Flowing matter

Preface

Contents

1 Numerical Approaches to Complex Fluids

2 Basic Concepts of Stokes Flows

2.1 Introduction
2.2 Navier–Stokes and Stokes Equations
- 2.2.1 Navier–Stokes Equations
- 2.2.2 Stokes Flows
2.3 Reversibility of Fluid Flows
- 2.3.1 Examples of Reversibility
- 2.3.2 Irreversible Trajectories in Stokes Flow
2.4 Minimum Energy Dissipation Theorem
- 2.4.1 Statement
- 2.4.2 An Application of the Minimum Energy Dissipation Theorem
2.5 Limits of the Stokes Approximation
- 2.5.1 Example of a System Where the Stokes Approximation Does Not Work
  - Other Linear Flow Equations
- 2.5.2 Departures from Reversibility Caused by Inertia
- 2.5.3 Accelerating Fluid Example
2.6 Conclusions
References

3 Mesoscopic Approach to Nematic Fluids

3.1 Introduction to Nematic Fluids
3.2 Nematic Order Parameters
3.3 Landau–de Gennes Free Energy Approach
- 3.3.1 Landau Theory of Nematic Phase Transition
- 3.3.2 Elastic Free Energy
- 3.3.3 Surface Anchoring
- 3.3.4 Electric Field Effects
- 3.3.5 Magnetic Field Effects
3.4 Topological Defects
- 3.4.1 Umbilic Defects
- 3.4.2 Basics of Topological Theory of Defects
3.5 Nematodynamics
- 3.5.1 Ericksen Stress Tensor
- 3.5.2 Ericksen–Leslie–Parodi Approach
- 3.5.3 Beris–Edwards Model
- 3.5.4 Qian–Sheng Model
- 3.5.5 Towards Active Nematics
3.6 Nematic Microfluidics
- 3.6.1 Nematic Flows in Channels
- 3.6.2 Nematic Microfluidic Junctions
- 3.6.3 Colloidal Particles in Nematic Microfluidic Environment
3.7 Nematic Colloids
- 3.7.1 Single Spherical Particle
- 3.7.2 Interparticle Interactions
- 3.7.3 Assembly and Self-assembly of Colloidal Structures
- 3.7.4 Complex-Shaped and Topological Colloids
3.8 Conclusions
References

4 Amphiphilic Janus Particles at Interfaces

Acronyms
4.1 Introduction
4.2 Short History of Asymmetric Janus Particles
4.3 General Synthetic Routes
- 4.3.1 Masking and Asymmetric Modification
- 4.3.2 Seeded Emulsion Polymerisation and Phase Separation
- 4.3.3 Microfluidic and Capillary Electro-Jetting Methods
- 4.3.4 Polymer Co-precipitation and Phase Separation
4.4 Tuning the Surface Polarity in JPs
4.5 Interfacial Activity and Adsorption at Interfaces
- 4.5.1 Contact Angle and Interfacial Adsorption Energies of HPs vs. JPs
- 4.5.2 Inter-Particle Interaction at Interfaces vs. Lowering the Interfacial Tension
- 4.5.3 Activation and Adsorption Energies of JPs Spontaneously Adsorbing at Interfaces
4.6 Pickering Emulsions: Arrested JPs at Interfaces
4.7 Self-Assembly of Janus Particles
4.8 JP-Based Nanomotors
4.9 Conclusions
References

5 Upscaling Flow and Transport Processes

5.1 Introduction
5.2 Flow Through Porous and Heterogeneous Media
- 5.2.1 Darcy's Law
- 5.2.2 Extensions of Darcy's Law
- 5.2.3 Heterogeneous Media
5.3 Macroscopic Transport Models
- 5.3.1 Fickian Dispersion
- 5.3.2 Anomalous Dispersion
  - Continuous Time Random Walks
  - Multi-Rate Mass Transfer
- 5.3.3 Mixing and Chemical Reactions
  - Mixing, Diffusion and Dispersion
  - Chemical Reactions
5.4 Multiphase and Surface Processes
- 5.4.1 Mass and Heat Transfer
  - From Surface Processes to Averaged Reaction Rates
5.5 Conclusions
Appendix A: Homogenisation and Two-Scale Expansions
Appendix B: Volume/Ensemble Averaging
References

6 Recent Developments in Particle Tracking Diagnosticsfor Turbulence Research

6.1 Introduction
6.2 A Model-Free Calibration Method
- 6.2.1 Principle
- 6.2.2 Practical Implementation
- 6.2.3 Results: Comparison with Tsai Model
- 6.2.4 Discussion
6.3 Particle Tracking Algorithms
- 6.3.1 Shadow Particle Tracking Velocimetry
  - Experimental Setup
  - The Trajectory Stereo-Matching Approach
  - Flow Measurements
- 6.3.2 Improved Four-Frame Best Estimate
6.4 Noise Reduction in Post-Processing Statistical Analysis
- 6.4.1 Lagrangian Auto-Correlation Functions
  - Results
  - Discussion
- 6.4.2 Eulerian Structure Functions
  - Method
  - Results
  - Discussion
6.5 Conclusions
References

7 Numerical Simulations of Active Brownian Particles

7.1 Introduction
7.2 Passive Brownian Motion
7.3 Active Particles
- 7.3.1 Active Brownian Motion
- 7.3.2 Run-and-Tumble Motion
- 7.3.3 Chiral Active Brownian Motion
- 7.3.4 Gaussian Noise Reorientation Model
7.4 More Complex Models
- 7.4.1 Non-Spherical Particles
- 7.4.2 External Fields
- 7.4.3 Interacting Particles
- 7.4.4 Multiplicative Noise
7.5 Numerical Examples
- 7.5.1 Living Crystals
- 7.5.2 Colloids with Short-Range Aligning Interaction
7.6 Conclusions
References

8 Active Fluids Within the Unified Coloured Noise Approximation

8.1 Introduction
- 8.1.1 The Genesis of the UCNA Model of Active Particles
8.2 The Unified Coloured Noise Approximation (UCNA)
- 8.2.1 Kinetic Approach
- 8.2.2 Stationary Solution in the Absence of Current
- 8.2.3 Fox Approximation
- 8.2.4 Entropy Production in UCNA
- 8.2.5 H-Theorem
8.3 Born–Green–Yvon Hierarchy in the Steady State
8.4 Active Pressure
8.5 Velocity Correlations
8.6 Simple Applications
- 8.6.1 Active Elastic Dumbbells
- 8.6.2 Pressure of N Noninteracting Active Particles Surrounded by Harshly Repulsive Walls
8.7 Active Particles in a Time-Dependent Potential
- 8.7.1 Effective Potential
- 8.7.2 Dynamical UCNA and Particle Density Profile
- 8.7.3 Average Drag Force
8.8 Conclusions
Appendix 1: Entropy Production and Heat Flux in the GCN
Appendix 2: Absence of Detailed Balance Condition in the GCN
References

9 Quadrature-Based Lattice Boltzmann Models for RarefiedGas Flow

9.1 Introduction
9.2 Generalities
9.3 One-Dimensional Quadrature-Based LB Models
- 9.3.1 Full-Range Gauss–Hermite Quadrature
- 9.3.2 Half-Range Gauss–Hermite Quadrature
9.4 LB Models in the Three-Dimensional Momentum Space
- 9.4.1 Reduced Distributions
- 9.4.2 Mixed Quadrature LB Models with Reduced Distribution Functions
- 9.4.3 The Lattice Boltzmann Equation
- 9.4.4 Non-Dimensionalisation Procedure
9.5 Simulation Results
- 9.5.1 Couette Flow Between Parallel Plates
- 9.5.2 Force-Driven Poiseuille Flow Between Parallel Plates
9.6 Conclusions
Appendix: Numerical Scheme
References

Index