RHEOLOGY OF POLYMERIC SYSTEMS PRINCIPLES AND APPLICATIONSPDF电子书下载

1 Introduction 1

1.1 Definitions and Classification 1

1.1-1 Purely Viscous or Inelastic Material 3

1.1-2 Perfectly Elastic Material 3

1.1-3 Viscoelastic Material 3

1.2 Non-Newtonian Phenomena 3

1.2-1 The Weissenberg Effect 4

1.2-2 Entry Flow, Extrudate Swell, Melt Fracture, and Vibrating Jet 4

1.2-3 Recoil 7

1.2-4 Drag Reduction 7

1.2-5 Hole Pressure Error 13

1.2-6 Mixing 14

1.2-7 Bubbles, Spheres, and Coalescence 15

2 Material Functions and Generalized Newtonian Fluid 18

2.1 Material Functions 19

2.1-1 Simple Shear Flow 19

2.1-2 Sinusoidal Shear Flow 25

2.1-3 Transient Shear Flows 26

2.1-4 Elongational Flow 32

2.2 Generalized Newtonian Models 35

2.2-1 Generalized Newtonian Fluid 36

2.2-2 The Power-Law Model (Ostwald, 1925) 37

2.2-3 The Ellis Model (Bird, Armstrong, and Hassager, 1977) 37

2.2-4 The Carreau Model (1972) 38

2.2-5 The Cross-Williamson Model (1965) 39

2.2-6 The Four-Parameter Carreau Model (Carreau et al., 1979b) 39

2.2-7 The De Kee Model (1977) 40

2.2-8 The Carreau-Yasuda Model (Yasuda, 1976) 41

2.2-9 The Bingham Model (1922) 41

2.2-10 The Casson Model (1959) 42

2.2-11 The Herschel-Bulkley Model (1926) 42

2.2-12 The De Kee-Turcotte Model (1980) 42

2.2-13 Viscosity Models for Complex Flow Situations 43

2.3 Thixotropy, Rheopexy, and Hysteresis 44

2.4 Relations Between Material Functions 48

2.5 Temperature, Pressure, and Molecular Weight Effects 50

2.5-1 Effect of Temperature on Viscosity 50

2.5-2 Effect of Pressure on Viscosity 52

2.5-3 Effect of Molecular Weight on Viscosity 52

2.6 Problems 57

3 Rheometry 61

3.1 Capillary Rheometry 62

3.1-1 Rabinowitsch Analysis 64

3.1-2 End Effects or Bagley Correction 68

3.1-3 Mooney Correction 72

3.1-4 Intrinsic Viscosity Measurements 73

3.2 Coaxial-Cylinder Rheometers 76

3.2-1 Calculation of Viscosity 77

3.2-2 End Effect Corrections 81

3.2-3 Normal Stress Determination 82

3.3 Cone-and-Plate Geometry 84

3.3-1 Viscosity Determination 86

3.3-2 Normal Stress Determination 88

3.3-3 Inertial Effects 90

3.3-4 Criteria for Transient Experiments 94

3.4 Concentric Disk Geometry 98

3.4-1 Viscosity Determination 99

3.4-2 Normal Stress Difference Determination 101

3.5 Yield Stress Measurements 103

3.6 Problems 106

4 Transport Phenomena in Simple Flows 112

4.1 Criteria for Using Purely Viscous Models 113

4.2 Isothermal Flow in Simple Geometries 114

4.2-1 Flow of a Shear-Thinning Fluid in a Circular Tube 114

4.2-2 Film Thickness for the Flow on an Inclined Plane 116

4.2-3 Flow in a Thin Slit 118

4.2-4 Helical Flow in an Annular Section 119

4.2-5 Flow in a Disk-Shaped Mold 122

4.3 Heat Transfer to Non-Newtonian Fluids 126

4.3-1 Convective Heat Transfer in Poiseuille Flow 126

4.3-2 Heat Generation in Poiseuille Flow 134

4.4 Mass Transfer to Non-Newtonian Fluids 138

4.4-1 Mass Transfer to a Power-Law Fluid Flowing on an Inclined Plate 138

4.4-2 Mass Transfer to a Power-Law Fluid in Poiseuille Flow 141

4.5 Boundary Layer Flows 144

4.5-1 Laminar Boundary Layer Flow of Power-Law Fluids over a Plate 144

4.5-2 Laminar Thermal Boundary Layer Flow over a Plate 149

4.6 Problems 152

5 Linear Viscoelasticity 162

5.1 Importance and Definitions 162

5.2 Linear Viscoelastic Models 163

5.2-1 The Maxwell Model 164

5.2-2 Generalized Maxwell Model 170

5.2-3 The Jeffreys Model 178

5.2-4 The Voigt-Kelvin Model 180

5.2-5 Other Linear Models 182

5.3 Relaxation Spectrum 184

5.4 Time-Temperature Superposition 186

5.5 Problems 189

6 Nonlinear Viscoelasticity 194

6.1 Nonlinear Deformations 195

6.1-1 Expressions for the Deformation and Deformation Rate 197

6.1-2 Pure Deformation or Uniaxial Elongation 200

6.1-3 Planar Elongation 204

6.1-4 Expansion or Compression 205

6.1-5 Simple Shear 205

6.2 Formulation of Constitutive Equations 208

6.2-1 Material Objectivity and Formulation of Constitutive Equations 209

6.2-2 Maxwell Convected Models 210

6.2-3 Generalized Newtonian Models 215

6.3 Differential Constitutive Equations 220

6.3-1 The De Witt Model 221

6.3-2 The Oldroyd Models 222

6.3-3 The White-Metzner Model 223

6.3-4 The Marrucci Model 230

6.3-5 The Phan-Thien-Tanner Model 232

6.4 Integral Constitutive Equations 234

6.4-1 The Lodge Model 235

6.4-2 The Carreau Constitutive Equation 239

6.4-3 The K-BKZ Constitutive Equation 247

6.4-4 The LeRoy-Pierrard Equation 254

6.5 Concluding Remarks 257

6.6 Problems 258

7 Constitutive Equations from Molecular Theories 263

7.1 Bead- and Spring-Type Models 264

7.1-1 Hookean Elastic Dumbbell 265

7.1-2 Finitely Extensible Nonlinear Elastic (FENE) Dumbbell 272

7.1-3 Rouse and Zimm Models 276

7.2 Network Theories 284

7.2-1 General Network Concept 284

7.2-2 Rubber-Like Solids 286

7.2-3 Elastic Liquids 288

7.2-4 Recent Developments 290

7.3 Reptation Theories 294

7.3-1 The Tube Model 294

7.3-2 The Doi-Edwards Model 296

7.3-3 The Curtiss-Bird Kinetic Theory 300

7.4 Conformation Tensor Rheological Models 304

7.4-1 Basic Description of the Conformation Model 304

7.4-2 FENE-Charged Macromolecules 307

7.4-3 Rod-Like and Worm-Like Macromolecules 312

7.4-4 Generalization of the Conformation Tensor Model 320

7.5 Problems 327

8 Multiphase Systems 329

8.1 Systems of Industrial Interest 330

8.2 Rheology of Suspensions 331

8.2-1 Viscosity of Dilute Suspensions of Rigid Spheres 332

8.2-2 Rheology of Emulsions 334

8.2-3 Rheology of Concentrated Suspensions of Non-Interactive Particles 343

8.2-4 Rheology of Concentrated Suspensions of Interactive Particles 347

8.2-5 Concluding Remarks 351

8.3 Flow About a Rigid Particle 352

8.3-1 Flow of a Power-Law Fluid Past a Sphere 352

8.3-2 Other Fluid Models 356

8.3-3 Viscoplastic Fluids 356

8.3-4 Viscoelastic Fluids 357

8.3-5 Wall Effects 357

8.3-6 Non-Spherical Particles 359

8.3-7 Drag-Reducing Fluids 360

8.3-8 Behavior in Confined Flows 361

8.4 Flow Around Fluid Spheres 362

8.4-1 Creeping Flow of a Power-Law Fluid Past a Gas Bubble 362

8.4-2 Experimental Results on Single Bubbles 363

8.5 Creeping Flow of a Power-Law Fluid Around a Newtonian Droplet 366

8.5-1 Experimental Results on Falling Drops 367

8.6 Flow in Packed Beds 368

8.6-1 Creeping Power-Law Flow in Beds of Spherical Particles: The Capillary Model 368

8.6-2 Other Fluid Models 373

8.6-3 Viscoelastic Effects 373

8.6-4 Wall Effects 374

8.6-5 Effects of Particle Shape 375

8.6-6 Submerged Objects' Approach to Fluid Flow in Packed Beds:Creeping Flow 376

8.7 Fluidized Beds 377

8.7-1 Minimum Fluidizafion Velocity 378

8.7-2 Bed Expansion Behavior 380

8.7-3 Heat and Mass Transfer in Packed and Fluidized Beds 382

8.8 Problems 383

9 Liquid Mixing 386

9.1 Introduction 387

9.2 Mechanisms of Mixing 388

9.2-1 Laminar Mixing 389

9.2-2 Turbulent Mixing 391

9.3 Scale-Up and Similarity Criteria 391

9.4 Power Consumption in Agitated Tanks 396

9.4-1 Low Viscosity Systems 396

9.4-2 High Viscosity Inelastic Fluids 397

9.4-3 Viscoelastic Systems 412

9.5 Flow Patterns 414

9.5-1 Class I Agitators 415

9.5-2 Class II Agitators 416

9.5-3 Class III Agitators 418

9.6 Mixing and Circulation Times 420

9.7 Gas Dispersion 423

9.7-1 Gas Dispersion Mechanisms 423

9.7-2 Power Consumption in Gas-Dispersed Systems 425

9.7-3 Bubble Size and Holdup 428

9.7-4 Mass Transfer Coefficient 429

9.8 Heat Transfer 430

9.8-1 Class Ⅰ Agitators 431

9.8-2 Class Ⅱ Agitators 432

9.8-3 Class Ⅲ Agitators 434

9.9 Mixing Equipment and its Selection 436

9.9-1 Mechanical Agitation 436

9.9-2 Extruders 436

9.10 Problems 439

Appendix A General Curvilinear Coordinate Systems and Higher Order Tensors 441

A.1 Cartesian Vectors and Summation Convention 442

A.2 General Curvilinear Coordinate Systems 445

A.2-1 Generalized Base Vectors 445

A.2-2 Transformation Rules for Vectors 449

A.2-3 Tensors of Arbitrary Order 452

A.2-4 Metric and Permutation Tensors 454

A.2-5 Physical Components 458

A.3 Covariant Differentiation 462

A.3-1 Definitions 462

A.3-2 Properties of Christoffel Symbols 464

A.3-3 Rules of Covariant Differentiation 465

A.3-4 Grad, Div, and Curl 468

A.4 Integral Transforms 474

A.5 Isotropic Tensors, Objective Tensors and Tensor-Valued Functions 476

A.5-1 Isotropic Tensors 476

A.5-2 Objective Tensors 478

A.5-3 Tensor-Valued Functions 480

A.6 Problems 483

Appendix B Equations of Change 487

B.1 The Equation of Continuity in Three Coordinate Systems 487

B.2 The Equation of Motion in Rectangular Coordinates (x, y, z) 487

B.2-1 In Terms of σ 487

B.2-2 In Terms of Velocity Gradients for a Newtonian Fluid with Constant ρ and μ 488

B.3 The Equation of Motion in Cylindrical Coordinates (r,？ , z) 488

B.3-1 In Terms of a 488

B.3-2 In Terms of Velocity Gradients for a Newtonian Fluid with Constant p and p 489

B.4 The Equation of Motion in Spherical Coordinates (r,？,φ) 490

B.4-1 In Terms of a 490

B.4-2 In Terms of Velocity Gradients for a Newtonian Fluid with Constant p and u 490

References 492

Notation 503

Subject Index 513