Spontaneous Oscillations and Synchronization of Active Droplets on a Water Surface via Marangoni Convection

Dynamic Oscillation and Motion of Oil-in-Water Emulsion Droplets

The interplay of interfacial tensions on droplets results in a range of self-powered motions that mimic those of living systems and serve as a tunable model to understand their complex non-equilibrium behavior. Spontaneous shape deformations and oscillations are crucial features observed in nature but difficult to incorporate in synthetic artificial systems. Here, we report sessile oil-in-water emulsions that exhibit rapid oscillating behavior. The oscillations depend on the nature and concentration of the surfactant, the chemical composition of the oil, and the wettability of the solid substrate. The rapid changes in the contact angle per oscillation are observed using side-view optical microscopy. We propose that the changes in the interfacial tension of the oil droplets is due to the partitioning of the surfactant into the oil phase and the movement of self-emulsified oil out of the parent droplets giving rise to the rhythmic variation in droplet contact-line. The ability to control and understand droplet oscillation can help model similar oscillations in out-of-equilibrium systems in nature and reproduce biomimetic behavior in artificial systems for various applications, such as microfluidic lab-on-a-chip and adaptive materials.

Bifurcation and Transposition of the Wicking Front of Binary Solutions Infiltrating into Chromatography Paper Associated with Their Evaporation

Nonequilibrium fluid patterns, such as Marangoni contraction, coffee rings, and tears of wine, are generated in binary solutions spread on a substrate during their evaporation. In this study, we observed another type of nonequilibrium behavior exhibited by binary solutions as they infiltrate porous materials and undergo evaporation. A binary solution comprising hexane and ethanol was brought into contact with the chromatography paper to facilitate infiltration into the paper's pores. Because the experimental setup was in an open environment, infiltration and evaporation occurred simultaneously. The wicking front exhibited an initial rapid advancement, followed by subsequent receding and readvancing. Additionally, the bifurcation of the wicking front after the onset of its readvancement was confirmed by monitoring the temporal evolution of the spatial luminance distribution and temperature distribution on the surface of the chromatography paper. Chromatographic development of a hydrophilic dye was conducted in this experimental setup in an open environment. Additionally, it was confirmed that the receding and readvancing of the wicking front represented the transposition of the bifurcated wicking fronts.

Nonreciprocal Cahn-Hilliard Model Emerges as a Universal Amplitude Equation

Oscillatory behavior is ubiquitous in out-of-equilibrium systems showing spatiotemporal pattern formation. Starting from a linear large-scale oscillatory instability-a conserved-Hopf instability-that naturally occurs in many active systems with two conservation laws, we derive a corresponding amplitude equation. It belongs to a hierarchy of such universal equations for the eight types of instabilities in homogeneous isotropic systems resulting from the combination of three features: large-scale vs small-scale instability, stationary vs oscillatory instability, and instability without and with conservation law(s). The derived universal equation generalizes a phenomenological model of considerable recent interest, namely, the nonreciprocal Cahn-Hilliard model, and may be of a similar relevance for the classification of pattern forming systems as the complex Ginzburg-Landau equation.

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.

Modes of synchrony in self-propelled pentanol drops

We report various modes of synchrony observed for a population of two, three and four pentanol drops in a rectangular channel at the air-water interface. Initially, the autonomous oscillations of a single 1-pentanol drop were studied in a ferroin DI water solution pre-mixed with some volume of pentanol. A pentanol drop performs continuous motion on the air-water interface due to Marangoni forces. A linear channel was prepared to study the uniaxial movement of the drop(s). Thereafter, a systematic study of the self-propelled motion of a 1-pentanol drop was reported as a function of the drop volume. Subsequently, the coupled dynamics were studied for two, three and four drops, respectively. We observed anti-phase oscillations in a pair of pentanol drops. In the case of three drops, relay synchronization was observed, wherein consecutive pairs of drops were exhibiting out-of-phase oscillations and alternate drops were performing in-phase oscillations. Four pentanol drops showed two different modes of synchrony: one was relay synchrony and the other was out-of-phase oscillations between two pairs of drops (within a pair, the drops exhibit in-phase oscillations).

Self-Synchronous Swinging Motion of a Pair of Autonomous Droplets

Synchronized motion between two self-running oil droplets floating on an aqueous phase is reported. We describe the results of our observation on the interference between a pair of centimeter-sized nitrobenzene droplets undergoing back-and-forth motion on a waterway. The two droplets exhibit a swinging type of synchronization when a thin glass capillary is placed at the midpoint of the waterway with a narrow rectangle shape. Furthermore, 2:1 synchronized oscillation of the periodicities of this back-and-forth motion is generated when the capillary is shifted away from the center of the waterway. We discuss the mechanism of the emergence of synchronized swinging motion for the pair of droplets based on a simple mathematical model with nonlinear coupled differential equations.

Biological active matter aggregates: Inspiration for smart colloidal materials

Aggregations of social organisms exhibit a remarkable range of properties and functionalities. Multiple examples, such as fire ants or slime mold, show how a population of individuals is able to overcome an existential threat by gathering into a solid-like aggregate with emergent functionality. Surprisingly, these aggregates are driven by simple rules, and their mechanisms show great parallelism among species. At the same time, great effort has been made by the scientific community to develop active colloidal materials, such as microbubbles or Janus particles, which exhibit similar behaviors. However, a direct connection between these two realms is still not evident, and it would greatly benefit future studies. In this review, we first discuss the current understanding of living aggregates, point out the mechanisms in their formation and explore the vast range of emergent properties. Second, we review the current knowledge in aggregated colloidal systems, the methods used to achieve the aggregations and their potential functionalities. Based on this knowledge, we finally identify a set of over-arching principles commonly found in biological aggregations, and further suggest potential future directions for the creation of bio-inspired colloid aggregations.

Information transmission by Marangoni-driven relaxation oscillations at droplets

Marangoni-driven relaxation oscillations can be observed in many systems where concentration gradients of surface-active substances exist. In the present paper, we describe the experimentally observed coupling between relaxation oscillations at neighboring droplets in a concentration gradient. By a numerical parameter study, we evaluate the oscillation characteristics depending on relevant material parameters and the pairwise droplet distance. Based on these findings, we demonstrate that hydrodynamic interaction in multidroplet configurations can lead to a synchronization of the oscillations over the whole ensemble. This effect has the potential to be used as a novel approach for information transmission in microfluidic applications.

Marangoni-driven flower-like patterning of an evaporating drop spreading on a liquid substrate

Drop motility at liquid surfaces is attracting growing interest because of its potential applications in microfluidics and artificial cell design. Here we report the unique highly ordered pattern that sets in when a millimeter-size drop of dichloromethane spreads on an aqueous substrate under the influence of surface tension, both phases containing a surfactant. Evaporation induces a Marangoni flow that forces the development of a marked rim at the periphery of the spreading film. At some point this rim breaks up, giving rise to a ring of droplets, which modifies the aqueous phase properties in such a way that the film recoils. The process repeats itself, yielding regular large-amplitude pulsations. Wrinkles form at the film surface due to an evaporative instability. During the dewetting stage, they emit equally spaced radial strings of droplets which, combined with those previously expelled from the rim, make the top view of the system resemble a flower.

In liquid–liquid systems, Marangoni effects induced by surface tension gradients may result in the formation of peculiar self-assembled patterns. Wodlei et al. utilize this effect to draw a ‘flower’ by letting an oil droplet evaporate on an aqueous substrate in the presence of a cationic surfactant.