Expand into collapse: gross and fine structures of an inflated balloon

Inflatable structures such as balloons harbor the interplay among pressure driving, mechanical response and geometrical constraint. We study such inflation by stitching two flat circular membranes, subject to a hydrostatic pressure. Regardless of the complex surface configuration, we report a simple shape assumed by the system, which can be understood quantitatively using coarse graining with a geometrical model. At a finer scale, on the other hand, the balloon surface collapses into deep folds with an increasing pressure. Using laser scattering, we measure the fold shape and obtain good agreement with our analytical prediction. We further compare our measured balloon cross sections with a simple toy-simulation to qualitatively study the emerging two-dimensional behavior embedded in an intrinsically three-dimensional setting. Our work is potentially applicable in scientific ballooning, parachuting and industrial encapsulation.