A Simple Theory for Separation of Gases by Thermal Diffusion

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Abstract
Equations are derived in a simple manner by equating the net bombardment of each species across a plane between two adjacent thin layers of the gas mixture to the amount of each species returned across the plane by a return flow, which flow is assumed necessary to keep the pressure constant and is assumed to carry back the various species in the proportions in which they exist in the neighborhood. The average temperatures of the layers differ by dT, but the bombardment of each species is assumed independent and calculable in any layer in the way the pressure of an ideal gas at constant temperature is calculated. The resulting equation for binary mixtures does better than give the order of magnitude of the observed separations. It appears to give an upper limit, either in agreement with data or somewhat higher—up to about twice the observed value—and to fit data somewhat better than does the approximate equation of Chapman. The agreement is poorest for mixtures containing hydrogen and also whenever the lower temperature is extremely low. The equations for mixtures of any number of species are simple. They indicate that the separation of two heavier species should be improved by addition of a light gas. An attempt to improve the equations by introduction of mean free paths is found profitless, unless arbitrary values are to be chosen.

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