Abstract
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.Graphical
Highlights
Ion-exchange membranes have several industrial applications, including fuel cells, the Chlor–Alkali process, and water electrolysis
We show how the membrane pore diameter increases and dead-end pores open up when the current density is increased
Graham et al have shown that the Nernst– Planck equation is valid in modeling diffusion of ions in ion-exchange resins of high concentrations (3–4 M) if taking into account the effective diffusivities [3]
Summary
Ion-exchange membranes have several industrial applications, including fuel cells, the Chlor–Alkali process, and water electrolysis. Rohman and Aziz have reviewed mathematical models of ion transport in electrodialysis They have proposed three types of phenomenological equations in their irreversible thermodynamic approach: (1) the Maxwell–Stefan (MS) equation which takes the interaction between each pair of components into account; (2) the Kedem–Katchalsky (KK) equation that considers the membrane as a geometric transition region between two homogenous compartments; and (3) the Nernst–Planck (NP) equation which describes diffusion and electro-migration in the ionic transport without taking into account the interaction between ions. Psaltis et al have compared the Nernst–Planck and Maxwell–Stefan approaches to transport predictions of ternary electrolytes They have concluded that using binary diffusivities (neglecting interaction between different solute species) and the full Maxwell–Stefan model does not affect the final steady-state concentrations profiles in the electrolyte solution of a multicomponent system. Graham et al have shown that the Nernst– Planck equation is valid in modeling diffusion of ions in ion-exchange resins of high concentrations (3–4 M) if taking into account the effective diffusivities [3]
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