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Formulation and a new solving approach to the problem of the wetting-induced deformation

ABSTRACT Although elastic deformation of substrate caused by wetting has been studied extensively, the influence of capillary effect and surface elasticity on the wetting-induced deformation is still an open question. This issue is investigated from the perspective of continuum mechanics. Based on the analysis of the composition of total energy, the self-energy of the triple contact line is introduced as a new energy form, and the governing equations of the wetting-induced deformation are derived from minimization of the total energy. Among them, two sets of new equations describe the equilibrium of the triple contact line in the non-pinned and pinned states, respectively. The results show that the equilibrium of the triple contact line depends not only on its capillary line tension and elastic line tension but also on its curvature. In particular, we discover that the surface/interface elastic stress and surface/interface tension are mutually independent in the equilibrium of the non-pinned triple contact line, while they are correlated with each other in the pinned state of the triple contact line. When the surface/interface elasticity is overlooked, the elastic deformation of a semi-infinite substrate caused by a cap-shaped droplet is calculated analytically through a new approach in which the deformed wetting interface is approximately taken as a rotational ellipsoid surface. The calculation reproduces the deformation pattern of the substrate observed in the soft-substrate wetting experiments.