Viscometric Flows of Non-Newtonian Fluids
Viscometric Flows of Non-Newtonian Fluids

Author: Bernard D. Coleman

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 139

ISBN-13: 3642886558

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We here attempt to give a complete but concise treatment of the theory of steady viscometric flows of simple (non-Newtonian) fluids and to use that theory to discuss the design and interpretation of ex periments. We are able to present the theory with less mathematical machinery than was used in our original papers, partly because this Tract has more limited aims than those papers, and partly because we employ a method, found by Noll and published here for the first time, for dealing with visco metric flows without the apparatus of rela tive Cauchy-Green tensors and reduced constitutive equations. To make the theory accessible to students not familiar with modern mathematics, we have added to our Tract an appendix explaining some of the mathe matical concepts essential to continuum physics. Pittsburgh, July 1965 BERNARD D. COLEMAN HERSHEL MARKOVITZ WALTER NOLL CONTENTS I. Introduction page 1. Limitations of the Classical Theory of Navier and Stokes. 1 5 2. Incompressible Simple Fluids. . . . . . . . . . . . 3. Plan and Scope of this Monograph . . . . . . . . . 7 II. Theory of Incompressible Simple Fluids 4. Kinematics. . . . . . . . . . . . 10 5. The Dynamical Equations . . . . . . . . . . . 12 6. The Principle of Material Objectivity . . . . . . 14 7. The Definition of an Incompressible Simple Fluid . 17 8. Static Behavior of Simple Fluids . . . . . . . . 19 III. General Theory of Viscometric Flows 9. The Kinematics of Simple Shearing Flow 21 10. The Viscometric Functions . . . . . . . . . . 22 11. The Dynamics of Simple Shearing Flow; Viscosity 26 12. The Definition of a Viscometric Flow 29 13. Curvilineal Flows. . . . . . . . 30 1. Kinematical Description . . . .

Non-Newtonian Fluid Mechanics
Non-Newtonian Fluid Mechanics

Author: G. Böhme

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 364

ISBN-13: 0444597573

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This volume is for use in technical universities, and for practising engineers who are involved with flow problems of non-Newtonian fluids. The treatment of the subject is based throughout on continuum mechanics model concepts and methods. Because in Non-Newtonian fluids the material properties operating depend critically on the kinematics of the flow, special attention is paid to the derivation and explanation of the adequate constitutive equations used. The book can be read without reference to other sources. It begins by considering some general principles of continuum mechanics, studies simple motions (steady and unsteady shear flows) and proceeds by degrees to kinematically more complex motions. Problems of various degrees of difficulty at the end of each chapter invite active participation by the reader. Numerous stimulating topics from the literature are considered in the book.

Rheology and Non-Newtonian Fluids
Rheology and Non-Newtonian Fluids

Author: Fridtjov Irgens

Publisher: Springer Science & Business Media

Published: 2013-07-25

Total Pages: 192

ISBN-13: 3319010530

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This book gives a brief but thorough introduction to the fascinating subject of non-Newtonian fluids, their behavior and mechanical properties. After a brief introduction of what characterizes non-Newtonian fluids in Chapter 1 some phenomena characteristic of non-Newtonian fluids are presented in Chapter 2. The basic equations in fluid mechanics are discussed in Chapter 3. Deformation kinematics, the kinematics of shear flows, viscometric flows, and extensional flows are the topics in Chapter 4. Material functions characterizing the behavior of fluids in special flows are defined in Chapter 5. Generalized Newtonian fluids are the most common types of non-Newtonian fluids and are the subject in Chapter 6. Some linearly viscoelastic fluid models are presented in Chapter 7. In Chapter 8 the concept of tensors is utilized and advanced fluid models are introduced. The book is concluded with a variety of 26 problems. Solutions to the problems are ready for instructors

Numerical Simulation of Non-Newtonian Flow
Numerical Simulation of Non-Newtonian Flow

Author: M.J. Crochet

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 367

ISBN-13: 0444598553

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Numerical Simulation of Non-Newtonian Flow focuses on the numerical simulation of non-Newtonian flow using finite difference and finite element techniques. Topics range from the basic equations governing non-Newtonian fluid mechanics to flow classification and finite element calculation of flow (generalized Newtonian flow and viscoelastic flow). An overview of finite difference and finite element methods is also presented. Comprised of 11 chapters, this volume begins with an introduction to non-Newtonian mechanics, paying particular attention to the rheometrical properties of non-Newtonian fluids as well as non-Newtonian flow in complex geometries. The role of non-Newtonian fluid mechanics is also considered. The discussion then turns to the basic equations governing non-Newtonian fluid mechanics, including Navier Stokes equations and rheological equations of state. The next chapter describes a flow classification in which the various flow problems are grouped under five main headings: flows dominated by shear viscosity, slow flows (slightly elastic liquids), small deformation flows, nearly-viscometric flows, and long-range memory effects in complex flows. The remainder of the book is devoted to numerical analysis of non-Newtonian fluids using finite difference and finite element techniques. This monograph will be of interest to students and practitioners of physics and mathematics.

Numerical Simulation of Non-Newtonian Flow
Numerical Simulation of Non-Newtonian Flow

Author: M.J. Crochet

Publisher: Elsevier Publishing Company

Published: 1984-02

Total Pages: 374

ISBN-13:

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Numerical Simulation of Non-Newtonian Flow focuses on the numerical simulation of non-Newtonian flow using finite difference and finite element techniques. Topics range from the basic equations governing non-Newtonian fluid mechanics to flow classification and finite element calculation of flow (generalized Newtonian flow and viscoelastic flow). An overview of finite difference and finite element methods is also presented. Comprised of 11 chapters, this volume begins with an introduction to non-Newtonian mechanics, paying particular attention to the rheometrical properties of non-Newtonian fluids as well as non-Newtonian flow in complex geometries. The role of non-Newtonian fluid mechanics is also considered. The discussion then turns to the basic equations governing non-Newtonian fluid mechanics, including Navier Stokes equations and rheological equations of state. The next chapter describes a flow classification in which the various flow problems are grouped under five main headings: flows dominated by shear viscosity, slow flows (slightly elastic liquids), small deformation flows, nearly-viscometric flows, and long-range memory effects in complex flows. The remainder of the book is devoted to numerical analysis of non-Newtonian fluids using finite difference and finite element techniques. This monograph will be of interest to students and practitioners of physics and mathematics.

Engineering Rheology
Engineering Rheology

Author: Roger I. Tanner

Publisher: OUP Oxford

Published: 2000-03-02

Total Pages: 590

ISBN-13: 0191590169

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This book sets out to provide a guide, with examples, for those who wish to make predictions about the mechanical and thermal behaviour of non-Newtonian materials in engineering and processing technology. After an introductory survey of the field and a review of basic continuum mechanics, the radical differences between elongational and shear behaviour are shown. Two chapters, one based on a continuum approach and the other using microstructural approaches, lead to useful mathematical desriptions of materials for engineering applications. As examples of nearly-viscometric and nearly-elongational flows, there is a discussion of lubrication and related shearing flows, and fibre- spinning and film-blowing respectively. A long chapter is devoted to the important new field of computational rheology, and this is followed by chapters on stability and turbulence and the all-important temperature effects in flow. This new edition contains much new material not available in book form elsewhere-for example wall slip, suspension rheology, computational rheology and new results in stability theory.