The aim of this paper is to describe the self-propulsion of a micro-robot (or micro-swimmer) consisting of $N$ spheres moving along a fixed line. The spheres are linked to each other by arms with the lengths changing periodically. For the derivation, we use the asymptotic procedure containing the two-timing method and a distinguished limit. We show that in the main approximation, the self-propulsion velocity appears as a linear combination of velocities of all possible triplets of spheres. Velocities and efficiencies of three-, four-, and five-swimmers are calculated.
The paper is devoted to H.K.Moffatt, who initiated the author's interests in low-Reynolds-number fluid dynamics.
We present here a comprehensive derivation for the speed of a small bottom-heavy sphere forced by a transverse acoustic field and thereby establish how density inhomogeneities may play a critical role in acoustic propulsion. The sphere is trapped at the pressure node of a standing wave whose wavelength is much larger than the sphere diameter. Due to its inhomogeneous density, the sphere oscillates in translation and rotation relative to the surrounding fluid. The perturbative flows induced by the sphere's rotation and translation are shown to generate a rectified inertial flow responsible for …
We describe experiments and simulations demonstrating the propulsion of a neutrally-buoyant swimmer that consists of a pair of spheres attached by a spring, immersed in a vibrating fluid. The vibration of the fluid induces relative motion of the spheres which, for sufficiently large amplitudes, can lead to motion of the center of mass of the two spheres. We find that the swimming speed obtained from both experiment and simulation agree and collapse onto a single curve if plotted as a function of the streaming Reynolds number, suggesting that the propulsion is related to streaming flows. There …
The propulsion of a liquid indium-tin micro-droplet by nanosecond-pulse laser impact is experimentally investigated. We capture the physics of the droplet propulsion in a scaling law that accurately describes the plasma-imparted momentum transfer, enabling the optimization of the laser-droplet coupling. The subsequent deformation of the droplet is described by an analytical model that accounts for the droplet's propulsion velocity and the liquid properties. Comparing our findings to those from vaporization-accelerated mm-sized water droplets, we demonstrate that the hydrodynamic response of la…
The paper carries on our previous investigations on the complementary version of Purcell's rotator: a low-Reynolds-number swimmer composed of three balls of equal radii. In the asymptotic regime of very long arms, the Stokes induced governing dynamics is derived and then experimented in the context of energy minimizing self-propulsion characterized in the first part of the paper.
Self-propulsion at low Reynolds number is notoriously restricted, a concept that is commonly known as the "scallop theorem". Here we present a truly self-propelled swimmer (force- and torque- free) that, while unable to swim in a Newtonian fluid due to the scallop theorem, propels itself in a non-Newtonian fluid as a result of fluid elasticity. This propulsion mechanism is demonstrated using a robotic swimmer, comprised of a "head" sphere and a "tail" sphere, whose swimming speed is shown to have reasonable agreement with a microhydrodynamic asymptotic theory and numerical simulations. Schlier…
In this paper we are interested in optimizing the shape of multi-flagellated helical microswimmers. Mimicking the propagation of helical waves along the flagella, they self-propel by rotating their tails. The swimmer's dynamics is computed using the Boundary Element Method, implemented in the open source Matlab library $Gypsilab$. We exploit a Bayesian optimization algorithm to maximize the swimmer's speeds through their shape optimization. Our results show that the optimal tail shapes are helices with large wavelength, such that the shape periodicity is disregarded. Moreover, the best propuls…
Self-propelling particles or microswimmers have opened a new field of investigation with both fundamental and practical perspectives. They represent very convenient model objects for experimental studies of active matter, and have implications in nano-robotics, drug delivery, and more. Here, we summarize recent advances in theoretical description of the self-propulsion of catalytic microswimmers that non-uniformly release ions, including its physical origins and the current switch in focus to non-linear effects, geometric tuning and more. In particular, we show that the ionic self-propulsion a…
The motion of microswimmers in complex flows is ruled by the interplay between swimmer propulsion and the dynamics induced by the fluid velocity field. Here we study the motion of a chiral microswimmer whose propulsion is provided by the spinning of a helical tail with respect to its body in a simple shear flow. Thanks to an efficient computational strategy that allowed us to simulate thousands of different trajectories, we show that the tail shape dramatically affects the swimmer's motion. In the shear dominated regime, the swimmers carrying an elliptical helical tail show several different J…
We study swimming of small spherical particles who regulate fluid flow on their surface by applying tangential squirming strokes. We derive translational and rotational velocities for any given stroke which is not restricted by axial symmetry as assumed usually. The formulation includes inertia of both the fluid and the swimmer, motivated by inertia's relevance for large Volvox colonies. We show that inertial contribution to mean speed comes from dynamic coupling between translation and rotation, which occurs only for strokes that break axial symmetry. Remarkably, this effect enables overcomin…
Studies of model microswimmers have significantly contributed to the understanding of the principles of self-propulsion we have today. However, only a small number of microswimmer types have been amenable to analytic modeling, and further development of such approaches is necessary to identify the key features of these active systems. Here we present a general perturbative calculation scheme for swimmers composed of beads interacting by harmonic potentials, driven by an arbitrary force protocol. The hydrodynamic interactions are treated using the Oseen and Rotne-Pragner approximations. We vali…
We report on the self-propulsion of boiling droplets which, despite their contact with viscous, immiscible oil films, attain high velocities comparable to those of levitating Leidenfrost droplets. Experiments and model reveal that droplet propulsion originates from a coupling between seemingly disparate short and long timescale phenomena due to microsecond fluctuations induced by boiling events at the droplet-oil interface. This interplay of phenomena leads to continuous asymmetric vapor release and momentum transfer for high droplet velocities.
Catalytic swimmers have attracted much attention as alternatives to biological systems for examining collective microscopic dynamics and the response to physico-chemical signals. Yet, understanding and predicting even the most fundamental characteristics of their individual propulsion still raises important challenges. While chemical asymmetry is widely recognized as the cornerstone of catalytic propulsion, different experimental studies have reported that particles with identical chemical properties may propel in opposite directions. Here, we show that, beyond its chemical properties, the det…
Self-diffusiophoretic particles exploit local concentration gradients of a solute species in order to self-propel at the micron scale. While an isolated chemically- and geometrically-isotropic particle cannot swim, we show that it can achieve self-propulsion through interactions with other individually-non-motile particles by forming geometrically-anisotropic clusters via phoretic and hydrodynamic interactions. This result 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 dynamics of…
In the study of microscopic flows, self-propulsion has been particularly topical in recent years, with the rise of miniature artificial swimmers as a new tool for flow control, low Reynolds number mixing, micromanipulation or even drug delivery. It is possible to take advantage of interfacial physics to propel these micro-robots, as demonstrated by recent experiments using the proximity of an interface, or the interface itself, to generate propulsion at low Reynolds number. This paper discusses how a nearby interface can provide the symmetry breaking necessary for propulsion. An overview of re…
Water vapor condensation is common in nature and widely used in industrial applications, including water harvesting, power generation, and desalination. As compared to traditional filmwise condensation, dropwise condensation on lubricant-infused surfaces (LIS) can lead to an order-of-magnitude increase in heat transfer rates. Small droplets (with the diameter below 100 $μ$m) account for nearly 85 percent of the total heat transfer and droplet sweeping plays a crucial role in clearing nucleation sites, allowing for frequent re-nucleation. Here, we focus on the dynamic interplay of microdroplets…
Oscillations of flagella and cilia play an important role in biology, which motivates the idea of functional mimicry as part of bio-inspired applications. Nevertheless, it still remains challenging to drive their artificial counterparts to oscillate via a steady, homogeneous stimulus. Combining theory and simulations, we demonstrate a strategy to achieve this goal by using an elasto-electro-hydrodynamic instability. In particular, we show that applying a uniform DC electric field can produce self-oscillatory motion of a microrobot composed of a dielectric particle and an elastic filament. Upon…
Active systems such as microorganisms and self-propelled particles show a plethora of collective phenomena, including swarming, clustering, and phase separation. Control over the propulsion direction and switchability of the interactions between the individual self-propelled units may open new avenues in designing of materials from within. Here, we present a self-propelled particle system, consisting of half-gold coated titania ($\mathrm{TiO}_2$) particles, in which we can fast and on-demand reverse the propulsion direction, by exploiting the different photocatalytic activities on both sides. …
Chemically active Janus particles generate tangential concentration gradients along their surface for self-propulsion. Although this is well studied in unbounded domains, the analysis in biologically relevant environments such as confinements is scarce. In this work, we study the motion of a Janus sphere in weak confinement. The particle is placed at an arbitrary location, with an arbitrary orientation between the two walls. Using the method of reflections, we study the effect of confining planar boundaries on the phoretic and hydrodynamic interactions, and their consequence on the Janus parti…
Swimming microorganisms often have to propel in complex, non-Newtonian fluids. We carry out experiments with self-propelling helical swimmers driven by an externally rotating magnetic field in shear-thinning, inelastic fluids. Similarly to swimming in a Newtonian fluid, we obtain for each fluid a locomotion speed which scales linearly with the rotation frequency of the swimmer, but with a prefactor which depends on the power index of the fluid. The fluid is seen to always increase the swimming speed of the helix, up to 50% faster and thus the strongest of such type reported to date. The maximu…
Synthetic microswimmers show great promise in biomedical applications such as drug delivery and microsurgery. Their locomotion, however, is subject to stringent constraints due to the dominance of viscous over inertial forces at low Reynolds number (Re) in the microscopic world. Furthermore, locomotory gaits designed for one medium may become ineffective in a different medium. Successful biomedical applications of synthetic microswimmers rely on their ability to traverse biological environments with vastly different properties. Here we leverage the prowess of machine learning to present an alt…
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…
We present a theory for the self-propulsion of symmetric, half spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air-water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion-advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary cond…
The temporal statistics of incompressible fluid velocity and passive scalar fields in developed turbulent conditions is investigated by means of direct numerical simulations along the trajectories of self-propelled point-like probes drifting in a flow. Such probes are characterised by a propulsion velocity which is fixed in intensity and direction; however, like vessels in a flow they are continuously deviated by their intended course as the result of local sweeping of the fluid flow. The recorded time-series by these moving probes represent the simplest realisation of transect measurements in…
