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The reduced 1D Poisson-Nernst-Planck (PNP) model of artificial nanopores inthe presence of a permanent charge on the channel wall is studied. Morespecifically, we consider the limit where the channel length exceed much theDebye screening length and channel's charge is sufficiently small. Iontransport is described by the nonequillibrium steady-state solution of the PNPsystem within a singular perturbation treatment. The quantities, 1/lambda --the ratio of the Debye length to a characteristic length scale and epsilon --the scaled intrinsic charge density, serve as the singular and the regularperturbation parameters, respectively. The role of the boundary conditions isdiscussed. A comparison between numerics and the analytical results of thesingular perturbation theory is presented.

A singular perturbation approach to the steady-state 1D Poisson-Nernst-Planck modeling