RHEOLOGICAL MEASUREMENT SECOND EDITION2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

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Part One Small Strain Measurements1

1 Oscillatory rheometry&G. Marin3

1.1 Linear viscoelastic functions in the frequency domain3

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 rheometry10

1.2.1 Controlled torque and controlled displacement11

1.2.2 Rheometers: orthogonal, balance and new designs16

1.2.3 Free oscillation rheometers23

1.2.4 Resonant methods26

1.2.5 Time domain mechanical spectroscopy26

1.2.6 Improvements in mechanical spectroscopic methods33

1.2.7 Sources of error35

1.3 Some important applications of oscillatory rheometry41

1.3.1 Molecular rheology42

1.3.2 Characterization of isothermal chemical reactions43

1.3.3 Thermomechanical analysis44

References45

2 Computer-aided methods in rheometry&H. H. Winter, M. Mours, M. Baumgartel and P. R. Soskey47

2.1 Introduction47

2.2 Parameters in rheological models50

2.2.1 Stress-strain relations50

2.2.2 Steady shear viscosity54

2.2.3 Rheology of the material at equilibrium57

2.2.4 Finite viscoelasticity (non-equilibrium)61

2.3 Determination of rheological material parameters64

2.3.1 Rheometric experiments64

2.3.2 Temperature shift factors66

2.3.3 Relaxation modulus and relaxation time spectrum72

2.4 Model calculations with relaxation time spectra79

2.5 Rheometry on samples that undergo changes85

2.6 Conclusions92

Appendix: definition of strain and stress tensors93

Acknowledgement95

References95

3 Rheological studies using a vibrating probe&R. A. Pethrick99

3.1 Introduction99

3.1.1 Application time, pot life and pour time101

3.1.2 Working life or working time101

3.1.3 Gel time102

3.1.4 Tack-free time, demould time102

3.1.5 Cure time102

3.2 Quality control methods103

3.2.1 Definition of the curing process103

3.2.2 Methods available for cure monitoring107

3.3 Vibrating needle curemeter (VNC)108

3.3.1 Amplitude attenuation for the VNC108

3.3.2 Output voltage and viscosity111

3.3.3 Monitoring viscous changes with the VNC113

3.3.4 Recognizing gelation characteristics with the VNC115

3.4 Strathclyde curemeter121

3.4.1 Calibration of the Strathclyde curemeter125

3.4.2 Thermally scanning curemeter126

3.4.3 Cure of an epoxy resin system128

3.4.4 Cure of powder resin systems130

3.4.5 Plastisol systems131

3.4.6 Other applications133

3.5 Conclusions134

Acknowledgements135

References135

4 Dynamic mechanical analysis using complex waveforms&B. I. Nelson and J. M. Dealy138

4.1 Introduction138

4.2 Frequency analysis of complex waveforms139

4.2.1 Time domain mechanical spectroscopy142

4.3 Properties of the discrete Fourier transform144

4.3.1 Aliasing146

4.3.2 Time and frequency domain scaling147

4.3.3 Leakage148

4.3.4 Alternating versus simultaneous data acquisition150

4.4 Some waveforms of special interest151

4.4.1 Multiple sine waves151

4.4.2 Equistrain waveforms152

4.4.3 Pulse-like strains153

4.4.4 PRBS waveforms155

4.5 A sample DMA experiment157

4.6 Conclusions163

References164

Part Two Large Strain Measurements165

5 Capillary rheometry&M. R. Mackley and R. P. G. Rutgers167

5.1 Introduction167

5.2 Physical aspects168

5.3 Level 1: viscometric capillary flow for simple constitutive equations172

5.3.1 Creeping flow solution for a Newtonian fluid172

5.3.2 Creeping flow solution for a power law fluid174

5.3.3 Creeping flow solution for a Bingham plastic fluid174

5.3.4 Apparent viscosity175

5.3.5 Entry flow corrections176

5.4 Level 2: numerical simulation of capillary flow178

5.4.1 Numerical simulation of Newtonian capillary flow178

5.4.2 Numerical simulation of power law capillary flow180

5.5 Level 3: modelling of complex rheological behaviour180

5.5.1 Viscoelastic constitutive equations181

5.5.2 Numerical simulation of viscoelastic flow182

5.6 Multipass rheometry185

5.7 Conclusions187

References188

6 Slit rheometry&Chang Dae Han190

6.1 Introduction190

6.2 Theory191

6.3 Method193

6.4 Discussion194

6.4.1 Correlations of Vexit and N1 with??194

6.4.2 Extent of flow disturbance near the die exit201

6.4.3 Extent of viscous shear heating205

6.5 Concluding remarks206

Notation208

References209

7 Viscous heating&R. C. Warren210

7.1 Effect of pressure on viscosity210

7.2 Equations of flow in capillaries211

7.3 Dimensionless numbers for non-isothermal flow213

7.4 Non-dimensional equations of flow215

7.5 Solution methods for the equations of flow215

7.5.1 Analytical methods215

7.5.2 Empirical methods216

7.5.3 Numerical methods217

7.6 Thermal boundary conditions at the die walls219

7.6.1 Adiabatic walls219

7.6.2 Isothermal walls219

7.6.3 Constant heat transfer coefficient at the die walls219

7.6.4 Effects of different thermal boundary conditions221

7.7 Fluid compressibility and expansion cooling224

7.8 Temperature rise due to viscous heating226

7.9 Temperature rises: theory versus experiment227

7.10 Effects of viscous heating on die swell229

7.10.1 Inelastic fluids230

7.10.2 Elastic fluids231

7.11 Concluding remarks233

Notation234

References235

8 Sliding plate and sliding cylinder rheometers&J. M. Dealy and A. J. Giacomin237

8.1 Introduction237

8.1.1 Limitations of pressure flow and rotational rheometers237

8.2 Sliding plate rheometers239

8.2.1 Basic features239

8.2.2 Basic equations240

8.2.3 Sources of error240

8.2.4 Use of shear stress transducers247

8.2.5 Applications249

8.2.6 High shear rate techniques252

8.3 Sliding cylinder rheometers253

8.3.1 Introduction253

8.3.2 Basic equations253

8.3.3 Applications255

References255

9 Rotational viscometry&R. L. Powell260

9.1 Introduction260

9.2 Conventional viscometers262

9.2.1 Cone and plate262

9.2.2 Parallel plates268

9.2.3 Concentric cylinders272

9.3 Sources of error277

9.3.1 Fluid inertia277

9.3.2 Flow geometry278

9.3.3 Viscous heating282

9.3.4 Sample instability283

9.3.5 Material effects284

9.3.6 Wall slip286

9.3.7 Experimental effects287

9.4 Novel rheometric flows288

9.4.1 Alternative cone and plate geometries288

9.4.2 Vane rheometer290

9.4.3 Helical screw rheometer292

Notation293

References296

10 Normal stress differences from hole pressure measurements&A. S. Lodge299

10.1 Summary299

10.2 Online measurements: high viscosity liquids299

10.3 Sample measurements: low viscosity liquids at high shear rates309

10.4 Circular holes317

10.5 Viscous heating318

Notation324

Acknowledgements324

References324

11 Using large-amplitude oscillatory shear&A. J. Giacomin and J. M. Dealy327

11.1 Introduction327

11.1.1 Simple shear327

11.1.2 Oscillatory shear328

11.1.3 Linear viscoelasticity328

11.1.4 Non-linear viscoelasticity330

11.1.5 Normal stress differences330

11.2 Experimental errors331

11.2.1 Fluid inertia331

11.2.2 Viscous heating333

11.2.3 Secondary flows333

11.3 Measurement techniques334

11.4 Methods of data analysis337

11.4.1 Spectral analysis337

11.4.2 Error analysis339

11.4.3 Response loops341

11.4.4 Analogue methods342

11.4.5 Time-domain analysis343

11.4.6 Approximate methods343

11.5 Plausible phase angles344

11.6 The Pipkin diagram344

11.7 Slip345

11.8 Limiting cases346

11.9 Interpreting non-linear behaviour347

11.10 Molecular origins351

Acknowledgements352

References353

12 Rate- or stress-controlled rheometry&W. GleijBle357

12.1 Introduction357

12.1.1 Contemporary examples of applied rheometry357

12.2 The problem359

12.3 Rate-controlled measurements360

12.4 Stress-controlled measurements363

12.5 Viscous and viscoelastic similarity366

12.6 Viscoelastic similarity and Bagley correction367

12.7 Experiments372

12.8 Conclusions377

12.9 Stress-controlled simultaneous measurement of viscosity and flow exponent378

12.9.1 Measurement technique379

12.9.2 Flow exponent and molecular weight distribution382

12.9.3 Experimental design and results383

12.9.4 Evaluation of flow data388

12.9.5 Conclusion390

References390

13 Transient rheometry&K. F. Wissbrun392

13.1 Introduction392

13.2 Transient test types and theoretical equations393

13.2.1 Constitutive equations394

13.2.2 Stress relaxation after imposition of step strain396

13.2.3 Creep after imposition of step stress397

13.2.4 Stress during start-up and after cessation of steady shear flow399

13.2.5 Elastic recoil (elastic or strain recovery)402

13.2.6 Multiple step strain tests404

13.2.7 Multiple shear rate step tests406

13.2.8 Continuously varied shear rate tests408

13.2.9 Superimposed dynamic tests410

13.3 Analysis of viscoelastic transient test data410

13.3.1 Determination of relaxation spectra410

13.3.2 Empirical approximate relations413

13.4 Experimental considerations415

13.4.1 Apparatus415

13.4.2 Sources of error415

13.4.3 Instrument response time and sample inertia416

13.4.4 Apparatus compliance419

13.4.5 Other sources of error and unusual phenomena421

References423

14 Commercial rotational rheometers&G. J. Brownsey427

14.1 Introduction427

14.2 Commercial rheometers431

14.2.1 Bohlin Instruments431

14.2.2 Brookfield Viscometers434

14.2.3 FANN436

14.2.4 Haake436

14.2.5 Kaltec Scientific440

14.2.6 Physica441

14.2.7 Reologica444

14.2.8 Rheometric Scientific446

14.2.9 TA Instruments449

14.3 Conclusion450

14.4 Useful addresses451

Part Three Extensional and Mixed Flows453

15 Converging dies&A. G. Gibson453

15.1 Introduction455

15.2 Behaviour of polymer melts, solutions and fibre suspensions458

15.2.1 Implications of fluid anisotropy459

15.2.2 Extensional behaviour of fibre suspensions462

15.3 Capillary flow experiments465

15.4 Treatment of capillary flow data467

15.5 Conical die flow472

15.5.1 Flow in convergences of shallow angle472

15.5.2 A convergent die model using spherical coordinates477

15.6 Power law equations for a wide range of die angles482

15.7 Design of injection mould gating485

15.8 Freely convergent flow: recirculation zones487

15.9 Conclusions488

Notation489

References490

16 Recoverable elastic strain and swelling ratio&R. I. Tanner492

16.1 Definition of recoverable elastic strain and swelling ratio492

16.2 Elastic theory of swelling494

16.3 Inelastic theory of swelling497

16.4 Computation of swelling for various rheological models498

16.4.1 Steady shear behaviour500

16.4.2 Steady elongational behaviour503

16.4.3 Results for the planar swelling problem504

16.5 Relation of rheology to swelling511

16.6 Conclusion and further investigations513

Notation513

References514

17 Elongational rheometers&R. K. Gupta and T. Sridhar516

17.1 Introduction516

17.2 Extensional flow kinematics518

17.2.1 Tensile viscosity518

17.3 Homogeneous stretching of polymer melts519

17.3.1 Constant stretch rate experiments520

17.3.2 Constant-stress experiments521

17.3.3 Constant sample length experiments523

17.3.4 Experimental results525

17.4 Non-uniform stretching of polymer melts528

17.4.1 Melt spinning of fibres529

17.4.2 Converging flows531

17.4.3 Miscellaneous methods532

17.5 Homogeneous stretching of polymer solutions533

17.5.1 Constant stretch rate experiments534

17.5.2 Experimental results536

17.6 Non-uniform stretching of polymer solutions538

17.6.1 Solution spinning of fibres538

17.6.2 The opposed nozzle rheometer542

17.6.3 Miscellaneous techniques544

17.7 Conclusions545

References545

18 Squeeze flow&A. G. Gibson, G. Kotsikos, J. H. Bland and S. Toll550

18.1 Introduction550

18.2 Theoretical treatment of squeeze flow552

18.2.1 Constant area squeeze flow552

18.2.2 Constant volume squeeze flow554

18.3 Squeeze flow of polymer melts555

18.3.1 Literature review555

18.3.2 Normal stresses and elastic effects in squeeze flow557

18.3.3 Experimental results559

18.4 Modelling squeeze flow of planar fibre suspensions563

18.4.1 Transversely isotropic power law model565

18.4.2 Limiting cases566

18.4.3 Variational approach566

18.4.4 Micromechanical approach570

18.4.5 Non-local constitutive equation573

18.4.6 Special cases: locality574

18.4.7 Squeeze flow with continuous tows575

18.5 Planar fibre suspension squeeze flow models579

18.6 Experimental squeeze flow of planar fibre suspensions581

18.6.1 Glass mat thermoplastics582

18.6.2 Sheet moulding compounds586

18.7 Conclusions and recommendations for further work589

Notation590

References591

Part Four Specialized Rheometers593

19 Flow visualization in rheometry&M. E. Mackay and D. V. Boger595

19.1 Introduction595

19.2 Birefringence measurements597

19.2.1 Stress-optic relation598

19.2.2 Measurement of birefringence599

19.2.3 Experimental studies using various geometries602

19.3 Streak-line observation and point velocity measurement616

19.3.1 Measurement techniques616

19.3.2 Tubular entry flows of viscoelastic fluids623

19.4 Conclusion629

Acknowledgements630

References630

20 Rheological measurements on small samples&M. E. Mackay635

20.1 Introduction635

20.2 Miniature torsional rheometers636

20.2.1 Cone and plate636

20.2.2 Parallel plates644

20.2.3 Concentric cylinders647

20.3 Falling ball rheometer650

20.4 Capillary rheometer653

20.5 Surface forces rheometer655

20.6 Prong rheometer658

20.7 Other rheorheters662

20.8 Concluding remarks663

Acknowledgements664

References664

21 Rheometry for process control&T. O. Broadhead and J. M. Dealy666

21.1 An overview of rheometry in manufacturing666

21.1.1 The value of rheological information666

21.1.2 Basic elements of a rheological measurement667

21.1.3 Rheological sensors for process control667

21.1.4 Instrument classification by method of installation669

21.2 Rheological behaviour and its measurement670

21.2.1 A survey of rheological behaviour670

21.2.2 Test requirements for various fluids674

21.2.3 Requirements for high pressure operation677

21.3 Capillary and other pressure flow rheometers677

21.3.1 Correlations with pressure drop sensors678

21.3.2 Capillary viscometers678

21.3.3 Slit rheometers684

21.4 Rotational process rheometers686

21.4.1 Common issues686

21.4.2 Concentric cylinder rheometers688

21.4.3 Parallel disc rheometers692

21.4.4 Cone and plate rheometers693

21.4.5 Rheometers based on lubrication flow694

21.5 Helical flow rheometers695

21.6 Piston-cup viscometers696

21.7 Vibrational rheometers697

21.8 Other rheometers699

21.9 Signal processing699

21.9.1 Calibration699

21.9.2 Temperature compensation700

21.9.3 Signal noise and filtering702

21.9.4 Sampling delay703

21.9.5 Process control using rheological sensors704

21.10 Selecting a process rheometer705

21.10.1 Nature of the material being processed705

21.10.2 Process conditions707

21.11 A final word708

Appendix: manufacturers of commercial instruments708

References720

22 Interfacial rheology&B. Warburton723

22.1 Introduction and history723

22.2 Definitions and theory725

22.3 Interfacial stress725

22.4 Interfacial strain726

22.5 Interfacial strain rate727

22.6 Interfacial elastic moduli727

22.7 Interfacial dilatational techniques728

22.7.1 Theory of dilatational interfacial rheology728

22.8 Interfacial shear rheology730

22.8.1 Continuous rotation730

22.8.2 Stationary and non-stationary interfacial films732

22.8.3 Interfacial shear under constant stress733

22.8.4 Interfacial shear oscillation734

22.8.5 Interfacial rheology on non-stationary interfacial films737

22.8.6 Solid films743

22.9 Immunological processes: cascade kinetics748

22.10 Summary and conclusions749

22.11 Names and addresses of instrument manufacturers749

Acknowledgements752

References752

Index755