On the Theory of Isotope Separation by Thermal Diffusion

We here develop the theory of the processes in an apparatus with two concentric tubes, such as that used by Brewer and Bramley. In the first section we describe the process of thermal diffusion in general, and review the theoretical information on the subject. In Section II we set up the equations for the convection and diffusion processes, and obtain an expression for the net transport of a single isotope which is valid for arbitrary macroscopic properties of the gas. The assumption that the viscosity and heat conductivity of a gas are proportional to the absolute temperature is usually a good approximation; in this case the expression reduces to a simple form. In Section III we apply the transport equation to questions of separation factor and speed of operation. This is done both for the case of discontinuous operation, in which the approach to equilibrium is allowed to reach a certain stage and then the contents of an end-reservoir are removed, and for the case of operation with a continuous flow of gas through the tube. The advantages of the two methods are compared. In the last section we apply the formulas to a numerical example: the concentration of the ${\mathrm{C}}^{13}$ isotope by the use of methane, in an apparatus of moderate dimensions and power consumption.