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arXiv · 2109.06683

Spreading equilibria under mildly singular potentials: pancakes versus droplets

Riccardo Durastanti·Lorenzo Giacomelli
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Abstract

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 $π/2$. 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.

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Riccardo Durastanti, Lorenzo Giacomelli. 2022-07-15. Spreading equilibria under mildly singular potentials: pancakes versus droplets. https://doi.org/10.1007/s00332-022-09826-5

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