Mathematical Modeling of Electrochemical Systems at Multiple Scales in Honor of Professor John Newman

Abstract

Newman's developments of electrochemical thermodynamics and transport phenomena are extended to account for changes in elastic or plastic deformation stress, as well as for varying pressure, temperature, and composition. The material, momentum, energy, and entropy balances from concentrated-solution transport theory are modified to include extended underpinning thermodynamic relationships. Various colligative properties describing electrolytic materials at equilibrium are identified through analysis of the Gibbs function, which also gives rise to state equations for volume, deformation strain, and entropy. A dynamical analysis on the continuum scale produces multiphysical versions of the equation of motion and the heat equation. The discussion concludes with a statement of the second law from the perspective of irreversible thermodynamics, providing a basis for the future development of transport constitutive laws for ion conductors with elastic, as well as viscous, character.