Finite-displacement elastic solution due to a triple contact line

Abstract

At the line of triple contact of an elastic body with two immiscible fluids, the body is subjected to a force concentrated on this line, the fluid-fluid surface tension. In the simple case of a semi-infinite body, limited by a plane, a straight contact line on this plane, and a fluid-fluid surface tension normal to the plane, the classical elastic solution leads to an infinite displacement at the contact line and an infinite elastic energy. By taking into account the body-fluid surface tension (i.e., isotropic surface stress), we present a new and more realistic solution concerning the semi-infinite body, which gives a finite displacement and a ridge at the contact line, and a finite elastic energy. This solution also shows that Green's formulae, in the volume and on the surfaces, are valid (these formulae play a central role in the theory).