Front Cover 1
Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions 4
Copyright Page 5
Table of Contents 6
Preface 10
Nomenclature 14
Chapter 1. Transport Equations 22
1.1 Basic Approach 22
1.2 Mass Balances 23
1.3 Momentum Balances 24
1.4 Energy Balances 28
1.5 Entropy Balance 31
1.6 Mixture Equations 32
1.7 Multicomponent Multiphase Flow 41
Chapter 2. One-Dimensional Steady Gas-Solid Flow 52
2.1 One-Dimensional, Steady Mixture Momentum Balance 52
2.2 One-Dimensional, Steady Gas Momentum Balance: Pressure Drop in Both Phases — Model A 54
2.3 Fluid Particle Drag 56
2.4 Buoyancy 58
2.5 Drag for Models B and C 60
2.6 Entrance Length in Pneumatic Transport 61
2.7 Pressure Drop 66
2.8 Pressure Drop Correlation in a Dilute Lift Line 72
Chapter 3. Drift Flux 82
3.1 Introduction 82
3.2 Hold-Up in Homogeneous and Slip Flow 82
3.3 Single Particle Analysis 83
3.4 Ergun Equation Prediction 84
3.5 Two Regimes in a Bubble Column 87
3.6 Other Applications 89
Chapter 4. Critical Granular Flow 94
4.1 One-Dimensional Granular Flow Momentum Balance 94
4.2 One-Dimensional Statics: Jannssen Equation 96
4.3 Incompressible, Frictionless Flow and Discharge 98
4.4 Thermodynamics of Powders: Compressibility 100
4.5 Critical Flow Theory for Granular Materials 103
4.6 Example of Critical Granular Flow 107
4.7 "Sound Speed" from Kinetic Theory 109
Chapter 5. The Fluidized State 118
5.1 Introduction: Fluidization Regimes 118
5.2 Minimum Fluidization Velocity 119
5.3 Geldart's Classification of Powders 125
5.4 Kinetic Energy Dissipation Analysis 127
Chapter 6. On the Origin of Bubbles 136
6.1 Introduction 136
6.2 Void Propagation in Incompressible Fluids 137
6.3 Shocks and Dispersion with No Solids Stress 140
6.4 Bubbling Criterion for Small Particles 142
Chapter 7. Inviscid Multiphase Flows: Bubbling Beds 150
7.1 Basic Equations 150
7.2 Compressible Granular Flow 152
7.3 Well-Posedness of Two-Phase Models 155
7.4 Homogeneous Flow and Pressure Propagation 160
7.5 Solids Vorticity and Void Propagation 162
7.6 Davidson Bubble Model 167
7.7 Computer Fluidization Models 170
7.8 Comparison of Computations to Observations 175
Chapter 8. Viscous Flow and Circulating Fluidized Beds 218
8.1 Introduction 218
8.2 Multiphase Navier-Stokes Equation Model 219
8.3 Dimensional Analysis: Scale Factors 222
8.4 CFB or Riser Flow: Experimental 228
8.5 Need for Clusters in One-D Modeling 235
8.6 Computation of Cluster Flow 237
8.7 Computation of Core-Annular Regime 245
8.8 Radial Profiles and Turbulence 249
Chapter 9. Kinetic Theory Approach 260
9.1 Introduction 260
9.2 Maxwellian Distribution for Particles 261
9.3 Properties of the Maxwellian State 263
9.4 Dynamics of an Encounter between Two Particles 265
9.5 The Frequency of Collisions 268
9.6 Mean Free Path 273
9.7 Elementary Treatment of Transport Coefficients 274
9.8 Boltzmann Integral-Differential Equation 277
9.9 Maxwell's Transport Equation 280
9.10 Conservation Laws with No Collisions 282
9.11 Second Approximation to the Frequency Distribution 284
9.12 Integral Equation Solver Strategy 293
9.13 Viscous Kinetic Stress Tensor 295
9.14 Dense Transport Theorem 297
9.15 Particulate Momentum Equation 300
9.16 Fluctuating Kinetic Energy Equation 302
9.17 Viscosity-Collisional Momentum Transfer 305
9.18 Granular Conductivity 311
Chapter 10. Applications of Kinetic Theory 318
10.1 Granular Shear Flow 318
10.2 Flow down a Chute 328
10.3 Bubbling Bed: Flow Patterns 332
10.4 Liquid-Solid Fluidization 339
10.5 Circulating Fluidized Bed Loop Simulation 345
10.6 Maximum Solids Circulation in a CFB 351
Chapter 11. Kinetic Theory of Granular Mixtures 358
11.1 Empirical Input: Restitution Coefficients 358
11.2 Boltzmann Equations for a Mixture 360
11.3 Dense Transport Theorem 360
11.4 Granular Temperatures and Applications 362
11.5 Particle-to-Particle Drag 364
11.6 Summary 366
Chapter 12. Sedimentation and Consolidation 376
12.1 Conservation of Particles 376
12.2 Settling in a Sedimentation Column: Introduction 378
12.3 Free Settling 381
12.4 Compression Settling 387
12.5 Consolidation: Relation to Osmotic Pressure 391
12.6 Electrokinetic Phenomenon: Zeta Potential 397
12.7 Effect of Zeta Potential on Sedimentation 400
Appendices: Formulation of Continuum Problems: Introduction 412
Appendix A: Overall (Macroscopic Balances) 414
Appendix B: Eulerian Approach: One-D Energy Balance 426
Appendix C: Leibniz Formula and Relation to Transport 432
Appendix D: Lagrangian Approach: One-D Conservation of Species and Population Balance 434
Appendix E: Reynolds Transport Theorem 444
Appendices: The Methods of Characteristics: Introduction 450
Appendix F: First Order Partial Differential Equation 452
Appendix G: Solution of a Hyperbolic System of First Order Partial Differential Equations 462
Index 478