We consider a model for vapor–liquid–solid growth of nanowires proposed in the physical literature. Liquid drops are described as local or global volume-constrained minimizers of the capillarity energy outside a semi-infinite convex obstacle modeling the nanowire. We first address the existence of global minimizers and then, in the case of rotationally symmetric nanowires, we investigate how the presence of a sharp edge affects the shape of local minimizers and the validity of Young’s law.
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Irene Fonseca, Nicola Fusco, Giovanni Leoni, Massimiliano Morini, Global and local energy minimizers for a nanowire growth model. Ann. Inst. H. Poincaré Anal. Non Linéaire 40 (2023), no. 4, pp. 919–957DOI 10.4171/AIHPC/54