Oscillatory pressure-driven rarefied binary gas mixture flow between parallel plates

The rarefied, oscillatory, pressure-driven binary gas mixture flow between parallel plates is computationally investigated in terms of the mixture molar fraction and molecular mass ratio of the species, in a wide range of gas rarefaction and oscillation frequency. Modeling is based on the McCormack kinetic model. The output quantities are in dimensionless form and include the flow rate, wall shear stress and pumping power of the mixture, as well as the velocity and shear stress distributions and flow rates of the species. The presented results are for He-Xe and Ne-Ar. The heavier species are affected more drastically than the lighter ones from the inertial forces, resulting to large differences between the flow rate amplitudes of the species, which are increased as the flow becomes less rarefied, provided that the oscillation frequency is adequately high. At very high frequencies the ratio of the flow rate amplitudes of the light over the heavy species tends to the inverse of their molecular mass ratio in the whole range of gas rarefaction. The velocity overshooting effect becomes more pronounced as the molecular mass is increased. The mixture flow rate amplitude is larger, while its phase angle is smaller, than the corresponding ones of single gas, and they both vary nonmonotonically with the molar fraction. The effect of the mixture composition on the wall shear stress and pumping power is small. The present work may be useful in the design of gas separation devices, operating at moderate and high frequencies in rarefied and dense atmospheres.

Figure 1

Velocity amplitude $u_{\alpha }^{\left(A\right)}\left(y\right)$ and phase angle $u_{\alpha }^{\left(P\right)}\left(y\right)$ (rad) of each species of He-Xe, with $C=0.5$, for $\delta =\left[0.1,10\right]$ and $\theta =0.1$ ($\square$), $\theta =1$ ($▵$), $\theta =10$ ($▿$) (He: solid lines, Xe: dashed lines).

Figure 2

Velocity amplitude $u_{\alpha }^{\left(A\right)}\left(y\right)$ and phase angle $u_{\alpha }^{\left(P\right)}\left(y\right)$ (rad) of each species of He-Xe, with $C=0$ ($\square$), $C=0.1$ ($▵$), $C=0.5$ ($\nabla$), $C=0.9$ ($◯$), for $\delta =1$ and $\theta =1$ (He: solid lines, Xe: dashed lines).

Figure 3

Velocity and shear stress amplitudes $u_{\alpha }^{\left(A\right)}\left(y\right)$ and ${\varpi }_{\alpha }^{\left(A\right)}\left(y\right)$ of each species of He-Xe, with $C=\left[0.1,0.4,0.7,0.9\right]$ for $\delta =10$ and $\theta =0.1$.

Figure 4

Mixture flow rate amplitude $G^{\left(A\right)}$ and phase angle $G^{\left(P\right)}$ (rad) of He-Xe in terms of $\delta \in \left[{10}^{-4},{10}^2\right]$, with $C=[0,0.25,0.5,0.75,0.9]$ and $\theta =\left[1,10,{10}^2\right]$.

Figure 5

Mixture flow rate amplitude $G^{\left(A\right)}$ and phase angle $G^{\left(P\right)}$ (rad) of He-Xe and Ne-Ar in terms of the molar fraction $C$ for $\delta =1$ and $\theta =\left[{10}^{-1},1,10,50,{10}^2\right]$.

Figure 6

Ratio of flow rate amplitudes $G_1^{\left(A\right)}/G_2^{\left(A\right)}$ of the species of He-Xe in terms of $\delta \in \left[{10}^{-4},{10}^2\right]$, with $C=\left[0,05,0.35,0.65,0.95\right]$ and $\theta =\left[0.1,1,10\right]$.

Figure 7

Ratio of flow rate amplitudes $G_1^{\left(A\right)}/G_2^{\left(A\right)}$ of the species of He-Xe and Ne-Ar, with $C=0.5$, in terms of $\theta \in \left[{10}^{-4},{10}^2\right]$ for $\delta =\left[0.1,1,10\right]$.

Figure 8

Difference of the flow rate phase angles $G_2^{\left(P\right)}-G_1^{\left(P\right)}$ (rad) of the species of He-Xe in terms of $\delta \in \left[{10}^{-4},{10}^2\right]$, with $C=\left[0.05,0.35,0.65,0.95\right]$ and $\theta =\left[0.1,1\right]$.

Figure 9

Time-dependent flow rates ${\tilde{G}}_1\left(t\right)$ of He, ${\tilde{G}}_2\left(t\right)$ of Xe and $\tilde{G}\left(t\right)$ of He-Xe, with $C=0.5$, over one cycle $t\in \left[0,2\pi \right]$ for $\delta =\left[0.1,10\right]$ and $\theta =\left[0.1,10\right]$.

Figure 10

Wall shear stress amplitude ${\varpi }_W^{\left(A\right)}$ and phase angle ${\varpi }_W^{\left(P\right)}$ (rad) of He-Xe in terms of $C$ for $\theta =\left[0.1,1,10,50,{10}^2\right]$ and $\delta =1$.

Figure 11

Normalized cycle-average pumping power $\overline{E}/dx$ of He-Xe and Ne-Ar in terms of $C$ for $\delta =1$ and $\theta =\left[0.1,1,10,{10}^2\right]$ (${\overline{E}}_S$ is the steady-state pumping power).