Separation of a Gas Mixture Flowing through a Long Tube at Low Pressure

Abstract

The separation of a binary gas mixture by diffusion through a capillary of radius $r$ depends on the fact that the molecules have different masses $m_i$ and mean speeds ${\overline{\nu }}_i$. When the inlet pressure is so low that the mean free path $\lambda$ is much greater than $r$, the flow is diffusive and the separation factor (at zero outlet pressure) has its maximum value ${\left(\frac{m_2}{m_1}\right)}^{\frac{1}{2}}$. At high pressures ($\lambda \ll r$) no separation occurs. This paper treats the intermediate case ($\lambda \approx r$) where the transfer of forward momentum from light to heavy molecules in unlike collisions equalizes the transport velocities and decreases the separation factor. As the inlet pressure rises, this effect makes the flow non-separative before it becomes viscous. Flow equations are derived by equating the momentum acquired by the light component from the pressure gradient to the momentum lost to the wall plus that transferred to the other component. The viscous effects are treated as a small additive perturbation on the flow. The integrated flow equations express the separation factor as a function of the inlet and outlet pressures.