RHEOLOGICAL MEASUREMENT SECOND EDITIONPDF电子书下载

Part One Small Strain Measurements 1

1 Oscillatory rheometry&G. Marin 3

1.1 Linear viscoelastic functions in the frequency domain 3

1.1.1 The complex shear modulus G(ω) 5

1.1.2 The complex compliance J(ω) 7

1.1.3 The complex viscosity η(ω) 9

1.2 Test methods in oscillatory rheometry 10

1.2.1 Controlled torque and controlled displacement 11

1.2.2 Rheometers: orthogonal, balance and new designs 16

1.2.3 Free oscillation rheometers 23

1.2.4 Resonant methods 26

1.2.5 Time domain mechanical spectroscopy 26

1.2.6 Improvements in mechanical spectroscopic methods 33

1.2.7 Sources of error 35

1.3 Some important applications of oscillatory rheometry 41

1.3.1 Molecular rheology 42

1.3.2 Characterization of isothermal chemical reactions 43

1.3.3 Thermomechanical analysis 44

References 45

2 Computer-aided methods in rheometry&H. H. Winter, M. Mours, M. Baumgartel and P. R. Soskey 47

2.1 Introduction 47

2.2 Parameters in rheological models 50

2.2.1 Stress-strain relations 50

2.2.2 Steady shear viscosity 54

2.2.3 Rheology of the material at equilibrium 57

2.2.4 Finite viscoelasticity (non-equilibrium) 61

2.3 Determination of rheological material parameters 64

2.3.1 Rheometric experiments 64

2.3.2 Temperature shift factors 66

2.3.3 Relaxation modulus and relaxation time spectrum 72

2.4 Model calculations with relaxation time spectra 79

2.5 Rheometry on samples that undergo changes 85

2.6 Conclusions 92

Appendix: definition of strain and stress tensors 93

Acknowledgement 95

References 95

3 Rheological studies using a vibrating probe&R. A. Pethrick 99

3.1 Introduction 99

3.1.1 Application time, pot life and pour time 101

3.1.2 Working life or working time 101

3.1.3 Gel time 102

3.1.4 Tack-free time, demould time 102

3.1.5 Cure time 102

3.2 Quality control methods 103

3.2.1 Definition of the curing process 103

3.2.2 Methods available for cure monitoring 107

3.3 Vibrating needle curemeter (VNC) 108

3.3.1 Amplitude attenuation for the VNC 108

3.3.2 Output voltage and viscosity 111

3.3.3 Monitoring viscous changes with the VNC 113

3.3.4 Recognizing gelation characteristics with the VNC 115

3.4 Strathclyde curemeter 121

3.4.1 Calibration of the Strathclyde curemeter 125

3.4.2 Thermally scanning curemeter 126

3.4.3 Cure of an epoxy resin system 128

3.4.4 Cure of powder resin systems 130

3.4.5 Plastisol systems 131

3.4.6 Other applications 133

3.5 Conclusions 134

Acknowledgements 135

References 135

4 Dynamic mechanical analysis using complex waveforms&B. I. Nelson and J. M. Dealy 138

4.1 Introduction 138

4.2 Frequency analysis of complex waveforms 139

4.2.1 Time domain mechanical spectroscopy 142

4.3 Properties of the discrete Fourier transform 144

4.3.1 Aliasing 146

4.3.2 Time and frequency domain scaling 147

4.3.3 Leakage 148

4.3.4 Alternating versus simultaneous data acquisition 150

4.4 Some waveforms of special interest 151

4.4.1 Multiple sine waves 151

4.4.2 Equistrain waveforms 152

4.4.3 Pulse-like strains 153

4.4.4 PRBS waveforms 155

4.5 A sample DMA experiment 157

4.6 Conclusions 163

References 164

Part Two Large Strain Measurements 165

5 Capillary rheometry&M. R. Mackley and R. P. G. Rutgers 167

5.1 Introduction 167

5.2 Physical aspects 168

5.3 Level 1: viscometric capillary flow for simple constitutive equations 172

5.3.1 Creeping flow solution for a Newtonian fluid 172

5.3.2 Creeping flow solution for a power law fluid 174

5.3.3 Creeping flow solution for a Bingham plastic fluid 174

5.3.4 Apparent viscosity 175

5.3.5 Entry flow corrections 176

5.4 Level 2: numerical simulation of capillary flow 178

5.4.1 Numerical simulation of Newtonian capillary flow 178

5.4.2 Numerical simulation of power law capillary flow 180

5.5 Level 3: modelling of complex rheological behaviour 180

5.5.1 Viscoelastic constitutive equations 181

5.5.2 Numerical simulation of viscoelastic flow 182

5.6 Multipass rheometry 185

5.7 Conclusions 187

References 188

6 Slit rheometry&Chang Dae Han 190

6.1 Introduction 190

6.2 Theory 191

6.3 Method 193

6.4 Discussion 194

6.4.1 Correlations of Vexit and N1 with?? 194

6.4.2 Extent of flow disturbance near the die exit 201

6.4.3 Extent of viscous shear heating 205

6.5 Concluding remarks 206

Notation 208

References 209

7 Viscous heating&R. C. Warren 210

7.1 Effect of pressure on viscosity 210

7.2 Equations of flow in capillaries 211

7.3 Dimensionless numbers for non-isothermal flow 213

7.4 Non-dimensional equations of flow 215

7.5 Solution methods for the equations of flow 215

7.5.1 Analytical methods 215

7.5.2 Empirical methods 216

7.5.3 Numerical methods 217

7.6 Thermal boundary conditions at the die walls 219

7.6.1 Adiabatic walls 219

7.6.2 Isothermal walls 219

7.6.3 Constant heat transfer coefficient at the die walls 219

7.6.4 Effects of different thermal boundary conditions 221

7.7 Fluid compressibility and expansion cooling 224

7.8 Temperature rise due to viscous heating 226

7.9 Temperature rises: theory versus experiment 227

7.10 Effects of viscous heating on die swell 229

7.10.1 Inelastic fluids 230

7.10.2 Elastic fluids 231

7.11 Concluding remarks 233

Notation 234

References 235

8 Sliding plate and sliding cylinder rheometers&J. M. Dealy and A. J. Giacomin 237

8.1 Introduction 237

8.1.1 Limitations of pressure flow and rotational rheometers 237

8.2 Sliding plate rheometers 239

8.2.1 Basic features 239

8.2.2 Basic equations 240

8.2.3 Sources of error 240

8.2.4 Use of shear stress transducers 247

8.2.5 Applications 249

8.2.6 High shear rate techniques 252

8.3 Sliding cylinder rheometers 253

8.3.1 Introduction 253

8.3.2 Basic equations 253

8.3.3 Applications 255

References 255

9 Rotational viscometry&R. L. Powell 260

9.1 Introduction 260

9.2 Conventional viscometers 262

9.2.1 Cone and plate 262

9.2.2 Parallel plates 268

9.2.3 Concentric cylinders 272

9.3 Sources of error 277

9.3.1 Fluid inertia 277

9.3.2 Flow geometry 278

9.3.3 Viscous heating 282

9.3.4 Sample instability 283

9.3.5 Material effects 284

9.3.6 Wall slip 286

9.3.7 Experimental effects 287

9.4 Novel rheometric flows 288

9.4.1 Alternative cone and plate geometries 288

9.4.2 Vane rheometer 290

9.4.3 Helical screw rheometer 292

Notation 293

References 296

10 Normal stress differences from hole pressure measurements&A. S. Lodge 299

10.1 Summary 299

10.2 Online measurements: high viscosity liquids 299

10.3 Sample measurements: low viscosity liquids at high shear rates 309

10.4 Circular holes 317

10.5 Viscous heating 318

Notation 324

Acknowledgements 324

References 324

11 Using large-amplitude oscillatory shear&A. J. Giacomin and J. M. Dealy 327

11.1 Introduction 327

11.1.1 Simple shear 327

11.1.2 Oscillatory shear 328

11.1.3 Linear viscoelasticity 328

11.1.4 Non-linear viscoelasticity 330

11.1.5 Normal stress differences 330

11.2 Experimental errors 331

11.2.1 Fluid inertia 331

11.2.2 Viscous heating 333

11.2.3 Secondary flows 333

11.3 Measurement techniques 334

11.4 Methods of data analysis 337

11.4.1 Spectral analysis 337

11.4.2 Error analysis 339

11.4.3 Response loops 341

11.4.4 Analogue methods 342

11.4.5 Time-domain analysis 343

11.4.6 Approximate methods 343

11.5 Plausible phase angles 344

11.6 The Pipkin diagram 344

11.7 Slip 345

11.8 Limiting cases 346

11.9 Interpreting non-linear behaviour 347

11.10 Molecular origins 351

Acknowledgements 352

References 353

12 Rate- or stress-controlled rheometry&W. GleijBle 357

12.1 Introduction 357

12.1.1 Contemporary examples of applied rheometry 357

12.2 The problem 359

12.3 Rate-controlled measurements 360

12.4 Stress-controlled measurements 363

12.5 Viscous and viscoelastic similarity 366

12.6 Viscoelastic similarity and Bagley correction 367

12.7 Experiments 372

12.8 Conclusions 377

12.9 Stress-controlled simultaneous measurement of viscosity and flow exponent 378

12.9.1 Measurement technique 379

12.9.2 Flow exponent and molecular weight distribution 382

12.9.3 Experimental design and results 383

12.9.4 Evaluation of flow data 388

12.9.5 Conclusion 390

References 390

13 Transient rheometry&K. F. Wissbrun 392

13.1 Introduction 392

13.2 Transient test types and theoretical equations 393

13.2.1 Constitutive equations 394

13.2.2 Stress relaxation after imposition of step strain 396

13.2.3 Creep after imposition of step stress 397

13.2.4 Stress during start-up and after cessation of steady shear flow 399

13.2.5 Elastic recoil (elastic or strain recovery) 402

13.2.6 Multiple step strain tests 404

13.2.7 Multiple shear rate step tests 406

13.2.8 Continuously varied shear rate tests 408

13.2.9 Superimposed dynamic tests 410

13.3 Analysis of viscoelastic transient test data 410

13.3.1 Determination of relaxation spectra 410

13.3.2 Empirical approximate relations 413

13.4 Experimental considerations 415

13.4.1 Apparatus 415

13.4.2 Sources of error 415

13.4.3 Instrument response time and sample inertia 416

13.4.4 Apparatus compliance 419

13.4.5 Other sources of error and unusual phenomena 421

References 423

14 Commercial rotational rheometers&G. J. Brownsey 427

14.1 Introduction 427

14.2 Commercial rheometers 431

14.2.1 Bohlin Instruments 431

14.2.2 Brookfield Viscometers 434

14.2.3 FANN 436

14.2.4 Haake 436

14.2.5 Kaltec Scientific 440

14.2.6 Physica 441

14.2.7 Reologica 444

14.2.8 Rheometric Scientific 446

14.2.9 TA Instruments 449

14.3 Conclusion 450

14.4 Useful addresses 451

Part Three Extensional and Mixed Flows 453

15 Converging dies&A. G. Gibson 453

15.1 Introduction 455

15.2 Behaviour of polymer melts, solutions and fibre suspensions 458

15.2.1 Implications of fluid anisotropy 459

15.2.2 Extensional behaviour of fibre suspensions 462

15.3 Capillary flow experiments 465

15.4 Treatment of capillary flow data 467

15.5 Conical die flow 472

15.5.1 Flow in convergences of shallow angle 472

15.5.2 A convergent die model using spherical coordinates 477

15.6 Power law equations for a wide range of die angles 482

15.7 Design of injection mould gating 485

15.8 Freely convergent flow: recirculation zones 487

15.9 Conclusions 488

Notation 489

References 490

16 Recoverable elastic strain and swelling ratio&R. I. Tanner 492

16.1 Definition of recoverable elastic strain and swelling ratio 492

16.2 Elastic theory of swelling 494

16.3 Inelastic theory of swelling 497

16.4 Computation of swelling for various rheological models 498

16.4.1 Steady shear behaviour 500

16.4.2 Steady elongational behaviour 503

16.4.3 Results for the planar swelling problem 504

16.5 Relation of rheology to swelling 511

16.6 Conclusion and further investigations 513

Notation 513

References 514

17 Elongational rheometers&R. K. Gupta and T. Sridhar 516

17.1 Introduction 516

17.2 Extensional flow kinematics 518

17.2.1 Tensile viscosity 518

17.3 Homogeneous stretching of polymer melts 519

17.3.1 Constant stretch rate experiments 520

17.3.2 Constant-stress experiments 521

17.3.3 Constant sample length experiments 523

17.3.4 Experimental results 525

17.4 Non-uniform stretching of polymer melts 528

17.4.1 Melt spinning of fibres 529

17.4.2 Converging flows 531

17.4.3 Miscellaneous methods 532

17.5 Homogeneous stretching of polymer solutions 533

17.5.1 Constant stretch rate experiments 534

17.5.2 Experimental results 536

17.6 Non-uniform stretching of polymer solutions 538

17.6.1 Solution spinning of fibres 538

17.6.2 The opposed nozzle rheometer 542

17.6.3 Miscellaneous techniques 544

17.7 Conclusions 545

References 545

18 Squeeze flow&A. G. Gibson, G. Kotsikos, J. H. Bland and S. Toll 550

18.1 Introduction 550

18.2 Theoretical treatment of squeeze flow 552

18.2.1 Constant area squeeze flow 552

18.2.2 Constant volume squeeze flow 554

18.3 Squeeze flow of polymer melts 555

18.3.1 Literature review 555

18.3.2 Normal stresses and elastic effects in squeeze flow 557

18.3.3 Experimental results 559

18.4 Modelling squeeze flow of planar fibre suspensions 563

18.4.1 Transversely isotropic power law model 565

18.4.2 Limiting cases 566

18.4.3 Variational approach 566

18.4.4 Micromechanical approach 570

18.4.5 Non-local constitutive equation 573

18.4.6 Special cases: locality 574

18.4.7 Squeeze flow with continuous tows 575

18.5 Planar fibre suspension squeeze flow models 579

18.6 Experimental squeeze flow of planar fibre suspensions 581

18.6.1 Glass mat thermoplastics 582

18.6.2 Sheet moulding compounds 586

18.7 Conclusions and recommendations for further work 589

Notation 590

References 591

Part Four Specialized Rheometers 593

19 Flow visualization in rheometry&M. E. Mackay and D. V. Boger 595

19.1 Introduction 595

19.2 Birefringence measurements 597

19.2.1 Stress-optic relation 598

19.2.2 Measurement of birefringence 599

19.2.3 Experimental studies using various geometries 602

19.3 Streak-line observation and point velocity measurement 616

19.3.1 Measurement techniques 616

19.3.2 Tubular entry flows of viscoelastic fluids 623

19.4 Conclusion 629

Acknowledgements 630

References 630

20 Rheological measurements on small samples&M. E. Mackay 635

20.1 Introduction 635

20.2 Miniature torsional rheometers 636

20.2.1 Cone and plate 636

20.2.2 Parallel plates 644

20.2.3 Concentric cylinders 647

20.3 Falling ball rheometer 650

20.4 Capillary rheometer 653

20.5 Surface forces rheometer 655

20.6 Prong rheometer 658

20.7 Other rheorheters 662

20.8 Concluding remarks 663

Acknowledgements 664

References 664

21 Rheometry for process control&T. O. Broadhead and J. M. Dealy 666

21.1 An overview of rheometry in manufacturing 666

21.1.1 The value of rheological information 666

21.1.2 Basic elements of a rheological measurement 667

21.1.3 Rheological sensors for process control 667

21.1.4 Instrument classification by method of installation 669

21.2 Rheological behaviour and its measurement 670

21.2.1 A survey of rheological behaviour 670

21.2.2 Test requirements for various fluids 674

21.2.3 Requirements for high pressure operation 677

21.3 Capillary and other pressure flow rheometers 677

21.3.1 Correlations with pressure drop sensors 678

21.3.2 Capillary viscometers 678

21.3.3 Slit rheometers 684

21.4 Rotational process rheometers 686

21.4.1 Common issues 686

21.4.2 Concentric cylinder rheometers 688

21.4.3 Parallel disc rheometers 692

21.4.4 Cone and plate rheometers 693

21.4.5 Rheometers based on lubrication flow 694

21.5 Helical flow rheometers 695

21.6 Piston-cup viscometers 696

21.7 Vibrational rheometers 697

21.8 Other rheometers 699

21.9 Signal processing 699

21.9.1 Calibration 699

21.9.2 Temperature compensation 700

21.9.3 Signal noise and filtering 702

21.9.4 Sampling delay 703

21.9.5 Process control using rheological sensors 704

21.10 Selecting a process rheometer 705

21.10.1 Nature of the material being processed 705

21.10.2 Process conditions 707

21.11 A final word 708

Appendix: manufacturers of commercial instruments 708

References 720

22 Interfacial rheology&B. Warburton 723

22.1 Introduction and history 723

22.2 Definitions and theory 725

22.3 Interfacial stress 725

22.4 Interfacial strain 726

22.5 Interfacial strain rate 727

22.6 Interfacial elastic moduli 727

22.7 Interfacial dilatational techniques 728

22.7.1 Theory of dilatational interfacial rheology 728

22.8 Interfacial shear rheology 730

22.8.1 Continuous rotation 730

22.8.2 Stationary and non-stationary interfacial films 732

22.8.3 Interfacial shear under constant stress 733

22.8.4 Interfacial shear oscillation 734

22.8.5 Interfacial rheology on non-stationary interfacial films 737

22.8.6 Solid films 743

22.9 Immunological processes: cascade kinetics 748

22.10 Summary and conclusions 749

22.11 Names and addresses of instrument manufacturers 749

Acknowledgements 752

References 752

Index 755