RHEOLOGY Principles, Measurements, and Applications. Christopher W. Macosko

Transcription

1 RHEOLOGY Principles, Measurements, and Applications

2 I '79~ VCH Publishers. Inc. New York

3 Part I. CONSTITUTIVE RELATIONS 1 1 l Elastic Solid Introduction The Stress Tensor Notation I Symmetry / Pressure /8 1.3 Principal Stresses and Invariants Finite Deformation Tensors Finger Tensor Strain Tensor Inverse Deformation Tensors Principal Strains Neo-Hookean Solid Uniaxial Extension Simple Shear General Elastic Solid Strain-Energy Function Anisotropy Rubber-like Liquids Equations of Motion Mass Balance Momentum Balance Boundary Conditions Summary Exercises 59 References 62 2 / Viscous Liquid Introduction Velocity Gradient Rate of Deformation Tensor Newtonian Fluid Uniaxial Extension General Viscous Fluid Power Law Cross Model 86

4 2.4.3 Other Viscous Models The Importance of 11,,, Extensional Thickening Models Plastic Behavior Other Viscoplastic Models Balance Equations Equations of Motion Boundary Conditions Energy Equation / Temperature and Pressure Dependence of Viscosity / Summary Exercises 105 References /06 3 / Linear Viscoelasticity Introduction General Linear Viscoelastic Model 1/ Relaxation Spectrum / Linear Viscoelasticity in Three Dimensions / Differential Form Small Strain Material Functions Stress Relaxation Creep Sinusoidal Oscillations 12/ 3.4 Exercises /26 Appendix 3A 127 Robert B. Secor Curve Fitting of Relaxation Modulus 127 Approximating Form /27 Error Measure /28 Search Procedures 129 References /33 4 / Nonlinear Viscoelasticity 135 Ronald G. Larson 4.1 Introduction / Nonlinear Phenomena / Normal Stress Difference in Shear Shear Thinning Interrelations Between Shear Functions Extensional Thickening /42

5 4.3 Simple Nonlinear Constitutive Equations / Second-Order Fluid / Upper-Convected Maxwell Equation Lodge Integral Equation / More Accurate Constitutive Equations Integral Constitutive Equations / Maxwell-Type Differential Constitutive Equations / Summary Exercises 17/ References 172 Part II. MEASUREMENTS: RHEOMETRY / Shear Rheometry: Drag flows Introduction Sliding Plates, Falling Ball / Falling Cylinder Falling Ball Rolling Ball / Concentric Cylinder Rheometer / Shear Stress / Shear Strain and Rate Normal Stresses in Couette Flow / Rod Climbing / End Effects Secondary Flows Shear Heating in Couette Flow Cone and Plate Rheometer Shear Stress Shear Strain Rate Normal Stresses Inertia and Secondary Flow Edge Effects with Cone and Plate 2/ Shear Heating 2/ Summary 2/6 5.5 Parallel Disks 2/ Normal Stresses 22/ 5.6 Drag Flow Indexers Rotating Disk in a Sea of Fluid Rotating Vane Helical Screw Rheometer Instrumented Mixers Eccentric Rotating Geometries Rotating Cantiliver Rod 227

6 5.7.2 Eccentric Rotating Disks Other Eccentric Geometries 23/ References / Shear Rheometry: Pressure- Driven Flows Introduction Capillary Rheometer Shear Rate Wall Slip, Melt Fracture True Shear Stress Shear Heating Extrudate Swell Melt Index Slit Rheometry Normal Stresses Exit Pressure 26/ Pressure Hole Other Pressure Rheometers Axial Annular Flow Tangential Annular Flow Tilted Open Channel Squeezing Flow Comparison of Shear Methods Summary 277 References / Extensional Rheometry Introduction Simple Extension End Clamps Rotating Clamps Buoyancy Baths Spinning Drop Lubricated Compression Planar Squeezing Sheet Stretching, Multiaxial Extension Rotating Clamps Inflation Methods Fiber Spinning Tubeless Siphon Bubble Collapse 3/7 7.7 Stagnation Flows Lubricated Dies 322

7 7.7.2 Unlubricated Dies Opposed Nozzles Entrance Flows Summary 332 References / Rheometer Design Introduction Drag Flow Rheometers Controlled Strain Torque Measurement Normal Stresses Alignment Controlled Stress Environmental Control Data Analysis Sinusoidal Oscillations Transient Pressure-Driven Rheometers Extensional Rheometers Process Line Rheometers Summary 373 References / Rheo-Optics: Flow Birefringence 379 Timothy P. Lodge 9.1 Introduction Review of Optical Phenomena 38/ Absorption and Emission Spectroscopies Scattering Techniques Birefringence and Dichroism Polarized Light Transmission Through a Series of Optical Elements Flow Birefringence: Principles and Practice The Stress-Optical Relation Range of Applicability of the Stress-Optical Relation Geometries for Measuring Flow Birefringence Birefringence in Steady and Transient Couette Flow Birefringence in Oscillatory Shear Flow Experimental Considerations 407

8 9.5 Flow Birefringence: Applications Stress Field Visualization Extensional Flow Dynamics of Isolated, Flexible Homopolymers Dynamics of Isolated Block Copolymers Dynamics of Block Copolymer Melts Dynamics of a Binary Blend Birefringence in Transient Flows Rheo-Optics of Suspensions Rotational Dynamics of Rigid Rods Summary 4/9 References 419 Part III. APPLICATIONS / Suspension Rheology 425 Jan Mewis and 10.1 Introduction Dilute Suspensions of Spheres Hard Spheres Particle Migration Emulsions Deformable Spheres Particle-Fluid Interactions: Dilute Spheroids Orientation Distribution Constitutive Relations for Spheroids Particle-Particle Interactions Dispersion Forces Electrostatic Forces Polymeric (Steric) Forces Scaling Brownian Hard Particles Monodisperse Hard Spheres Particle Size Distribution Nonspherical Particles Non-Newtonian Media Extensional Flow of Ellipsoids Stable Colloidal Suspensions Electrostatic Stabilization Polymeric (Steric) Stabilization Flocculated Systems Structure in Flocculated Dispersions Static Properties Flow Behavior 468

9 10.8 Summary 470 References 47/ 11 / Rheology of Polymeric Liquids 475 Matthew Tirrell 11.1 Introduction Polymer Chain Conformation Zero Shear Viscosity Dilute Solution Nondilute Polymeric Liquids Coil Overlap Rheology of Dilute Polymer Solutions Elastic Dumbbell Rouse and Other Multihead Models Concentrated Solutions and Melts Entanglements Reptation Model Effects of Long Chain Branching Effect of Molecular Weight Distribution Temperature Dependence 5/ Summary 5/2 References 512 Appendix / Solutions to Exercises Index 535 Chapter I 515 Chapter Chapter Chapter 4 53/