FRG: Collaborative Research: Dynamics of Thin Liquid Films: Mathematics and Experiments

近年来，液体薄膜科学发展迅速，在涂层流体、生物流体、微流体工程和医学等领域得到了广泛的应用。在这个项目中，我们将使用数学建模、分析和数值模拟相结合的方法，结合精心选择的定量实验，重点研究三组自由表面流动问题。这三个领域是：(i)由表面张力梯度驱动的流动，（ii）惯性在润滑不足以模拟薄膜流动的情况下的作用，以及（iii）振动薄膜。我们对围绕这些流动建模的理论问题的理解的进步，以及通过实验探索流动的新特征，将直接应用于改善高科技产业和生物医学系统中制造过程的控制和可靠性。薄液体层或薄膜的流动发生在工业涂层流动、微流体工程和医学等领域。在这个项目中，我们重点研究了薄液体薄膜的特性，如表面张力在驱动流动中的作用，以及薄层在快速振动下的行为。表面张力是肺黏液层动力学的重要机制，也是表面活性剂替代疗法治疗早产儿的核心。通过表面张力的温度依赖性或使用快速振动来控制薄层流动，有可能消除工业涂层过程中破坏性的不均匀性。这些领域和应用中的每一个都提出了重大的科学挑战，需要数学家和物理学家的共同努力，共同探索理论和实验方法。该项目包括对研究生和本科生进行跨学科研究计划的培训，以开发物理、工程和应用数学方面的协调先进技能。

The science of thin liquid films has developed rapidly in recent years, with applications to coating flows, biofluids, microfluidic engineering, and medicine. In this project, we will focus on three groups of free-surface flow problems using a combination of mathematical modeling, analysis and numerical simulation, coupled to carefully chosen quantitative experiments. The three areas are: (i) flows driven by surface tension gradients, (ii) the role of inertia in regimes where lubrication is inadequate to model thin film flow, and (iii) vibrating thin films. Advances in our understanding of theoretical issues surrounding modeling these flows, and the exploration of new features of the flows through experiments will have direct applications to improving control and reliability of manufacturing processes in high-tech industries and to biomedical systems. The flow of thin liquid layers or films occurs in contexts including industrial coating flows, microfluidic engineering, and medicine. In this project, we focus on properties of thin liquid films such as the role of surface tension in driving flow, and the behavior of thin layers under rapid vibration. Surface tension is an important mechanism in the dynamics of mucus layers in the lung, and is central to the treatment of premature infants by surfactant replacement therapy. The control of thin layer flow, through the temperature dependence of surface tension or using rapid vibrations, has the potential to eliminate damaging nonuniformities in industrial coating processes. Each of these areas and applications pose substantial scientific challenges that will be met with a collaborative effort between mathematicians and physicists, exploring theoretical and experimental methods in tandem. The project includes graduate and undergraduate student training in an interdisciplinary research program thatwill develop coordinated advanced skills in physics, engineering, and applied mathematics.