The equilibrium and stability of a sessile droplet laid on a spherical substrate in the presence of line tension are studied within a continuum approach. The destabilizing role played by the substrate’s curvature is analysed in detail for both positive and negative line tensions. In the former case, several bifurcation diagrams exist which show, among other things, that stable equilibria can fail to exist when the droplet size, the substrate size and the ratio between the line and the surface tension are comparable to one another. When line tension is negative, the substrate’s curvature enhances the destabilization of sessile droplets.
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