Silong Zong | York University
An Electro-Neutral Model for ion transport
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 talk, we present 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 to the original PNP system, therefore it would also be easier to derive macroscopic models for cellular structures using EN models. We will consider the general multi-ion case with either Dirichlet boundary conditions or flux boundary conditions. The derivation is based on matched asymptotics, and the key idea is to bring back higher order contributions into the effective boundary conditions. The EN model will be verified by some numerical examples, including a concrete example for neural axon to simulate action potential.