Richard Dunkel

Operating electrodialysis (ED) processes beyond the limiting current density offers the potential for reduced capital costs and improved energy efficiency, but is fundamentally constrained by concentration polarization and the associated increase in electrical resistance. Spacer geometries are commonly employed to manipulate hydrodynamics in ED channels and enhance mass transfer; however, their impact on overlimiting ion transport remains insufficiently understood. In this study, we systematically investigate how specifically designed spacer geometries influence limiting and overlimiting current behavior by coupling electrochemical measurements with three-dimensional computational fluid dynamics (CFD) simulations. Custom spacer structures were fabricated by 3D printing and evaluated using current--voltage (I--V) characteristics and chronopotentiometric measurements under buoyancy-stable and buoyancy-unstable configurations. The simulations resolve spacer-induced flow fields, near-membrane shear distributions, ion transport, and current-density patterns, enabling direct correlation with experimental performance. While all spacer geometries enhance average mass transfer compared to a spacerless reference, their electrochemical effectiveness strongly depends on the spatial overlap between regions of increased near-membrane shear and electrically active membrane area. Spacer designs that generate strong local mixing but simultaneously induce electric-field shadowing lead to highly non-uniform current distributions, early local ion depletion, and modest gains in effective limiting and overlimiting currents. In contrast, geometries that promote a more homogeneous alignment of shear enhancement and electric driving force delay concentration polarization and stabilize overlimiting operation, particularly under buoyancy-stable conditions where forced convection dominates. These findings allow us to rationalize why spacer geometries that perform well in terms of classical mass-transfer metrics do not necessarily translate into improved overlimiting electrodialysis performance.

The coupling between ion transport, fluid flow, and electrostatics may give rise to electroconvection, a physical phenomenon in which the buildup of charge near selective surfaces leads to hydrodynamic instability, eventually transitioning to an unsteady and chaotic flow. Though electroconvection contains a wide range of spatiotemporal scales, averaging of the ion concentration, velocity, and electric potential fields may produce a lower-dimensional and smoother representation while still capturing the essential performance metrics: ion current density and mean applied voltage, for example. The Poisson–Nernst–Planck–Stokes equations are known to capture the chaotic dynamics of electroconvection accurately. However, there is as of yet no way to directly compute the mean fields, since the application of the well-known Reynolds-averaging procedure leads to a closure problem. In this work, we combine the macroscopic forcing method, a numerical technique for measurement of closure operators in Reynolds-averaged equations, with high-fidelity experimental data to close the equations for the mean fields in chaotic electroconvection. We show that the unclosed fluxes in the Reynolds-averaged equations may be represented to the leading order as a gradient-diffusion term, with a spatially varying eddy diffusivity that we directly measure from experimental velocity fields. As a result, we are able to directly solve for the mean ion concentration and electric potential fields by supplementing the 1D Poisson–Nernst–Planck equations with an eddy diffusivity that captures the averaged effects of mixing due to chaotic, 3D electroconvection. The resulting current-voltage curve exhibits strong agreement with experiments. Our method allows for the study of electroconvection with orders-of-magnitude cost savings by obviating the need for expensive direct numerical simulations. Additionally, our measured eddy diffusivity profiles provide a benchmark for the development of stand-alone reduced-order models of electroconvection.