Thin Layer Flow: Experiments, Modeling, and Analysis

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ShearerDMS-0604047 Recent results suggest that there are strong connectionsbetween the science and mathematics of thin liquid films and theflow of thin layers of granular materials. The investigatorsexplores these connections through modeling, analysis, numericalsimulation and experiments. They study multidimensionalnonlinear systems of partial differential equations of avalanchemodels, and the connection to experiments, to gain new insightsinto fundamental aspects of granular and avalanche mechanics. Inrelated studies, the investigators formulate and analyze systemsof partial differential equations for thin liquid films driven bysurfactants or controlled by temperature. These equations giverise to mathematical theory addressing new wave structuresobserved in experiments and simulations. The investigators explore strong connections between thescience and mathematics of thin liquid films and the flow of thinlayers of granular materials. Thin films are important inmedical applications such as surfactant replacement therapy, andin microscopic coating flows that arise in industry andmanufacturing. Granular materials occur over a large range oflength scales, from pharmaceuticals and agricultural grains torocks and gravel in landslides. The results of this projectfurther the understanding of issues of both specializedscientific interest and of broad significance to society, such asthe identification of mechanisms of wave propagation and patternsin surfactant transport in human lungs, and the separation bysize of rocks and other particles in avalanches. This projectincorporates training of mathematics and physics graduate andundergraduate students in mathematics, simulation, andexperimental physics in a multidisciplinary research program. The participation of under-represented groups builds on recentsuccesses. Results from this project are disseminated throughjournal publications, special sessions and lectures atinternational conferences, articles in popular sciencepublications, and through a project web page.