Transport phenomena

Abstract

R Byron BirdR. Byron Bird (known as “Bob” to his friends) is well known for his pioneering research in non-Newtonian fluid dynamics, especially as it relates to polymers, as well as macromolecular kinetic theory and transport phenomena. He is the coauthor of four widely used books (the backgrounds of which are described in the following Retrospective) and approximately 125 research papers and 50 review articles which involve these research areas. Professor Bird received a BS in Chemical Engineering from the University of Illinois in 1947, and his PhD in Chemistry from the University of Wisconsin in 1950. His long career in the Chemical Engineering Department at Wisconsin began in 1953, where he became full Professor in 1957, was Department Chairman 1964–1968, and Vilas Research Professor until 1992, when he “retired” from the university. He has also been visiting professor at Kyoto University, Nagoya University, University of California at Berkeley, Huadong Huagong Xueyuan (Shanghai), Technische Universiteit Delft, Universite´ Catholique de Louvain, and Technical University of Denmark (Lyngby). His outstanding research has been recognized world-wide, resulting in many honors and awards. Among his awards are the Wm. H. Walker Award (1962), Warren K. Lewis Award (1974), and the Founders Award (1989) from the American Institute of Chemical Engineers; the Bingham Medal (1974) from the Society of Rheology; and the Eringen Medal (1983) of the Society of Engineering Science. In 1987, President Reagan presented him with the National Medal of Science. Professor Bird is a Member of the National Academy of Engineering (since 1969) and the National Academy of Sciences of the United States, a Foreign Member of the Royal Dutch Academy of Sciences and the Royal Flemish Academy Belgium for Sciences and the Arts, and a Fellow of the American Physical Society (since 1970), the American Academy of Mechanics, and the American Academy of Arts and Sciences. He has received honorary doctorates from nine universities. Although Professor Bird retired officially from his university position nine years ago, he remains very active in research. During the past five years, he has published papers on, for example, statistical mechanics of transport phenomena, multicomponent diffusion in polymeric liquids, and thermal conductivity of chainlike polymer solutions. He is very interested in languages, having published research papers in several languages, two Dutch readers and three books dealing with translation of technical Japanese texts. He is “addicted to” wilderness canoe trips in Canada; the most unforgettable of his 70 or so trips was a 3-week 320-mile trip down Coppermine River in the Northwest Territory in 1971, ending up at the Arctic Ocean. by Arthur LeissaThe term transport phenomena is used to describe processes in which mass, momentum, angular momentum, and energy move about in matter. Thus it includes diffusional phenomena, fluid dynamics, and heat transport. The subject may be treated from a molecular point of view (kinetic theory), from a microscopic point of view (continuum mechanics), or from a macroscopic point of view (equipment description). Parts of the subject of transport phenomena have been around for a long time: Inviscid fluid dynamics was studied in the 1700s by Bernoulli and Euler, and Newton enunciated his comments on momentum flux in the 1680s, although it was not until the 1820s that the Navier-Stokes equations were formulated. Fourier established the equations for heat flux and heat conduction in the 1820s, and in the century that followed the equations for heat convection and thermal radiation had been established. Fick’s first and second laws of diffusion date back to the 1850s, but it was not until a half-century later that convective mass transport was studied. On the other hand, many topics are of newer vintage. In the 1930s (Onsager), 1940s (Eckart), and 1950s (Kirkwood and Crawford, Hirschfelder and Curtiss, Prigogine, and others) worked on the cross effects, such as thermal diffusion, the diffusion-thermo effect, and forced diffusion. Although the theoretical bases for the transport phenomena were virtually complete by the 1950s, the continuum theory of transport phenomena was not much used in chemical engineering because of the apparent intractability of the equations. Only relatively simple problems could be solved analytically, and computing machines were quite primitive by today’s standards. There was a similar development of the molecular theory of transport phenomena. Both Maxwell and Boltzmann had succeeded before the beginning of the 20th century in drafting formal theories of a rigorous kinetic theory of monatomic gases at low density, and they had established the connection with the equations of change for velocity, concentration, and temperature. But it was not until the second decade of the 20th century that the Boltzmann integrodifferential equation was solved (independently by Chapman and Enskog) and only in the late 1940s that transport properties were computed for realistic intermolecular interactions. By the 1950s, Kirkwood and his students were hard at work on developing a similar formal theory for monatomic liquids, but it has yet to be used in making numerical calculations. In the 1990s, Curtiss and Bird showed how to extend Kirkwood’s formalism to polymer solutions and undiluted polymers. I was fortunate to have studied chemical engineering as an undergraduate (at the University of Maryland and the University of Illinois) and particularly lucky to have had Professor Joseph O. Hirschfelder as my mentor in the chemistry department in graduate school (at the University of Wisconsin) and to have become acquainted with Professor Charles F. Curtiss when he was a young faculty member. Both “Joe” and “Chuck” had worked on many practical problems during and after the war (flames, combustion, detonations, effects of atomic weapons, etc). They were among the leaders in the emerging field of theoretical chemistry and knew how to apply their knowledge to the solution of complex physicochemical problems. Among Joe’s academic descendants there are professors of chemical engineering, mechanical engineering, aeronautical engineering, and fuel technology, as well as in physics and chemistry, attesting to Joe’s wide range of interests. Probably the most important thing we learned from Joe is the importance of the interactions among various branches of science and engineering, and that the “boundaries” between the various fields are very unimportant and best ignored. Joe’s Theoretical Chemistry Institute at the University of Wisconsin attracted talent from all corners of the world, and his graduate students had the opportunity to interact with them and learn from them. This, then, was the milieu in which I spent my graduate years (1947-1950). During the summer of 1950, we began working on a book, summarizing the various research activities of Joe and Chuck—a book that would also influence very strongly my later research, teaching, and bookwriting: Molecular Theory of Gases and Liquids, by Hirschfelder, Curtiss, and Bird, published by John Wiley and Sons in 1954, and in a corrected edition in 1964 (this book would come to be referred to simply as “MTGL”). In 1950-1951, I spent the academic year with Professor Jan de Boer, Director of the Institute for Theoretical Physics in Amsterdam. From him I learned about the quantum theory of transport phenomena, and also a great deal about the technique of presenting complicated scientific ideas to beginners and colleagues. The year in Amsterdam was a very important part of my education. Then in 1951-1952, I returned to Madison to work full time for one year on the manuscript for MTGL. We completely reorganized and rewrote the manuscript, grouping the chapters into three parts: equilibrium properties, nonequilibrium properties, and intermolecular forces. The fact that this book is still in print attests to the durability of the contents and the usefulness of the presentation. During the galley proof and page proof stages, I was at Cornell University in the chemistry department (September 1952 to June 1953) and, in the summer months, at the Du Pont Experimental Station in Wilmington, Delaware. These were very busy months, which contributed importantly to my scientific background. At Cornell, I taught quantitative analysis and quantum chemistry, and at Du Pont, I was introduced to the field of polymer rheology. At Du Pont, I found that many engineers were inadequately prepared to tackle some of their assigned problems because of a lack of training in transport phenomena. One example will make this point clear. At that time, one of the current problems was to understand the phenomenon of viscous heating in flowing polymers. Most engineers were puzzled about the origin of this heating effect and how to describe it. They were unaware that there is a term in the equation of change for temperature that accounts for viscous heating. This term had, in fact, been well known to physicists for some time, and it had been included in Chapter 11 of MTGL. In 1953, when I returned to the University of Wisconsin to teach in the chemical engineering department, I found that much of the teaching of fluid dynamics, heat transfer, and mass transfer was done by means of working a number of sample problems using charts and formulas of ill-defined ancestry. As an undergraduate, I had been taught in the same way. This method of teaching does enable the student to solve some fairly complex and important problems, but often with little real understanding. The situation was further exacerbated by the fact that virtually no fluid dynamics and heat conduction were being taught in the physics department, and only scant information on diffusion was being given in the physical chemistry courses. These topics had been either discarded or soft-pedaled in order to make way (quite appropriately) for the newer and exciting areas involving nuclear physics and quantum phenomena. But the result of these changes had been disastrous for the chemical engineering undergraduate students. Therefore, in 1957 we implemented a junior-level course on transport phenomena for chemical engineering and nuclear engineering students, and in the course of the academic year 1957-1958 we prepared Notes on Transport Phenomena, which was published in 1958 by John Wiley and Sons. This was a “preliminary edition” and was tested at four universities. In the spring of 1958, I gave the course at the Technical University in Delft in Dutch, to try out the ideas on an entirely different audience. During that period, I had close contact with Professor Hans Kramers and his students, and from them I learned much. Back at the University of Wisconsin in the fall of 1958, we began rewriting the notes based on our own teaching experiences and also using the comments of the users at other schools. Finally, in 1960 the textbook Transport Phenomena by Bird, Stewart, and Lightfoot, emerged (it is usually referred to as BS&L). This book has enjoyed over 60 printings, and there is little doubt that it has influenced the teaching of chemical engineering in the US and abroad. The summer of 2001 saw the publication of a second edition of the book, with the same authorship as for the first edition. As might be expected after 42 years of teaching this material, we had become acutely aware of the shortcomings of the first edition, and hence a complete revision was long overdue. The unique features of our book are: a) the parallel presentation of momentum, energy, and mass transport, emphasizing the similarities, but also pointing out the differences; and b) the discussions at three different scales—the molecular scale, the microscopic (or continuum) scale, and the macroscopic scale (describing process equipment). We have also not shied away from the use of vector and tensor notation, differential equations, and other intermediate topics of mathematics. The main reason for the success of Transport Phenomena as a textbook is, I think, the fact that the three authors came from quite different backgrounds and have strikingly different personalities. Ed Lightfoot (BS and PhD at Cornell), is very imaginative and iconoclastic, and a firm believer that the usefulness of the theory must be demonstrated by realistic problems. Warren Stewart (BS and MS at the University of Wisconsin, and ScD at MIT) was a brilliant student in chemical engineering, with thorough training in numerical analysis and boundary-layer computations. He has since developed powerful techniques for solving transport and reaction-engineering problems and has an extensive knowledge of the scientific and engineering literature, making him a very valuable member of the writing enterprise. My own contribution seems to have been my belief that complex material can be taught to undergraduates if it is organized and presented properly, with uniform approaches and notation throughout. Also, I supplied the “feeling of impatience” without which no book manuscript can be completed. We had many heated arguments while writing the book, but, in the end, it is the reader who profits from our resolving the differences of opinions. We made several attempts to get a second edition off the ground, but various other activities interfered. It was not until all three of us had “retired” that it would become feasible. Work began on January 1, 1998, and the last of the page proofs were corrected on June 6, 2001. Preparing the second edition was not without its problems. In the intervening years, the three of us had gone off in different directions. My own research was on the transport phenomena in polymeric fluids—both from the continuum point of view and the molecular point of view (in the latter, I had about 15 years of collaboration with Chuck Curtiss, who is absolutely unfazed by extremely complex problems). Warren Stewart had worked on a wide variety of problems, including boundary-layer theory, diffusion with chemical reaction, multicomponent mass transfer, Fourier analysis of turbulent heat and mass transfer, parameter estimation, statistics, and applied mathematics (in particular, the method of orthogonal collocation). Ed Lightfoot has been concerned with separations processes for biological systems, electrochemical problems, diffusion in porous media, metabolic pathways, evolutionary science, and topics even further afield, but all closely associated with biochemical and biomedical processes. By the end of the century, each of us had developed his own distinctive style, his own prejudices, his own favorite topics, and his own unique objectives. For a while, it seemed as though the project would not be workable. But by perseverance, loyalty to the subject and to each other, and some good-natured cajoling, we did succeed in establishing a modus operandi enabling each of us to contribute his own strengths without too seriously offending the others. Now for a few words about that portion of my career dealing with polymers. As a result of my brief experience at Du Pont in 1953, I became aware of the field of polymer rheology, in which there were many unsolved problems. In addition, in the 1970s and 1980s I was a regular consultant at Union Carbide, and the problems I encountered there provided a constant source of research ideas. From 1953 to 1968, I worked largely on the continuum mechanics of polymers, with emphasis on fluid mechanics and heat-transfer problems. In my early work on polymer rheology, I found the papers by Professor James G. Oldroyd (University of Liverpool) to be very inspiring, and I also particularly enjoyed my interactions with my colleagues, Professor Millard W. Johnson and Professor Arthur S. Lodge, in the Department of Engineering Mechanics, and Professor John L. Schrag and Professor John D. Ferry of the Chemistry Department. In 1968, I joined with these four colleagues to form the Rheology Research Center, which is still functioning today. Polymer fluid dynamics is similar to turbulence, in that the key problem is the lack of knowledge about the stress tensor itself. In both fields, one is forced to “back out” this information from experimental data on different classes of flows. However, for polymers we can get additional information—and very valuable information indeed—by using crude molecular models and elementary kinetic theories. In this regard, we have a great advantage over the fluid dynamicists studying turbulence. This led me, in 1968 (after serving four years as department chairman), to reorient my research efforts and to study polymer rheology from a molecular viewpoint. Polymer chemists had been active in the molecular theory for some time, but their efforts were largely restricted to linear viscoelasticity. For nonlinear problems, Dr. Anton Peterlin (at the National Bureau of Standards) and Professor Hanswalter Giesekus (Universita¨t Dortmund) were the main contributors to the molecular theory of nonlinear viscoelasticity; I studied their works and found interacting with them to be very helpful. In about 1971, I started team-teaching a course on kinetic theory of polymers jointly with Professor Curtiss (and, initially also with Johnson and Lodge). This activity continued until the 1990s, and numerous joint publications resulted from this cooperative activity. In 1974, two of my PhD students, Robert C. Armstrong (currently chairman of the chemical engineering department at MIT) and Ole Hassager (now professor at the Technical University of Denmark) announced that they wanted to write a book with me on the continuum and molecular theories of polymer rheology, building on a set of notes that I had prepared. Later we were joined by Chuck Curtiss in this effort, and the result was the two-volume treatise Dynamics of Polymeric Liquids, the first edition of which appeared in 1977 (with a vastly revised edition in 1987). A few years before my retirement in 1992, it became apparent that the seemingly intractable problems in polymer kinetic theory could best be solved by molecular dynamics or Brownian dynamics simulation. Several students made good inroads in this area, and this approach has since been developed and exploited extensively by others. After my retirement in 1992, Chuck Curtiss and I returned to the subject of kinetic theory of polymeric liquids. In our earlier work, we had developed a kinetic theory for polymers using very general molecular models, including models with constraints (that is, bead-rod-spring structures in which there could be constant bond lengths or constant bond angles), which necessitated the use of generalized coordinates. In 1994, we decided to eliminate the constraints (ie, the rods) and work with bead-spring models, thereby simplifying the formalism. We also decided to study nonisothermal systems (most polymer processing problems involve nonisothermal flow) as well as multicomponent mixtures (most polymeric fluids are in fact polydisperse, and therefore essentially multicomponent). In the period from 1994 to 1999, we worked intensively on formulating this general theory, so that we now have expressions for the mass, momentum, and energy fluxes, including all the possible cross effects, including the effect of velocity gradients on the heat flux and mass fluxes. Using the general theory thus developed, we have been able to solve a number of important problems: the development of an equation of change for temperature; derivation of an expression for the thermal conductivity of dilute solutions of bead-spring chains, and showing that a generalization of the Maxwell-Stefan equations can describe multicomponent diffusion. This development has spawned a whole collection of problems that will provide future workers with a supply of research ideas. No doubt Brownian dynamics and molecular dynamics will be needed to implement the theory. The lesson to learn from our work on transport phenomena is the importance of the interplay between industry and academia, the connection between continuum mechanics and molecular theory, and the cross-fertilization of experiment and theory. After all, it is the experimental work that provides the inspiration for the theoretical development, and it is the theory that provides guidance for the next stage of experimentation.