MATHEON-ICM WORKSHOP on Free Boundaries and Materials Modeling - Abstract
Kimmerle, Sven-Joachim
Based on a thermodynamical consistent model for precipitation in GaAs crystals including surface tension and bulk stresses by Dreyer and Duderstadt, we propose a diffusion model with sharp interfaces to describe the radii evolution of liquid droplets in a crystalline solid. The problem exhibits different scales for typical particle distances and typical radii of liquid droplets which motivates a mean field model. Our model takes conservation of mass and substance into account and generalises the well-known LSW model for Ostwald ripening for which a lot of rigorous results already exist.
Precisely, we concentrate here on As-rich liquid spherical droplets and assume a homogeneous liquid. The model leads to a parabolic nonlinear PDE for the chemical potential. The barycentric velocity, which enters into the PDE, is determined from a mechanical BVP. The boundaries of the droplets are free boundaries and their radii evolve under Stefan conditions depending on a small parameter. A mean field ansatz reduces the problem to a large system of ODE's coupled by a mean field.
Further members of the Matheon-project: W. Dreyer (WIAS), F. Duderstadt (WIAS), M. Herrmann (HU), M. Naldzhieva (WIAS), B. Niethammer (HU/Oxford)