We theoretically investigate the fluid mechanics of self-propelled (or swimming) bodies. An important factor concerning the hydrodynamics of locomotion concerns the relative strength of inertial to viscous forces experienced by the swimmer, the ratio of which is quantified by the Reynolds number, Re. Particular attention is given to the regime where Re is intermediate, where viscous and inertial forces are both relevant to fluid motion. We study two broad classes of swimmers: ‘pushers’ and ‘pullers’. Pushers produce thrust from the rear of their body, while pullers generate thrust from the front. We first investigate the near-field flow due to pushers and pullers by numerically solving the Navier-Stokes equations for Re of 0.01–1000. We show that, although the locomotion of pushers and pullers is similar at small Re, drastic differences due to fluid inertia arise as Re is increased. Most remarkably, flow instabilities develop at much smaller Re for a puller than a pusher. Further, we investigate the large scale fluid transport induced by a swimmer as a function of Re in the context of the induced ‘drift volume’. The drift volume quantifies the volume of fluid swept out by a ‘dyed’ fluid plane that is initially perpendicular to the body’s path. However, we first address the previously unsolved problem of the drift volume due to a body that is towed by an external force at finite Re. While the drift volume is comparable to the body volume in inviscid flow (Re ! 1), it is much larger when Re is finite due to viscous effects. The drift volume due to a swimmer is smaller than that due to a towed body because swimmers generate a weaker far-field flow. However, it is still potentially large compared to the volume of the swimmer’s body in the viscously dominated small-Re regime. However, the drift volume of a swimmer quickly diminishes as Re is increased.

La nageoire caudale des animaux aquatiques peut être modélisée par un foil oscillant qui produit de la poussée. Le sillage moyen d'un tel foil oscillant est un jet de quantité de mouvement nette positive. Il a été proposé que les caractéristiques de stabilité de ces sillages moyens sont liées à l'efficacité de la propulsion des animaux aquatiques. Dans cet étude, nous reprenons cette question en tenant compte à la fois de la poussée et de la traînée exercée sur un corps auto-propulsé lorsqu'il nage. Nous étudions la stabilité d'une famille de sillages ayant une quantité de mouvement nulle, construit comme l'approximation d'Oseen d'un doublet de force se déplaçant à vitesse constante. En effectuant une analyse de stabilité locale, nous montrons d'abord que ces sillages subissent une transition convectif-absolu. En utilisant une approche "time-stepper" et intégrant le système de Navier-Stokes linéarisé, nous étudions la stabilité globale et mettons en évidence des effets non-parallèles de l'écoulement principal, ainsi que le rôle de la région absolument instable dans l'écoulement. Pour compléter le scénario d'instabilité globale, nous abordons l'évolution non linéaire d'une perturbation injectée dans le sillage. Ces résultats sont ensuite discutés dans le contexte de la nage d'un animal aquatique. Selon les résultats de stabilité, les sillages de quantité de mouvement nulle produit par les animaux aquatiques sont généralement stables, tandis que le sillage qui correspondrait à la poussée seule est instable. Il est essentiel de considérer toutes les forces exercées sur un animal auto-propulsé lors de l'examen de la stabilité de son sillage et l'efficacité de sa propulsion. / The caudal fin of swimming animals can be modelled as a thrust-producing flapping foil. When considered alone, such a foil produces on average a jet wake with a positive net momentum. It has been argued that the instability characteristics of these averaged wakes are linked to the propulsion efficiency of swimming animals. Here, we reconsider this question by taking into account both the thrust and the drag exerted on a self-propelled swimming body. To do so, we study the stability of a family of momentumless wakes, constructed as the Oseen approximation of a force doublet moving at constant velocity. By performing a local stability analysis, we first show that these wakes undergo a transition from absolute to convective instability. Then, using the time-stepper approach by integrating the linearised Navier-Stokes system, we investigate the global stability and reveal the influence of a non-parallel base flow as well as the role of the locally absolutely unstable upstream region in the wake. Finally, to complete the global scenario, we address the nonlinear evolution of the wake disturbance. These results are then discussed in the context of aquatic locomotion. According to the present stability results, the momentumless wake of aquatic animals is generally stable, whereas the corresponding thrust part is unstable. It is therefore essential to consider all forces exerted on a self-propelled animal when discussing its wake stability and its propulsion efficiency.

The remarkable efficacy with which normal surface mass transpiration (blowing and suction) alters a given base flow to achieve a desired predefined objective has motivated several investigations on drag reduction, self-propulsion and suppression of separation and wake unsteadiness in bluff body flows. However, the energetic efficiency, a critical parameter that determines the true efficacy and in particular practical feasibility of this control strategy, has received significantly less attention. In this work, we determine the optimal zero net mass transpiration blowing and suction profiles that minimize net power consumption while reducing drag or enabling self-propulsion in typical bluff body flows. We establish the influence of prescribed blowing and suction profiles on the hydrodynamic loads and net power consumption for a representative bluff body flow involving flow past a stationary two-dimensional circular cylinder. Using analysis based on Oseen’s equations, we find that all the symmetric modes, except the first one, lead to an increase in the net power consumption without affecting hydrodynamic drag. The optimal blowing and suction profile that yields minimum power consumption is such that the normal stress acting on the cylinder surface vanishes identically. Furthermore, we show that a self-propelling state corresponding to zero net drag force is attained when the first mode of blowing and suction profile is such that the flow field be-comes irrigational. Based on these findings we employ direct numerical simulation tools to decipher the Reynolds number dependence of the optimal profiles and the associated power consumption for both drag reduction and self-propulsion. For a typical Reynolds number, the time-averaged drag coefficient first decreases due to vortex shedding suppression, then increases and eventually decreases again after attaining a local maximum as the strength of the first mode is increased. The net power consumption continues to decrease with an increase in the strength of the first mode before reaching a minima after which it rises continuously. For a Reynolds number of 1000 over fifteen fold reduction in drag is achieved for an optimal blowing and suction profile with a maximum radial surface velocity that is nearly 1.97 times the free stream velocity. Next, to establish whether or not higher modes play a role in decreasing net power consumption at finite Reynolds number, we perform theoretical analysis of a configuration similar to the one described above for a spherical body. At zero Reynolds number, as a result of mode independence, we show that surface blow-ing and suction of any form that involves second or higher order axisymmetric or non-axisymmetric modes does not contribute to drag and only leads to an increase in total power consumption. However, at finite Reynolds number, using analysis based on Oseen’s equations, we find that the second and higher modes contribute substantially to the optimal profiles. Finally to understand the effects of a change in shape we consider generalization of the above analysis to axisymmetric prolate and oblate spheroidal bodies. We find that for a general axisymmetric body with non-constant curvature, the optimal drag reducing and self-propelling blowing and suction profiles for minimum power consumption contain second and higher-order modes along with the first mode even when the Reynolds number is zero. The net decrease in power consumption with the use of second and higher order modes exceeds 33% for a disk-like low aspect ratio self-propelling oblate spheroid. Moreover, we perform comparisons between blowing and suction and tangential surface velocity based boundary deformation propulsion mechanisms. Below an aspect ratio of 0.56 we find blowing and suction mechanism to be more efficient for self-propulsion of an oblate spheroid. In contrast, for a self-propelling pro-late spherical micro-swimmer, we show that the tangential surface tread milling consumes less power irrespective of the aspect ratio.

L'objectif de ce travail est d'étudier l'effet thermoélectrique à l'échelle nanométrique des nanostructures chauffées. Dans un premier temps, nous étudions les mécanismes d'autopropulsion thermo-électrophorétique de particules Janus chauffées par laser. Ce mécanisme d'autopropulsion est principalement induit par l'effet Seebeck ou l'effet thermoélectrique. Cet effet provient de la séparation des charges survenues lorsqu'un gradient de température est présent dans la solution d'électrolyte: Une forte absorption du laser par la partie métallisée de la particule génère un gradient de température qui en retour agit sur les espèces ioniques (positive et négative) et les conduits vers les zones chaudes ou les zones froides. Ce mouvement d'ions entraine la création d'un champ électrique dipolaire qui, à proximité de la particule, dépend fortement des propriétés de surface. Ce changement de comportement de ce champ électrique sur une surface isolant ou conductrice n'affecte pas la vitesse de la particule. Dans un second temps, nous étudions les effets d'interactions hydrodynamiques et de la condensation des contre-ions sur la thermophorèse des polymères d'ADN. Comme résultat principal, la mobilité thermophorétique montre, en fonction de la longueur de la chaîne, un comportement non-monotone et se compose de deux contributions induites par les forces conductrices dominantes que sont l'effet Seebeck et le gradient de permittivité. À la fin, nous comparons notre résultat théorique avec une récente expérience sur l'ADN / The aim of this work is to study the nanoscale Seebeck effect at hot nanostructures. At first, we study the thermo-electrophoresis self-propulsion mechanism for a heated metal capped Janus colloid. The self-propulsion mechanism is mainly induced by the electrolyte Seebeck effect or thermoelectric effect. This effect takes its origin from the separation of charges occurring while a temperature gradient is present in a electrolyte solution: A strong absorption of laser light by the metal side of the particle creates a temperature gradient which in turn acts on ion-species (positive and negative) and drives them to the hot or the cold region. This motion of ion results in a dipolar electric field which, close to the particle, depends strongly on the surface properties. The change of behavior of the electric field at the insulating or conducting surface does not affect the velocity of the particle. At second, we study the effect of hydrodynamic interactions and counterion condensation in thermophoresis for DNA polymer. As the main result, the thermophoretic mobility shows, in function of the chain length, a non-monotonuous behavior and consists of two contributions induced by the dominant driving forces which are the thermally induced permittivity-gradient and the electrolyte Seebeck effect. At the end, we compare our theoretical result with recent experiment on single-stranded DNA.

<div>In many natural and industrial processes, bubbles are exposed to surface-active contaminants (surfactants) that may cover the whole or part of the bubble interface. A partial coverage of the bubble interface results in a spontaneous self-propulsion mechanism, which is yet poorly understood.</div><div>The main goal of this study is to enhance the understanding of the flow and interfacial mechanisms underlying the self-propulsion of small surfactant contaminated bubbles. The focus is on characterizing the self-propulsion regimes generated by the presence of surface-active species, and the influence of surfactant activity and surface coverage on the active bubble motion. </div><div>The study was developed by simultaneously solving the full system of partial differential equations governing the free-surface flow physics and the surfactant transport on the deforming bubble interface using multi-scale numerical simulation. </div><div>Results show in microscopic detail how surface tension gradients (Marangoni stresses) induced by the uneven interfacial coverage produce spontaneous hydrodynamics flows (Marangoni flows) on the surrounding liquid, leading to bubble motion. Results also establish the influence of both surfactant activity and interfacial coverage on total displacement and average bubble velocity at the macroscale. </div><div>Findings from this research improve the fundamental understanding of the free-surface dynamics of self-propulsion and the associated transport of surface-active species, which are critical to important natural and technological processes, ranging from the Marangoni propulsion of microorganisms to the active motion of bubbles and droplets in microfluidic devices. Overall, the findings advance our understanding of active matter behavior; that is, the behavior of material systems with members able to transduce surface energy and mass transport into active movement.</div>

Propulsionar cadeira de rodas (CR) está relacionado a altas incidências de dores e lesões em usuários de cadeira de rodas (UCR). Embora seja reconhecida como uma forma de baixa eficiência para se locomover, representa fundamental importância para o desempenho dessas pessoas nas atividades de vida diária, ocupacionais, de lazer e em sua participação social. Ao longo dos estudos sobre a propulsão nas últimas décadas, foi notado recentemente em especial, que a propulsão inicial que retira o sistema usuário-cadeira de rodas do repouso, o colocando em movimento, apresentam a maiores solicitações mecânicas. Considerando que esta situação é executada várias vezes durante o uso típico da cadeira de rodas, torna-a relevante objeto de estudo. Como até o momento, pouco foram os estudos sobre a fase inicial da autopropulsão e que do ponto de vista da neuroativação, esse movimento não foi abordado, este estudo tem como objetivo descrever o gesto da fase inicial da autopropulsão de cadeira de rodas manual de UCR, por meio da eletromiografia, apresentando os níveis atingidos de ativação muscular e o perfil do comportamento de ativação ao longo da execução do gesto da autopropulsão. Para isso foram avaliados oito grupos musculares envolvidos nesse gesto de onze UCR. Os sinais eletromiográficos foram coletados dos oito grupos musculares, simultaneamente, durante a execução de dez propulsões, partindo do repouso, de cada UCR participante da pesquisa. Com relação aos níveis de ativações musculares, foi introduzido um método alternativo de normalização. Esse método consiste na realização do teste de contração isométrica máxima na própria CR. Os resultados foram apresentados em boxplot a fim de demonstrar o pico de ativação bem como a distribuição dos demais níveis de ativação. Como o novo método proposto demonstrou limitações, inviabilizou a interpretação dos resultados quanto as intensidades calculadas. Sobre o perfil de acionamento muscular ao longo da execução da autopropulsão, os resultados foram expostos em gráficos normalizados pelo pico dinâmico e em relação ao período de um ciclo de propulsão, evidenciando o comportamento ativado em cada instante do ciclo. Segundo os resultados dessa segunda metodologia, entre os oito grupos musculares examinados, os que apresentaram os maiores picos de ativação foram: deltoide anterior (80,27%), o peitoral maior (79,27%), os flexores de punho (78,93%) e os extensores de punho (80,65%). Os achados colaboram com estudos anteriores de outros autores de que os principais grupos musculares efetores na propulsão de CR são o deltóide anterior (DA) e peitoral maior (PM). / Propelling wheelchair (CR) is related to high incidences of pain and injury in wheelchair users (WCU). Although this locomotion way be known as low efficient locomotion mode, it represents fundamental importance for these people performance in daily living activities, occupational, leisure and in their social participation. Over the studies course on propulsion in recent decades, it has recently been noted, particularly, that the initial stage of wheelchair propulsion which retires the user-wheelchair system from resting, putting it into motion, presents greater mechanical stresses. It considering this situation is executed several times during the typical wheelchair usage, it makes this relevant study object. As until current moment, there are few studies about initial stage of wheelchair propulsion and, from the neuroactivation point of view, this movement was not approached, this study aims to describe the gesture of initial stage of manual wheelchair propulsion from WCU, across electromyography, presenting the muscular activation levels achieved and the recruited behavior profile during the propulsion gesture execution. For this problem, eight muscle groups involved in this gesture were evaluated from eleven WCU. Electromyographic signals were collected from these eight muscle groups, simultaneously, during ten propulsions execution, starting from resting, of each WCU participant of the research. Regarding the muscular activation levels, an alternative normalization method was introduced. This method consists in performing the maximum isometric contraction test on the wheelchair itself. The results were showed in boxplot in order to demonstrate the activation peak as well as the remaining activation levels distribution. As the new method proposed showed limitations, a better results interpretation was not possible on calculated intensities. Regarding the muscular activation profile during the propulsion execution, the results were exposed in graphs normalized by the dynamic peak as well as in relation to a single propulsion cycle, evidencing the activated behavior at each cycle moment. According to the results based on second methodology, among the eight muscle groups examined, the ones which presented the highest activation peaks values were: the anterior deltoid (80.27%), the pectoralis major (79.27%), the wrist flexors (78, 93%) and the wrist extensors (80.65%). The findings agree with previous studies by other authors that the main effector muscle groups in CR propulsion are anterior deltoid (DA) and pectoralis major (PM).

Propulsionar cadeira de rodas (CR) está relacionado a altas incidências de dores e lesões em usuários de cadeira de rodas (UCR). Embora seja reconhecida como uma forma de baixa eficiência para se locomover, representa fundamental importância para o desempenho dessas pessoas nas atividades de vida diária, ocupacionais, de lazer e em sua participação social. Ao longo dos estudos sobre a propulsão nas últimas décadas, foi notado recentemente em especial, que a propulsão inicial que retira o sistema usuário-cadeira de rodas do repouso, o colocando em movimento, apresentam a maiores solicitações mecânicas. Considerando que esta situação é executada várias vezes durante o uso típico da cadeira de rodas, torna-a relevante objeto de estudo. Como até o momento, pouco foram os estudos sobre a fase inicial da autopropulsão e que do ponto de vista da neuroativação, esse movimento não foi abordado, este estudo tem como objetivo descrever o gesto da fase inicial da autopropulsão de cadeira de rodas manual de UCR, por meio da eletromiografia, apresentando os níveis atingidos de ativação muscular e o perfil do comportamento de ativação ao longo da execução do gesto da autopropulsão. Para isso foram avaliados oito grupos musculares envolvidos nesse gesto de onze UCR. Os sinais eletromiográficos foram coletados dos oito grupos musculares, simultaneamente, durante a execução de dez propulsões, partindo do repouso, de cada UCR participante da pesquisa. Com relação aos níveis de ativações musculares, foi introduzido um método alternativo de normalização. Esse método consiste na realização do teste de contração isométrica máxima na própria CR. Os resultados foram apresentados em boxplot a fim de demonstrar o pico de ativação bem como a distribuição dos demais níveis de ativação. Como o novo método proposto demonstrou limitações, inviabilizou a interpretação dos resultados quanto as intensidades calculadas. Sobre o perfil de acionamento muscular ao longo da execução da autopropulsão, os resultados foram expostos em gráficos normalizados pelo pico dinâmico e em relação ao período de um ciclo de propulsão, evidenciando o comportamento ativado em cada instante do ciclo. Segundo os resultados dessa segunda metodologia, entre os oito grupos musculares examinados, os que apresentaram os maiores picos de ativação foram: deltoide anterior (80,27%), o peitoral maior (79,27%), os flexores de punho (78,93%) e os extensores de punho (80,65%). Os achados colaboram com estudos anteriores de outros autores de que os principais grupos musculares efetores na propulsão de CR são o deltóide anterior (DA) e peitoral maior (PM). / Propelling wheelchair (CR) is related to high incidences of pain and injury in wheelchair users (WCU). Although this locomotion way be known as low efficient locomotion mode, it represents fundamental importance for these people performance in daily living activities, occupational, leisure and in their social participation. Over the studies course on propulsion in recent decades, it has recently been noted, particularly, that the initial stage of wheelchair propulsion which retires the user-wheelchair system from resting, putting it into motion, presents greater mechanical stresses. It considering this situation is executed several times during the typical wheelchair usage, it makes this relevant study object. As until current moment, there are few studies about initial stage of wheelchair propulsion and, from the neuroactivation point of view, this movement was not approached, this study aims to describe the gesture of initial stage of manual wheelchair propulsion from WCU, across electromyography, presenting the muscular activation levels achieved and the recruited behavior profile during the propulsion gesture execution. For this problem, eight muscle groups involved in this gesture were evaluated from eleven WCU. Electromyographic signals were collected from these eight muscle groups, simultaneously, during ten propulsions execution, starting from resting, of each WCU participant of the research. Regarding the muscular activation levels, an alternative normalization method was introduced. This method consists in performing the maximum isometric contraction test on the wheelchair itself. The results were showed in boxplot in order to demonstrate the activation peak as well as the remaining activation levels distribution. As the new method proposed showed limitations, a better results interpretation was not possible on calculated intensities. Regarding the muscular activation profile during the propulsion execution, the results were exposed in graphs normalized by the dynamic peak as well as in relation to a single propulsion cycle, evidencing the activated behavior at each cycle moment. According to the results based on second methodology, among the eight muscle groups examined, the ones which presented the highest activation peaks values were: the anterior deltoid (80.27%), the pectoralis major (79.27%), the wrist flexors (78, 93%) and the wrist extensors (80.65%). The findings agree with previous studies by other authors that the main effector muscle groups in CR propulsion are anterior deltoid (DA) and pectoralis major (PM).

Equilibrium statistical mechanics has a remarkable property: the steady state probability distribution can be calculated by a procedure independent of the detailed dynamics of the system under consideration. The partition function contains the complete thermodynamics of the system. The calculation of the partition function itself might be a daunting task and one might need to resort to approximate methods in practice. But there is no problem in principle on how to do the statistical mechanics of a system that is at thermal equilibrium. Nonequilibrium statistical mechanics is a completely different story. There is no general formalism, even in principle, the application of which is guaranteed to yield the probability distribution, even for stationary states, without explicit consideration of the dynamics of the system. Instead, there are several methods of wide applicability drawn from experience which work for particular classes of systems. Frequently, one writes down phenomenological equations of motion based on general principles of conservation and symmetry and attempts to extract the dynamical response and correlations. The motivation for studying nonequilibrium systems is the very simple fact that they are ubiquitous in nature and exhibit very rich, diverse and often counter-intuitive phenomenon. We ourselves are an example of a very complex nonequilibrium system. This thesis examines three problems which illustrate the generic features of a typical driven system maintained out of thermal equilibrium. The first chapter provides a very brief discussion of nonequilibrium systems. We outline the tools that are commonly employed in the theoretical description of driven systems, and discuss the response of physical systems to applied perturbations. Chapter two considers a very simple model for a single self-propelled particle with an internal asymmetry, and nonequilibrium energy input in the form of Gaussianwhite noise. Our model connects three key nonequilibrium quantities – drift velocity, mean internal force and position-velocity correlations. We examine this model in detail and solve it using perturbative, numerical and exact methods. We begin chapter three with a brief introduction to the sedimentation of particle-fluid suspensions. Some peculiarities of low Reynolds number hydrodynamics are discussed with particular emphasis on the sedimentation of colloidal particles in a viscous fluid. We then introduce the problem of velocity fluctuations in steady sedi-mentation. The relevance of the current study to an earlier model and improvements made in the present work are then discussed. A physical understanding of our model and the conclusions that result from its analysis are an attempt to resolve the old problem of divergent velocity fluctuations in steadily sedimentating suspensions. The fourth chapter is a study to probe the nature of the fluctuations in a driven suspension of point-particles. Fluctuation relations that characterise large-deviations are a current topic of intense study. We show in this chapter that the random dynamics of suspended particles in a driven suspension occasionally move against the driving force, and that the probability of such rare events obeys a steady state fluctuation relation. In the final chapter, we summarise the models studied and point out the common features that they display. We conclude by pointing out some ways in which the problems discussed in this thesis can be extended upon in the future.

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.