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

对粘性薄膜和流体界面动力学的基本问题进行了实验、分析和计算相结合的研究。最近在驱动薄膜中发现了稳定的欠压缩波，这为实验和数学理论之间的独特合作创造了机会。这项研究计划将包括固体-液体-蒸汽界面、移动接触线和表面张力效应的相关研究。分析和计算研究将与一系列实验相结合，这些实验包括在旋转涂层几何结构中寻找欠压缩波、接触线在室温临界点附近的运动，以及对流体界面有限时间破裂中奇点形成的动力学进行高速视频成像。数学分析将包括薄膜破裂的模型、驱动接触线的稳定性以及计算这些问题的方案的数值分析。液膜和移动接触线出现在从涂料的工业设计和微芯片制造到包括隐形眼镜和肺部衬里的医疗应用的一系列问题中。所有这些问题都涉及到不同长度尺度的相互作用，其中的物理规律并没有被清楚地理解。这是杜克大学数学系(Bertozzi，Witelski)和物理系(Behringer)和北卡罗来纳州立大学(Sheeller)数学系的研究人员合作的结果。这项工作将数学建模、分析和数值模拟与新的实验室实验相结合，以研究驱动膜和移动接触线的基本问题。计算和数学模型将指导实验设计，研究旋涂过程和除湿薄膜中的新现象。该项目将涉及本科生、研究生、博士后助理和来自其他机构的来访科学家。这项研究将促进杜克大学数学系、物理系和非线性与复杂系统中心的课程发展。

0073841ShearerA 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.