2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134626We prove the invariance of the contact angle in liquid-solid wetting phenomena : an electrified droplet is spreading on a solid surface. The drop is minimizing its energy. We express the differential of this energy with respect to the shape of the drop and deduce necessary conditions for optimality . By variational method, using well-chosen test functions, we obtain the main result about the contact angle between the drop and the solid.28 pages, 9 figuresClassical Analysis and ODEsOptimization and Control49K10, 49K20, 49K30text