Half-range analysis of a counter-current separator (Q1192532)

We analyze the mathematical model of a single-interface counter-current separator introduced by \textit{V. Fitt}, \textit{J. R. Ockendon} and \textit{M. Shillor} [Int. J. Heat Mass Transfer 28, 753-759 (1985; Zbl 0566.76104)] for relatively long reactors. For such reactors, the mathematical model, which is a forward/backward diffusion system, can be solved by eigenfunction expansions. We construct these expansions using complex variable methods developed for kinetic theory. From this analysis we obtain explicit formulas for the power of the reactor, both in terms of the average purity of the output stream and in terms of the equivalent number of theoretical plates.