Aperiodic bursting dynamics of active rotors

Run-and-tumble like motion of a camphor-infused Marangoni swimmer

'Run-and-tumble' (RT) motion has been a subject of intense research for several decades. Many organisms, such as bacteria, perform such motion in the presence or absence of local chemical concentration gradients and it is found to be advantageous in search processes. Although there are previous reports involving the successful design of non-living self-propelled particles exhibiting such motion in the presence of external stimuli (chemical/mechanical), RT motion with 'rest' has not yet been observed for autonomous non-living active particles. We have designed a swimmer that performs motion using a combination of 'run', 'tumble', and 'rest' states with stochastic transitions. In the present scenario, it arises solely due to self-generated local surface tension gradients. We quantify the residence time statistics by analyzing the swimmer trajectories from the experimental data, which suggests that the 'rest' and 'tumble' states are more frequent than 'run'. Then, we quantify the motion properties by computing the mean squared displacement, which shows that the swimmer performs ballistic motion on a short time scale and then slows down due to tumbling and resting. To validate the observed transport properties, we introduce a minimal model of a chiral active Brownian particle, stochastically switching between three internal states. The model parameters were extracted from the experiments, which rendered a good agreement between the experiments and simulations.

Pathway selection by an active droplet

We report the movement of an active 1-pentanol drop within a closed Y-shaped channel subjected to geometrical and chemical asymmetry. A Y-shaped channel was configured with an angle of 120° between any two arms, which serves as the closed area of movement for the active drop. The arm where the 1-pentanol drop is introduced in the beginning is considered the source arm, and the center of the Y-shaped structure is the decision region. The drop always selects a specific route to move away from the decision region. The total probability of pathway selection excludes the possibility of the drop choosing the source channel. Remarkably, the active drop exhibits a strong sense of navigation for both geometrically and chemically asymmetric environments with accuracy rates of 80% and 100%, respectively. The pathway selection in a chemically asymmetric channel is a demonstration of the artificial negative chemotaxis, where the extra confined drop acts as a chemo-repellent. To develop a better understanding of our observations, a numerical model is constructed, wherein the particle is subjected to a net force which is a combined form of - (i) Yukawa-like repulsive interaction force (acting between the drop and the walls), (ii) a self-propulsion force, (iii) a drag, and (iv) a stochastic force. The numerics can capture all the experimental findings both qualitatively and quantitatively. Finally, a statistical analysis validates conclusions derived from both experiments and numerics.

In-phase and mixed-phase measure synchronization of camphor rotors

The numerical, analytical, and experimental analyses are presented for synchronizing two rotors under the Yukawa interaction. We report that the rotors exhibit in-phase and mixed-phase measure synchronizations for a pair of coupled rotors. Here, the analytical condition for synchronization is derived, tested numerically, and confirmed experimentally using coupled camphor infused rotors as a test bed. Moreover, the concept of measure synchronization is discussed. We report that, in conservative systems, not only the critical coupling parameter but initial conditions also play an essential role for estimating the measure synchronization region.

Mathematical modeling for the synchronization of two interacting active rotors

We investigate the synchronization of active rotors. A rotor is composed of a free-rotating arm with a particle that releases a surface-active chemical compound. It exhibits self-rotation due to the surface tension gradient originating from the concentration field of the surface-active compound released from the rotor. In a system with two active rotors, they should interact through the concentration field. Thus, the interaction between them does not depend only on the instantaneous positions, but also on the dynamics of the concentration field. By numerical simulations, we show that in-phase and antiphase synchronizations occur depending on the distance between the two rotors. The stability of the synchronization mode is analyzed based on phase reduction theorem through the calculation of the concentration field in the co-rotating frame with the active rotor. We also confirm that the numerical results meet the prediction by theoretical analyses.

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.

Phase-flip transition in volume-mismatched pairs of coupled 1-pentanol drops

We have explored a variety of synchronization domains and observed phase-flip transition in a pair of coupled 1-pentanol drops as a function of the volume mismatch. Both experimental observations and numerical studies are presented. The experiments were carried out in a rectangular channel in a ferroin deionized water solution premixed with some volume of pentanol. A single pentanol drop (≥ 3μL) performs back and forth oscillations along the length of the channel due to the well-known Marangoni forces. In the present work, for a pair of drops, the drop 1 volume was changed from 3 to 5 μL in steps of 1μL, whereas the drop 2 volume was varied from 1 to 3 μL in steps of 0.5μL. A systematic investigation of all the possible combinations of the drop volumes showed the presence of three different types of synchrony-in-phase, antiphase, and phase-switched. In-phase synchronization was robust for a volume mismatch of >3.0μL between the two drops. On the other hand, antiphase synchronization was robust when the volume mismatch was <2.0μL. The phase-switched state is a synchronized state involving a phase-flip transition in the time domain. This state was observed for the intermediate range of volume mismatch. Numerically, the system has been investigated using two Stuart-Landau oscillators interacting via a coupling function in the form of Lennard-Jones potential. The numerical results suitably capture both in-phase and antiphase oscillations for a pair of volume-mismatched pentanol drops.

Generation of aperiodic motion due to sporadic collisions of camphor ribbons

We present numerical and experimental results for the generation of aperiodic motion in coupled active rotators. The numerical analysis is presented for two point particles constrained to move on a unit circle under the Yukawa-like interaction. Simulations exhibit that the collision among the rotors results in chaotic motion of the rotating point particles. Furthermore, the numerical model predicts a route to chaotic motion. Subsequently, we explore the effect of separation between the rotors on their chaotic dynamics. The numerically calculated fraction of initial conditions which led to chaotic motion shed light on the observed effects. We reproduce a subset of the numerical observations with two self-propelled ribbons rotating at the air-water interface. A pinned camphor rotor moves at the interface due to the Marangoni forces generated by surface tension imbalance around it. The camphor layer present at the common water surface acts as chemical coupling between two ribbons. The separation distance of ribbons (L) determines the nature of coupled dynamics. Below a critical distance (L_{T}), rotors can potentially, by virtue of collisions, exhibit aperiodic oscillations characterized via a mixture of co- and counterrotating oscillations. These aperiodic dynamics qualitatively matched the chaotic motion observed in the numerical model.