Geometric motion for a degenerate Allen-Cahn/Cahn-Hilliard system: The partial wetting case
✍ Scribed by Amy Novick-Cohen; Lydia Peres Hari
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 431 KB
- Volume
- 209
- Category
- Article
- ISSN
- 0167-2789
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✦ Synopsis
Using formal asymptotics we demonstrate that in a low temperature coarsening limit, a degenerate Allen-Cahn/Cahn-Hilliard system yields a geometric problem in which small particles whose shape evolves according to surface diffusion move along a surface where the chemical potential is quasi-static, which itself moves by motion by mean curvature. The degenerate Allen-Cahn/Cahn-Hilliard system was developed in [J.W. Cahn, A. Novick-Cohen, Evolution equations for phase separation and ordering in binary alloys, J. Stat. Phys. 76 (1994) 877-909] to describe simultaneous ordering and phase separation, and within this context the particles which contain a minor disordered phase are embedded along grain boundaries which partition the system into two ordered phase variants. The limiting problem, though, can also be viewed as a diffuse interface approximation for various problems in materials science in which surface diffusion and motion by mean curvature are coupled, see, for example, [