  We show that a modified version of the Dukhin number is an appropriate
scaling parameter for the ionic selectivity of uniformly charged nanopores. The
modified Dukhin number is an unambiguous function of the variables $\sigma$
(surface charge), $R$ (pore radius), and $c$ (salt concentration), and defined
as $\mathrm{mDu}=|\sigma|/e(R/\lambda)$, where $\lambda$ is the screening
length of the electrolyte carrying the $c$ dependence ($\lambda\sim c^{-1/2}$).
Scaling means that the device function (selectivity) is a smooth and (in this
case) monotonic function of mDu. The original Dukhin number defined as
$\mathrm{Du}=|\sigma|/eRc$ ($c^{-1}$ dependence) was introduced to indicate
whether the surface or the volume conduction is dominant in the pore. The
modified version satisfies scaling and characterizes selectivity in the
intermediate regime, where both surface and bulk conductions are present and
the pore is neither perfectly selective, nor perfectly non-selective. Our
modeling study using the Local Equilibrium Monte Carlo method and the
Poisson-Nernst-Planck theory provides the radial flux profiles from which the
radial selectivity profile can be computed. These profiles show in which region
of the nanopore the surface or the volume conduction dominates for a given
combination of the variables $\sigma$, $R$, and $c$. We show that the
inflection point of the scaling curve may be used to characterize the
transition point between the surface and volume conductions.
