Dr PJ Cullen is a lecturer in?the Faculty of Engineering at the University of New South Wales. His current research interests include rheology, mixing, chemical imaging and non-thermal plasmas for biological applications in food. He has published over 35 journal papers, 15 book chapters and edited 1 book on food mixing.

Professor Rodolfo J. Romañach is Professor of Chemistry at the University of Puerto Rico. He has over 20 years of experience in vibrational spectroscopy, and worked in Puerto Rico's pharmaceutical industry for 12 years prior to joining the UPR-Mayagüez faculty. In the pharmaceutical industry he worked extensively in assay and cleaning validation, and in providing analytical support for API and pharmaceutical process related problems.

Professor Nicolas Abatzaglou is Director of the?Chemical Engineering and Biotechnological Engineering Department and Holder of the Pfizer Chair: PAT in Pharmaceutical Engineering at the Universite de Sherbrooke, Canada. He is the current recipient of Quebec's Minister of Education (MELS Chantier II) Fellowship award for his excellence in research and teaching.

Professor Chris Rielly is Head of the Department of Chemical Engineering at Loughborough University. He has taught chemical engineering for over 20 years at Cambridge and Loughborough Universities and is a Fellow of the Institution of Chemical Engineers with more than 20 years of experience working in experimental and computational fluid mechanics. His interests include multi-phase flow, mass transfer and turbulent mixing in chemical processing equipment. He has served on the Scientific Committees of the European Conference on Mixing, the International Conference on Gas-Liquid-Solid Reaction Engineering and the Process Innovation and Intensification Conference. He is an academic consultant to BHR Group's Fluid Mixing Processes Industrial Consortium and Chairman of the IChemE's Fluid Mixing Subject Group. He has previously edited books.

Preface xvii

Part I Fundamentals of Mixing 1

1 Mixing Theory 3
Chris D. Rielly

1.1 Introduction 3

1.2 Describing Mixtures 5

1.3 Scale of Scrutiny 6

1.4 Quantifying Mixedness for Coarse and Fine‐Grained Mixtures 8

1.4.1 Coarse and Fine‐Grained Mixtures 8

1.4.2 Scale and Intensity of Segregation 9

1.5 Determining the End‐Point of Mixing: Comparison of Mixing Indices 15

1.6 Continuous Flow Mixers 19

1.6.1 Idealized Mixing Patterns 19

1.6.2 Residence Time Distributions 21

1.6.3 Back‐Mixing and Filtering of Disturbances Using a CSTR 23

References 24

2 Turbulent Mixing Fundamentals 27
Suzanne M. Kresta

2.1 Introduction 27

2.2 The Velocity Field and Turbulence 28

2.3 Circulation and Macro‐Mixing 29

2.4 Fully Turbulent Limits and the Scaling of Turbulence 32

2.5 The Spectrum of Turbulent Length Scales, Injection of a Scalar (Either Reagent or Additive) and the Macro‐, Meso‐ and Micro‐Scales of Mixing 34

2.6 Turbulence and Mixing of Solids, Liquids, and Gases 37

2.7 Specifying Mixing Requirements for a Process 38

2.8 Conclusions 39

Notation 39

Roman Characters 39

Greek Characters 40

References 40

3 Laminar Mixing Fundamentals 43
P.J. Cullen and N.N. Misra

3.1 Laminar Flows 43

3.2 Mixing in Laminar Flows 44

3.2.1 Chaos and Laminar Chaotic Mixing 45

3.2.2 Granular Chaotic Mixing 50

3.3 Recent Advances 53

References 54

4 Sampling and Determination of Adequacy of Mixing 57
Rodolfo J. Romañach

4.1 Introduction, Process Understanding, and Regulations 57

4.2 Theory of Sampling 59

4.3 Sampling of Pharmaceutical Powder Blends 63

4.4 Stratified Sampling Approach 65

4.5 Testing 67

4.6 Process Knowledge/Process Analytical Technology 68

4.7 Real Time Spectroscopic Monitoring of Powder Blending 70

4.8 Looking Forward, Recommendations 73

4.9 Conclusion 74

4.10 Acknowledgments 75

References 75

Part II Applications 79

5 Particles and Blending 81
Reuben D. Domike and Charles L. Cooney

5.1 Introduction 81

5.2 Particle Geometry 82

5.2.1 Particle Size and Size Distribution 82

5.2.2 Particle Shape and Shape Distribution 83

5.3 Particle Interactions 84

5.3.1 van der Waals Forces 84

5.3.2 Electrostatic Forces 85

5.3.3 Adsorbed Liquid Layers and Liquid Bridges 85

5.3.4 Solid Bridges 86

5.3.5 Use of AFM to Measure Interparticle Forces 87

5.3.6 Interparticle Friction 89

5.4 Empirical Investigations of Particles and Blending 90

5.4.1 Blending of Powders 90

5.4.2 Impact of Particle Geometry on Blending 92

5.4.3 Impact of Interparticle Forces on Blending 93

5.4.4 Impact of Blender Conditions on Blending 95

5.5 Simulation Techniques 95

5.5.1 Full Physics Models Using Discrete Element Modeling 96

5.5.2 Continuum Models 97

5.5.3 Cellular Automata 98

References 98

6 Continuous Powder Mixing 101
Juan G. Osorio, Aditya U. Vanarase, Rodolfo J. Romañach, and Fernando J. Muzzio

6.1 Introduction 101

6.2 Overview 102

6.3 Theoretical Characterization 107

6.3.1 Residence Time Distribution (RTD) Modeling 107

6.3.2 Variance Reduction Ratio 108

6.4 Experimental Characterization 108

6.4.1 Hold‐Up 109

6.4.2 Residence Time Distribution (RTD) Measurements 109

6.4.3 Mean Strain 110

6.5 Continuous Mixing Efficiency 110

6.5.1 Variance Reduction Ratio 110

6.5.2 Blend Homogeneity 111

6.6 Effects of Process Parameters on Mixing Behavior and Performance 112

6.6.1 Hold‐Up 113

6.6.2 RTD Measurements 113

6.7 Mixing Performance 118

6.7.1 Modeling 120

6.7.2 PAT, QbD, and Control 122

6.8 Conclusions and Continuing Efforts 124

References 125

7 Dispersion of Fine Powders in Liquids: Particle Incorporation and Size Reduction 129
Gül N. Özcan-Taşkın

7.1 Particle Incorporation into Liquids 129

7.1.1 Wetting 130

7.1.2 Stirred Tanks for Particle Incorporation 132

7.1.3 In‐Line Devices Used for Particle Incorporation 140

7.2 Break Up of Fine Powder Clusters in Liquids 143

7.2.1 Mechanisms of Break Up 146

7.2.2 Process Devices for Deagglomeration\Size Reduction of Agglomerates 147

References 150

8 Wet Granulation and Mixing 153
Karen P. Hapgood and Rachel M. Smith

8.1 Introduction 153

8.2 Nucleation 154

8.2.1 Drop Penetration Time 156

8.2.2 Dimensionless Spray Flux 158

8.2.3 Nucleation Regime Map 160

8.3 Consolidation and Growth 162

8.3.1 Granule Consolidation 162

8.3.2 Granule Growth Behaviour 164

8.3.3 Granule Growth Regime Map 165

8.4 Breakage 167

8.4.1 Single Granule Strength and Deformation 167

8.4.2 In‐Granulator Breakage Studies 170

8.4.3 Aiding Controlled Granulation via Breakage 172

8.5 Endpoint Control 174

8.5.1 Granulation Time 175

8.5.2 Impeller Power Consumption 176

8.5.3 Online Measurement of Granule Size 176

8.5.4 NIR and Other Spectral Methods 177

References 178

9 Emulsions 183
Andrzej W. Pacek

9.1 Introduction 183

9.2 Properties of Emulsions 185

9.2.1 Morphology 185

9.2.2 Volumetric Composition 185

9.2.3 Drop Size Distributions and Average Drop Sizes 186

9.2.4 Rheology 191

9.3 Emulsion Stability and Surface Forces 195

9.3.1 Surface Forces 195

9.3.2 Emulsion Stability 199

9.4 Principles of Emulsion Formation 203

9.4.1 Low Energy Emulsification 204

9.4.2 High Energy Emulsification 205

9.5 Emulsification Equipment 216

9.5.1 Stirred Vessels 216

9.5.2 Static Mixers 218

9.5.3 High Shear Mixers 219

9.5.4 High‐Pressure Homogenizers 223

9.5.5 Ultrasonic Homogenizers 225

9.6 Concluding Remarks 226

Nomenclature 226

Greek symbols 228

References 228

10 Mixing of Pharmaceutical Solid‐Liquid Suspensions 233
Mostafa Barigou and Frans L. Muller

10.1 Introduction 233

10.1.1 Linking Solid‐Liquid Processing to Critical Quality Attributes 233

10.1.2 Material Properties and Composition 234

10.1.3 Impact of Blending and Homogenization 234

10.1.4 Impact of Turbulence 237

10.1.5 Impact of Heat Transfer 237

10.2 Scale‐Up of Operations Involving Solid Suspensions 237

10.2.1 The Nature of Suspensions 237

10.2.2 Scale‐Up and Scale‐Down Rules 239

10.2.3 Identification of Agitator Duties 240

10.2.4 Solid‐Liquid Unit Operations 242

10.3 General Principles of Solid‐Liquid Suspensions 243

10.3.1 Rheological Behaviour of the Continuous Phase 243

10.3.2 Rheology of Suspensions 246

10.3.3 Terminal Velocity of Particles 249

10.3.4 Turbulence 254

10.4 Solids Charging 257

10.4.1 Charging to Batch Vessels 257

10.4.2 Charging Difficult Powders 261

10.5 Solid Suspension 261

10.5.1 States of Solid Suspension 261

10.5.2 Prediction of Minimum Speed for Complete Suspension 262

10.6 Solid Distribution 269

10.6.1 Agitator Speed 269

10.6.2 Homogeneity 270

10.6.3 Geometry 271

10.6.4 Practical Guidelines 272

10.7 Blending in Solid‐Liquid Systems 272

10.7.1 Mixing Time 272

10.7.2 Viscoplastic Slurries Yield Stress and Cavern Formation 272

10.8 Mass Transfer 275

10.9 Size Reduction, Deagglomeration and Attrition 277

10.9.1 Breaking Particles through Turbulent Forces 277

10.9.2 Breaking Particles through Impact 278

Nomenclature 281

Greek symbols 281

Abbreviations 282

References 282

Part III Equipment 287

11 Powder Blending Equipment 289
David S. Dickey

11.1 Introduction 289

11.2 Blending Mechanisms 290

11.3 Blend Time 290

11.4 Fill Level 291

11.5 Segregation 291

11.6 Powder Processing Difficulties 292

11.7 Blender Classification 292

11.7.1 Tumble Blenders 293

11.7.2 Rotating Element Blenders 298

11.7.3 Granulators 303

11.7.4 Other Blenders – Mullers and Custom Blenders 304

11.8 Continuous Blenders 305

11.9 Blender Selection 306

11.10 Equipment Specifications 307

11.10.1 Materials of Construction 309

11.10.2 Electrical Classification 309

11.10.3 Drives and Seals 309

References 310

12 Fluid Mixing Equipment Design 311
David S. Dickey

12.1 Introduction 311

12.2 Equipment Description 312

12.2.1 Laboratory Mixers 312

12.2.2 Development Mixers 313

12.2.3 Portable Mixers 313

12.2.4 Top-Entering Mixers 315

12.2.5 High-Shear Dispersers 318

12.2.6 High Viscosity Mixers 319

12.2.7 Multi-Shaft Mixers 319

12.2.8 Bottom-Entering Mixers 320

12.2.9 Glass-Lined Mixers and Vessels 321

12.2.10 Side-Entering Mixers 322

12.2.11 Vessel Geometry 322

12.2.12 Baffles 323

12.3 Measurements 323

12.3.1 Power 324

12.3.2 Torque 326

12.3.3 Tip Speed 327

12.3.4 Blend Time 327

12.4 Mixing Classifications 328

12.4.1 Liquid Mixing 328

12.4.2 Solids Suspension 330

12.4.3 Gas Dispersion 332

12.4.4 Viscous Mixing 333

12.5 Mechanical Design 334

12.5.1 Shaft Design 334

12.5.2 Shaft Seals 335

12.5.3 Materials of Construction 336

12.5.4 Surface Finish 337

12.5.5 Motors 338

12.5.6 Drives 339

12.6 Static Mixers 339

12.6.1 Twisted Element 339

12.6.2 Structured Element 339

12.6.3 Basic Design 340

12.7 Challenges and Troubleshooting 341

12.7.1 Careful Observations 341

12.7.2 Process Problems 341

Nomenclature 342

Greek 343

References 343

13 Scale‐Up 345
David S. Dickey

13.1 Introduction 345

13.2 Similarity and Scale‐Up Concepts 346

13.2.1 Dimensional Analysis 346

13.2.2 Similarity 347

13.2.3 Applied Scale‐Up 349

13.3 Testing Methods 350

13.4 Observation and Measurement 352

13.5 Scale‐Up Methods 354

13.5.1 Scale‐Up with Geometric Similarity 354

13.5.2 Example of Geometric Similarity Scale‐Up 358

13.5.3 Scale‐Up Without Geometric Similarity 359

13.5.4 Example of Non‐Geometric Scale‐Up 361

13.5.5 Scale‐Up for Powder Mixing 364

13.6 Summary 367

Nomenclature 367

Greek 368

References 368

14 Equipment Qualification, Process and Cleaning Validation 369
Ian Jones and Chris Smalley

14.1 Introduction 369

14.2 Blending Equipment Commissioning and Qualification 370

14.2.1 Outline of the Verification Approach 370

14.2.2 Requirements Phase 371

14.2.3 Specifications and Design Review Phase 373

14.2.4 Verification Phase 375

14.3 Blending and Mixing Validation 380

14.3.1 Why do You Need to Validate Pharmaceutical Blends/Mixes? 382

14.3.2 When do You Need to Validate Blending/Mixing? 384

14.3.3 Components of Blending/Mixing Validation 385

14.3.4 What to Validate 386

14.4 Blending Cleaning Validation 389

14.4.1 Cleaning Development Studies 389

14.4.2 Cleaning Validation 395

14.5 Conclusion 398

14.6 Acknowledgements 399

References 399

Part IV Optimization and Control 401

15 Process Analytical Technology for Blending 403
Nicolas Abatzoglou

15.1 Introduction 403

15.1.1 The Role of PAT in Pharmaceutical Manufacturing: Is PAT Really New? 404

15.1.2 Why PAT is Feasible 405

15.1.3 Where PAT can be Applied in Pharmaceutical Manufacturing 406

15.1.4 The Regulatory Framework 406

15.2 Chemometrics and Data Management 408

15.2.1 PAT Data Management and Interpretation 409

15.3 Near‐Infrared Spectroscopy (NIRS) 412

15.4 Raman Spectroscopy (RS) 419

15.5 Image Analysis 422

15.6 LIF Spectroscopy 424

15.7 Effusivity 426

15.8 Other Potential Sensor Technologies 426

15.9 Comments on PAT in Liquid Formulation Mixing 427

References 427

16 Imaging Fluid Mixing 431
Mi Wang

16.1 Introduction 431

16.2 Point Measurement Techniques 433

16.3 Photographic Imaging 435

16.4 Digital Particle Image Velocimetry 439

16.5 Magnetic Resonance Imaging 443

16.6 Positron Emission Particle Tracking Imaging 444

16.7 Electrical Process Tomography 446

References 452

17 Discrete Element Method (DEM) Simulation of Powder Mixing Process 459
Ali Hassanpour and Mojtaba Ghadiri

17.1 Introduction to DEM and its Application in Pharmaceutical Powder Processing 459

17.2 DEM Simulation of Powder Mixing 461

17.3 Validation and Comparison with the Experiments 468

17.4 Concluding Remarks 474

References 475

Index 479

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