Polymer Rheology: Fundamentals and Applications

  • ID: 3260053
  • Book
  • 237 pages
  • Carl Hanser Verlag GmbH & Co. KG
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Rheology unites the seemingly unrelated fields of plasticity and non-Newtonian fluids by recognizing that both these types of materials are unable to support a shear stress in static equilibrium. In this sense, a plastic solid is a fluid. Granular rheology refers to the continuum mechanical description of granular materials.

One of the tasks of rheology is to empirically establish the relationships between deformations and stresses, respectively their derivatives by adequate measurements. These experimental techniques are known as rheometry and are concerned with the determination with well-defined rheological material functions. Such relationships are then amenable to mathematical treatment by the established methods of continuum mechanics.

In this book, rheology - the study of the deformation and flow of matter - deals primarily with the stresses generated during the flow of complex materials such as polymers, colloids, foams, and gels. A rapidly growing and industrially important field, it plays a significant role in polymer processing, food processing, coating and printing, and many other manufacturing processes.
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1 Introduction to Rheology
1.1 The Field of Rheology
1.2 Viscous Liquids or the Newtonian Fluid
1.3 Linear Elasticity or the Hookean Spring
1.4 Viscoelasticity and the Maxwell Model
1.5 Time Scale and the Deborah Number
1.6 Deformation, Rate of Deformation, and the Deviatoric Stress Tensors
1.7 Guide to the Book

2 Structure and Properties of Deforming Polymers
2.1 Molecular Structure of Polymers
2.2 Stress Relaxation Behavior
2.3 Shear Thinning Behavior
2.4 Normal Stresses in Shear Flow
2.5 Stress Overshoot during Start-up Flow
2.6 Melt Strength or Melt Fracture
2.7 Dynamic Response

3 Generalized Newtonian Fluid (GNF) Models
3.1 Temperature Dependence of Viscosity
3.2 Viscous Flow Models
3.2.1 The Power Law Model
3.2.2 The Bird-Carreau-Yasuda Model
3.2.3 The Cross-WLF Model
3.2.4 The Bingham Model
3.2.5 The Herschel-Bulkley Model
3.2.6 Accounting for Pressure Dependence in Viscous Flow Models . 73 Power Law Carreau-WLF Cross-WLF Universal Temperature and Pressure Invariant Viscosity Function
3.3 Elongational Viscosity
3.4 Suspension Rheology
3.5 Chemo-Rheology

4 Transport Phenomena
4.1 Dimensionless Groups
4.2 Balance Equations
4.2.1 The Mass Balance or Continuity Equation
4.2.2 The Material or Substantial Derivative
4.2.3 The Momentum Balance or Equation of Motion
4.2.4 The Energy Balance or Equation of Energy
4.3 Model Simplification
4.3.1 Reduction in Dimensionality
4.3.2 Lubrication Approximation
4.4 Viscometric Flows
4.4.1 Pressure Driven Flow of a Newtonian Fluid through a Slit
4.4.2 Flow of a Power Law Fluid in a Straight Circular Tube (Hagen-Poiseuille Equation)
4.4.3 Volumetric Flow Rate of a Power Law Fluid in Axial Annular Flow
4.4.4 Circular Annular Couette Flow of a Power Law Fluid
4.4.5 Squeezing Flow of a Newtonian Fluid between Two Parallel Circular Discs
4.4.6 Flow of a Power Law Fluid between Two Parallel Circular Discs

5 Viscoelasticity
5.1 Linear Viscoelasticity
5.1.1 Relaxation Modulus
5.1.2 The Boltzmann Superposition Principle
5.1.3 The Maxwell Model - Relaxation
5.1.4 Kelvin Model
5.1.5 Jeffrey’s Model
5.1.6 Standard Linear Solid Model
5.1.7 The Generalized Maxwell Model
5.1.8 Dynamic Tests
5.2 Non-Linear Viscoelasticity
5.2.1 Objectivity
5.2.2 Differential Viscoelastic Models
5.2.3 Integral Viscoelastic Models

6 Rheometry
6.1 The Sliding Plate Rheometer
6.2 The Cone-Plate Rheometer
6.3 The Parallel-Plate Rheometer
6.4 The Capillary Rheometer
6.4.1 Computing Viscosity Using the Bagley and Weissenberg-Rabinowitsch Equations
6.4.2 Viscosity Approximation Using the Representative Viscosity Method
6.5 The Melt Flow Indexer
6.6 Extensional Rheometry
6.7 High Pressure Rheometers
6.8 Integrated Mold Sensors for Quality Control

Subject Index
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Tim A. Osswald is Kuo and Cindy F. Wang Professor at the University of Wisconsin-Madison College of Engineering and Honorary Professor of Plastics Technology at the University of Erlangen-Nuremberg and the National University of Colombia. He is author of many books and book chapters, as well as over 100 papers in the field of plastics technology.

Natalie Rudolph is Team Leader at the Fraunhofer-Gesellschaft and was formerly Chief Engineer at the University of Wisconsin-Madison.
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