Application of the Level-Set Method to a Mixed-Mode and Curvature Driven Stefan Problem

This study focuses on the dissolution and growth of small possibly initially non-smooth particles within a diffusive phase. The dissolution or growth of the particle is assumed to be affected by concentration gradients of a single chemical element within the diffusive phase at the particle boundary caused by diffusion and by an interface reaction. The combined formulation results in a mixed-mode formulation. The moving boundary problem is solved using a level-set method and finite-element techniques such as SUPG. The appropriate meshes are derived using a fixed background mesh and the level-set function. We experimentally show that these techniques give mass-conserving solutions in the limit of infinite resolution, give a linear experimental order of convergence, can handle arbitrary particles and give the possibility to incorporate surface tensions using the Gibbs-Thomson effect and the local curvature.