Self-propelled motion of a fluid droplet under chemical reaction

Emergence of inertia in the low-Reynolds regime of self-diffusiophoretic motion

For isotropic swimming particles driven by self-diffusiophoresis at zero Reynolds number (where particle velocity responds instantaneously to applied force), the diffusive timescale of emitted solute can produce an emergent quasi-inertial behavior. These particles can orbit in a central potential and reorient under second-order dynamics, not the first-order dynamics of classical zero-Reynolds motion. They are described by a simple effective model that embeds their history-dependent behavior as an effective inertia, this being the most primitive expression of memory. The system can be parameterized with dynamic quantities such as particle size and swimming speed, without detailed knowledge of the diffusiophoretic mechanism.

Self-emergent vortex flow of microtubule and kinesin in cell-sized droplets under water/water phase separation

By facilitating a water/water phase separation (w/wPS), crowded biopolymers in cells form droplets that contribute to the spatial localization of biological components and their biochemical reactions. However, their influence on mechanical processes driven by protein motors has not been well studied. Here, we show that the w/wPS droplet spontaneously entraps kinesins as well as microtubules (MTs) and generates a micrometre-scale vortex flow inside the droplet. Active droplets with a size of 10-100 µm are generated through w/wPS of dextran and polyethylene glycol mixed with MTs, molecular-engineered chimeric four-headed kinesins and ATP after mechanical mixing. MTs and kinesin rapidly created contractile network accumulated at the interface of the droplet and gradually generated vortical flow, which can drive translational motion of a droplet. Our work reveals that the interface of w/wPS contributes not only to chemical processes but also produces mechanical motion by assembling species of protein motors in a functioning manner.

Hydrodynamics of a confined active Belousov-Zhabotinsky droplet

Self-sustained locomotion of synthetic droplet swimmers has been of great interest due to their ability to mimic the behavior of biological swimmers. Here we harness the Belousov-Zhabotinsky (BZ) reaction to induce Marangoni stresses on the fluid-droplet interface and elucidate the spontaneous locomotion of active BZ droplets in a confined two-dimensional channel. Our approach employs the lattice Boltzmann method to simulate a coupled system of multiphase hydrodynamics and BZ-reaction kinetics. Our investigation reveals the mechanism underlying the propulsion of active BZ droplets, in terms of convective and diffusive fluxes and deformation of the droplets. Furthermore, we demonstrate that by manipulating the degree of confinement, strength, and nature of coupling between surface tension and active species' concentration, the motion of the BZ droplet can be directed. In addition, we are able to capture two different kinds of droplet behaviors, namely, sustained and stationary, and establish conditions for the sustained long-time motion. We envisage that our findings can be used not only to understand the mechanics of biological swimmers but also to design reaction-driven self-propelled systems for a variety of biomimetic applications.

pH-Sensitive Controlled Motion of Micrometer-sized Oil Droplets in a Solution of Surfactants Containing Fumaric Acid Derivatives

Self-propelled droplets are of considerable interest as an appropriate model for understanding the self-propulsion of objects in the fields of nonequilibrium physics and nonlinear science. Several research groups have reported the monodirectional motion of droplets, that is, chemotaxis, using stimuli-responsive materials. However, the precise control of chemotaxis remains challenging from the perspective of synthetic chemistry because chemotactic motion is primarily induced by the consumption of reactive oil or surfactants. Herein, we report a chemical system containing pH-responsive fumaric acid derivatives, in which the oil droplet exhibited positive chemotaxis over a wide pH range-from basic to acidic conditions. From the measurements of the interfacial tension between the oil and aqueous phases, it was deduced that the positive chemotaxis was due to heterogeneity in the interfacial tension of the droplet surface, which was accompanied by the production of surface-active compounds in the pH gradient in a linear-type channel.

Pairing-induced motion of source and inert particles driven by surface tension

We experimentally and theoretically investigate systems with a pair of source and inert particles that interact through a concentration field. The experimental system comprises a camphor disk as the source particle and a metal washer as the inert particle. Both are floated on an aqueous solution of glycerol at various concentrations, where the glycerol modifies the viscosity of the aqueous phase. The particles form a pair owing to the attractive lateral capillary force. As the camphor disk spreads surface-active molecules at the aqueous surface, the camphor disk and metal washer move together, driven by the surface tension gradient. The washer is situated in the front of the camphor disk, keeping the distance constant during their motion, which we call a pairing-induced motion. The pairing-induced motion exhibited a transition between circular and straight motions as the glycerol concentration in the aqueous phase changed. Numerical calculations using a model that considers forces caused by the surface tension gradient and lateral capillary interaction reproduced the observed transition in the pairing-induced motion. Moreover, this transition agrees with the result of the linear stability analysis on the reduced dynamical system obtained by the expansion with respect to the particle velocity. Our results reveal that the effect of the particle velocity cannot be overlooked to describe the interaction through the concentration field.

Statistics for an object actively driven by spontaneous symmetry breaking into reversible directions

Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained until a large enough impulse by an additional stochastic force reverses it. Examples may be provided by self-propelled droplets, gliding bacteria stochastically reversing their propulsion direction, or nonpolar vibrated hoppers. The magnitude of active forcing is regarded as constant, and we include the effect of inertial contributions. Interestingly, this situation can formally be mapped to stochastic motion under (dry, solid) Coulomb friction, however, with a negative friction parameter. Diffusion coefficients are calculated by formal mapping to the situation of a quantum-mechanical harmonic oscillator exposed to an additional repulsive delta-potential. Results comprise a ditched or double-peaked velocity distribution and spatial statistics showing outward propagating maxima when starting from initially concentrated arrangements.

Modeling of chemically active particles at an air-liquid interface

The collective motion of chemically active particles at an air-liquid interface is studied theoretically as a dynamic self-organization problem. Based on a physical consideration, we propose a minimal model for self-propelled particles by combining hydrodynamic interaction, capillary interaction, driving force by Marangoni effect, and Marangoni flow. Our model has successfully captured the features of chemically active particles, that represent dynamic self-organized states such as crystalline, chain, liquid-like and spreading states.

Spontaneous Mode Switching of Self-Propelled Droplet Motion Induced by a Clock Reaction in the Belousov-Zhabotinsky Medium

Interfacial chemical dynamics on a droplet generate various self-propelled motions. For example, ballistic and random motions arise depending on the physicochemical conditions inside the droplet and its environment. In this study, we focus on the relationship between oxidant concentrations in an aqueous droplet and its mode of self-propelled motion in an oil phase including surfactant. We demonstrated that the chemical conditions inside self-propelled aqueous droplets were changed systematically, indicating that random motion appeared at higher concentrations of oxidants, which were H₂SO₄ and BrO₃^-, and ballistic motion at lower concentrations. In addition, spontaneous mode switching from ballistic to random motion was successfully demonstrated by adding malonic acid, wherein the initially observed reduced state of the aqueous solution suddenly changed to the oxidized state. Although we only observed one-time transition and have not yet succeeded to realize alternation between ballistic (reduced state) and random motion (oxidized state), such spontaneous transitions are fundamental steps in realizing artificial cells and understanding the fundamental mechanisms of life-like behavior, such as bacterial chemotaxis originating from periodical run-and-tumble motion.

Spontaneous Motion and Rotation of Acid Droplets on the Surface of a Liquid Metal

Self-propulsion of droplets is of great significance in many fields. The spontaneous horizontal motion and self-jumping of droplets have been well realized in various ways. However, there is still a lack of an effective method to enable a droplet to rotate spontaneously and steadily. In this paper, by employing an acid droplet and a liquid metal, the spontaneous and steady rotation of droplets is achieved. For an acid droplet, it may spontaneously move when it is deposited on the surface of the liquid metal. By adjusting experimental parameters to the proper range, the self-rotation of droplet happens. This phenomenon originates from the fluctuation of the droplet boundary and the collective movement of bubbles that are generated by the chemical reactions between the acid droplet and liquid metal. This rotation has a simpler implementation method and more steady rotation state. Its angular velocity is much higher than that driven by other mechanisms. Moreover, the movements of acid droplets on the liquid metal are classified according to experimental conditions. The internal flow fields, the movements and distribution of bubbles, and the fluctuation of the droplet boundary are also explored and discussed. The theoretical model describing the rotational droplet is given. Our work may deepen the understanding of the physical system transition affected by chemical reactions and provide a new way for the design of potential applications, e.g., micro- and nanodevices.

Photochemical motion control of surface active Belousov-Zhabotinsky droplets

Photochemical control of the motion of surface active Belousov-Zhabotinsky (BZ) droplets in an oil-surfactant medium is carried out with illumination intensity gradients. Droplet motion is analyzed under conditions of constant uniform illumination and a constant illumination gradient. Control of droplet motion is developed by testing different illumination gradients. Complex hypotrochoid target trajectories are tracked by BZ droplets illuminated with two-dimensional V-shaped gradients.

Kinetics of active water/ethanol Janus droplets

Droplets made of a water/ethanol mixture spontaneously self-propel in an oil/surfactant solution and, depending on the initial ethanol concentration at the time of production, may evolve in up to three stages. Upon self-propulsion the droplets absorb surfactant molecules during their continuous motion in the oily phase. In combination with the continuous loss of ethanol this mass exchange with the ambient phase may lead to a spontaneous phase separation of the water/ethanol mixture, and eventually to the formation of characteristic Janus droplets. Supported by experimental evidence, we propose a simple model that is able to explain the propulsion velocity and its scaling with the droplet radius in the last stage of the droplet evolution.

Droplets as Carriers for Flexible Electronic Devices

Coupling soft bodies and dynamic motions with multifunctional flexible electronics is challenging, but is essential in satisfying the urgent and soaring demands of fully soft and comprehensive robotic systems that can perform tasks in spite of rigorous spatial constraints. Here, the mobility and adaptability of liquid droplets with the functionality of flexible electronics, and techniques to use droplets as carriers for flexible devices are combined. The resulting active droplets (ADs) with volumes ranging from 150 to 600 µL can conduct programmable functions, such as sensing, actuation, and energy harvesting defined by the carried flexible devices and move under the excitation of gravitational force or magnetic force. They work in both dry and wet environments, and adapt to the surrounding environment through reversible shape shifting. These ADs can achieve controllable motions at a maximum velocity of 226 cm min-1 on a dry surface and 32 cm min-1 in a liquid environment. The conceptual system may eventually lead to individually addressable ADs that offer sophisticated functions for high-throughput molecule analysis, drug assessment, chemical synthesis, and information collection.

Start of Micrometer-Sized Oil Droplet Motion through Generation of Surfactants

Self-propelled motion of micrometer-sized oil droplets in surfactant solution has drawn much attention as an example of nonlinear life-like dynamics under far-from-equilibrium conditions. The driving force of this motion is thought to be induced by Marangoni convection based on heterogeneity in the interfacial tension at the droplet surface. Here, to clarify the required conditions for the self-propelled motion of oil droplets, we have constructed a chemical system, where oil droplet motion is induced by the production of 1,2,3-triazole-containing surfactants through the Cu-catalyzed azide-alkyne cycloaddition reaction. From the results of the visualization and analysis of flow fields around the droplet, the motion of the droplets could be attributed to the formation of flow fields, which achieved sufficient strength caused by the in situ production of surfactants at the droplet surface.

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.

Self-propulsion of an active polar drop

We investigate the self-propulsive motion of a drop containing an active polar field. The drop demonstrates spontaneous symmetry breaking from a uniform orientational order into a splay or bend instability depending on the types of active stress, namely, contractile or extensile, respectively. We develop an analytical theory of the mechanism of this instability, which has been observed only in numerical simulations. We show that both contractile and extensile active stresses result in the instability and self-propulsive motion. We also discuss asymmetry between contractile and extensile stresses and show that extensile active stress generates chaotic motion even under a simple model of the polarity field coupled with motion and deformation of the drop.

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.

Theoretical model of chirality-induced helical self-propulsion

We recently reported the experimental realization of a chiral artificial microswimmer exhibiting helical self-propulsion [T. Yamamoto and M. Sano, Soft Matter 13, 3328 (2017)1744-683X10.1039/C7SM00337D]. In the experiment, cholesteric liquid crystal (CLC) droplets dispersed in surfactant solutions swam spontaneously, driven by the Marangoni flow, in helical paths whose handedness is determined by the chirality of the component molecules of CLC. To study the mechanism of the emergence of the helical self-propelled motion, we propose a phenomenological model of the self-propelled helical motion of the CLC droplets. Our model is constructed by symmetry argument in chiral systems, and it describes the dynamics of CLC droplets with coupled time-evolution equations in terms of a velocity, an angular velocity, and a tensor variable representing the symmetry of the helical director field of the droplet. We found that helical motions as well as other chiral motions appear in our model. By investigating bifurcation behaviors between each chiral motion, we found that the chiral coupling terms between the velocity and the angular velocity, the structural anisotropy of the CLC droplet, and the nonlinearity of model equations play a crucial role in the emergence of the helical motion of the CLC droplet.

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.

Marangoni Effect-Driven Motion of Miniature Robots and Generation of Electricity on Water

The well-known Marangoni effect perfectly supports the dynamic mechanism of organic solvent-swollen gels on water. On this basis, we report a series of energy conversion processes of concentrated droplets of polyvinylidene fluoride/dimethyl formamide (PVDF/DMF) that can transfer chemical-free energy to kinetic energy to rapidly rotate itself on water. This droplet (22.2 mg) is capable to offer kinetic energy of 0.099 μJ to propel an artificial paper rocket of 31.8 mg to move over 560 cm on water at an initial velocity of 7.9 cm s^-1. As the droplet increases to 35.0 mg, a paper goldfish of 10.6 mg can be driven to swim longer at a higher initial velocity of 20 cm s^-1. The kinetic energy of the droplet can be further converted to electrical energy through an electromagnetic generator, in which as a 0.5 MΩ resistor is loaded, the peak output reaches 6.5 mV that corresponds to the power density of 0.293 μW kg^-1. We believe that this report would open up a promising avenue to exploit energies for applications in miniature robotics.

Anchoring-driven spontaneous rotations in active gel droplets

We study the dynamics of an active gel droplet with imposed orientational anchoring (normal or planar) at its surface. We find that if the activity is large enough droplets subject to strong anchoring spontaneously start to rotate, with the sense of rotation randomly selected by fluctuations. Contractile droplets rotate only for planar anchoring and extensile ones only for normal anchoring. This is because such a combination leads to a pair of stable elastic deformations which creates an active torque to power the rotation. Interestingly, under these conditions there is a conflict between the anchoring promoted thermodynamically and that favoured by activity. By tuning activity and anchoring strength, we find a wealth of qualitatively different droplet morphologies and spatiotemporal patterns, encompassing steady rotations, oscillations, and more irregular trajectories. The spontaneous rotations we observe are fundamentally different from previously reported instances of rotating defects in active fluids as they require the presence of strong enough anchoring and entail significant droplet shape deformations.

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.

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.

Surface-dependent scenarios for dissolution-driven motion of growing droplets

Nano-droplets on a foreign substrate have received increasing attention because of their technological possible applications, for instance to catalyse the growth of nanowires. In some cases the droplets can move as a result of a reaction with the substrate. In this work we show that the substrate orientation, the surface morphology and the shape of the pits etched in the substrate by the droplets affect the droplet motion, so that a single mechanism (droplet-induced substrate dissolution) may lead to several unexpected droplet dynamics. The experiments are carried out by low energy electron microscopy on Au-Si and Au-Ge, which are model systems for studying liquid droplet alloys. Studying in-situ the behaviour of Au droplets on various Si and Ge surfaces, we describe a subtle interplay between the substrate orientation, the surface defects, and the droplet motion. Our observations allow a deep understanding of the interfacial mechanisms at the origin of the alloy formation and the associated droplet motion. These mechanisms are based on events of substrate dissolution/recrystallization. The outcomes of this work highlight the importance of the etching anisotropy on the droplet-substrate behaviours, and are essential in the perspective of positioning liquid alloy droplets used for instance as nanowire catalysts.

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.

Mathematical model for self-propelled droplets driven by interfacial tension

We propose a model for the spontaneous motion of a droplet induced by inhomogeneity in interfacial tension. The model is derived from a variation of the Lagrangian of the system and we use a time-discretized Morse flow scheme to perform its numerical simulations. Our model can naturally simulate the dynamics of a single droplet, as well as that of multiple droplets, where the volume of each droplet is conserved. We reproduced the ballistic motion and fission of a droplet, and the collision of two droplets was also examined numerically.

Molecular System for the Division of Self-Propelled Oil Droplets by Component Feeding

Unique dynamics using inanimate molecular assemblies have drawn a great amount of attention for demonstrating prebiomimetic molecular systems. For the construction of an organized logic combining two fundamental dynamics of life, we demonstrate here a molecular system that exhibits both division and self-propelled motion using oil droplets. The key molecule of this molecular system is a novel cationic surfactant containing a five-membered acetal moiety, and the molecular system can feed the self-propelled oil droplet composed of a benzaldehyde derivative and an alkanol. The division dynamics of the self-propelled oil droplets were observed through the hydrolysis of the cationic surfactant in bulk solution. The mechanism of the current dynamics is argued to be based on the supply of "fresh" oil components in the moving oil droplets, which is induced by the Marangoni instability. We consider this molecular system to be a prototype of self-reproducing inanimate molecular assembly exhibiting self-propelled motion.

Controlled motion of Janus particles in periodically phase-separating binary fluids

We numerically investigate the propelled motions of a Janus particle in a periodically phase-separating binary fluid mixture. In this study, the surface of the particle tail prefers one of the binary fluid components and the particle head is neutral in the wettability. During the demixing period, the more wettable phase is selectively adsorbed to the particle tail. Growths of the adsorbed domains induce the hydrodynamic flow in the vicinity of the particle tail, and this asymmetric pumping flow drives the particle toward the particle head. During the mixing period, the particle motion almost ceases because the mixing primarily occurs via diffusion and the resulting hydrodynamic flow is negligibly small. Repeating this cycle unboundedly moves the Janus particle toward the head. The dependencies of the composition and the repeat frequency on the particle motion are discussed.

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

We report spontaneous motion in a fully biocompatible system consisting of pure water droplets in an oil-surfactant medium of squalane and monoolein. Water from the droplet is solubilized by the reverse micellar solution, creating a concentration gradient of swollen reverse micelles around each droplet. The strong advection and weak diffusion conditions allow for the first experimental realization of spontaneous motion in a system of isotropic particles at sufficiently large Péclet number according to a straightforward generalization of a recently proposed mechanism [S. Michelin, E. Lauga, and D. Bartolo, Phys. Fluids 25, 061701 (2013); S. Michelin and E. Lauga, J. Fluid Mech. 747, 572 (2014)]. Experiments with a highly concentrated solution of salt instead of water, and tetradecane instead of squalane, confirm the above mechanism. The present swimming droplets are able to carry external bodies such as large colloids, salt crystals, and even cells.

Spontaneous motility of passive emulsion droplets in polar active gels

We study by computer simulations the dynamics of a droplet of passive, isotropic fluid, embedded in a polar active gel. The latter represents a fluid of active force dipoles, which exert either contractile or extensile stresses on their surroundings, modelling for instance a suspension of cytoskeletal filaments and molecular motors. When the polarisation of the active gel is anchored normal to the droplet at its surface, the nematic elasticity of the active gel drives the formation of a hedgehog defect; this defect then drives an active flow which propels the droplet forward. In an extensile gel, motility can occur even with tangential anchoring, which is compatible with a defect-free polarisation pattern. In this case, upon increasing activity the droplet first rotates uniformly, and then undergoes a discontinuous nonequilibrium transition into a translationally motile state, powered by bending deformations in the surrounding active medium.

Spontaneous motion and deformation of a self-propelled droplet

The time evolution equation of motion and shape are derived for a self-propelled droplet driven by a chemical reaction. The coupling between the chemical reaction and motion makes an inhomogeneous concentration distribution as well as a surrounding flow leading to the instability of a stationary state. The instability results in spontaneous motion by which the shape of the droplet deforms from a sphere. We found that the self-propelled droplet is elongated perpendicular to the direction of motion and is characterized as a pusher.

Perspective: nanomotors without moving parts that propel themselves in solution

Self-propelled nanomotors use chemical energy to produce directed motion. Like many molecular motors they suffer strong perturbations from the environment in which they move as a result of thermal fluctuations and do not rely on inertia for their propulsion. Such tiny motors are the subject of considerable research because of their potential applications, and a variety of synthetic motors have been made and are being studied for this purpose. Chemically powered self-propelled nanomotors without moving parts that rely on asymmetric chemical reactions to effect directed motion are the focus of this article. The mechanisms they use for propulsion, how size and fuel sources influence their motion, how they cope with strong molecular fluctuations, and how they behave collectively are described. The practical applications of such nanomotors are largely unrealized and the subject of speculation. Since molecular motors are ubiquitous in biology and perform a myriad of complex tasks, the hope is that synthetic motors might be able to perform analogous tasks. They may have the potential to change our perspective on how chemical dynamics takes place in complex systems.

Spontaneous motion of an elliptic camphor particle

The coupling between deformation and motion in a self-propelled system has attracted broader interest. In the present study, we consider an elliptic camphor particle for investigating the effect of particle shape on spontaneous motion. It is concluded that the symmetric spatial distribution of camphor molecules at the water surface becomes unstable first in the direction of a short axis, which induces the camphor disk motion in this direction. Experimental results also support the theoretical analysis. From the present results, we suggest that when an elliptic particle supplies surface-active molecules to the water surface, the particle can exhibit translational motion only in the short-axis direction.

Rotational motion of a droplet induced by interfacial tension

Spontaneous rotation of a droplet induced by the Marangoni flow is analyzed in a two-dimensional system. The droplet with the small particle which supplies a surfactant at the interface is considered. We calculated flow field around the droplet using the Stokes equation and found that advective nonlinearity breaks symmetry for rotation. Theoretical calculation indicates that the droplet spontaneously rotates when the radius of the droplet is an appropriate size. The theoretical results were validated through comparison with the experiments.

Spinning motion of a deformable self-propelled particle in two dimensions

We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from symmetry arguments for three kinds of variable. One is a vector which represents the velocity of the center of mass. The second is a traceless symmetric tensor representing deformation. The third is an antisymmetric tensor for spinning degree of freedom. By numerical simulations, we have obtained a variety of dynamical states due to interplay between the spinning motion and the deformation. The bifurcations of these dynamical states are analyzed by the simplified equations of motion.

Drift instability in the motion of a fluid droplet with a chemically reactive surface driven by Marangoni flow

We theoretically derive the amplitude equations for a self-propelled droplet driven by Marangoni flow. As advective flow driven by surface tension gradient is enhanced, the stationary state becomes unstable and the droplet starts to move. The velocity of the droplet is determined from a cubic nonlinear term in the amplitude equations. The obtained critical point and the characteristic velocity are well supported by numerical simulations.