Mechanics of pendant drops and axisymmetric membranes

Drop shape analysis of pendant drops is a commonly used technique to measure the interfacial tension of liquid-vapor or liquid-liquid interfaces. The technique is increasingly being used to investigate the mechanical response of molecular structures that form at these interfaces as well, utilizing analysis techniques developed by the solid mechanics community. The aim of this highlight is to summarize the formal analysis methods needed to analyze these types of experiments and to make the connection between liquid-like behavior of the interface, and the more general solid-like case where the two principal interfacial tensions are not necessarily equal to one another. Several illustrative examples are used to accomplish this, including protein complexes formed at the oil-water interface, ionically crosslinked block copolymer monolayers at oil-water interfaces, and block copolymer-based thermoplastic elastomers at the air-water interface. In addition to describing the mechanical analysis of these types of experiments, we provide a stability map that defines the experimental window within which useful pendant drop experiments can be conducted for interfacial layers with liquid-like behavior.