Table Of ContentColloidal Active
Matter
What do bird flocks, bacterial swarms, cell tissues, and cytoskeletal fluids
have in common? They are all examples of active matter. This book ex-
plores how scientists in various disciplines, from physics to biology, have
collated a solid corpus of experimental designs and theories during the last
two decades to decipher active systems.
The book addresses, from a multidisciplinary viewpoint, the field of ac-
tive matter at a colloidal scale. Concepts, experiments, and theoretical
models are put side by side to fully illuminate the subtilities of active sys-
tems. A large variety of subjects, from microswimmers or driven colloids
to self-organized active fluids, are analysed within a unified perspective.
Generic collective effects of self-propelled or driven colloids, such as motil-
ity-induced flocking, and new paradigms, such as the celebrated concept
of active nematics in reconstituted protein-based fluids, are discussed us-
ing well-known experimental scenarios and recognized theories. Topics are
covered with rigor and in a self-consistent way, reaching both practitioners
and newcomers to the field.
The diversity of topics and conceptual challenges in active matter have long
hampered the chance to explore the field with a general perspective. This
monograph, the first single-authored title on active matter, is intended to
fill this gap by bridging disparate experimental and theoretical interests
from colloidal soft matter to cell biophysics.
Francesc Sagués Mestre, Universitat de Barcelona.
Advances in Biochemistry and Biophysics
This monograph series offers expert summaries of cutting edge topics across all
areas of biological physics. Individual titles address such topics as molecular bio-
physics, statistical biophysics, molecular modeling, single-molecule biophysics,
and chemical biophysics. The goal of the series is to facilitate interdisciplinary
research by training biologists and biochemists in quantitative aspects of modern
biomedical research and to teach key biological principles to advanced students
in physical sciences and engineering.
Pulling Rabbits Out of Hats
Using Mathematical Modeling in the Material, Biophysical, Fluid Mechanical,
and Chemical Sciences
David Wollkind, Bonni J. Dichone
Colloidal active matter
Concepts, experimental realizations and models
Francesc Sagués Mestre
Colloidal Active
Matter
Concepts, Experimental
Realizations, and Models
Francesc Sagués Mestre
First edition published 2023
by CRC Press
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© 2023 Francesc Sagués Mestre
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ISBN: 978-1-032-28894-9 (hbk)
ISBN: 978-1-032-29840-5 (pbk)
ISBN: 978-1-003-30229-2 (ebk)
DOI: 10.1201/9781003302292
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Publisher’s note: This book has been prepared from camera-ready copy provided by the authors.
To my dog
and my cat.
Contents
Preface xi
List of Figures xv
Symbols xix
1 Introduction 1
2 Fundamental Concepts: Isotropic and Anisotropic Colloidal
Suspensions 3
2.1 Isotropic Dilute Suspensions . . . . . . . . . . . . . . . . . . 5
2.1.1 Microscopic Colloidal Behavior: Diffusion,
Sedimentation and Random Walk Models . . . . . . . 5
2.1.2 The Boundary Layer Concept: Electrically Charged
Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.3 Effects of Polymers on Colloidal Stability . . . . . . . 10
2.2 Anisotropic Dense Suspensions: Colloidal Liquid Crystals . . 12
2.2.1 The Role of Colloid Shape and Concentration . . . . . 12
2.2.2 Basic Concepts of Liquid Crystals: Phases and Order
Parameter . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.3 Long- and Short-Range Order: Orientational
Distortions and Defects . . . . . . . . . . . . . . . . . 16
2.3 A Composite System: Nematic Colloids . . . . . . . . . . . . 18
3 Particle-based Active Systems 23
3.1 Self-propelled Swimmers . . . . . . . . . . . . . . . . . . . . 25
3.1.1 Self-phoretic Swimmers and their Active Brownian
Particle (ABP) Models. . . . . . . . . . . . . . . . . . 26
3.1.1.1 General Concepts . . . . . . . . . . . . . . . 26
3.1.1.2 Experimental Realizations of Phoretic
Swimmers. . . . . . . . . . . . . . . . . . . . 29
3.1.1.3 Basic Statistical Properties of Self-phoretic
Swimmers: Diffusion and Sedimentation . . . 32
3.1.1.4 The Active Brownian Model . . . . . . . . . 34
3.1.2 Swimmers Based on Marangoni Flows . . . . . . . . . 38
3.1.3 Biological Microswimmers . . . . . . . . . . . . . . . . 40
3.1.3.1 Flagellated Bacteria . . . . . . . . . . . . . . 40
vii
viii Contents
3.1.3.2 Other Biological Microswimmers . . . . . . . 41
3.2 Colloids Driven to Swim . . . . . . . . . . . . . . . . . . . . 42
3.2.1 Magnetic Forcing . . . . . . . . . . . . . . . . . . . . . 42
3.2.1.1 A Doublet Roller. . . . . . . . . . . . . . . . 43
3.2.1.2 A Magnetically Driven Magnetic Snake . . . 46
3.2.1.3 Magnetic Spinners . . . . . . . . . . . . . . . 47
3.2.2 Electric Forcing: Quincke Rollers under DC Driving . 50
3.2.3 ElectricForcing:ClassicalFixed-ChargeElectroosmotic
Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.4 Induced-Charge Electrophoresis under AC Driving . . 55
3.2.4.1 Induced-Charge Electrophoresis . . . . . . . 55
3.2.4.2 Liquid Crystal-Enabled Electrophoresis . . . 57
3.2.4.3 AnomalousStatisticalCharacteristicsofDriven
Nematic Colloids . . . . . . . . . . . . . . . . 61
3.3 Brief Commented List of Selected Review Papers . . . . . . 67
4 Protein-based Active Fluids 71
4.1 Active Gels Based on Filamentary Proteins . . . . . . . . . . 72
4.1.1 Active Gels Based on Actin Filaments . . . . . . . . . 72
4.1.2 Active Gels Based on Microtubules . . . . . . . . . . . 73
4.1.2.1 Historic Antecedents . . . . . . . . . . . . . . 73
4.1.2.2 The Brandeis Approach . . . . . . . . . . . . 74
4.2 Two-dimensional Active Nematics . . . . . . . . . . . . . . . 77
4.2.1 Active Nematics Based on Microtubules . . . . . . . . 77
4.2.2 Active Nematics Based on Actin Filaments . . . . . . 83
4.3 The Effect of the Interface on Two-Dimensional Active
Nematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.3.1 Aqueous Active Nematics Interfaced with Isotropic Oils 84
4.3.2 Aqueous Active Nematics Interfaced with Anisotropic
Oils . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.4 Effects of Spatial Confinement . . . . . . . . . . . . . . . . . 93
4.4.1 Encapsulated Active Nematics . . . . . . . . . . . . . 93
4.4.2 Geometric Confinement of Active Nematics . . . . . . 99
4.4.3 A New Concept: Active Boundary Layers . . . . . . . 103
4.4.4 Geometric Confinement of Active Gels . . . . . . . . . 106
4.5 Recent Advances in the Preparation of Active Gels and Active
Nematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5 Emerging Concepts in Active Matter 115
5.1 Dynamic Clustering and Swarming Behavior . . . . . . . . . 116
5.1.1 Experimental Observations of Dynamic Clustering . . 117
5.1.2 Modeling Approaches to Clustering of Microswimmers 121
5.2 Motility-Induced Phase Separation . . . . . . . . . . . . . . . 122
5.3 Active Turbulence . . . . . . . . . . . . . . . . . . . . . . . . 128
5.4 Thermodynamic Concepts in Active Matter . . . . . . . . . . 132
Contents ix
5.4.1 Active Temperature . . . . . . . . . . . . . . . . . . . 132
5.4.2 Active Pressure . . . . . . . . . . . . . . . . . . . . . . 133
6 Modeling Active Fluids 139
6.1 Linearized Leslie-Ericksen Theories for Active Polar Fluids . 140
6.1.1 General Scheme of Equations . . . . . . . . . . . . . . 141
6.1.2 Analysis of +1 Defects: Asters, Vortices, and Spirals . 146
6.1.3 Activity-Induced Flows from Aligned States . . . . . . 148
6.1.4 MinimalVersionforaTwo-DimensionalActiveNematic
in Absence of Flow-Alignment . . . . . . . . . . . . . 151
6.2 A Beris-Edwards Approach to Model Active Nematics . . . . 155
6.2.1 General Scheme of Equations . . . . . . . . . . . . . . 155
6.2.2 A Simplified Analysis of Defect Dynamics . . . . . . . 157
6.2.3 Theoretical Description of Active Nematic Turbulence 160
6.3 Modeling Interfaced Active Fluids . . . . . . . . . . . . . . . 163
6.4 Modeling Confined Active Fluids . . . . . . . . . . . . . . . . 171
6.4.1 Modeling Active Flows in Thin Films and Droplets . . 171
6.4.1.1 Thin Active Films . . . . . . . . . . . . . . . 171
6.4.1.2 Active Droplets . . . . . . . . . . . . . . . . 174
6.4.2 Modeling Active Flows under Geometric Confinement 179
6.5 Brief Commented List of Selected Review Papers . . . . . . 183
7 Concepts and Models for Dry Active Matter 187
7.1 Hydrodynamic-like Theories . . . . . . . . . . . . . . . . . . 189
7.1.1 Flocking of Active Polar Particles. . . . . . . . . . . . 189
7.1.1.1 Giant Number Fluctuations . . . . . . . . . . 192
7.1.2 Particles Interacting Nematically on a Substrate . . . 194
7.1.3 Self-Propelled Rods with Nematic Alignment . . . . . 197
7.2 Microscopic-like Theories . . . . . . . . . . . . . . . . . . . . 199
7.2.1 Particle-Based Models for Dry Systems . . . . . . . . 199
7.2.2 Common Rationale: Phase-Separated Regimes . . . . 202
7.2.3 Specific Class-Dependent Features . . . . . . . . . . . 203
7.2.3.1 Traveling Bands in Polar Class . . . . . . . . 203
7.2.3.2 Unstable Nematic Bands . . . . . . . . . . . 204
7.2.4 Properties of the Liquid Ordered Phase . . . . . . . . 205
8 Appendix 1: Microswimming in Constrained and Disordered
Environments 207
8.1 Microswimming under Constrained Motion . . . . . . . . . . 207
8.2 Microswimming under the Effects of Noise and Disorder . . . 211
9 Appendix 2: Microswimming in Complex Fluids 217
9.1 Motion of Microorganisms in Complex Fluids . . . . . . . . . 217
9.2 Artificial Microswimmers Performing in Complex Fluids . . . 219
9.3 Theoretical Approaches to Microswimming in Complex Fluids 222
