Deionization shocks in crossflow

Shock electrodialysis is a recently developed electrochemical water treatment method that shows promise for water deionization and ionic separations. Although simple models and scaling laws have been proposed, a predictive theory has not yet emerged to fit experimental data and enable system design. Here, we extend and analyze existing "leaky membrane" models for the canonical case of a steady shock in crossflow, as in recent experimental prototypes. Two-dimensional numerical solutions are compared with analytical boundary-layer approximations and experimental data. The boundary-layer theory accurately reproduces the simulation results for desalination, and both models predict the data collapse of the desalination factor with dimensionless current, scaled to the incoming convective flux of cations. The numerical simulation also predicts the water recovery increase with current. Nevertheless, neither approach can quantitatively fit the transition from normal to over-limiting current, which suggests gaps in our understanding of extreme electrokinetic phenomena in porous media.