Phase field approximation of a kinetic moving-boundary problem modelling dissolution and precipitation
The authors consider a phase field model describing a one-phase free boundary problem (Stefan-like problem) with a kinetic condition at the moving boundary. The motivating background is the modelling of a process involving transport of solutes by diffusion in a fluid undergoing a precipitation/dissolution reaction. This process can also be modelled by a sharp interface free boundary problem. Using a formal asymptotic analysis the authors are able to prove that the phase field model approximates in the limit \(\varepsilon \rightarrow 0\) the sharp interface model. Herein \(\varepsilon \) denotes the thickness of an interfacial layer containing the moving boundary. The existence and uniqueness of solutions to the phase field model is investigated in detail. Numerical experiments demonstrate the approximating behaviour of the phase field model. The bibliography contains 16 items.
scientific article; zbMATH DE number 5903240