Martin Rhodes, PhD, is Professor Emeritus in the Department of Chemical and Biological Engineering, Monash University, Australia and has published extensively on particle technology.

Jonathan Seville, PhD, is Professor of Formulation Engineering at the School of Chemical Engineering, University of Birmingham, UK. Formerly editor of the journal Powder Technology, he has published several books on particle technology. He is past President of the Institution of Chemical Engineers and a Fellow of the Royal Academy of Engineering.

About the Authors xi

Preface to the Third Edition xii

Preface to the Second Edition xiii

Preface to the First Edition xiv

Acknowledgements xvii

About the Website xviii

Introduction xix

1 Particle Analysis 1

1.1 Particle Size 1

1.2 Description of Populations of Particles 4

1.3 Conversion Between Distributions 4

1.4 Describing the Population by a Single Number 7

1.5 Equivalence of Means 9

1.6 Common Methods of Displaying Size Distributions 11

1.6.1 Normal Distribution 11

1.6.2 Log-normal Distribution 11

1.7 Methods of Particle Size Measurement 12

1.7.1 Image Analysis 13

1.7.2 Light Scattering 13

1.7.3 Dynamic Light Scattering 15

1.7.4 Scanning Mobility Particle Sizer 15

1.7.5 Other Methods 16

1.8 Surface Area Measurement 17

1.8.1 Adsorption Isotherms 17

1.8.2 The BET Technique 17

1.9 Sampling 19

1.10 Worked Examples 19

Test Yourself 28

Exercises 29

2 Mechanical Properties of Particles 32

2.1 Introduction to Material Properties 33

2.2 Particle-Particle Contact for Elastic Materials 36

2.3 Contact in the Presence of Surface Forces 38

2.3.1 Cohesion and Adhesion 38

2.3.2 Surface Roughness and Contamination 41

2.3.3 Comparison of Cohesion with Particle Weight 41

2.3.4 Measurement of Cohesion and Adhesion 42

2.4 Friction 43

2.5 Impact and Bounce 45

2.5.1 Impacts in the Normal Direction 45

2.5.2 Oblique Impacts 47

2.6 Liquid Bridges 47

2.7 Worked Examples 52

Test Yourself 54

Exercises 54

3 Motion of Particles in a Fluid 56

3.1 Single Particles in a Fluid 56

3.1.1 Motion of Single Solid Particles in a Fluid 56

3.1.2 Particles Falling Under Gravity Through a Fluid 59

3.1.3 Effect of Boundaries on Terminal Velocity 63

3.1.4 Unsteady Motion 64

3.1.5 Further Reading 65

3.1.6 Worked Examples on the Motion of Single Particles in a Fluid 66

Test Yourself - Single Particles in a Fluid 74

3.2 Settling of a Suspension of Particles 75

3.2.1 Introduction 75

3.2.2 Settling Flux as a Function of Suspension Concentration 77

3.2.3 Sharp Interfaces in Sedimentation 79

3.2.4 The Batch Settling Test 80

3.2.5 Relationship Between the Height-Time Curve and the Flux Plot 83

3.2.6 Worked Examples on Settling of a Suspension of Particles 85

Test Yourself - Settling of a Suspension Particles 92

Exercises - Single Particles in a Fluid 92

Exercises - Settling of a Suspension of Particles 95

4 Discrete Element Method Modelling 102

4.1 Introduction 102

4.2 Principles - The "Hard-Sphere" and "Soft-Sphere" Approaches 104

4.3 Updating Particle Positions -'Time-Stepping' 107

4.4 Contact Detection 109

4.5 Contact Modelling 110

4.5.1 Linear Spring-Dashpot Model 111

4.5.2 Hertzian Model 112

4.5.3 Elastoplastic Models 112

4.5.4 Cohesive Models 113

4.6 Coupling with Computational Fluid Dynamics (CFD-DEM) 114

4.7 Calibration 115

4.8 Modelling Large Systems 118

4.9 Modelling Aspherical Particles 119

4.10 Data Analysis and Visualization 121

4.11 Validation 123

4.12 Worked Examples 124

Exercises 132

Interactive Exercises 132

5 Colloids, Aerosols and Fine Particles 133

5.1 Introduction 133

5.2 Brownian Motion 134

5.3 Surface Forces 136

5.3.1 van der Waals Forces 137

5.3.2 Electrical Double-Layer Forces 139

5.3.3 Adsorbing Polymers, Bridging and Steric Forces 144

5.3.4 Net Interaction Force 145

5.4 Effect of Surface Forces on Behaviour in Air and Water 145

5.5 Influences of Particle Size and Surface Forces on Solid/Liquid Separation by Sedimentation 148

5.5.1 Sedimentation Rate 148

5.5.2 Sediment Concentration and Consolidation 149

5.6 Gas-Solid Separation 151

5.7 Suspension Rheology 152

5.8 Influence of Surface Forces on Suspension Flow 157

5.8.1 Repulsive Forces 157

5.8.2 Attractive Forces 158

5.9 Nanoparticles 162

5.10 Worked Examples 163

Test Yourself 166

Exercises 167

6 Packed Beds and Fluidized Beds 170

6.1 Fluid Flow Through a Packed Bed of Particles 170

6.1.1 Pressure Drop-Flow Relationship 170

6.1.2 Further Reading 174

6.1.3 Worked Examples 174

Test Yourself - Fluid Flow through Packed Beds 176

6.2 Fluidization 176

6.2.1 Fundamentals 176

6.2.2 Relevant Powder and Particle Properties 179

6.2.3 Bubbling and Non-Bubbling Fluidization 181

6.2.4 Classification of Powders 183

6.2.5 Expansion of a Fluidized Bed 187

6.2.6 Entrainment 191

6.2.7 Heat Transfer in Fluidized Beds 195

6.2.8 A Simple Model for the Bubbling Fluidized Bed Reactor 201

6.2.9 High Velocity Fluidization 205

6.2.10 Some Practical Considerations 210

6.2.11 Applications of Fluidized Beds 213

6.2.12 Worked Examples 220

Test Yourself - Fluidization 226

Exercises - Fluid Flow through Packed Beds 227

Exercises - Fluidization 228

7 Pneumatic Transport and Standpipes 233

7.1 Pneumatic Transport 233

7.1.1 Dilute Phase and Dense Phase Transport 234

7.1.2 The Choking Velocity in Vertical Transport 234

7.1.3 The Saltation Velocity in Horizontal Transport 236

7.1.4 Fundamentals 237

7.1.5 Design for Dilute Phase Transport 240

7.1.6 Dense Phase Transport 245

7.1.7 Matching the System to the Powder 250

7.2 Standpipes 251

7.2.1 Standpipes in Packed Bed Flow 252

7.2.2 Standpipes in Fluidized Bed Flow 252

7.2.3 Pressure Balance During Standpipe Operation 255

7.2.4 Further Reading 257

7.3 Worked Examples 258

Test Yourself 263

Exercises 264

8 Separation of Particles from a Gas 266

8.1 Gas Cyclones 267

8.1.1 Flow Characteristics of Cyclones 268

8.1.2 Efficiency of Separation of Cyclones 268

8.1.3 Scale-up of Cyclones 272

8.1.4 Range of Operation of Cyclones 275

8.1.5 Some Practical Design and Operation Details of Cyclones 276

8.2 Filtration 279

8.3 Worked Examples 282

Test Yourself 285

Exercises 286

9 Storage and Flow of Powders - Hopper Design 288

9.1 Mass Flow and Core Flow 288

9.2 The Design Philosophy 290

9.2.1 Flow - No Flow Criterion 291

9.2.2 The Hopper Flow Factor ff 291

9.2.3 Unconfined Yield Stress ¿y 291

9.2.4 Powder Flow Function 292

9.2.5 Critical Conditions for Flow 292

9.2.6 Critical Outlet Dimension 293

9.2.7 Summary 294

9.3 Shear Cell Test 294

9.4 Analysis of Shear Cell Test Results 296

9.4.1 Mohr's Circle - in Brief 296

9.4.2 Application of Mohr's Circle to the Analysis of the Yield Locus 297

9.4.3 Determination of ¿y and ¿c 298

9.4.4 Determination of ¿ from Shear Cell Tests 298

9.4.5 The Kinematic Angle of Friction between Powder and Hopper Wall, ¿W 299

9.4.6 Determination of the Hopper Flow Factor, ff 300

9.5 Summary of Design Procedure 304

9.6 Discharge Aids 304

9.7 Pressure on the Base of a Tall Cylindrical Bin 304

9.8 Mass Flow Rates 307

9.9 Conclusions 308

9.10 Worked Examples 309

Test Yourself 314

Exercises 314

10 Mixing and Segregation 319

10.1 Types of Mixture 319

10.2 Segregation 320

10.2.1 Causes and Consequences of Segregation 320

10.2.2 Mechanisms of Segregation 321

10.3 Reduction of Segregation 324

10.4 Equipment for Particulate Mixing 325

10.4.1 Mechanisms of Mixing 325

10.4.2 Types of Mixer 326

10.5 Analysis of Mixer Performance 328

10.5.1 Simple V-Mixer 328

10.5.2 Analysing More Complex Mixers 331

10.6 Assessing the Mixture 332

10.6.1 Quality of a Mixture 332

10.6.2 Sampling 333

10.6.3 Statistics Relevant to Mixing 333

10.7 Worked Examples 335

Test Yourself 340

Exercises 341

11 Particle Size Reduction 343

11.1 Mechanisms of Particle Size Reduction 344

11.1.1 Breakage 344

11.1.2 Abrasion 348

11.1.3 Stressing Mechanisms for Size Reduction 348

11.2 Model Predicting Energy Requirement and Product Size Distribution 349

11.2.1 Energy Requirement 349

11.2.2 Prediction of the Product Size Distribution 352

11.3 Attrition 354

11.3.1 Sources of Attrition in Processes 355

11.3.2 Measurement of the Degree of Attrition Within a Process 355

11.3.3 Measurement Methods 356

11.3.4 Energy Requirement for Attrition 356

11.4 Types of Comminution Equipment 357

11.4.1 Stressing Mechanism 357

11.4.2 Particle Size 362

11.4.3 Material Properties 363

11.4.4 Carrier Medium 364

11.4.5 Mode of Operation 364

11.4.6 Combination with Other Operations 364

11.4.7 Types of Milling Circuit 364

11.5 Worked Examples 366

Test Yourself 368

Exercises 369

12 Size Enlargement 372

12.1 Introduction 372

12.2 Crystallization 373

12.2.1 Crystal Structure 373

12.2.2 Solubility and Saturation 374

12.2.3 Nucleation and Growth 376

12.2.4 Crystallizer Design 378

12.3 Granulation 378

12.3.1 Introduction 378

12.3.2 Granulation Rate Processes 380

12.3.3 Simulation of the Granulation Process 388

12.3.4 Granulation Equipment 391

12.4...