Nernst-Planck transport theory for (reverse) electrodialysis: I. Effect of co-ion transport through the membranes

Electrodialysis (ED) and Reverse Electrodialysis (RED) are related technologies for water desalination and energy conversion, both based on the selective transport of ions through ion exchange membranes. Fundamental understanding of these processes requires the description of ion transfer phenomena both along and through the membranes. We develop a simple 2D model valid for ED and RED, extending the approach by Sonin and Probstein (Desalination 5, 1968, 293) by using the Nernst–Planck equation not only in the flow channels but also in the membranes. This model requires as only input parameters the geometrical features of the system, the membrane charge density, and the diffusion coefficients of ions in the channel and in the membrane. The effect of non-ideal behavior of the membrane due to the co-ion transport is discussed, evaluating the performance of the processes in terms of current efficiency and energy consumption (for ED), and salt flux efficiency and power density (for RED). Membrane properties such as permselectivity are calculated as outputs of the model, and depend on position in the channel.

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