In this paper we study the self-propulsion of a symmetric V-shape micro-robot (or V-robot) which consists of three spheres connected by two arms with an angle between them; the arms' lengths and the angle are changing periodically. Using an asymptotic procedure containing two-timing method and a distinguished limit, we obtain analytic expressions for the self-propulsion velocity and Lighthill's efficiency. The calculations show that a version of V-robot, aligned perpendicularly to the direction of self-swimming, is both the fastest one and the most efficient one. We have also shown that such $V$-robot is faster and more efficient than a linear three-sphere micro-robot. At the same time the maximal self-propulsion velocity of V-robots is significantly smaller than that of comparable microorganisms.
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…
In this paper we study the self-propulsion of a triangular micro-robot (or triangle-robot) which consists of three spheres connected by three rods; the rods' lengths are changing independently and periodically. Using the asymptotic procedure containing the two-timing method and distinguished limit arguments, we obtain analytic expressions for self-propulsion velocity the angular velocity. Our calculations show that a triangle-robot rotates with constant angular velocity around its centroid, while the centroid moves in a circle. The important special case of zero angular velocity represents rec…
The aim of this paper is to derive an analytical expression for the self-propulsion velocity of a micro-swimmer that consists of N spheres moving along a fixed line. The spheres are linked to each other by the rods of the prescribed lengths changing periodically. For the derivation we use the asymptotic procedure containing the two-timing method and a distinguished limit. Our final formula shows that in the main approximation the self-propulsion velocity is determined by the interactions between all possible triplets of spheres.
In this paper we study the self-propulsion of a dumbbell micro-robot submerged in a viscous fluid. The micro-robot consists of two rigid spherical beads connected by a rod or a spring; the rod's/spring's length is changing periodically. The constant density of each sphere differs from the density of a fluid, while the whole micro-robot has neutral buoyancy. An effective oscillating gravity field is created via rigid-body oscillations of the fluid. Our calculations show that the micro-robot undertakes both translational and rotational motion. Using an asymptotic procedure containing a two-timin…
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 self-propulsion of a sphere immersed in a polar liquid or ferrofluid is studied on the basis of ferrohydrodynamics. In the electrical case an oscillating charge density located inside the sphere generates an electrical field which polarizes the fluid. The lag of polarization with respect to the electrical field due to relaxation generates a time-independent electrical torque density acting on the fluid causing it to move. The resulting propulsion velocity of the sphere is calculated in perturbation theory to second order in powers of the charge density.
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…
Combining geometric mechanics theory, laboratory robotic experiment and numerical simulation, we study the locomotion in granular media (GM) of the simplest non-inertial swimmer, the Purcell three-link swimmer. Using granular resistive force laws as inputs, the theory relates translation and rotation of the body to shape changes (movements of the links). This allows analysis, visualization, and prediction of effective movements that are verified by experiment. The geometric approach also facilitates comparison between swimming in GM and in viscous fluids.
Among the many types of artificial motile nano- and microparticles that have been developed in the past, colloidal particles that exhibit propulsion when they are exposed to ultrasound are particularly advantageous. Their properties, however, are still largely unexplored. For example, the dependence of the propulsion on the particle shape and the structure of the flow field generated around the particles are still unknown. In this article, we address the propulsion mechanism of ultrasound-propelled nano- and microparticles in more detail. Based on direct computational fluid dynamics simulation…
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…
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…
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-propulsion of a Janus droplet in a solution of surfactant, which reacts on a half of a drop surface, is studied theoretically. The droplet acts as a catalytic motor creating a concentration gradient, which generates its surface-tension-driven motion; the self-propulsion speed is rather high, $60\; {\rm μm/s}$ and more. This catalytic motor has several advantages over other micromotors: simple manufacturing, easily attained neutral buoyancy. In contrast to a single-fluid droplet, which demonstrates a self-propulsion as a result of symmetry breaking instability, for Janus one no stability t…
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. …
The move to high performance applications greatly increases the demand to produce large instantaneous fluid forces for high-speed maneuvering and improved power efficiency for sustained propulsion. Animals achieve remarkable feats of maneuvering and efficiency by changing their body shape to generate unsteady fluid forces. Inspired by this, we have studied a range of immersed bodies which drastically change their shape to produce fluid forces. These include relatively simple shape- changes, such as quickly changing the angle of attack of a foil to induce emergency stops and the use of tandem f…
We study self-propulsion of a half-metal coated colloidal particle under laser irradiation. The motion is caused by self-thermophoresis: i.e. absorption of laser at the metal-coated side of the particle creates local temperature gradient which in turn drives the particle by thermophoresis. To clarify the mechanism, temperature distribution and a thermal slip flow field around a micro-scale Janus particle are measured for the first time. With measured temperature drop across the particle, the speed of self-propulsion is corroborated with the prediction based on accessible parameters. As an appl…
Shear-thinning is an important rheological property of many biological fluids, such as mucus, whereby the apparent viscosity of the fluid decreases with shear. Certain microscopic swimmers have been shown to progress more rapidly through shear-thinning fluids, but is this behavior generic to all microscopic swimmers, and what are the physics through which shear-thinning rheology affects a swimmer's propulsion? We examine swimmers employing prescribed stroke kinematics in two-dimensional, inertialess Carreau fluid: shear-thinning "Generalized Stokes" flow. Swimmers are modeled, using the method…
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…
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…
