Ion-size-dependent electroconvective transport in confined channels.

Electroconvective flow near ion-selective surfaces is a fundamental phenomenon in electrochemistry that has attracted significant attention across disciplines such as membrane science, drug delivery, and ion transport. Despite this interest, a comprehensive understanding of electroconvective transport across the transition from weakly to strongly confined channels remains elusive. In this study, we investigate electroconvective transport in charged confined channels containing an embedded ion-selective membrane using direct numerical simulations. The Poisson-Nernst-Planck equations are modified to incorporate ionic steric effects. This work focuses on how variations in the steric parameter influence electroconvection across channels with varying degrees of confinement and electric double layer (EDL) overlap, while maintaining a fixed electrohydrodynamic coupling parameter. Under strong confinement, where EDLs overlap, electroconvective transport is primarily governed by steric effects. In this regime, the average ion concentration exhibits an inverse relationship with the steric parameter. In contrast, under weak confinement-where EDLs do not overlap-electroconvective flow dominates the transport mechanism. Here, a decrease in the dimensionless Debye number leads to an increase in the velocity of electroconvective vortices. Above a critical dimensionless Debye number, the transition in transport mechanism-from electroconvective flow to steric (ion size) effects-can be captured through an asymptotic scaling law involving both the dimensionless Debye number and the dimensionless steric parameter. These results establish a framework that connects the behavior of electroconvective transport in weakly and strongly confined channels.