Separation of a Gas Mixture Flowing Through a Long Tube at Low Pressure
U.S. Atomic Energy Commission, Technical Information Branch, 1949 - Gases - 12 pages
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 sub i and mean speeds v sub 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 (m sub 1/m sub 2)(1/2). At high pressures (lambda (less than or equal 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 nonseparative 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.
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adding additive Appendix approximation assumed average axis becomes calculation capillary tube coefficient collisions comparable component composition concentration Consider constant cross section curve cylindrical element decreases denote depends diffusion diffusive flow drift velocity effect entire equal equation 11 Evidently experiments express follows fore-pressure formula free-molecule flow function gas mixture gases given Hence ideal independent indicate inlet integration intermediate intermolecular collision Introducing inversely isotopic mixture Knudsen laminar flow light lighter low pressures mass mean free path measured method molecular mass molecules momentum transfer neglected nonseparative numerical obtained orifice outlet Phys Pollard porous medium Present pressure pressure gradient proportional pure radius range ratio readily seen region relative represented result separation separation factor similar simply term Theory tion total flow transition transport velocities treated unit unit area unit volume unlike molecules viscous flow wall zero