Thin sheets achieve optimal wrapping of liquids

A liquid drop can wrap itself in a sheet using capillary forces [Py et al., PRL 98, 2007]. However, the efficiency of ``capillary origami'' at covering the surface of a drop is hampered by the mechanical cost of bending the sheet. Thinner sheets deform more readily by forming small-scale wrinkles and stress-focussing patterns, but it is unclear how coverage efficiency competes with mechanical cost as thickness is decreased, and what wrapping shapes will emerge. We place a thin ($\sim 100$ nm) polymer film on a drop whose volume is gradually decreased so that the sheet covers an increasing fraction of its surface. The sheet exhibits a complex sequence of axisymmetric and polygonal partially- and fully- wrapped shapes. Remarkably, the progression appears independent of mechanical properties. The gross shape, which neglects small-scale features, is correctly predicted by a simple geometric approach wherein the exposed area is minimized. Thus, simply using a thin enough sheet results in maximal coverage.