Problems in non-Newtonian and free surface flows

非牛顿流和自由表面流中的问题

• 批准号: 0405810
• 负责人: Michael Renardy
• 金额: $ 12.5万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0405810&HistoricalAwards=false
• 关键词: Problems; non; Newtonian; free; surface

The study of flow problems in polymeric liquids poses numerous challenges for mathematical analysis. The topics addressed in this project include asymptotic analysis of the breakup of liquid jets, analysis of stability and control of viscoelastic flows, and numerical simulation of drop breakup under shear, a fundamental process in the formation of emulsions. Applications of viscoelastic flows arise in manufacturing of plastics, foods, and other products, as well as in biological problems such as blood flow. The effect of polymer additives in suppressing breakup of drops is exploited both in nature (in spider webs) and in technology (to control sizes of drops in the spraying of liquids). Instabilities in the flow of complex fluids often pose limits for polymer processing techniques. The research carried on under this project will clarify fundamental mathematical issues underlying such phenomena to enable a better understanding of these flows and the development of methods for their simulation.

聚合物液体流动问题的研究对数学分析提出了许多挑战。本课题的主题包括液体射流破碎的渐近分析，粘弹性流动的稳定性分析和控制，以及剪切作用下液滴破碎的数值模拟，这是乳状液形成的一个基本过程。粘弹性流动的应用出现在塑料、食品和其他产品的制造中，也出现在生物问题中，如血液流动。聚合物添加剂在抑制液滴破碎方面的作用在自然界（在蜘蛛网中）和技术上（在喷射液体时控制液滴的大小）都得到了利用。复杂流体流动的不稳定性常常对聚合物加工技术构成限制。在这个项目下进行的研究将澄清这些现象背后的基本数学问题，以便更好地理解这些流动并开发模拟它们的方法。