  The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion
transport. In many applications, e.g., ions in biological tissues, the presence
of thin boundary layers poses both modelling and computational challenges. In
this paper, we derive simplified electro-neutral (EN) models where the thin
boundary layers are replaced by effective boundary conditions. There are two
major advantages of EN models. First of all, it is much cheaper to solve them
numerically. Secondly, EN models are easier to deal with compared with the
original PNP, therefore it is also easier to derive macroscopic models for
cellular structures using EN models.
  Even though the approach is applicable to higher dimensional cases, this
paper mainly focuses on the one-dimensional system, including the general
multi-ion case. Using systematic asymptotic analysis, we derive a variety of
effective boundary conditions directly applicable to EN system for the bulk
region. This EN system can be solved directly and efficiently without computing
the solution in the boundary layer. The derivation is based on matched
asymptotics, and the key idea is to bring back higher order contributions into
effective boundary conditions. For Dirichlet boundary conditions, the higher
order terms can be neglected and classical results (continuity of
electrochemical potential) are recovered. For flux boundary conditions,
however, neglecting higher contribution leads to physically incorrect solutions
since they account for accumulation of ions in boundary layer. The validity of
our EN model is verified by several examples and numerical computation. In
particular, our EN model is much more efficient than the original PNP model
when applied to the computation of membrane potential.
