Phase field approximation of a kinetic moving-boundary problem modelling dissolution and precipitation

We present a phase field model which approximates a one-phase Stefan-like problem with a kinetic condition at the moving boundary, and which models a dissolution and precipitation reaction. The concentration of dissolved particles is variable on one side of the free boundary and jumps across the free boundary to a fixed value given by the constant concentration of the particles in the precipitate. Using a formal asymptotic analysis we show that the phase field model approximates the appropriate sharp interface limit. The existence and uniqueness of solutions to the phase field model is studied. By numerical experiments the approximating behaviour of the phase field model is investigated.