Combined Influence of Membrane Profiling and Wing-Shaped Spacers on Ion Transport: A Two-Dimensional Potentiodynamic Study

Membrane profiling and near-membrane spacers modify concentration polarization by altering fluid flow and the membrane–solution interface. This study examines their combined influence using a two-dimensional Nernst–Planck–Poisson–Navier–Stokes model with a voltage ramp of 5 mV/s. The geometries comprise a smooth membrane without spacers, a profiled membrane without spacers, and six wing arrangements adjacent to a profiled membrane. The feed concentration is 0.01 mol/m3, the protrusion radius is 0.5 mm, and the center-to-center pitch is 1.5 mm. Current data from five identifiable model files are compared over a common interval up to 1.2 V using a dimensionless domain-integrated current. Wing placement affects the current response, while profiling increases the geometric membrane contour by 28.54%. An analytical reference limiting current is calculated using the Levêque equation. The comparison with published three-dimensional results provides qualitative support for the transport mechanism. Systematic numerical uncertainty assessment, quantitative three-dimensional validation, geometry optimization, and energy comparisons at equal salt removal are identified as further research beyond the scope of the present study.