Energy stability of droplets and dry spots in a thin film model of hanging drops

Cheung, Ka Luen; Chou, Kai Seng

doi:10.1007/s00033-017-0852-2

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Droplets Of the Thin Film Equation1

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2022

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Cited by 2 publications

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“…Therefore, only a radially symmetric droplet with zero contact angle could be energy stable. Examples of energy stable droplets with zero contact angle can be found in [10]. In fact, in the model studied in this work, these droplets are global minimizers of the energy.…”

Section: Droplets Of the Thin Film Equationmentioning

confidence: 93%

A symmetry result for an elliptic problem arising from the 2-D thin film equation

Cheung

Chou

2016

Proc. Amer. Math. Soc.

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Section: Droplets Of the Thin Film Equationmentioning

confidence: 93%

A symmetry result for an elliptic problem arising from the 2-D thin film equation

Cheung

Chou

2016

Proc. Amer. Math. Soc.

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Spreading Equilibria Under Mildly Singular Potentials: Pancakes Versus Droplets

Durastanti

Giacomelli

2022

J Nonlinear Sci

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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 $$\pi /2$$ 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 for purely repulsive potentials. 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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Energy stability of droplets and dry spots in a thin film model of hanging drops

Cited by 2 publications

References 13 publications

A symmetry result for an elliptic problem arising from the 2-D thin film equation

A symmetry result for an elliptic problem arising from the 2-D thin film equation

Spreading Equilibria Under Mildly Singular Potentials: Pancakes Versus Droplets

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