《RHEOLOGY PRINCIPLES，MEASUREMENTS，AND APPLICATIONS》

Part Ⅰ.CONSTITUTIVE RELATIONS1

1Elastic SolidChristopher W.Macosko5

1.1 Introduction5

1.2The Stress Tensor8

1.2.1 Notation11

1.2.2 Symmetry16

1.2.3 Pressure18

1.3 Principal Stresses and Invariants20

1.4Finite Deformation Tensors24

1.4.1 Finger Tensor29

1.4.2 Strain Tensor32

1.4.3 Inverse Deformation Tensors32

1.4.4 Principal Strains34

1.5Neo-Hookean Solid37

1.5.1 Uniaxial Extension38

1.5.2 Simple Shear40

1.6General Elastic Solid40

1.6.1 Strain-Energy Function42

1.6.2 Anisotropy44

1.6.3 Rubber-like Liquids45

1.7Equations of Motion45

1.7.1 Mass Balance45

1.7.2 Momentum Balance47

1.8 Boundary Conditions52

1.9 Summary58

1.10Exercises59

References62

2Viscous LiquidChristopher W.Macosko65

2.1 Introduction65

2.2Velocity Gradient68

2.2.1 Rate of Deformation Tensor72

2.3Newtonian Fluid77

2.3.1 Uniaxial Extension79

2.4General Viscous Fluid83

2.4.1 Power Law84

2.4.2 Cross Model86

2.4.3 Other Viscous Models86

2.4.4 The Importance of II 2D89

2.4.5 Extensional Thickening Models91

2.5Plastic Behavior92

2.5.1 Other Viscoplastic Models95

2.6Balance Equations98

2.6.1 Equations of Motion99

2.6.2 Boundary Conditions99

2.6.3 Energy Equation100

2.6.4 Temperature and Pressure Dependence of Viscosity100

2.7 Summary104

2.8Exercises105

References106

3Linear ViscoelasticityChristopher W.Macosko109

3.1 Introduction109

3.2General Linear Viscoelastic Model111

3.2.1 Relaxation Spectrum115

3.2.2 Linear Viscoelasticity in Three Dimensions115

3.2.3 Differential Form115

3.3Small Strain Material Functions117

3.3.1 Stress Relaxation118

3.3.2 Creep119

3.3.3 Sinusoidal Oscillations121

3.4 Exercises126

Appendix 3ARobert B.Secor127

Curve Fitting of Relaxation Modulus127

Approximating Form127

Error Measure128

Search Procedures129

References133

4Nonlinear ViscoelasticityRonald G.Larson135

4.1 Introduction135

4.2Nonlinear Phenomena138

4.2.1 Normal Stress Difference in Shear138

4.2.2 Shear Thinning139

4.2.3 Interrelations Between Shear Functions140

4.2.4 Extensional Thickening142

4.3Simple Nonlinear Constitutive Equations146

4.3.1 Second-Order Fluid146

4.3.2 Upper-Convected Maxwell Equation149

4.3.3 Lodge Integral Equation153

4.4More Accurate Constitutive Equations158

4.4.1 Integral Constitutive Equations158

4.4.2 Maxwell-Type Differential Constitutive Equations166

4.5 Summary170

4.6Exercises171

References172

Part Ⅱ.MEASUREMENTS：RHEOMETRY175

5Shear Rheometry：Drag FlowsChristopher W.Macosko181

5.1 Introduction181

5.2Sliding Plates，Falling Ball184

5.2.1 Falling Cylinder185

5.2.2 Falling Ball187

5.2.3 Rolling Ball187

5.3Concentric Cylinder Rheometer188

5.3.1 Shear Stress190

5.3.2 Shear Strain and Rate191

5.3.3 Normal Stresses in Couette Flow195

5.3.4 Rod Climbing198

5.3.5 End Effects200

5.3.6 Secondary Flows202

5.3.7 Shear Heating in Couette Flow203

5.4Cone and Plate Rheometer205

5.4.1 Shear Stress206

5.4.2 Shear Strain Rate207

5.4.3 Normal Stresses208

5.4.4 Inertia and Secondary Flow209

5.4.5 Edge Effects with Cone and Plate213

5.4.6 Shear Heating216

5.4.7 Summary216

5.5Parallel Disks217

5.5.1 Normal Stresses221

5.6Drag Flow Indexers222

5.6.1 Rotating Disk in a Sea of Fluid223

5.6.2 Rotating Vane224

5.6.3 Helical Screw Rheometer224

5.6.4 Instrumented Mixers225

5.7Eccentric Rotating Geometries226

5.7.1 Rotating Cantiliver Rod227

5.7.2 Eccentric Rotating Disks227

5.7.3 Other Eccentric Geometries231

References231

6Shear Rheometry：Pressure-Driven FlowsChristopher W.Macosko237

6.1 Introduction237

6.2Capillary Rheometer238

6.2.1 Shear Rate240

6.2.2 Wall Slip，Melt Fracture244

6.2.3 True Shear Stress247

6.2.4 Shear Heating252

6.2.5 Extrudate Swell254

6.2.6 Melt Index256

6.3Slit Rheometry257

6.3.1 Normal Stresses260

6.3.2 Exit Pressure261

6.3.3 Pressure Hole262

6.4Other Pressure Rheometers266

6.4.1 Axial Annular Flow266

6.4.2 Tangential Annular Flow267

6.4.3 Tilted Open Channel268

6.4.4 Squeezing Flow270

6.5 Comparison of Shear Methods275

6.6Summary277

References280

7Extensional RheometryChristopher W.Macosko285

7.1 Introduction285

7.2Simple Extension288

7.2.1 End Clamps291

7.2.2 Rotating Clamps292

7.2.3 Buoyancy Baths294

7.2.4 Spinning Drop296

7.3Lubricated Compression297

7.3.1 Planar Squeezing303

7.4Sheet Stretching，Multiaxial Extension303

7.4.1 Rotating Clamps304

7.4.2 Inflation Methods306

7.5Fiber Spinning308

7.5.7 Tubeless Siphon315

7.6 Bubble Collapse317

7.7Stagnation Flows320

7.7.1 Lubricated Dies322

7.7.2 Unlubricated Dies322

7.7.3 Opposed Nozzles323

7.8 Entrance Flows326

7.9Summary332

References333

8Rheometer DesignChristopher W.Macosko337

8.1 Introduction337

8.2Drag Flow Rheometers338

8.2.1 Controlled Strain339

8.2.2 Torque Measurement342

8.2.3 Normal Stresses345

8.2.4 Alignment347

8.2.5 Controlled Stress349

8.2.6 Environmental Control352

8.3Data Analysis357

8.3.1 Sinusoidal Oscillations359

8.3.2 Transient363

8.4 Pressure-Driven Rheometers364

8.5 Extensional Rheometers368

8.6 Process Line Rheometers370

8.7Summary373

References374

9Rheo-Optics：Flow BirefringenceTimothy P.Lodge379

9.1 Introduction379

9.2Review of Optical Phenomena381

9.2.1 Absorption and Emission Spectroscopies382

9.2.2 Scattering Techniques382

9.2.3 Birefringence and Dichroism384

9.3Polarized Light386

9.3.1 Transmission Through a Series of Optical Elements390

9.4Flow Birefringence：Principles and Practice393

9.4.1 The Stress-Optical Relation393

9.4.2 Range of Applicability of the Stress-Optical Relation397

9.4.3 Geometries for Measuring Flow Birefringence400

9.4.4 Birefringence in Steady and Transient Couette Flow403

9.4.5 Birefringence in Oscillatory Shear Flow405

9.4.6 Experimental Considerations407

9.5Flow Birefringence：Applications408

9.5.1 Stress Field Visualization408

9.5.2 Extensional Flow409

9.5.3 Dynamics of Isolated，Flexible Homopolymers409

9.5.4 Dynamics of Isolated Block Copolymers412

9.5.5 Dynamics of Block Copolymer Melts415

9.5.6 Dynamics of a Binary Blend415

9.5.7 Birefringence in Transient Flows416

9.5.8 Rheo-Optics of Suspensions416

9.5.9 Rotational Dynamics of Rigid Rods417

9.6Summary419

References419

Part Ⅲ.APPLICATIONS423

10Suspension RheologyJan Mewis and Christopher W.Macosko425

10.1 Introduction425

10.2Dilute Suspensions of Spheres428

10.2.1 Hard Spheres428

10.2.2 Particle Migration430

10.2.3 Emulsions434

10.2.4 Deformable Spheres437

10.3Particle-Fluid Interactions：Dilute Spheroids439

10.3.1 Orientation Distribution440

10.3.2 Constitutive Relations for Spheroids443

10.4Particle-Particle Interactions449

10.4.1 Dispersion Forces450

10.4.2 Electrostatic Forces451

10.4.3 Polymeric（Steric）Forces452

10.4.4 Scaling454

10.5Brownian Hard Particles455

10.5.1 Monodisperse Hard Spheres455

10.5.2 Particle Size Distribution458

10.5.3 Nonspherical Particles459

10.5.4 Non-Newtonian Media460

10.5.5 Extensional Flow of Ellipsoids460

10.6Stable Colloidal Suspensions461

10.6.1 Electrostatic Stabilization462

10.6.2 Polymeric（Steric）Stabilization464

10.7Flocculated Systems465

10.7.1 Structure in Flocculated Dispersions465

10.7.2 Static Properties467

10.7.3 Flow Behavior468

10.8Summary470

References471

11Rheology of Polymeric LiquidsMatthew Tirrell475

11.1 Introduction475

11.2 Polymer Chain Conformation476

11.3Zero Shear Viscosity479

11.3.1 Dilute Solution479

11.3.2 Nondilute Polymeric Liquids480

11.3.3 Coil Overlap482

11.4Rheology of Dilute Polymer Solutions487

11.4.1 Elastic Dumbbell487

11.4.2 Rouse and Other Multihead Models495

11.5Concentrated Solutions and Melts497

11.5.1 Entanglements497

11.5.2 Reptation Model502

11.5.3 Effects of Long Chain Branching505

11.5.4 Effect of Molecular Weight Distribution506

11.6 Temperature Dependence510

11.7Summary512

References512

AppendixSolutions to Exercises515

Chapter 1515

Chapter 2521

Chapter 3527

Chapter 4531

Index535