Nonequilibrium thermodynamic foundation of the grand-potential phase field model

TL;DR

This paper establishes a thermodynamic foundation for the grand-potential phase field model, highlighting its implications for mass exchange and equilibrium conditions in phase transformations.

Contribution

It demonstrates that the grand-potential phase field model minimizes the Helmholtz free energy under mass conservation, providing a thermodynamic basis for its use.

Findings

Grand-potential model minimizes Helmholtz free energy at equilibrium

In the grand-potential model, the grand potential does not decrease monotonically

Mass exchange with surroundings invalidates mass conservation in the model

Abstract

Choosing the correct free energy functional is critical when developing thermodynamically consistent phase field models. We show that the grand-potential phase field model minimizes the Helmholtz free energy when mass conservation is imposed. While both functionals are at a minimum at equilibrium, the Helmholtz free energy decreases monotonically with time in the grand-potential phase field model, whereas the grand potential does not. Minimizing the grand potential implies a different problem where a system can exchange mass with its surroundings at every point, leading to a condition of isochemical potential and invalidating mass conservation of the system.