Viscoelasticity and Rheology
eBook - ePub

Viscoelasticity and Rheology

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 16–18, 1984

  1. 456 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Viscoelasticity and Rheology

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 16–18, 1984

About this book

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.

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Yes, you can access Viscoelasticity and Rheology by Arthur S. Lodge,Michael Renardy,John A. Nohel in PDF and/or ePUB format, as well as other popular books in Technology & Engineering & Engineering General. We have over one million books available in our catalogue for you to explore.

THE MOTION OF VISCOELASTIC FLUIDS AROUND SPHERES AND BUBBLES

Ole Hassager, Danmarks Tekniske HØjskole, Lyngby, Denmark and Mathematics Research Center and Chemical Engineering Department, University of Wisconsin, Madison, Wisconsin

Publisher Summary

This chapter discusses the translation of bubbles and solid spheres in a viscoelastic fluid. The motion is assumed to be caused by a gravitational field or an imposed force. The chapter presents some experimental observations of bubble shapes, velocity fields, and friction coefficients. One of the most striking features of translating air bubbles in viscoelastic fluids is that they develop a cusp at the rear pole. Often this effect may be observed in an almost full shampoo bottle by rapidly turning it upside down and watching an air bubble rise. More controlled experiments by Astarita and Apuzzo with a series of bubbles of increasing volume show a transition from a spherical bubble shape to an elongated ellipsoidal shape and the development of the cusp at the rear pole. They also measured the rise velocity of the bubbles as a function of the volume, and showed that for some viscoelastic fluids there is a critical volume at which the rise velocity appears to have a discontinuous increase when plotted as function of the volume.

INTRODUCTION

This paper is concerned with the translation of bubbles and solid spheres in a viscoelastic fluid. The motion is assumed to be caused by a gravitational field or an imposed force, and we will consider the situations in which the motion takes place in an unbounded fluid, quiescent far from the object as well as the situation in which the motion takes place in a finite container (a cylinder). First we will review some experimental observations of bubble shapes, velocity fields and friction coefficients. In the next section we then consider perturbation solutions for motions that are so slow...

Table of contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Inside Front Cover
  5. Copyright
  6. Contributors
  7. Preface
  8. Chapter 1: THE MOTION OF VISCOELASTIC FLUIDS AROUND SPHERES AND BUBBLES
  9. Chapter 2: WAVE PROPAGATION IN VISCOELASTIC SOLIDS
  10. Chapter 3: OVERVIEW OF MACROSCOPIC VISCOELASTIC FLOW
  11. Chapter 4: NECKING PHENOMENA AND COLD DRAWING
  12. Chapter 5: POLYMERIC LIQUIDS: FROM MOLECULAR MODELS TO CONSTITUTIVE EQUATIONS
  13. Chapter 6: ON SLOW-FLOW APPROXIMATIONS TO FLUIDS WITH FADING MEMORY
  14. Chapter 7: A COMPARISON OF MOLECULAR AND NETWORK-CONSTITUTIVE THEORIES FOR POLYMER FLUIDS
  15. Chapter 8: ON USING RUBBER AS A GUIDE FOR UNDERSTANDING POLYMERIC LIQUID BEHAVIOR
  16. Chapter 9: ON VISCOPLASTIC MODELS
  17. Chapter 10: DISSIPATION IN MATERIALS WITH MEMORY
  18. Chapter 11: HYPERBOLIC PHENOMENA IN THE FLOW OF VISCOELASTIC FLUIDS
  19. Chapter 12: ABSORBING BOUNDARIES FOR VISCOELASTICITY
  20. Chapter 13: RECENT DEVELOPMENTS AND OPEN PROBLEMS IN THE MATHEMATICAL THEORY OF VISCOELASTICITY
  21. Chapter 14: EVALUATION OF CONSTITUTIVE EQUATIONS: MATERIAL FUNCTIONS AND COMPLEX FLOWS OF VISCOELASTIC FLUIDS
  22. Chapter 15: FINITE ELEMENT METHODS FOR VISCOELASTIC FLOW
  23. Chapter 16: CONSTITUTIVE EQUATIONS FOR THE COMPUTING PERSON
  24. Index