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 xviiSECTION I FLUID FLOWS 11 Drop Generation in Controlled Fluid Flows 3Elena Castro Hernandez, Josefa Guerrero, Alberto Fernandez-Nieves, & Jose M. Gordillo1.1 Introduction, 31.2 Coflow, 41.2.1 Problem and Dimensionless Numbers, 41.2.2 Dripping and Jetting, 51.2.3 Narrowing Jets, 61.2.4 Unified Scaling of the Drop Size in Both Narrowing and Widening Regimes, 71.2.5 Convective Versus Absolute Instabilities, 91.3 Flow Focusing, 121.4 Summary and Outlook, 15References, 152 Electric Field Effects 19Francisco J. Higuera2.1 Introduction, 192.2 Mathematical Formulation and Estimates, 202.2.1 Conical Meniscus, 222.2.2 Cone-to-Jet Transition Region and Beyond, 232.2.3 Very Viscous Liquids, 242.3 Applications and Extensions, 242.3.1 Multiplexing, 242.3.2 Coaxial Jet Electrosprays, 252.3.3 Electrodispersion in Dielectric Liquid Baths, 262.4 Conclusions, 27References, 273 Fluid Flows for Engineering Complex Materials 29Ignacio G. Loscertales3.1 Introduction, 293.2 Single Fluid Micro- or Nanoparticles, 303.2.1 Flows Through Micron-Sized Apertures, 313.2.2 Microflows Driven by Hydrodynamic Focusing, 333.2.3 Micro- and Nanoflows Driven by Electric Forces, 343.3 Steady-state Complex Capillary Flows for Particles with Complex Structure, 363.3.1 Hydrodynamic Focusing, 363.3.2 Electrified Coaxial Jet, 383.4 Summary, 39Acknowledgments, 41References, 41SECTION II COLLOIDS IN EXTERNAL FIELDS 434 Fluctuations in Particle Sedimentation 45P.N. Segrè4.1 Introduction, 454.2 Mean Sedimentation Rate, 454.2.1 Brownian Sedimentation, 464.2.2 Non-Brownian Sedimentation, 474.3 Velocity Fluctuations, 484.3.1 Introduction, 48Caflisch and Luke Divergence Paradox, 484.3.2 Thin Cells and Quasi Steady-State Sedimentation, 49Hydrodynamic Diffusion, 514.3.3 Thick Cells, Time-Dependent Sedimentation, and Stratification, 52Time-Dependent Sedimentation, 52Stratification Scaling Model, 544.3.4 Stratification Model in a Fluidized Bed, 554.4 Summary, 56References, 575 Particles in Electric Fields 59Todd M. Squires5.1 Electrostatics in Electrolytes, 605.1.1 The Poisson–Boltzmann Equation, 615.1.2 Assumptions Underlying the Poisson–Boltzmann Equation, 625.1.3 Alternate Approach: The Electrochemical Potential, 635.1.4 Electrokinetics, 645.2 The Poisson–Nernst–Planck–Stokes Equations, 655.3 Electro-Osmotic Flows, 665.3.1 Alternate Approach: The Electrochemical Potential, 675.4 Electrophoresis, 685.4.1 Electrophoresis in the Thick Double-Layer Limit, 695.4.2 Electrophoresis in the Thin Double-Layer Limit, 695.4.3 Electrophoresis for Arbitrary Charge and Screening Length, 715.4.4 Concentration Polarization, 725.5 Nonlinear Electrokinetic Effects, 755.5.1 Induced-Charge Electrokinetics, 755.5.2 Dielectrophoresis, 765.5.3 Particle Interactions and Electrorheological Fluids, 775.6 Conclusions, 77References, 786 Colloidal Dispersions in Shear Flow 81Minne P. Lettinga6.1 Introduction, 816.2 Basic Concepts of Rheology, 826.2.1 Definition of Shear Flow, 826.2.2 Scaling the Shear Rate, 836.2.3 Flow Instabilities, 846.3 Effect of Shear Flow on Crystallization of Colloidal Spheres, 866.3.1 Equilibrium Phase Behavior, 876.3.2 Nonequilibrium Phase Behavior, 876.3.3 The Effect on Flow Behavior, 916.4 Effect of Shear Flow on Gas–Liquid Phase Separating Colloidal Spheres, 926.4.1 Equilibrium Phase Behavior, 926.4.2 Nonequilibrium Phase Behavior, 956.4.3 The Effect on Flow Behavior, 986.5 Effect of Shear Flow on the Isotropic–Nematic Phase Transition of Colloidal Rods, 996.5.1 Equilibrium Phase Behavior: Isotropic–Nematic Phase Transition from a Dynamical Viewpoint, 1006.5.2 Nonequilibrium Phase Behavior of Sheared Rods: Theory, 1026.5.3 Nonequilibrium Phase Behavior of Sheared Rods: Experiment, 1046.5.4 The Effect of the Isotropic–Nematic Transition on the Flow Behavior, 1076.6 Concluding Remarks, 108References, 1097 Colloidal Interactions with Optical Fields: Optical Tweezers 111David McGloin, Craig McDonald, & Yuri Belotti7.1 Introduction, 1117.2 Theory, 1127.3 Experimental Systems, 1147.3.1 Optical Tweezers, 1147.3.2 Force Measuring Techniques, 1167.3.3 Radiation Pressure Traps, 1207.3.4 Beam Shaping Techniques, 1217.4 Applications, 1227.4.1 Colloidal Science, 1227.4.2 Nanoparticles, 1237.4.3 Colloidal Aerosols, 1237.5 Conclusions, 125References, 125SECTION III EXPERIMENTAL TECHNIQUES 1318 Scattering Techniques 133Luca Cipelletti, Véronique Trappe, & David J. Pine8.1 Introduction, 1338.2 Light and Other Scattering Techniques, 1348.3 Static Light Scattering, 1358.3.1 Static Structure Factor, 1368.3.2 Form Factor, 1378.4 Dynamic Light Scattering, 1388.4.1 Conventional Dynamic Light Scattering, 1388.4.2 Diffusing Wave Spectroscopy, 1398.4.3 Dynamic Light Scattering from Nonergodic Media, 1428.4.4 Multispeckle Methods, 1438.4.5 Time-Resolved Correlation, 1438.5 Imaging and Scattering, 1458.5.1 Photon Correlation Imaging, 1458.5.2 Near Field Scattering, 1468.5.3 Differential Dynamic Microscopy, 147References, 1489 Rheology of Soft Materials 149Hans M. Wyss9.1 Introduction, 1499.2 Deformation and Flow: Basic Concepts, 1509.2.1 Importance of Timescales, 1509.3 Stress Relaxation Test: Time-Dependent Response, 1519.3.1 The Linear Response Function G(t), 1529.4 Oscillatory Rheology: Frequency-Dependent Response, 1539.4.1 Storage Modulus G′ and Loss Modulus G′′, 1539.4.2 Relation Between Frequency- and Time-Dependent Measurements, 1549.5 Steady Shear Rheology, 1549.6 Nonlinear Rheology, 1559.6.1 Large Amplitude Oscillatory Shear (LAOS) Measurements, 1559.6.2 Lissajous Curves and Geometrical Interpretation of LAOS Data, 1559.6.3 Fourier Transform Rheology, 1579.7 Examples of Typical Rheological Behavior for Different Soft Materials, 1579.7.1 Soft Glassy Materials, 1579.7.2 Gel Networks, 1599.7.3 Biopolymer Networks: Strain-Stiffening Behavior, 1609.8 Rheometers, 1609.8.1 Rotational Rheometers, 1609.8.2 Measuring Geometries, 1609.8.3 Stress- and Strain-Controlled Rheometers, 1619.9 Conclusions, 162References, 16210 Optical Microscopy of Soft Matter Systems 165Taewoo Lee, Bohdan Senyuk, Rahul P. Trivedi, & Ivan I. Smalyukh10.1 Introduction, 16510.2 Basics of Optical Microscopy, 16610.3 Bright Field and Dark Field Microscopy, 16710.4 Polarizing Microscopy, 16910.5 Differential Interference Contrast and Phase Contrast Microscopies, 17010.6 Fluorescence Microscopy, 17110.7 Fluorescence Confocal Microscopy, 17210.8 Fluorescence Confocal Polarizing Microscopy, 17410.9 Nonlinear Optical Microscopy, 17610.9.1 Multiphoton Excitation Fluorescence Microscopy, 17610.9.2 Multiharmonic Generation Microscopy, 17710.9.3 Coherent Anti-Stokes Raman Scattering Microscopy, 17810.9.4 Coherent Anti-Stokes Raman Scattering Polarizing Microscopy, 17910.9.5 Stimulated Raman Scattering Microscopy, 18010.10 Three-Dimensional Localization Using Engineered Point Spread Functions, 18110.11 Integrating Three-Dimensional Imaging Systems With Optical Tweezers, 18210.12 Outlook and Perspectives, 183References, 184SECTION IV COLLOIDAL PHASES 18711 Colloidal Fluids 189José Luis Arauz-Lara11.1 Introduction, 18911.2 Quasi-Two-Dimensional Colloidal Fluids, 19011.3 Static Structure, 19011.4 Model Pair Potential, 19311.5 The Ornstein–Zernike Equation, 19511.6 Static Structure Factor, 19611.7 Self-Diffusion, 19711.8 Dynamic Structure, 19811.9 Conclusions, 200Acknowledgments, 200References, 20012 Colloidal Crystallization 203Zhengdong Cheng12.1 Crystallization and Close Packing, 20312.1.1 van der Waals Equation of State and Hard Spheres as Model for Simple Fluids, 20412.1.2 The Realization of Colloidal Hard Spheres, 20512.2 Crystallization of Hard Spheres, 20812.2.1 Phase Behavior, 20812.2.2 Equation of State of Hard Spheres, 21012.2.3 Crystal Structures, 21512.2.4 Crystallization Kinetics, 21812.3 Crystallization of Charged Spheres, 22912.3.1 Phase Behavior, 22912.3.2 Crystallization Kinetics, 23512.4 Crystallization of Microgel Particles, 23712.4.1 Phase Behavior, 23812.4.2 Crystallization and Melting Kinetics, 23812.5 Conclusions and New Directions, 241Acknowledgments, 242References, 24213 The Glass Transition 249Johan Mattsson13.1 Introduction, 24913.2 Basics of Glass Formation, 25013.2.1 Basics of Glass Formation in Molecular Systems, 25013.2.2 Basics of Glass Formation in Colloidal Systems, 25213.3 Structure of Molecular or Colloidal Glass-Forming Systems, 25213.4 Dynamics of Glass-Forming Molecular Systems, 25413.4.1 Relaxation Dynamics as Manifested in the Time Domain, 25413.4.2 Relaxation Dynamics as Manifested in the Frequency Domain, 25613.4.3 The Structural Relaxation Time, 25813.4.4 The Stretching of the Structural Relaxation, 25913.4.5 The Dynamic Crossover, 25913.5 Dynamics of Glass-Forming Colloidal Systems, 26213.5.1 General Behavior, 26213.5.2 The Structural Relaxation, 26313.5.3 The Dynamic Crossover, 26413.5.4 “Fragility” in Colloidal Systems, 26513.5.5 Glassy “Secondary” Relaxations, 26613.6 Further Comparisons Between Molecular and Colloidal Glass Formation, 26713.6.1 Dynamic Heterogeneity, 26713.6.2 Decoupling of Translational and Rotational Diffusion, 26913.6.3 The Vibrational Properties and the Boson Peak, 27013.7 Theoretical Approaches to Understand Glass Formation, 27113.7.1 Above the Dynamic Crossover: Mode Coupling Theory, 27113.7.2 Below the Dynamic Crossover: Activated Dynamics, 27313.8 Conclusions, 275References, 27614 Colloidal Gelation 279Emanuela Del Gado, Davide Fiocco, Giuseppe Foffi, Suliana Manley, Veronique Trappe, & Alessio Zaccone14.1 Introduction: What Is a Gel? 27914.1.1 An Experimental Summary: How Is a Gel Made? 28014.2 Colloid Interactions: Two Important Cases, 28014.2.1 “Strong” Interactions: van der Waals Forces, 28014.2.2 “Weak” Interactions: Depletion Interactions, 28214.2.3 Putting It All Together, 28514.3 Routes to Gelation, 28514.3.1 Dynamic Scaling, 28514.3.2 Fractal Aggregation, 28714.4 Elasticity of Colloidal Gels, 28814.4.1 Elasticity of Fractal Gels, 28814.4.2 Deformations and Connectivity, 28914.5 Conclusions, 290References, 290SECTION V OTHER SOFT MATERIALS 29315 Emulsions 295Sudeep K. Dutta, Elizabeth Knowlton, & Daniel L. Blair15.1 Introduction, 29515.1.1 Background, 29515.2 Processing and Purification, 29615.2.1 Creation and Stability, 29615.2.2 Destabilization and Aggregation, 29815.2.3 Coarsening, 29815.2.4 Purification: Creaming and Depletion, 29915.3 Emulsion Science, 30015.3.1 Microfluidics: Emulsions on a Chip, 30015.3.2 Dense Emulsions and Jamming, 30015.3.3 The Jammed State, 30115.3.4 The Flowing State, 30415.4 Conclusions, 305References, 30516 An Introduction to the Physics of Liquid Crystals 307Jan P. F. Lagerwall16.1 Overview of This Chapter, 30716.2 Liquid Crystal Classes and Phases, 30816.2.1 The Foundations: Long-Range Order, the Nematic Phase, and the Director Concept, 30816.2.2 Thermotropics and Lyotropics: The Two Liquid Crystal Classes, 30816.2.3 The Smectic and Lamellar Phases, 31116.2.4 The Columnar Phases, 31316.2.5 Chiral Liquid Crystal Phases, 31416.2.6 Liquid Crystal Polymorphism, 31616.3 The Anisotropic Physical Properties of Liquid Crystals, 31716.3.1 The Orientational Order Parameter, 31716.3.2 Optical Anisotropy, 31816.3.3 Dielectric, Conductive, and Magnetic Anisotropy and the Response to Electric and Magnetic Fields, 32116.3.4 The Viscous Properties of Liquid Crystals, 32316.4 Deformations and Singularities in The Director Field, 32516.4.1 Liquid Crystal Elasticity, 32516.4.2 The Characteristic Topological Defects of Liquid Crystals, 32716.5 The Special Physical Properties of Chiral Liquid Crystals, 33016.5.1 Optical Activity and Selective Reflection, 33016.6 Some Examples From Present-Day Liquid Crystal Research, 33216.6.1 Colloid Particles in Liquid Crystals and Liquid Crystalline Colloid Particles, 33316.6.2 Biodetection with Liquid Crystals, 33316.6.3 Templating and Nano-/Microstructuring Using Liquid Crystals, 33416.6.4 Liquid Crystals for Photovoltaic and Electromechanical Energy Conversion, 33416.6.5 Lipidomics and the Liquid Crystal Phases of Cell Membranes, 33616.6.6 Active Nematics, 336References, 33617 Entangled Granular Media 341Nick Gravish & Daniel I. Goldman17.1 Granular Materials, 34217.1.1 Dry, Convex Particles, 34217.1.2 Cohesion through Fluids, 34317.1.3 Cohesion through Shape, 34317.1.4 Characterize the Rheology of Granular Materials, 34417.2 Experiment, 34517.2.1 Experimental Apparatus, 34517.2.2 Packing Experiments, 34617.2.3 Collapse Experiments, 34617.3 Simulation, 34817.3.1 Random Contact Model of Rods, 34817.3.2 Packing Simulations, 35017.4 Conclusions, 352Acknowledgments, 352References, 35218 Foams 355Reinhard Ḧohler & Sylvie Cohen-Addad18.1 Introduction, 35518.2 Equilibrium Structures, 35618.2.1 Equilibrium Conditions, 35618.2.2 Geometrical and Topological Properties, 35818.2.3 Static Bubble Interactions, 35818.3 Aging, 35918.3.1 Drainage, 35918.3.2 Coarsening, 36018.3.3 Coalescence, 36118.4 Rheology, 36118.4.1 Elastic Response, 36118.4.2 Linear Viscoelasticity, 36218.4.3 Yielding and Plastic Flow, 36318.4.4 Viscous Flow, 36418.4.5 Rheology near the Jamming Transition, 365References, 366SECTION VI ORDERED MATERIALS IN CURVED SPACES 36919 Crystals and Liquid Crystals Confined to Curved Geometries 371Vinzenz Koning, & Vincenzo Vitelli19.1 Introduction, 37119.2 Crystalline Solids and Liquid Crystals, 37319.3 Differential Geometry of Surfaces, 37319.3.1 Preliminaries, 37319.3.2 Curvature, 37419.3.3 Monge Gauge, 37519.4 Elasticity on Curved Surfaces and in Confined Geometries, 37519.4.1 Elasticity of a Two-Dimensional Nematic Liquid Crystal, 37519.4.2 Elasticity of a Two-Dimensional Solid, 37619.4.3 Elasticity of a Three-dimensional Nematic Liquid Crystal, 37719.5 Topological Defects, 37719.5.1 Disclinations in a Nematic, 37719.5.2 Disclinations in a Crystal, 37819.5.3 Dislocations, 37819.6 Interaction Between Curvature and Defects, 37919.6.1 Coupling in Liquid Crystals, 37919.6.2 Coupling in Crystals, 37919.6.3 Screening by Dislocations and Pleats, 38119.6.4 Geometrical Potentials and Forces, 38119.7 Nematics in Spherical Geometries, 38119.7.1 Nematic Order on the Sphere, 38119.7.2 Beyond Two Dimensions: Spherical Nematic Shells, 38219.8 Toroidal Nematics, 38319.9 Concluding Remarks, 383References, 38320 Nematics on Curved Surfaces – Computer Simulations of Nematic Shells 387Martin Bates20.1 Introduction, 38720.2 Theory, 38820.3 Experiments on Spherical Shells, 38920.3.1 Nematics, 38920.3.2 Smectics, 39120.4 Computer Simulations – Practicalities, 39220.4.1 Introduction, 39220.4.2 Monte Carlo Simulations, 39320.5 Computer Simulations of Nematic Shells, 39520.5.1 Spherical Shells, 39520.5.2 Nonspherical Shells, 39720.6 Conclusions, 399References, 401Index 403