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Collective dynamics of self-propelled particles : waves, vortex, swarm, braiding Jean-Baptiste Caussin To cite this version: Jean-Baptiste Caussin. Collective dynamics of self-propelled particles : waves, vortex, swarm, braiding. Other [cond-mat.other]. Ecole normale sup´erieurede lyon - ENS LYON, 2015. En- glish. <NNT : 2015ENSL0996>. <tel-01170988> HAL Id: tel-01170988 https://tel.archives-ouvertes.fr/tel-01170988 Submitted on 2 Jul 2015 HAL is a multi-disciplinary open access L'archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destin´eeau d´ep^otet `ala diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publi´esou non, lished or not. The documents may come from ´emanant des ´etablissements d'enseignement et de teaching and research institutions in France or recherche fran¸caisou ´etrangers,des laboratoires abroad, or from public or private research centers. publics ou priv´es. THÈSE en vue de l’obtention du grade de Docteur de l’Université de Lyon, délivré par l’École Normale Supérieure de Lyon Discipline : PHYSIQUE Laboratoire de Physique de l’ENS de LYON École Doctorale de Physique et d’Astrophysique de Lyon Dynamique collective de particules auto-propulsées : ondes, vortex, essaim, tressage Collective dynamics of self-propelled particles: waves, vortex, swarm, braiding Présentée par Jean-Baptiste CAUSSIN Directeur de thèse : Denis BARTOLO Présentée et soutenue publiquement le 24 juin 2015 Après avis de: M. Eric BERTIN M. Luca GIOMI Devant la commission d’examen formée de: M. Jean-Louis BARRAT Examinateur M. Denis BARTOLO Directeur de thèse M. Eric BERTIN Rapporteur M. Luca GIOMI Rapporteur M. Emmanuel TRIZAC Examinateur Table of contents Introduction 1 1 Polar active matter ....................................... 2 2 The paradigmatic numerical framework: Vicsek-like models .............. 3 3 Hydrodynamic description of active populations ..................... 7 4 From theoretical models to actual systems ......................... 10 5 Goals and organization of this thesis ............................. 13 1 Emergence of macroscopic polar phases in a model colloidal system 17 1 Designing a population of self-propelled colloids ..................... 18 2 Microscopic dynamics of a population of rollers ...................... 24 3 From microscopic to macroscopic dynamics ........................ 30 Article: Emergence of macroscopic directed motion in populations of motile colloids . 43 Article: Emergent vortices in populations of colloidal rollers . 66 Article: Tailoring the interactions between self-propelled bodies . 79 2 Emergent spatial structures in flocking models 91 1 Emergent polar patterns at the transition to collective motion ............. 92 2 A phenomenological hydrodynamic description ...................... 94 3 Shape of the band pattern: a dynamical-system insight ................. 96 4 Band patterns in a more realistic model ........................... 100 Article: Emergent spatial structures in flocking models: a dynamical system insight . 105 3 Geometry of interacting trajectories in a flock 117 1 Why is a geometric approach relevant? ........................... 118 2 Geometric description of the individual dynamics .................... 118 3 Geometric description of the mixing dynamics ...................... 119 Trajectories of aligning self-propelled particles: geometric characterization . 122 Article: Braiding a flock: winding statistics of interacting flying spins . 134 Perspectives and open questions 143 Appendix Non-equilibrium dynamics of confined suspensions 147 Article: Hydrodynamic fluctuations in confined particle-laden fluids . 149 Article: Hydrodynamics of confined active fluids ......................... 156 References 176 Introduction Some of the most spectacular examples of collective motion are provided by animal popula- tions that self-assemble into coherently-moving groups. The spontaneous emergence of coordi- nated motion at large scale is observed in systems as diverse as bird flocks, fish shoal or locust swarms (see Fig. 1). From a physical perspective, this robust observation has raised an intense interest over the past 20 years. Such ensembles of motile individuals were shown to display rich physical properties, which strongly differ from all equilibrium systems. A variety of theoretical models are now available, together with a number of experimental realizations. They unveiled a large diversity of phenomenologies, and define the field of “active matter” [136, 216]. In this introduction, we situate more precisely this thesis in the broad area of active matter. In the first section, we specify the subclass of systems which we consider: populations displaying po- lar structures, i.e. directed motion at large scale. We then introduce, in section 2, the paradigmatic framework of active matter, which we refer to as “Vicsek-like models”. In section 3, we recall the standard hydrodynamic approaches used to describe the large-scale dynamics of active popula- tions. Section 4 is devoted to the connection between theoretical models and actual experimental systems. Finally, we conclude in section 5 with a general outline of the thesis. (a) (b) (c) Figure 1 – Coherent motion in animal groups. (a) Populations of locusts form swarms that cover hun- dreds of km2. (b) Thousands of starlings move coherently within a flock. (c) Millions of sardines migrate collectively by forming large shoals [218]. 2 INTRODUCTON 1 Polar active matter Before we describe the theoretical background of this thesis, it is useful to specify the subclass of active systems that we have in mind. In a physical perspective, the motile individuals that we mentioned in Fig. 1 are examples of self-propelled particles. Irrespective of the mechanisms they use to achieve their motion, they share two main features [168]. (i) Each individual converts energy, which is stored or homogeneously supplied to the system, into net translational motion. The local spend or injection of energy keeps the population out of equilibrium. (ii) Each individual propels itself along its own direction. Self-propelled bodies are polar parti- cles which carry an orientation (although their geometric shape can be isotropic). As a matter of fact, this general definition encompasses a variety of systems. A number of biological situations involve active elements to generate motion, from animal flocks to the inter- nal dynamics of cells [30, 121, 187, 223]. In addition, much effort has been devoted over the past 8 years to building synthetic systems in the lab. Several strategies are now available to prepare self-propelled particles, either extracted from biological materials or purely artificial. All the fun- damental components of soft-matter have been motorized: polymers [115, 188, 190, 201], emul- sions [52, 102, 110, 209, 210, 213], colloids [39, 105, 112, 149–151, 204], and grains [68, 120, 122, 144]. Synthetic active populations are then obtained by assembling these self-propelled units. As an illustration of the diversity of recent active materials, three examples of experimental systems are shown in Fig. 2: bacteria swimming in thin films of liquid [227], colloids propelled by self-phoretic effects [151], and microtubule filaments driven by molecular motors [188]. We will not enter the details of the propulsion and interaction mechanisms. However, comparing the ex- perimental pictures (Fig. 2) to the initial flocking problem (Fig. 1) yields a striking remark: none of these examples display coherent flocks akin to those observed in animal populations. In con- trolled experiments, more complex spatio-temporal patterns have been systematically reported, such as clustering [151, 204], swirling [68, 73], nematic organization with dynamical defects [115, 188, 201] etc. Stable directed motion is not observed at the entire population scale. This rich phenomenology shows that the terms “collective motion” and “active matter” en- compass very diverse behaviors. We have to be more precise in specifying the class of systems we study. More specifically, in this thesis we focus on polar active matter. We are interested in active populations which display stable directed motion, akin to the animal groups shown in Fig. 1. Lo- cally, the individuals align their orientations and move coherently along the same local direction. Until recently, the physical descriptions of this subclass of systems were mostly restricted to theo- (a) (b) (c) Figure 2 – Illustration of the diversity of active patterns. (a) Moving clusters in suspensions of motile bac- teria (reproduced from [227]). (b) Dynamical crystals in a suspension of self-propelled colloids (reproduced from [151]). (c) Nematic order in a suspension of microtubules driven by molecular motors, confined at an oil-water interface. The arrows denote disclination defects (reproduced from [188]). The paradigmatic numerical framework: Vicsek-like models 3 retical and numerical approaches. From this perspective, the emergence of polar structures is well accounted for by a simple numerical framework, that we now describe. 2 The paradigmatic numerical framework: Vicsek-like models 2.1 The Vicsek model: aligning self-propelled spins The physics of active matter was initiated by the seminal work of Vicsek et al. in 1995 [215]. The numerical model that they proposed can be introduced from a simple remark. The emer- gence of directed motion is observed in a variety of living systems, which obviously involve very different interaction mechanisms, see Fig.

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