Periodical alternation between precipitation and dissolution of camphor solid film on an ethanol solution.

Rhythmic behaviors are generally observed in nonlinear chemical reactions such as the Belousov-Zhabotinsky reaction and enzymatic reactions. Similarly, a simple phase change can also lead to rhythmic behavior. It has been reported previously that camphor solid films alternate between generation and disappearance on ethanol (EtOH) solution, and a phenomenological mechanism has been suggested for this. The evaporation of EtOH decreases the temperature on the surface of the solution via vaporization heat and induces precipitation in the camphor solid film. At this time, the film prevents evaporation, and thus, the surface temperature increases due to thermal diffusion from the atmosphere, resulting in dissolution of the solid film. To verify the previously suggested phenomenological mechanism, we controlled the evaporation rate of EtOH using a porous plastic cover. As a result, the period of oscillation increased with decreasing pore diameter, and finally, the oscillation did not occur without pore in the cover, where the camphor solid film was not observed. Additionally, a new mathematical model was proposed, and the numerical calculations agreed well with experimental observations. Linear stability and bifurcation analyses revealed the detailed mechanism of this phenomenon, which agreed well with the phenomenological explanation mentioned above.

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.

Periodic Precipitation in a Confined Liquid Layer.

Pattern formation is a ubiquitous phenomenon in animate and inanimate systems generated by mass transport and reaction of chemical species. The Liesegang phenomenon is a self-organized periodic precipitation pattern always studied in porous media such as hydrogels and aerogels for over a century. The primary consideration of applying the porous media is to prevent the disintegration of the precipitation structures due to the sedimentation of the precipitate and induced fluid flow. Here, we show that the periodic precipitation patterns can be engineered using a Hele-Shaw cell in a confined liquid phase, restricting hydrodynamic instability. The patterns generated in several precipitation reaction systems exhibit spatiotemporal properties consistent with patterns obtained in solid hydrogels. Furthermore, analysis considering the Rayleigh-Darcy number emphasizes the crucial role of fluidity in generating periodic precipitation structures in a thin liquid film. This exploration promises breakthroughs at the intersection of fundamental understanding and practical applications.

Reproduction of bacterial chemotaxis by a non-living self-propelled object.

Taxic behavior as a response to an external stimulus is a fundamental function of living organisms. Some bacteria successfully implement chemotaxis without directly controlling the direction of movement. They periodically alternate between run and tumble, i.e., straight movement and change in direction, respectively. They tune their running period depending on the concentration gradient of attractants around them. Consequently, they respond to a gentle concentration gradient stochastically, which is called "bacterial chemotaxis." In this study, such a stochastic response was reproduced by a non-living self-propelled object. We used a phenanthroline disk floating on an aqueous solution of Fe[Formula: see text]. The disk spontaneously alternated between rapid motion and rest, similar to the run-and-tumble motion of bacteria. The movement direction of the disk was isotropic independent of the concentration gradient. However, the existing probability of the self-propelled object was higher at the low-concentration region, where the run length was longer. To explain the mechanism underlying this phenomenon, we proposed a simple mathematical model that considers random walkers whose run length depends on the local concentration and direction of movement against the gradient. Our model adopts deterministic functions to reproduce the both effects, which is instead of stochastic tuning the period of operation used in the previous reports. This allows us to analyze the proposed model mathematically, which indicated that our model reproduces both positive and negative chemotaxis depending on the competition between the local concentration effect and it's gradient effect. Owing to the newly introduced directional bias, the experimental observations were reproduced numerically and analytically. The results indicate that the directional bias response to the concentration gradient is an essential parameter for determining bacterial chemotaxis. This rule might be universal for the stochastic response of self-propelled particles in living and non-living systems.

Bioconvection pattern of Euglena under periodical illumination.

Microorganisms respond to environmental conditions and often spontaneously form highly ordered convection patterns. This mechanism has been well-studied from the viewpoint of self-organization. However, environmental conditions in nature are usually dynamic. Naturally, biological systems respond to temporal changes in environmental condition. To elucidate the response mechanisms in such a dynamic environment, we observed the bioconvection pattern of Euglena under periodical changes in illumination. It is known that Euglena shows localized bioconvection patterns under constant homogeneous illumination from the bottom. Periodical changes in light intensity induced two different types of spatiotemporal patterns: alternation of formation and decomposition over a long period and complicated transition of pattern over a short period. Our observations suggest that pattern formation in a periodically changing environment is of fundamental importance to the behavior of biological systems.

Long-time behavior of swimming Euglena gracilis in a heterogenous light environment.

The cell motion of Euglena gracilis in homogeneous and heterogeneous light environments was analyzed. Homogeneous and heterogeneous environments were prepared, with only a red color or with a red circle surrounded by brighter white regions, respectively. In a heterogeneous environment, the cells move into the red circle. Swimming orbits at 1/25 s intervals for 120 s were analyzed. The speed distribution of the 1 s-averaged cell orbits in a homogeneous environment was different from that in a heterogeneous environment, where the faster swimming fraction was enhanced. The relationship between speed and curvature radius was analyzed using a joint histogram. Histograms for short timescale motion, constructed by 1 s-averaged orbits, suggest that the cell swimming curves are not biased, while those for long timescale motion, constructed by 10 s-averaged orbits, suggest that the cell swimming curves are biased in the clockwise direction. Furthermore, the curvature radius determines the speed, which does not seem to depend on the light environment. The mean squared displacement in a heterogeneous environment is larger than that in a homogeneous environment on a 1 s timescale. These results will be the basis for constructing a model for the long-time behavior of photomovement for light differences.

Appearance and suppression of Turing patterns under a periodically forced feed.

Turing instability is a general and straightforward mechanism of pattern formation in reaction-diffusion systems, and its relevance has been demonstrated in different biological phenomena. Still, there are many open questions, especially on the robustness of the Turing mechanism. Robust patterns must survive some variation in the environmental conditions. Experiments on pattern formation using chemical systems have shown many reaction-diffusion patterns and serve as relatively simple test tools to study general aspects of these phenomena. Here, we present a study of sinusoidal variation of the input feed concentrations on chemical Turing patterns. Our experimental, numerical and theoretical analysis demonstrates that patterns may appear even at significant amplitude variation of the input feed concentrations. Furthermore, using time-dependent feeding opens a way to control pattern formation. The patterns settled at constant feed may disappear, or new patterns may appear from a homogeneous steady state due to the periodic forcing.

Visual Sensing System to Investigate Self-Propelled Motion and Internal Color of Multiple Aqueous Droplets.

This study proposes a visual sensing system to investigate the self-propelled motions of droplets. In the visual sensing of self-propelled droplets, large field-of-view and high-resolution images are both required to investigate the behaviors of multiple droplets as well as chemical reactions in the droplets. Therefore, we developed a view-expansive microscope system using a color camera head to investigate these chemical reactions; in the system, we implemented an image processing algorithm to detect the behaviors of droplets over a large field of view. We conducted motion tracking and color identification experiments on the self-propelled droplets to verify the effectiveness of the proposed system. The experimental results demonstrate that the proposed system is able to detect the location and color of each self-propelled droplet in a large-area image.

Coexistence of oscillatory and reduced states on a spherical field controlled by electrical potential.

The Belousov-Zhabotinsky (BZ) reaction was investigated to elucidate features of oscillations depending on the applied electrical potential, E. A cation-exchange resin bead loaded with the catalyst of the BZ reaction was placed on a platinum plate as a working electrode and then E was applied. We found that global oscillations (GO) and a reduced state coexisted on the bead at a negative value of E and that the source point of GO changed depending on E. The thickness of the reduced state was determined by a yellow colored region which corresponded to the distribution of Br2. The present studies suggest that the distribution of the inhibitor, Br-, which is produced from Br2, plays an important role in the existence of the reduced state and GO, and the source point of GO.

Instability of the Homogeneous Distribution of Chemical Waves in the Belousov-Zhabotinsky Reaction.

Chemical traveling waves play an important role in biological functions, such as the propagation of action potential and signal transduction in the nervous system. Such chemical waves are also observed in inanimate systems and are used to clarify their fundamental properties. In this study, chemical waves were generated with equivalent spacing on an excitable medium of the Belousov-Zhabotinsky reaction. The homogeneous distribution of the waves was unstable and low- and high-density regions were observed. In order to understand the fundamental mechanism of the observations, numerical calculations were performed using a mathematical model, the modified Oregonator model, including photosensitive terms. However, the homogeneous distribution of the traveling waves was stable over time in the numerical results. These results indicate that further modification of the model is required to reproduce our experimental observations and to discover the fundamental mechanism for the destabilization of the homogeneous-distributed chemical traveling waves.

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.

Dendrite Pattern Formation of Sodium Chloride Crystal.

A variety of crystal structures is found in nature, not only equilibrium structures reflecting molecular structures, but also non-equilibrium structures which depend on the physicochemical conditions occurring during the crystal growth. In this paper, we focus on the dendrite structure of sodium chloride (NaCl) formed by the simple evaporation of an aqueous NaCl solution. The characteristics of the growth structures were measured as a function of the initial concentration of NaCl. In addition, the crystal growth process was measured using optical microscopy. As a result, the growth rate was not constant but was found to oscillate over time and synchronize with the wetting of the crystal. Our observations indicate that dendrite structures are more easily generated at higher initial concentrations. The detailed mechanism for dendrite pattern formation is still under investigation.

Switching between Two Oscillatory States Depending on the Electrical Potential.

Various spatiotemporal patterns were created on the surface or in the body of cation-exchange resin beads which were loaded with the catalyst of the Belousov-Zhabotinsky (BZ) reaction. Either global oscillations (GO) or traveling waves (TW) and the switching between them were observed in the previous papers, but it was not clear how chemicals contribute to the reaction inside/around the BZ bead. In this paper, we scanned the electrical potential, E, from +1 to -1 V (negative scan) and then turned from -1 to +1 V (positive scan) to control the switching between GO and TW. We found that the electrical switching potential from TW to GO, ETG, and from GO to TW, EGT, depended on the scanning direction of E and the diameter of the bead, d. The present study suggests that the electrode-induced increase of the inhibitor, Br-, and the activator, HBrO2, around the BZ bead plays an important role in determining ETG and EGT.

Electric field assisted motion of a mercury droplet.

Field-assisted self-assembly, motion, and manipulation of droplets have gained much attention in the past decades. We exhibit an electric field manipulation of the motion of a liquid metal (mercury) droplet submerged in a conductive liquid medium (a solution of sulfuric acid). A mercury droplet moves toward the cathode and its path selection is always given by the steepest descent of the local electric field potential. Utilizing this unique behavior, we present several examples of droplet motions, including maze solving, electro-levitation, and motion on a diverted path between parallel electrodes by controlling the conductivity of the medium. We also present an experimental demonstration of Fermat's principle in a non-optical system, namely a mercury droplet moving along a refracted path between electrodes in a domain having two different conductivities.

Effect of a product on spontaneous droplet motion driven by a chemical reaction of surfactant.

We focus on the self-propelled motion of an oil droplet within an aqueous phase or an aqueous droplet within an oil phase, which originates from an interfacial chemical reaction of surfactant. The droplet motion has been explained by mathematical models, which require the assumption that the chemical reaction increases the interfacial tension. However, several experimental reports have demonstrated self-propelled motion with the chemical reaction decreasing the interfacial tension. Our motivation is to construct an improved mathematical model, which explains these experimental observations. In this process, we consider the concentrations of the reactant and product on the interface and of the reactant in the bulk. Our numerical calculations indicate that the droplet potentially moves in the cases of both an increase and a decrease in the interfacial tension. In addition, the reaction rate and size dependencies of the droplet speed observed in experiments were well reproduced using our model. These results indicate the potential of our model as a universal one for droplet motion.

Interfacial Dynamics in the Spontaneous Motion of an Aqueous Droplet.

Self-propelled droplets can spontaneously move using chemical energy. In several reports of self-propelled droplets, interfacial chemical reactions occur at the oil/aqueous interface to induce the Marangoni flow. While the dynamics of interfacial tension is essential to the droplet motion, there are few reports that quantitatively discuss the moving mechanism based on interfacial tension measurements. In this study, we focused on the self-propelled motion of an aqueous droplet in the oil phase, where the surfactant monoolein reacts with bromine at the interface, and estimated the physicochemical parameters related to the droplet motion based on the time series of interfacial tension. These results may reveal the general mechanism for the self-propelled motion of aqueous/oil droplets driven by the interfacial chemical reaction.

Chemical Wave Propagation in the Belousov-Zhabotinsky Reaction Controlled by Electrical Potential.

The Belousov-Zhabotinsky (BZ) reaction is an important experimental model for the study of chemical oscillations and waves far from the thermodynamic equilibrium. Earlier studies had observed that individual BZ microbeads can show both global oscillations and traveling waves, but failed to select these different dynamic states. Here, we report experiments, in which this control was achieved by an externally applied electrical potential. The spherical microbeads were first loaded with the catalyst, then immersed into a catalyst-free BZ solution, and finally placed onto a planar platinum electrode. For positive electrical potentials, we observed global oscillations, whereas negative potentials resulted in traveling waves. The spatio-temporal characteristics of these phenomena are discussed in relation to the activator, HBrO2, which is produced by an electrochemical reaction.

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.

Self-Propelled Motion of a Coumarin Disk Characteristically Changed in Couple with Hydrolysis on an Aqueous Phase.

In this study, a coumarin disk was examined as a simple self-propelled object under a chemical reaction. A coumarin disk placed on an aqueous phase containing Na3PO4 as a base exhibited continuous and oscillatory motion at lower and higher initial concentrations of Na3PO4, [Na3PO4]0, respectively. In addition, the period of the oscillation between rest and motion increased with increasing [Na3PO4]0. The mechanism of mode bifurcation between continuous and oscillatory motion and a change in the period of oscillation were discussed in terms of hydrolysis of coumarin and the surface tension of the aqueous solution as a driving force. A reduced mathematical model based on the reaction kinetics of coumarin around the air/aqueous interface, which adequately reproduced the experimental observation, was constructed. These results suggest that the characteristics of the self-propelled motion were determined by the kinetics of hydrolysis.

Competition between global feedback and diffusion in coupled Belousov-Zhabotinsky oscillators.

The Belousov-Zhabotinsky (BZ) reaction is a famous experimental model for chemical oscillatory reaction and pattern formation. We herein study a diffusive coupled system of two oscillators with global feedback using the photosensitive BZ reaction both experimentally and theoretically. The coupled oscillator showed in-phase and antiphase oscillations depending on the strength of diffusive coupling and light feedback. Moreover, we analyzed our model to locate the bifurcational origin and found the reconnection of the bifurcation branches for antiphase oscillation, which was induced by the competition between global feedback and the diffusion effect.