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arXiv · 2302.06269

Effects of surface tension and elasticity on critical points of the Kirchhoff-Plateau problem

Giulia Bevilacqua·Chiara Lonati
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Abstract

We introduce a modified Kirchhoff-Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic midline. In a specific setting, we characterize quantitatively some properties of minimizers. Indeed, choosing three different geometrical shapes for the cross-section, we derive Euler-Lagrange equations for a planar version of the Kirchhoff-Plateau problem. We show that in the physical range of the parameters, there exists a unique critical point satisfying the imposed constraints. Finally, we analyze the effects of the surface tension on the shape of the cross-sections at the equilibrium.

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Giulia Bevilacqua, Chiara Lonati. 2023-02-13. Effects of surface tension and elasticity on critical points of the Kirchhoff-Plateau problem. https://doi.org/10.1007/s40574-023-00392-6

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