Self-propelled Objects Research Articles

Emergent dynamics due to chemo-hydrodynamic self-interactions in active polymers

The field of synthetic active matter has, thus far, been led by efforts to create point-like, isolated (yet interacting) self-propelled objects (e.g. colloids, droplets, microrobots) and understanding their collective dynamics. The design of flexible, freely jointed active assemblies from autonomously powered sub-components remains a challenge. Here, we report freely-jointed active polymers created using self-propelled droplets as monomeric units. Our experiments reveal that the self-shaping chemo-hydrodynamic interactions between the monomeric droplets give rise to an emergent rigidity (the acquisition of a stereotypical asymmetric C-shape) and associated ballistic propulsion of the active polymers. The rigidity and propulsion of the chains vary systematically with their lengths. Using simulations of a minimal model, we establish that the emergent polymer dynamics are a generic consequence of quasi two-dimensional confinement and auto-repulsive trail-mediated chemical interactions between the freely jointed active droplets. Finally, we tune the interplay between the chemical and hydrodynamic fields to experimentally demonstrate oscillatory dynamics of the rigid polymer propulsion. Altogether, our work highlights the possible first steps towards synthetic self-morphic active matter.

Reciprocal microswimming in fluctuating and confined environments

From bacteria and sperm cells to artificial microrobots, self-propelled microscopic objects at low Reynolds numbers often perceive fluctuating mechanical and chemical stimuli and contact exterior wall boundaries both in nature and the laboratory. In this paper, we theoretically investigate the fundamental features of microswimmers by focusing on their reciprocal deformation. Although the scallop theorem prohibits the net locomotion of reciprocal microswimmers, by analyzing a two-sphere swimmer model, we show that in a fluctuating and geometrically confined environment, reciprocal deformations can afford a statistically average displacement. After designing the shape gait, a reciprocal swimmer can migrate in any direction, even in the statistical sense, while the statistical average of passive rigid particles statistically diffuses in a particular direction in the presence of external boundaries. To elucidate this symmetry breakdown, by introducing an impulse response function, we derive a general formula for predicting the nonzero net displacement of a reciprocal swimmer. Using this theory, we determine the relation between the shape gait and net locomotion as well as the net diffusion constant increase and decrease, owing to a reciprocal deformation. Based on these findings and a theoretical formulation, we provide a fundamental basis for environment-coupled statistical locomotion. Thus, this paper is valuable for understanding biophysical phenomena in fluctuating environments, designing artificial microrobots, and conducting laboratory experiments. Published by the American Physical Society 2024

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.

The influence of obstacles on the collective motion of self-propelled objects

The influence of obstacles on the collective motion of self-propelled objects

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.

Recursively positive and negative chemotaxis coupling with reaction kinetics in self-organized inanimate motion

Reconstructing recursive chemotaxis in inanimate self-propelled objects is inevitable in the development of recursively and autonomously artificial mass transport systems. However, the fabrication of inanimately recursive chemotaxis has been extremely challenging because of the difficulty in introducing competitive positive and negative feedback into an inanimate self-propelled object. Herein, a coumarin derivative (coumarin, 4-methylcoumarin (4-MC), or 6-methylcoumarin (6-MC))-based disk floated on water as a self-propelled object exhibited characteristic features of motion; these features include continuous motion, repetition between positive and negative chemotaxis to the Na3PO4 powder as a base stimulus, and oscillatory motion above the Na3PO4 powder depending on the Na3PO4 density of the powder and the functional group of coumarin derivatives. The mechanism of the characteristic features of motion to the base stimulus is discussed in relation to the surface tension of the coumarin derivatives as the driving force of motion and the reaction rate of the hydrolysis between coumarin derivatives and OH– obtained from Na3PO4. This study suggests a novel avenue for developing a recursive chemotactic system coupled with reaction kinetics in self-organized motion.

Configuration and dynamics of a self-propelled diblock copolymer chain.

Active polymers are slender or chain-like self-propelled objects. Synthetic chains of self-propelled colloidal particles are one of the examples, which provide a potential way to develop varied active polymers. Here, we study the configuration and dynamics of an active diblock copolymer chain. Our focus is on the competition and the cooperation between the equilibrium self-assembly due to chain heterogeneity and the dynamic self-assembly due to propulsion. Simulations show that an active diblock copolymer chain can form the spiral(+)/tadpole(+) states under forward propulsion and the spiral(-)/tadpole(-)/bean states under backward propulsion. Interestingly, it is easier for the backward-propelled chain to form a spiral. The transitions between the states can be analyzed in terms of work and energy. For forward propulsion, we found a key quantity, i.e. the chirality of the packed self-attractive A block, which determines the configuration of the whole chain and the dynamics. However, no such quantity is found for the backward propulsion. Our results set the foundation for further study of the self-assembly of multiple active copolymer chains and provide a reference for the design and application of polymeric active materials.

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.

3D single cell migration driven by temporal correlation between oscillating force dipoles.

Directional cell locomotion requires symmetry breaking between the front and rear of the cell. In some cells, symmetry breaking manifests itself in a directional flow of actin from the front to the rear of the cell. Many cells, especially in physiological 3D matrices, do not show such coherent actin dynamics and present seemingly competing protrusion/retraction dynamics at their front and back. How symmetry breaking manifests itself for such cells is therefore elusive. We take inspiration from the scallop theorem proposed by Purcell for micro-swimmers in Newtonian fluids: self-propelled objects undergoing persistent motion at low Reynolds number must follow a cycle of shape changes that breaks temporal symmetry. We report similar observations for cells crawling in 3D. We quantified cell motion using a combination of 3D live cell imaging, visualization of the matrix displacement, and a minimal model with multipolar expansion. We show that our cells embedded in a 3D matrix form myosin-driven force dipoles at both sides of the nucleus, that locally and periodically pinch the matrix. The existence of a phase shift between the two dipoles is required for directed cell motion which manifests itself as cycles with finite area in the dipole-quadrupole diagram, a formal equivalence to the Purcell cycle. We confirm this mechanism by triggering local dipolar contractions with a laser. This leads to directed motion. Our study reveals that these cells control their motility by synchronizing dipolar forces distributed at front and back. This result opens new strategies to externally control cell motion as well as for the design of micro-crawlers.

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.

Fast-Moving Self-Propelled Droplets of a Nanocatalyzed Belousov-Zhabotinsky Reaction.

Self-sustained locomotion by virtue of an internalized chemical reaction is a characteristic feature of living systems and has inspired researchers to develop such self-moving biomimetic systems. Here, we harness a self-oscillating Belousov-Zhabotinsky (BZ) reaction, a well-known chemical oscillator, with enhanced kinetics by virtue of our graphene-based catalytic mats, to elucidate the spontaneous locomotion of BZ reaction droplets. Specifically, our nanocatalysts comprise ruthenium nanoparticle decorations on graphene oxide, reduced graphene oxide, and graphene nanosheets, thereby creating 0D-2D heterostructures. We demonstrate that when these nanocatalyzed droplets of the BZ reaction are placed in an oil-surfactant medium, they exhibit a macroscopic translatory motion at the velocities of few millimeters per second. This motion is brought about by the combination of enhanced kinetics of the BZ reaction and the Marangoni effect. Our investigations reveal that the velocity of locomotion increases with the electrical conductivity of our nanocomposites. Moreover, we also show that the positive feedback generated by the reaction-diffusion phenomena results in an asymmetric distribution of surface tension that, in turn, facilitates the self-propelled motion of the BZ droplets. Finally, we explore a system of multiple nanocatalyzed BZ droplets and reveal a variety of motions caused by their mutual interactions. Our findings suggest that through the use of 0D-2D hybrid nanomaterials, it is possible to design fast-moving self-propelled synthetic objects for a variety of biomimetic applications.

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.

Alternate Route Selection of Self-Propelled Filter Papers Impregnated with Camphor for Two-Branched Water Channels.

The route selection of self-propelled filter papers impregnated with camphor for two-branched water channels was investigated. The two-branched water channel was composed of a stem channel and two branch channels, and the branch channels were connected to the stem channel at a junction. When a single camphor paper reached the junction from the stem channel, it selected one of the two routes equivalently. Three or five camphor papers which were placed on a stem channel exhibited either alternate or random route selection depending on the characteristic length between the leading and following papers, Lc. That is, the alternate route selection of the camphor papers for the two-branched water channels was observed at Lc ≤ 25 mm. By contrast, the alternate route selection was broken at Lc > 25 mm. The physicochemical meaning of the threshold value, Lth ∼ 26 mm, between the alternate and random route selections was discussed based on the experimental results. In addition, the distribution length of camphor molecules developed from the leading camphor paper and the change in the spatial gradient of surface tension around the junction supports the value of Lth. These results suggest that autonomous phenomena using inanimate self-propelled objects are important to understand collective motion in living organisms.

A Perfect Plastic Material for Studies on Self-Propelled Motion on the Water Surface.

We describe a novel plastic material composed of camphene, camphor, and polypropylene that seems perfectly suited for studies on self-propelled objects on the water surface. Self-motion is one of the attributes of life, and chemically propelled objects show numerous similarities with animated motion. One of important questions is the relationship between the object shape and its motility. In our paper published in 2019, we presented a novel hybrid material, obtained from the solution of camphor in camphene, that allowed making objects of various shapes. This hybrid material has wax-like mechanical properties, but it has a very high tackiness. Here, we report that a small amount of polypropylene removed this undesirable feature. We investigated the properties of camphor–camphene–polypropylene plastic by performing the statistical analysis of a pill trajectory inside a Petri dish and compared them with those of camphor-camphene wax. The plastic showed the stable character of motion for over an hour-long experiment. The surface activity of objects made of plastic did not significantly depend on the weight ratios of the compounds. Such a significant increase in usefulness came from the polypropylene, which controlled the dissipation of camphor and camphene molecules.

Self-propelled slender objects can measure flow signals net of self-motion

The perception of hydrodynamic signals by self-propelled objects is a problem of paramount importance ranging from the field of bio-medical engineering to bio-inspired intelligent navigation. By means of a state-of-the-art fully resolved immersed boundary method, we propose different models for fully coupled self-propelled objects (swimmers, in short), behaving either as “pusher” or as “puller.” The proposed models have been tested against known analytical results in the limit of Stokes flow, finding excellent agreement. Once tested, our more realistic model has been exploited in a chaotic flow field up to a flow Reynolds number of 10, a swimming number ranging between zero (i.e., the swimmer is freely moving under the action of the underlying flow in the absence of propulsion) and one (i.e., the swimmer has a relative velocity with respect to the underlying flow velocity of the same order of magnitude as the underlying flow), and different swimmer inertia measured in terms of a suitable definition of the swimmer Stokes number. Our results show the following: (i) pusher and puller reach different swimming velocities for the same, given, propulsive force: while for pusher swimmers, an effective slender body theory captures the relationship between swimming velocity and propulsive force, this is not for puller swimmers. (ii) While swimming, pusher and puller swimmers possess a different distribution of the vorticity within the wake. (iii) For a wide range of flow/swimmer Reynolds numbers, both pusher and puller swimmers are able to sense hydrodynamic signals with good accuracy.

Time-dependent inertia of self-propelled particles: The Langevin rocket.

Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics, which involve inertia, friction, and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation are manifold, ranging from minirockets (which are self-propelled by burning their own mass), to dust particles in plasma (which lose mass by evaporating material), to walkers with expiring activity. Here we present analytical solutions for several dynamical correlation functions, such as mean-square displacement and orientational and velocity autocorrelation functions. If the parameters exhibit a slow power law in time, we obtain anomalous superdiffusion with a nontrivial dynamical exponent. Finally, we constitute the "Langevin rocket" model by including orientational fluctuations in the traditional Tsiolkovsky rocket equation. We calculate the mean reach of the Langevin rocket and discuss different mass ejection strategies to maximize it. Our results can be tested in experiments on macroscopic robotic or living particles or in self-propelled mesoscopic objects moving in media of low viscosity, such as complex plasma.

Anomalous Behavior of Highly Active Helical Swimmers

Artificially designed self-propelled objects can allow studying active matter phenomena with great detail that is not possible in natural, e.g. biological systems. Here, we show experimental results on helical shaped, magnetically actuated, reciprocal swimmers, where the degree of randomness in the reciprocal sequence plays an important role in determining their effective motility. Here, for the first time we show the results at high activity levels where the degree of randomness is further affected by the presence of the surface, which in turn results in a non-monotonic increase of motility as a function of magnetic drive. It will be interesting to extend these studies to denser systems where the swimmers can interact with each other through hydrodynamic forces.

A particle-field approach bridges phase separation and collective motion in active matter

Whereas self-propelled hard discs undergo motility-induced phase separation, self-propelled rods exhibit a variety of nonequilibrium phenomena, including clustering, collective motion, and spatio-temporal chaos. In this work, we present a theoretical framework representing active particles by continuum fields. This concept combines the simplicity of alignment-based models, enabling analytical studies, and realistic models that incorporate the shape of self-propelled objects explicitly. By varying particle shape from circular to ellipsoidal, we show how nonequilibrium stresses acting among self-propelled rods destabilize motility-induced phase separation and facilitate orientational ordering, thereby connecting the realms of scalar and vectorial active matter. Though the interaction potential is strictly apolar, both, polar and nematic order may emerge and even coexist. Accordingly, the symmetry of ordered states is a dynamical property in active matter. The presented framework may represent various systems including bacterial colonies, cytoskeletal extracts, or shaken granular media.

Prosocial attention in children with and without autism spectrum disorder: Dissociation between anticipatory gaze and internal arousal.

From an early age children help othersyet the underlying mechanisms of children's prosocial attention remain understudied. Comparing the attentional and physiological mechanisms of prosocial attention of typically developing and atypically developing children contributes to our understanding of the ontogeny of prosocial development. We presented typically developing (TD) children and children with Autism Spectrum Disorder(ASD), who often have difficulty developing prosocial behaviour, with scenarios in which an adult needed a dropped object to finish a task but was subsequently not helped by a second adult. In a perceptually matched non-social control scenario, children saw self-propelled objects move and drop without any adult present in the scene. Results showed a dissociation between arousal (pupil dilation) and the anticipation of the individual's need (gaze patterns), such that only TD children looked longer at the correct solution to the adult's need prior to the resolution of the situation. In contrast, following the resolution of the scene, both groups showed greater arousal when the adult was not helped compared to when the non-social situation remained unresolved. For the ASD group, this effect was greatest for children with higher developmental quotients. These results suggest that, despite similarities in prosocial attention between TD and ASD children, previously documented reduced prosocial behaviour in children with ASD may be in part due to a specific impairment in anticipating prosocial behaviour.

Model Estimates of Circulating Flow around Objects in the Marine Medium and Atmosphere

Model studies of force action on streamlined fragments of technical structures by a stratified sea current have been carried out. Analytical expressions are obtained for the hydrodynamic load on a point dipole during its circulation flow around a two-layer fluid flow of finite depth. The dependences of the wave resistance and the lifting force on the velocity of the current and circulation are investigated. It is shown that taking into account the velocity circulation can significantly affect the force effect on the dipole. The effect of a sharp (reversible) change in the direction of lift in a relatively narrow range of the flow velocity of a pipeline fragment simulated by a dipole has been found. The effect can also appear when moving self-propelled underwater objects and aircraft in the atmosphere.