Ion Transport in Charged Membranes: Linking Electric-Field-Driven Mechanisms to Pore Size via Perturbation Analysis

Ion-exchange membranes are a critical component in electrochemical systems. Nevertheless, the understanding and modeling of ion transport within these porous structures have been limited by particular complexity reductions, either ignoring the dimensionality of their porous network architecture or imposing geometric assumptions (i.e., overlapping double layers). Before addressing this morphology-transport gap, a framework that relates the driving forces of transport to the geometry of a single pore is required. In this work, our modeling domain consists of a two-dimensional single pore with charged walls, connecting two identical electrolyte reservoirs. Using the Poisson-Nernst-Planck equations and regular perturbation theory, we decouple the electric fields and analyze the driving forces of ion transport, specifically electromigration and induced electroosmosis within the pore. These processes are described as analytical functions of the interaction aspect ratio, κ, defined as the ratio of the pore radius to the Debye length. Using this parameter, our study (i) describes the interplay between electromigrative and electroosmotic mechanisms that set ionic conductivity, (ii) identifies a dimensionless group of intrinsic electrolyte properties that indicates the predominant driving force, and (iii) provides a qualitative, confinement-dependent perspective on selectivity in ion-conducting membranes.