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Droplets Like to Wear Thin Polygonal Dresses
A flat sheet must deform to wrap a liquid drop. Thin sheets (∼ 100 nm) wrap using small-scale wrinkles and folds, unlike thick sheets, which only bend over large scales. These features cost little mechanical energy but give considerable freedom to deform without stretching. We demonstrate that the global wrapped shape (ignoring the local features) is obtained by minimizing the exposed liquid area under the constraint that the sheet cannot stretch, independent of the mechanical properties of the sheet. This purely geometrical approach accounts for the complex sequence of axisymmetric and polygonal wrapped shapes observed in our experiments. Surface tension alone thus drives axisymmetry breaking and a wrinkle to fold transition.