Free Boundary Problems with Surface Tension

表面张力的自由边界问题

• 批准号: 0600870
• 负责人: Gieri Simonett
• 金额: $ 13.57万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-15 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600870&HistoricalAwards=false
• 关键词: Free; Boundary; Problems; Surface; Tension

Free Boundary Problems with Surface Tension.Abstract of Proposed ResearchGerri Simonett Over the last decades, the subject of free boundary problems has attracted increasing attention because of its theoretical interest, and because of its numerous applications in the natural and engineering sciences. Free boundary problems are important in many fields such as material sciences, fluid mechanics, hydrodynamics, thermo-mechanics, magneto-dynamics, solid state physics, geology, chemistry, and the biological and medical sciences. The appropriate numerical and analytical treatment is a major challenge, both to the engineer and to the mathematician. Typically, a free boundary problem consists of one or more partial differential equations which have to be solved in a domain that is a priori unknown and that has to be determined as part of the problem. Free boundary problems are in general harder to solve, both analytically and numerically, than the underlying differential equations would be in a prescribed domain. They have an inherent nonlinear structure, as two separate solutions cannot be superposed. In this project, the PI proposes a systematic investigation of various free boundary problems with moving contact lines in the presence of surface tension. Moving contact lines occur in many situations, for example in processes such as the coating of solid surfaces by a viscous fluid, spin coating of micro chips, the displacement of one fluid by another fluid along a solid boundary, the spreading of drops on solid surfaces, the motion of a fluid (or a fluid-liquid system) in a container where the free surface is in contact with the wall of the container. The modeling and characterization of contact line motion is one of the major unsolved problems of capillary theory.

具有表面张力的自由边界问题。拟议研究摘要Gerri Simonett 在过去的几十年中，自由边界问题因其理论兴趣以及在自然科学和工程科学中的众多应用而引起了越来越多的关注。自由边界问题在材料科学、流体力学、流体力学、热力学、磁动力学、固态物理、地质学、化学以及生物和医学等许多领域都很重要。对于工程师和数学家来说，适当的数值和分析处理都是一个重大挑战。通常，自由边界问题由一个或多个偏微分方程组成，这些方程必须在先验未知的域中求解，并且必须将其确定为问题的一部分。自由边界问题通常比规定域中的基本微分方程更难解析和数值求解。它们具有固有的非线性结构，因为两个单独的解决方案不能叠加。 在该项目中，PI 提出对存在表面张力的情况下移动接触线的各种自由边界问题进行系统研究。移动接触线在许多情况下都会发生，例如在用粘性流体涂覆固体表面、旋涂微芯片、一种流体沿固体边界被另一种流体置换、液滴在固体表面上扩散等过程中。 ，容器中流体（或液-液系统）的运动，其中自由表面与容器壁接触。接触线运动的建模和表征是毛细管理论未解决的主要问题之一。