  Fundamental understanding of ionic transport at the nanoscale is essential
for developing biosensors based on nanopore technology and new generation
high-performance nanofiltration membranes for separation and purification
applications. We study here ionic transport through single putatively neutral
hydrophobic nanopores with high aspect ratio (of length L=6 \mu m with
diameters ranging from 1 to 10 nm) and with a well controlled cylindrical
geometry. We develop a detailed hybrid mesoscopic theoretical approach for the
electrolyte conductivity inside nanopores, which considers explicitly ion
advection by electro-osmotic flow and possible flow slip at the pore surface.
By fitting the experimental conductance data we show that for nanopore
diameters greater than 4 nm a constant weak surface charge density of about
10$^{-2}$ C m$^{-2}$ needs to be incorporated in the model to account for
conductance plateaus of a few pico-Siemens at low salt concentrations. For
tighter nanopores, our analysis leads to a higher surface charge density, which
can be attributed to a modification of ion solvation structure close to the
pore surface, as observed in the molecular dynamics simulations we performed.
