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.