Roles of solution conductivity mismatch in transient current and fluid transport in electrolyte displacement by electro-osmotic flow

Electro-osmotically driven displacement between two solutions having a conductivity mismatch is theoretically examined. Internal pressures induced by the conductivity mismatch can affect the propagation of the solution interface and the behavior of the transient current. Combining Ohm's law and fluid mass conservation, we derive a coupled set of length-averaged equations accounting for how the electric current and the traveling distance of the solution interface vary with time, electric field, and the solution conductivities. Extension to successive displacements involving multiple solution zones is made to reveal non-monotonic and stagewise changes in transient currents. For the first time, critical roles of surface conductance on displacements in highly charged channels are unraveled. We show that if the lower conductivity solution has a greater valence than the higher one, the effective conductivity of the former can exceed that of the latter when the channel height is below some critical value. The resulting transient current behavior can turn opposite to that usually observed in the large-channel case, offering a new paradigm for gauging the importance of surface conductance in submicron charged channels. Possible impacts of diffusion smearing and hydrodynamic dispersion are also discussed by including the additional mixing zone into the analysis. Having shown good agreement with the existing experimental data, our analysis not only captures the natures of solution displacement by electro-osmotic flow (EOF), but also extends the applicability of the current monitoring method for measuring surface zeta potentials of microchannels.