are difficult to be applied to complex gas mixtures. In this work, we employ two widely used molecular simulation methods, i.e., direct simulation Monte Carlo (DSMC) and molecular dynamics (MD), to calculate the spontaneous RBS spectra of binary gas mixtures. We validate these two methods by comparing the simulation results for mixtures of argon and helium with the experimental results. Then we extend the RBS calculations to gas mixtures involving polyatomic gases. The rotational relaxation numbers specific to each species pair in DSMC are determined by fitting the DSMC spectra to the MD spectra. Our results show that all the rotational relaxation numbers for air composed of ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ increase with temperature in the range of 300–750 K. We further calculate the RBS spectra for binary mixtures composed of ${\mathrm{N}}_2$ and one noble monatomic gas, and the simulation results show that the rotational relaxation of ${\mathrm{N}}_2$ is greatly affected by the mass of the noble gas atoms. This work demonstrates that RBS is a promising and alternative way to study the rotational relaxation process in gas mixtures.

Figure 1

Schematic of the spontaneous RBS experiments. $\vec{q}$ and $f$ represent the scattering wave vector and frequency in both directions for Stokes and anti-Stokes scattering.

Figure 2

RBS spectra of argon gas corresponding to different Y values. The spectra are obtained using the DSMC method (see Sec. 3a). Y is increased by changing pressure P from 0.5 to 3 bars, while the other parameters are fixed (${\lambda }_{\mathrm{in}}=403\mathrm{nm}$, $\theta ={40}^{\circ }$, $T=300\mathrm{K}$).

Figure 3

Schematic of the RBS calculation procedure. The simulation domain is displayed in the x-y plane.

Figure 4

Panels (a–d) show the comparison of MD calculated RBS spectra (blue solid line) with those measured from the experiments [28] (green square) under conditions presented in Table 6, and panels (e–h) show the corresponding residuals (solid line). Panel (c) also displays the RBS spectrum calculated by kinetic model equations [28] (red dotted line), and the residuals between kinetic model and MD results (dashed line) are shown in panel (g).

Figure 5

Comparison of DSMC (line) and MD (square) spectra under conditions given in Table 6.

Figure 6

Panels (a–c) show the comparison of MD calculated RBS spectra (line) with those measured from the experiments [22] (square) for the first group of conditions presented in Table 7, and panels (d–f) show the corresponding residuals.

Figure 7

Comparison of DSMC and MD spectra for ${\mathrm{N}}_2$ at (a) $T=297.3\mathrm{K}$, (b) $T=500\mathrm{K}$, and (c) $T=750\mathrm{K}$. The DSMC spectra correspond to the best fitting values of $Z_{{\mathrm{N}}_2\text{−}{\mathrm{N}}_2}$.

Figure 8

Comparison of DSMC and MD spectra for ${\mathrm{O}}_2$ at (a) $T=297.6\mathrm{K}$, (b) $T=500\mathrm{K}$, and (c) $T=750\mathrm{K}$. The DSMC spectra correspond to the best fitting values of $Z_{{\mathrm{O}}_2\text{−}{\mathrm{O}}_2}$.

Figure 9

The equilibrium rotational relaxation numbers $Z_{{\mathrm{N}}_2\text{−}{\mathrm{N}}_2}$ (a) and $Z_{{\mathrm{O}}_2\text{−}{\mathrm{O}}_2}$ (b) obtained from RBS calculations.

Figure 10

Comparison of DSMC and MD spectra for air at (a) $T=296.8\mathrm{K}$, (b) $T=500\mathrm{K}$, and (c) $T=750\mathrm{K}$.

Figure 11

(a) The $Z_{{\mathrm{N}}_2\text{−}{\mathrm{N}}_2}$, $Z_{{\mathrm{O}}_2\text{−}{\mathrm{O}}_2}$, $Z_{{\mathrm{N}}_2\text{−}{\mathrm{O}}_2}$, and $Z_{{\mathrm{O}}_2\text{−}{\mathrm{N}}_2}$ obtained from the RBS calculations. (b) The ${\mu }_b$ of ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and air calculated from the rotational relaxation numbers.

Figure 12

Comparison of DSMC and MD spectra for the ${\mathrm{N}}_2$-Ne (a) and ${\mathrm{N}}_2$-Ar (b) gas mixtures. Panels (c,d) show the corresponding residuals for the best fitting values of $Z_{{\mathrm{N}}_2\text{−}x}$.

Figure 13

Comparison of DSMC and MD spectra for the ${\mathrm{N}}_2$-Kr (a) and ${\mathrm{N}}_2$-Xe (b) gas mixtures. Panels (c,d) show the corresponding residuals for the best fitting values of $Z_{{\mathrm{N}}_2\text{−}x}$.

Figure 14

The changes of $Z_{{\mathrm{N}}_2\text{−}x}$, $Z_{{\mathrm{N}}_2-{\mathrm{N}}_2}$, and $Z_{{\mathrm{N}}_2,\mathrm{total}}$ against the mass ratio between species $x$ and ${\mathrm{N}}_2$. The error bars of the obtained $Z_{{\mathrm{N}}_2\text{−}x}$ are also displayed.