Problems in non-Newtonian and free surface flows

聚合物液体中流动问题的研究对数学分析提出了许多挑战。该项目所涉及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以及血液流动等生物问题上。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(在喷洒液体时控制液滴的大小)中都得到了利用。复杂流体流动中的不稳定性往往对聚合物加工技术构成限制。在该项目下进行的研究将澄清这些现象背后的基本数学问题，使人们能够更好地了解这些流动及其模拟方法的发展。

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.