Electroconvective instability near an ion-selective membrane: Scaling law from extended space charge dynamics

Abstract

Electroconvective (EC) instability, driven by strong electric fields near ion-selective surfaces, plays a vital role in various electrochemical systems but remains incompletely understood. Combining linear stability and scaling analysis, we systematically investigate the effects of ion valence and diffusivity on EC instability thresholds, alongside electrolyte viscosity and concentration. We predict the size of the extended space charge (ESC) layer where the instability originates, and quantify its associated potential drop, providing key insight into the onset mechanisms of EC instability. Moreover, unlike previous studies that primarily analyzed eigenfunctions in the electroneutral bulk region, we focused on the ESC layer, demonstrating that instability originates there, emphasizing the role of localized eigenfunctions and ion types within the ESC layer in the early development of instability. Based on these insights, we propose a scaling law that predicts critical conditions for instability onset. We further identified a critical electric Rayleigh number (RaE,cr = 36) that governs instability across varying ion transport properties and membrane types, showing improved agreement compared to previous theoretical predictions. This work provides a robust theoretical framework for understanding and optimizing ion-selective systems in electrochemical applications.