Analysis of a Poisson–Nernst–Planck–Fermi model for Ion Transport in Biological Channels and nanopores

Abstract

In this talk, we analyse a Poisson-Nernst-Planck-Fermi model to describe the evolution of a mixture of finite size ions in liquid electrolytes, which move through biological membranes or nanopores. The ion concentrations solve a cross-diffusion system in a bounded domain with mixed Dirichlet-Neumann boundary conditions. A drift term due to the electric potential is also present in the equations. The latter is coupled to the concentrations through a Poisson-Fermi equation. The novelty and the advantage of this model is to take into account ion-ion correlations, which is really important in case of strong electrostatic coupling and high ion concentrations. The global-in-time existence of bounded weak solutions is proved, employing the boundedness-by-entropy method, extended to nonhomogeneous boundary conditions. Furthermore, the weak-strong uniqueness result is also presented.