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Thin elastic sheets at three-dimensional liquid interfaces
The interaction of a thin elastic object, such as a polymeric sheet, with a liquid interface occurs in a range of problems : from the everyday case of wet dog hairs clumping to the stiction of components during the fabrication of Microelectromechanical System (MEMS). Much previous work has focussed on understanding this interaction in two-dimensions. Here, a key simplification is that the elastic object is able to bend without changing its length. However, in three-dimensions, things are qualitatively different : a naturally flat object cannot bend in more than one direction without stretching. This geometrical restriction has consequences for a number of apparently simple problems, including the gentle poking of a floating elastic sheet and the equilibrium of a liquid droplet on a thin, supported membrane. (This latter problem has recently received renewed attention as a means of measuring pre-tensions within polymeric sheets.) I will discuss the consequences of three-dimensional deformations, focussing in particular on how and why intuitive ideas about the stresses in such sheets may break down.