A redefined energy functional to prevent mass loss in phase-field methods

Phase-field modeling has gained considerable attention for the study of two-phase systems. The method consists of introducing a field that can represent the state of matter or the atomic species concentration. In this way, the fields identify locally the phase present at a given point and also the location of interfaces. However, a well-known limitation of phase-field methods is (enclosed) mass loss and bulk diffusion, which has motivated numerous approaches in order to counteract these issues. In this work, it is shown that both issues can be attributed to a nonphysical term originating from the definition of the energy functional, which causes mass change by mean curvature. Therefore, a redefined energy functional is presented, which ensures a proper energy balance. While avoiding the nonphysical bulk diffusion, it achieves conservation of (enclosed) mass as well. Furthermore, overall system dynamics remain comparable to the classic energy functional. The redefined energy potential is still able to model spinodal decomposition, while it matches sharp interface results better when applied to a two-phase system.