Steady-state electrical response of homogeneous cation-exchange membrane systems under bi-ionic conditions

- The steady-state electric response of bi-ionic membrane systems is investigated.
- Analytical expressions for the limiting currents in bi-ionic systems are readapted.
- Concentrations of counter-ions inside the membrane strongly vary with current.
- The ionic fluxes reach a limiting value as the current increases.

This paper aims to numerically study the steady-state electrical response of ion-exchange membrane systems under bi-ionic conditions. The considered particular system is constituted by a membrane with negative fixed charge and two diffusion boundary layers on both sides of the membrane. The system is bathed by two solutions with a common co-ion but different counter-ion. The ionic transport processes of a ternary electrolyte are described by the Nernst-Planck-Poisson equations not only in the membrane but also in the diffusion layers, including the electric double layers at the interfaces. The numerical results are obtained by using the network simulation method. The steady-state voltage-current characteristics are analysed for cation-exchange membrane systems with monovalent ions and systems with a divalent counter-ion. The co-ion concentration polarization phenomena in the electroneutral regions of the diffusion boundary layers of these systems are analysed and discussed in detail. The electroneutral profiles of the counter-ionic concentrations inside the membrane and the counter-ionic fluxes are also analysed for different values of the electric current through the systems.

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