Ionic flow through ion channels is a complex multi-scale process of electrodiffusion that depends on nonlinear interaction of many physical parameters such as channel structures (channel shape and spatial distribution of permanent charges), boundary concentrations, electric potential differences, diffusion coefficients, dielectric properties, ionic sizes, etc. Among those physical parameters, the permanent charge is arguably the most important factor for rich dynamical phenomena of ionic flows.

In this talk, we will focus on effects of permanent charges on ionic flow via a geometric singular perturbation analysis of Poisson-Nernst-Planck models and will report a number of findings, some are counter-intuitive.