Thin Layer Flow: Experiments, Modeling, and Analysis

North Carolina State University, Raleigh NC

Investigators

Abstract

Shearer DMS-0604047 Recent results suggest that there are strong connections between the science and mathematics of thin liquid films and the flow of thin layers of granular materials. The investigators explores these connections through modeling, analysis, numerical simulation and experiments. They study multidimensional nonlinear systems of partial differential equations of avalanche models, and the connection to experiments, to gain new insights into fundamental aspects of granular and avalanche mechanics. In related studies, the investigators formulate and analyze systems of partial differential equations for thin liquid films driven by surfactants or controlled by temperature. These equations give rise to mathematical theory addressing new wave structures observed in experiments and simulations. The investigators explore strong connections between the science and mathematics of thin liquid films and the flow of thin layers of granular materials. Thin films are important in medical applications such as surfactant replacement therapy, and in microscopic coating flows that arise in industry and manufacturing. Granular materials occur over a large range of length scales, from pharmaceuticals and agricultural grains to rocks and gravel in landslides. The results of this project further the understanding of issues of both specialized scientific interest and of broad significance to society, such as the identification of mechanisms of wave propagation and patterns in surfactant transport in human lungs, and the separation by size of rocks and other particles in avalanches. This project incorporates training of mathematics and physics graduate and undergraduate students in mathematics, simulation, and experimental physics in a multidisciplinary research program. The participation of under-represented groups builds on recent successes. Results from this project are disseminated through journal publications, special sessions and lectures at international conferences, articles in popular science publications, and through a project web page.