Polymer Processing

PREFACE

TABLE OF CONTENTS

INTRODUCTION

I.1 MODELING AND SIMULATION

I.2 MODELING PHILOSOPHY

I.3 NOTATION

I.4 CONCLUDING REMARKS

REFERENCES

PART I BACKGROUND

CHAPTER 1 POLYMER MATERIALS SCIENCE

1.1 CHEMICAL STRUCTURE

1.2 MOLECULAR WEIGHT

1.3 CONFORMATION AND CONFIGURATION OF POLYMER MOLECULES

1.4 MORPHOLOGICAL STRUCTURE

1.4.1 Copolymers and Polymer Blends

1.5 THERMAL TRANSITIONS

1.6 VISCOELASTIC BEHAVIOR OF POLYMERS

1.6.1 Stress Relaxation

1.6.2 Time-Temperature Superposition (WLF-Equation)

1.7 EXAMPLES OF COMMON POLYMERS

1.7.1 Thermoplastics

1.7.2 Thermosetting Polymers

1.7.3 Elastomers

Problems

REFERENCES

CHAPTER 2 PROCESSING PROPERTIES

2.1 THERMAL PROPERTIES

2.1.1 Thermal Conductivity

2.1.2 Specific Heat

2.1.3 Density

2.1.4 Thermal Diffusivity

2.1.5 Linear Coefficient of Thermal Expansion

2.1.6 Thermal Penetration

2.1.7 Measuring Thermal Data

2.2 CURING PROPERTIES

2.3 RHEOLOGICAL PROPERTIES

2.3.1 Flow Phenomena

2.3.2 Viscous Flow Models

2.3.3 Viscoelastic Constitutive Models

2.3.4 Rheometry

2.3.5 Surface Tension

2.4 PERMEABILITY PROPERTIES

2.4.1 Sorption

2.4.2 Diffusion and Permeation

2.4.3 Measuring S, D, and P

2.4.4 Diffusion of Polymer Molecules and Self-Diffusion

2.5 FRICTION PROPERTIES

Problems

REFERENCES

CHAPTER 3 POLYMER PROCESSES

3.1 EXTRUSION

3.1.1 The Plasticating Extruder

3.1.2 Extrusion Dies

3.2 MIXING PROCESSES

3.2.1 Distributive Mixing

3.2.2 Dispersive Mixing

3.2.3 Mixing Devices

3.3 INJECTION MOLDING

3.3.1 The Injection Molding Cycle

3.3.2 The Injection Molding Machine

3.3.3 Related Injection Molding Processes

3.4 SECONDARY SHAPING

3.4.1 Fiber Spinning

3.4.2 Film Production

3.4.3 Thermoforming

3.5 CALENDERING

3.6 COATING

3.7 COMPRESSION MOLDING

3.8 FOAMING

3.9 ROTATIONAL MOLDING

REFERENCES

PART II PROCESSING FUNDAMENTALS

CHAPTER 4 DIMENSIONAL ANALYSIS AND SCALING

4.1 DIMENSIONAL ANALYSIS

4.2 DIMENSIONAL ANALYSIS BY MATRIX TRANSFORMATION

4.3 PROBLEMS WITH NON-LINEAR MATERIAL PROPERTIES

4.4 SCALING AND SIMILARITY

Problems

REFERENCES

CHAPTER 5 TRANSPORT PHENOMENA IN POLYMER PROCESSING

5.1 BALANCE EQUATIONS

5.1.1 The Mass Balance or Continuity Equation

5.1.2 The Material or Substantial Derivative

5.1.3 The Momentum Balance or Equation of Motion

5.1.4 The Energy Balance or Equation of Energy

5.2 MODEL SIMPLIFICATION

5.2.1 Reduction in Dimensionality

5.2.2 Lubrication Approximation

5.3 SIMPLE MODELS IN POLYMER PROCESSING

5.3.1 Pressure Driven Flow of a Newtonian Fluid Through a Slit

5.3.2 Flow of a Power Law Fluid in a Straight Circular Tube (Hagen-Poiseuille Equation)

5.3.3 Flow of a Power Law Fluid in a Slightly Tapered Tube

5.3.4 Volumetric Flow Rate of a Power Law Fluid in Axial Annular Flow

5.3.5 Radial Flow Between two Parallel Discs — Newtonian Model

5.3.6 The Hele-Shaw model

5.3.7 Cooling or Heating in Polymer Processing

Problems

REFERENCES

CHAPTER 6 ANALYSES BASED ON ANALYTICAL SOLUTIONS

6.1 SINGLE SCREW EXTRUSION—ISOTHERMAL FLOW PROBLEMS

6.1.1 Newtonian Flow in the Metering Section of a Single Screw Extruder

6.1.2 Cross Channel Flow in a Single Screw Extruder

6.1.3 Newtonian Isothermal Screw and Die Characteristic Curves

6.2 EXTRUSION DIES—ISOTHERMAL FLOW PROBLEMS

6.2.1 End-Fed Sheeting Die

6.2.2 Coat Hanger Die

6.2.3 Extrusion Die with Variable Die Land Thicknesses

6.2.4 Pressure Flow of Two Immiscible Fluids with Different Viscosities

6.2.5 Fiber Spinning

6.2.6 Viscoelastic Fiber Spinning Model

6.3 PROCESSES THAT INVOLVE MEMBRANE STRETCHING

6.3.1 Film Blowing

6.3.2 Thermoforming

6.3.2 Thermoforming

6.4 CALENDERING — ISOTHERMAL FLOW PROBLEMS

6.4.1 Newtonian Model of Calendering

6.4.2 Shear Thinning Model of Calendering

6.4.3 Calender Fed with a Finite Sheet Thickness

6.5 COATING PROCESSES

6.5.1 Wire Coating Die

6.5.2 Roll Coating

6.6 MIXING — ISOTHERMAL FLOW PROBLEMS

6.6.1 Effect of Orientation on Distributive Mixing ? Erwin’s Ideal Mixer

6.6.2 Predicting the Striation Thickness in a Couette Flow System — Shear Thinning Model

6.6.3 Residence Time Distribution of a Fluid Inside a Tube

6.6.4 Residence Time Distribution Inside the Ideal Mixer

6.7 INJECTION MOLDING—ISOTHERMAL FLOW PROBLEMS

6.7.1 Balancing the Runner System in Multi-Cavity Injection Molds

6.7.2 Radial Flow Between Two Parallel discs

6.8 NON-ISOTHERMAL FLOWS

6.8.1 Non-Isothermal Shear Flow

6.8.2 Non-Isothermal Pressure Flow Through a Slit

6.9 MELTING AND SOLIDIFICATION

6.9.1 Melting with Pressure Flow Melt Removal

6.9.2 Melting with Drag Flow Melt Removal

6.9.3 Melting Zone in a Plasticating Single Screw Extruder

6.10 CURING REACTIONS DURING PROCESSING

6.11 CONCLUDING REMARKS

Problems

REFERENCES

PART III NUMERICAL TECHNIQUES

CHAPTER 7 INTRODUCTION TO NUMERICAL ANALYSIS

7.1 DISCRETIZATION AND ERROR

7.2 INTERPOLATION

7.2.1 Polynomial and Lagrange Interpolation

7.2.2 Hermite Interpolations

7.2.3 Cubic Splines

7.2.4 Global and Radial Interpolation

7.3 NUMERICAL INTEGRATION

7.3.1 Classical Integration Methods

7.3.2 Gaussian Quadratures

7.4 DATA FITTING

7.4.1 Least Squares Method

7.4.2 The Levenberg-Marquardt Method

7.5 METHOD OF WEIGHTED RESIDUALS

Problems

REFERENCES

CHAPTER 8 FINITE DIFFERENCE METHOD

8.1 TAYLOR-SERIES EXPANSIONS

8.2 NUMERICAL ISSUES

8.3 THE INFO-TRAVEL CONCEPT

8.4 STEADY-STATE PROBLEMS

8.5 TRANSIENT PROBLEMS

8.5.1 Higher Order Approximation Techniques

8.6 THE RADIAL FLOW METHOD

8.7 FLOW ANALYSIS NETWORK

8.8 PREDICTING FIBER ORIENTATION — THE FOLGAR-TUCKER MODEL

8.9 CONCLUDING REMARKS

Problems

REFERENCES

CHAPTER 9 FINITE ELEMENT METHOD

9.1 ONE-DIMENSIONAL PROBLEMS

9.1.1 One-Dimensional Finite Element Formulation

9.1.2 Numerical Implementation of a One-Dimenional Finite Element Formulation

9.1.3 Matrix Storage Schemes

9.1.4 Transient Problems

9.2 TWO-DIMENSIONAL PROBLEMS

9.2.1 Solution of Posisson’s equation Using a Constant Strain Triangle

9.2.2 Transient Heat Conduction Problem Using Constant Strain Triangle

9.2.3 Solution of Field Problems Using Isoparametric Quadrilateral Elements.

9.2.4 Two Dimensional Penalty Formulation for Creeping Flow Problems

9.3 THREE-DIMENSIONAL PROBLEMS

9.3.1 Three-dimensional Elements

9.3.2 Three-Dimensional Transient Heat Conduction Problem With Convection

9.3.3 Three-Dimensional Mixed Formulation for Creeping Flow Problems

9.4 MOLD FILLING SIMULATIONS USING THE CONTROL VOLUME APPROACH

9.4.1 Two-Dimensional Mold Filling Simulation of Non-Planar Parts (2.5D Model)

9.4.2 Full Three-Dimensional Mold Filling Simulation

9.5 VISCOELASTIC FLUID FLOW

Problems

REFERENCES

CHAPTER 10 BOUNDARY ELEMENT METHOD

10.1 SCALAR FIELDS

10.1.1 Green’s Identities

10.1.2 Green’s Function or Fundamental Solution

10.1.3 Integral Formulation of Poisson’s Equation

10.1.4 BEM Numerical Implementation of the 2D Laplace Equation

10.1.5 2D Linear Elements.

10.1.6 2D Quadratic Elements

10.1.7 Three-Dimensional Problems

10.2 MOMENTUM EQUATIONS

10.2.1 Green’s Identities for the Momentum Equations

10.2.2 Integral Formulation for the Momentum Equations

10.2.3 BEM Numerical Implementation of the Momentum Balance Equations

10.2.4 Numerical Treatment of the Weakly Singular Integrals

10.2.5 Solids in Suspension

10.3 COMMENTS OF NON-LINEAR PROBLEMS

10.4 OTHER BOUNDARY ELEMENT APPLICATIONS

Problems

REFERENCES

CHAPTER 11 RADIAL FUNCTIONS METHOD

11.1 THE KANSA COLLOCATION METHOD

11.2 APPLYING RFM TO BALANCE EQUATIONS IN POLYMER PROCESSING

11.2.1 Energy Balance

11.2.2 Flow problems

Problems

REFERENCES

INDEX