This book is about two special topics in rheological fluid mechanics: the elasticity of liquids and asymptotic theories of constitutive models. The major emphasis of the book is on the mathematical and physical consequences of the elasticity of liquids; seventeen of twenty chapters are devoted to this. Constitutive models which are instantaneously elastic can lead to some hyperbolicity in the dynamics of flow, waves of vorticity into rest (known as shear waves), to shock waves of vorticity or velocity, to steady flows of transonic type or to short wave instabilities which lead to ill-posed problems. Other kinds of models, with small Newtonian viscosities, give rise to perturbed instantaneous elasticity, associated with smoothing of discontinuities as in gas dynamics. There is no doubt that liquids will respond like elastic solids to impulses which are very rapid compared to the time it takes for the molecular order associated with short range forces in the liquid, to relax. After this, all liquids look viscous with signals propagating by diffusion rather than by waves. For small molecules this time of relaxation is estimated as lQ-13 to 10-10 seconds depending on the fluids. Waves associated with such liquids move with speeds of 1 QS cm/s, or even faster. For engineering applications the instantaneous elasticity of these fluids is of little interest; the practical dynamics is governed by diffusion, ·say, by the Navier-Stokes equations. On the other hand, there are other liquids which are known to have much longer times of relaxation.

The areas of suspension mechanics, stability and computational rheology have exploded in scope and substance in the last decade. The present book is one of the first of a comprehensive nature to treat these topics in detail. The aim of the authors has been to highlight the major discoveries and to present a number of them in sufficient breadth and depth so that the novice can learn from the examples chosen, and the expert can use them as a reference when necessary.The first two chapters, grouped under the category General Principles, deal with the kinematics of continuous media and the balance laws of mechanics, including the existence of the stress tensor and extensions of the laws of vector analysis to domains bounded by fractal curves or surfaces. The third and fourth chapters, under the heading Constitutive Modelling, present the tools necessary to formulate constitutive equations from the continuum or the microstructural approach. The last three chapters, under the caption Analytical and Numerical Techniques, contain most of the important results in the domain of the fluid mechanics of viscoelasticity, and form the core of the book.A number of topics of interest have not yet been developed to a theoretical level from which applications can be made in a routine manner. However, the authors have included these topics to make the reader aware of the state of affairs so that research into these matters can be carried out. For example, the sections which deal with domains bounded by fractal curves or surfaces show that the existence of a stress tensor in such regions is still open to question. Similarly, the constitutive modelling of suspensions, especially at high volume concentrations, with the corresponding particle migration from high to low shear regions is still very sketchy.

Most books on continuum mechanics focus on elasticity and fluid mechanics. But whether student or practicing professional, modern engineers need a more thorough treatment to understand the behavior of the complex materials and systems in use today. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity offers a complete tour of the subject th

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.

Engineering Viscoelasticity covers all aspects of the thermo- mechanical response of viscoelastic substances that a practitioner in the field of viscoelasticity would need to design experiments, interpret test data, develop stress-strain models, perform stress analyses, design structural components, and carry out research work. The material in each chapter is developed from the elementary to the esoteric, providing the background in mathematics and mechanics that are central to understanding the subject matter being presented. This book also examines how viscoelastic materials respond to the application of loads, and provides practical guidelines to use them in the design of commercial, military and industrial applications.

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.

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.

Fluid Mechanics, Second Edition deals with fluid mechanics, that is, the theory of the motion of liquids and gases. Topics covered range from ideal fluids and viscous fluids to turbulence, boundary layers, thermal conduction, and diffusion. Surface phenomena, sound, and shock waves are also discussed, along with gas flow, combustion, superfluids, and relativistic fluid dynamics. This book is comprised of 16 chapters and begins with an overview of the fundamental equations of fluid dynamics, including Euler's equation and Bernoulli's equation. The reader is then introduced to the equations of motion of a viscous fluid; energy dissipation in an incompressible fluid; damping of gravity waves; and the mechanism whereby turbulence occurs. The following chapters explore the laminar boundary layer; thermal conduction in fluids; dynamics of diffusion of a mixture of fluids; and the phenomena that occur near the surface separating two continuous media. The energy and momentum of sound waves; the direction of variation of quantities in a shock wave; one- and two-dimensional gas flow; and the intersection of surfaces of discontinuity are also also considered. This monograph will be of interest to theoretical physicists.

The pursuit of the golden balance between oversimplification and overload with theory has always been the primary goal of every author of book on rheology. Rheology: Concepts, Methods, and Applications, Second Edition is a tool for chemists and chemical engineers to solve many practical problems. They have to learn what to measure, how to measure, and what to do with the data. But, the learning process should not take users away from their major goals, such as manufacturing quality products, developing new materials, analysis of material durability. In the book various aspects of theoretical rheology as well as methods of measurement and raw data treatment and how to use rheological methods in different groups of products are discusses. The authors share their experiences of many years of experimental studies and teaching to show use of rheology in studies of materials. They and were very meticulous in giving historical background of contributors to rheology as a science and as the method of solving many practical problems. This book is very useful as a teaching tool in universities and colleges because it is consistent with programs of rheology courses. Practicality of this book will prepare students for typical tasks in industry. Equally it serves the industry and accomplished rheologists because it contains expert advice of two very famous and accomplished scientists and teachers who know discoveries first-hand because they may have taken part in some of them. introductory rheology for students and scientists easy to understand many practical examples