Abstract

"Rheology and Fluid Mechanics of Polymer Solutions Undergoing Rapid Elongational Deformations"

Bead-spring kinetic theory models, which we illustrate in this talk by elastic dumbbells, have proven to be very useful in describing the rheological behavior of polymeric liquids and for understanding the response of these liquids in complex flows. In this talk we consider two experiments in which simple bead-spring models have failed to capture key physical observations, and we discuss improvements to the models motivated by these failures. The first experiment is filament stretching, which consists of the sudden startup of uniaxial elongational flow followed by stress relaxation. When stress is plotted against birefringence in this experiment, hysteresis is observed between the growth and relaxation parts of the experiment. Simple bead-spring models do not capture this hysteretic behavior. We analyze the Kramer's chain, a fine-scale model for polymer dynamics, in order to assess the validity of the coarser-grained bead-spring models in these deformations. Whereas the spring force is a simple function of the dumbbell length for customary nonlinear elastic springs, we find that the relationship between the ensemble averaged end-to-end force and the extension for a Kramer's chain depends on the kinematic history to which it has been subjected. We find that it is essential for a dumbbell model to have an end-to-end force that depends upon the deformation history in order to capture hysteresis in the filament stretching experiment.

We then turn to a discussion of a complex flow, namely flow around a linear, periodic array of cylinders. Viscoelastic liquids in this flow undergo a transition from steady, two-dimensional flow to a spatially periodic, three-dimensional flow at a critical flow rate. Simple bead-spring models do not correctly capture this flow transition, and we believe that this shortcoming is due to the failure of these models to describe well the rapid elongational flow in the wake behind the cylinders. In order to address this problem we construct a new bead-spring model that is simple enough to be used in finite element simulations, and yet captures correctly the dynamics of hysteresis observed in the first experiment. The new model describes a polymer molecule as a set of identical segments where each segment represents a fragment of the polymer that is short enough so that it can sample its entire configuration space on the time scale of the deformation and therefore stretches in reverse. As the molecule unravels, the number of segments decreases but the maximum length of each segment increases so that the model accounts for the constant maximum contour length of the parent molecule. The behavior of this new model in the flow around cylinders will be presented.

Abstract

"Frontiers in Chemical Engineering Education"

A dramatic shift in chemical engineering undergraduate education is envisioned, based on discipline-wide workshop discussions that have taken place over the last two years. Faculty from more than 53 universities and industry representatives from 5 companies participated. Through this process broad consensus has been developed regarding basic principles for chemical engineering undergraduate education in the future; these principles address fundamental knowledge, skills and attributes, and methods of engagement with the students. From these principles a new set of organizing principles emerged for the discipline: molecular transformations, broadly interpreted to include chemical and biological systems and physical as well as chemical structural changes; multiscale analysis, from sub-molecular through super-macroscopic scales for physical, chemical, and biological systems; and a systems approach, addressed to all scales and supplying tools to deal with dynamics, complexity, uncertainty, and external factors. The curriculum integrates all organizing principles and basic supportive sciences throughout the educational sequence and moves from simple to complex. The curriculum is consistently infused with relevant and demonstrative laboratory experiences, and opportunities for teaming experiences and use of communication skills (written and oral) are included throughout. The curriculum is also designed so as to address different learning styles and to include a first-year chemical engineering experience. Finally an important theme is a consistent infusion with relevant and demonstrative examples, which provide open-ended problems and case studies and supply frequent integrative opportunities for students.

This radically different curriculum would produce more versatile chemical engineers, which are needed to meet the challenges and opportunities of creating products and processes, manipulating complex systems, and managing technical operations in industries increasingly reliant on molecular understanding and manipulation. Another benefit of the new curriculum is that it reconnects undergraduate education with ongoing research in chemical engineering in a way that has not been present for the past 40 years. This reconnection will serve us well as an engineering discipline in attracting the best and brightest students and in reopening the path to continual renewal of the curriculum.