  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.
