Nernst-Planck transport theory for (reverse) electrodialysis: II. Effect of water transport through ion-exchange membranes

TL;DR

This paper develops a two-dimensional Maxwell-Stefan-based model to analyze water and ion transport in ion-exchange membranes during electrodialysis and reverse electrodialysis, validated with experimental data and used to study operational effects.

Contribution

It extends previous transport theory by incorporating water transport in a 2D model, linking ion and water fluxes with frictional interactions, and validating against experimental data.

Findings

Water and ion fluxes are self-consistently calculated in the model.

Water and coion leakage significantly affect membrane performance.

The model accurately predicts experimental results for ED and RED.

Abstract

Transport of water through ion-exchange membranes is of importance both for electrodialysis (ED) and reverse electrodialysis (RED). In this work, we extend our previous theory [J. Membrane Sci., 510, (2016) 370-381] and include water transport in a two-dimensional model for (R)ED. Following a Maxwell-Stefan (MS) approach, ions in the membrane have friction with the water, pore walls, and one another. We show that when ion-ion friction is neglected, the MS-approach is equivalent to the hydrodynamic theory of hindered transport, for instance applied to nanofiltration. After validation against experimental data from literature for ED and RED, the model is used to analyze single-pass seawater ED, and RED with highly concentrated solutions. In the model, fluxes and velocities of water and ions in the membranes are self-consistently calculated as function of the driving forces. We investigate the influence of water and coion leakage under different operational conditions.