Camphor Disk Research Articles

Self-propelled motion controlled by ionic liquids.

We studied the self-propulsion of a camphor disk floating on a water surface using two types of ionic liquids (hexylammonium-trifluoroacetate (HHexam-TFA) and hexylethylenediaminium-trifluoroacetate (HHexen-TFA)). Bifurcation between continuous, oscillatory, and no motion was observed depending on the concentration of the ionic liquid. The bifurcation concentration between oscillatory and no motion for HHexam-TFA was lower than that for HHexen-TFA. The different bifurcation concentrations are discussed in relation to the surface tension and Fourier transform infrared spectra of the mixtures of camphor and ionic liquids. These results suggest that the interaction between the ionic liquid molecules at the air/water interface is weakened by the addition of camphor molecules and the features of self-propulsion vary due to the change in the driving force.

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.

Stochastic migrations of Marangoni surfers between two lobes of a dumbbell-shaped confinement.

We report an experimental investigation on the stochastic migration dynamics of Marangoni surfers (camphor-infused paper disks) between the two lobes of a dumbbell-shaped chamber. We characterize the migration dynamics using survival analysis of a configuration, wherein a configuration represents a distinct distribution of disks between the lobes. We observe that a configuration's stability decreases with increasing pairwise interactions. Consequently, the configuration with equal partitioning of disks between the lobes-that is exactly one-half of disks in each lobe for even-numbered systems but with one extra disk in either of the lobes for odd-numbered systems-has the lowest pairwise interactions, thus is always the most stable configuration. Furthermore, all configurations exhibit a stretched exponential decay with time, which is ascribed to a disk's activity decay with time or "aging"-a phenomenon validated by modeling a camphor disk as a chiral active particle (CAP) as initially proposed by Cruz et al.

Self-propulsion of an elliptical phoretic disk emitting solute uniformly

Self-propulsion of chemically active droplets and phoretic disks has been studied widely; however, most research overlooks the influence of disk shape on swimming dynamics. Inspired by experimentally observed prolate composite droplets and elliptical camphor disks, we employ simulations to investigate the phoretic dynamics of an elliptical disk that emits solutes uniformly in the creeping flow regime. By varying the disk's eccentricity $e$ and the Péclet number $Pe$ , we distinguish five disk behaviours: stationary, steady, orbiting, periodic and chaotic. We perform a linear stability analysis (LSA) to predict the onset of instability and the most unstable eigenmode when a stationary disk transitions spontaneously to steady self-propulsion. In addition to the LSA, we use an alternative approach to determine the perturbation growth rate, illustrating the competing roles of advection and diffusion. The steady motion features a transition from a puller-type to a neutral-type swimmer as $Pe$ increases, which occurs as a bimodal concentration profile at the disk surface shifts to a polarized solute distribution, driven by convective solute transport. An elliptical disk achieves an orbiting motion through a chiral symmetry-breaking instability, wherein it repeatedly follows a circular path while simultaneously rotating. The periodic swinging motion, emerging from a steady motion via a supercritical Hopf bifurcation, is characterized by a wave-like trajectory. We uncover a transition from normal diffusion to superdiffusion as eccentricity $e$ increases, corresponding to a random-walking circular disk and a ballistically swimming elliptical counterpart, respectively.

On the reaction–diffusion type modelling of the self-propelled object motion

In this study, we propose a mathematical model of self-propelled objects based on the Allen–Cahn type phase-field equation. We combine it with the equation for the concentration of surfactant used in previous studies to construct a model that can handle self-propelled object motion with shape change. A distinctive feature of our mathematical model is that it can represent both deformable self-propelled objects, such as droplets, and solid objects, such as camphor disks, by controlling a single parameter. Furthermore, we demonstrate that, by taking the singular limit, this phase-field based model can be reduced to a free boundary model, which is equivalent to the L^2-gradient flow model of self-propelled objects derived by the variational principle from the interfacial energy, which gives a physical interpretation to the phase-field model.

Survival strategies of artificial active agents

Artificial cells can be engineered to display dynamics sharing remarkable features in common with the survival behavior of living organisms. In particular, such active systems can respond to stimuli provided by the environment and undertake specific displacements to remain out of equilibrium, e.g. by moving towards regions with higher fuel concentration. In spite of the intense experimental activity aiming at investigating this fascinating behavior, a rigorous definition and characterization of such “survival strategies” from a statistical physics perspective is still missing. In this work, we take a first step in this direction by adapting and applying to active systems the theoretical framework of Transition Path Theory, which was originally introduced to investigate rare thermally activated transitions in passive systems. We perform experiments on camphor disks navigating Petri dishes and perform simulations in the paradigmatic active Brownian particle model to show how the notions of transition probability density and committor function provide the pivotal concepts to identify survival strategies, improve modeling, and obtain and validate experimentally testable predictions. The definition of survival in these artificial systems paves the way to move beyond simple observation and to formally characterize, design and predict complex life-like behaviors.

Center manifold theory for the 1-dimensional collective motions of camphor disks with delta functions in the <inline-formula><tex-math id="M1">$ L^2 $</tex-math></inline-formula>-framework

Camphor boat and disk are types of interfacial self-propellers that rely on the modification of forces present at the air-liquid interface. In a one-dimensional circuit, self-organized congestion and clustering phenomena are observed experimentally and numerically [11,43]. Although the center manifold theories proposed in [5,7] are useful in the analysis of collective motions, the requirement in the reduction process is not fulfilled because the linearized operator involves Dirac delta functions. To overcome such mathematical difficulties, a theory in the $ (H^1)^* $-framework was developed in [17]. However, the reduced equation does not include any nonlinearity. Thus, information on the collective motions could not be obtained. The objectives of the present study are to propose a new approach to establish the existence and uniqueness of a center manifold in a system with delta functions in the $ L^2 $-framework and to derive a reduced system with suitable nonlinearity from the original model in [33].

Height-dependent oscillatory motion of a plastic cup with a camphor disk floated on water.

We have developed a self-propelled object, which is composed of a plastic cup and a camphor disk, on water to reflect its three-dimensional shape in the nature of motion. The self-propelled object, of which the driving force of motion is the difference in the surface tension, exhibited oscillatory motion between motion and rest. The period and the maximum speed of oscillatory motion increased and decreased depending on the height of the cup, h, respectively. Two types of diffusion coefficients were estimated based on the diffusion of camphor molecules which were indirectly visualized using 7-hydroxycoumarin. The experimental result on the period of oscillatory motion depending on h could be reproduced by the numerical calculation based on the diffusion of camphor molecules around the object and the diffusion coefficients which were experimentally estimated. The experimental results suggest that characteristic features of motion can be created based on the three-dimensional shape of the object.

Synchronized motion of two camphor disks on a water droplet levitated under microgravity

Two camphor disks, as self-propelled objects, were placed on a water droplet levitated under microgravity to understand the nature of their self-propelled motion on a sphere field without a boundary. When a single camphor disk was placed on the droplet, unidirectional rotation with a constant speed was observed. When two camphor disks were placed on the droplet, synchronized motion occurred; that is, the two disks exhibited unidirectional motion while the distance between them was maintained. The characteristic features of the self-propelled motion are discussed in relation to the camphor molecules developed from the disk as the source of both the driving force of motion and the repulsive force between the disks. The present study suggests that self-propelled objects can exhibit cooperative motion in a field without boundary.

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.

Self-Propelled Motion of the Camphor Float With n-Fold Rotational Symmetry

It is known that a camphor particle at a water surface exhibits self-propulsion since it releases camphor molecules at the surface and reduces the surface tension, and the gradient of surface tension drives the camphor particle itself. Such a motion is considered to be driven by the concentration field of the chemicals emitted by the particle itself. It is also known that the shape of the particle seriously affects the mode of motion. In order to understand the universal mechanism on the effect of the shape on such a self-propelled motion, we theoretically investigated the bifurcation structure of the motion of the camphor float with n-fold rotational symmetry, which comprises n camphor disks attached to a rigid light circular plate along a periphery with an equivalent spacing. Here, we mainly studied the cases with n = 2 and 3. We found that the camphor float with n = 2 moves in the direction perpendicular to the line connecting the two camphor disks, while that with n = 3 changes its direction of motion depending on the size of the camphor float.

Multidimensional Self-Propelled Motion Based on Nonlinear Science

Self-propelled objects, which exhibit characteristic features of motion, are proposed based on nonlinear science. At first, a self-propelled object with length like undulatory swimming is designed, i.e., the phase of oscillation at several points on the object is propagated in the opposite direction of motion. Second, the vertical oscillation of a camphor disk is created at an amphiphilic molecular layer developed on water. The proposed systems suggest that nonlinearity can enhance the autonomy of self-propelled objects as multidimensional motion.

On a numerical bifurcation analysis of a particle reaction-diffusion model for a motion of two self-propelled disks

AbstractTheoretical analysis using mathematical models is often used to understand a mechanism of collective motion in a self-propelled system. In the experimental system using camphor disks, several kinds of characteristic motions have been observed due to the interaction of two camphor disks. In this paper, we understand the emergence mechanism of the motions caused by the interaction of two self-propelled bodies by analyzing the global bifurcation structure using the numerical bifurcation method for a mathematical model. Finally, it is also shown that the irregular motion, which is one of the characteristic motions, is chaotic motion and that it arises from periodic bifurcation phenomena and quasi-periodic motions due to torus bifurcation.

Self-propelled camphor disk dependent on the depth of the sodium dodecyl sulfate aqueous phase

We studied the self-propulsion of a camphor disk placed on a surfactant solution to clarify the relationship between the speed of motion and the depth of the aqueous phase. At lower concentrations of sodium dodecyl sulfate (SDS) in the aqueous phase, the speed of motion for the deeper aqueous phase was higher than that for the shallower aqueous phase. However, this relationship was reversed at higher SDS concentrations. The surface tension of the aqueous phase and diffusion rate around the camphor disk were measured to determine this reverse relationship at higher SDS concentrations. Numerical calculation considering the flow field coupled with the concentration field qualitatively reproduced the experimental results on the diffusion rate depending on the SDS concentration. These results suggest that the amount of camphor dissolved in the aqueous phase plays an important role in reversing the speed of motion depending on the depth of the aqueous phase.

Self-Propelled Motion Sensitive to the Chemical Structure of Amphiphilic Molecular Layer on an Aqueous Phase.

Two novel amphiphiles, N-(3-nitrophenyl)stearamide (MANA) and N,N′-(4-nitro-1,3-phenylene)distearamide (OPANA), were synthesized by reacting nitroanilines with one or two equivalents of stearic acid. We investigated how the molecular structures of these compounds influenced the characteristics of a self-propelled camphor disk placed on a monolayer of the synthesized amphiphiles. Three types of motion were observed at different surface pressures (Π): continuous motion (Π < 4 mN m−1), deceleration (4 mN ≤ Π ≤ 20 mN m−1), and no motion (Π > 20 mN m−1). The speed of the motion of the camphor disks was inversely related to Π for both MANA and OPANA at the temperatures tested, when Π increased in the respective molecular layers under compression. The spectroscopic evidence from UV-Vis, NMR, and ESI-TOF-MS revealed that the dependence of the speed of the motion on Π originates from the intermolecular interactions that are present in the monolayers. This study suggests that it is possible to control the self-propelled motion by manipulating contributing factors at the molecular level.

Oscillatory Motion of a Camphor Object on a Surfactant Solution.

The mode bifurcation between oscillatory motion and no motion of a camphor object floating on surfactant aqueous solution was investigated. The camphor and surfactant were used as the sources of driving and suppressing forces, respectively. A circular plastic sheet was attached to the center of the bottom of a camphor disk, which served as the self-propelled object; further, the contact area between the disk and the solution (S) was varied to control the amount of camphor molecules from the disk that dissolved in the solution. Motion features, that is, the maximum speed, frequency of oscillatory motion, and mode bifurcation, varied depending on S. We discussed the relationship between these motion features and the kinetics of camphor and surfactant molecules around the object. The results suggest that the nature of the oscillatory motion depends on the amount of camphor molecules accumulated at the base of the self-propelled object.

Mixing and unmixing induced by active camphor particles

In this experimental study, we report on the mixing properties of interfacial colloidal floaters (glass bubbles) by chemical and hydrodynamical currents generated by self-propelled camphor disks swimming at the air-water interface. Despite reaching a statistically stationary state for the glass bubbles distribution, those floaters always remain only partially mixed. This intermediate state results from a competition between (i) the mixing induced by the disordered motion of many camphor swimmers and (ii) the unmixing promoted by the chemical cloud attached to each individual self-propelled disk. Mixing/unmixing is characterized globally using the standard deviation of concentration and spectra, but also more locally by averaging the concentration field around a swimmer. Besides the demixing process, the system develops a "turbulent-like" concentration spectra, with a large-scale region, an inertial regime and a Batchelor region. We show that unmixing is due to the Marangoni flow around the camphor swimmers, and is associated to compressible effects.

Existence and non-existence of asymmetrically rotating solutions to a mathematical model of self-propelled motion

Mathematical models for self-propelled motions are often utilized for understanding the mechanism of collective motions observed in biological systems. Indeed, several patterns of collective motions of camphor disks have been reported in experimental systems. In this paper, we show the existence of asymmetrically rotating solutions of a two-camphor model and give necessary conditions for their existence and non-existence. The main theorem insists that the function describing the surface tension should have a concave part so that asymmetric motions of two camphor disks appear. Our result provides a clue for the dependence between the surfactant concentration and the surface tension in the mathematical model, which is difficult to be measured in experiments.

Self-Propelled Motion of a Camphor Disk on a Nervonic Acid Molecular Layer and Its Dependence on Phase Transition.

We studied the self-propelled motion of a camphor disk placed on water developed with a nervonic acid molecular layer to investigate the dependence of types of motion on the properties of amphiphilic compounds. The surface pressure (Π) versus area (A) isotherm exhibited a transition point corresponding to a phase transition between the fluid (F) and fluid/condensed (F/C) phases of nervonic acid. The type of motion was determined by not only the surface pressure of the nervonic acid molecular layer but also the phase, either F or F/C. When the temperature of water was varied through the phase transition temperature Tp40 (∼23 °C), with an area of 40 Å2 per nervonic acid molecule in the molecular layer, no motion and oscillatory motion were observed reversibly above and below Tp40, respectively. Our results suggest that the features of camphor motion depend on not only the surface pressure but also the nature of the phase in the nervonic acid molecular layer.

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.