We present a mathematical model for Joule heating of an electrolytic solution in a nanopore. The model couples the electrical and thermal dynamics responsible for rapid and extreme superheating of the electrolyte within the nanopore. The model is implemented numerically with a finite element calculation, yielding a time and spatially resolved temperature distribution in the nanopore region. Temperatures near the thermodynamic limit of superheat are predicted to be attained just before the explosive nucleation of a vapor bubble is observed experimentally. Knowledge of this temperature distribution enables the evaluation of related phenomena including bubble nucleation kinetics, relaxation oscillation, and bubble dynamics.
