A special case study of boundary layer effects via Poisson-Nernst-Planck systems with permanent charges

摘要

In this work, we study a quasi-one-dimensional classical Poisson-Nernst-Planck model with oppositely charged ion species. A simple profile of permanent charges: zeros at the two end regions and a constant over the middle region is included. Of particular interest is the effect on ionic flows from the permanent charge (small) with boundary layers. The nonlinear interplay among system parameters is characterized in great details, which provides insights into the qualitative properties of ionic flows of interest.