CAREER: Macromolecular Fluid Flow: Experiments, Equations, and Education

该项目由宾夕法尼亚州立大学数学系W. G. Pritchard实验室进行的复杂流体流动的综合研究、推广和教育工作组成。研究部分将大分子流体动力学的实验研究与建模方程的数学研究相结合。边界附近的聚合物溶液和熔体等流体的流动是非牛顿流体动力学领域中最有趣和最具挑战性的问题之一，特别是在自由、可变形的界面上。该研究将探索几种不同的现象：聚合物溶液中上升气泡的界面动力学，蠕虫状胶束流体的应力诱导振荡，以及由水滴形成的长细丝。这些实验涉及许多不同的流体，包括电荷屏蔽聚电解质聚合物和蠕虫状胶束溶液。将使用视频成像对流体的流动和界面以及流体的局部速度和双折射应力进行定量测量。这些测量的结果将与流体的流变特性相关联。研究者希望阐明流体的宏观流动与其组成分子的微观特性之间的联系。推广工作有两个组成部分。首先，中学数学教师的继续教育是通过周末工作坊进行的，包括迷你课程、非正式讨论和互动实验演示。第二部分包括一名高中数学教师参与暑期实验室研究项目，作为“中学教师研究经验”试点项目的一部分。这个项目的教育元素包括开发一门高级本科建模课程，其中包括一个实验室部分。本课程的目的是让学生了解研究的真正周期，从建模到分析和测量，再回到建模。这些活动还包括继续在普里查德实验室进行本科生研究的一对一教学。该项目包括对复杂流体的行为和性质的综合研究-推广-教育工作。具有复杂微观结构的流动流体的研究不仅对食品、塑料和其他工业具有重要的技术意义，而且也是一个具有挑战性的数学问题。这项工作结合了复杂流体的实验研究和建模方程的数学研究，在宾夕法尼亚州立大学数学系的实验设施W. G. Pritchard实验室进行。该研究探讨了几个方面，包括在聚合物溶液中气泡的形状动力学，以及类聚合物洗涤剂的行为。流动和边界形状的定量测量将与流体性质相关联，试图阐明宏观流动与流体分子微观特征之间的联系。这个项目的外联工作包括两个部分。第一部分通过包括迷你课程、非正式讨论和互动实验演示在内的周末研讨会讨论中学数学教师的继续教育。第二个部分涉及一位高中数学老师的暑期实验室研究项目。这是“中学教师研究经验”试点项目的一部分，该项目受到美国国家科学基金会本科生暑期项目的启发。该提案的教育元素涉及开发一门新的本科建模课程，其中包括实验室部分，以及涉及本科生研究的一对一教学。

This project consists of an integrated research, outreach, and educational effort on the flow of complex fluids, performed in the W. G. Pritchard Laboratories of the Department of Mathematics of Pennsylvania State University. The research part combines an experimental study of macromolecular fluid dynamics with the mathematical study of the modeling equations. The flow of fluids such as polymer solutions and melts near a boundary is among the most interesting and challenging problems in the field of non-Newtonian fluid dynamics, particularly at free, deformable interfaces. The research will explore several different phenomena: interface dynamics of rising bubbles in polymer solutions, stress-induced oscillations of wormlike micellar fluids, and the long filaments formed by falling drops. These experiments involve a number of different fluids including charge-screened polyelectrolyte polymers and wormlike micellar solutions. Quantitative measurements will be made of the flow and interface using video imaging, as well as of the local velocity and birefringent stress of the fluid. The results of these measurements will be correlated with the rheological properties of the fluid. The investigator hopes to elucidate the connection between the macroscopic fluid flow and the microscopic character of its component molecules. The outreach effort has two components. In the first, the continuing education of secondary school mathematics teachers is pursued through weekend workshops which include minicourses, informal discussions, and interactive experimental demonstrations. The second part consists of the involvement of a high school mathematics teacher in a summer laboratory research project as part of a pilot "Research Experiences for Secondary School Teachers" program. The educational element of this project includes the development of an advanced undergraduate course on modeling, which includes a laboratory component. The purpose of this course is to expose students to the true cycle of research, from modeling to analysis and measurement and back to modeling. These activities also include continuing the one-on-one teaching involved in undergraduate research in the Pritchard Lab. This project consists of an integrated research-outreach-educational effort on the behavior and properties of complex fluids. The study of flowing fluids which possess a complex microscopic structure is not only of great technological importance to the food, plastics, and other industries, but it also presents a challenging mathematical problem. The work combines the experimental study of complex fluids with the mathematical study of the equations which model them, performed in the W. G. Pritchard Laboratories, an experimental facility in the Mathematics Department of Pennsylvania State University. The research explores several aspects including the shape dynamics of bubbles rising in polymer solutions, and the behavior of polymer-like detergent fluids. Quantitative measurements of the flow and boundary shape will be correlated with the fluid properties, in an attempt to elucidate the connection between the macroscopic flow and the microscopic character of the fluid molecules. This project's outreach effort consists of two parts. The first part addresses the continuing education of secondary school mathematics teachers through weekend workshops which include minicourses, informal discussions, and interactive experimental demonstrations. The second component involves a high school mathematics teacher in a summer laboratory research project. This is part of a pilot program "Research Experiences for Secondary School Teachers," inspired by the NSF's summer program for undergraduates. The educational element of the proposal involves the development of a new undergraduate course on modeling which includes a laboratory component, and the one-on-one teaching involved in undergraduate research.