s (MSPRF) program and therefore had two overarching goals (1) to provide scientific development of the PI through post-doctoral experience and (2) to advance the state of mathematical science through the outcomes the proposed project. The post-doctoral research was carried out in the Mathematics Department at MIT under the sponsorship of Professor John Bush. The Mathematics Department at MIT is one of only a few math departments in the world to have a dedicated experimental lab facility. The facility allows the mathematicians to carry out physical experiments that can provide insight into mathematical models. The research project proposed in this grant combined theory and experiments carried out in this facility. The nature of the project was to mathematically model and investigate the shape of thin, liquid films as they retract under the influence of surface tension. The initial focus was on the popping dynamics of large, viscous interfacial bubbles. Gas that is entrained in a liquid will rise to the surface of a liquid, producing a thin-film bubble that eventually ruptures. Over a decade ago, scientists observed that if these bubbles are sufficiently viscous, they will wrinkle as they pop. It was believed that this wrinkling was the result the fixed surface area being crumpled by an external force (here gravity). Indeed, the phenomenon is referred to as the "parachute instability," as the published mathematical models have all been analogous to those that would model a collapsing parachute wrinkling under its own weight. However, the results from this NSF-funded project have demonstrated that gravity is negligible in this process, and instead that surface responsible for neither the collapse nor the resulting instability that wrinkles the film. Using a combination of experiments and theory, we investigated why capillary forces display attributes that are normally exclusive to gravitational forces. The results are intellectually interesting because typically wrinkling can be rationalized by quasi-static calculations; in this particular case, a quasi-static analysis does not lead to wrinkling, suggesting a dynamic origin. Such dynamics may be relevant to natural and industrial processes that involve bubbling viscous material, such as volcanoes and glass manufacturing. A later focus of the project shifted to the retraction of liquid films on superhydrophobic surfaces, as this retraction time is important in the overall contact time of a drop on a non-wetting solid. When a drop impacts a non-wetting surface, it spreads and then can retract so rapidly that it completely leaves the surface. These dynamics have been mathematically modeled; however, there has been a tacit assumption that the dynamics are axisymmetric, leading to a theoretical minimum in the contact time. In collaboration with a team in Mechanical Engineering at MIT, we demonstrated both theoretically and experimentally, that it was possible to overcome this assumed minimum by breaking radial symmetry during the thin-film recoil. These findings have broad implications for applications in which it is advantageous to minimize drop contact time, such as preventing ice buildup on airplane wings. The experiments and mathematical model were published in Nature in 2013.
