A thin polymer film with an annular shape that is floating on water. As the surface tension pulling on the outer edge is lowered, the sheet forms wrinkles and then two folds. The sheet is 394 nm thick and 16 mm wide.

Wrinkles are all around us — on hanging curtains, the skin of drying fruit, or a surprised forehead. The more a material is squished, the deeper and taller the wrinkles become, until they collapse into a fold. Typically, this process depends strongly on the materials in question, for example the thickness of the skin, or the softness of the flesh underneath. However, we show that a wrinkle-to-fold transition may be affected only by the shape of the compressed object, rather than by any mechanical properties!

We investigated an ultrathin elastic annulus (the shape and diameter of a large metal washer, but a thousand times thinner than a human hair) floating on water. When we varied the surface tension that pulls at the inner and outer edges, we found that wrinkles grow outwards from the central hole and then merge and collapse into a few folds. Strikingly, the process does not depend on the film’s thickness or the liquid density. Instead, it depends strongly on the sheet’s initial shape, which in turn deforms to reduce the exposed surface area of the fluid. Thus, a tricky mechanics problem becomes a simple geometry problem. This understanding gives a new path to controlling thin elastic sheets in natural and technological settings.

Geometry-driven folding of a floating annular sheet. J. D. Paulsen, V. Démery, K. B. Toga, Z. Qiu, T. Russell, B. Davidovitch, and N. Menon, Physical Review Letters 118, 048004 (2017).  pdf  link  bibtex