Viscoelasticity and Rheology covers the proceedings of a symposium by the same title, conducted by the Mathematics Research Center held at the University of Wisconsin-Madison on October 16-18, 1984. The contributions to the symposium are divided into four broad categories, namely, experimental results, constitutive theories, mathematical analysis, and computation. This 16-chapter work begins with experimental topics, including the motion of bubbles in viscoelastic fluids, wave propagation in viscoelastic solids, flows through contractions, and cold-drawing of polymers. The next chapters covering constitutive theories explore the molecular theories for polymer solutions and melts based on statistical mechanics, the use and limitations of approximate constitutive theories, a comparison of constitutive laws based on various molecular theories, network theories and some of their advantages in relation to experiments, and models for viscoplasticity. These topics are followed by discussions of the existence, regularity, and development of singularities, change of type, interface problems in viscoelasticity, existence for initial value problems and steady flows, and propagation and development of singularities. The remaining chapters deal with the numerical simulation of flow between eccentric cylinders, flow around spheres and bubbles, the hole pressure problem, and a review of computational problems related to various constitutive laws. This book will prove useful to chemical engineers, researchers, and students.

In this book, the necessary background for understanding viscoelasticity is covered; both the continuum and microstructure approaches to modelling viscoelastic materials are discussed, since neither approach alone is sufficient.

This text introduces the subject of rheology in terms understandable to non-experts and describes the application of rheological principles to many industrial products and processes.

This book offers a comprehensive introduction to polymer rheology with a focus on the viscoelastic characterization of polymeric materials. It contains various numerical algorithms for the processing of viscoelastic data, from basic principles to advanced examples which are hard to find in the existing literature. The book takes a multidisciplinary approach to the study of the viscoelasticity of polymers, and is self-contained, including the essential mathematics, continuum mechanics, polymer science and statistical mechanics needed to understand the theories of polymer viscoelasticity. It covers recent achievements in polymer rheology, such as theoretical and experimental aspects of large amplitude oscillatory shear (LAOS), and numerical methods for linear viscoelasticity, as well as new insights into the interpretation of experimental data. Although the book is balanced between the theoretical and experimental aspects of polymer rheology, the author’s particular interest in the theoretical side will not remain hidden. Aimed at readers familiar with the mathematics and physics of engineering at an undergraduate level, the multidisciplinary approach employed enables researchers with various scientific backgrounds to expand their knowledge of polymer rheology in a systematic way.

If one dismisses the Prophetess Deborah who in her famous song after the victory over the Philistines sang "The mountains melted before the Lord" and her contemporary (on our time scale), the Egyptian Amenemhet, who designed the water clock, which was in fact the prototype of the capillary viscometer, the beginnings of modern rheology should be linked up with the works of the classics of natural sciences of the 19th century: J ames Clerk Maxwell, Lord Kelvin, and Ludwig Boltzmann, whose names are associated with the origination of the fundamental concepts of rheology. The founda tions of experimental rheology were also laid in the nineteenth century in the works of J. M. L. Poiseuille, T. Schwedoff, and others. The next step in the advancement of rheology dates back to the twenties of this century when E. C. Bingham, G. W. Scott-Blair, A. Nadai, and M. Reiner developed the fundamentals of the engineering approach to the technological properties of real materials, thereby outlining the numerous potential applications of rheology. The progress of polymer rheology was especially vigorous after World War II when polymeric materials found their way into industry and the home. Today, rheology is 60-70 per cent concerned with investigations of this kind of materials. Polymer rheology has evolved as an independent science over the last 10-15 years and is in its various aspects intimately entwined with molecular physics, continuum mechanics, and the processing of polymeric materials.

Rheology: Theory and Applications, Volume 5 focuses on overtly fluid behavior of polymers, including the theory of large deformations, thermoelastic effects, elastic phenomena observed during the extrusion of polymeric melts, and theories of the structure of liquids and glasses. The selection first elaborates on the application of large deformation theory to the thermomechanical behavior of rubberlike polymers and unstable flow of molten polymers. Discussions focus on the mechanism proposed for unstable flow, ripple and associated effects, direct observation of waviness phenomena, empirical behavior of porous, unfilled, and filled rubberlike polymers, and problems connected with the interpretation of mechanical response parameters. The text then examines elasticity effects in polymer extrusion and strength and extensibility of elastomers. The publication takes a look at free volume and polymer rheology and studies of the deformation of crystalline polymers. Topics include the contribution of the two orientation processes to the birefringence, deformation of superstructure, rate of orientation of crystalline regions, free volume and physical state, glass transition and free volume, and reappraisal of time-temperature superposition. The manuscript also elaborates on the deformation and dissipative processes in high polymeric solids and the thermodynamics of deformation. The selection is a vital source of data for researchers interested in the theories and applications of rheology.

This book contains notes for a one-semester course on viscoelasticity given in the Division of Applied Mathematics at Brown University. The course serves as an introduction to viscoelasticity and as a workout in the use of various standard mathematical methods. The reader will soon find that he needs to do some work on the side to fill in details that are omitted from the text. These are notes, not a completely de tailed explanation. Furthermore, much of the content of the course is in the prob lems assigned for solution by the student. The reader who does not at least try to solve a good many of the problems is likely to miss most of the point. Much that is known about viscoelasticity is not discussed in these notes, and references to original sources are usually not given, so it will be difficult or impossible to use this book as a reference for looking things up. Readers wanting something more like a treatise should see Ferry's Viscoelastic Properties of Polymers, Lodge's Elastic Liquids, the volumes edited by Eirich on Rheology, or any issue of the Transactions of the Society of Rheology. These works emphasize physical aspects of the subject. On the mathematical side, Gurtin and Sternberg's long paper On the Linear Theory of Viscoelasticity (ARMA~, 291(1962)) remains the best reference for proofs of theorems.