Dynamics of extended space charge in concentration polarization

This paper is concerned with ionic currents from an electrolyte solution into a charge selective solid, such as an electrode, an ion exchange membrane or an array of nanochannels in a microfluidic system. All systems of this kind have characteristic voltage-current curves with segments in which current nearly saturates at some plateau values due to concentration polarization--formation of solute concentration gradients under the passage of a dc current. A number of seemingly different phenomena occurring in that range, such as anomalous rectification in cathodic copper deposition from a copper sulfate solution, superfast vortexes near an ion-exchange granule, overlimiting conductance in electrodialysis and the recently observed nonequilibrium electro-osmotic instability, result from formation of an additional extended space charge layer next to that of a classical electrical double layer at the solid/liquid interface or, rather, from the peculiar features of the extended space charge distinguishing it from that of a common diffuse electrical double layer. In this paper we discuss the nature and origin of the extended space charge and analyze its peculiar steady state and time-dependent properties important for understanding nonequilibrium electrokinetic phenomena in ionic systems.