The science of thin liquid films has developed rapidly in recent years, with applications to coating flows, biofluids, microfluidic engineering, and medicine. In this project, we will focus on three groups of free-surface flow problems using a combination of mathematical modeling, analysis and numerical simulation, coupled to carefully chosen quantitative experiments. The three areas are: (i) flows driven by surface tension gradients, (ii) the role of inertia in regimes where lubrication is inadequate to model thin film flow, and (iii) vibrating thin films. Advances in our understanding of theoretical issues surrounding modeling these flows, and the exploration of new features of the flows through experiments will have direct applications to improving control and reliability of manufacturing processes in high-tech industries and to biomedical systems.
The flow of thin liquid layers or films occurs in contexts including industrial coating flows, microfluidic engineering, and medicine. In this project, we focus on properties of thin liquid films such as the role of surface tension in driving flow, and the behavior of thin layers under rapid vibration. Surface tension is an important mechanism in the dynamics of mucus layers in the lung, and is central to the treatment of premature infants by surfactant replacement therapy. The control of thin layer flow, through the temperature dependence of surface tension or using rapid vibrations, has the potential to eliminate damaging nonuniformities in industrial coating processes. Each of these areas and applications pose substantial scientific challenges that will be met with a collaborative effort between mathematicians and physicists, exploring theoretical and experimental methods in tandem. The project includes graduate and undergraduate student training in an interdisciplinary research program that will develop coordinated advanced skills in physics, engineering, and applied mathematics.
