This book presents a compilation of self-contained chapters covering a wide range of topics within the broad field of soft condensed matter. Each chapter starts with basic definitions to bring the reader up-to-date on the topic at hand, describing how to use fluid flows to generate soft materials of high value either for applications or for basic research. Coverage includes topics related to colloidal suspensions and soft materials and how they differ in behavior, along with a roadmap for researchers on how to use soft materials to study relevant physics questions related to geometrical frustration.
Table of Contents:
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
About the Author :
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.
