  We revisit the theory of ion transport in parallel-plate channels and also
discuss how the wettability of a solid and the mobility of adsorbed surface
charges impact the transport of ions. It is shown that depending on the ratio
of the electrostatic disjoining pressure to the excess osmotic pressure at the
walls two different regimes occur. In the thick channel regime this ratio is
small and the channel effectively behaves as thick, even when the diffuse
layers strongly overlap. The latter is possible for highly charged channels
only. In the thin channel regime the disjoining pressure is comparable to the
excess osmotic pressure at the wall, which implies relatively weakly charged
walls. We derive simple expressions for the mean conductivity of the channel in
these two regimes, highlighting the role of electrostatic and
electro-hydrodynamic boundary conditions. Our theory provides a simple
explanation of the high conductivity observed experimentally in hydrophilic
channels, and allows one to obtain rigorous bounds on its attainable value and
scaling with salt concentration. Our results also show that further dramatic
amplification of conductivity is possible if hydrophobic slip is involved, but
only in the thick channel regime provided the walls are sufficiently highly
charged and the most of adsorbed charges are immobile. However, for weakly
charged surfaces the massive conductivity amplification due to hydrodynamic
slip is impossible in both regimes. Interestingly, in this case the moderate
slip-driven contribution to conductivity can monotonously decrease with the
fraction of immobile adsorbed charges. These results provide a framework for
tuning the conductivity of nanochannels by adjusting their surface properties
and bulk electrolyte concentrations.
