Oscillating electroosmotic flow in channels and capillaries with modulated wall charge distribution

Electrolyte-filled channels with modulated wall charge distribution subjected to an applied DC electric field, form time-independent vortices whose sense of circulation is determined by the field direction [Physical Review Letters $\mathbf{75}, 755, (1995)$]. In this paper we show that an electrolyte in a channel or cylindrical capillary subjected to an external \emph{alternating} (AC) electric field gives rise to various laminar flow structures, including vortices whose sense of circulation changes with the period of oscillation of the applied AC field. The introduction of a period of oscillation lifts certain degeneracies associated with its time-independent counterpart. Although, in general, the mass flux vanishes, the charge flux is nonzero. The flow is accompanied by a longitudinal (oscillating) advective current that displays hysteresis accompanied by a diverging and negative self-similar conductance that depends on the applied voltage [Nano Letters $\mathbf{10}, 2674, (2010)$]. We show that this behavior can be interpreted with respect to a ``memory retention time'', that depends on frequency, viscosity and the Debye length and could thus form the impetus for investigating control protocols of signal carriers.