Controlling electroconvective flow via circular geometry

Electroconvection near perfectly ion-selective membranes governs ion and fluid transport and plays a vital role in desalination, energy storage, and electrochemical systems. Although electroconvection has been extensively examined in planar and macroelectrode systems, the influence of electrode curvature on instability regulation remains insufficiently investigated. This study conducts direct numerical simulations of the Poisson–Nernst–Planck–Stokes equations to investigate the regulatory impact of curvature in needle-shaped circular electrodes (cathodes) on electroconvection behavior. As the radius of the needle-shaped electrode decreases, the electric field demonstrates a line charge singularity, substantially amplifying the local electric field intensity. This enhancement in the electric field drives a greater number of cations from the membrane interface into the finite domain, increasing the charge density within the extended space charge layer and reducing the onset voltage required for electroconvective instability. The geometric constraint imposed by smaller radii compresses fluid motion and mitigates chaotic flow dynamics. Larger radii augment the average external electric field, generating irregular flow structures. Scaling analysis indicated that the root mean square vortex velocity in annular geometries follows a power-law scaling with voltage, with the scaling exponent varying between 1 and 2 depending on curvature. However, ion flux scaling retains linear invariance regardless of geometric variation. These results present a tunable strategy for manipulating ion transport by controlling instability through needle-shaped electrodes, contributing to the design and optimization of electroconvective systems for microfluidic and energy-related applications.