R Y1 YX1 XR E ?1àln11 à? Y XX(1 X)BASIC SEPARATION THEORYDOE-HDBK-1015/1-93Appendix ACH-01Rev. 0Page A-4The actual separation achieved by a stage is expressed in terms of the mol fraction of thelight component and for the purpose of this discussion is designated by the capital letterR. It can be defined as follows: if Y is the concentration of light component in theenriched stream leaving a converter and X is its concentration in the depleted streamleaving the same converter, then.This definition is similar to that of the separation factor, but, as shown in Figure A-1, thevalue of R is based on the overall separation of a stage while that of the separation factoris based on the performance of the barrier alone. The relation between the two is givenby the following equation.E is a correction factor called the mixing efficiency. It can be explained as follows:since the light component passes through the barrier more rapidly than the heavycomponent, the layer of gas at the surface on the high pressure side of the barrierbecomes more depleted in the light component than the bulk of the gas on the highpressure side. Thus, there is a concentration gradient perpendicular to the surface of thebarrier which results in a decrease in separation. In the particular process of separationof uranium isotopes, the value of R in the preceding equation differs very little from unity(R = 1.003) and is somewhat inconvenient for use in calculations. By subtracting 1 fromeach side of the equation, equating the symbol ? (psi) to R - 1, and by making a slightapproximation, the equation becomes.This equation is used frequently in the plant in making separation tests.