Nernst-Planck modeling of multicomponent ion transport in a Nafion membrane at high current density

S. Moshtari Khah, N.A.W. Oppers, M.T. de Groot, J.T.F. Keurentjes, J.C. Schouten, J. van der Schaaf

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21 Citations (Scopus)
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A mathematical model of multicomponent ion transport through a cation-exchange membrane is developed based on the Nernst–Planck equation. A correlation for the non-linear potential gradient is derived from current density relation with fluxes. The boundary conditions are determined with the Donnan equilibrium at the membrane–solution interface, taking into account the convective flow. Effective diffusivities are used in the model based on the correlation of tortuosity and ionic diffusivities in free water. The model predicts the effect of an increase in current density on the ion concentrations inside the membrane. The model is fitted to the previously published experimental data. The effect of current density on the observed increase in voltage drop and the decrease in permselectivity has been analyzed using the available qualitative membrane swelling theories. The observed non-linear behavior of the membrane voltage drop versus current density can be explained by an increase in membrane pore diameter and an increase in the number of active pores. We show how the membrane pore diameter increases and dead-end pores open up when the current density is increased.
Original languageEnglish
Pages (from-to)51-62
Number of pages12
JournalJournal of Applied Electrochemistry
Issue number1
Publication statusPublished - Jan 2017


  • High current density
  • Membrane resistivity
  • Membrane selectivity
  • Multicomponent ion transport
  • Nernst–Planck


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