Taxis of Artificial Swimmers in a Spatio-Temporally Modulated Activation Medium

Contrary to microbial taxis, where a tactic response to external stimuli is controlled by complex chemical pathways acting like sensor-actuator loops, taxis of artificial microswimmers is a purely stochastic effect associated with a non-uniform activation of the particles' self-propulsion. We study the tactic response of such swimmers in a spatio-temporally modulated activating medium by means of both numerical and analytical techniques. In the opposite limits of very fast and very slow rotational particle dynamics, we obtain analytic approximations that closely reproduce the numerical description. A swimmer drifts on average either parallel or anti-parallel to the propagation direction of the activating pulses, depending on their speed and width. The drift in line with the pulses is solely determined by the finite persistence length of the active Brownian motion performed by the swimmer, whereas the drift in the opposite direction results from the combination of ballistic and diffusive properties of the swimmer's dynamics.Comment: 19 pages, 6 figures; Entropy (in press

Self-propelled particles with inhomogeneous activity

Movement is an essential feature of life. It allows organisms to move towards a more favorable environment and to search for food. There are many biological systems that fall under the category active matter, from molecular motors walking on microtubules inside cells to flocks of birds. What these systems have in common is that each of its constituents converts energy into directed motion, that is, they propel themselves forward. Besides the many biological examples, there is also synthetic active matter, these are self-propelled particles made in a laboratory. These are typically colloidal sized particles that can propel themselves forward by self-phoresis. In this work the focus is on the low Reynolds number regime, meaning that the typical size of the constituents is less than a few micrometers. The models that are used to describe such active matter are can be viewed as nonequilibrium extensions to Brownian motion (the thermal motion of small particles dissolved in a fluid). In many systems the self-propulsion speed (activity) is not homogeneous in space: the particles swim faster in some areas than in others. The main topic of this dissertation is how a single active particle, or a few active particles tied together by a potential, behave in such systems. It is known that a single active particle without any steering mechanism spends most time in the regions where it moves slowly, or in other words, they spend most time in regions where they are less active. However, here it is shown that, even though they spend most time in the less active regions, dynamical properties, such as the probability to move towards the more active regions is higher than moving towards the less active regions. Furthermore, when the active particles are connected to a passive Brownian 'cargo' particle, chained together to form a colloidal sized polymer, or fixed to another active particle, the resulting active dimers or polymers either accumulate in the high activity regions or the low activity regions, depending on the friction of the cargo particle, the number of monomers in the polymer, or the relative orientation of active particles. Lastly, when the activity is both time- and space-dependent, a steady drift of active particles can be induced, without any coupling between the self-propulsion direction and the gradient in the activity. This phenomenon can be used to position the particles depending on their size.:1. Brownian Motion 2. Active Matter 3. Modeling Active Matter 4. Introduction: Inhomogeneous activity 5. Pseudochemotaxis 6. Cargo-Carrying Particles 7. Active Colloidal Molecules 8. Time-Varying Activity Fields Appendix: Hydrodynamic

Active Emulsions: Physicochemical Hydrodynamics and Collective Behavior

Active matter is a collection of constituent elements that constantly consume energy, convert it to mechanical work, and interact with their counterparts. These materials operate out of equilibrium and exhibit fascinating collective dynamics such as spontaneous pattern formation. Self-organization of bio-polymers within a cell, collective migration of bacteria in search of nutrition, and the bird flocks are paragons of active living matter and the primary source of our knowledge on it. To understand the overarching physical principles of active matter, it is desirable to build artificial systems that are capable of imitating living active matter while ruling out the biological complexities. The goal of this thesis is to study active micro-droplets as a paradigm for biomimetic artificial active particles, using fundamental principles of fluid dynamics and statistical physics. The Marangoni-driven motility in these droplets is reminiscent of the locomotion of some protozoal organisms, known as squirmers. The main scientific objectives of this research are to (i) investigate the potential biomimetic features of active droplets including compartmentalization, adaptability (e.g. multi-gait motility), and information processing (signaling and sensing) and (ii) study the implications of those features in the collective dynamics of active emulsions governed by hydrodynamic and autochemotactic interactions. These objectives are addressed experimentally using microfluidics and microscopy, integrated with quantitative image analysis. The quantitative experimental results are then compared with the predictions from theory or simulations. The findings of this thesis are presented in five chapters. First, we address the challenge of compartmentalizing active droplets. We use microfluidics to generate liquid shells (double emulsions). We propose and successfully prove the use of a nematic liquid crystal oil to stabilize the liquid shells, which are otherwise susceptible to break up during motility. We investigate the propulsion dynamics and use that insight to put forward routes to control shell motion via topology, chemical signaling, and topography. In the second results chapter, we establish the bimodal dynamics of chaotic motility in active droplets; a regime that emerges as a response to the increase of viscosity in the swimming medium. To establish the physical mechanism of this dynamical transition, we developed a novel technique to simultaneously visualize the hydrodynamic and chemical fields around the droplet. The results are rationalized by quantitative comparison to established advection-diffusion models. We further observe that the droplets undergo self-avoiding random walks as a result of interaction with the self-generated products of their activity, secreted in the environment. The third results chapter presents a review of the dynamics of chemotactic droplets in complex environments, highlighting the effects of self-generated chemical interactions on the droplet dynamics. In the fourth results chapter, we investigate how active droplets sense and react to the chemical gradients generated by their counterparts--- a behavior known as autochemotaxis. Then, we study the collective dynamics governed by these autochemotactic interactions, in two and three dimensions. For the first time, we report the observation of ‘history caging’, where swimmers are temporarily trapped in an evolving network of repulsive chemical trails. The caging results in a plateau in the mean squared displacement profiles as observed for dense colloidal systems near the glass transition. In the last results chapter, we investigate the collective dynamics in active emulsions, governed by hydrodynamic interactions. We report the emergence of spontaneously rotating clusters. We show that the rotational dynamics originates from a novel symmetry breaking mechanism for single isotropic droplets. By extending our understanding to the collective scale, we show how the stability and dynamics of the clusters can be controlled by droplet activity and cluster size. The experimental advancements and the findings presented in this thesis lay the groundwork for future investigations of emergent dynamics in active emulsions as a model system for active matter. In the outlook section, we present some of the new questions that have developed in the course of this research work and discuss a perspective on the future directions of the research on active droplets.2022-01-1

Self-propulsion of chemically-active droplets

Microscopic active droplets are able to swim autonomously in viscous flows: this puzzling feature stems from solute exchanges with the surrounding fluid via surface reactions or their spontaneous solubilisation, and the interfacial flows resulting from these solutes' gradients. Contrary to asymmetric active colloids, these isotropic droplets swim spontaneously by exploiting the nonlinear coupling of solute transport with self-generated Marangoni flows, which is also responsible for secondary transitions to more complex individual and collective dynamics. Thanks to their simple design and their sensitivity to physico-chemical signals, they are fascinating physicists, chemists, biologists and fluid dynamicists alike to analyse viscous self-propulsion and collective dynamics in active matter systems, to develop synthetic cellular models or to perform targeted biomedical or engineering applications. I review here the most recent and significant developments of this rapidly-growing field, focusing on the mathematical and physical modelling of these intringuing droplets, together with its experimental design and characterisation.Comment: 26 pages, 8 figures, to appear in Annual Review of Fluid Mechanic

Thermophoretic microswimmers: Interplay of phoresis, geometry and hydrodynamics

The term swimmer refers to biological or artificial structures that are capable of self-propel by drawing energy from the surrounding environment. The typical size of a swimmer ranges orders of magnitude, from the macroscopic world of a blue whale in the ocean, to the microscopic of a bacteria. Microscopic swimmers, or microswimmers, live in an environment where the viscosity of the fluid dominates their motion, suppressing the inertia that we are so familiar with. Phoresis refers to the physical mechanism in which colloidal particles migrate due to the presence of a solvent gradient, such as thermal, chemical or magnetic. Phoretic colloids have recently emerged as a promising avenue for the design of artificial microswimmers. Thermophoretic colloids are partially coated with a high heat conductivity material, such as gold, which heats faster under laser illumination, creating then a local thermal gradient. The non-coated surface reacts to the difference in temperatures and displays the thermophoretic response to it, driving the motion of the swimmer. The motion of colloids immersed in fluid produce long-ranged flows, which can infere in the motion of further colloids. These fluid-mediated interactions are known as hydrodynamic interactions. Since the colloid is found in solvent, phoresis and propulsion are linked to a hydrodynamic flow field. These fluid-mediated interactions are deeply influenced by the geometry and surface properties of the colloid, and play a major role in the interaction between swimmers. This dissertation addresses the study of self-thermophoretic dimeric and trimeric colloidal swimmers by means of mesoscale computer simulations. In order to precisely understand the debated role of hydrodynamic interactions in these systems, two computational approaches are hereby presented. We use a full hydrodynamic approach, which includes thermophoresis, and a second method which neglects fluid-mediated effects while accounting for thermophoretic interactions. Hydrodynamic simulations are performed via the combination of molecular dynamics (MD) and multi-particle collision dynamics (MPC), which has proven to include hydrodynamics and heat transport. We furthermore propose a thermophoretic Brownian dynamics method for the dry systems, with phoresis implemented by means of pair potential interactions. The advantage of this method respect to regular Brownian methods is that the propulsion mechanism and intermolecular phoretic interactions are described by the same potential. This ensures a correct description of the thermophoretic interactions, disregarding only the hydrodynamics in the system, thus allowing for a fair comparative study. In this thesis we have dealt with multimeric structures made of one heated bead, which creates a local thermal gradient, adjacent to one or two thermophoretic beads. Dimeric swimmers only have one phoretic bead, whereas trimers are build with two phoretic beads. The first trimers have been constructed with all the beads placed rod-like, with the heated bead in the middle. In order to achieve ballistic motion, the two phoretic beads need to have different phoretic responses, thus the phoretic forces sharing orientation. Trimers can moreover be built with two phoretic beads of the same nature, in which the linear structure is no longer useful for propulsion. The three beads are then placed in a triangular lattice, recovering the ballistic propulsion. Changing one of the phoretic beads of this structure to the opposite phoretic behaviour leads to a rotational behaviour due to a phoretic torque, thus to a rotor swimmer. Ensembles of dimeric and trimeric swimmers are studied besides the single swimmer properties, showing that the interplay of phoresis, hydrodynamics and geometry is key to the correct understanding of their collective behaviour. Thermophoresis either helps aggregation, as in the case of thermophilic swimmers, in which phoretic beads try to cluster around heat sources; or strongly prevents clustering when thermophobic beads get repelled by heat sources. These dimers and trimers change their hydrodynamic behaviour when varying the aspect ratio between the phoretic and heated beads’ radii. Interestingly, the effects of hydrodynamics have shown to have distinct impacts on different systems. In some cases, hydrodynamics enhances aggregation, like it is the case for symmetric thermophilic dimers. In other cases, clustering is penalised due to repulsive fluid-mediated interactions, as it is the case for thermophobic dimers and triangular trimers. These effects are further enhanced or diminished by phoretic and steric effects. Furthermore, steric effects lead to alignment or aggregation on the system. The results presented in this dissertation contribute to the understanding of thermophoretically driven artificial microswimmers. The large variety of behaviours which we have seen is which may offer more versatile tools in various systems such as micro-fluidic systems, or even devices with applications in medicine given the biocompatibility of small thermal gradients with most organisms

When droplets deform, break up and propel microswimmers

This thesis investigates the motion and breakup of droplets in low-Reynolds-number flows, focusing on two aspects. In the first part, we study the breakup of droplets in subcritical flow conditions, when there exists a linearly stable solution for the droplet shape, but a finite amplitude perturbation might trigger instabilities. Thus, there exists a finite basin of attraction of the stable solution, whose boundary separates droplets that break from those recovering the stable shape. Our effort is mostly devoted to the exploration of the state space in which the basin boundary is defined. To this end, we proceed by adapting theories initially developed to study laminar-turbulent transition, namely nonmodal analysis and edge tracking. We study the influence of non-normal effects in the breakup of a rising droplet, showing that the optimal shapes found with nonmodal analysis are more efficient in triggering breakup than initially ellipsoids droplets. Afterwards, we investigate the relevance of edge state in the breakup of droplet in uni-axial extensional flows, finding that edge states select the path toward breakup. The exploration of the bifurcation diagram reveals a similar situation for bi-axial extensional flows, where droplets are squeezed along the axis instead of being extended. In the second part we develop a joint chemical-hydrodynamics model to study the motion of bubble-propelled conical microswimmers. We conclude that the chemistry and the hydrodynamics partially decouple. In fact, chemistry dictates the time scale at which the microswimmer moves while the hydrodynamics governs the attained displacement. We furthermore find the geometrical and chemical parameters that optimize the swimming velocity. The effects of bubble deformability are then included. In this case, the swimming velocity is optimal for small cone opening angles. Furthermore, we find that the swimming efficiency, measured in displacement attained per fuel consumption, decreases when the bubble is more deformable. Finally, we study the motion of a sphere inflating close to a wall, which is relevant to the study of conical microswimmers and allows us to revisit the classical settling sphere problem. We find that depending on the boundary conditions imposed on the sphere, whether it is a rigid shell or a perfect free-shear bubble, the sphere-wall gap will close or open in time

Jet propulsion without inertia

A body immersed in a highly viscous fluid can locomote by drawing in and expelling fluid through pores at its surface. We consider this mechanism of jet propulsion without inertia in the case of spheroidal bodies, and derive both the swimming velocity and the hydrodynamic efficiency. Elementary examples are presented, and exact axisymmetric solutions for spherical, prolate spheroidal, and oblate spheroidal body shapes are provided. In each case, entirely and partially porous (i.e. jetting) surfaces are considered, and the optimal jetting flow profiles at the surface for maximizing the hydrodynamic efficiency are determined computationally. The maximal efficiency which may be achieved by a sphere using such jet propulsion is 12.5%, a significant improvement upon traditional flagella-based means of locomotion at zero Reynolds number. Unlike other swimming mechanisms which rely on the presentation of a small cross section in the direction of motion, the efficiency of a jetting body at low Reynolds number increases as the body becomes more oblate, and limits to approximately 162% in the case of a flat plate swimming along its axis of symmetry. Our results are discussed in the light of slime extrusion mechanisms occurring in many cyanobacteria

Activation processes in biology

Many processes in physics and biology can be understand through the framework of escape from a metastable state, including (but not limited to) the rates of chemical reactions, the unfolding of proteins, the nucleation of bubbles, and the condensation of gases. To understand the kinetics of these processes, we have to be able to calculate the rate of escape. In this thesis, I solve several of such of escape problems, each addressing a specific physical or biological system. I first show how the forced unfolding of heteropolymers could be a process with non-exponential kinetics, developing ideas about the importance of unfolding pathways in determining kinetics of unfolding. Then, I consider forced unfolding when a molecule is attached to a yielding (viscoelastic) substrate, and a constant force is applied. I show that the rates of unfolding depend on both the elastic and viscous response of the substrate. This problem is related to the biological process of mechanosensing, when the unfolding `sensor' protein exposes catalytic residues and generates a chemical signal to the cell. Related to this is the analysis of population-dynamics study of cells adhesion on substrates, which allows me to extract key characteristics and parameters of the adhesome complex. Then, I apply the ideas of escape from a metastable state to ask about the rates of a ligand at the end of a tethered polymer binding to a surface receptor, using a mean field approach to reduce the problem to one dimension. I show that there is a trade-off between the entropic cost of reaching to a receptor vs the volumetric cost of expanding the tether length. I then show that for a Gaussian chain with multiple ligands along its length, there exists a finite, non-zero optimal number of ligands to minimise the time taken for the end of the chain to bind to the surface. Finally, I consider the problem of microswimmers in an obstacle lattice, calculating their transport properties, and showing how we can use lattices to examine the underlying stochastic dynamics.I was funded through an EPSRC studentship: EP/M508007/1

Flagellated and Ciliated Microswimmers

The propulsion mechanism and the swimming dynamics of various ciliated microorganisms are investigated. Ciliated microswimmers, ranging from a single flagellated sperm cell to multiciliated microswimmers, propel themselves by cilia attached to their cell membrane. The underlying complex biomachinery of a cilium, the axoneme, employs an evolutionary developed mechanism, which is tailored to generate an optimal beating pattern to propel the swimmer through the environment it encounters. In this work mesoscale hydrodynamics simulations are used to simulate the whip-like motion of the cilium at low Reynolds numbers. The particle-based approach of multi-particle collision dynamics enables simulations of self-propelled microswimmers in complex confinements where steric and hydrodynamic interactions strongly influence the swimming dynamics. Details of cilia arrangement and beat shape are critical in understanding propulsion and surface attraction. The axonemal beating of cilia and flagella is modeled by a semi-flexible polymer with periodically changing intrinsic curvature. In the spirit of a minimalistic modeling approach, the axoneme is only bend along one degree of freedom, creating a defined beat plane. The first part discusses surface attraction and guidance of sperm cells swimming in confinement. In particular, the motion of sperm in geometrically structured (zigzag) microchannels provides an interesting geometry for the manipulation and sorting of sperm cells. Sperm swim along the channel walls, but are deflected from the sidewall at sharp bends. The simulation results are in qualitative agreement with recent microfluidic experiments and provide a better insight into the mechanisms of sperm navigation under strong confinement. The effective adhesion of a sperm cell to a flat surface depends both on the envelope of its planar beat shape and on the orientation of its beat plane. A proposed self-propelled steric model explains the average deflection around corners. Further investigation of various beat patterns with increasing wavelength results in complex surface attraction dynamics of the sperm cell. The insight from the steric model helps to understand the surface attraction in terms of the beat-shape envelope. It is found that when the beat pattern exceeds a critical wavelength, the flagellum buckles and beats in a complex three-dimensional shape, which strongly increases surface attraction. Indeed, the analysis of three-dimensional experimental holographic data of freely swimming human sperm cells shows that on average the beat pattern is relatively planar but exhibits regular nonplanar components twice per beat. By comparing this high-resolution experimental data with simulation results, a possible explanation for the nonplanar beating is obtained. Simulated sperm with imposed planar bends and two orders of magnitude smaller twist than bending rigidity undergo a twist instability and exhibit a three-dimensional beat pattern. Simulations allow to map the phase space of the twist instability, which shows no dependence on the bending rigidity, but a sharp transition from planar to three-dimensional beating below a critical twist rigidity. A localized twist wave goes through the cilium, which twists the cilium at a very narrow segment close to the point of minimal in-plane bending. This creates essentially two beat planes, separating the cilium in two segments of planar beating before and after the twisting region. In the second part, propulsion and synchronization of multi-ciliated spherical swimmers with different cilia densities and arrangements are studied. Instead of pre-imposing the intrinsic curvature, a ratchet-like mechanism drives the ciliary beat pattern. Therefore, the beat period can be influenced by the flow generated from the motion of the other cilia. The propulsion velocity of ciliated spherical swimmers increases sub-linearly with increasing cilia density. Large differences in propulsion speed for equal numbers of cilia with different arrangements on the sphere are found. For symmetric ciliated swimmers, the emergence of a stable synchronization state is found to depend on the initial condition. In some symmetric 9-cilia swimmers, long stable phases of synchronization emerge. Swimmers whose phase difference increases due to phase slips have a slower propulsion velocity than swimmers which develop a constant phase-lag between cilia. Turning to an oscillator model for cilia synchronization, the emergence of metachronal coordination in different topologies above a surface is studied. The oscillators are modeled as hydrodynamically interacting spheres propelled along a circular trajectory. Non-dimensionalization of the model provides the radial confinement strength as the only control parameter. Boundary effects influence the synchronization as well as the confinement strength. In open chains of oscillators as well as in circular arrangements, stable large-scale patterns of synchronization emerge until a critical confinement strength. No long-term coordination emerges above a critical confinement strength in any of the studies topologies. Finally, the cilium model is used to simulate a tuft of cilia, modeled to describe the placement of cilia in brain ventricles of mice. It is found that the particle flux towards the surface is located in hot-spots where the flux is significantly enhanced compared to purely diffusive transport. This shows the important role of ciliary beating in molecular transport towards primary cilia on the surface of the ventricles

Target search of active particles in complex environments

Microswimmers are microscopic active agents capable of harvesting energy from the surrounding environment and converting it into self-propulsion and directed motion. This peculiar feature characterizes them as out-of-equilibrium systems that break microscopic reversibility. The problem of finding a specific target in a complex environment is essential for these agents since it is employed for a variety of purposes, from foraging nourishment to escaping potential threats. Here, we provide a detailed study of the target search process for microswimmers exploring complex environments. To this end, we generalize Transition Path Theory, the rigorous statistical mechanics description of transition processes, to the target-search problem. One of the main results of this thesis is the generalization to non-equilibrium systems of the Transition Path Sampling (TPS) algorithm, which was originally designed to simulate rare transitions in passive systems. The TPS algorithm relies on microscopic reversibility for its functioning, therefore its generalization to out-of-equilibrium systems lacking detailed balance and microscopic reversibility has remained a major challenge. Within this work, we generalize the TPS algorithm to the case of an active Brownian particle, i.e. a paradigmatic model for microswimmers, and we obtain a first insight into the counterintuitive target-search pathways explored by these agents. The second result of this thesis is a systematic characterization of the target-search path ensemble for an active particle exploring an energy landscape. The third and final original contribution of this Ph.D. thesis is the generalization of the concept of the committor function to target-search problems, with a validation of our theory against experiments of a camphor self-propelled disk.Comment: Ph.D. thesi