Discontinuous curvature in a thin-film profile near a three-phase contact line

The contact line at a solid-liquid-vapor interface is a region of localized forces. However, if the solid phase is thick and stiff, the consequent singularity in the otherwise smooth interfacial surfaces is barely noticeable. In this work, we address the nature of such a singular behavior when the solid phase is very stiff but also highly bendable. We study a system consisting of a thin polymer film partly floating on water with one end lifted up in the air, whose one-dimensional nature simplifies considerably the theory as well as collecting and analyzing high-quality data. Observing the contact line at capillary length scale (millimetres), over which the solid elasticity has a negligible effect, we show that the slope jumps at the three-phase contact line, and the shape is accurately described by the classical Young-Laplace equation. When observing the contact line over the bendo-capillary scale (~10-100 micrometres in our experiment), where bending energy is comparable to surface energy, we find that the discontinuity in the slope of the polymer film is regularised and the profile looks smooth. However, we find that even at this bendo-capillary scale, a higher-order discontinuity exists in the derivative of the curvature.