Drop Spreading and Confinement in Swelling-Driven Folding of Thin Films

Surface instabilities are a versatile method for generating three-dimensional (3D) surface microstructure. When an elastomeric film weakly bonded to a substrate is swollen with solvent, buckle delamination and subsequent sliding of the film on the substrate lead to the formation of tall, self-contacting, and permanent folds. This paper explores the mechanics of fold development when such folding is induced by placing a drop on the surface of the film. We show that capillary effects can induce a strong coupling between folding and drop spreading: as folds develop, they wick the solvent toward the periphery of the drop, further propagating radially aligned folds. Accordingly, a solvent drop spreads far more on films that are weakly adhered to the substrate. As drop size reduces and folding becomes increasingly confined, debonding propagates along the perimeter of the wetted region, thus leading to corral-shaped fold patterns. On the other hand, as drop size increases and confinement effects weaken, isotropically oriented folds appear at a spacing that reduces as swelling increases. The spacing between the folds and the size of the corrals are both determined by the extent to which a single fold relieves compressive stress in its vicinity by sliding. We develop a model for folding which explicitly accounts for the fact that folds must initiate with near-zero volume under the buckle. The model shows that folds can appear even at very low swelling if there are large pre-existing debonded regions at the film-substrate interface.