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

0073841 ShearerA相结合的实验，分析和计算研究的基本问题，在薄粘性膜和流体界面的动力学。 最近在驱动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。本研究计划将包括固-液-气界面、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，包括在旋涂几何形状中搜索欠压缩波，室温临界点附近接触线的运动，以及流体界面有限时间破裂中奇点形成动力学的高速视频成像。数学分析将包括膜破裂的模型，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。液体膜和移动接触线出现在从油漆和微芯片制造的工业设计到医疗应用，包括隐形眼镜和肺衬里的问题。所有这些问题都涉及到各种不同长度尺度的相互作用，其中的物理定律还没有被清楚地理解。这是来自杜克大学数学系（Bertozzi，Witelski）和物理系（Behringer）以及北卡罗来纳州州立大学数学系（Shearer）的研究人员之间的合作。这项工作结合了数学建模，分析和数值模拟与新的实验室实验，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的设计，研究旋涂工艺和去湿膜中的新现象。该计划将涉及本科生，研究生，博士后助理，并访问其他机构的科学家。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开发。

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.