The electroneutrality constraint in nonlocal models

Area of Science:

• Computational chemistry
• Physical chemistry
• Chemical engineering

Background:

• Multicomponent ionic systems involve complex reaction and diffusion dynamics.
• Modeling ion transport across membranes requires accounting for induced electric fields.
• Strict electroneutrality is a key criterion in ionic system simulations.

Purpose of the Study:

• To develop and apply a nonlocal Nernst-Planck model for multicomponent ionic systems.
• To investigate the performance of charge conservation and Gauss' law in modeling electric fields.
• To assess the adherence to strict electroneutrality under various initial conditions.

Main Methods:

• Development of a nonlocal Nernst-Planck model.
• Application to a one-dimensional liquid junction problem with a permeable membrane.
• Modeling induced electric fields using nonlocal charge conservation and Gauss' law.
• Analysis of four different initial scenarios to evaluate electroneutrality.

Main Results:

• Both charge conservation and Gauss' law provide similar results when initial conditions satisfy strict electroneutrality.
• Gauss' law demonstrates superior numerical stability, especially when species concentrations approach zero.
• Gauss' law is computationally more efficient than charge conservation.
• Insights into electroneutrality conditions for nonlocal peridynamic models were gained.

Conclusions:

• Gauss' law offers significant advantages in numerical stability and computational cost for modeling ionic systems.
• The study provides crucial insights for handling evolving charges in nonlocal reaction-diffusion and corrosion models.
• The developed model and findings are applicable to various electrochemical and materials science problems.