Coupled Concentration Polarization and Electroosmotic Circulation near Micro/Nanointerfaces: Taylor–Aris Model of Hydrodynamic Dispersion and Limits of Its Applicability

Abstract

Mismatches in electrokinetic properties between micro- and nanochannels give rise to superposition of electroosmotic and pressure-driven flows in the microchannels. Parabolic or similar flow profiles are known to cause the so-called hydrodynamic dispersion, which under certain conditions can be formally assimilated to an increase in the solute diffusivity (Taylor-Aris model). It is demonstrated theoretically that taking into account these phenomena modifies considerably the pattern of current-induced concentration polarization of micro/nanointerfaces as compared to the classical model of unstirred boundary layer. In particular, the hydrodynamic dispersion leads to disappearance of limiting current. At essentially "over-limiting" current densities, the time-dependent profiles of salt concentration in microchannels behave like sharp concentration "fronts" moving away from the interface until they reach the reservoir end of the microchannel. Under galvanostatic conditions postulated in this study, these "fronts" move with practically constant speed directly proportional to the current density. The sharp transition from a low-concentration to a high-concentration zone can be useful for the analyte preconcentration via stacking. The pattern of moving sharp concentration "fronts" has been predicted for the first time for relatively broad microchannels with negligible surface conductance. The Taylor-Aris approach to the description of hydrodynamic dispersion is quantitatively applicable only to the analysis of sufficiently "slow" processes (as compared to the characteristic time of diffusion relaxation in the transversal direction). A posteriori estimates reveal that the condition of "slow" processes is typically not satisfied close to current-polarized micro/nanointerfaces. Accordingly, to make the description quantitative, one needs to go beyond the Taylor-Aris approximation, which will be attempted in future studies. It is argued that doing so would make even stronger the dampening impact of hydrodynamic dispersion on the current-induced concentration polarization of micro/nanointerfaces.

Concentration polarization, surface currents, and bulk advection in a microchannel

“…As pointed out in Refs. [29,[41][42][43], the effects of bulk advection can to some extent be understood in terms of a Taylor-Aris-like model of hydrodynamic dispersion. However, in those papers surface conduction and surface advection is neglected on account of their small contribution to the total current in the investigated limits.…”

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

“…The theory predicts a transition between two new mechanisms, surface conduction (SC) and electroosmotic flow (EOF), that dominate in nanochannels and microchannels, respectively. The EOF mechanism is driven by large electro-osmotic slip in the depleted region on the sidewalls (not the membrane at the end of the channel) [33], leading to "wall fingers" of salt transported by vortices faster than transverse diffusion [31,34]. This new mode of surface convection thus cannot be described by classical Taylor-Aris dispersion [33,34].…”

“…The EOF mechanism is driven by large electro-osmotic slip in the depleted region on the sidewalls (not the membrane at the end of the channel) [33], leading to "wall fingers" of salt transported by vortices faster than transverse diffusion [31,34]. This new mode of surface convection thus cannot be described by classical Taylor-Aris dispersion [33,34]. The EOF mechanism, extended for "eddy fingers" in a random porous medium, has been confirmed indirectly by experiments measuring the current-voltage relation, scaling with salt concentration or surface charge, and desalination efficiency of "shock electrodialysis" [35].…”