Self-propulsion of pure water droplets by spontaneous Marangoni-stress-driven motion

Separation of Floating Oil Drops Based on Drop-Liquid Substrate Interfacial Tension

Though various strategies exist for the transport of oil drops suspended on a liquid substrate, selective manipulation of different kinds of drops based on their respective characteristics remains a challenge. In practice, it is possible to have multiple drops having different wetting states with the liquid substrate, whose separation is desired. In this work, we exploit curvature-induced capillary forces for the selective manipulation (transport as well as separation) of oil droplets based on their interfacial tension (IFT) with the underlying liquid substrate. To demonstrate this, we have selected two oils having different IFTs with the aqueous liquid substrate and tuned their curvature-induced capillary interaction (inward or outward from the source) by controlled addition of the surfactant. We experimentally realize three droplet manipulation regimes: repulsion, attraction, and separation regime. In the repulsion and attraction regimes, both the drops behave in a similar manner. Strikingly, in the separation regime, drops can be effectively separated based on their IFT; low IFT droplets are attracted toward the source, while high IFT droplets do the reverse.

Self-Synchronous Swinging Motion of a Pair of Autonomous Droplets

Synchronized motion between two self-running oil droplets floating on an aqueous phase is reported. We describe the results of our observation on the interference between a pair of centimeter-sized nitrobenzene droplets undergoing back-and-forth motion on a waterway. The two droplets exhibit a swinging type of synchronization when a thin glass capillary is placed at the midpoint of the waterway with a narrow rectangle shape. Furthermore, 2:1 synchronized oscillation of the periodicities of this back-and-forth motion is generated when the capillary is shifted away from the center of the waterway. We discuss the mechanism of the emergence of synchronized swinging motion for the pair of droplets based on a simple mathematical model with nonlinear coupled differential equations.

Universal optimal geometry of minimal phoretic pumps

Unlike pressure-driven flows, surface-mediated phoretic flows provide efficient means to drive fluid motion on very small scales. Colloidal particles covered with chemically-active patches with nonzero phoretic mobility (e.g. Janus particles) swim using self-generated gradients, and similar physics can be exploited to create phoretic pumps. Here we analyse in detail the design principles of phoretic pumps and show that for a minimal phoretic pump, consisting of 3 distinct chemical patches, the optimal arrangement of the patches maximizing the flow rate is universal and independent of chemistry.

Self-propulsion of symmetric chemically active particles: Point-source model and experiments on camphor disks

Solid undeformable particles surrounded by a liquid medium or interface may propel themselves by altering their local environment. Such nonmechanical swimming is at work in autophoretic swimmers, whose self-generated field gradient induces a slip velocity on their surface, and in interfacial swimmers, which exploit unbalance in surface tension. In both classes of systems, swimmers with intrinsic asymmetry have received the most attention but self-propulsion is also possible for particles that are perfectly isotropic. The underlying symmetry-breaking instability has been established theoretically for autophoretic systems but has yet to be observed experimentally for solid particles. For interfacial swimmers, several experimental works point to such a mechanism, but its understanding has remained incomplete. The goal of this work is to fill this gap. Building on an earlier proposal, we first develop a point-source model that may be applied generically to interfacial or phoretic swimmers. Using this approximate but unifying picture, we show that they operate in very different regimes and obtain analytical predictions for the propulsion velocity and its dependence on swimmer size and asymmetry. Next, we present experiments on interfacial camphor disks showing that they indeed self-propel in an advection-dominated regime where intrinsic asymmetry is irrelevant and that the swimming velocity increases sublinearly with size. Finally, we discuss the merits and limitations of the point-source model in light of the experiments and point out its broader relevance.

Physics of active emulsions

Phase separating systems that are maintained away from thermodynamic equilibrium via molecular processes represent a class of active systems, which we call active emulsions. These systems are driven by external energy input, for example provided by an external fuel reservoir. The external energy input gives rise to novel phenomena that are not present in passive systems. For instance, concentration gradients can spatially organise emulsions and cause novel droplet size distributions. Another example are active droplets that are subject to chemical reactions such that their nucleation and size can be controlled, and they can divide spontaneously. In this review, we discuss the physics of phase separation and emulsions and show how the concepts that govern such phenomena can be extended to capture the physics of active emulsions. This physics is relevant to the spatial organisation of the biochemistry in living cells, for the development of novel applications in chemical engineering and models for the origin of life.

Active Particles Powered by Quincke Rotation in a Bulk Fluid

Dielectric particles suspended in a weakly conducting fluid are known to spontaneously start rotating under the action of a sufficiently strong uniform dc electric field due to the Quincke rotation instability. This rotation can be converted into translation when the particles are placed near a surface providing useful model systems for active matter. Using a combination of numerical simulations and theoretical modeling, we demonstrate that it is possible to convert this spontaneous Quincke rotation into spontaneous translation in a plane perpendicular to the electric field in the absence of surfaces by relying on geometrical asymmetry instead.

Bouncing Oil Droplet in a Stratified Liquid and its Sudden Death

Droplets can self-propel when immersed in another liquid in which a concentration gradient is present. Here we report the experimental and numerical study of a self-propelling oil droplet in a vertically stratified ethanol-water mixture: At first, the droplet sinks slowly due to gravity, but then, before having reached its density matched position, jumps up suddenly. More remarkably, the droplet bounces repeatedly with an ever increasing jumping distance, until all of a sudden it stops after about 30 min. We identify the Marangoni stress at the droplet-liquid interface as responsible for the jumping: its strength grows exponentially because it pulls down ethanol-rich liquid, which in turn increases its strength even more. The jumping process can repeat because gravity restores the system. Finally, the sudden death of the jumping droplet is also explained. Our findings have demonstrated a type of prominent droplet bouncing inside a continuous medium with no wall or sharp interface.

Friction on water sliders

A body in motion tends to stay in motion but is often slowed by friction. Here we investigate the friction experienced by centimeter-sized bodies sliding on water. We show that their motion is dominated by skin friction due to the boundary layer that forms in the fluid beneath the body. We develop a simple model that considers the boundary layer as quasi-steady, and is able to capture the experimental behaviour for a range of body sizes, masses, shapes and fluid viscosities. Furthermore, we demonstrate that friction can be reduced by modification of the body's shape or bottom topography. Our results are significant for understanding natural and artificial bodies moving at the air-water interface, and can inform the design of aerial-aquatic microrobots for environmental exploration and monitoring.

Self-assembling outside equilibrium: emergence of structures mediated by dissipation

Self-assembly under non-equilibrium conditions may give rise to the formation of structures not available at equilibrium.

Surface swimmers, harnessing the interface to self-propel

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 microrobots, 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 recent experiments illustrates how forces at the interface can be used to generate locomotion. Surface swimmers ranging from the microscopic scale to typically the capillary length are covered. Two systems are then discussed in greater detail. The first is composed of floating ferromagnetic spheres that assemble through capillarity into swimming structures. Two previously studied configurations, triangular and collinear, are discussed and contrasted. A new interpretation for the triangular swimmer is presented. Then, the non-monotonic influence of surface tension and viscosity is evidenced in the collinear case. Finally, a new system is introduced. It is a magnetically powered, centimeter-sized piece that swims similarly to water striders.

Clustering-induced self-propulsion of isotropic autophoretic particles

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 identical and homogeneous active particles. Using full numerical simulations as well as theoretical modelling of the clustering process, the statistics of the propulsion properties are obtained for arbitrary initial arrangement of the particles. The robustness of these results to thermal noise, and more generally the effect of Brownian motion of the particles, is also discussed.

Vapor-Induced Attraction of Floating Droplets

Droplets partially submersed in an immiscible liquid pool attract each other. We experimentally study the interaction of floating droplets containing aqueous solution of a volatile liquid. A droplet affects its neighbors by generating a vapor gradient to the surroundings and responds by evaporating asymmetrically over its exposed cap. We show that the induced asymmetric temperature distribution causes a surface tension gradient driving the attracting motion. We highlight that the attracting dynamics starts with an accelerating stage, followed by a decelerating stage. We finally provide a theoretical model that quantitatively captures the interactive forces between droplets and predicts essential features of the attracting motion.

Interaction of Pure Marangoni Convection with a Propagating Reactive Interface under Microgravity

A reactive interface in the form of an autocatalytic reaction front propagating in a bulk phase can generate a dynamic contact line upon reaching the free surface when a surface tension gradient builds up due to the change in chemical composition. Experiments in microgravity evidence the existence of a self-organized autonomous and localized coupling of a pure Marangoni flow along the surface with the reaction in the bulk. This dynamics results from the advancement of the contact line at the surface that acts as a moving source of the reaction, leading to the reorientation of the front propagation. Microgravity conditions allow one to isolate the transition regime during which the surface propagation is enhanced, whereas diffusion remains the main mode of transport in the bulk with negligible convective mixing, a regime typically concealed on Earth because of buoyancy-driven convection.

Locomotion Mode of Micrometer-Sized Oil Droplets in Solutions of Cationic Surfactants Having Ester or Ether Linkages

Micrometer-sized self-propelled oil droplets under a far-from-equilibrium condition have drawn much attention because of their potential as a dynamic model for the chemical machinery in living organisms. To clarify the effect of interactions between the system components (surfactant, oil, and water) on the locomotion mode of droplets, we investigated the behaviors of oil droplets composed of n-heptyloxybenzaldehyde (HBA) in solutions of cationic surfactants having or not having an ester or an ether linkage. It was observed that in solutions of cationic surfactants having an ester or an ether linkage, spherical HBA droplets self-propelled by changing their direction frequently. On the other hand, when this functional group is absent, a slow self-propelled motion of the oil droplets concurrent with the evolution of aggregates on their surface was observed. From the results of measurement of interfacial tension and assessment of self-emulsification, we determined that the attractive interactions of cationic surfactants without an ester or an ether linkage with HBA are stronger than those having the linkage. The difference in the locomotion mode of oil droplets is probably explained from the viewpoint of the interactions among the system components.

Blood Crystal: Emergent Order of Red Blood Cells Under Wall-Confined Shear Flow

Driven or active suspensions can display fascinating collective behavior, where coherent motions or structures arise on a scale much larger than that of the constituent particles. Here, we report numerical simulations and an analytical model revealing that deformable particles and, in particular, red blood cells (RBCs) assemble into regular patterns in a confined shear flow. The pattern wavelength concurs well with our experimental observations. The order is of a pure hydrodynamic and inertialess origin, and it emerges from a subtle interplay between (i) hydrodynamic repulsion by the bounding walls that drives deformable cells towards the channel midplane and (ii) intercellular hydrodynamic interactions that can be attractive or repulsive depending on cell-cell separation. Various crystal-like structures arise depending on the RBC concentration and confinement. Hardened RBCs in experiments and rigid particles in simulations remain disordered under the same conditions where deformable RBCs form regular patterns, highlighting the intimate link between particle deformability and the emergence of order.

Self-propelled motion switching in nematic liquid crystal droplets in aqueous surfactant solutions

The self-propelled motions of micron-sized nematic liquid crystal droplets in an aqueous surfactant solution have been studied by tracking individual droplets over long time periods. Switching between self-propelled modes is observed as the droplet size decreases at a nearly constant dissolution rate: from random to helical and then straight motion. The velocity of the droplet decreases with its size for straight and helical motions but is independent of size for random motion. The switching between helical and straight motions is found to be governed by the self-propelled velocity, and is confirmed by experiments at various surfactant concentrations. The helical motion appears along with a shifting of a point defect from the self-propelled direction of the droplet. The critical velocity for this shift of the defect position is found to be related with the Ericksen number, which is defined by the ratio of the viscous and elastic stresses. In a thin cell whose thickness is smaller than that of the initial droplet size, the droplets show more complex trajectories, including "figure-8s" and zigzags. The appearance of those characteristic motions is attributed to autochemotaxis of the droplet.

Flow-induced phase separation of active particles is controlled by boundary conditions

Active particles, including swimming microorganisms, autophoretic colloids, and droplets, are known to self-organize into ordered structures at fluid-solid boundaries. The entrainment of particles in the attractive parts of their spontaneous flows has been postulated as a possible mechanism underlying this phenomenon. Here, combining experiments, theory, and numerical simulations, we demonstrate the validity of this flow-induced ordering mechanism in a suspension of active emulsion droplets. We show that the mechanism can be controlled, with a variety of resultant ordered structures, by simply altering hydrodynamic boundary conditions. Thus, for flow in Hele-Shaw cells, metastable lines or stable traveling bands can be obtained by varying the cell height. Similarly, for flow bounded by a plane, dynamic crystallites are formed. At a no-slip wall, the crystallites are characterized by a continuous out-of-plane flux of particles that circulate and re-enter at the crystallite edges, thereby stabilizing them. At an interface where the tangential stress vanishes, the crystallites are strictly 2D, with no out-of-plane flux. We rationalize these experimental results by calculating, in each case, the slow viscous flow produced by the droplets and the long-ranged, many-body active forces and torques between them. The results of numerical simulations of motion under the action of the active forces and torques are in excellent agreement with experiments. Our work elucidates the mechanism of flow-induced phase separation in active fluids, particularly active colloidal suspensions, and demonstrates its control by boundaries, suggesting routes to geometric and topological phenomena in an active matter.

Microfluidic Devices Developed for and Inspired by Thermotaxis and Chemotaxis

Taxis has been reported in many cells and microorganisms, due to their tendency to migrate toward favorable physical situations and avoid damage and death. Thermotaxis and chemotaxis are two of the major types of taxis that naturally occur on a daily basis. Understanding the details of the thermo- and chemotactic behavioral response of cells and microorganisms is necessary to reveal the body function, diagnosing diseases and developing therapeutic treatments. Considering the length-scale and range of effectiveness of these phenomena, advances in microfluidics have facilitated taxis experiments and enhanced the precision of controlling and capturing microscale samples. Microfabrication of fluidic chips could bridge the gap between in vitro and in situ biological assays, specifically in taxis experiments. Numerous efforts have been made to develop, fabricate and implement novel microchips to conduct taxis experiments and increase the accuracy of the results. The concepts originated from thermo- and chemotaxis, inspired novel ideas applicable to microfluidics as well, more specifically, thermocapillarity and chemocapillarity (or solutocapillarity) for the manipulation of single- and multi-phase fluid flows in microscale and fluidic control elements such as valves, pumps, mixers, traps, etc. This paper starts with a brief biological overview of the concept of thermo- and chemotaxis followed by the most recent developments in microchips used for thermo- and chemotaxis experiments. The last section of this review focuses on the microfluidic devices inspired by the concept of thermo- and chemotaxis. Various microfluidic devices that have either been used for, or inspired by thermo- and chemotaxis are reviewed categorically.

Chemotactic droplet swimmers in complex geometries

Chemotaxis¹ and auto-chemotaxis are key mechanisms in the dynamics of micro-organisms, e.g. in the acquisition of nutrients and in the communication between individuals, influencing the collective behaviour. However, chemical signalling and the natural environment of biological swimmers are generally complex, making them hard to access analytically. We present a well-controlled, tunable artificial model to study chemotaxis and autochemotaxis in complex geometries, using microfluidic assays of self-propelling oil droplets in an aqueous surfactant solution (Herminghaus et al 2014 Soft Matter 10 7008-22; Krüger et al 2016 Phys. Rev. Lett. 117). Droplets propel via interfacial Marangoni stresses powered by micellar solubilisation. Moreover, filled micelles act as a chemical repellent by diffusive phoretic gradient forces. We have studied these chemotactic effects in a series of microfluidic geometries, as published in Jin et al (2017 Proc. Natl Acad. Sci. 114 5089-94): first, droplets are guided along the shortest path through a maze by surfactant diffusing into the maze from the exit. Second, we let auto-chemotactic droplet swimmers pass through bifurcating microfluidic channels and record anticorrelations between the branch choices of consecutive droplets. We present an analytical Langevin model matching the experimental data. In a previously unpublished experiment, pillar arrays of variable sizes and shapes provide a convex wall interacting with the swimmer and, in the case of attachment, bending its trajectory and forcing it to revert to its own trail. We observe different behaviours based on the interplay of wall curvature and negative autochemotaxis, i.e. no attachment for highly curved interfaces, stable trapping at large pillars, and a narrow transition region where negative autochemotaxis makes the swimmers detach after a single orbit.

Lattice Boltzmann study of chemically-driven self-propelled droplets

We numerically study the behavior of self-propelled liquid droplets whose motion is triggered by a Marangoni-like flow. This latter is generated by variations of surfactant concentration which affect the droplet surface tension promoting its motion. In the present paper a model for droplets with a third amphiphilic component is adopted. The dynamics is described by Navier-Stokes and convection-diffusion equations, solved by the lattice Boltzmann method coupled with finite-difference schemes. We focus on two cases. First, the study of self-propulsion of an isolated droplet is carried on and, then, the interaction of two self-propelled droplets is investigated. In both cases, when the surfactant migrates towards the interface, a quadrupolar vortex of the velocity field forms inside the droplet and causes the motion. A weaker dipolar field emerges instead when the surfactant is mainly diluted in the bulk. The dynamics of two interacting droplets is more complex and strongly depends on their reciprocal distance. If, in a head-on collision, droplets are close enough, the velocity field initially attracts them until a motionless steady state is achieved. If the droplets are vertically shifted, the hydrodynamic field leads to an initial reciprocal attraction followed by a scattering along opposite directions. This hydrodynamic interaction acts on a separation of some droplet radii otherwise it becomes negligible and droplets motion is only driven by the Marangoni effect. Finally, if one of the droplets is passive, this latter is generally advected by the fluid flow generated by the active one.

Remotely Triggered Locomotion of Hydrogel Mag-bots in Confined Spaces

In this study, soft hydrogel crawlers with remote magnetic-responsive motility in confined spaces have been developed. Inspired by the motion of maggots, the hydrogel crawlers can reversibly contract and elongate their body controlled by repeatedly switching on/off an alternating magnetic field. Based on the cyclic deformation, the hydrogel crawlers can move peristaltically in a confined space that is coated with asymmetric micro-patterns. The dependence of the hydrogel motility on the pattern structures and lubrication is characterized using experimental measurements. Such a hydrogel system pioneers the study of active motile systems in porous media and has the potential to impact the fields of targeted drug delivery and active actuators.

Spontaneous Oscillations and Synchronization of Active Droplets on a Water Surface via Marangoni Convection

Shape-oscillations and synchronization are intriguing phenomena in many biological and physical systems. Here, we report the rhythmic mechanical oscillations and synchronization of aniline oil droplets on a water phase, which is induced by Marangoni convection during transfer of the solute. The repetitive increase and decrease in the surface concentration in the vicinity of the contact line leads to the oscillations of droplets through an imbalance in surface tensions. The nature of the oscillations depends on the diameter of the droplet, the depth of the bulk aqueous phase, and the concentration of the aqueous phase. A numerical simulation reproduces the essential behaviors of active oscillations of a droplet. Droplets sense each other through a surface tension gradient and advection, and hydrodynamic coupling in the bulk solution induces the synchronization of droplet oscillations.

Thermo- and soluto-capillarity: Passive and active drops

A survey is provided of a variety of problems where a passive or an active drop experiences directed motion consequence of the action of an external or internal agent or a combination of both. An active drop is capable of reacting by engendering autonomous, self-propelled motion in favor or against the agent. The phenomena involved offer diverse complexity but one way or another the drop motion finally rests on thermo- or soluto-capillarity hence on interfacial tension gradients. Accordingly, here a minimal mathematical framework underlying such drop motions is provided when direct external temperature or solute gradients, illumination, internal heat generation or surface chemical reaction are incorporated into the physico-chemical-hydrodynamics.

Solute-mediated interactions between active droplets

Concentration gradients play a critical role in embryogenesis, bacterial locomotion, as well as the motility of active particles. Particles develop concentration profiles around them by dissolution, adsorption, or the reactivity of surface species. These gradients change the surface energy of the particles, driving both their self-propulsion and governing their interactions. Here, we uncover a regime in which solute gradients mediate interactions between slowly dissolving droplets without causing autophoresis. This decoupling allows us to directly measure the steady-state, repulsive force, which scales with interparticle distance as F∼1/r^{2}. Our results show that the dissolution process is diffusion rather than reaction rate limited, and the theoretical model captures the dependence of the interactions on droplet size and solute concentration, using a single fit parameter, l=16±3nm, which corresponds to the length scale of a swollen micelle. Our results shed light on the out-of-equilibrium behavior of particles with surface reactivity.

Swinging motion of active deformable particles in Poiseuille flow

Dynamics of active deformable particles in an external Poiseuille flow is investigated. To make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical shape deformation. First, we clarify the relation of our model to that of rigid active particles. Then, we study the dynamical modes that active deformable particles exhibit by changing the strength of the external flow. We emphasize the difference between the active particles that tend to self-propel parallel to the elliptical shape deformation and those self-propelling perpendicularly. In particular, a swinging motion around the centerline far from the channel walls is discussed in detail.

Camphor-Engine-Driven Micro-Boat Guides Evolution of Chemical Gardens

A micro-boat self-propelled by a camphor engine, carrying seed crystals of FeCl₃, promoted the evolution of chemical gardens when placed on the surface of aqueous solutions of potassium hexacyanoferrate. Inverse chemical gardens (growing from the top downward) were observed. The growth of the “inverse” chemical gardens was slowed down with an increase in the concentration of the potassium hexacyanoferrate. Heliciform precipitates were formed under the self-propulsion of the micro-boat. A phenomenological model, satisfactorily describing the self-locomotion of the camphor-driven micro-boat, is introduced and checked.

Self-Propulsion and Shape Restoration of Aqueous Drops on Sulfobetaine Silane Surfaces

The motion of droplets on typical surfaces is generally halted by contact line pinning associated with contact angle hysteresis. In this study, it was shown that, on a zwitterionic sulfobetaine silane (SBSi)-coated surface, aqueous drops with appropriate solutes can demonstrate hysteresis-free behavior, whereas a pure water drop shows spontaneous spreading. By adding solutes such as polyethylene glycol, 2(2-butoxy ethoxy) ethanol, or sodium n-dodecyl sulfate, an aqueous drop with a small contact angle (disappearance of spontaneous spreading) was formed on SBSi surfaces. The initial drop shape was readily relaxed back to a circular shape (hysteresis-free behavior), even upon severe disturbances. Moreover, it was interesting to observe the self-propulsion of such a drop on horizontal SBSi surfaces in the absence of externally provided stimuli. The self-propelled drop tends to follow a random trajectory, and the continuous movement can last for at least 10 min. This self-propelled random motion can be attributed to the combined effects of the hysteresis-free surface and the Marangoni stress. The former comes from the total wetting property of the surface, while the latter originates from surface tension gradient due to fluctuating evaporation rates along the drop border.

Self-Propelled Motion of Monodisperse Underwater Oil Droplets Formed by a Microfluidic Device

We evaluated the speed profile of self-propelled underwater oil droplets comprising a hydrophobic aldehyde derivative in terms of their diameter and the surrounding surfactant concentration using a microfluidic device. We found that the speed of the oil droplets is dependent on not only the surfactant concentration but also the droplet size in a certain range of the surfactant concentration. This tendency is interpreted in terms of combination of the oil and surfactant affording spontaneous emulsification in addition to the Marangoni effect.

Chirality-induced helical self-propulsion of cholesteric liquid crystal droplets

We report the first experimental realization of a chiral artificial microswimmer exhibiting helical motion without any external fields. We discovered that a cholesteric liquid crystal (CLC) droplet with a helical director field swims in a helical path driven by the Marangoni flow in an aqueous surfactant solution. We also showed that the handedness of the helical path is reversed when that of the CLC droplet is reversed by replacing the chiral dopant with the enantiomer. In contrast, nematic liquid crystal (NLC) droplets exhibited ballistic motions. These results suggest that the helical motion of the CLC droplets is driven by chiral couplings between the Marangoni flow and rotational motion via the helical director field of CLC droplets.

Chemotaxis and autochemotaxis of self-propelling droplet swimmers

Chemotaxis and autochemotaxis play an important role in many essential biological processes. We present a self-propelling artificial swimmer system that exhibits chemotaxis as well as negative autochemotaxis. Oil droplets in an aqueous surfactant solution are driven by interfacial Marangoni flows induced by micellar solubilization of the oil phase. We demonstrate that chemotaxis along micellar surfactant gradients can guide these swimmers through a microfluidic maze. Similarly, a depletion of empty micelles in the wake of a droplet swimmer causes negative autochemotaxis and thereby trail avoidance. We studied autochemotaxis quantitatively in a microfluidic device of bifurcating channels: Branch choices of consecutive swimmers are anticorrelated, an effect decaying over time due to trail dispersion. We modeled this process by a simple one-dimensional diffusion process and stochastic Langevin dynamics. Our results are consistent with a linear surfactant gradient force and diffusion constants appropriate for micellar diffusion and provide a measure of autochemotactic feedback strength vs. stochastic forces. This assay is readily adaptable for quantitative studies of both artificial and biological autochemotactic systems.

Liquid Marbles, Elastic Nonstick Droplets: From Minireactors to Self-Propulsion

Liquid marbles are nonstick droplets wrapped by micro- or nanometrically scaled colloidal particles, representing a platform for a variety of chemical, biological, and microfluidics applications. Liquid marbles demonstrate elastic properties and do not coalesce when bounced or pressed. The effective surface tension and Young modulus of liquid marbles are discussed. Physical sources of the elasticity of liquid marbles are considered. Liquids and powders used for the fabrication of liquid marbles are surveyed. This feature article reviews properties and applications of liquid marbles. Liquid marbles demonstrate potential as microreactors, microcontainers for growing micro-organisms and cells, and microfluidics devices. The Marangoni-flow-driven self-propulsion of marbles supported by liquids is addressed.

‘Fuelled’ motion: phoretic motility and collective behaviour of active colloids

Phoretic motility is a propulsion mechanism used to design active particles which display complex collective behaviours, characterised experimentally and theoretically.

Can phoretic particles swim in two dimensions?

Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be used to study the physics of collective motion in active matter and might have promising applications in bioengineering. In the case of self-diffusiophoresis, the classical physical model relies on a steady solution of the diffusion equation, from which chemical gradients, phoretic flows, and ultimately the swimming velocity may be derived. Motivated by disk-shaped particles in thin films and under confinement, we examine the extension to two dimensions. Because the two-dimensional diffusion equation lacks a steady state with the correct boundary conditions, Laplace transforms must be used to study the long-time behavior of the problem and determine the swimming velocity. For fixed chemical fluxes on the particle surface, we find that the swimming velocity ultimately always decays logarithmically in time. In the case of finite Péclet numbers, we solve the full advection-diffusion equation numerically and show that this decay can be avoided by the particle moving to regions of unconsumed reactant. Finite advection thus regularizes the two-dimensional phoretic problem.

Oscillation of Speed of a Self-Propelled Belousov-Zhabotinsky Droplet

Self-propelled objects can become potential biomimetic micromachines, but a versatile strategy is required to add the desired functions. Introducing a characteristic chemical reaction is a simple answer; however, the problem is how the chemical reaction is coupled to the self-propelled motion. We propose a strategy to select the chemical reaction so that its product or intermediate affects the driving force of a self-propelled object. To demonstrate this strategy, we put an aqueous droplet of nonlinear chemical reaction, the Belousov-Zhabotinsky (BZ) reaction, into an oil phase including a surfactant, where an aqueous droplet was driven by an interfacial reaction of the surfactant and bromine. The results exhibited oscillation of speed, and it was synchronized with the redox oscillation of the BZ reaction in the droplet. Bromine is one of the intermediates of the BZ reaction, and thus the droplet motion well-reflected the characteristics of the BZ reaction.

Active Brownian motion of emulsion droplets: Coarsening dynamics at the interface and rotational diffusion

A micron-sized droplet of bromine water immersed in a surfactant-laden oil phase can swim (S. Thutupalli, R. Seemann, S. Herminghaus, New J. Phys. 13 073021 (2011). The bromine reacts with the surfactant at the droplet interface and generates a surfactant mixture. It can spontaneously phase-separate due to solutocapillary Marangoni flow, which propels the droplet. We model the system by a diffusion-advection-reaction equation for the mixture order parameter at the interface including thermal noise and couple it to fluid flow. Going beyond previous work, we illustrate the coarsening dynamics of the surfactant mixture towards phase separation in the axisymmetric swimming state. Coarsening proceeds in two steps: an initially slow growth of domain size followed by a nearly ballistic regime. On larger time scales thermal fluctuations in the local surfactant composition initiates random changes in the swimming direction and the droplet performs a persistent random walk, as observed in experiments. Numerical solutions show that the rotational correlation time scales with the square of the inverse noise strength. We confirm this scaling by a perturbation theory for the fluctuations in the mixture order parameter and thereby identify the active emulsion droplet as an active Brownian particle.

Curling Liquid Crystal Microswimmers: A Cascade of Spontaneous Symmetry Breaking

We report curling self-propulsion in aqueous emulsions of common mesogenic compounds. Nematic liquid crystal droplets self-propel in a surfactant solution with concentrations above the critical micelle concentration while undergoing micellar solubilization [Herminghaus et al., Soft Matter 10, 7008 (2014)]. We analyzed trajectories both in a Hele-Shaw geometry and in a 3D setup at variable buoyancy. The coupling between the nematic director field and the convective flow inside the droplet leads to a second symmetry breaking which gives rise to curling motion in 2D. This is demonstrated through a reversible transition to nonhelical persistent swimming by heating to the isotropic phase. Furthermore, autochemotaxis can spontaneously break the inversion symmetry, leading to helical trajectories in 3D.

Dimensionality matters in the collective behaviour of active emulsions

The behaviour of artificial microswimmers consisting of droplets of a mesogenic oil immersed in an aqueous surfactant solution depends qualitatively on the conditions of dimensional confinement; ranging from only transient aggregates in Hele-Shaw geometries to hexagonally packed, convection-driven clusters when sedimenting in an unconfined reservoir. We study the effects of varying the swimmer velocity, the height of the reservoir, and the buoyancy of the droplet swimmers. Two simple adjustments of the experimental setting lead to a suppression of clustering: either a decrease of the reservoir height below a certain value, or a match of the densities of droplets and surrounding phase, showing that the convection is the key mechanism for the clustering behaviour.

Tactic, reactive, and functional droplets outside of equilibrium

Droplets subject to non-equilibrium conditions can exhibit a range of biomimetic and “intelligent” behaviors.

Geometric pumping in autophoretic channels

Many microfluidic devices use macroscopic pressure differentials to overcome viscous friction and generate flows in microchannels. In this work, we investigate how the chemical and geometric properties of the channel walls can drive a net flow by exploiting the autophoretic slip flows induced along active walls by local concentration gradients of a solute species. We show that chemical patterning of the wall is not required to generate and control a net flux within the channel, rather channel geometry alone is sufficient. Using numerical simulations, we determine how geometric characteristics of the wall influence channel flow rate, and confirm our results analytically in the asymptotic limit of lubrication theory.

Droplets: unconventional protocell model with life-like dynamics and room to grow

Over the past few decades, several protocell models have been developed that mimic certain essential characteristics of living cells. These protocells tend to be highly reductionist simplifications of living cells with prominent bilayer membrane boundaries, encapsulated metabolisms and/or encapsulated biologically-derived polymers as potential sources of information coding. In parallel with this conventional work, a novel protocell model based on droplets is also being developed. Such water-in-oil and oil-in-water droplet systems can possess chemical and biochemical transformations and biomolecule production, self-movement, self-division, individuality, group dynamics, and perhaps the fundamentals of intelligent systems and evolution. Given the diverse functionality possible with droplets as mimics of living cells, this system has the potential to be the first true embodiment of artificial life that is an orthologous departure from the one familiar type of biological life. This paper will synthesize the recent activity to develop droplets as protocell models.