Abstract:

The Variable Dielectric Poisson-Nernst-Planck (VDPNP) equations are models that describe ion transport behavior in electrolyte solutions. These equations extend the classical Poisson-Nernst-Planck (PNP) equations by introducing a dependence of the dielectric constant on ion concentration, which allows for a better description of the complex dynamic processes in electrolyte solutions. To investigate the impact of the VDPNP equations on system interactions, this paper first solves the VDPNP model using the Gummel finite element method. Subsequently, numerical simulations of nanopore systems are performed. The simulation results show that, in mixed solutions, the traditional PNP equations cannot distinguish between sodium and potassium ions based on concentration, whereas the VDPNP models can clearly differentiate between sodium and potassium ions. Furthermore, the distinguishing effect becomes more pronounced as the surface charge increases.

Key words: variable Dielectric Poisson-Nernst-Planck equations, finite element method, numerical simulation