Collaborative proposal: Focused Research Group on Fundamental Problems in the Dynamics of Thin Viscous Films and Fluid Interfaces

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0074049BertozziA combined experimental, analytical, and computational study of fundamental problems in the dynamics of thin viscous films and fluid interfaces is proposed. The recent discovery of stable undercompressive waves in driven films has created the opportunity for a unique collaboration between experiments and mathematical theory. This research program will include related studies of solid-liquid-vapor interfaces, moving contact lines, and surface tension effects. Analytical and computational studies will be integrated with a series of experiments that includes a search for undercompressive waves in a spin coating geometry, motion of contact lines near room- temperature critical points, and high-speed video imaging of the dynamics of singularity formation in finite-time rupture of fluid interfaces. Mathematical analysis will include models for film rupture, stability of driven contact lines, and numerical analysis of schemes for computing these problems.Liquid films and moving contact lines arise in problems ranging from industrial design of paints and microchip fabrication to medical applications including contact lenses and the lining of the lung. All of these problems involve interactions across widely different length-scales in which the physical laws are not clearly understood. This is a collaboration between researchers from the Mathematics (Bertozzi, Witelski) and Physics (Behringer) Departments at Duke University and the Mathematics Department at North Carolina State University (Shearer). This effort combines mathematical modeling, analysis, and numerical simulation with new laboratory experiments to study fundamental problems in driven films and moving contact lines. Computational and mathematical models will direct the design of experiments investigating new phenomena in spin coating processes and dewetting films. The program will involve undergraduates, graduate students, postdoctoral associates, and visiting scientists from other institutions. This research will foster curriculum developments in the Departments of Mathematics, Physics and the Center for Nonlinear and Complex Systems at Duke University