A Maxwell-Ampère Nernst-Planck Framework for Modeling Charge Dynamics
arXiv:2202.07366 · doi:10.1137/22M1477891
Abstract
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 the description of charge dynamics. The MANP model with a curl-free condition on the electric displacement is shown to be energy dissipative with respect to a convex free-energy functional, and demonstrated to be equivalent to the Poisson-Nernst-Planck model. By the energy dissipation law, the steady state of the MANP model reproduces the charge conserving Poisson--Boltzmann (PB) theory, providing an alternative energy stable approach to study the PB theory. In order to achieve the curl-free condition, a companion local curl-free relaxation algorithm, which is shown to naturally preserve the discrete Gauss's law and converge robustly with linear computational complexity, is developed for the MANP model. One of the main advantages of our development is that it can efficiently deal with space-dependent permittivity instead of solving the variable-coefficient Poisson's equation. Many-body effects such as ionic steric effects and Coulomb correlations can be incorporated within the MANP framework to derive modified MANP models for problems in which the mean-field approximation fails. Numerical results on the charge dynamics with such beyond mean-field effects in inhomogeneous dielectric environments are presented to demonstrate the performance of the MANP models in the description of charge dynamics, illustrating that the proposed MANP model provides a general framework for modeling charge dynamics.
References in corpus (16)
- Diffuse-Charge Dynamics in Electrochemical Systems
- Steric Effects in Electrolytes: A Modified Poisson-Boltzmann Equation
- An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm
- Local Simulation Algorithms for Coulomb Interaction
- Local Molecular Dynamics with Coulombic Interaction
- Ionic channels in biological membranes. Electrostatic analysis of a natural nanotube
- Coulomb Interactions via Local Dynamics: A Molecular--Dynamics Algorithm
- Simulation of Electric Double Layers around Charged Colloids in Aqueous Solution of Variable Permittivity
- Computing Coulomb Interaction in Inhomogeneous Dielectric Media via a Local Electrostatics Lattice Algorithm
- Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches
- Dynamics of a Local Algorithm for Simulating Coulomb Interactions
- A Continuum,O(N) Monte-Carlo algorithm for charged particles
- A minimizing principle for the Poisson-Boltzmann equation
- Simple and Robust Solver for the Poisson-Boltzmann Equation
- Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media
- Linear-Scaling Selected Inversion based on Hierarchical Interpolative Factorization for Self Green's Function for Modified Poisson-Boltzmann Equation in Two Dimensions