Multicomponent Space-Charge Transport Model for Ion-Exchange Membranes Yahan Yang and Peter N. Pintauro Dept. of Chemical Engineering, Tulane University, New Orleans, LA 70118 A multicomponent space-charge transport model for ion-exchange membranes was de®eloped, where the membrane structure was modeled as an array of cylindrical pores with a uniform distribution of fixed-charge sites on the pore walls. Ion rfixed-charge site electrostatic interactions, electric-field-induced water dipole orientation, ion-hydration free-energy changes during ion partitioning, and concentration-dependent transport pa- rameters were considered in the analysis. The model predicted experimental concentra- tion ®s. time data accurately for Donnan dialysis separations with a DuPont Nafion 117 cation-exchange membrane, where the membrane separated a dilute H SO solution 2 4 from an aqueous mixture of either Cs SO q Li SO or Cs SO q Na SO . Both 2 4 2 4 2 4 2 4 computer predictions and experimental measurements showed that the alkali metal ( ) cation with the larger hard-sphere radius lower surface charge density was selecti®ely absorbed in and transported across the membrane during a multicomponent separation. The cation r cation transport permselecti®ity was less than the selecti®ity for equilibrium uptake due to slow ion transport near the pore wall, where discrimination between like-charge cations was greatest. Introduction The design of ion-exchange membranes can be greatly aided by ion and solvent structurer function transport models Ž. that contain 1 a mathematical description of the membrane Ž. microstructure; 2 relationships describing macroscopic Ž . measurable solute r solvent partitioning and the transport of Ž . Ž. ion species and water solvent ; and 3 fundamental theories relating the membrane structure to species fluxes and perm- selectivity, through molecular-level ionr solventr polymer in- teractions. Such models can be used to propose new ion-ex- change membranes with specific ion and solvent transport Ž characteristics for a given electrochemical device that is, a . battery, fuel cell, andr or reactor or separation process Ž . that is, electrodialysis or Donnan dialysis . Additionally, a structurer function model could be used to simulate the per- formance of a given membrane in a particular electrochemi- cal or separation application. It is generally recognized that the overall permselectivity of salts by an ion-exchange membrane is governed by partition- Correspondence concerning this article should be addressed to P. N. Pintauro. Present address of Y. Yang: Exxon Production Research Company, P. O. Box 2189, Houston, TX 77252. ing events at the upstream and downstream membrane r solu- tion interfaces and transport through the interior of the membrane. Numerous theories have been proposed and tested to describe such sorption and transport events. One such ‘‘space-charge’’model predefines the micro-level struc- Ž ture of an ion-exchange membrane as an arrayof pores usu- . ally cylindrical of known size with a specified distribution of ion-exchange sites on the pore walls. Model equations based on this structure include the Nernst-Planck and Navier-Stokes equations for the solute flux and solvent velocity, respec- tively. Electroneutrality in the pore fluid is not assumed and the Poisson-Boltzmann equation is used to calculate the ra- dial-direction variations in electric potential and ion charge density. A nonzero space charge produces coupling between electrical forces, mass transfer, and fluid flow within the pore, Ž. which manifests itself in two ways: a the interaction of fluid flow and the electric field generates a body-force term in the Ž. momentum balance equation, and b the electrostatic poten- tial in the space-charge region of the pore causes counterion enrichment and coion exclusion. Also, the interaction be- tween the space-charge region and the driving forces for transport directed parallel to the pore wall results in such June 2000 Vol. 46, No. 6 AIChE Journal 1177