(6ez) Electrokinetic Instability in Microchannel-Nanochannel Devices: A Comparison of Slip-Velocity and Full-Formulation

In systems containing ion-selective membranes or nanochannels, concentration polarization (CP) under DC voltage beyond the classical Levich limit leads to the breakdown of local electroneutrality over micron or larger scales at the salt-depleted interface. This manifests itself in the growth of an extended space charge (ESC) region, which becomes unstable above a critical voltage drop. The instability results in the formation of a fast-flowing vortex system with complex, often chaotic, dynamics. In unconfined systems, i.e. large electrolytic cells, this contributes strongly to the overlimiting conductance (OLC) of the system. However, both the role of the instability in OLC as well as its origin and onset become more complicated in highly confined systems such as microchannel devices. The problem of instability under geometric confinement has been studied both analytically and numerically using two different approaches. The first approach considers the ESC to be negligibly thin. Thus it is replaced by a slip boundary condition for the hydrodynamics and boundary values for the concentration and potential obtained from asymptotic analysis. This yields directly a marginal stability curve and critical parameters for the onset of instability. The second approach employs a direct numerical calculation of the stability problem resulting in a growth-rate surface from which marginal stability and critical parameters may be extracted. While both show suppression of the instability with increasing confinement, there are some interesting discrepancies between the features which merits further consideration.