Multiscale thermodynamics of charged mixtures

Petr Vágner,Michal Pavelka,Oğul Esen

doi:10.1007/s00161-020-00900-5

Abstract

A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization, and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely geometric way by means of semidirect products. This leads to a complex Hamiltonian system with a new Poisson bracket, which can be used in principle with any energy functional. The thermodynamic (irreversible) part is added as gradient dynamics, generated by derivatives of a dissipation potential, which makes the theory part of the GENERIC framework. Subsequently, Dynamic MaxEnt reductions are carried out, which lead to reduced GENERIC models for smaller sets of state variables. Eventually, standard engineering models are recovered as the low-level limits of the detailed theory. The theory is then compared to recent literature.

Highlights

Theoretical electrochemistry aims to describe and predict behavior of chemically reacting systems of charged substances
This paper aims to develop a hierarchy of continuum models on different levels of description using the framework of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) [1,2,3,4]
Müller in [67] published a comprehensive analysis of fluid mixtures coupled with electromagnetic fields, including polarization and magnetization which will be further referred as the DGM approach

Summary

Introduction

Theoretical electrochemistry aims to describe and predict behavior of chemically reacting systems of charged substances. The modeling methods vary according to the characteristic times, lengths and details of the observed electrochemical systems. This paper aims to develop a hierarchy of continuum models on different levels of description using the framework of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) [1,2,3,4]. Consider an isolated system described by state variables x. The state variables can be for instance position and momentum of a particle, field of probability density on phase space, Communicated by Andreas Öchsner.

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Conclusion