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| Bird/Stewart/Lightfoot Lecture 2004-05 |
Lecture by Robert K. Prud'homme
Department of Chemical Engineering, Princeton University
Thursday, April 21, 2005
Room 1800 Engineering Hall
Lecture at 4:00 p.m.
Refreshments at 3:45 p.m.
We present two problems involving polymer dynamics and confinement. One is “old” — a problem of polymer flow through porous media that arises in chromatographic separations. This was one of the problems I tackled as a young faculty member at Princeton. The velocity of a polymer coil, and therefore its apparent “size,” during flow through a tortuous porous media is a strong function of the Deborah number, De. We went to the simpler system of very large DNA in a 20 micron capillary to avoid the complexity of the flow field in a packed bed. Quite surprisingly, the effect of De was equally strong in this simpler flow. There was no theory that could adequately explain the results. But Ed Lightfoot had just published a paper on capillary electrophoretic separations that showed the mathematical relationship between the peak broadening and the mean velocity for any convective-flow-diffusion process. We used the theory and showed that the results were consistent with a diffusion process where the diffusivity is a function of De. Now, many years later Mike Graham and Juan de Pablo at Wisconsin have just completed beautiful simulations of DNA in small capillaries that qualitatively show the radial migration observed in our experiments. We are collaborating to close this 20 year gap in understanding flow of polymers in confined geometries. The second “new” problem involves the entry of “polymers” into small pores. But in this case the polymers are self-assembling surfactants that form “living worm-like chains.” These fluids have the characteristics of classical polymer solutions that can be described by single time constant Maxwell fluids. These fluids are used in oil recovery operations involving flow into porous media because they are immune to irreversible mechanical degradation. When the confinement length scales are comparable to the length of the micelles, unexpected “filtration” phenomena are observed. The entry into the pores occurs at a critical flux, not a critical stress. The critical flux is independent of pore size over a ten-fold range of pore sizes, and is independent of bulk fluid viscosity over a hundred-fold range of viscosity. An instability occurs where the flux through the holes varies over two orders of magnitude at constant pressure. The origin of this behavior is found in a simple model by de Gennes that considers the balance of hydrodynamic drag on a “blob” of the chain entering a pore and the force associated with the confinement of the blob in the pore. This model predicts the lack of dependence on pore size, and on the bulk fluid rheology. This is the first step in the process of understanding the flow of these dynamic objects in flow through porous media.
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Robert K. Prud’homme is a professor in the Department of Chemical Engineering at Princeton University and the Director of the Engineering Biology Program. He received his BS at Stanford University and his PhD from the University of Wisconsin–Madison. His research interests include self-assembly of complex fluids. Systems of interest are biopolymer solutions and gels, surfactant mesophases, and polymer/surfactant mixtures, liposomes for DNA and controlled drug delivery. He has served as the undergraduate representative in the Chemical Engineering Department and on numerous departmental and university committees. He has served on the boards of directors of the American Institute of Chemical Engineers Materials Science Division, the U.S. Society of Rheology, and Dow Chemical Company’s Materials Science Advisory Board. He is the recipient of an Engineering School Excellence in Teaching Award. |
As the chemical engineering profession developed in the first half of the 20th century, the concept of "unit operations" arose as the natural organizing principle in educating chemical engineers. Particularly in undergraduate education, underlying theories of mass, momentum and energy transfer were presented only to the extent necessary for a narrow range of applications. Following World War II, chemical engineers moved into a number of new areas in which problem definitions and solutions required a deeper knowledge of the fundamentals of transport phenomena than those provided in the textbooks on unit operations.
In the 1950's, R. Byron Bird, Warren E. Stewart, and Edwin N. Lightfoot stepped forward to develop an undergraduate course at the University of Wisconsin to integrate the teaching of fluid flow, heat transfer, and diffusion. From this beginning, they prepared the landmark textbook, Transport Phenomena, published in 1960 by John Wiley & Sons.
This textbook, referred to by generations of chemical engineers simply as BSL after its authors, would remain in print for 41 years and see five translations. BSL has changed fundamentally the organizing principle in virtually all chemical engineering curricula worldwide. The enduring strength of BSL is testimony to the vision and attention to detail of its authors.
In "retirement," the three authors found time to thoroughly revise BSL, the second edition of which appeared in the summer of 2001. With new or revised discussions of such topics as two-phase systems, angular momentum, Taylor dispersion and turbulence, the revision promises to help prepare students well into the 21st century. The BSL Lecture was inaugurated in the fall of 2001 to honor the achievements of these outstanding chemical engineers.
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Copyright 2004 The Board of Regents of the University of Wisconsin System Date last modified: 08-Apr-2005 Date created: 07-Apr-2005 Content by: che@che.wisc.edu Markup by: diaz@engr.wisc.edu Thank you for visiting! |
