Geometric tools for complex interfaces: from lung surfactant to the mussel byssus

Interfaces are ubiquitous in nature and absolutely key for life as illustrated by such complex interfaces as the cell membrane and the endothelial and epithelial linings of tissues. The mechanical properties of these interfaces play an important role in their biological functions. In this highlight, we describe our recent work (Pocivavsek et al., Science, 2008, 320, 912) using geometry as a tool for studying the behavior of complex interfaces. General scaling laws emerging from studying the shape of elastic interfaces can in turn be used in their characterization. Interfacial wrinkling is a well known phenomenon, however, the geometric patterns seen at biological interfaces are often far from idealized sinusoidal wrinkles. We show how more complex and non-linear patterns naturally emerge from wrinkles and how material properties can be extracted from these non-linear geometries.