期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 29, 期 12, 页码 2183-2223出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202519500441
关键词
Young-Dupre; contact angle; wetting; triple junctions; thin films; sharp-interface model; transmission problems
资金
- Center for Nonlinear Analysis (NSF) [DMS-0635983]
- Austrian Science Fund (FWF) [P 27052, P 29681]
- Vienna Science and Technology Fund (WWTF)
- Berndorf Privatstiftung [MA16-005]
- SFB project F65 Taming complexity in partial differential systems
- City of Vienna
We present here an analysis of the regularity of minimizers of a variational model for epitaxially strained thin-films. The regularity of energetically-optimal film profiles is studied by extending previous methods and by developing new ideas based on transmission problems. The achieved regularity results relate to both the Stranski-Krastanow and the Volmer-Weber modes, the possibility of different elastic properties between the film and the substrate, and the presence of the surface tensions of all three involved interfaces: film/gas, substrate/gas, and film/substrate. Finally, geometrical conditions are provided for the optimal wetting angle, i.e. the angle formed at the contact point of films with the substrate. In particular, the Young-Dupre law is shown to hold, yielding what appears to be the first analytical validation of such law for a thin-film model in the context of Continuum Mechanics.
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