Rheology of Particulate Dispersions and Composites 1st Edition by Rajinder Pal 1000713474 9781000713473

PART I Introduction

Chapter 1 Applications of Particulate Dispersions and Composites

1.1 Particulate Dispersions

1.1.1 Ceramics

1.1.2 Particulate Recording Media

1.1.3 Nanotechnological Applications

1.1.4 Biomedical Applications

1.1.5 Biotechnological Applications

1.1.6 Paints

1.1.7 Marine Oil Spills

1.1.8 Food Applications

1.1.9 Pipeline Transportation of Materials

1.1.10 Petroleum Production

1.1.11 Cosmetics and Toiletries

1.1.12 Geological Applications

1.2 Composites

1.2.1 Particulate Composites and Their Applications

1.2.1.1 Coarse-Particle Composites

1.2.1.2 Fine-Particle Composites

1.2.2 Fiber-Reinforced Composites and Their Applications

References

Chapter 2 Brief Review of Mechanics of Fluids, Solids, and Interfaces

2.1 Basic Concepts of Continuum Mechanics

2.1.1 Continuum Model of Matter

2.1.2 Kinematics

2.1.2.1 Lagrangian and Eulerian Descriptions of Deformation and Flow

2.1.2.2 Displacement Gradient Tensors

2.1.2.3 Deformation Gradient Tensors

2.1.2.4 Finite Strain Tensors

2.1.2.5 Material Time Derivative of a Spatial Function

2.1.2.6 Material Time Derivative of a Volume Integral (Reynolds Transport Theorem)

2.1.2.7 Velocity Gradient Tensor

2.1.2.8 Rate of Deformation Tensor and Vorticity Tensor

2.1.2.9 Shear Rate Tensor

2.1.3 Stress Vector and Stress Tensor

2.1.3.1 Stress Vector

2.1.3.2 Stress Tensor

2.1.4 Constitutive Equation

2.2 Mechanics of Fluids

2.2.1 The Continuity Equation

2.2.2 The Equation of Motion

2.2.3 The Navier–Stokes Equation

2.2.4 Creeping–Flow Equations

2.3 Mechanics of Solids

2.4 Mechanics of Interfaces

2.4.1 Definitions of Important Terms

2.4.1.1 Surface Unit Tensor and Surface Gradient Operator

2.4.1.2 Surface Deformation Gradient Tensor

2.4.1.3 Surface Strain Tensor

2.4.1.4 Surface Rate of Strain Tensor

2.4.1.5 Surface Stress Vector

2.4.1.6 Surface Stress Tensor

2.4.2 Surface Divergence Theorem

2.4.3 Force Balance on Interfacial Film

2.4.4 Interfacial Rheology

Notation

Supplemental Reading

Chapter 3 Bulk Stress in Particulate Dispersions and Composites

3.1 Dispersed System as a Continuum

3.2 Ensemble vs. Volume Averaging

3.3 Bulk Stress in Dispersions and Composites

3.3.1 Dispersions

3.3.1.1 Dipole Strength of Rigid Particles

3.3.1.2 Dipole Strength of Droplets with Interfacial Film

3.3.2 Composites

3.4 Constitutive Equations for Dispersed Systems

3.4.1 Dilute System of Nonspherical Particles

3.4.2 Dilute System of Spherical Particles

3.5 Nonhydrodynamic Effects in Dispersions

Notation

References

PART II Rheology of Dispersions of Rigid Particles

Chapter 4 Dispersions of Rigid Spherical Particles

4.1 Introduction

4.2 Dispersions of Solid Spherical Particles

4.3 Dispersion of Porous Rigid Particles

4.4 Dispersions of Electrically Charged Solid Particles

4.4.1 Fundamental Equations

4.4.2 The Bulk Stress

4.4.3 Constitutive Equation

Notation

References

Chapter 5 Dispersions of Rigid Nonspherical Particles

5.1 Introduction

5.2 Motion of a Single Isolated Spheroidal Particle in Shear Flow

5.3 Rheology of Suspension of Non-Brownian Axisymmetric Particles

5.4 Effects of Brownian Motion on the Rheology of Axisymmetric Particles

Notation

References

Chapter 6 Dispersions of Rigid (Spherical and Nonspherical) Magnetic Particles

6.1 Introduction

6.2 Suspensions of Spherical Dipolar Particles

6.2.1 Motion of a Single Isolated Dipolar Particle in Shear Flow

6.2.2 Rheology of Suspensions of Spherical Dipolar Particles

6.2.2.1 Effect of Rotary Brownian Motion

6.3 Suspensions of Nonspherical Dipolar Particles

Notation

References

PART III Rheology of Dispersions of Nonrigid Particles

Chapter 7 Dispersions of Soft (Deformable) Solid Particles

7.1 Introduction

7.2 Fundamental Equations

7.2.1 Constitutive Equation of the Particle Material

7.3 Rheology of Dispersions of Soft, Solid-Like Elastic Particles

7.4 Rheology of Dispersions of Soft Solid-Like Viscoelastic Particles

Notation

References

Chapter 8 Dispersions of Liquid Droplets

8.1 Introduction

8.2 Deformation and Breakup of Droplets

8.3 Fundamental Equations

8.4 Rheology of Emulsions

8.4.1 Zero-Order Deformation Solution

8.4.2 First-Order Deformation Solution

8.4.3 Second-Order Deformation Solution

8.5 Effect of Surfactants on Emulsion Rheology

Notation

References

Chapter 9 Dispersions of Bubbles

9.1 Introduction

9.2 Dilational Viscosity of Bubbly Suspensions

9.2.1 Normal Force at the Cell Boundary

9.2.2 Normal Force at the Boundary of the Equivalent Homogeneous Fluid

9.2.3 Equation for Dilational Viscosity

9.3 Constitutive Equation for Bubbly Suspensions

9.4 Effect of Surfactants on the Rheology of Bubbly Suspensions

Notation

References

Chapter 10 Dispersions of Capsules

10.1 Introduction

10.2 Fundamental Equations

10.3 Membrane Mechanics

10.3.1 Strain Energy Function of Membrane Material

10.3.1.1 Mooney–Rivlin (MR) Type Membrane

10.3.1.2 RBC-Type Membrane

10.4 Instantaneous Shape of Initially Spherical Capsule

10.4.1 Deformation of a Capsule in Steady Irrotational Flow

10.4.2 Deformation of a Capsule in Steady Simple Shear Flow

10.4.2.1 Capsule with a Mooney–Rivlin-Type Membrane

10.4.2.2 Capsule with an RBC-Type Membrane

10.5 Rheological Constitutive Equation for Dispersion of Capsules

10.5.1 Steady Irrotational Flow

10.5.2 Steady Simple Shear Flow

10.5.2.1 Capsule with a Mooney–Rivlin-Type Membrane

10.5.2.2 Capsule with an RBC-Type Membrane

Notation

References

Chapter 11 Dispersions of Core–Shell Particles

11.1 Introduction

11.2 Rheology of Dispersions of Core–shell Particles

11.2.1 Dispersions of Solid Core–Hairy Shell Particles

11.2.2 Dispersions of Solid Core–Liquid Shell Particles

11.2.3 Dispersions of Liquid Core–Liquid Shell (Double-Emulsion) Droplets

Notation

References

PART IV Rheology of Composites

Chapter 12 Particulate Composites

12.1 Introduction

12.2 Constitutive Equation for Particulate Composites

12.3 Dipole Strength of Spherical Particles

12.4 Effective Elastic Moduli of Particulate Composites with Spherical Particles

12.4.1 Composites with Rigid Spherical Particles

12.4.2 Composites with Incompressible Matrix

12.4.3 Composites with Pores

12.5 Effective Elastic Moduli of Particulate Composites with Disk-shaped Particles

12.6 Bounds for the Effective Elastic Properties of Particulate Composites

Notation

References

Chapter 13 Fiber-Reinforced Composites

13.1 Introduction

13.2 Elastic Behavior of Continuous-Fiber Composites

13.2.1 Unidirectional Continuous-Fiber Composites

13.2.1.1 Elementary Models

13.2.1.2 Improved Models

13.2.1.3 Bounds on the Elastic Properties of Unidirectional Continuous-Fiber Composites

13.2.2 Randomly Oriented Continuous-Fiber Composites

13.3 Elastic Behavior of Discontinuous Short-fiber Composites

13.3.1 Unidirectional Short-Fiber Composites

13.3.2 Randomly Oriented Short-Fiber Composites

Notation

References

PART V Linear Viscoelasticity of Particulate Dispersions and Composites

Chapter 14 Introduction to Linear Viscoelasticity

14.1 Linear Viscoelasticity

14.2 Oscillatory Shear

14.3 Maxwell Model

Notation

References

Chapter 15 Dynamic Viscoelastic Behavior of Particulate Dispersions

15.1 Dispersions of Soft Rubberlike Solid Particles

15.1.1 Generalization of Frohlich and Sack Model

15.2 Dispersions of Deformable Liquid Droplets with Pure Interface

15.2.1 Generalization of Oldroyd Model

15.3 Dispersions Of Deformable Liquid Droplets Coated With Additive

15.3.1 Droplets Coated with Purely Viscous Films

15.3.2 Droplets Coated with Purely Elastic Films

15.3.3 Droplets Coated with Viscoelastic Films

15.3.3.1 Palierne Model

15.3.4 Droplets Coated with Films Possessing Bending Rigidity

15.3.5 Droplets Coated with Liquid Films

Notation

References

Chapter 16 Dynamic Viscoelastic Behavior of Composites

16.1 Introduction

16.2 Elastic-Viscoelastic Correspondence Principle

16.3 Complex Moduli of Viscoelastic Particulate Composites

16.4 Complex Moduli of Viscoelastic Fiber-Reinforced Composites

Notation

References

PART VI Appendices

Appendix A Equations Related to Mechanics of Fluids and Solids in Different Coordinate Systems

A.1 Equations Related to Fluid Mechanics

A.1.1 Continuity Equation in Different Coordinate Systems

A.1.2 Equations of Motion in Different Coordinate Systems

A.1.3 Rate of Strain Tensor (E¯¯) in Different Coordinate Systems

A.1.4 Shear Rate Tensor (γ˙¯¯)in Different Coordinate Systems

A.1.5 Vorticity Tensor (Ω¯¯) in Different Coordinate Systems

A.1.6 Viscous Stress Tensor (τ¯¯) for Newtonian Fluids in Different Coordinate Systems

A.1.7 Navier–Stokes Equations in Different Coordinate Systems

A.2 Equations Related to Mechanics of Solids

A.2.1 Infinitesimal Strain Tensor (e¯¯) in Different Coordinate Systems

A.2.2 Equilibrium Equation in Different Coordinate Systems

A.2.3 Hooke’s Law in Different Coordinate Systems

A.2.4 Navier–Cauchy Equations in Different Coordinate Systems

Appendix B Vector and Tensor Operations in Index Notation

B.1 Vector Operations

B.2 Tensor Operations

B.3 Some Useful Relations

Appendix C Gauss Divergence Theorem

Appendix D Symmetric Deviator of Fourth-Order Tensor

Index