Geometry-driven folding transitions in floating thin films

When a thin elastic sheet is compressed, it forms wrinkles to gather excess material, while deforming the fluid or solid substrate by only a small amount. Upon further compression, the sheet may fold, in order to lower the mechanical energy of the system$^1$. Here we demonstrate a folding transition that is independent of the mechanical properties of the sheet. We study the deformations of a thin polymer film that has an annular shape, floating on a planar air-water interface. By controlling the concentration of a surfactant outside the film, we vary the tension pulling on the outer boundary of the annulus. The sheet spontaneously folds at a threshold ratio of inner to outer surface tension that depends on the geometry of the sheet, but is independent of its bending rigidity. Our results are consistent with a simple geometric principle: the sheet adopts the unstretched shape that minimizes the interfacial energy of the exposed liquid$^2$. Finally, we consider the application of this geometric principle to the folding of a floating indented film.\\\\ 1. Pocivavsek et al., Science 320, 912 (2008).\\ 2. Paulsen et al., Nature Materials, doi:10.1038/nmat4397 (2015).