Handbook of industrial mixing : science and practice

Introduction xxxiii Edward L. Paul, Victor A. Atiemo-Obeng, and Suzanne M. Kresta Mixing in Perspective xxxiv Scope of Mixing Operations xxxvi Residence Time Distributions: Chapter 1 xxxvii Mixing Fundamentals: Chapters 1–5 xxxix Mixing Equipment: Chapters 6, 7, 8, and 21 xxxix Miscible Liquid Blending: Chapters 3, 7, 9, and 16 xl Solid–Liquid Suspension: Chapters 10, 17, and 18 xl Gas–Liquid Contacting: Chapter 11 xli Liquid–Liquid Mixing: Chapter 12 xlii Mixing and Chemical Reactions/Reactor Design: Chapters 13 and 17 xlii Heat Transfer and Mixing: Chapter 14 xliii Specialized Topics for Various Industries: Chapters 15–20 xliii Conversations Overheard in a Chemical Plant xliv The Problem xliv Competitive-Consecutive Reaction xlv Gas–Liquid Reaction xlvi Solid–Liquid Reaction xlvi Liquid–Liquid Reaction xlvii Crystallization xlvii Using the Handbook xlix Diagnostic Charts l Mixing Nomenclature and Unit Conversions lv Acknowledgments lix References lx v vi CONTENTS 1 Residence Time Distributions 1 E. Bruce Nauman 1-1 Introduction 1 1-2 Measurements and Distribution Functions 2 1-3 Residence Time Models of Flow Systems 5 1-3.1 Ideal Flow Systems 5 1-3.2 Hydrodynamic Models 6 1-3.3 Recycle Models 7 1-4 Uses of Residence Time Distributions 9 1-4.1 Diagnosis of Pathological Behavior 9 1-4.2 Damping of Feed Fluctuations 9 1-4.3 Yield Prediction 10 1-4.4 Use with Computational Fluid Dynamic Calculations 14 1-5 Extensions of Residence Time Theory 15 Nomenclature 16 References 16 2 Turbulence in Mixing Applications 19 Suzanne M. Kresta and Robert S. Brodkey 2-1 Introduction 19 2-2 Background 20 2-2.1 Definitions 20 2-2.2 Length and Time Scales in the Context of Turbulent Mixing 24 2-2.3 Relative Rates of Mixing and Reaction: The Damkoehler Number 32 2-3 Classical Measures of Turbulence 38 2-3.1 Phenomenological Description of Turbulence 39 2-3.2 Turbulence Spectrum: Quantifying Length Scales 45 2-3.3 Scaling Arguments and the Energy Budget: Relating Turbulence Characteristics to Operating Variables 53 2-4 Dynamics and Averages: Reducing the Dimensionality of the Problem 61 2-4.1 Time Averaging of the Flow Field: The Eulerian Approach 62 2-4.2 Useful Approximations 63 CONTENTS vii 2-4.3 Tracking of Fluid Particles: The Lagrangian Approach 69 2-4.4 Experimental Measurements 71 2-5 Modeling the Turbulent Transport 72 2-5.1 Time-Resolved Simulations: The Full Solution 74 2-5.2 Reynolds Averaged Navier–Stokes Equations: An Engineering Approximation 78 2-5.3 Limitations of Current Modeling: Coupling between Velocity, Concentration, Temperature, and Reaction Kinetics 81 2-6 What Have We Learned? 81 Nomenclature 82 References 83 3 Laminar Mixing: A Dynamical Systems Approach 89 Edit S. Szalai, Mario M. Alvarez, and Fernando J. Muzzio 3-1 Introduction 89 3-2 Background 90 3-2.1 Simple Mixing Mechanism: Flow Reorientation 90 3-2.2 Distinctive Properties of Chaotic Systems 92 3-2.3 Chaos and Mixing: Some Key Contributions 94 3-3 How to Evaluate Mixing Performance 96 3-3.1 Traditional Approach and Its Problems 96 3-3.2 Measuring Microstructural Properties of a Mixture 99 3-3.3 Study of Microstructure: A Brief Review 102 3-4 Physics of Chaotic Flows Applied to Laminar Mixing 103 3-4.1 Simple Model Chaotic System: The Sine Flow 103 3-4.2 Evolution of Material Lines: The Stretching Field 108 3-4.3 Short-Term Mixing Structures 108 3-4.4 Direct Simulation of Material Interfaces 110 3-4.5 Asymptotic Directionality in Chaotic Flows 110 3-4.6 Rates of Interface Growth 112 3-4.7 Intermaterial Area Density Calculation 114 3-4.8 Calculation of Striation Thickness Distributions 116 3-4.9 Prediction of Striation Thickness Distributions 117 3-5 Applications to Physically Realizable Chaotic Flows 119 3-5.1 Common 3D Chaotic System: The Kenics Static Mixer 119 viii CONTENTS 3-5.2 Short-Term Mixing Structures 120 3-5.3 Asymptotic Directionality in the Kenics Mixer 120 3-5.4 Computation of the Stretching Field 123 3-5.5 Rates of Interface Growth 124 3-5.6 Intermaterial Area Density Calculation 125 3-5.7 Prediction of Striation Thickness Distributions in Realistic 3D Systems 128 3-6 Reactive Chaotic Flows 130 3-6.1 Reactions in 3D Laminar Systems 134 3-7 Summary 138 3-8 Conclusions 139 Nomenclature 140 References 141 4 Experimental Methods 145 Part A: Measuring Tools and Techniques for Mixing and Flow Visualization Studies 145 David A. R. Brown, Pip N. Jones, and John C. Middleton 4-1 Introduction 145 4-1.1 Preliminary Considerations 146 4-2 Mixing Laboratory 147 4-2.1 Safety 147 4-2.2 Fluids: Rheology and Model Fluids 148 4-2.3 Scale of Operation 154 4-2.4 Basic Instrumentation Considerations 155 4-2.5 Materials of Construction 156 4-2.6 Lab Scale Mixing in Stirred Tanks 156 4-2.7 Lab Scale Mixing in Pipelines 160 4-3 Power Draw Or Torque Measurement 161 4-3.1 Strain Gauges 162 4-3.2 Air Bearing with Load Cell 164 4-3.3 Shaft Power Measurement Using a Modified Rheometer 164 4-3.4 Measurement of Motor Power 164 4-4 Single-Phase Blending 164 4-4.1 Flow Visualization 165 4-4.2 Selection of Probe Location 167 4-4.3 Approximate Mixing Time Measurement with Colorimetric Methods 167 4-4.4 Quantitative Measurement of the Mixing Time 169 CONTENTS ix 4-4.5 RTD for CSTR 174 4-4.6 Local Mixedness: CoV, Reaction, and LIF 174 4-5 Solid–Liquid Mixing 177 4-5.1 Solids Distribution 177 4-5.2 Solids Suspension: Measurement of Njs 182 4-6 Liquid–Liquid Dispersion 187 4-6.1 Cleaning a Liquid–Liquid System 187 4-6.2 Measuring Interfacial Tension 188 4-6.3 Njd for Liquid–Liquid Systems 189 4-6.4 Distribution of the Dispersed Phase 189 4-6.5 Phase Inversion 190 4-6.6 Droplet Sizing 190 4-7 Gas–Liquid Mixing 194 4-7.1 Detecting the Gassing Regime 194 4-7.2 Cavity Type 194 4-7.3 Power Measurement 196 4-7.4 Gas Volume Fraction (Hold-up) 196 4-7.5 Volumetric Mass Transfer Coefficient, kLa 196 4-7.6 Bubble Size and Specific Interfacial Area 199 4-7.7 Coalescence 199 4-7.8 Gas-Phase RTD 200 4-7.9 Liquid-Phase RTD 200 4-7.10 Liquid-Phase Blending Time 200 4-7.11 Surface Aeration 200 4-8 Other Techniques 201 4-8.1 Tomography 201 Part B: Fundamental Flow Measurement 202 George Papadopoulos and Engin B. Arik 4-9 Scope of Fundamental Flow Measurement Techniques 202 4-9.1 Point versus Full Field Velocity Measurement Techniques: Advantages and Limitations 203 4-9.2 Nonintrusive Measurement Techniques 206 4-10 Laser Doppler Anemometry 207 4-10.1 Characteristics of LDA 208 4-10.2 Principles of LDA 208 4-10.3 LDA Implementation 212 4-10.4 Making Measurements 220 4-10.5 LDA Applications in Mixing 224 x CONTENTS 4-11 Phase Doppler Anemometry 226 4-11.1 Principles and Equations for PDA 226 4-11.2 Sensitivity and Range of PDA 230 4-11.3 Implementation of PDA 233 4-12 Particle Image Velocimetry 237 4-12.1 Principles of PIV 237 4-12.2 Image Processing 239 4-12.3 Implementation of PIV 243 4-12.4 PIV Data Processing 246 4-12.5 Stereoscopic (3D) PIV 247 4-12.6 PIV Applications in Mixing 249 Nomenclature 250 References 250 5 Computational Fluid Mixing 257 Elizabeth Marden Marshall and Andr´e Bakker 5-1 Introduction 257 5-2 Computational Fluid Dynamics 259 5-2.1 Conservation Equations 259 5-2.2 Auxiliary Models: Reaction, Multiphase, and Viscosity 268 5-3 Numerical Methods 273 5-3.1 Discretization of the Domain: Grid Generation 273 5-3.2 Discretization of the Equations 277 5-3.3 Solution Methods 281 5-3.4 Parallel Processing 284 5-4 Stirred Tank Modeling Using Experimental Data 285 5-4.1 Impeller Modeling with Velocity Data 285 5-4.2 Using Experimental Data 289 5-4.3 Treatment of Baffles in 2D Simulations 289 5-4.4 Combining the Velocity Data Model with Other Physical Models 290 5-5 Stirred Tank Modeling Using the Actual Impeller Geometry 292 5-5.1 Rotating Frame Model 292 5-5.2 Multiple Reference Frames Model 292 5-5.3 Sliding Mesh Model 295 5-5.4 Snapshot Model 300 5-5.5 Combining the Geometric Impeller Models with Other Physical Models 300 CONTENTS xi 5-6 Evaluating Mixing from Flow Field Results 302 5-6.1 Graphics of the Solution Domain 303 5-6.2 Graphics of the Flow Field Solution 304 5-6.3 Other Useful Solution Variables 310 5-6.4 Mixing Parameters 313 5-7 Applications 315 5-7.1 Blending in a Stirred Tank Reactor 315 5-7.2 Chemical Reaction in a Stirred Tank 316 5-7.3 Solids Suspension Vessel 318 5-7.4 Fermenter 319 5-7.5 Industrial Paper Pulp Chests 321 5-7.6 Twin-Screw Extruders 322 5-7.7 Intermeshing Impellers 323 5-7.8 Kenics Static Mixer 325 5-7.9 HEV Static Mixer 326 5-7.10 LDPE Autoclave Reactor 328 5-7.11 Impeller Design Optimization 330 5-7.12 Helical Ribbon Impeller 332 5-7.13 Stirred Tank Modeling Using LES 333 5-8 Closing Remarks 336 5-8.1 Additional Resources 336 5-8.2 Hardware Needs 336 5-8.3 Learning Curve 337 5-8.4 Common Pitfalls and Benefits 337 Acknowledgments 338 Nomenclature 339 References 341 6 Mechanically Stirred Vessels 345 Ramesh R. Hemrajani and Gary B. Tatterson 6-1 Introduction 345 6-2 Key Design Parameters 346 6-2.1 Geometry 347 6-2.2 Impeller Selection 354 6-2.3 Impeller Characteristics: Pumping and Power 358 6-3 Flow Characteristics 364 6-3.1 Flow Patterns 366 6-3.2 Shear 368 6-3.3 Impeller Clearance and Spacing 371 6-3.4 Multistage Agitated Tanks 372 xii CONTENTS 6-3.5 Feed Pipe Backmixing 375 6-3.6 Bottom Drainage Port 376 6-4 Scale-up 376 6-5 Performance Characteristics and Ranges of Application 378 6-5.1 Liquid Blending 379 6-5.2 Solids Suspension 380 6-5.3 Immiscible Liquid–Liquid Mixing 381 6-5.4 Gas–Liquid Dispersion 382 6-6 Laminar Mixing in Mechanically Stirred Vessels 383 6-6.1 Close-Clearance Impellers 385 Nomenclature 388 References 389 7 Mixing in Pipelines 391 Arthur W. Etchells III and Chris F. Meyer 7-1 Introduction 391 7-2 Fluid Dynamic Modes: Flow Regimes 393 7-2.1 Reynolds Experiments in Pipeline Flow 393 7-2.2 Reynolds Number and Friction Factor 394 7-3 Overview of Pipeline Device Options by Flow Regime 396 7-3.1 Turbulent Single-Phase Flow 398 7-3.2 Turbulent Multiphase Flow 399 7-3.3 Laminar Flow 401 7-4 Applications 404 7-4.1 Process Results 404 7-4.2 Pipeline Mixing Applications 405 7-4.3 Applications Engineering 405 7-4.4 Sample of Industrial Applications 407 7-5 Blending and Radial Mixing in Pipeline Flow 409 7-5.1 Definition of Desired Process Result 410 7-5.2 Importance of Physical Properties 417 7-6 Tee Mixers 419 7-7 Static Or Motionless Mixing Equipment 422 7-7.1 Types of Static Mixers 426 7-7.2 Static Mixer Design Options by Flow Regime and Application 429 7-7.3 Selecting the Correct Static Mixer Design 429 CONTENTS xiii 7-8 Static Mixer Design Fundamentals 429 7-8.1 Pressure Drop 429 7-8.2 Blending Correlations for Laminar and Turbulent Flow 432 7-8.3 Which In-line Mixer to Use 437 7-8.4 Examples 438 7-9 Multiphase Flow in Motionless Mixers and Pipes 441 7-9.1 Physical Properties and Drop Size 441 7-9.2 Dispersion of Particulate Solids: Laminar Flow 450 7-9.3 Pressure Drop in Multiphase Flow 451 7-9.4 Dispersion versus Blending 452 7-9.5 Examples 452 7-10 Transitional Flow 459 7-11 Motionless Mixers: Other Considerations 460 7-11.1 Mixer Orientation 460 7-11.2 Tailpipe/Downstream Effects 460 7-11.3 Effect of Inlet Position 462 7-11.4 Scale-up for Motionless Mixers 462 7-12 In-line Mechanical Mixers 463 7-12.1 Rotor–Stator 464 7-12.2 Extruders 464 7-13 Other Process Results 465 7-13.1 Heat Transfer 465 7-13.2 Mass Transfer 470 7-14 Summary and Future Developments 473 Acknowledgments 473 Nomenclature 473 References 475 8 Rotor–Stator Mixing Devices 479 Victor A. Atiemo-Obeng and Richard V. Calabrese 8-1 Introduction 479 8-1.1 Characteristics of Rotor–Stator Mixers 479 8-1.2 Applications of Rotor–Stator Mixers 480 8-1.3 Summary of Current Knowledge 480 8-2 Geometry and Design Configurations 482 8-2.1 Colloid Mills and Toothed Devices 482 xiv CONTENTS 8-2.2 Radial Discharge Impeller 482 8-2.3 Axial Discharge Impeller 483 8-2.4 Mode of Operation 485 8-3 Hydrodynamics of Rotor–Stator Mixers 489 8-3.1 Power Draw in Batch Mixers 489 8-3.2 Pumping Capacity 491 8-3.3 Velocity Field Information 491 8-3.4 Summary and Guidelines 496 8-4 Process Scale-up and Design Considerations 496 8-4.1 Liquid–Liquid Dispersion 498 8-4.2 Solids and Powder Dispersion Operations 501 8-4.3 Chemical Reactions 501 8-4.4 Additional Considerations for Scale-up and Comparative Sizing of Rotor–Stator Mixers 502 8-5 Mechanical Design Considerations 503 8-6 Rotor–Stator Mixing Equipment Suppliers 504 Nomenclature 505 References 505 9 Blending of Miscible Liquids 507 Richard K. Grenville and Alvin W. Nienow 9-1 Introduction 507 9-2 Blending of Newtonian Fluids in the Turbulent and Transitional Regimes 508 9-2.1 Literature Survey 508 9-2.2 Development of the Design Correlation 508 9-2.3 Use of the Design Correlation 510 9-2.4 Impeller Efficiency 511 9-2.5 Shaft Torque, Critical Speed, and Retrofitting 512 9-2.6 Nonstandard Geometries: Aspect Ratios Greater Than 1 and Multiple Impellers 513 9-2.7 Other Degrees of Homogeneity 513 9-2.8 Examples 514 9-3 Blending of Non-Newtonian, Shear-Thinning Fluids in the Turbulent and Transitional Regimes 516 9-3.1 Shear-Thinning Fluids 516 9-3.2 Literature Survey 517 9-3.3 Modifying the Newtonian Relationships for Shear-Thinning Fluids 518 9-3.4 Use of the Design Correlation 520 9-3.5 Impeller Efficiency 520 CONTENTS xv 9-3.6 Cavern Formation and Size in Yield Stress Fluids 521 9-3.7 Examples 522 9-4 Blending in the Laminar Regime 527 9-4.1 Identifying the Operating Regime for Viscous Blending 528 9-4.2 Impeller Selection 529 9-4.3 Estimation of Power Draw 529 9-4.4 Estimation of Blend Time 530 9-4.5 Effect of Shear-Thinning Behavior 530 9-4.6 Design Example 530 9-5 Jet Mixing in Tanks 531 9-5.1 Literature Review 532 9-5.2 Jet Mixer Design Method 533 9-5.3 Jet Mixer Design Steps 535 9-5.4 Design Examples 536 Nomenclature 538 References 539 10 Solid–Liquid Mixing 543 Victor A. Atiemo-Obeng, W. Roy Penney, and Piero Armenante 10-1 Introduction 543 10-1.1 Scope of Solid–Liquid Mixing 544 10-1.2 Unit Operations Involving Solid–Liquid Mixing 544 10-1.3 Process Considerations for Solid–Liquid Mixing Operations 545 10-2 Hydrodynamics of Solid Suspension and Distribution 548 10-2.1 Settling Velocity and Drag Coefficient 550 10-2.2 States of Solid Suspension and Distribution 556 10-3 Measurements and Correlations for Solid Suspension and Distribution 557 10-3.1 Just Suspended Speed in Stirred Tanks 558 10-3.2 Cloud Height and Solids Distribution 562 10-3.3 Suspension of Solids with Gas Dispersion 562 10-3.4 Suspension of Solids in Liquid-Jet Stirred Vessels 563 10-3.5 Dispersion of Floating Solids 564 10-4 Mass Transfer in Agitated Solid–Liquid Systems 565 10-4.1 Mass Transfer Regimes in Mechanically Agitated Solid–Liquid Systems 565 xvi CONTENTS 10-4.2 Effect of Impeller Speed on Solid–Liquid Mass Transfer 568 10-4.3 Correlations for the Solid–Liquid Mass Transfer 569 10-5 Selection, Scale-up, and Design Issues for Solid–Liquid Mixing Equipment 573 10-5.1 Process Definition 573 10-5.2 Process Scale-up 574 10-5.3 Laboratory or Pilot Plant Experiments 575 10-5.4 Tips for Laboratory or Pilot Plant Experimentation 576 10-5.5 Recommendations for Solid–Liquid Mixing Equipment 577 10-5.6 Baffles 579 10-5.7 Selection and Design of Impeller 579 10-5.8 Impeller Speed and Power 580 10-5.9 Shaft, Hub, and Drive 580 Nomenclature 581 References 582 11 Gas–Liquid Mixing in Turbulent Systems 585 John C. Middleton and John M. Smith 11-1 Introduction 585 11-1.1 New Approaches and New Developments 586 11-1.2 Scope of the Chapter 586 11-1.3 Gas–Liquid Mixing Process Objectives and Mechanisms 589 11-2 Selection and Configuration of Gas–Liquid Equipment 591 11-2.1 Sparged Systems 595 11-2.2 Self-Inducers 595 11-2.3 Recommendations for Agitated Vessels 596 11-3 Flow Patterns and Operating Regimes 599 11-3.1 Stirred Vessels: Gas Flow Patterns 599 11-3.2 Stirred Vessels: Liquid Mixing Time 605 11-4 Power 607 11-4.1 Static Mixers 607 11-4.2 Gassed Agitated Vessels, Nonboiling 607 11-4.3 Agitated Vessels, Boiling, Nongassed 612 11-4.4 Agitated Vessels, Hot Gassed Systems 617 11-4.5 Prediction of Power by CFD 619 11-5 Gas Hold-up or Retained Gas Fraction 620 11-5.1 In-line Mixers 620 CONTENTS xvii 11-5.2 (Cold) Agitated Vessels, Nonboiling 620 11-5.3 Agitated Vessels, Boiling (Nongassed) 622 11-5.4 Hold-up in Hot Sparged Reactors 623 11-6 Gas–Liquid Mass Transfer 626 11-6.1 Agitated Vessels 627 11-6.2 In-line Mixers 630 11-6.3 Gas–Liquid Mass Transfer with Reaction 631 11-7 Bubble Size 632 11-8 Consequences of Scale-up 633 Nomenclature 634 References 635 12 Immiscible Liquid–Liquid Systems 639 Douglas E. Leng and Richard V. Calabrese 12-1 Introduction 639 12-1.1 Definition of Liquid–Liquid Systems 639 12-1.2 Practical Relevance 640 12-1.3 Fundamentals: Breakup, Coalescence, Phase Inversion, and Drop Size Distribution 641 12-1.4 Process Complexities in Scale-up 646 12-1.5 Classification by Flow Regime and Liquid Concentration 647 12-1.6 Scope and Approach 649 12-2 Liquid–Liquid Dispersion 649 12-2.1 Introduction 649 12-2.2 Breakup Mechanism and Daughter Drop Production in Laminar Flow 651 12-2.3 Drop Dispersion in Turbulent Flow 656 12-2.4 Time to Equilibrium and Transient Drop Size in Turbulent Flow 668 12-2.5 Summary 679 12-3 Drop Coalescence 679 12-3.1 Introduction 679 12-3.2 Detailed Studies for Single or Colliding Drops 687 12-3.3 Coalescence Frequency in Turbulent Flow 692 12-3.4 Conclusions, Summary, and State of Knowledge 696 12-4 Population Balances 697 12-4.1 Introduction 697 12-4.2 History and Literature 698 12-4.3 Population Balance Equations 698 xviii CONTENTS 12-4.4 Application of PBEs to Liquid–Liquid Systems 700 12-4.5 Prospects and Limitations 700 12-5 More Concentrated Systems 704 12-5.1 Introduction 704 12-5.2 Differences from Low Concentration Systems 705 12-5.3 Viscous Emulsions 706 12-5.4 Phase Inversion 707 12-6 Other Considerations 710 12-6.1 Introduction 710 12-6.2 Suspension of Drops 711 12-6.3 Interrelationship between Suspension, Dispersion, and Coalescence 713 12-6.4 Practical Aspects of Dispersion Formation 714 12-6.5 Surfactants and Suspending Agents 715 12-6.6 Oswald Ripening 717 12-6.7 Heat and Mass Transfer 717 12-6.8 Presence of a Solid Phase 718 12-6.9 Effect of a Gas Phase 719 12-7 Equipment Selection for Liquid–Liquid Operations 719 12-7.1 Introduction 719 12-7.2 Impeller Selection and Vessel Design 719 12-7.3 Power Requirements 727 12-7.4 Other Considerations 727 12-7.5 Recommendations 729 12-8 Scale-up of Liquid–Liquid Systems 730 12-8.1 Introduction 730 12-8.2 Scale-up Rules for Dilute Systems 731 12-8.3 Scale-up of Concentrated, Noncoalescing Dispersions 732 12-8.4 Scale-up of Coalescing Systems of All Concentrations 735 12-8.5 Dispersion Time 735 12-8.6 Design Criteria and Guidelines 736 12-9 Industrial Applications 737 12-9.1 Introduction 737 12-9.2 Industrial Applications 737 12-9.3 Summary 742 Nomenclature 742 References 746 CONTENTS xix 13 Mixing and Chemical Reactions 755 Gary K. Patterson, Edward L. Paul, Suzanne M. Kresta, and Arthur W. Etchells III 13-1 Introduction 755 13-1.1 How Mixing Can Cause Problems 757 13-1.2 Reaction Schemes of Interest 758 13-1.3 Relating Mixing and Reaction Time Scales: The Mixing Damkoehler Number 761 13-1.4 Definitions 764 13-2 Principles of Reactor Design for Mixing-Sensitive Systems 766 13-2.1 Mixing Time Scales: Calculation of the Damkoehler Number 766 13-2.2 How Mixing Affects Reaction in Common Reactor Geometries 778 13-2.3 Mixing Issues Associated with Batch, Semibatch, and Continuous Operation 780 13-2.4 Effects of Feed Point, Feed Injection Velocity, and Diameter 782 13-2.5 Mixing-Sensitive Homogeneous Reactions 785 13-2.6 Simple Guidelines 790 13-3 Mixing and Transport Effects in Heterogeneous Chemical Reactors 790 13-3.1 Classification of Reactivity in Heterogeneous Reactions 794 13-3.2 Homogeneous versus Heterogeneous Selectivity 795 13-3.3 Heterogeneous Reactions with Parallel Homogeneous Reactions 800 13-3.4 Gas Sparged Reactors 800 13-3.5 Liquid–Liquid Reactions 809 13-3.6 Liquid–Solid Reactions 818 13-4 Scale-up and Scale-down of Mixing-Sensitive Systems 821 13-4.1 General Mixing Considerations 822 13-4.2 Scale-up of Two-Phase Reactions 824 13-4.3 Scale-up Protocols 826 13-5 Simulation of Mixing and Chemical Reaction 833 13-5.1 General Balance Equations 834 13-5.2 Closure Equations for the Correlation Terms in the Balance Equations 836 13-5.3 Assumed Turbulent Plug Flow with Simplified Closure 839 xx CONTENTS 13-5.4 Blending or Mesomixing Control of Turbulently Mixed Chemical Reactions 843 13-5.5 Lamellar Mixing Simulation Using the Engulfment Model 846 13-5.6 Monte Carlo Coalescence–Dispersion Simulation of Mixing 848 13-5.7 Paired-Interaction Closure for Multiple Chemical Reactions 850 13-5.8 Closure Using β-PFD Simulation of Mixing 853 13-5.9 Simulation of Stirred Reactors with Highly Exothermic Reactions 854 13-5.10 Comments on the Use of Simulation for Scale-up and Reactor Performance Studies 856 13-6 Conclusions 857 Nomenclature 859 References 861 14 Heat Transfer 869 W. Roy Penney and Victor A. Atiemo-Obeng 14-1 Introduction 869 14-2 Fundamentals 870 14-3 Most Cost-Effective Heat Transfer Geometry 873 14-3.1 Mechanical Agitators 874 14-3.2 Gas Sparging 874 14-3.3 Vessel Internals 874 14-4 Heat Transfer Coefficient Correlations 878 14-4.1 Correlations for the Vessel Wall 880 14-4.2 Correlations for the Bottom Head 880 14-4.3 Correlations for Helical Coils 881 14-4.4 Correlations for Vertical Baffle Coils 881 14-4.5 Correlations for Plate Coils 881 14-4.6 Correlations for Anchors and Helical Ribbons 881 14-5 Examples 882 Nomenclature 883 References 884 15 Solids Mixing 887 Part A: Fundamentals of Solids Mixing 887 Fernando J. Muzzio, Albert Alexander, Chris Goodridge, Elizabeth Shen, and Troy Shinbrot 15-1 Introduction 887 CONTENTS xxi 15-2 Characterization of Powder Mixtures 888 15-2.1 Ideal Mixtures versus Real Mixtures 888 15-2.2 Powder Sampling 891 15-2.3 Scale of Scrutiny 895 15-2.4 Quantification of Solids Mixing: Statistical Methods 896 15-3 Theoretical Treatment of Granular Mixing 898 15-3.1 Definition of the Granular State 899 15-3.2 Mechanisms of Mixing: Freely-Flowing Materials 901 15-3.3 Mechanisms of Mixing: Weakly Cohesive Material 904 15-3.4 De-mixing 906 15-4 Batch Mixers and Mechanisms 909 15-4.1 Tumbling Mixers 909 15-4.2 Convective Mixers 912 15-5 Selection and Scale-up of Solids Batch Mixing Equipment 917 15-5.1 Scaling Rules for Tumbling Blenders 917 15-5.2 Final Scale-up and Scale-down Considerations 922 15-6 Conclusions 923 Acknowledgments 923 Part B: Mixing of Particulate Solids in the Process Industries 924 Konanur Manjunath, Shrikant Dhodapkar, and Karl Jacob 15-7 Introduction 924 15-7.1 Scope of Solid–Solid Mixing Tasks 925 15-7.2 Key Process Questions 925 15-8 Mixture Characterization and Sampling 926 15-8.1 Type of Mixtures 926 15-8.2 Statistics of Random Mixing 928 15-8.3 Interpretation of Measured Variance 931 15-8.4 Sampling 931 15-9 Selection of Batch and Continuous Mixers 933 15-9.1 Batch Mixing 934 15-9.2 Continuous Mixing 934 15-9.3 Comparison between Batch and Continuous Mixing 934 15-9.4 Selection of Mixers 936 xxii CONTENTS 15-10 Fundamentals and Mechanics of Mixer Operation 936 15-10.1 Mixing Mechanisms 936 15-10.2 Segregation Mechanisms 939 15-10.3 Mixer Classification 940 15-11 Continuous Mixing of Solids 965 15-11.1 Types of Continuous Mixers 967 15-12 Scale-up and Testing of Mixers 968 15-12.1 Principle of Similarity 969 15-12.2 Scale-up of Agitated Centrifugal Mixers 969 15-12.3 Scale-up of Ribbon Mixers 972 15-12.4 Scale-up of Conical Screw Mixers (Nauta Mixers) 973 15-12.5 Scaling of Silo Blenders 974 15-12.6 Specifying a Mixer 974 15-12.7 Testing a Mixer 975 15-12.8 Testing a Batch Mixer 977 15-12.9 Testing a Continuous Mixer 977 15-12.10 Process Safety in Solids Mixing, Handling, and Processing 977 Nomenclature 981 References 982 16 Mixing of Highly Viscous Fluids, Polymers, and Pastes 987 David B. Todd 16-1 Introduction 987 16-2 Viscous Mixing Fundamentals 987 16-2.1 Challenges of High Viscosity Mixing 987 16-2.2 Dispersive and Distributive Mixing 988 16-2.3 Elongation and Shear Flows 989 16-2.4 Power and Heat Transfer Aspects 992 16-3 Equipment for Viscous Mixing 994 16-3.1 Batch Mixers 994 16-3.2 Continuous Mixers 1000 16-3.3 Special Mixers 1017 16-4 Equipment Selection 1020 16-5 Summary 1022 Nomenclature 1023 References 1024 CONTENTS xxiii 17 Mixing in the Fine Chemicals and Pharmaceutical Industries 1027 Edward L. Paul, Michael Midler, and Yongkui Sun 17-1 Introduction 1027 17-2 General Considerations 1028 17-2.1 Batch and Semibatch Reactors 1029 17-2.2 Batch and Semibatch Vessel Design and Mixing 1030 17-2.3 Multipurpose Design 1032 17-2.4 Batch and Semibatch Scale-up Methods 1035 17-2.5 Continuous Reactors 1035 17-2.6 Reaction Calorimetry 1036 17-3 Homogeneous Reactions 1038 17-3.1 Mixing-Sensitive Reactions 1039 17-3.2 Scale-up of Homogeneous Reactions 1042 17-3.3 Reactor Design for Mixing-Sensitive Homogeneous Reactions 1043 17-4 Heterogeneous Reactions 1044 17-4.1 Laboratory Scale Development 1045 17-4.2 Gas–Liquid and Gas–Liquid–Solid Reactions 1045 17-4.3 Liquid–Liquid Dispersed Phase Reactions 1050 17-4.4 Solid–Liquid Systems 1052 17-5 Mixing and Crystallization 1057 17-5.1 Aspects of Crystallization that Are Subject to Mixing Effects 1059 17-5.2 Mixing Scale-up in Crystallization Operations 1062 References 1064 18 Mixing in the Fermentation and Cell Culture Industries 1071 Ashraf Amanullah, Barry C. Buckland, and Alvin W. Nienow 18-1 Introduction 1071 18-2 Scale-up/Scale-down of Fermentation Processes 1073 18-2.1 Interaction between Liquid Hydrodynamics and Biological Performance 1073 18-2.2 Fluid Dynamic Effects of Different Scale-up Rules 1076 18-2.3 Influence of Agitator Design 1089 18-2.4 Mixing and Circulation Time Studies 1090 18-2.5 Scale-down Approach 1094 18-2.6 Regime Analysis 1095 xxiv CONTENTS 18-2.7 Effects of Fluctuating Environmental Conditions on Microorganisms 1096 18-2.8 Required Characteristics of a Model Culture for Scale-down Studies 1103 18-2.9 Use of Bacillus subtilis as an Oxygen- and pH-Sensitive Model Culture 1104 18-2.10 Experimental Simulations of Dissolved Oxygen Gradients Using Bacillus subtilis 1104 18-2.11 Experimental Simulations of pH Gradients Using Bacillus subtilis 1110 18-3 Polysaccharide Fermentations 1113 18-3.1 Rheological Characterization of Xanthan Gum 1114 18-3.2 Effects of Agitation Speed and Dissolved Oxygen in Xanthan Fermentations 1115 18-3.3 Prediction of Cavern Sizes in Xanthan Fermentations Using Yield Stress and Fluid Velocity Models 1116 18-3.4 Influence of Impeller Type and Bulk Mixing on Xanthan Fermentation Performance 1119 18-3.5 Factors Affecting the Biopolymer Quality in Xanthan and Other Polysaccharide Fermentations 1123 18-4 Mycelial Fermentations 1124 18-4.1 Energy Dissipation/Circulation Function as a Correlator of Mycelial Fragmentation 1127 18-4.2 Dynamics of Mycelial Aggregation 1132 18-4.3 Effects of Agitation Intensity on Hyphal Morphology and Product Formation 1133 18-4.4 Impeller Retrofitting in Large Scale Fungal Fermentations 1137 18-5 Escherichia coli Fermentations 1137 18-5.1 Effects of Agitation Intensity in E. coli Fermentations 1138 18-6 Cell Culture 1139 18-6.1 Shear Damage and Kolmogorov’s Theory of Isotropic Turbulence 1139 18-6.2 Cell Damage Due to Agitation Intensity in Suspension Cell Cultures 1141 18-6.3 Bubble-Induced Cell Damage in Sparged Suspension Cultures 1144 18-6.4 Use of Surfactants to Reduce Cell Damage Due to Bubble Aeration in Suspension Culture 1146 CONTENTS xxv 18-6.5 Cell Damage Due to Agitation Intensity in Microcarrier Cultures 1148 18-6.6 Physical and Chemical Environment 1149 18-7 Plant Cell Cultures 1152 Nomenclature 1154 References 1157 19 Fluid Mixing Technology in the Petroleum Industry 1171 Ramesh R. Hemrajani 19-1 Introduction 1171 19-2 Shear-Thickening Fluid for Oil Drilling Wells 1173 19-3 Gas Treating for CO2 Reduction 1174 19-4 Homogenization of Water in Crude Oil Transfer Lines 1175 19-4.1 Fixed Geometry Static Mixers 1176 19-4.2 Variable Geometry In-line Mixer 1177 19-4.3 Rotary In-line Blender 1178 19-4.4 Recirculating Jet Mixer 1179 19-5 Sludge Control in Crude Oil Storage Tanks 1179 19-5.1 Side-Entering Mixers 1180 19-5.2 Rotating Submerged Jet Nozzle 1181 19-6 Desalting 1183 19-7 Alkylation 1185 19-8 Other Applications 1185 Nomenclature 1186 References 1186 20 Mixing in the Pulp and Paper Industry 1187 Chad P. J. Bennington 20-1 Introduction 1187 20-2 Selected Mixing Applications in Pulp and Paper Processes: Nonfibrous Systems 1189 20-2.1 Liquid–Liquid Mixing 1189 20-2.2 Gas–Liquid Mixing 1189 20-2.3 Solid–Liquid Mixing 1192 20-2.4 Gas–Solid–Liquid Mixing 1194 20-3 Pulp Fiber Suspensions 1196 20-3.1 Pulp Suspension Mixing 1196 20-3.2 Characterization of Pulp Suspensions 1196 20-3.3 Suspension Yield Stress 1199 20-3.4 Turbulent Behavior of Pulp Suspensions 1201 20-3.5 Turbulence Suppression in Pulp Suspensions 1203 20-3.6 Gas in Suspension 1204 xxvi CONTENTS 20-4 Scales of Mixing in Pulp Suspensions 1206 20-5 Macroscale Mixing/Pulp Blending Operations 1206 20-5.1 Homogenization and Blending 1206 20-5.2 Repulping 1210 20-5.3 Lumen Loading 1213 20-6 Mixing in Pulp Bleaching Operations 1214 20-6.1 Pulp Bleaching Process 1214 20-6.2 Mixing Equipment in Pulp Bleaching Objectives 1221 20-6.3 Mixing Assessment in Pulp Suspensions 1231 20-6.4 Benefits of Improved Mixing 1237 20-7 Conclusions 1238 Nomenclature 1238 References 1240 21 Mechanical Design of Mixing Equipment 1247 David S. Dickey and Julian B. Fasano 21-1 Introduction 1247 21-2 Mechanical Features and Components of Mixers 1248 21-2.1 Impeller-Type Mixing Equipment 1249 21-2.2 Other Types of Mixers 1254 21-3 Motors 1258 21-3.1 Electric Motors 1258 21-3.2 Air Motors 1267 21-3.3 Hydraulic Motors 1267 21-4 Speed Reducers 1267 21-4.1 Gear Reducers 1268 21-4.2 Belt Drives 1277 21-5 Shaft Seals 1278 21-5.1 Stuffing Box Seals 1278 21-5.2 Mechanical Seals 1280 21-5.3 Lip Seals 1285 21-5.4 Hydraulic Seals 1285 21-5.5 Magnetic Drives 1286 21-6 Shaft Design 1287 21-6.1 Designing an Appropriate Shaft 1287 21-6.2 Shaft Design for Strength 1289 21-6.3 Hollow Shaft 1292 21-6.4 Natural Frequency 1293 21-7 Impeller Features and Design 1308 21-7.1 Impeller Blade Thickness 1309 21-7.2 Impeller Hub Design 1310 CONTENTS xxvii 21-8 Tanks and Mixer Supports 1310 21-8.1 Beam Mounting 1311 21-8.2 Nozzle Mounting 1313 21-8.3 Other Structural Support Mounting 1317 21-9 Wetted Materials of Construction 1318 21-9.1 Selection Process 1318 21-9.2 Selecting Potential Candidates 1319 21-9.3 Corrosion–Fatigue 1320 21-9.4 Coatings and Coverings 1327 Nomenclature 1329 References 1330 22 Role of the Mixing Equipment Supplier 1333 Ronald J. Weetman 22-1 Introduction 1333 22-2 Vendor Experience 1334 22-2.1 Equipment Selection and Sizing 1334 22-2.2 Scale-up 1337 22-3 Options 1338 22-3.1 Impeller Types 1338 22-3.2 Capital versus Operating Costs: Torque versus Power 1343 22-4 Testing 1343 22-4.1 Customer Sample Testing 1343 22-4.2 Witness Testing 1344 22-4.3 Laser Doppler Velocimetry 1345 22-4.4 Computational Fluid Dynamics 1345 22-5 Mechanical Reliability 1347 22-5.1 Applied Loads Due to Fluid Forces 1347 22-5.2 Manufacturing Technologies 1348 22-6 Service 1349 22-6.1 Changing Process Requirements 1349 22-6.2 Aftermarket and Worldwide Support 1350 22-7 Key Points 1351 References 1352 Index 1353