Flows in Polymers, Reinforced Polymers and Composites (eBook)

Preface 7
Acknowledgments 8
Contents 9
1 Multi-scale Modeling and Simulation of Polymer Flow 12
1.1 Introduction 12
1.1.1 Rheology and Structure 12
1.1.2 A Hierarchy of Modeling Approaches 13
1.1.3 The Role of Computational Rheology 15
1.2 Macroscopic Modeling and Simulations 16
1.2.1 Governing Equations and Numerical Challenges 17
1.2.2 A Spectrum of Numerical Methods and Applications 19
1.3 Multi-scale Kinetic Theory of Viscoelastic Flow 20
1.3.1 Probability Distribution of Molecular Configurations 20
1.3.2 Fokker-Planck Equation and Kramers Relation 21
1.3.3 Exploiting the Multi-scale Model: Three Basic Approaches 23
1.3.4 Illustrative Examples of Kinetic Theory Models 24
1.4 Micro-Macro Simulations Using the Stochastic Approach 28
1.4.1 CONNFFESSIT 28
1.4.2 Numerical Challenges 29
1.4.3 Brownian Configuration Fields 31
1.4.4 Lagrangian Particle Methods 32
1.4.5 Variance Reduction 34
1.5 Micro-Macro Simulations Using the Fokker-Planck Approach 34
1.5.1 Proper Generalized Decomposition 35
1.5.2 PGD Simulations of the Multi-bead-Spring FENE Model 36
1.5.3 Fokker-Planck Simulations of Complex Flows 38
1.6 The Impact of Closure Approximations 39
1.7 Illustrative Examples of Complex Flow Simulations 42
1.7.1 Early Macroscopic Simulations 42
1.7.2 Macroscopic Simulations with Advanced Models 44
1.7.3 Impact of Closure Approximations in Complex Flows 47
1.8 Discussion 47
1.8.1 From Numbers to Rheology 48
1.8.2 The Infamous HWNP and Mesh Convergence 49
1.9 Conclusions 50
References 51
2 Complex Flows of Micro/Nano Structured Fluids: Reinforced Polymer Composites 54
2.1 Introduction 54
2.2 Dilute and Semi-dilute Suspensions 57
2.2.1 Multi-scale Description of Non-brownian Rod Suspensions 57
2.2.2 Multi-scale Description of Brownian Rods Suspensions 63
2.2.3 Semi-concentrated Regime 69
2.3 Processing Flow Simulation 70
2.3.1 Fixed Mesh Description of the Fluid Domain Evolution and Flow Front Tracking by Using a Volume of Fluid---VoF---Technique 71
2.3.2 Updated Lagrangian Meshless Simulation 76
2.4 Concentrated Suspensions Involving Rod Clusters 80
2.4.1 Rigid Clusters 80
2.4.2 Deformable Clusters 85
2.5 Advanced Topics 91
2.5.1 On the Solution of the Fokker-Plank Equation 91
2.5.2 Descriptions Based on Higher-Order Kinematics 95
2.5.3 Accounting for Rod Bending 101
2.5.4 Delaying Orientation Mechanisms 107
2.5.5 Collective Effects 109
2.5.6 Orientation Induced by an Electric Field 112
References 116
3 Flows of Simple Fluids in Complex Microstructures: Composite Processing of Structural Polymer Composites 120
3.1 Introduction 120
3.2 Description of Fibrous Microstructures in Composites 124
3.2.1 Monodisperse Porosity Medium 126
3.2.2 Bidisperse Porosity Medium 130
3.3 Governing Equations for Flows in Porous Media 132
3.3.1 Pore-Scale Isothermal Flow Description 133
3.3.2 Macroscopic Scale: Upscaling 133
3.4 Flow of Simple Fluids in Non-deformable Fibrous Microstructures 139
3.4.1 Negligible Inertia and Single-Scale Porosity Medium 139
3.4.2 Negligible Inertia and Double-Scale Porosity Medium 143
3.4.3 Fluid Inertia 145
3.5 Flow of Complex Fluids in Non-deformable Fibrous Microstructures 146
3.5.1 Slightly Compressible Fluids 146
3.5.2 Reactive Fluids 148
3.6 Numerical Simulation 149
References 150