On the Propagation of Concentration Polarization from Microchannel−Nanochannel Interfaces Part I: Analytical Model and Characteristic Analysis

Abstract

We develop two models to describe ion transport in microchannels and nanochannels. For the first model, we obtain a one-dimensional (unsteady) partial differential equation governing flow and charge transport through a shallow and wide electrokinetic channel. In this model, the effects of electric double layer (EDL) on axial transport are taken into account using exact solutions of the Poisson-Boltzmann equation. The second simpler model, which is approachable analytically, assumes that the EDLs are confined to near-wall regions. Using a characteristics analysis, we showed that the latter model captures concentration polarization (CP) effects and provides useful insight into its dynamics. Two distinct CP regimes are identified: CP with propagation in which enrichment and depletion shocks propagate outward; and CP without propagation where polarization effects stay local to micro-nanochannel interfaces. The existence of each regime is found to depend on a nanochannel Dukhin number and mobility of the co-ion nondimensionalized by electroosmotic mobility. Interestingly, microchannel dimensions and axial diffusion are found to play an insignificant role in determining whether CP propagates. The steady state condition of propagating CP is shown to be controlled by channel heights, surface chemistry and co-ion mobility instead of the reservoir condition. Both models are validated against experimental results in Part II of this two paper series.

Effect of geometry on concentration polarization in realistic heterogeneous permselective systems

“…Such a geometry realistically describes systems that have been the subject of numerous recent experimental and numerical works [6,11,12,15,21,[27][28][29][30][31][32][34][35][36][37]41,42]. Additionally, this geometry can also describe a periodic array of permselective regions (e.g.…”

Analysis of electrolyte transport through charged nanopores

“…It is well known that interfaces between charged membranes or nanochannels and unsupported bulk electrolytes lead to ion concentration polarization outside the membrane, e.g., in classical electrodialysis [33][34][35], but complex nonequilibrium electrokinetic phenomena resulting from strong concentration polarization have recently been discovered inside membrane pores or microchannels, such as deionization shock waves [32,[36][37][38][39][40][41] and overlimiting current sustained by surface conduction (electromigration) and electro-osmotic flow [42][43][44][45] with applications to nanotemplated electrodeposition [46] and water desalination by "shock electrodialysis" [47]. In most situations for nanochannels, the ions remain in local quasiequilibrium, since electromigration FIG.…”

Experimental Verification of Overlimiting Current by Surface Conduction and Electro-Osmotic Flow in Microchannels

“…(6) The salt concentration tends to form very sharp gradients between the depleted and concentrated regions (on the anodic, depleted side of the membrane), perhaps first observed a decade ago [25]. In micronanofluidic device in which steady over-limiting current has been observed [26], salt gradients propagate as shock waves, [6,27] or "deionization shocks" [28][29][30] at constant current, due to the nonlinear effect of ion transport in the electric double layers of the sidewalls. These observations suggest that multiple transport mechanisms may be involved when overlimiting current occurs under strong confinement.…”