Micron scale robots going inside our body and curing various ailments is a technolog¬ical dream that easily captures our imagination. However, with the advent of novel nanofabrication and nanocharacterization tools there has been a surge in the research in this field over the last decade. In order to achieve locomotion (swim) at these small length scales, special strategies need to be adopted, that is able to overcome the large viscous damping that these microbots have to face while moving in the various bod¬ily fluids. Thus researchers have looked into the swimming strategies found in nature like that of bacteria like E.coli found in our gut or spermatozoa in the reproductive mucus. Biomimetic swimmers that replicate the motion of these small microorganisms hold tremendous promise in a host of biomedical applications like targeted drug delivery, microsurgery, biochemical sensing and disease diagnosis. In one such method of swimming at very low Reynolds numbers, a micron scale helix has been fabricated and rendered magnetic by putting a magnetic material on it. Small rotating magnetic fields could be used then to rotate the helix, which translated as a result of the intrinsic translation rotation coupling in a helix. The present work focussed on the development of such a system of nanopropellers, a few microns in length, the characterization of its dynamics and velocity fluctuations originating from thermal noise. The work has also showed a possible application of the nanopropellers in microrheology where it could be used as a new tool to measure the rheological characteristics of a complex heterogeneous environment with very high spatial and temporal resolutions. A generalized study of the dynamics of these propellers under a rotating field, has showed the existence of a variety of different dynamical configurations. Rigid body dynamics simulations have been carried out to understand the behaviour. Significant amount of insight has been gained by solving the equations of motion of the object analytically and it has helped to obtain a complete understanding, along with providing closed form expressions of the various characteristics frequencies and parameters that has defined the motion. A study of the velocity fluctuations of these chiral nanopropellers has been carried out, where the nearby wall of the microfluidic cell was found to have a dominant effect on the fluctuations. The wall has been found to enhance the average level of fluctuations apart from bringing in significant non Gaussian effects. The experimentally obtained fluctuations has been corroborated by a simulation in which a time evolution study of the governing 3D Langevin dynamics equations has been done. A closer look at the various sources of velocity fluctuations and a causality study thereof has brought out a minimum length scale below which helical propulsion has become impractical to achieve because of the increased effect of the orientational fluctuations of the propeller at those small length scales. An interesting bistable dynamics of the propeller has been observed under certain experimental conditions, in which the propeller randomly switched between the different dynamical states. This defied common sense because of the inherent deterministic nature of the governing Stokes equation. Rigid body dynamics simulations and stability analysis has shown the existence of time scales in which two different dynamical states of the propeller have become stable. Thus the intrinsic dynamics of the system has been found to be the reason behind the bistable behaviour, randomness being brought about by the thermal fluctuations present in the system. Finally, in a novel application of the propellers, they have been demonstrated as a tool for microrheological mapping in a complex fluidic environment. The studies done in this work have helped to develop this method of active microrheology in which the measurement times are orders of magnitude smaller than its existing counterparts.

What is flagellar swimming? Cilia and flagella are whip-like cell appendages that can exhibit regular bending waves. This active process emerges from the non-equilibrium dynamics of molecular motors distributed along the length of cilia and flagella. Eukaryotic cells can possess many cilia and flagella that beat in a coordinated fashion, thus transporting fluids, as in mammalian airways or the ventricular system inside the brain. Many unicellular organisms posses just one or two flagella, rendering them microswimmers that are propelled through fluids by the flagellar beat including sperm cells and the biflagellate green alga Chlamydomonas. Objectives. In this thesis in theoretical biological physics, we seek to understand the nonlinear dynamics of flagellar swimming and synchronization. We investigate the flow fields induced by beating flagella and how in turn external hydrodynamic flows change speed and shape of the flagellar beat. This flagellar load-response is a prerequisite for flagellar synchronization. We want to find the physical principals underlying stable synchronization of the two flagella of Chlamydomonas cells. Results. First, we employed realistic hydrodynamic simulations of flagellar swimming based on experimentally measured beat patterns. For this, we developed analysis tools to extract flagellar shapes from high-speed videoscopy data. Flow-signatures of flagellated swimmers are analysed and their effect on a neighboring swimmer is compared to the effect of active noise of the flagellar beat. We were able to estimate a chemomechanical energy efficiency of the flagellar beat and determine its waveform compliance by comparing findings from experiments, in which a clamped Chlamydomonas is exposed to external flow, to predictions from an effective theory that we designed. These mechanical properties have interesting consequences for the synchronization dynamics of Chlamydomonas, which are revealed by computer simulations. We propose that direct elastic coupling between the two flagella of Chlamydomonas, as suggested by recent experiments, in combination with waveform compliance is crucial to facilitate in-phase synchronization of the two flagella of Chlamydomonas.:1 Introduction 1.1 Physics of cell motility: flagellated swimmers as model system 2 1.1.1 Tissue cells and unicellular eukaryotic organisms have cilia and flagella 2 1.1.2 The conserved architecture of flagella 3 1.1.3 Synchronization in collections of flagella 5 1.2 Hydrodynamics at the microscale 9 1.2.1 Navier-Stokes equation 10 1.2.2 The limit of low Reynolds number 10 1.2.3 Multipole expansion of flow fields 11 1.3 Self-propulsion by viscous forces 13 1.3.1 Self propulsion requires broken symmetries 13 1.3.2 Signatures of flowfields: pusher & puller 15 1.4 Overview of the thesis 16 2 Flow signatures of flagellar swimming 2.1 Self-propulsion of flagellated swimmers 20 2.1.1 Representation of flagellar shapes 20 2.1.2 Computation of hydrodynamic friction forces 21 2.1.3 Material frame and rigid-body transformations 22 2.1.4 The grand friction matrix 23 2.1.5 Dynamics of swimming 23 2.2 The hydrodynamic far field: pusher and puller 26 2.2.1 The flow generated by a swimmer 26 2.2.2 Force dipole characterization 27 2.2.3 Flagellated swimmers alternate between pusher and puller 29 2.2.4 Implications for two interacting Chlamydomonas cells 31 2.3 Inertial screening of oscillatory flows 32 2.3.1 Convection and oscillatory acceleration 33 2.3.2 The oscilet: fundamental solution of unsteady flow 35 2.3.3 Screening length of oscillatory flows 35 2.4 Energetics of flagellar self-propulsion 36 2.4.1 Impact of inertial screening on hydrodynamic dissipation 37 2.4.2 Case study: the green alga Chlamydomonas 38 2.4.3 Discussion: evolutionary optimization and the number of molecular motors 38 2.5 Summary 39 3 The load-response of the flagellar beat 3.1 Experimental collaboration: flagellated swimmers exposed to flows 41 3.1.1 Description of the experimental setup 42 3.1.2 Computed flow profile in the micro-fluidic device 43 3.1.3 Image processing and flagellar tracking 43 3.1.4 Mode decomposition and limit-cycle reconstruction 47 3.1.5 Changes of limit-cycle dynamics: deformation, translation, acceleration 49 3.2 An effective theory of flagellar oscillations 50 3.2.1 A balance of generalized forces 50 3.2.2 Hydrodynamic friction in generalized coordinates 51 3.2.3 Intra-flagellar friction 52 3.2.4 Calibration of active flagellar driving forces 52 3.2.5 Stability of the limit cycle of the flagellar beat 53 3.2.6 Equations of motion 55 3.3 Comparison of theory and experiment 56 3.3.1 Flagellar mean curvature 57 3.3.2 Susceptibilities of phase speed and amplitude 57 3.3.3 Higher modes and stalling of the flagellar beat at high external load 59 3.3.4 Non-isochrony of flagellar oscillations 63 3.4 Summary 63 4 Flagellar load-response facilitates synchronization 4.1 Synchronization to external driving 65 4.2 Inter-flagellar synchronization in the green alga Chlamydomonas 67 4.2.1 Equations of motion for inter-flagellar synchronization 68 4.2.2 Synchronization strength for free-swimming and clamped cells 70 4.2.3 The synchronization strength depends on energy efficiency and waveform compliance 73 4.2.4 The case of an elastically clamped cell 74 4.2.5 Basal body coupling facilitates in-phase synchronization 75 4.2.6 Predictions for experiments 78 4.3 Summary 80 5 Active flagellar fluctuations 5.1 Effective description of flagellar oscillations 84 5.2 Measuring flagellar noise 84 5.2.1 Active phase fluctuations are much larger than thermal noise 84 5.2.2 Amplitude fluctuations are correlated 85 5.3 Active flagellar fluctuations result in noisy swimming paths 86 5.3.1 Effective diffusion of swimming circles of sperm cell 86 5.3.2 Comparison of the effect of noise and hydrodynamic interactions 87 5.4 Summary 88 6 Summary and outlook 6.1 Summary of our results 89 6.2 Outlook on future work 90 A Solving the Stokes equation A.1 Multipole expansion 95 A.2 Resistive-force theory 96 A.3 Fast multipole boundary element method 97 B Linearized Navier-Stokes equation B.1 Linearized Navier-Stokes equation 101 B.2 The case of an oscillating sphere 102 B.3 The small radius limit 103 B.4 Greens function 104 C Hydrodynamic friction C.1 A passive particle 107 C.2 Multiple Particles 107 C.3 Generalized coordinates 108 D Data analysis methods D.1 Nematic filter 111 D.1.1 Nemat 111 D.1.2 Nematic correlation 111 D.2 Principal-component analysis 112 D.3 The quality of the limit-cycle projections of experimental data 113 E Adler equation F Sensitivity analysis for computational results F.1 The distance function of basal coupling 117 F.2 Computed synchronization strength for alternative waveform 118 F.3 Insensitivity of computed load-response to amplitude correlation time 118 List of Symbols List of Figures Bibliography

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Les microrobots magnétiques, qui nagent en utilisant des modes de propulsion bio-inspirées, apparaissent très prometteurs pour la manipulation et la caractérisation d'objets à l'échelle microscopique dans des environnements confinés et très restreints, contrairement aux méthodes de micromanipulation classiques. La littérature propose une variété de microrobots avec des formes géométriques et des propriétés magnétiques différentes. Les commandes en mouvement proposées restent cependant simples, peu précises et insuffisamment robustes pour la réalisation de tâches réelles. De plus, il subsiste une incertitude sur le fait que tous ces micronageurs artificiels peuvent accomplir les mêmes tâches avec une performance égale. L'objectif de cette thèse consiste alors à proposer : des commandes de mouvement génériques par asservissement visuel dans l'espace pour tous les types de micronageurs avec des contraintes non holonomes afin d'améliorer les performances de ces micronageurs, un ensemble de critères de comparaison entre des robots avec une topologie ou un mode de propulsion différents pour le choix du micronageur le plus performant pour réaliser une tâche particulière. Des lois de commande de suivi de chemin dans l'espace sont synthétisées et validées expérimentalement sur des nageurs hélicoïdal et flexible sous différentes conditions. Ces robots évoluent dans un fluide à faible nombre de Reynolds, imitant respectivement le mécanisme de locomotion des bactéries et des spermatozoïdes et sont actionnés par un champ magnétique uniforme. Ces deux classes de nageurs possèdent une géométrie et un mode d'actionnement différents. Leurs performances sont ainsi comparées. / Magnetic microrobots, which swim using bio-inspired propulsion modes, appear very promising for manipulation and characterization of objects at microscopic scale inside confined and very restricted environments, unlike conventional micromanipulation methods. The literature proposes a variety of microrobots with different geometric shapes and magnetic properties. However, the motion controls proposed remain simple, imprecise and insufficiently robust for performing real tasks. In addition, there is still uncertainty that all these artificial microswimmers can accomplish the same tasks with equal performance. The objective of this thesis is thus to propose : generic motion controls by visual servoing in space for all kinds of microswimmers with nonholonomic constraints in order to improve the microswimmer performances, a set of comparison criteria between robots with a different topology or propulsion mode for choosing the most efficient microswimmer in order to perform a specific task. Path following control laws in space are synthesized and experimentally validated on helical and flexible swimmers under different conditions. These robots operate in low Reynolds number fluid, imitating respectively bacteria and spermatozoa and are actuated with uniform magnetic field. These two classes of swimmers have different actuation mode and geometric shape. Their performances are thus compared according to the task to be performed, the environment in which the robots evolve and the manufacturing constraints.

Since the highly cited paper by Purcell postulating the “Scallop theorem” almost 50 years ago, asymmetry is an unavoidable part of micromotors. It is frequently induced by self-shadowing or self-masking, resulting in so-called Janus colloids. This strategy works very reliably, but turns into a bottleneck once up-scaling becomes important. Herein, existing alternatives are discussed and a novel synthetic pathway yielding active swimmers in a one-pot synthesis is presented. To understand the resulting mobility from a single material, the geometric asymmetry is evaluated using a python based algorithm and this process is automated in an open access tool.

Die Fähigkeit künstlicher Mikroschwimmer, auf äußere Reize zu reagieren und deren mechanistische Ursprünge, gehören zu den umstrittensten Fragen der interdisziplinären Wissenschaft. Die Erzeugung chemischer Gradienten ist dabei eine technische Herausforderung, da sie aufgrund von Diffusion schnell abflachen. Inspiriert von ‘Stop-flow’ Experimenten aus der chemischen Kinetik zeigen wir, dass die Erzeugung eines mikrofluidischen Gradienten durch Kombination mit einer Druckrückkopplungsschleife zur präzisen Kontrolle des Stoppens erfolgen kann. Das ermöglicht es uns, die mechanistischen Details der Chemotaxis von künstlichen katalytischen Janus-Mikromotoren zu untersuchen. Wir stellen fest, dass diese Kupfer-Janus-Partikel eine chemotaktische Bewegung entlang des Konzentrationsgradienten sowohl in positiver als auch in negativer Richtung zeigen, und wir demonstrieren die mechanische Reaktion der Partikel auf unausgewogene Widerstandskräfte, die dieses Verhalten erklären.

The ability of artificial microswimmers to respond to external stimuli and the mechanistical details of their origins belong to the most disputed challenges in interdisciplinary science. Therein, the creation of chemical gradients is technically challenging, because they quickly level out due to diffusion. Inspired by pivotal stopped flow experiments in chemical kinetics, we show that microfluidics gradient generation combined with a pressure feedback loop for precisely controlling the stop of the flows, can enable us to study mechanistical details of chemotaxis of artificial Janus micromotors, based on a catalytic reaction. We find that these copper Janus particles display a chemotactic motion along the concentration gradient in both, positive and negative direction and we demonstrate the mechanical reaction of the particles to unbalanced drag forces, explaining this behaviour.

Catalytic microswimmers that move by a phoretic mechanism in response to a self-induced chemical gradient are often obtained by the design of spherical janus microparticles, which suffer from multi-step fabrication and low yields. Approaches that circumvent laborious multi-step fabrication include the exploitation of the possibility of nonuniform catalytic activity along the surface of irregular particle shapes, local excitation or intrinsic asymmetry. Unfortunately, the effects on the generation of motion remain poorly understood. In this work, single crystalline BiVO₄ microswimmers are presented that rely on a strict inherent asymmetry of charge-carrier distribution under illumination. The origin of the asymmetrical flow pattern is elucidated because of the high spatial resolution of measured flow fields around pinned BiVO₄ colloids. As a result the flow from oxidative to reductive particle sides is confirmed. Distribution of oxidation and reduction reactions suggests a dominant self-electrophoretic motion mechanism with a source quadrupole as the origin of the induced flows. It is shown that the symmetry of the flow fields is broken by self-shadowing of the particles and synthetic surface defects that impact the photocatalytic activity of the microswimmers. The results demonstrate the complexity of symmetry breaking in nonspherical microswimmers and emphasize the role of self-shadowing for photocatalytic microswimmers. The findings are leading the way toward understanding of propulsion mechanisms of phoretic colloids of various shapes.