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

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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.