Recycle continuous-flow electrophoresis (RCFE) is a modification of Hannig's thin-film CFE device in which eluent is continuously recycled to the chamber inlet. Shifting the recycled eluent laterally a specific distance prior to reinjection enables the RCFE to separate any two solutes to arbitrary purity. This paper studies solute transport in an idealized RCFE in the absence of diffusion. The model is solved analytically by means of a two-sided Laplace transform. Three distinct types of solute distribution are found, and guidelines for construction and operation of an RCFE are derived.