A finite element solver for a thermodynamically consistent electrolyte model

2025-05-22

AI Summary

Classical Nernst–Planck models suffer from thermodynamic inconsistency in highly concentrated electrolytes due to coupled steric hindrance, explicit solvation, and fluid compressibility under pressure. Method: We develop a thermodynamically consistent finite-element solver for multicomponent electrolytes, adopting atomic fractions, electric potential, and pressure as primary variables. Our formulation rigorously enforces mass conservation, electroneutrality, and non-negative entropy production, and—uniquely—integrates steric effects, explicit solvation, and fluid compressibility within a unified variational framework. Implemented modularly in FEniCSx, it couples the Poisson equation, modified species conservation laws, and thermodynamically grounded constitutive relations in one- and two-dimensional settings. Results: The solver demonstrates robust convergence under strong concentration gradients and high pressure differentials. It accurately reproduces double-layer evolution and ionic rectification, and quantitatively elucidates the coupled influence of solvation number, Debye length, and bulk compressibility on ion transport.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Learning on the Edge & Model Compression
• Multiagent Systems: Distributed Problem Solving

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Economics, Online Markets and Human Computation: Sustainability of Web economics

Abstract

In this study, we present a finite element solver for a thermodynamically consistent electrolyte model that accurately captures multicomponent ionic transport by incorporating key physical phenomena such as steric effects, solvation, and pressure coupling. The model is rooted in the principles of non-equilibrium thermodynamics and strictly enforces mass conservation, charge neutrality, and entropy production. It extends beyond classical frameworks like the Nernst-Planck system by employing modified partial mass balances, the electrostatic Poisson equation, and a momentum balance expressed in terms of electrostatic potential, atomic fractions, and pressure, thereby enhancing numerical stability and physical consistency. Implemented using the FEniCSx platform, the solver efficiently handles one- and two-dimensional problems with varied boundary conditions and demonstrates excellent convergence behavior and robustness. Validation against benchmark problems confirms its improved physical fidelity, particularly in regimes characterized by high ionic concentrations and strong electrochemical gradients. Simulation results reveal critical electrolyte phenomena, including electric double layer formation, rectification behavior, and the effects of solvation number, Debye length, and compressibility. The solver's modular variational formulation facilitates its extension to complex electrochemical systems involving multiple ionic species with asymmetric valences.

Problem

• Develops finite element solver for thermodynamically consistent electrolyte transport
• Captures steric effects, solvation, and pressure coupling in ionic transport
• Enhances numerical stability and physical consistency beyond classical frameworks

Innovation

• Finite element solver for consistent electrolyte model
• Incorporates steric effects and solvation phenomena
• Modular variational formulation for complex systems