We analyze limiting capabilities of mechanical separation processes using finite-time thermodynamics and obtain estimates for the lower bound of the energy consumption for systems of a given productivity. We show that this consumption does not tend to zero when the molar fraction of one of the components tends to unity. The estimates obtained are used to analyze multistage separation processes, containing recycles, especially, isotope separation systems. For such systems we obtain relations between fluxes, mass transfer surfaces, and stage number. These relations are deduced from the condition of minimum dissipation, assuming that the enrichment factor is constant. We also obtain the optimality condition for the sequence of separations needed for a multicomponent mixture in a mechanical separation systems.