This is a research paper on efficiencies of physically separating gases of different densities, using turbulence at relatively low rotational speeds. Simple density separators need very high rotation, calling for extremely expensive bearings and motors, that usually need to be special made to order.
The gases described in the paper are methane and carbon dioxide, 0.000554 and 0.001836 g/cm³ at stp. Detailed schematics of the mesh employed to deliver better separation, resulting in high purity, are described and drawn, together with the test results.
As it happens, atmospheric gases, principally oxygen and nitrogen, are much farther apart in density, at 1.429 and 0.0012506 g/cm³ at stp respectively. The principal trace compound is carbon dioxide, whose density is much closer to nitrogen than oxygen, and which can therefore be expected to be found in much higher concentrations in the nitrogen ‘waste’ fraction than the desired high purity oxygen, after separation.
An added advantage to separating oxygen from the atmosphere is that (apart from the handy source) nitrogen exhausted or vented from the separator is mostly harmless. This compares favorably with electrolysis of water, which is relatively simple to fabricate from everyday hardware found in workshops, but needs very high maintenance to minimise the risk of explosive fires.