Energetic Variational Approach for Prediction of Thermal Electrokinetics in Charging and Discharging Processes of Electrical Double Layer Capacitors

TL;DR

This paper introduces a thermodynamically consistent variational model to predict thermal electrokinetics in EDLCs, capturing heat generation, temperature oscillations, and ion transport dynamics during charging and discharging.

Contribution

It develops a novel energetic variational approach combining thermodynamics and electrokinetics to model non-isothermal ion transport in EDLCs.

Findings

Successfully predicts temperature oscillations during charging/discharging.

Shows thermal electrokinetics cannot follow rapid surface potential changes.

Identifies hysteresis effects in ion transport at high scan rates.

Abstract

This work proposes a new variational, thermodynamically consistent model to predict thermal electrokinetics in electric double layer capacitors (EDLCs) by using an energetic variational approach. The least action principle and maximum dissipation principle from the non-equilibrium thermodynamics are employed to develop modified Nernst-Planck equations for non-isothermal ion transport with temperature inhomogeneity. Laws of thermodynamics are employed to derive a temperature evolution equation with heat sources due to thermal pressure and electrostatic interactions. Numerical simulations successfully predict temperature oscillation in the charging-discharging processes of EDLCs, indicating that the developed model is able to capture reversible and irreversible heat generations. The impact of ionic sizes and scan rate of surface potential on ion transport, heat generation, and charge current is systematically assessed in cyclic voltammetry simulations. It is found that the thermal electrokinetics in EDLCs cannot follow the surface potential with fast scan rates, showing delayed dynamics with hysteresis diagrams. Our work thus provides a useful tool for physics-based prediction of thermal electrokinetics in EDLCs.