Dynamic Self-Assembly in Ensembles of Camphor Boats

Narrow escape for active camphor particles: facilitated escape and aging

In this work, we experimentally investigate the narrow escape problem using self-propelled camphor-infused discs, which have the possibility to escape from a bounded circular domain through an opening in the boundary. To analyze the statistical properties of the escape problem, we proposed two experimental protocols: first, a control setup within a closed circular domain where the disc encounters a target simulating an opening on the boundary, and a second setup where a real opening is placed on the boundary of the circular domain. These two setups allow us to compare how the statistical properties of escape differ between simulated (or fictitious) escape and the actual escape of camphor particles. Our results suggest that the presence of an actual opening in the wall alters the interactions between the particle and the boundary. Notably, we observe the counterintuitive phenomenon that introducing a real door in the boundary makes less accessible the escape from the domain. We further contrast and analyze several qualitative and quantitative properties of the system, including chiral flips, bouncing behavior, arrival angle distribution, as well as first passage time and exit time distributions, among other dynamical properties.

Dynamics of Aggregation in Systems of Self-Propelled Rods

We highlight camphene-camphor-polypropylene plastic as a useful material for self-propelled objects that show aggregation while floating on a water surface. We consider self-propelled rods as an example of aggregation of objects characterized by non-trivial individual shapes with low-symmetry interactions between them. The motion of rods made of the camphene-camphor-polypropylene plastic is supported by dissipation of the surface-active molecules. The physical processes leading to aggregation and the mathematical model of the process are discussed. We analyze experimental data of aggregate formation dynamics and relate them to the system's properties. We speculate that the aggregate structure can be represented as a string of symbols, which opens the potential applicability of the phenomenon for information processing if objects floating on a water surface are regarded as reservoir computers.

Positional Information-Based Organization of Surfactant Droplet Swarms Emerging from Competition Between Local and Global Marangoni Effects

Positional information is key for particles to adapt their behavior based on their position in external concentration gradients, and thereby self-organize into complex patterns. Here, position-dependent behavior of floating surfactant droplets that self-organize in a pH gradient is demonstrated, using the Marangoni effect to translate gradients of surface-active molecules into motion. First, fields of surfactant microliter-droplets are generated, in which droplets floating on water drive local, outbound Marangoni flows upon dissolution of surfactant and concomitantly grow myelin filaments. Next, a competing surfactant based on a hydrolysable amide is introduced, which is more surface active than the myelin surfactant and thereby inhibits the local Marangoni flows and myelin growth from the droplets. Upon introducing a pH gradient, the amide surfactant hydrolyses in the acidic region, so that the local Marangoni flows and myelin growth are reestablished. The resulting combination of local and global surface tension gradients produces a region of myelin-growing droplets and a region where myelin growth is suppressed, separated by a wave front of closely packed droplets, of which the position can be controlled by the pH gradient. Thereby, it is shown how "French flag"-patterns, in synthetic settings typically emerging from reaction-diffusion systems, can also be established via surfactant droplet systems.

Surface tension gradient invoked path selection

Certain active particles execute continuous self-propelled motion at the air-water interface due to Marangoni forces. Here, we report motion of camphor and pentanol infused disks in an L-shaped two path and a Y-shaped three path channel. These channels are open to the sink. In both the cases, these channels have asymmetry in arm-lengths while the arm-widths are equal. The active disks are introduced in the decision region (center) of the channel from where they elect to move along a particular path towards the sink. We observe that these active disks show a preference for reaching the sink along the minimal (in length) path. The camphor disk prefers the minimal path 80% of the time in the two-path and 68% of the time in the three-path channels, while for the pentanol disk, the preference rates for the minimal path selection are 88% and 74%, respectively. Furthermore, we perform numerical analysis to validate the experimental observations.

A Miniaturized, Fuel-Free, Self-Propelled, Bio-Inspired Soft Actuator for Copper Ion Removal

We present a novel miniaturized, gear-shaped, fuel-free actuator capable of autonomously propelling itself in an aquatic environment to absorb heavy metals, such as copper ions. While hydrogel-based absorbents are promising solutions for cationic pollutant remediation, their stationary nature limits their effectiveness in areas where contaminants are unevenly distributed. To address this, we developed a bio-inspired soft actuator that mimics natural propulsion mechanisms. The Marangoni effect, driven by its inherent chemical properties, demonstrated a self-propelled motion without requiring external fuel. The proof-of-concept actuator generated a plane motion lasting up to 2 h and swept over an area approximately 400 times bigger than its size. By harnessing the chemical and optical properties of the hydrogel, we efficiently removed and quantitatively analyzed copper ions through a colorimetric method. This innovative integration of self-propelled movement and efficient copper ion absorption underscores its potential for advancing miniaturized devices in environmental remediation, paving the way for more active and efficient pollutant removal systems in challenging aquatic environments.

Quorum Sensing in Emulsion Droplet Swarms Driven by a Surfactant Competition System

Quorum sensing enables unicellular organisms to probe their population density and perform behavior that exclusively occurs above a critical density. Quorum sensing is established in emulsion droplet swarms that float at a water surface and cluster above a critical density. The design involves competition between 1) a surface tension gradient that is generated upon release of a surfactant from the oil droplets, and thereby drives their mutual repulsion, and 2) the release of a surfactant precursor from the droplets, that forms a strong imine surfactant which suppresses the surface tension gradient and thereby causes droplet clustering upon capillary (Cheerios) attraction. The production of the imine-surfactant depends on the population density of the droplets releasing the precursor so that the clustering only occurs above a critical population density. The pH-dependence of the imine-surfactant formation is exploited to trigger quorum sensing upon a base stimulus: dynamic droplet swarms are generated that cluster and spread upon spatiotemporally varying acid and base conditions. Next, the clustering of two droplet subpopulations is coupled to a chemical reaction that generates a fluorescent signal. It is foreseen that quorum sensing enables control mechanisms in droplet-based systems that display collective responses in contexts of, e.g., sensing, optics, or dynamically controlled droplet-reactors.

Can self-propelled objects escape from compression stimulation?

We studied circular papers impregnated with camphor (CPs) and CPs with magnets (MCPs) as self-propelled objects floating on water under the compression of the water surface as an inanimate system for evacuation in an emergency. Two water chambers-Cin and Cout-were connected via a plastic gate, and eight CPs or eight MCPs were placed on Cin. We monitored the movement of the CPs or MCPs from Cin to Cout when the gate was opened and the area of Cin (Ain) was decreased using a barrier. When Ain was large, CPs moved stochastically from Cin to Cout while exhibiting random motion. The escape probability from Cin to Cout (P) at time t = 20 s increased with a decrease in Ain, and the rate of increase in P increased depending on the width of the gate (Wg). By contrast, clustering was observed for MCPs. Consequently, P of MCPs was lower than that of CPs. The difference in the surface tension between Cin and Cout (Δγ) increased with a decrease in Ain. P is discussed in relation to Δγ as the driving force for emergencies and the repulsive forces between CPs or attractive forces between MCPs. These results suggest that the repulsive force enhances the self-propulsion of objects towards the gate, that is, as a result, higher values of P are obtained.

Shaping active matter from crystalline solids to active turbulence

Active matter drives its constituent agents to move autonomously by harnessing free energy, leading to diverse emergent states with relevance to both biological processes and inanimate functionalities. Achieving maximum reconfigurability of active materials with minimal control remains a desirable yet challenging goal. Here, we employ large-scale, agent-resolved simulations to demonstrate that modulating the activity of a wet phoretic medium alone can govern its solid-liquid-gas phase transitions and, subsequently, laminar-turbulent transitions in fluid phases, thereby shaping its emergent pattern. These two progressively emerging transitions, hitherto unreported, bring us closer to perceiving the parallels between active matter and traditional matter. Our work reproduces and reconciles seemingly conflicting experimental observations on chemically active systems, presenting a unified landscape of phoretic collective dynamics. These findings enhance the understanding of long-range, many-body interactions among phoretic agents, offer new insights into their non-equilibrium collective behaviors, and provide potential guidelines for designing reconfigurable materials.

Modulating photothermocapillary interactions for logic operations at the air-water interface

We demonstrate a system for performing logical operations (OR, AND, and NOT gates) at the air-water interface based on Marangoni optical trapping and repulsion between photothermal particles. We identify a critical separation distance at which the trapped particle assemblies become unstable, providing insight into the potential for scaling to larger arrays of logic elements.

Spatial programming of self-organizing chemical systems using sustained physicochemical gradients from reaction, diffusion and hydrodynamics

Living organisms employ chemical self-organization to build structures, and inspire new strategies to design synthetic systems that spontaneously take a particular form, via a combination of integrated chemical reactions, assembly pathways and physicochemical processes. However, spatial programmability that is required to direct such self-organization is a challenge to control. Thermodynamic equilibrium typically brings about a homogeneous solution, or equilibrium structures such as supramolecular complexes and crystals. This perspective addresses out-of-equilibrium gradients that can be driven by coupling chemical reaction, diffusion and hydrodynamics, and provide spatial differentiation in the self-organization of molecular, ionic or colloidal building blocks in solution. These physicochemical gradients are required to (1) direct the organization from the starting conditions (e.g. a homogeneous solution), and (2) sustain the organization, to prevent it from decaying towards thermodynamic equilibrium. We highlight four different concepts that can be used as a design principle to establish such self-organization, using chemical reactions as a driving force to sustain the gradient and, ultimately, program the characteristics of the gradient: (1) reaction-diffusion coupling; (2) reaction-convection; (3) the Marangoni effect and (4) diffusiophoresis. Furthermore, we outline their potential as attractive pathways to translate chemical reactions and molecular/colloidal assembly into organization of patterns in solution, (dynamic) self-assembled architectures and collectively moving swarms at the micro-, meso- and macroscale, exemplified by recent demonstrations in the literature.

Self-Organization Emerging from Marangoni and Elastocapillary Effects Directed by Amphiphile Filament Connections

Self-organization of meso- and macroscale structures is a highly active research field that exploits a wide variety of physicochemical phenomena, including surface tension, Marangoni flow, and (elasto)capillary effects. The release of surface-active compounds generates Marangoni flows that cause repulsion, whereas capillary forces attract floating particles via the Cheerios effect. Typically, the interactions resulting from these effects are nonselective because the gradients involved are uniform. In this work, we unravel the mechanisms involved in the self-organization of amphiphile filaments that connect and attract droplets floating at the air-water interface, and we demonstrate their potential for directional gradient formation and thereby selective interaction. We simulate Marangoni flow patterns resulting from the release and depletion of amphiphile molecules by source and drain droplets, respectively, and we predict that these flow patterns direct the growth of filaments from the source droplets toward specific drain droplets, based on their amphiphile depletion rate. The interaction between such droplets is then investigated experimentally by charting the flow patterns in their surroundings, while the role of filaments in source-drain attraction is studied using microscopy. Based on these observations, we attribute attraction of drain droplets and even solid objects toward the source to elastocapillary effects. Finally, the insights from our simulations and experiments are combined to construct a droplet-based system in which the composition of drain droplets regulates their ability to attract filaments and as a consequence be attracted toward the source. Thereby, we provide a novel method through which directional attraction can be established in synthetic self-organizing systems and advance our understanding of how complexity arises from simple building blocks.

Complexity and bifurcations in the motion of a self-propelled rectangle confined in a circular water chamber

We consider the motion of a self-propelled object of rectangular shape inside a circular water chamber. The mathematical model of self-motion includes equations for the orientation and location of the rectangle and reaction-diffusion equation with an effective diffusion coefficient for the time evolution of the surface concentration of active molecules. Numerical simulations of motion were performed for different values of the ratio between the supply rate S and the evaporation rate a of active molecules. Treating S₀ = S/a as a control parameter, we found the critical behavior in variables characterizing the trajectory and identified different types of motion. If the value of S₀ is small, the rectangle rests at the chamber center. For larger S₀, a reciprocal motion during which the rectangle passes through the center is observed. At yet higher supply rates, the star-polygonal motion appears, and the trajectory remains at a distance from the chamber center. In the experiments with a rectangle made of camphor-camphene-polypropylene plastic moving in a Petri dish, we observed the transition from the star-polygonal motion to the reciprocal motion in time. This transition can be understood on the basis of the developed model if we assume that the supply rate decreases in time.

Motion of a chemically reactive bimetal motor in a magnetic field

The wide research interest in nano-, micro-, and macromotors is due to the diverse range of applied problems in engineering, biomedicine, and ecology. At the same time, the amount of known mechanisms responsible for the locomotion of motors is limited. Here, we demonstrate a novel method of motor locomotion, which can be contingently called "chemical magnetism". The phenomenon considered here is based on the fact that any current loop in the magnetic field is affected by a force. "Chemical magnet" represents a bimetal surfer swimming at the electrolyte surface. When the redox reaction proceeds, a current loop emerges. That defines the action of the additional magnetic force on the surfer in the non-uniform magnetic field. The magnetic properties of the surfer can be varied in a wide range by changing the concentration of the electrolyte solution, its temperature, and the pair of metals composing the surfer. The phenomenon of "chemical magnetism" considered here widens a list of known mechanisms of motor locomotion.

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.

Micro-object manipulation by decanol liquid lenses

The flexible and precise manipulation of droplets on an air-liquid interface with complex functions remains challenging. Herein, we propose a smart strategy for excellently manipulating target droplets by decanol liquid lenses. A moveable surface tension gradient field generated by decanol liquid lenses is responsible for realizing various functions of transportation, launching and splitting of target droplets. With such fascinating features, directional long-distance transportation and on-demand droplet coalescence are enabled. Moreover, paw-like liquid lenses are constructed, which realizes a complex process, including collection, capture, transportation and release of target droplets. Remarkably, this strategy can also be applied to manipulate particles and liquid marbles other than droplets, eliminating the limitation of object properties. This work offers a smart strategy for manipulating micro-objects, which shows great potential in applications such as lab-on-a-chip, diagnostics, analytical chemistry and bioengineering, etc.

Two-dimensional numerical model of Marangoni surfers: From single swimmer to crystallization

We numerically study the dynamics of an ensemble of Marangoni surfers in a two-dimensional and unconfined space. The swimmers are modeled as Gaussian sources of surfactant generating surface tension gradients and are shown to follow the Marangoni flow filtered at their spatial scale in the lubrication regime, an unstable situation leading to spontaneous motion as soon as the Marangoni effect is intense enough. As the system is fully unconstrained, it is possible to study the various dynamical regimes from single swimmer, two-body interaction, to the many-particles case characterized by an efficient particle dispersion. We show that, although the present model is very simple, it reproduces the experimentally observed transition between a regime of dispersion by random agitation when the number of swimmers is moderate to the regime of crystallization with imperfect hexagonal lattice at high density.

A remotely controlled Marangoni surfer

Inspired by creatures that have naturally mastered locomotion on the air-water interface, we developed and built a self-powered, remotely controlled surfing robot capable of traversing this boundary by harnessing surface tension modification for both propulsion and steering through a controlled release of isopropyl alcohol. In this process, we devised and implemented novel release valve and steering mechanisms culminating in a surfer with distinct capabilities. Our robot measures about 110 mm in length and can travel as fast as 0.8 body length per second. Interestingly, we found that the linear speed of the robot follows a 1/3 power law with the release rate of the propellant. Additional maneuverability tests also revealed that the robot is able to withstand 20 mm s^-2in centripetal acceleration while turning. Here, we thoroughly discuss the design, development, performance, overall capabilities, and ultimate limitations of our robotic surfer.

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.

Oscillating Motion of Oil Droplets in the Emulsion Near the Air-Water Interface

Numerous living organisms as well as artificially created self-propelled objects can form dissipative structures due to the nonlinear effects and nonequilibrium of the system. Here we present an active oil-in-water emulsion in which the oil droplets take part in the reciprocating motion under the action of Marangoni flow near the air-water interface. The droplet dynamics in the emulsion is governed by the chemical reaction proceeding between quiescent copper particles and ammonia and by the convective mixing of a surfactant. We established that the reciprocating motion of droplets in the emulsion arises as a result of a periodic change in the Marangoni flow direction at the air-water interface. The feature of the considered system is that the reciprocating motion of droplets is realized only when the surface area fraction of droplets in the emulsion is close to the density of a two-dimensional colloid crystal. Oscillations degenerate under the reduction in surface area fraction to the critical value of ∼50% since the existence of oscillations in the emulsion requires a suppression of the surfactant convective mixing between the inner layers of liquid film and the air-water interface.

Surfactant-loaded capsules as Marangoni microswimmers at the air-water interface: Symmetry breaking and spontaneous propulsion by surfactant diffusion and advection

We present a realization of a fast interfacial Marangoni microswimmer by a half-spherical alginate capsule at the air-water interface, which diffusively releases water-soluble spreading molecules (weak surfactants such as polyethylene glycol (PEG)), which act as "fuel" by modulating the air-water interfacial tension. For a number of different fuels, we can observe symmetry breaking and spontaneous propulsion although the alginate particle and emission are isotropic. The propulsion mechanism is similar to soap or camphor boats, which are, however, typically asymmetric in shape or emission to select a swimming direction. We develop a theory of Marangoni boat propulsion starting from low Reynolds numbers by analyzing the coupled problems of surfactant diffusion and advection and fluid flow, which includes surfactant-induced fluid Marangoni flow, and surfactant adsorption at the air-water interface; we also include a possible evaporation of surfactant. The swimming velocity is determined by the balance of drag and Marangoni forces. We show that spontaneous symmetry breaking resulting in propulsion is possible above a critical dimensionless surfactant emission rate (Peclet number). We derive the relation between Peclet number and swimming speed and generalize to higher Reynolds numbers utilizing the concept of the Nusselt number. The theory explains the observed swimming speeds for PEG-alginate capsules, and we unravel the differences to other Marangoni boat systems based on camphor, which are mainly caused by surfactant evaporation from the liquid-air interface. The capsule Marangoni microswimmers also exhibit surfactant-mediated repulsive interactions with walls, which can be qualitatively explained by surfactant accumulation at the wall.

From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

We present a theory for the self-propulsion of symmetric, half-spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air-water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion-advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary conditions. We derive novel results for concentration profiles under constant flux boundary conditions and for the Nusselt number (the dimensionless ratio of total emitted flux and diffusive flux). Based on these results, we analyze the Marangoni boat for small Marangoni propulsion (low Peclet number) and show that two swimming regimes exist, a diffusive regime at low velocities and an advection-dominated regime at high swimmer velocities. We describe both the limit of large Marangoni propulsion (high Peclet number) and the effects from evaporation by approximative analytical theories. The swimming velocity is determined by force balance, and we obtain a general expression for the Marangoni forces, which comprises both direct Marangoni forces from the surface tension gradient along the air-water-swimmer contact line and Marangoni flow forces. We unravel whether the Marangoni flow contribution is exerting a forward or backward force during propulsion. Our main result is the relation between Peclet number and swimming velocity. Spontaneous symmetry breaking and, thus, swimming occur for a perfectly symmetrical swimmer above a critical Peclet number, which becomes small for large system sizes. We find a supercritical swimming bifurcation for a symmetric swimmer and an avoided bifurcation in the presence of an asymmetry.

Imperfect bifurcation in the rotation of a propeller-shaped camphor rotor

We investigated the bifurcation structure on the self-propelled motion of a camphor rotor at a water surface. The center of the camphor rotor was fixed by the axis, and it showed rotational motion around it. Due to the chiral asymmetry of its shape, the absolute values of the angular velocities in clockwise and counterclockwise directions were different. This asymmetry in the angular velocities implies an imperfect bifurcation. From the numerical simulation results, we discuss the condition for the occurrence of the imperfect bifurcation.

Autonomous mesoscale positioning emerging from myelin filament self-organization and Marangoni flows

Out-of-equilibrium molecular systems hold great promise as dynamic, reconfigurable matter that executes complex tasks autonomously. However, translating molecular scale dynamics into spatiotemporally controlled phenomena emerging at mesoscopic scale remains a challenge-especially if one aims at a design where the system itself maintains gradients that are required to establish spatial differentiation. Here, we demonstrate how surface tension gradients, facilitated by a linear amphiphile molecule, generate Marangoni flows that coordinate the positioning of amphiphile source and drain droplets floating at air-water interfaces. Importantly, at the same time, this amphiphile leads, via buckling instabilities in lamellar systems of said amphiphile, to the assembly of millimeter long filaments that grow from the source droplets and get absorbed at the drain droplets. Thereby, the Marangoni flows and filament organization together sustain the autonomous positioning of interconnected droplet-filament networks at the mesoscale. Our concepts provide potential for the development of non-equilibrium matter with spatiotemporal programmability.

Self-Propelled Supracolloidal Fibers from Multifunctional Polymer Surfactants and Droplets

Advanced synthetic materials are needed to produce nano- and mesoscale structures that function autonomously, catalyze reactions, and convert chemical energy into motion. This paper describes supracolloidal fiber-like structures that are composed of self-adhering, or "sticky," oil-in-water emulsion droplets. Polymer zwitterion surfactants serve as the key interfacial components of these materials, enabling multiple functions simultaneously, including acting as droplet-stabilizing surfactants, interdroplet adhesives, and building blocks of the fibers. This fiber motion, a surprising additional feature of these supracolloidal structures, is observed at the air-water interface and hinged on the chemistry of the polymer surfactant. The origin of this motion is hypothesized to involve transport of polymer from the oil-water interface to the air-water interface, which generates a Marangoni (interfacial) stress. Harnessing this fiber motion with functional polymer surfactants, and selection of the oil phase, produced worm-like objects capable of rotation, oscillation, and/or response to external fields. Overall, these supracolloidal fibers fill a design gap between self-propelled nano/microscale particles and macroscale motors, and have the potential to serve as new components of soft, responsive materials structures.

First passage of an active particle in the presence of passive crowders

We experimentally study the stochastic transport of a self-propelled camphor boat, driven by Marangoni forces, through a crowd of passive paper discs floating on water. We analyze the statistics of the first passage times of the active particle to travel from the center of a circular container to its boundary. While the mean times rise monotonically as a function of the covered area fraction φ of the passive paper discs, their fluctuations show a non-monotonic behavior - being higher at low and high value of φ compared to intermediate values. The reason is traced to an interplay of two distinct sources of fluctuations - one intrinsic to the dynamics, while the other due to the crowding.

Life-Like Motion of Oil Drops at the Air-Liquid Interface

Generally, interactions of oil drops at the air-liquid interface mainly have two features, namely, attraction and repulsion. However, in our study, we find that the oil drops at the air-liquid interface have other interacting features, that is, the atomic-like motion and the "capture" motion. For the atomic-like motion, oil drops attract each other at a long distance, but repel when they are about to come into contact with each other. For the "capture" motion, a big oil drop can actively "capture" oil droplets like a zooplankton. In our research, we analyze interfacial forces among the oil drops. Based on the experiments and analyses, we demonstrate that the atomic-like motion of oil drops is mainly due to the lateral capillary force and the surface tension force, and the "capture" motion is mainly due to the unbalanced impact force of flow fluid around the drops. In addition, based on our results, we use the oil drops to perform many functions at the air-liquid interface. For example, the oil drops can drive an object with linear and rotational motion. When a carbon tetrachloride drop is suspended above the air-liquid interface, it can be used to control an oil droplet to pass through serpentine grooves and obstacles. In addition, the suspended carbon tetrachloride drops also can be used to rank multiple droplets with a special shape. Based on the results, our study makes it possible to use oil drops to transport materials, drive objects, and even collect droplets at the air-liquid interface.

A hybrid camphor-camphene wax material for studies on self-propelled motion

A new material that combines the self-propelling properties of camphor with the malleability of camphene is reported. It has wax-like mechanical properties at room temperature and can be formed into required shapes. The speed of the self-propelled objects and the trajectory depend on the shape and camphor-camphene weight ratio.

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.

Spreading dynamics of reactive surfactants driven by Marangoni convection

We consider the spreading dynamics of some insoluble surface-active species along an aqueous interface. The model includes both diffusion, Marangoni convection and first-order reaction kinetics. An exact solution of the nonlinear transport equations is derived in the regime of large Schmidt number, where viscous effects are dominant. We demonstrate that the variance of the surfactant distribution increases linearly with time, providing an unambiguous definition for the enhanced diffusion coefficient observed in the experiments. The model thus presents new insight regarding the actuation of camphor grains at the water-air interface.

Rotational motion of a camphor disk in a circular region

In a two-dimensional axisymmetric system, the system symmetry allows rotational or oscillatory motion as stable stationary motion for a symmetric self-propelled particle. In the present paper, we studied the motion of a camphor disk confined in a two-dimensional circular region. By reducing the mathematical model describing the dynamics of the motion of a camphor disk and the concentration field of camphor molecules on a water surface, we analyzed the reduced equations around a bifurcation point where the rest state at the center of the system becomes unstable. As a result, we found that rotational motion is stably realized through the double-Hopf bifurcation from the rest state. The theoretical results were confirmed by numerical calculation and corresponded well to the experimental results.

Rotational synchronization of camphor ribbons

Experiments on interacting pinned self-propelled rotators are presented. The rotators are made from paper with camphor infused in its matrix. The ribbons rotate due to Marangoni effect driven forces arising by virtue of surface tension gradients. Two such self-rotating camphor ribbons are observed to experience a repulsive coupling via the camphor layer in the common water medium. Lag synchronization in both corotating (same sense of rotation) and counterrotating (opposite sense of rotation) ribbons is reported for the experiments. This synchronization is found to be dependent on the pivot to pivot distance l. For distances less than the span of both the ribbons, l_{c}, the rotators successfully synchronize. Furthermore, it is experimentally perceived that synchronization in the counterrotating ribbons is more robust than in the corotating ribbons. We rationalize the mechanism of this synchronization via a theoretical model involving a Yukawa type interaction which is analyzed numerically.

Bifurcation in the angular velocity of a circular disk propelled by symmetrically distributed camphor pills

We studied rotation of a disk propelled by a number of camphor pills symmetrically distributed at its edge. The disk was put on a water surface so that it could rotate around a vertical axis located at the disk center. In such a system, the driving torque originates from surface tension difference resulting from inhomogeneous surface concentration of camphor molecules released from the pills. Here, we investigated the dependence of the stationary angular velocity on the disk radius and on the number of pills. The work extends our previous study on a linear rotor propelled by two camphor pills [Y. Koyano et al., Phys. Rev. E 96, 012609 (2017)]. It was observed that the angular velocity dropped to zero after a critical number of pills was exceeded. Such behavior was confirmed by a numerical model of time evolution of the rotor. The model predicts that, for a fixed friction coefficient, the speed of pills can be accurately represented by a function of the linear number density of pills. We also present bifurcation analysis of the conditions at which the transition between a standing and a rotating disk appears.

Power law observed in the motion of an asymmetric camphor boat under viscous conditions

We investigated the velocity of an asymmetric camphor boat moving on aqueous solutions with glycerol. The viscosity was controlled by using several concentrations of glycerol into the solution. The velocity decreased with an increase in the glycerol concentration. We proposed a phenomenological model, and we showed that the velocity decreased with an increase in the viscosity according to power law. Our experimental result agreed with the one obtained from our model. These results suggest that a decay length of the camphor concentration at the front side of the boat is sufficiently shorter than that of the rear side.

Experimental Investigation of the Self-Propelled Motion of a Sodium Oleate Tablet and Boat at an Oil-Water Interface

The self-propelled behaviors of macroscopic inanimate objects at surfaces and interfaces are ubiquitous phenomena of fundamental interest in interface science. However, given the existence of a large variety of systems with their own inherent chemical properties, the kinematics of the self-propelled motion and the dynamics of the forces driving these systems often remain largely unknown. Here, we experimentally investigate the spontaneous motion of a sodium oleate tablet at a water-nitrobenzene interface, under nonequilibrium and global isothermal conditions, through measurements of the interfacial tension with the noninvasive, quasi-elastic laser scattering method. The sodium oleate tablet was self-propelled due to an imbalance in the interfacial tension induced by the inhomogeneous adsorption of oleate/oleic acid molecules. The kinetics of the self-propelled motion of a boat-shaped plastic sheet bearing sodium oleate tablets at a sodium oleate aqueous solution-nitrobenzene interface was also studied. The interfacial tension difference between the front and rear of the boat was quantitatively identified as the force pushing the boat forward, although the Marangoni flow due to the uneven distribution of the interfacial tension behind the boat tended to decelerate the motion.

From dynamic self-assembly to networked chemical systems

Although dynamic self-assembly, DySA, is a relatively new area of research, the past decade has brought numerous demonstrations of how various types of components - on scales from (macro)molecular to macroscopic - can be arranged into ordered structures thriving in non-equilibrium, steady states. At the same time, none of these dynamic assemblies has so far proven practically relevant, prompting questions about the field's prospects and ultimate objectives. The main thesis of this Review is that formation of dynamic assemblies cannot be an end in itself - instead, we should think more ambitiously of using such assemblies as control elements (reconfigurable catalysts, nanomachines, etc.) of larger, networked systems directing sequences of chemical reactions or assembly tasks. Such networked systems would be inspired by biology but intended to operate in environments and conditions incompatible with living matter (e.g., in organic solvents, elevated temperatures, etc.). To realize this vision, we need to start considering not only the interactions mediating dynamic self-assembly of individual components, but also how components of different types could coexist and communicate within larger, multicomponent ensembles. Along these lines, the review starts with the discussion of the conceptual foundations of self-assembly in equilibrium and non-equilibrium regimes. It discusses key examples of interactions and phenomena that can provide the basis for various DySA modalities (e.g., those driven by light, magnetic fields, flows, etc.). It then focuses on the recent examples where organization of components in steady states is coupled to other processes taking place in the system (catalysis, formation of dynamic supramolecular materials, control of chirality, etc.). With these examples of functional DySA, we then look forward and consider conditions that must be fulfilled to allow components of multiple types to coexist, function, and communicate with one another within the networked DySA systems of the future. As the closing examples show, such systems are already appearing heralding new opportunities - and, to be sure, new challenges - for DySA research.

Hydrodynamic Signatures of Stationary Marangoni-Driven Surfactant Transport

We experimentally study steady Marangoni-driven surfactant transport on the interface of a deep water layer. Using hydrodynamic measurements, and without using any knowledge of the surfactant physicochemical properties, we show that sodium dodecyl sulphate and Tergitol 15-S-9 introduced in low concentrations result in a flow driven by adsorbed surfactant. At higher surfactant concentration, the flow is dominated by the dissolved surfactant. Using camphoric acid, whose properties are a priori unknown, we demonstrate this method's efficacy by showing its spreading is adsorption dominated.

Antiswarming: Structure and dynamics of repulsive chemically active particles

Chemically active Brownian particles with surface catalytic reactions may repel each other due to diffusiophoretic interactions in the reaction and product concentration fields. The system behavior can be described by a "chemical" coupling parameter Γ_{c} that compares the strength of diffusiophoretic repulsion to Brownian motion, and by a mapping to the classical electrostatic one component plasma (OCP) system. When confined to a constant-volume domain, body-centered cubic (bcc) crystals spontaneously form from random initial configurations when the repulsion is strong enough to overcome Brownian motion. Face-centered cubic (fcc) crystals may also be stable. The "melting point" of the "liquid-to-crystal transition" occurs at Γ_{c}≈140 for both bcc and fcc lattices.

Metal-Organic Framework "Swimmers" with Energy-Efficient Autonomous Motility

Placed at a water/air interface, particles of porphyrin-based MOFs (metal-organic frameworks) cut from large-area films display efficient, multiple-use autonomous motility powered by release of solvents incorporated in the MOF matrix and directionality dictated by their shapes. The particles can be refueled multiple times and can achieve speeds of ca. 200 mm·s^-1 with high kinetic energy per unit of chemical "fuel" expended (>50 μJ·g^-1). Efficiency of motion depends on the nature of the fuel used as well as the microstructure and surface wettability of the MOF surface. When multiple movers are present at the interface, they organize into "open" structures that exhibit collective, time-periodic motions.

Relationship between the size of a camphor-driven rotor and its angular velocity

We consider a rotor made of two camphor disks glued below the ends of a plastic stripe. The disks are floating on a water surface and the plastic stripe does not touch the surface. The system can rotate around a vertical axis located at the center of the stripe. The disks dissipate camphor molecules. The driving momentum comes from the nonuniformity of surface tension resulting from inhomogeneous surface concentration of camphor molecules around the disks. We investigate the stationary angular velocity as a function of rotor radius ℓ. For large ℓ the angular velocity decreases for increasing ℓ. At a specific value of ℓ the angular velocity reaches its maximum and, for short ℓ it rapidly decreases. Such behavior is confirmed by a simple numerical model. The model also predicts that there is a critical rotor size below which it does not rotate. Within the introduced model we analyze the type of this bifurcation.

Unidirectional motion of a camphor disk on water forced by interactions between surface camphor concentration and dynamically changing boundaries

Dynamically changing boundaries induce unidirectional motion of a camphor disk on water, which is regarded as a signal diode.