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Abstract

Hollow-fiber membrane reactive extraction and facilitated supported liquid membrane processes for the separation of charged species are analyzed theoretically. A mathematical model incorporating laminar flow, Nemst-Planck diffusion, buffer effect, ion strength, interfacial reaction kinetics and/or equilibria, diffusivity of species in the membrane phase, shell resistances, and shell concentration is deueloped and solued numerically. When the lumen mass-transfer resistance is dominant, the predicted remoual rate of a single ion or the separation rate of a mixture of ions by a simplified model with Fickian diffusion deuiates greatly from the prediction with the present model. For instance, when the concentration of triualent ions in the feed decreases to half of its initial ualue, the membrane length calculated using Fickian diffusion is 75% higher than the length predicted by Nemst-Planck diffusion. Thus, the Leueque equation based on Fick's law does not adequately describe the mass transfer of the charged species in the lumen feed. The effect of buffer ions and diffusiuity of species in the membrane phase on the mass transfer of the species is also discussed.