This dissertation examines the motion of colloids in a temperature gradient, a non-equilibrium phenomenon also known as thermophoresis. Chapter 1 gives an introduction to the existing applications and basic concepts of thermophoresis and outlines some of the experimental and theoretical challenges that serve as a motivation for this PhD project. In Chapter 2, a general theoretical description for thermophoresis is formulated using the theory of non-equilibrium thermodynamics. The colloidal flux is split up into an interfacial single-colloid contribution and a bulk contribution, followed by a determination of transport coefficients based on Onsager’s reciprocal relations. It is further shown how the phenomenological expression of the thermophoretic flux can be recovered when the fluid is at steady-state. The results issuing from this description are then discussed and compared to other existing approaches, some of which are shown to neglect the hydrodynamic character of colloidal thermophoresis. Chapter 3 is dedicated to the validation of the introduced theoretical framework by means of computer simulations, using a simulation technique known as multi-particle collision dynamics. More specifically, the dependence of the thermophoretic force on different system parameters is examined and deviations from the theoretical prediction are explained by an advective distortion of interfacial fluid properties at the colloidal surface. Chapter 4 presents steady-state measurements of functionalised colloids in a temperature gradient, showing how the addition of molecular surface groups increases the experimental complexity of thermophoretic motion. The relaxation process behind this steady-state is also studied, to determine how the relaxation speed depends on the applied temperature gradient. In chapter 5, a general conclusion is drawn from the presented work and its implications are briefly discussed in relation to the current state of knowledge. Finally, the discussion is closed with an outlook on remaining challenges in understanding colloidal motion that could be the subject of future research.

In this thesis we have studied systems that driven by mechanisms broadly known as phoresis. More specifically, in the second chapter we calculate the excess noise in electrophoresis of a colloid due to microion fluctuations. In the next three chapters we study in detail a system of self-phoretic colloids, propelled by the energy released when an ambient fuel molecule makes contact with a catalytic region on the particle’s surface. We start with the behaviour of a single particle in a linear substrate gradient, then go on to study interactions between two particles due to their diffusion clouds, and finally obtain the collective equations of motion by a systematic coarse-graining of the microscopic Langevin dynamics. To understand the role of nonequilibrium fluctuations in an electrophoretic system we have theoretically analyzed the dynamics of a single colloidal particle in an externally applied electric field. We have studied the colloidal dynamics in two scenarios: a particle free to move in an unbounded fluid and a colloid near a wall which is stationary due to a balance between gravity and the electric field. The thermal motions of microions lead to an anisotropic, nonequilibrium noise, proportional to the field, in the effective Langevin equation for the colloid. The fluctuation-dissipation ratio depends strongly on frequency, in contrast to an equilibrium system, and the colloid if displaced from its steady-state position relaxes with a velocity not proportional to the gradient of the logarithm of the steady-state probability. Other measurable effects of this noise are a superdiffusive peak at short times and an enhanced diffusity at long times. We have then studied the effective potential and obtained a non-dimensional measure of the size of the excess noise. Possible extensions of this study to include the behaviour of the mean and fluctuation properties in the case of an applied alternating potential, and the effect of the excess noise on electrohydrodynamic aggregation of colloids. We next turn to a phoretic system that has been much studied in the recent years – active Janus colloids . On one hand these colloids are an important contribution to the general class of problems on self-propulsion at low Reynolds number. On the other hand since their behaviour can be tuned at the level of single particle we can ask how their collective behaviour depends on the swimmer design. This makes it a very rich field with lots of challenging questions. We first study the single particle behaviour of an active Janus colloid in an imposed substrate gradient, then build the two-particle interactions and ultimately the collective equations of motion by a generalisation of these results. Our work presents a new approach to active matter. We show theoretically how to design particles that are not only motile but can reorient in response to gradients, thus mimicking chemotaxis. We outline the collective behaviour emerging from these single-particle properties, including colloidal realisations of gravitational collapse, plasma oscillations and spontaneously ringing states, and present a phase diagram, in terms of single particle parameters, that can be tested in experiments. This provides a template to design collective behaviours of interest by tuning the surface properties of the colloids. We can also control the range of the interaction by varying the concentration of reactant. Our coarse-grained equations of motion for the polar orientation and number density fields for a collection of colloids propelled by and interacting through long-ranged dif-fusion fields are novel in a number of ways. This is the first example in active matter literature of a microscopic derivation of collective dynamics for particles interacting via long-ranged diffusion fields. The instabilities and possible phases that we predict are different from those in traditional flocking models, which consider only short-ranged aligning interactions. The long-ranged interactions of interest here cannot produce a globally polar ordered state, and we work in a concentration regime where steric and collisional interactions are not important. Instabilities towards flocking, and the advective nonlinearities of the Toner-Tu model, although not ruled out by the symmetries of our model, do not play a significant role in our system. The collective behaviour we predict will not be seen in purely locally interacting active-particle systems. The mechanisms at work in the “saturated” case where reactant is abundant cannot be viewed as totally generic features of collections of self-driven particles; they require interactions mediated by the production or consumption of long-ranged diffusing solute fields. Earlier work on saturated systems resolved neither interactions mediated by the polarity of the objects nor chemotactic effects. Their treatment truncated the equations at the level of the concentration [1]. In the “unsaturated” case more than one mechanism operates. One is related to the motility-induced phase separation discussed phenomenologically in refs. [2,3] (for which our system provides an important microscopic realisation). The other is due to chemo-taxis and phoresis which we report for the first time. Our expression of the various coefficients in the equaions of motion in terms of the single particle properties can also be used to design systems in which one or the other of these mechanisms dominate. We are now planning to study a collection of these particles in a fluid and examine the diffusion of a tracer particle as was done by Yeomans et al. [4] for hydrodynamic interactions. The Levy flights obtained in [4] is due to the long-ranged nature of the hydrodynamic fields, which cause effects like entrainment leading to interesting tracer dynamics. In this thesis we have considered colloids in which the symmetry axis of the colloid and the catalytic coat coincide. It might be of interest to consider cases when the axes are at an angle making the swimmer biaxial, or more complicated arrangements leading to chirality and thus rotation. Collective dynamics and two particle interaction between such swimmers can also be interesting. The formalism developed for the study of interaction between two active colloids through their diffusion fields and hydrodynamics can be extended to study their interaction with extended passive surfaces like walls or spheres. The collective dynamics of this class of active systems when it is confined between parallel walls is also of interest. Work in progress includes studies of the motion of the swimmer in a periodic array of passive colloids. In this study of collective dynamics, we have ignored the role of hydrodynamics, as the slowest decay of the field is 1/r3, which is subdominant to the decay of the chemical fields and in the dilute limit is expected to change things only qualitatively. However their role would be more important when we consider the stability of ordered structures like an aster in the saturated case. Another effect of hydrodynamics is to stir the fluid. It might be interesting to study the finite-P´eclet number regime [5, 6] of our system particularly in the unscreened region when advection of the scalar fields s and p by the velocity can affect clustering. We have derived the form of the nonlinear equations of motion in both the saturated and the unsaturated regimes. It will be interesting to investigate their relevance in the dynamics and phases that this extremely rich system can form. Even in the overdamped limit where we obtain an effective density equation it is not clear that the dynamics will resemble that of the Keller-Segel model due to the presence of the interesting nonlinear terms. Also, in this thesis, we have only looked at the fluid-like state of the system. We have just started exploring the high concentration regime where we can check the propensity of the system to develop crystalline order. In the screened limit where we obtain a condensation due a negative squared sound speed, it is posssible to study the condensation phenomenon in greater detail. In future we also plan to examine whether the tendency to condense at nonzero wavenumber (See Fig 5.1), i.e., microphase separation, can lead to liquid-crystalline phases like smectics. The systems described in this thesis are extremely rich and the few ideas mentioned above form just a small subset of the plethora of exciting theoretical and experimental explorations that can be performed with them. Since they can be “designed”, unlike biological substances, they can also become a test-bed for testing theoretical predictions of the nonequilibrium statistical mechanics of self-propelled systems.

Les invasions biologiques se sont intensifiées au cours des dernières décennies en raison d’une accélération des échanges commerciaux. Ces invasions représentent une menace pour les écosystèmes et de nombreuses activités anthropiques, il est donc crucial de comprendre les mécanismes qui les sous-tendent afin de mieux prévoir et limiter leurs impacts. Dans cette thèse, j’aborde la question du potentiel dispersif d’espèces natives et non natives impliquées dans une association phorétique nouvellement formée. En particulier, je me focalise sur le cas de l’association entre un nématode invasif ravageur des pinèdes, le nématode du pin (Bursaphelenchus xylophilus) et son insecte vecteur endémique en Europe (Monochamus galloprovincialis). J’ai tout d’abord étudié les flux de gènes de l’insecte vecteur seul afin d’identifier les barrières à sa dispersion. J’ai ensuite simulé l’expansion spatiale du couple nématode-vecteur à l’aide d’un modèle de dispersion, en intégrant l’effet synergique de cette nouvelle association. Les résultats obtenus au cours de cette thèse montrent qu’il existe un important potentiel de dispersion du nématode invasif en Europe par le biais de cette association phorétique. En revanche, certains paramètres de l’environnement tels que les reliefs et les températures basses qui leur sont associées, ainsi que les fortes densités en pins constituent des barrières à la dispersion du vecteur et donc des obstacles potentiels à l’expansion du nématode invasif. Au-delà des apports relatifs au modèle d’étude, cette thèse a conduit au développement de plusieurs méthodes pouvant être adaptées à d’autres cas d’associations phorétiques nouvelles et, par extension, contribuer à la compréhension de la dispersion des espèces au sein de ces systèmes complexes et peu étudiés. / Biological invasions dramatically increased over the last decades due to the intensification of international trade. These invasions constitute a threat for ecosystems and many anthropic activities, therefore it is crucial to understand underlying processes in order to better predict and manage their impacts. In this PhD thesis, I explore the potential of dispersion of native and non-native species involved in a novel phoretic association. I focus on the case of the association between a pest for pine forests, the pinewood nematode (Bursaphelenchus xylophilus) introduced in Europe, and its endemic insect vector (Monochamus galloprovincialis). I first estimated gene flows of the insect vector alone in order to identify the barriers and corridors to dispersal of this species. Then I have simulated the spatial spread of the nematode-vector couple using a spread model, and accounting for the synergistic effect of this novel association. The results obtained during this PhD showed that the invasive nematode has an important potential to spread through this phoretic association. However, some environmental features such as elevation, areas with low temperatures, and the high pine densities constitute barriers to dispersal of the vector and so, potential obstacles to the spread of the invasive nematode. Beyond these results focused on the model of study, this thesis has led to the development of several methods that may be adapted to other cases of novel phoretic association and, by extension, may contribute to a better understanding of dispersal of species involved in those complex and poorly known systems.

La phorèse est un mécanisme physico-chimique par lequel certains colloïdes microscopiques dérivent à travers les gradients d'un champ de concentration de soluté dans un fluide. Ce mécanisme est exploité par des particules autophorétiques, ou colloïdes actifs chimiquement, pour auto-propulser. Ces particules influencent les mouvements de leurs voisines par le biais d'interactions chimiques et hydrodynamiques et sont donc étudiées pour leur comportement collectif. La modélisation de ces interactions a fait l'objet de recherches approfondies au cours des dernières années, à la fois d'un point de vue physique pour comprendre les mécanismes précis des interactions, et d'un point de vue expérimental pour expliquer les observations de la formation de structures cohérentes à grande échelle. Cependant, une modélisation exacte de ces suspensions actives est difficile en raison des interactions à grand nombre de particules. Jusqu'à présent, la plupart des modèles proposés reposent sur la superposition d'approximations de champ lointain pour les signatures chimiques et hydrodynamiques de chaque particule, qui ne sont valides que de manière asymptotique dans la limite de suspensions très diluées. Un cadre analytique systématique et unifié basé sur la méthode classique de réflexion (MoR) est développé ici pour les problèmes de Laplace et de Stokes afin d'obtenir les interactions entre particules phorétiques et les vitesses résultantes avec un ordre de précision arbitraire en terme du rapport du rayon et de la distance typique entre deux particules voisines.Un système comprenant uniquement des particules autophorétiques homogènes et isotropes chimiquement et géométriquement est ensuite considéré en détail. On sait que de telles particules isotropes ne peuvent se propulser seules; cependant, en présence d'autres particules identiques, la symétrie du champ de concentration est brisée et les particules forment spontanément des agrégats ou clusters denses. De manière remarquable, ceux-ci peuvent s'auto-propulser si leur arrangement est présente une asymétrie. Ce résultat identifie donc une nouvelle voie pour briser la symétrie du champ de concentration et ainsi générer un mouvement, qui ne repose pas sur une conception anisotrope des particules individuelles, mais sur les interactions collectives de particules actives identiques et homogènes. Un argument pour l'origine de ce comportement auto-propulsif des clusters, basé sur la MoR, est proposé. De plus, en utilisant des simulations numériques complètes combinées à un modèle théorique réduit, nous caractérisons les propriétés statistiques de l'autopropulsion. / Diffusiophoresis is a physico-chemical mechanism by which certain microscopic colloids drift through gradients of a solute concentration field in a fluid. This mechanism is exploited by autophoretic particles, which are chemically active synthetic colloids, to achieve self-propulsion. These particles influence each others' motion through chemical and hydrodynamic interactions and are hence known to exhibit collective behaviour. Modeling these interactions is a subject of intense research over the past decades, both from a physical perspective to understand the precise mechanisms of the interactions, as well as from an experimental point of view to explain the observations of formation of coherent large-scale structures. However, an exact modeling of is difficult due to multi-body interactions and surface effects. Most efforts so far rely on the superposition of far-field approximations for each particle's signature, which are only valid asymptotically in the dilute suspension limit. A systematic and unified analytical framework based on the classical Method of Reflections (MoR) is developed here for both Laplace and Stokes' problems to obtain the multi-body interactions and the resulting velocities of phoretic particles, up to any order of accuracy in the radius-to-distance ratio of the particles.A system comprising only of chemically- and geometrically-isotropic autophoretic particles is then considered in detail. It is known that such isotropic particles cannot self-propel in isolation; however, in the presence of other identical particles, the symmetry of the concentration field is broken and the particles spontaneously form close packed clusters. Remarkably, these clusters are observed to self-propel based on their geometric arrangement. This result thus identifies a new route to symmetry-breaking for the concentration field and to self-propulsion, that is not based on an anisotropic design, but on the collective interactions of identical and homogeneous active particles. An argument for origin of this self-propulsive behaviour of clusters is made based on MoR. Furthermore, using full numerical simulations and theoretical model for clustering, we characterize the statistical properties of self-propulsion of the system.

No description available.

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.