A Maxwell–Ampère Nernst–Planck Framework for Modeling Charge Dynamics

Understanding the properties of charge dynamics is crucial to many practical applications, such as electrochemical energy devices and transmembrane ion channels. This work proposes a Maxwell–Ampère Nernst–Planck (MANP) framework for description dynamics. The MANP model with curl-free condition on electric displacement shown be dissipative respect convex free-energy functional, demonstrated equivalent Poisson–Nernst–Planck model. By dissipation law, steady state reproduces conserving Poisson–Boltzmann (PB) theory, providing an alternative stable approach study PB theory. In order achieve condition, companion local relaxation algorithm, which naturally preserve discrete Gauss’s law converge robustly linear computational complexity, developed One main advantages our development that it can efficiently deal space-dependent permittivity instead solving variable-coefficient Poisson’s equation. Many-body effects ionic steric Coulomb correlations incorporated within derive modified models problems in mean-field approximation fails. Numerical results beyond inhomogeneous dielectric environments are presented demonstrate performance dynamics, illustrating proposed provides general modeling