A Nernst-Planck analysis on the contributions of the ionic transport in permeable ion-exchange membranes to the open circuit voltage and the membrane resistance in reverse electrodialysis stacks

摘要

The contributions of the ionic transport through a cation-exchange membrane, with perfectly stirred bathing solutions, on the open circuit voltage and the membrane ohmic resistance under reverse electrodialysis conditions, have been theoretically investigated. The Nernst-Planck flux equations, together with the Donnan equilibrium relations and the electrical neutrality condition, are numerically solved by using the network simulation method. On the one hand, the voltage-current characteristic, the polarization curves and the contributions of the ion-exchange membrane to the open circuit voltage and the membrane resistance are studied in a single system with NaCl solutions. The results are compared to those analytically obtained by using linear variations of ionic concentrations inside the membrane. On the other hand, a similar study is done for a membrane immersed in solutions constituted by a mixture of NaCl and MgCl2. The uphill transport of the divalent cation against its concentration gradient is considered in the interpretation of the results. The numerical results are compared to those analytically obtained by considering the hypothesis of total co-ion exclusion inside the membrane. (C) 2017 Elsevier Ltd. All rights reserved.