Swarming of self-propelled camphor boats

How to capture active Marangoni surfers

Surfers at the air-water interface form a large subset of the domain of active matter systems. They range from the water strider in the biological world to soluto-capillary effect driven artificial boats. In this work, we propose a general protocol to capture soluto-capillary effect driven interfacial surfers. By locally modifying the air-water interface using the perturbation from a micro-air-pump, these boats are reliably captured in the region of influence (ROI) of the perturbation. The surfers begin to explore the available space freely again once the perturbation is switched off. This method is successfully generalized to a couple of distinct surface-active chemicals used as fuel for the boats. Control experiments involving passive particles validate the results as being significantly better than purely mechanical "herding" of the particles. A possible mechanism behind the observed "trapping" is proposed.

Time-Resolved Measurements of Interfacial Tension and Flow Speed of the Inclined Water Surface around a Self-propelled Camphor Boat by the Quasi-elastic Laser Scattering Method

An inclined liquid surface, such as a meniscus, plays an important role in advection and transport phenomena at a liquid's surface. However, there is no time-resolved measurement method for the interfacial tension of an inclined liquid-air interface. Here, a noninvasive method for simultaneous measurements of the interfacial tension and surface flow speed for an inclined water surface is described. This is an upgrade of the quasi-elastic laser scattering method with a closed-loop control system that introduces the dynamically tracked scattered and referential light into the detector. For the evaluation of the tilt compensation by dynamic tracking, the relationship between the apparent interfacial tension and surface inclination was examined for a water meniscus at 0-5° inclinations. It was also demonstrated that simultaneous measurements of the interfacial tension and surface flow speed around a self-propelled camphor boat on a pure water surface inclined by >3° at the back end of the boat are difficult to conduct accurately without dynamic tracking. Both the interfacial tension difference and the backward flow speed increased as the boat speed increased to 0.1 m/s; that had not been evaluated to date because of the high velocity of the boat and the surface inclination of the water around it. The direct experimental evaluation of the interfacial tension and the flow speed supported the model that the driving force of the camphor boat is the interfacial tension difference and the resistance force proportional to the boat velocity reduces its acceleration.

Revealing the deterministic components in active avalanche-like dynamics

Avalanche dynamics in an ensemble of self-propelled camphor boats are studied. The self-propelled agents are camphor infused circular paper disks moving on the surface of water. The ensemble exhibits bursts of activity in the autonomous state triggered by stochastic fluctuations. This type of dynamics has been previously reported in a slightly different system (J. Phys. Soc. Jpn., 2015, 84, 034802). Fourier analysis of the autonomous ensemble's average speed reveals a unimodal spectrum, indicating the presence of a preferred time scale in the dynamics. We therefor, entrain such an ensemble by external forcing by using periodic air perturbations on the surface of the water. This forcing is able to replace the stochastic fluctuations which trigger a burst in the autonomous ensemble, thus entraining the system. Upon varying the periodic forcing frequency, an optimal frequency is revealed at which the quality of entrainment of the ensemble by the forcing is augmented. This optimal frequency is found to be in the vicinity of the Fourier spectrum peak of the autonomous ensemble's average speed. This indicates the existence of an underlying deterministic component in the apparent aperiodic bursts of motion of the autonomous ensemble of active particles. A qualitative reasoning for the observed phenomenon is presented.

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.

Periodic oscillations in a string of camphor infused disks

The rhythmic beating motion of autonomously motile filaments has many practical applications. Here, we present an experimental study on a filament made of camphor infused paper disks, stitched together adjacent to each other using nylon thread. The filament displays spontaneous translatory motion when it is placed on the surface of water due to the surface tension gradients created by camphor molecules on the water surface. When this filament is clamped on one end, we obtain regular oscillatory motion instead of translation. The filament shows qualitatively different dynamics at different activity levels, which is controlled by the amount of camphor infused into the paper disks. For a better physical understanding of the filament dynamics, we develop a minimal numerical model involving a semi-flexible filament made of active polar disks, where the polarity is coupled to the instantaneous velocity of the particle. This model qualitatively reproduces different oscillatory modes of the filament. Moreover, our model reveals a rich dynamical state diagram of the system, as a function of filament activity and the coupling strength.

Reduced model of a reaction-diffusion system for the collective motion of camphor boats

The unidirectional motion of a camphor boat along an annular water channel is observable. When camphor boats are placed in a water channel, both homogeneous and inhomogeneous states occur as collective motions, depending on the number of boats. The inhomogeneous state is a type of congestion, that is, the velocities of the boats change with temporal oscillation, and the shock wave appears along the line of travel of the boats. The unidirectional motion of a single camphor boat and the homogeneous state can be represented by traveling wave solutions in a mathematical model. Because the experimental results described here are thought of as a type of bifurcation phenomenon, the destabilization of traveling wave solutions may indicate the emergence of congestion. We previously attempted to study a linearized eigenvalue problem associated with a traveling wave solution. However, the problem is too difficult to analyze rigorously, even for just two camphor boats. Therefore we developed a center manifold theory and derived a reduced model in our previous work. In the present paper, we study the reduced model and show that the original model and our reduced model qualitatively exhibit the same properties by applying numerical techniques. Moreover, we demonstrate that the numerical results obtained in our models for camphor boats are quite similar to those in a car-following model, the OV model, but there are some different features between our reduced model and a typical OV model.

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.

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.

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.

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.

Critical dynamics of the jamming transition in one-dimensional nonequilibrium lattice-gas models

We consider several one-dimensional driven lattice-gas models that show a phase transition in the stationary state between a high-density fluid phase in which the typical length of a hole cluster is of order unity and a low-density jammed phase where a hole cluster of macroscopic length forms in front of a particle. Using a hydrodynamic equation for an interface growth model obtained from the driven lattice-gas models of interest here, we find that in the fluid phase, the roughness exponent and the dynamic exponent that, respectively, characterize the scaling of the saturation width and the relaxation time of the interface with the system size are given by the Kardar-Parisi-Zhang exponents. However, at the critical point, we show analytically that when the equal-time density-density correlation function decays slower than inverse distance, the roughness exponent varies continuously with a parameter in the hop rates, but it is one-half otherwise. Using these results and numerical simulations for the density-density autocorrelation function, we further find that the dynamic exponent z=3/2 in all cases.

Physicochemical design and analysis of self-propelled objects that are characteristically sensitive to environments

The development of self-propelled motors that mimic biological motors is an important challenge for the transport of either themselves or some material in a small space, since biological systems exhibit high autonomy and various types of responses, such as taxis and swarming. In this perspective, we review non-living systems that behave like living matter. We especially focus on nonlinearity to enhance autonomy and the response of the system, since characteristic nonlinear phenomena, such as oscillation, synchronization, pattern formation, bifurcation, and hysteresis, are coupled to self-motion of which driving force is the difference in the interfacial tension. Mathematical modelling based on reaction-diffusion equations and equations of motion as well as physicochemical analysis from the point of view of the molecular structure are also important for the design of non-living motors that mimic living motors.

Maze solving using temperature-induced Marangoni flow

A temperature gradient can be utilized for maze solving using a temperature-induced Marangoni flow. Induced liquid flow drags passive tracers such as small dye particles, which dissolve in a water phase thus visualizing the shortest path.

Collective motion of symmetric camphor papers in an annular water channel

We investigate the collective motion of symmetric self-propelled objects that are driven by a difference in the surface tension. The objects move around an annular water channel spontaneously and interact through the camphor layer that develops on the water surface. We found that two collective motion modes, discrete and continuous density waves, are generated depending on the number of self-propelled objects. The two modes are characterized by examining the local and global dynamics, and the collective motion mechanism is discussed in relation to the distribution of camphor concentration in the annular water channel. We conclude that the difference between these two modes originates from that of the driving mechanism that pushes a camphor paper away from a cluster, through which mechanism density waves are generated and maintained.

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.