Permanent charge effects on Current-Voltage relations via classical Poisson-Nernst-Planck systems under relaxed electroneutrality boundary conditions.

This work investigates the dynamics of ionic flows through a classical Poisson-Nernst-Planck model incorporating two oppositely charged ion species and small permanent charges. By integrating boundary layer effects into current-voltage relations, we analyze how ionic flow dynamics are influenced by the interplay of physical parameters including permanent charge, channel geometry, and ion diffusion coefficients. Within a simplified modeling framework, we identify several critical potentials that offer mechanistic insights into electrodiffusion processes in biological channels. Extending the work presented in [Membranes 2023, 13, 131], we examine the sequence of these critical potentials and characterize how small permanent charges affect ion flux within the boundary layer. Numerical simulations are conducted to illustrate the analytical results intuitively.