  Possible mechanisms of overlimiting current in unsupported electrolytes,
exceeding diffusion limitation, have been intensely studied for their
fundamental significance and applications to desalination, separations,
sensing, and energy storage. In bulk membrane systems, the primary physical
mechanism is electro-convection, driven by electro-osmotic instability on the
membrane surface. It has recently been predicted that confinement by charged
surfaces in microchannels or porous media favors two new mechanisms,
electro-osmotic flow (EOF) and surface conduction (SC), driven by large
electric fields in the depleted region acting on the electric double layers on
the sidewalls. Here, we provide the first direct evidence for the transition
from SC to EOF above a critical channel height, using in situ particle tracking
and current-voltage measurements in a micro/nanofluidic device. The dependence
of the over-limiting conductance on channel depth (d) is consistent with
theoretical predictions, scaling as d^-1 for SC and d^4/5 for EOF with a
transition around d=8um. This complete picture of surface-driven over-limiting
current can guide engineering applications of ion concentration polarization
phenomena in microfluidics and porous media.
