How to model surface diffusion using the phase-field approach
Abstract
It is demonstrated that the description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach previously used in the literature is shown to fail to produce the correct asymptotics, albeit in a subtle manner. An apparently obvious alternative fails for a complementary reason. Finally, a model is constructed that asymptotically approaches known sharp-interface equations without adding undesired constraints. In order to provide a complete physical example, the model is exhibited for the elastically induced Grinfeld instability with material transport by surface diffusion. The whole analysis is carried out for three-dimensional systems to pave the way for simulations in 3D.
Cite
@article{arxiv.cond-mat/0607823,
title = {How to model surface diffusion using the phase-field approach},
author = {Klaus Kassner},
journal= {arXiv preprint arXiv:cond-mat/0607823},
year = {2007}
}
Comments
Submitted to "Multiscale Modeling and Simulation"