| |
| |
| Preface | |
| |
| |
| |
| Introduction: How Much Do I Need to Learn about Rheology? | |
| |
| |
| |
| Shear Thinning/Shear Thickening | |
| |
| |
| |
| Yield Stress | |
| |
| |
| |
| Elastic/Viscoelastic Effects | |
| |
| |
| |
| Rheology as Spectroscopy | |
| |
| |
| |
| Process Modeling | |
| |
| |
| |
| Vector and Tensor Operations | |
| |
| |
| |
| Scalars | |
| |
| |
| |
| Vectors | |
| |
| |
| |
| Tensors | |
| |
| |
| |
| Differential Operations with Vectors and Tensors | |
| |
| |
| |
| Curvilinear Coordinates | |
| |
| |
| |
| Vector and Tensor Integral Theorems | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Newtonian Fluid Mechanics | |
| |
| |
| |
| Conservation of Mass | |
| |
| |
| |
| Conservation of Momentum | |
| |
| |
| |
| The Newtonian Constitutive Equation | |
| |
| |
| |
| The Navier-Stokes Equation | |
| |
| |
| |
| Example Flow Problems: Incompressible Newtonian Fluids | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Standard Flows for Rheology | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Simple Shear Flow | |
| |
| |
| |
| Simple Shear-Free (Elongational) Flows | |
| |
| |
| |
| Forms of the Stress Tensor in Standard Flows | |
| |
| |
| |
| Measuring Stresses in Standard Flows | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Material Functions | |
| |
| |
| |
| Introduction and Definitions | |
| |
| |
| |
| Shear Flow | |
| |
| |
| |
| Elogational Flow | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Experimental Data | |
| |
| |
| |
| Steady Shear Flow | |
| |
| |
| |
| Unsteady Shear FLow | |
| |
| |
| |
| Steady Elongational Flow | |
| |
| |
| |
| Unsteady Elongational Flow | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Problems | |
| |
| |
| |
| No Memory: Generalized Newtonian Fluids | |
| |
| |
| |
| Constitutive Constraints | |
| |
| |
| |
| The GNF Constitutive Equation | |
| |
| |
| |
| Material Function Predictions | |
| |
| |
| |
| Example Flow Problems: Power-Law Generalized Newtonian Fluid | |
| |
| |
| |
| Limitations on GNF Models | |
| |
| |
| |
| Memory Effects: Generalized Linear-Visoelastic Fluids | |
| |
| |
| |
| Memory Effects | |
| |
| |
| |
| The Maxwell Models | |
| |
| |
| |
| The GLVE Constitutive Equation | |
| |
| |
| |
| Example Flow Problems: GLVE Fluid | |
| |
| |
| |
| Limitations on the GLVE Model | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Introduction to More Advanced Constitutive Modeling | |
| |
| |
| |
| Finite Strain Measures | |
| |
| |
| |
| Lodge Equation | |
| |
| |
| |
| Convected Derivatives | |
| |
| |
| |
| Other Constitutive Approaches | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Rheometry | |
| |
| |
| |
| Shear Flow | |
| |
| |
| |
| Elongational Flows | |
| |
| |
| |
| Flow Birefringence | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Nomenclature | |
| |
| |
| |
| Glossary | |
| |
| |
| |
| Mathemats | |
| |
| |
| |
| Math Hints | |
| |
| |
| |
| Differential Operations in Curvlinear Coordinates | |
| |
| |
| |
| Projection of a Plane | |
| |
| |
| |
| Finite Deformation Tensors in Curvlinear Coordinates | |
| |
| |
| |
| Coordinate Transformations of Orthonormal Bases | |
| |
| |
| |
| Finding Principal Values | |
| |
| |
| |
| Contravariant/Covariant Transformations of Tensors | |
| |
| |
| |
| Problems--Mathematics Appendix | |
| |
| |
| |
| Predictions of Constitutive Equations | |
| |
| |
| |
| Optics of Birefringence | |
| |
| |
| |
| Light in a Vacuum | |
| |
| |
| |
| Light in an Isotropic Medium | |
| |
| |
| |
| Light in an Anisotropic Medium | |
| |
| |
| |
| Summary | |
| |
| |
| |
| Problems | |
| |
| |
| References | |
| |
| |
| Index | |