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Updated: Jul 19, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
Published on: May 18, 2021
Transient finite element analysis of electric double layer using Nernst-Planck-Poisson equations with a modified
Jongil Lim1, John Whitcomb, James Boyd
1Department of Aerospace Engineering, Texas A & M University, College Station, TX 77843, USA.
Abstract:
A finite element implementation of the transient nonlinear Nernst-Planck-Poisson (NPP) and Nernst-Planck-Poisson-modified Stern (NPPMS) models is presented. The NPPMS model uses multipoint constraints to account for finite ion size, resulting in realistic ion concentrations even at high surface potential. The Poisson-Boltzmann equation is used to provide a limited check of the transient models for low surface potential and dilute bulk solutions. The effects of the surface potential and bulk molarity on the electric potential and ion concentrations as functions of space and time are studied. The ability of the models to predict realistic energy storage capacity is investigated. The predicted energy is much more sensitive to surface potential than to bulk solution molarity.
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