  Ion flow in charged nanopores is strongly influenced by the ratio of the
Debye length to the pore radius. We investigate the asymptotic behaviour of
solutions to the Poisson-Nernst-Planck (PNP) system in narrow pore like
geometries and study the influence of the pore geometry and surface charge on
ion transport. The physical properties of real pores motivate the investigation
of distinguished asymptotic limits, in which either the Debye length and pore
radius are comparable or the pore length is very much greater than its radius.
This results in a Quasi-1D PNP model which can be further simplified, in the
physically relevant limit of strong pore wall surface charge, to a fully
one-dimensional model. Favourable comparison is made to the two-dimensional PNP
equations in typical pore geometries. It is also shown that, for physically
realistic parameters, the standard 1D Area Averaged PNP model for ion flow
through a pore is a very poor approximation to the (real) two-dimensional
solution to the PNP equations. This leads us to propose that the Quasi-1D PNP
model derived here, whose computational cost is significantly less than
two-dimensional solution of the PNP equations, should replace the use of the 1D
Area Averaged PNP equations as a tool to investigate ion and current flows in
ion pores.
