Table of Contents. Mixing and Compounding of Polymers. Theory and Practice. Herausgegeben von Ica Manas-Zloczower ISBN:

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1 Table of Mixing and Compounding of Polymers Theory and Practice Herausgegeben von Ica Manas-Zloczower ISBN: For further information and order see or contact your bookseller. Carl Hanser Verlag, München

2 In loving memory of tanti Frieda

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4 Foreword Mixing is a very important and complex component of practically every polymer processing operation. Yet, mixing principles and mixing understanding are relevant to many disciplines as well as many manufacturing processes. Given the complexity of the subject and its outmost relevance to many fields in science and engineering, the format of this book as a monograph seems mostly appropriate. Each chapter in the book is written by recognized experts in the field and I would like to express my utmost appreciation to all the authors for their contribution. Special thanks to Dr. Christine Strohm for her tremendous help in the final shaping of the book. This book was intended to be an updated edition of the first book on Mixing and Compounding of Polymers edited by Zehev Tadmor and myself published as part of the Progress in Polymer Processing Series in I would like to express my sincere gratitude and appreciation to Zehev Tadmor who was and continues to be an important mentor and role model for my professional career and who entrusted me to undertake solely the task of the second edition of the book. Last, but not least I would like to thank my husband Iani for his continuous and unconditional support along these years. Ica Manas-Zloczower Cleveland January 2009

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6 Foreword... VII PART I Mechanisms and Theory Basic Concepts... 3 Ica Manas-Zloczower, Zehev Tadmor 2 Mixing of Miscible Liquids... 5 Charles Tucker III 2.1 Introduction Continuum Analysis of Stretching Deformation Analysis Rate Analysis Interface Stretching in Simple Flows Simple Shear: Deformation Analysis Simple Shear: Rate Analysis Planar Elongation: Deformation Analysis Planar Elongation: Rate Analysis Stretching Behavior and Mixing Flows Chaos and Chaotic Flows An Example Flow Poincaré Sections Lyapunov Exponents Periodic Points Mixing in Chaotic Flows Global Chaos Universal Stretching Properties Growth of Average Stretch Global Stretching Distribution Spatial Distribution of Stretch Implications for Flow Selection Other Considerations Rheological Effects Molecular Diffusion Summary Acknowledgements References... 38

7 X 3 Mixing of Immiscible Liquids Han E. H. Meijer, Jos M. H. Janssen and Patrick D. Anderson 3.1 Introduction Mixing Mechanisms Distributive Mixing (Ca >> Ca crit ) Affine Deformation Efficient Mixing: Stretching, Folding, and Reorienting Static Mixers Multiflux Ross Sulzer Kenics Optimization Kenics Mixers Optimizing RL Designs Optimizing for Non-Newtonian Fluids Optimizing RR Designs Scale-up: Use of Structure Radius and Scale of Segregation Mapping the Structure Conclusions Dynamic Mixers Co-Rotating Twin-Screw Extruders Single Screw Extruders The Rotational Arc Mixer (RAM) Understanding Mixing: the Lid-Driven Cavity Flow Geometry Periodic Points The Mapping Method Accuracy of the Mapping Method Optimization by Using the Mapping Method Adding Inertia D Cavity Dispersive Mixing Ca Ca crit Rayleigh Disturbances Disintegration of Threads at Rest Disintegration of Threads During Flow Flow Classification Drop Deformation and Breakup Step-Wise Equilibrium versus Dynamic Breakup Two Mechanisms Plane Hyperbolic Flow Simple Shear Flow Theoretical Models for Drop Evolution Coalescence and Influence of Surfactants Collision of Drops

8 XI Film Drainage Theoretical Restrictions of the Drainage Models Drainage Probability Experimental Coalescence Probability Combination of Breakup and Coalescence Influence of Surfactants on Deformation Surface Tension Gradients Equation of State Drop Shapes Modes of Drop Breakage Influence of Surfactants on Coalescence Polymer Blending in Practice A Two-Zone Model Principle Numerical Approach Effective Viscosity Results Influence of Material Parameters Influence of Processing Conditions Passage through a Die Phase Inversion Journal Bearing: a Second Model Flow Dynamics of Mixing Rheology and Morphology Constitutive Modeling of Dispersive Mixtures Diffuse Interface Modeling Conclusions APPENDIX 3.A: Determination of Interfacial Tension Nomenclature References Dispersive Mixing of Solid Additives Ica Manas-Zloczower and Donald L. Feke 4.1 Introduction Continuum Dispersion Models Agglomerate Structure and Cohesiveness Models for Agglomerate Dispersion Discrete Dispersion Models Dispersion Mechanisms and Modelling Based on Experimental Observations Concluding Remarks Nomenclature References

9 XII 5 A Kinematic Approach to Distributive Mixing J. F. Agassant, A. Poitou and R. Valette 5.1 Introduction Kinematic Approach to Distributive Mixing Application to Simple Flow Configurations Simple Shear Flow Pure Elongational Flow Application to a Two-Dimensional Flow Configuration Experimental Study of a Two-Dimensional, Nonstationary Flow Application to Three-Dimensional Flow Configurations Periodic Shearing Flow Non-Stationary Flow within an Internal Mixer Discussion Nomenclature References Number of Passage Distribution Functions Z. Tadmor 6.1 Introduction Theory of Number of Passage Distribution (NPD) Functions NPD Functions in Batch and Flow Recirculating Systems NPD Functions in Some Model Systems Well-Stirred Batch Vessel with Recirculation Plug Flow with Recirculation Well-Stirred Continuous Mixing Vessel with Recirculation Applications of NPD Functions to Dispersive Mixing Dispersive Mixing Modeling of Mixers Acknowledgment References Mixing Measures Ica Manas-Zloczower and Miron Kaufman 7.1 Introduction Entropic Measures Shannon Entropy Renyi Entropies Applications Multi-Component Shannon Entropy Application: Simultaneous Dispersive and Distributive Mixing Index Modified Multi-Component Shannon Entropy Applications to Extruders Applications to Micromixers

10 XIII Renyi Generalized Entropies and Fractal Properties Applications Summary References PART II Mixing Equipment Modeling, Simulation, Visualization Flow Field Analysis of a Banbury Mixer Haur-Horng Yang and Ica Manas-Zloczower 8.1 Introduction Flow Simulations Description of Method Velocity Profiles and Pressure Distributions Flow Field Characterization Dispersive Mixing Distributive Mixing Summary and Conclusions Nomenclature References CFD Simulations of Static Mixers: A Survey Philippe A. Tanguy, Louis Fradette, Mourad Heniche and Shaffiq A. Jaffer 9.1 Static Mixers in the Polymer Industry Performance Criteria Pressure Drop Shearing Action Mixing Performance Mixing Homogeneity CFD Methods Numerical Modelling Principles Simulation Flowchart Equations of Change Discretization Solvers Particle Tracking Summary of the Main Hydrodynamic Predictions Pressure Drop Poincaré Maps Residence Time Distribution Overall Deformation and Shear Transverse Flow Summary of the Main Results on Mixing Evaluation

11 XIV Segregation Scale Intensity of Segregation Chaos Theory Mixer Performance Comparison Other Mixing Evaluation Studies Simulation Methods, Software Tools Industrial Perspective and what the Future Holds Single Phase Fluids Multiphase Fluids Multi-Scale Modeling Nomenclature References Flow Visualization in Internal Mixers Kyonsuku Min 10.1 Introduction Historical Development of Internal Mixers Flow Visualization Flow Visualization by Various Sensors Flow Visualization through Transparent Windows References Continuous Equipment Simulation Single Screw Seppo Syrjälä 11.1 Introduction General Equations for the Creeping Flows of Generalized-Newtonian Fluids Geometrical Considerations and Approximations Overview of Previous Work Description of Applied Modeling Approaches Two-Dimensional Formulation Three-Dimensional Formulation Predicted Results Isothermal Flow of a Newtonian Fluid Isothermal Flow of a Power-Law Non-Newtonian Fluid Non-Isothermal Flow of Non-Newtonian Fluids Nomenclature References Modeling Flow in Twin Screw Extrusion James L. White, Kyunha Ban, Sug Hun Bumm, Qibo Jiang 12.1 Introduction Modular Self-Wiping Co-Rotating Twin Screw Extruders Technology

12 XV Flow in Individual Elements Heat Balance Melting Composite Modular Machine Behavior Global Machine Software Tangential Counter-Rotating Twin Screw Extruders Technology Flow in Individual Elements Heat Balance Composite Modular Machine Behavior Intermeshing Counter-Rotating Twin Screw Extruders Technology Flow in Individual Elements Melting Composite Modular Machine Behavior Continuous Mixers Technology Flow Modeling References Continuous Equipment Simulation Co-Kneader P. H. M. Elemans 13.1 Introduction Machine Geometry and Working Principle Screw Elements, Pins, and Barrel Liners Melting Modeling the Co-Kneader Newtonian, Isothermal Analysis of Continuous Mixers Twin-Screw Extruders The Co-Kneader Mixing Experimental Throughput versus Pressure Characteristic Filled Length Pressure Gradients Residence Time Distribution Nonisothermal, Non-Newtonian Analysis Outlook Nomenclature References Continuous Equipment Simulation Mixing Devices Alejandro Londoño-Hurtado, Juan Pablo Hernandez-Ortiz, Tim A. Osswald 14.1 Static Mixers

13 XVI 14.2 Mixing Heads in Single Screw Extrusion Conclusions References Continuous Process Visualization: Visual Observation, On-Line Monitoring, Model-Fluid Extrusion and Simulation Chi-Kai Shih and Mark D. Wetzel 15.1 Introduction Overview Techniques for Visualization of Polymer Extrusion and Compounding Experimental Simulation with a Simple Mixer and Real Material Melting of Polymer Pellets Melting of Polymer Powders Melting of Polymer Blends Melting of Polymer/Rubber Blends Visualization of Morphological Transformations during Mixed Melting: the Phase Inversion Phenomenon Visualization of Morphological Transformations during Mixed Melting: Direct Observation and Torque Monitoring of Miscible Blends with Extremely Low Viscosity Ratio ( 0.01) Model Fluid Extrusion: Real Mixer with a Simple Fluid Visualization of Flow in Extruders using Model Fluids Visualization of Glass Fiber Dispersion in a Model Fluid Processing with Continuous Equipment and Real Polymers Visualization of the Extrudate at the Die Exit Visualization of Fluid Flows in a Fixed Geometry In-Line Sampling On-Line Microscopy Point Measurements: Characterization of Melting and Mixing Time with the Residence Time Distribution Visualization of Solid Transport and the Onset of Melting by Direct Observation Visualization of the Melting Zone by Direct Observation Visualization and On-line Monitoring using Highly- Instrumented Extruders Visualization of the Melting of Polymer Blends Visualization of Phase Inversion during Polymer Blending Visualization of Mixing of Polymer Pellets with Mineral Filler Characterization of Energy Dissipation in the Melting Zone: Pulse Perturbation Method and Dynamic Monitoring Characterization of the Twin Screw Extrusion Process from the Steady-State Compounding Principles and Practical Examples

14 XVII Melting Zone Extrusion and Mixing Melting of Polymer/Polymer Blends Melting of Polymer/Filler Blends Mixing after Melting Dispersive Mixing with Phase Inversion Mixing of Plastic/Rubber Blends with High Viscosity Ratio (> 3.5) Mixing of Plastic/Rubber Blends with Low Viscosity Ratio (< 0.28) Mixing of Plastic/Rubber Blends with Extremely Low Viscosity Ratio ( 0.1) Mixing of Plastic/Rubber Blends: Blending with in situ Grafting Melting and Mixing Dynamics in Extrusion Unstable Flow during Single Screw Extrusion Unstable Flow during Twin Screw Extrusion Visualization and Monitoring Applied to Process Control Summary Concluding Remarks References Scale-Up of Mixing Equipment Helmut Potente 16.1 Similarity Systems Dimensionless Groups Global Treatment Zone-Based Treatment Melt Conveying Section Melting Sections Compact Solid Bed Dispersive Melting Solid Conveying Sections Mixing in Melt Conveying Sections Miscible Melts Immiscible Melts Solid/Melt Systems Scale-Up, Scale-Down Rules Continuous, Steady-State Processes Melt Extruder and Melt-Dominated Smooth-Barrel Plasticizing Extruder Identical Melt Output Temperatures and Identical Temperature Profiles over the Dimensionless Extruder Length

15 XVIII Different Temperatures for the Model and Main Machine Rubber Extruder Grooved Barrel Extruder Co-Rotating Twin Screw Extruder Counter Rotating Twin Screw Extruder Non-Intermeshing Counter Rotating Twin Screw Kneader Buss Kneader Mixing Rolls Mixing Elements Discontinuous Processes Internal Mixers Mechanically Agitated Vessels References Scale-Down of Mixing Equipment: Microfluidics Patrick D. Anderson and Han E. H. Meijer 17.1 Introduction Mixing at Small Scales: Dimensionless Groups Distributive Mixing at Small Scales Passive versus Active Actuation Passive Mixers: Design Options Staggered Herringbone Mixer Barrier-Embedded Static Mixers Serpentine Channels Active Mixers: Design Options Neutral Beads Magnetic Beads Coupled Electrostatics and Hydrodynamics Artificial Cilia Dispersive Mixing at Small Scales Experimental Observations Boundary Integral Simulations Small Deformation Theory Conclusions References PART III Compounding Compounding (Theory and Practice) Prof. Marino Xanthos 18.1 Introduction

16 XIX 18.2 Types and Characteristics of Compounds Polymer Blends Polymer Formulations Filled Polymers (Polymer Composites) Compounding Practice General Polymer Blends and Polymer Formulations Filled Polymers Setting Up a Compounding Line Low Aspect Ratio Fillers High Aspect Ratio Fillers Nanoclays Concluding Remarks Abbreviations References Solid Additives Alberto Scurati 19.1 Introduction Synthesis and Chemical Properties of Amorphous Silica Synthesis of Amorphous Silica Chemistry and Properties of Silica Surfaces Silica Mixing and Compounding Morphology of Filler Agglomerates Particle and Pore Size Distribution Dispersibility of Fine Particle Agglomerates The Fractal Nature of Filler Particulates Filler Reinforcement Concluding Remarks References Compatibilizers Mechanisms and Theory Prof. Marino Xanthos 20.1 Introduction Parameters Affecting Wetting, Dispersion, and Adhesion Fillers Surface Modification and Interfacial Agents Compatibilizers for Polymer Blends Abbreviations References Dispersion of Two-Dimensional Nanoparticles in Polymer Melts Alejandra Reyna-Valencia and Mosto Bousmina 21.1 Introduction Clay Particle Characteristics

17 XX Structure Characterisation by X-Ray Diffraction Surface Interactions Intercalation by Organic Surfactants Exfoliation Process Stability of the Exfoliated Structure Role of Exfoliation On Macroscopic Behavior Special Case: Clay Dispersion in Multiphase Systems Modeling of Rheological Behavior Concluding Remarks Acknowledgements References Effect of Mixing on Properties of Compounds Yoshiyuki Suetsugu 22.1 Types of Aggregation and Interaction between Particles Determination of Dispersion and Dispersion Index Mixing and Dispersion in Practice Agglomerate Dispersion Profile of Dispersed Phase Effect of Mixing Conditions Effect of Surface Treatment Fiber Mixing Mixing of Clay Nanocomposite Dispersion and Properties Mechanical Properties Effect of Agglomerate Dispersion Effect of Interface Electrical Properties Properties of Clay Nanocomposites Properties of Other Nanocomposites Summary Nomenclature References PART IV Mixing Practices Internal Mixers Kimio Inoue 23.1 Introduction Mixing Mechanism of Internal Mixer Structure of Internal Mixer

18 XXI Mixing Steps for Mixing of Polymers and Fillers Dispersion Mechanism of Fillers Studies of Mixing Mechanism by Model Tests Two-Dimensional and Three-Dimensional Model Tests Improvement of Rotors by Model Tests Development of New Rotor for Internal Mixers Rotor in Tangential Type Internal Mixer Four-Wing Rotor (4WN) ST Rotor Tangential Type 6-Wing Rotor (6WI) Development of Rotors for Intermeshing Mixers Intermeshing Mixers VIC Mixer Partial Intermeshing Mixer Improvement of Internal Mixers Summary References Mixing in Single-Screw Extruders Chris Rauwendaal 24.1 Introduction Laminar Mixing in Melt Conveying Effect of Reorientation Backmixing Cross Sectional Mixing and Axial Mixing Residence Time Distribution RTD in Screw Extruders Methods to Improve Backmixing Conclusions Chaotic Mixing Mixing Devices in Extrusion Distributive Mixing Elements The Vortex Intermeshing Pin (VIP) Mixer Description of the VIP Mixer Experimental Results Dispersive Mixing Sections Design of Dispersive Mixing Devices Using the TSE Mixing Mechanism in Single Screw Extruders Nomenclature References Mixing Practices in Co-Rotating Twin Screw Extruders Dr. Paul G. Andersen 25.1 Introduction

19 XXII 25.2 Building Blocks for Mixing Extruder Geometry Element Geometry Typical Process Mixing Tasks Polymer/Polymer Polymer/Low Aspect Ratio Filler Elastomer Elastomer/Low Aspect Ratio Filler Polymer/High Aspect Ratio Filler (Fiber) Polymer/Nano Scale Filler Polymer/Low Viscosity Additives Summary References Intermeshing Twin Screw Extruders Tadamoto Sakai 26.1 Outline Total Compounding System Outline of the Total System Typical Machine Specifications and Output Capacities Extrusion Performance Simulation Melting Mechanism Analysis Twin Screw Extrusion Characteristics Simulation Compounding Applications Inorganic Filler Compounding Glass-Fiber Compounding Short Glass Fiber Compounding Long Glass Fiber Compounding and Molding Polymer Nano-Composite Compounding Polymer Blending Miscible Polymer Blending Immiscible Polymer Blending Reactive Extrusion Advantages of Reactive Extrusion Typical Chemical Reactions Recycling Applications PET Direct Extrusion PET Modification for Producing Foamed Sheet Combination of Reactive Processing and Injection Molding Devolatilization Effects of Water Addition High Concentration Devolatilization References

20 XXIII 27 Reactive Compounding Guo-Hua Hu, Sandrine Hoppe, Lian-Fang Feng, Christian Fonteix 27.1 Introduction Free Radical Grafting of Monomers onto Polymers Overall Reaction Scheme Free Radical Grafting in a Batch Mixer Effect of Comonomers Effect of Temperature Effect of Mixing Free Radical Grafting in a Twin Screw Extruder Effect of Screw Design Effect of Plastication/Melting Effect of Feeding Mode Recent Developments Fractional Feeding Concept of Nano-Reactors Reactive Blending General Features of Morphology Development Reactive Blending in Batch Mixers or Analogues Effect of the Copolymer Formation Kinetics Effect of Mixing Time Effect of Mixing Intensity Reactive Blending in Screw Extruders Non-Reactive versus Reactive Blends Effect of Screw Configuration Effect of the Compatibilizer Content Adverse Effect of Mixing One-Step versus Two-Step Reactive Blending Comparison of in situ Compatibilization to Separate Copolymer Addition Polymerized Blends Intractable Engineering Plastics/Monomer Systems Nano-Blends Compounding of Polymer Nanocomposites Multi-Scale Structures of Montmorillonite (MMT) Mechanisms of Dispersion of MMT in Polymers Factors Affecting the Rate and Scale of Dispersion of MMT in Polymers Water-Assisted MMT Dispersion in Polymers Summary References

21 XXIV 28 Continuous Mixers Eduardo L. Canedo and Lefteris N. Valsamis 28.1 Introduction Structure and Principles of Operation Solids Conveying Melting Mixing Devolatilization Pumping Modeling Circumferential Flow Global Flow Models Scale-Up Considerations Rotor Design Single-Stage Rotors Two-Stage Rotors Conclusion List of Symbols Abreviations References Subject Index