Flows of Free Liquid Fibers and Sheets

自由液体纤维和片材的流动

• 批准号: 0709197
• 负责人: Thomas Hagen
• 金额: $ 3.82万
• 依托单位: University of Memphis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-15 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0709197&HistoricalAwards=false
• 关键词: Flows; Free; Liquid; Fibers; Sheets

This project is concerned with the formation and evolution of free liquid filaments, jets and sheets of viscous, viscoelastic, and viscoplastic fluids under the influence of internal and external forces. The formulation of these fluid flows involves an unknown free surface that describes the region in an ambient medium occupied by the fluid. Understanding how these free surfaces evolve, what flow scenarios and material parameters are prone to trigger flow instabilities, and how the transition to flow catastrophes such as capillary breakup proceeds is a fundamental challenge in mathematics and the sciences. Capillary, inertial and viscoelastic forces or balances thereof are known to stabilize or destabilize fluid filaments. In the case of highly viscous fluids, liquid filaments thin uniformly before breakup occurs and drops are formed, while in contrast viscoelasticity is expected to induce a beads-on-string morphology of the liquid filaments. The inherently nonlinear nature and the high degree of complexity of the cascade of events leading to thinning, necking, breakup or other transient patterns are topics that this project addresses. It encompasses a rigorous derivation and justification of averaged lower-dimensional equations for thin filaments and sheets indicating boundaries of validity of these models, a discussion of capillary thinning and breakup of viscoplastic fluid jets, and stability studies in the context of fiber spinning and film drawing for viscous and viscoelastic liquids. Analyzing and justifying mathematical models of fiber and film flows and explaining observed flow phenomena arising in capillary thinning and engineering applications requires the development of new mathematical tools, combining machinery from partial differential equations, stability theory, asymptotic analysis and multiscale analysis. A variety of high-tech applications, including food processing, ink-jet printing, atomization of paints and aerosols, jet stabilization, fiber spinning, and electrospinning of nanofibers, are all characterized by similar objectives: to either induce breakup of thin fluid filaments (or sheets) in a controlled manner, to suppress it or to keep flow instabilities from occurring. To reach these objectives, a deep mathematical understanding of the physical mechanisms and rheological parameters governing the onset of instabilities and the transition to flow catastrophes is necessary. The investigator develops the mathematical framework to derive, analyze, and justify flow models describing the evolution of free liquid filaments and sheets. Under examination are the occurrence of flow instabilities, the transition to breakup, and novel rheological phenomena in several exemplary flows. This research has the potential to significantly enhance our knowledge of the physical principles and limitations governing flows in these vital areas of engineering and science. The project also serves the purpose to train both graduate and undergraduate students in mathematical fluid mechanics and applied analysis in general and fiber/sheet forming flows in particular.

该项目关注的是在内部和外部力的影响下，粘性、粘弹性和粘塑性流体的自由液体细丝、射流和薄片的形成和演化。这些流体流的公式涉及一个未知的自由表面，它描述了周围介质中被流体占据的区域。了解这些自由表面如何演变，什么样的流动场景和材料参数容易触发流动不稳定性，以及如何过渡到流动灾难，如毛细管破裂的进展是数学和科学的一个基本挑战。 已知毛细管力、惯性力和粘弹性力或其平衡使流体细丝稳定或不稳定。在高粘性流体的情况下，液体长丝均匀地变薄之前发生分裂和液滴形成，而在相反的粘弹性预计将诱导珠串形态的液体长丝。固有的非线性性质和高度复杂的事件级联导致变薄，颈缩，分裂或其他瞬态模式的主题，这个项目的地址。它包括一个严格的推导和理由的平均低维方程的细丝和片材表示这些模型的有效性的边界，毛细管变薄和崩溃的粘塑性流体射流的讨论，和稳定性研究的背景下，纤维纺丝和薄膜拉伸的粘性和粘弹性液体。分析和证明纤维和薄膜流动的数学模型，并解释所观察到的流动现象中出现的毛细管变薄和工程应用需要开发新的数学工具，结合机械偏微分方程，稳定性理论，渐近分析和多尺度分析。各种高科技应用，包括食品加工，喷墨打印，油漆和气溶胶的雾化，射流稳定，纤维纺丝和纳米纤维的静电纺丝，都具有相似的目标：以受控的方式诱导细流体长丝（或片材）的分解，抑制它或防止流动不稳定性发生。为了达到这些目标，一个深刻的数学理解的物理机制和流变参数控制的不稳定性的开始和过渡到流动灾难是必要的。研究人员开发的数学框架来推导，分析和证明流动模型描述自由液体长丝和片材的演变。正在检查的是几个示例性流动中流动不稳定性的发生、向破裂的转变以及新的流变现象。这项研究有可能显着提高我们的知识的物理原理和限制，在这些重要的工程和科学领域的流动。该项目还服务于培养研究生和本科生的数学流体力学和应用分析一般和纤维/片材成型流动特别的目的。