Spreading equilibria under mildly singular potentials: pancakes versus droplets
| Autor: | Riccardo Durastanti, Lorenzo Giacomelli |
|---|---|
| Přispěvatelé: | Durastanti, Riccardo, Giacomelli, Lorenzo |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Physical sciences
Alt–Phillips functional Pancake Free boundary problems Scaling law Spreading coefficient Droplet Effective contact angle Mathematics - Analysis of PDEs FOS: Mathematics Singular minimization problem Alt–Caffarelli functional Asymptotic behavior Attractive-repulsive potential Complete wetting Inter-molecular potential Lubrication theory Macroscopic contact angle Mass constraint Partial wetting Precursor Singular potential Thin-film equation Uniqueness Mathematical Physics Applied Mathematics General Engineering Mathematical Physics (math-ph) Modeling and Simulation Analysis of PDEs (math.AP) |
| Popis: | We study global minimizers of a functional modeling the free energy of thin liquid layers over a solid substrate under the combined effect of surface, gravitational, and intermolecular potentials. When the latter ones have a mild repulsive singularity at short ranges, global minimizers are compactly supported and display a microscopic contact angle of $\pi/2$. Depending on the form of the potential, the macroscopic shape can either be droplet-like or pancake-like, with a transition profile between the two at zero spreading coefficient. These results generalize, complete, and give mathematical rigor to de Gennes' formal discussion of spreading equilibria. Uniqueness and non-uniqueness phenomena are also discussed. Comment: 46 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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