Fluids, Colloids and Soft Materials

Alberto Fernandez-Nieves received his Ph.D. in Physics from the University of Granada and is Assistant Professor of Physics at the Georgia Institute of Technology. Before joining GeorgiaTech, he was Lecturer of Physics at the University of Almeria and studies the physics of soft materials with a focus on the connection between microscopic order and macroscopic properties.

Preface xv List of Contributors xvii

SECTION I FLUID FLOWS 1

1 Drop Generation in Controlled Fluid Flows 3
Elena Castro Hernandez, Josefa Guerrero, Alberto Fernandez-Nieves, & Jose M. Gordillo

1.1 Introduction, 3

1.2 Coflow, 4

1.2.1 Problem and Dimensionless Numbers, 4

1.2.2 Dripping and Jetting, 5

1.2.3 Narrowing Jets, 6

1.2.4 Unified Scaling of the Drop Size in Both Narrowing and Widening Regimes, 7

1.2.5 Convective Versus Absolute Instabilities, 9

1.3 Flow Focusing, 12

1.4 Summary and Outlook, 15

References, 15

2 Electric Field Effects 19
Francisco J. Higuera

2.1 Introduction, 19

2.2 Mathematical Formulation and Estimates, 20

2.2.1 Conical Meniscus, 22

2.2.2 Cone-to-Jet Transition Region and Beyond, 23

2.2.3 Very Viscous Liquids, 24

2.3 Applications and Extensions, 24

2.3.1 Multiplexing, 24

2.3.2 Coaxial Jet Electrosprays, 25

2.3.3 Electrodispersion in Dielectric Liquid Baths, 26

2.4 Conclusions, 27

References, 27

3 Fluid Flows for Engineering Complex Materials 29
Ignacio G. Loscertales

3.1 Introduction, 29

3.2 Single Fluid Micro- or Nanoparticles, 30

3.2.1 Flows Through Micron-Sized Apertures, 31

3.2.2 Microflows Driven by Hydrodynamic Focusing, 33

3.2.3 Micro- and Nanoflows Driven by Electric Forces, 34

3.3 Steady-state Complex Capillary Flows for Particles with Complex Structure, 36

3.3.1 Hydrodynamic Focusing, 36

3.3.2 Electrified Coaxial Jet, 38

3.4 Summary, 39

Acknowledgments, 41

References, 41

SECTION II COLLOIDS IN EXTERNAL FIELDS 43

4 Fluctuations in Particle Sedimentation 45
P.N. Segrè

4.1 Introduction, 45

4.2 Mean Sedimentation Rate, 45

4.2.1 Brownian Sedimentation, 46

4.2.2 Non-Brownian Sedimentation, 47

4.3 Velocity Fluctuations, 48

4.3.1 Introduction, 48

Caflisch and Luke Divergence Paradox, 48

4.3.2 Thin Cells and Quasi Steady-State Sedimentation, 49

Hydrodynamic Diffusion, 51

4.3.3 Thick Cells, Time-Dependent Sedimentation, and Stratification, 52

Time-Dependent Sedimentation, 52

Stratification Scaling Model, 54

4.3.4 Stratification Model in a Fluidized Bed, 55

4.4 Summary, 56

References, 57

5 Particles in Electric Fields 59
Todd M. Squires

5.1 Electrostatics in Electrolytes, 60

5.1.1 The Poisson–Boltzmann Equation, 61

5.1.2 Assumptions Underlying the Poisson–Boltzmann Equation, 62

5.1.3 Alternate Approach: The Electrochemical Potential, 63

5.1.4 Electrokinetics, 64

5.2 The Poisson–Nernst–Planck–Stokes Equations, 65

5.3 Electro-Osmotic Flows, 66

5.3.1 Alternate Approach: The Electrochemical Potential, 67

5.4 Electrophoresis, 68

5.4.1 Electrophoresis in the Thick Double-Layer Limit, 69

5.4.2 Electrophoresis in the Thin Double-Layer Limit, 69

5.4.3 Electrophoresis for Arbitrary Charge and Screening Length, 71

5.4.4 Concentration Polarization, 72

5.5 Nonlinear Electrokinetic Effects, 75

5.5.1 Induced-Charge Electrokinetics, 75

5.5.2 Dielectrophoresis, 76

5.5.3 Particle Interactions and Electrorheological Fluids, 77

5.6 Conclusions, 77

References, 78

6 Colloidal Dispersions in Shear Flow 81
Minne P. Lettinga

6.1 Introduction, 81

6.2 Basic Concepts of Rheology, 82

6.2.1 Definition of Shear Flow, 82

6.2.2 Scaling the Shear Rate, 83

6.2.3 Flow Instabilities, 84

6.3 Effect of Shear Flow on Crystallization of Colloidal Spheres, 86

6.3.1 Equilibrium Phase Behavior, 87

6.3.2 Nonequilibrium Phase Behavior, 87

6.3.3 The Effect on Flow Behavior, 91

6.4 Effect of Shear Flow on Gas–Liquid Phase Separating Colloidal Spheres, 92

6.4.1 Equilibrium Phase Behavior, 92

6.4.2 Nonequilibrium Phase Behavior, 95

6.4.3 The Effect on Flow Behavior, 98

6.5 Effect of Shear Flow on the Isotropic–Nematic Phase Transition of Colloidal Rods, 99

6.5.1 Equilibrium Phase Behavior: Isotropic–Nematic Phase Transition from a Dynamical Viewpoint, 100

6.5.2 Nonequilibrium Phase Behavior of Sheared Rods: Theory, 102

6.5.3 Nonequilibrium Phase Behavior of Sheared Rods: Experiment, 104

6.5.4 The Effect of the Isotropic–Nematic Transition on the Flow Behavior, 107

6.6 Concluding Remarks, 108

References, 109

7 Colloidal Interactions with Optical Fields: Optical Tweezers 111
David McGloin, Craig McDonald, & Yuri Belotti

7.1 Introduction, 111

7.2 Theory, 112

7.3 Experimental Systems, 114

7.3.1 Optical Tweezers, 114

7.3.2 Force Measuring Techniques, 116

7.3.3 Radiation Pressure Traps, 120

7.3.4 Beam Shaping Techniques, 121

7.4 Applications, 122

7.4.1 Colloidal Science, 122

7.4.2 Nanoparticles, 123

7.4.3 Colloidal Aerosols, 123

7.5 Conclusions, 125

References, 125

SECTION III EXPERIMENTAL TECHNIQUES 131

8 Scattering Techniques 133
Luca Cipelletti, Véronique Trappe, & David J. Pine

8.1 Introduction, 133

8.2 Light and Other Scattering Techniques, 134

8.3 Static Light Scattering, 135

8.3.1 Static Structure Factor, 136

8.3.2 Form Factor, 137

8.4 Dynamic Light Scattering, 138

8.4.1 Conventional Dynamic Light Scattering, 138

8.4.2 Diffusing Wave Spectroscopy, 139

8.4.3 Dynamic Light Scattering from Nonergodic Media, 142

8.4.4 Multispeckle Methods, 143

8.4.5 Time-Resolved Correlation, 143

8.5 Imaging and Scattering, 145

8.5.1 Photon Correlation Imaging, 145

8.5.2 Near Field Scattering, 146

8.5.3 Differential Dynamic Microscopy, 147

References, 148

9 Rheology of Soft Materials 149
Hans M. Wyss

9.1 Introduction, 149

9.2 Deformation and Flow: Basic Concepts, 150

9.2.1 Importance of Timescales, 150

9.3 Stress Relaxation Test: Time-Dependent Response, 151

9.3.1 The Linear Response Function G(t), 152

9.4 Oscillatory Rheology: Frequency-Dependent Response, 153

9.4.1 Storage Modulus G′ and Loss Modulus G′′, 153

9.4.2 Relation Between Frequency- and Time-Dependent Measurements, 154

9.5 Steady Shear Rheology, 154

9.6 Nonlinear Rheology, 155

9.6.1 Large Amplitude Oscillatory Shear (LAOS) Measurements, 155

9.6.2 Lissajous Curves and Geometrical Interpretation of LAOS Data, 155

9.6.3 Fourier Transform Rheology, 157

9.7 Examples of Typical Rheological Behavior for Different Soft Materials, 157

9.7.1 Soft Glassy Materials, 157

9.7.2 Gel Networks, 159

9.7.3 Biopolymer Networks: Strain-Stiffening Behavior, 160

9.8 Rheometers, 160

9.8.1 Rotational Rheometers, 160

9.8.2 Measuring Geometries, 160

9.8.3 Stress- and Strain-Controlled Rheometers, 161

9.9 Conclusions, 162

References, 162

10 Optical Microscopy of Soft Matter Systems 165
Taewoo Lee, Bohdan Senyuk, Rahul P. Trivedi, & Ivan I. Smalyukh

10.1 Introduction, 165

10.2 Basics of Optical Microscopy, 166

10.3 Bright Field and Dark Field Microscopy, 167

10.4 Polarizing Microscopy, 169

10.5 Differential Interference Contrast and Phase Contrast Microscopies, 170

10.6 Fluorescence Microscopy, 171

10.7 Fluorescence Confocal Microscopy, 172

10.8 Fluorescence Confocal Polarizing Microscopy, 174

10.9 Nonlinear Optical Microscopy, 176

10.9.1 Multiphoton Excitation Fluorescence Microscopy, 176

10.9.2 Multiharmonic Generation Microscopy, 177

10.9.3 Coherent Anti-Stokes Raman Scattering Microscopy, 178

10.9.4 Coherent Anti-Stokes Raman Scattering Polarizing Microscopy, 179

10.9.5 Stimulated Raman Scattering Microscopy, 180

10.10 Three-Dimensional Localization Using Engineered Point Spread Functions, 181

10.11 Integrating Three-Dimensional Imaging Systems With Optical Tweezers, 182

10.12 Outlook and Perspectives, 183

References, 184

SECTION IV COLLOIDAL PHASES 187

11 Colloidal Fluids 189
José Luis Arauz-Lara

11.1 Introduction, 189

11.2 Quasi-Two-Dimensional Colloidal Fluids, 190

11.3 Static Structure, 190

11.4 Model Pair Potential, 193

11.5 The Ornstein–Zernike Equation, 195

11.6 Static Structure Factor, 196

11.7 Self-Diffusion, 197

11.8 Dynamic Structure, 198

11.9 Conclusions, 200

Acknowledgments, 200

References, 200

12 Colloidal Crystallization 203
Zhengdong Cheng

12.1 Crystallization and Close Packing, 203

12.1.1 van der Waals Equation of State and Hard Spheres as Model for Simple Fluids, 204

12.1.2 The Realization of Colloidal Hard Spheres, 205

12.2 Crystallization of Hard Spheres, 208

12.2.1 Phase Behavior, 208

12.2.2 Equation of State of Hard Spheres, 210

12.2.3 Crystal Structures, 215

12.2.4 Crystallization Kinetics, 218

12.3 Crystallization of Charged Spheres, 229

12.3.1 Phase Behavior, 229

12.3.2 Crystallization Kinetics, 235

12.4 Crystallization of Microgel Particles, 237

12.4.1 Phase Behavior, 238

12.4.2 Crystallization and Melting Kinetics, 238

12.5 Conclusions and New Directions, 241

Acknowledgments, 242

References, 242

13 The Glass Transition 249
Johan Mattsson

13.1 Introduction, 249

13.2 Basics of Glass Formation, 250

13.2.1 Basics of Glass Formation in Molecular Systems, 250

13.2.2 Basics of Glass Formation in Colloidal Systems, 252

13.3 Structure of Molecular or Colloidal Glass-Forming Systems, 252

13.4 Dynamics of Glass-Forming Molecular Systems, 254

13.4.1 Relaxation Dynamics as Manifested in the Time Domain, 254

13.4.2 Relaxation Dynamics as Manifested in the Frequency Domain, 256

13.4.3 The Structural Relaxation Time, 258

13.4.4 The Stretching of the Structural Relaxation, 259

13.4.5 The Dynamic Crossover, 259

13.5 Dynamics of Glass-Forming Colloidal Systems, 262

13.5.1 General Behavior, 262

13.5.2 The Structural Relaxation, 263

13.5.3 The Dynamic Crossover, 264

13.5.4 “Fragility” in Colloidal Systems, 265

13.5.5 Glassy “Secondary” Relaxations, 266

13.6 Further Comparisons Between Molecular and Colloidal Glass Formation, 267

13.6.1 Dynamic Heterogeneity, 267

13.6.2 Decoupling of Translational and Rotational Diffusion, 269

13.6.3 The Vibrational Properties and the Boson Peak, 270

13.7 Theoretical Approaches to Understand Glass Formation, 271

13.7.1 Above the Dynamic Crossover: Mode Coupling Theory, 271

13.7.2 Below the Dynamic Crossover: Activated Dynamics, 273

13.8 Conclusions, 275

References, 276

14 Colloidal Gelation 279
Emanuela Del Gado, Davide Fiocco, Giuseppe Foffi, Suliana Manley, Veronique Trappe, & Alessio Zaccone

14.1 Introduction: What Is a Gel? 279

14.1.1 An Experimental Summary: How Is a Gel Made? 280

14.2 Colloid Interactions: Two Important Cases, 280

14.2.1 “Strong” Interactions: van der Waals Forces, 280

14.2.2 “Weak” Interactions: Depletion Interactions, 282

14.2.3 Putting It All Together, 285

14.3 Routes to Gelation, 285

14.3.1 Dynamic Scaling, 285

14.3.2 Fractal Aggregation, 287

14.4 Elasticity of Colloidal Gels, 288

14.4.1 Elasticity of Fractal Gels, 288

14.4.2 Deformations and Connectivity, 289

14.5 Conclusions, 290

References, 290

SECTION V OTHER SOFT MATERIALS 293

15 Emulsions 295
Sudeep K. Dutta, Elizabeth Knowlton, & Daniel L. Blair

15.1 Introduction, 295

15.1.1 Background, 295

15.2 Processing and Purification, 296

15.2.1 Creation and Stability, 296

15.2.2 Destabilization and Aggregation, 298

15.2.3 Coarsening, 298

15.2.4 Purification: Creaming and Depletion, 299

15.3 Emulsion Science, 300

15.3.1 Microfluidics: Emulsions on a Chip, 300

15.3.2 Dense Emulsions and Jamming, 300

15.3.3 The Jammed State, 301

15.3.4 The Flowing State, 304

15.4 Conclusions, 305

References, 305

16 An Introduction to the Physics of Liquid Crystals 307
Jan P. F. Lagerwall

16.1 Overview of This Chapter, 307

16.2 Liquid Crystal Classes and Phases, 308

16.2.1 The Foundations: Long-Range Order, the Nematic Phase, and the Director Concept, 308

16.2.2 Thermotropics and Lyotropics: The Two Liquid Crystal Classes, 308

16.2.3 The Smectic and Lamellar Phases, 311

16.2.4 The Columnar Phases, 313

16.2.5 Chiral Liquid Crystal Phases, 314

16.2.6 Liquid Crystal Polymorphism, 316

16.3 The Anisotropic Physical Properties of Liquid Crystals, 317

16.3.1 The Orientational Order Parameter, 317

16.3.2 Optical Anisotropy, 318

16.3.3 Dielectric, Conductive, and Magnetic Anisotropy and the Response to Electric and Magnetic Fields, 321

16.3.4 The Viscous Properties of Liquid Crystals, 323

16.4 Deformations and Singularities in The Director Field, 325

16.4.1 Liquid Crystal Elasticity, 325

16.4.2 The Characteristic Topological Defects of Liquid Crystals, 327

16.5 The Special Physical Properties of Chiral Liquid Crystals, 330

16.5.1 Optical Activity and Selective Reflection, 330

16.6 Some Examples From Present-Day Liquid Crystal Research, 332

16.6.1 Colloid Particles in Liquid Crystals and Liquid Crystalline Colloid Particles, 333

16.6.2 Biodetection with Liquid Crystals, 333

16.6.3 Templating and Nano-/Microstructuring Using Liquid Crystals, 334

16.6.4 Liquid Crystals for Photovoltaic and Electromechanical Energy Conversion, 334

16.6.5 Lipidomics and the Liquid Crystal Phases of Cell Membranes, 336

16.6.6 Active Nematics, 336

References, 336

17 Entangled Granular Media 341
Nick Gravish & Daniel I. Goldman

17.1 Granular Materials, 342

17.1.1 Dry, Convex Particles, 342

17.1.2 Cohesion through Fluids, 343

17.1.3 Cohesion through Shape, 343

17.1.4 Characterize the Rheology of Granular Materials, 344

17.2 Experiment, 345

17.2.1 Experimental Apparatus, 345

17.2.2 Packing Experiments, 346

17.2.3 Collapse Experiments, 346

17.3 Simulation, 348

17.3.1 Random Contact Model of Rods, 348

17.3.2 Packing Simulations, 350

17.4 Conclusions, 352

Acknowledgments, 352

References, 352

18 Foams 355
Reinhard Ḧohler & Sylvie Cohen-Addad

18.1 Introduction, 355

18.2 Equilibrium Structures, 356

18.2.1 Equilibrium Conditions, 356

18.2.2 Geometrical and Topological Properties, 358

18.2.3 Static Bubble Interactions, 358

18.3 Aging, 359

18.3.1 Drainage, 359

18.3.2 Coarsening, 360

18.3.3 Coalescence, 361

18.4 Rheology, 361

18.4.1 Elastic Response, 361

18.4.2 Linear Viscoelasticity, 362

18.4.3 Yielding and Plastic Flow, 363

18.4.4 Viscous Flow, 364

18.4.5 Rheology near the Jamming Transition, 365

References, 366

SECTION VI ORDERED MATERIALS IN CURVED SPACES 369

19 Crystals and Liquid Crystals Confined to Curved Geometries 371
Vinzenz Koning, & Vincenzo Vitelli

19.1 Introduction, 371

19.2 Crystalline Solids and Liquid Crystals, 373

19.3 Differential Geometry of Surfaces, 373

19.3.1 Preliminaries, 373

19.3.2 Curvature, 374

19.3.3 Monge Gauge, 375

19.4 Elasticity on Curved Surfaces and in Confined Geometries, 375

19.4.1 Elasticity of a Two-Dimensional Nematic Liquid Crystal, 375

19.4.2 Elasticity of a Two-Dimensional Solid, 376

19.4.3 Elasticity of a Three-dimensional Nematic Liquid Crystal, 377

19.5 Topological Defects, 377

19.5.1 Disclinations in a Nematic, 377

19.5.2 Disclinations in a Crystal, 378

19.5.3 Dislocations, 378

19.6 Interaction Between Curvature and Defects, 379

19.6.1 Coupling in Liquid Crystals, 379

19.6.2 Coupling in Crystals, 379

19.6.3 Screening by Dislocations and Pleats, 381

19.6.4 Geometrical Potentials and Forces, 381

19.7 Nematics in Spherical Geometries, 381

19.7.1 Nematic Order on the Sphere, 381

19.7.2 Beyond Two Dimensions: Spherical Nematic Shells, 382

19.8 Toroidal Nematics, 383

19.9 Concluding Remarks, 383

References, 383

20 Nematics on Curved Surfaces – Computer Simulations of Nematic Shells 387
Martin Bates

20.1 Introduction, 387

20.2 Theory, 388

20.3 Experiments on Spherical Shells, 389

20.3.1 Nematics, 389

20.3.2 Smectics, 391

20.4 Computer Simulations – Practicalities, 392

20.4.1 Introduction, 392

20.4.2 Monte Carlo Simulations, 393

20.5 Computer Simulations of Nematic Shells, 395

20.5.1 Spherical Shells, 395

20.5.2 Nonspherical Shells, 397

20.6 Conclusions, 399

References, 401

Index 403