PoissonNernstPlancksystem
PoissonNernstPlancksystem, commonly referred to as the Poisson–Nernst–Planck (PNP) system, is a continuum model that describes the spatiotemporal evolution of ionic concentrations and electric potential in electrolytes under the influence of an electric field. It treats ions as charged species undergoing diffusion and migration in response to electrostatic forces, and it couples the Poisson equation for the electric potential with Nernst-Planck equations for each ionic species.
For each species i, with concentration c_i(x,t), valence z_i, diffusion coefficient D_i, and elementary charge e,
Boundary conditions may specify fixed concentrations or fluxes, and electrode surfaces may impose a specified potential
Applications include modeling ion transport in microfluidic channels, nanopores, and biological ion channels, as well as