Self-propelled Droplets Research Articles

Dynamics of a self-propelled compound droplet

A recent experiment by Wang et al. (Soft Matt., vol. 17, 2021, pp. 2985–2993) shows that a self-propelled compound drop in a surfactant-laden solution can autonomously change its motion from a straight line to a spiraling trajectory, enhancing its capability for chemical detection, catalytic reaction and pollutant removal in a large fluid region. To understand the underlying physics of this peculiar motion, we develop a two-dimensional minimal model to study the swimming dynamics of a compound droplet driven by a self-generated Marangoni stress. We find that, depending on the Péclet number ( $Pe$ ) and the viscosity and volume ratios of the two compound phases, the drop can swim in a variety of trajectories, including straight lines, circles, zigzag curves and chaotic trajectories. The drop moves in circles when its two components have comparable volumes. Otherwise, it shows other types of motions depending on $Pe$ . Our simulation results for the circular motion at small $Pe$ are qualitatively comparable to the experiment. The transition between zigzag and circular trajectories is mainly determined by the orientation of high-order modes with respect to the drop's swimming direction. For most compound drops, the speed decays as $Pe^{-1/3}$ at high Péclet numbers as it does for a single-phase drop. A drop with two equal components undergoes a run-and-reorient motion due to the competition between the even and odd modes.

Precursor film of self-propelled droplets: Inducing motion of a static droplet

Acetic and propionic acids on glass show a total wetting behavior with a large exponent beyond Tanner’s law. However, incorporating the Silwet L-77 surfactant into the droplet of acids causes the wetting behavior to change from spreading to random motion. The directed motion of the self-propelled droplet can be achieved on a linear runway constructed by coating polysilazane on glass. The absence of contact line pinning can be attributed to a thin film extending from the edge of the bulk droplet. Two simple methods are proposed to observe the precursor film associated with the spreading droplet and the self-running Silwet-laden droplet: (i) the color change of nearby water droplets containing a pH indicator, and (ii) the noncontact interaction observed using an optical microscope. Because of the precursor film, the self-running droplet can induce the motion of a static droplet without direct contact between their contact lines. This interesting finding may be explained using the interfacial tension gradient associated with the Marangoni stress due to the contact between the precursor film and the static droplet.

Dropwise condensation heat transfer on vertical superhydrophobic surfaces with gradient microgrooves in humid air

Self-propelled droplet removal contributes vitally to the enhancement of condensation heat transfer performance. Here, inspired by the prickle tip of the cactus, we design and fabricate a gradient groove superhydrophobic surface. A visualization system in humid air has been established to investigate the droplet dynamic behaviors and heat transfer performance on the vertical gradient groove superhydrophobic surface. The dropwise condensation is also analyzed and compared to that on the plane and square groove superhydrophobic surfaces. The results indicate that the gradient groove superhydrophobic surface has the highest condensation heat flux among the three mentioned superhydrophobic surfaces with the increasing subcooling. The gradient grooves facilitate the condensed droplets departure under the synergistic effect of the dual-Laplace induced jumping and gravity-driven sliding removal even at higher subcooling. The dual-Laplace induced jumping possesses greater driving force, conducting the smaller droplet departure diameter and smaller angle between initial velocity and surface wall, which effectively improves the surface refreshment and further strengthens the surface heat transfer.

Fabrication of Metallic Superhydrophobic Surfaces with Tunable Condensate Self-Removal Capability and Excellent Anti-Frosting Performance.

Laser fabrication of metallic superhydrophobic surfaces (SHSs) for anti-frosting has recently attracted considerable attention. Effective anti-frosting SHSs require the efficient removal of condensed microdroplets through self-propelled droplet jumping, which is strongly influenced by the surface morphology. However, detailed analyses of the condensate self-removal capability of laser-structured surfaces are limited, and guidelines for laser processing parameter control for fabricating rationally structured SHSs for anti-frosting have not yet been established. Herein, a series of nanostructured copper-zinc alloy SHSs are facilely constructed through ultrafast laser processing. The surface morphology can be properly tuned by adjusting the laser processing parameters. The relationship between the surface morphologies and condensate self-removal capability is investigated, and a guideline for laser processing parameterization for fabricating optimal anti-frosting SHSs is established. After 120 min of the frosting test, the optimized surface exhibits less than 70% frost coverage because the remarkably enhanced condensate self-removal capability reduces the water accumulation amount and frost propagation speed (<1 μm/s). Additionally, the material adaptability of the proposed technique is validated by extending this methodology to other metals and metal alloys. This study provides valuable and instructive insights into the design and optimization of metallic anti-frosting SHSs by ultrafast laser processing.

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.

Statistics for an object actively driven by spontaneous symmetry breaking into reversible directions.

Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained until a large enough impulse by an additional stochastic force reverses it. Examples may be provided by self-propelled droplets, gliding bacteria stochastically reversing their propulsion direction, or nonpolar vibrated hoppers. The magnitude of active forcing is regarded as constant, and we include the effect of inertial contributions. Interestingly, this situation can formally be mapped to stochastic motion under (dry, solid) Coulomb friction, however, with a negative friction parameter. Diffusion coefficients are calculated by formal mapping to the situation of a quantum-mechanical harmonic oscillator exposed to an additional repulsive delta-potential. Results comprise a ditched or double-peaked velocity distribution and spatial statistics showing outward propagating maxima when starting from initially concentrated arrangements.

Chemotactic self-caging in active emulsions

A common feature of biological self-organization is how active agents communicate with each other or their environment via chemical signaling. Such communications, mediated by self-generated chemical gradients, have consequences for both individual motility strategies and collective migration patterns. Here, in a purely physicochemical system, we use self-propelling droplets as a model for chemically active particles that modify their environment by leaving chemical footprints, which act as chemorepulsive signals to other droplets. We analyze this communication mechanism quantitatively both on the scale of individual agent-trail collisions as well as on the collective scale where droplets actively remodel their environment while adapting their dynamics to that evolving chemical landscape. We show in experiment and simulation how these interactions cause a transient dynamical arrest in active emulsions where swimmers are caged between each other's trails of secreted chemicals. Our findings provide insight into the collective dynamics of chemically active particles and yield principles for predicting how negative autochemotaxis shapes their navigation strategy.

Time dependence of the dominant mechanisms of self-propelled droplets by Leidenfrost phenomenon on Zn plate surfaces with and without ZnO nanorods

For an earlier study, using Zn plates with a specific pitch and height, we analyzed the self-propulsion of water droplets caused by the Leidenfrost phenomenon. The results demonstrated the existence of two modes: volume expansion (partial contact mode), which accompanies nucleate boiling; and gravity (gravity mode), which water droplets receive. The dominant mode depends on the temperature. The findings also suggested that proper arrangement of ZnO nanorods onto the ratchet structure might provide synergistic effects between the two modes. Continuing from that earlier study, we analyzed water droplets that were self-propelled by the Leidenfrost phenomenon on Zn plates with double the height and double the pitch of the ratchet structures. Similarly to the structure studied earlier, the self-propulsive behavior of water droplets on these samples was produced by partial contact mode and gravity mode. Furthermore, when the time change of the dominant propulsive force was examined along with data of the earlier report, the high propulsive force found mainly in the partial contact mode at the initial stage of self-propulsion tended to shift to the gravity mode over time. The initial high propulsion duration was also confirmed as becoming shorter as the sample temperature rises. This temperature dependence is regarded as related to the time dependence of the vapor film formation process with the temperature rise of water droplets. The time change of the dominant propulsive force was clarified as dependent on the ratchet structure and surface modification by ZnO nanorods. These facts and related findings demonstrated that the self-propulsion of water droplets attributable to the Leidenfrost phenomenon is controllable by the solid surface design.

Spontaneous emergence of a spin state for an emitter in a time-varying medium

Time-varying media can dramatically modify the emission of embedded sources by producing time reversed waves refocusing on the source. Here, we show that such a back action can create an angular momentum by setting the source in a spontaneous spin state. We experimentally implement this coupling using self-propelled bouncing droplets sources coupled to the surface waves they emit on a parametrically excited bath. The spin state dynamics result from a self-organized interplay between the source motion and the time reversed waves. The discrete stability analysis agrees with the experimental observations. In addition, we show that these spin states provide a unique opportunity for an experimental access to parameters enabling comparison and calibration of the various existing models.

Chemical design of self-propelled Janus droplets

Chemical design of self-propelled Janus droplets

Swimming dynamics of a self-propelled droplet

Chemically active droplets often show intriguing self-propulsion behaviour in a surfactant solution. The drop motion is controlled by the nonlinear coupling among chemical transport in the bulk fluid, consumption of surfactant at the drop surface, and the fluid flow driven by the self-generated Marangoni stress. To quantify the underlying hydrodynamics, this work investigates the swimming motion of a two-dimensional drop that is determined by two dimensionless parameters, the Péclet number ($Pe$) and Damköhler number ($Da$). The weakly nonlinear analysis shows that near the instability threshold, the drop undergoes a supercritical bifurcation with velocity $U\sim \sqrt {Pe-Pe_c}$, where $Pe_c$ is the critical Péclet number for the onset of dipole mode. In the highly nonlinear regime, the drop transits from steady translation of pusher swimming to unsteady motion of mixed pusher–puller swimming along zigzaging trajectories of quadrangle and/or triangle waves. Mode decomposition shows that the zigzag motion is directly related to the interaction between the secondary wake of low surfactant concentration and the primary wake.

Analysis of different self-propulsion types of oil droplets based on electrostatic interaction effects.

This study aims to investigate electrical effects in self-propelled oil droplets and analyze the motion caused by electrical interactions between two droplets. We examine the motion of self-propelled oil droplets in terms of electrical effects; no similar analyses have been reported to date. When an oleic acid droplet is introduced into a surfactant solution, oleic acid is adsorbed at the droplet surface; as a result, the surface becomes negatively charged. However, the electrostatic interaction between oil droplets has not been studied so far. We focus on the chargeability of self-propelled oil droplets, and propose that their motion can be controlled by changing the charge state at the oil/water interface. This is realized by controlling the pH of the surfactant solution. We prepared several aqueous solutions with slightly different pH values, and introduced two oil droplets into each solution to investigate the relationship between the pH value and the correlated motion of the oil droplets. In an aqueous solution at pH 12.00, the two oil droplets showed two types of motion (follow-up and parallel motion), while in an aqueous solution at pH 12.10 they exhibited only one type of motion, i.e., repulsive motion. In order to analyze the three types of motion, we investigated electrical effects on the surface of the oil droplets. First, we measured the zeta potentials of aqueous solutions at pH 12.00 and 12.10, and analyzed the relationship between pH and charge. Furthermore, we calculated the amount of charge and the repulsive force generated on the surface of the oil droplets. For the pH 12.10 solution, the charge of one oil droplet and the repulsive force generated by the charge were found to be −30.79 pC and 282 nN, respectively. Taking into account the driving forces controlling the motion of oil droplets reported in previous studies, this repulsive force could be the driving force of the observed repulsive motion. Based on the experimental results, we inferred that the three types of self-propulsive motion were controlled by electrical effects at the oil/water interface. To further examine these motions, we analyzed the time dependences of the total distance traveled by a droplet and of the distance between oil droplets, as well as the droplet velocities and images of internal convection of oil droplets.

PH-Sensitive Controlled Motion of Micrometer-sized Oil Droplets in a Solution of Surfactants Containing Fumaric Acid Derivatives.

Self-propelled droplets are of considerable interest as an appropriate model for understanding the self-propulsion of objects in the fields of nonequilibrium physics and nonlinear science. Several research groups have reported the monodirectional motion of droplets, that is, chemotaxis, using stimuli-responsive materials. However, the precise control of chemotaxis remains challenging from the perspective of synthetic chemistry because chemotactic motion is primarily induced by the consumption of reactive oil or surfactants. Herein, we report a chemical system containing pH-responsive fumaric acid derivatives, in which the oil droplet exhibited positive chemotaxis over a wide pH range-from basic to acidic conditions. From the measurements of the interfacial tension between the oil and aqueous phases, it was deduced that the positive chemotaxis was due to heterogeneity in the interfacial tension of the droplet surface, which was accompanied by the production of surface-active compounds in the pH gradient in a linear-type channel.

Spontaneously rotating clusters of active droplets.

We report on the emergence of spontaneously rotating clusters in active emulsions. Ensembles of self-propelling droplets sediment and then self-organise into planar, hexagonally ordered clusters which hover over the container bottom while spinning around the plane normal. This effect exists for symmetric and asymmetric arrangements of isotropic droplets and is therefore not caused by torques due to geometric asymmetries. We found, however, that individual droplets exhibit a helical swimming mode in a small window of intermediate activity in a force-free bulk medium. We show that by forming an ordered cluster, the droplets cooperatively suppress their chaotic dynamics and turn the transient instability into a steady rotational state. We analyse the collective rotational dynamics as a function of droplet activity and cluster size and further propose that the stable collective rotation in the cluster is caused by a cooperative coupling between the rotational modes of individual droplets in the cluster.

Peculiar encounter between self-propelled droplet and static droplet: swallow, rerouting, and recoil

Understanding the outcome and mechanism of droplet–droplet collision is important in digital microfluidics, especially for the encounter between the self-propelled and static droplets. Observation of the collision process between a self-propelled droplet and another static liquid droplet on a poly(methyl methacrylate) substrate. The former is a mixture of dimethylformamide and 10 wt% Silwet L-77, while the latter can be either miscible or immiscible with the former. Four types of interesting outcomes after the encounter are identified: (i) swallow-and-run (liquid paraffin), (ii) swallow-run-pinning (olive oil), (iii) rerouting-and-run (water), and (iv) recoil-and-run (glycerol). The swallow behavior is observed as the two droplets are immiscible, but the rebound behavior is acquired as they are miscible. The former can be explained by the two spreading coefficients, while the latter may be attributed to the buildup of the gradient of the interfacial tension upon contact.

Self-preserving mechanisms in motile oil droplets: a computational model of abiological self-preservation.

Recent empirical work has characterized motile oil droplets—small, self-propelled oil droplets whose active surface chemistry moves them through their aqueous environment. Previous work has evaluated in detail the fluid dynamics underlying the motility of these droplets. This paper introduces a new computational model that is used to evaluate the behaviour of these droplets as a form of viability-based adaptive self-preservation, whereby (i) the mechanism of motility causes motion towards the conditions beneficial to that mechanism’s persistence; and (ii) the behaviour automatically adapts to compensate when the motility mechanism’s ideal operating conditions change. The model simulates a motile oil droplet as a disc that moves through a two-dimensional spatial environment containing diffusing chemicals. The concentration of reactants on its surface change by way of chemical reactions, diffusion, Marangoni flow (the equilibriation of surface tension) and exchange with the droplet’s local environment. Droplet motility is a by-product of Marangoni flow, similar to the motion-producing mechanism observed in the lab. We use the model to examine how the droplet’s behaviour changes when its ideal operating conditions vary.

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.

Lattice Boltzmann and Jones matrix calculations for the determination of the director field structure in self-propelling nematic droplets.

Nematic droplets immersed in aqueous surfactant solutions can show a self-propelled motion induced by a Marangoni flow in the droplet surface. In addition to the self-propulsion, the Marangoni flow induces within the droplet a convective flow which considerably influences the nematic director field of the droplet. We report numerical simulations aiming at the determination of the director field in the self-propelling droplet. The convective flow and the resulting structure of director field are described by a lattice Boltzmann model. The reliability of the obtained structures is proved by subsequent Jones matrix calculations which enable the direct comparison of experimental polarizing microscopy images of self-propelling droplets with calculated images based on the simulated structures.

In situ observation of droplet nanofluidics for yielding low-dimensional nanomaterials

Droplet based micro/nanofluidics has been demonstrated as a versatile tool in a wide range of fields. In particular, seeded growth of planar low-dimensional nanomaterials often relies on crawling metal droplets as catalytic media where nucleation and crystal growth proceed. However, direct observations of nanomaterials growth led by self-propelled droplet transport remain rare, which leaves many open questions on droplet behavior during growth. Here, we report in situ observations of in-plane Si nanowire growth in a transmission electron microscope, where an indium droplet migrates on a silicon nitride membrane coated by a layer of hydrogenated amorphous silicon (a-Si:H), dissolves the a-Si:H coating film on the membrane, and results in the production of a crystalline Si nanowire in its trail. This in situ observation, combined with the geometric investigation of the nanowires, presents nice consistency with de Gennes’ theoretical prediction of reactive wetting induced droplet motion. Interestingly, we recorded a nanoflake-to-nanowire transition when the growth rate was increased by heating the membrane from 350 °C to 400 °C. This work directly unveils rich transport mechanism of catalytic droplets, which are expected to be a new platform for producing diverse low-dimensional nanomaterials and promote their potential applications in nanoscience and technologies.

Ultrafast self-propelled water droplet transport on a graphene-covered nanocone

Cacti, a common drought-tolerant plant, enable the directional transport of droplets from the tip of the spikes to the roots in order to collect moisture from the air, creating conditions for cactus survival in arid areas. Inspired by this interesting natural phenomenon, a novel design for a monolayer graphene-covered nanocone (GNC) is proposed to realize ultrafast water droplet transport from the tip to the end of the GNC. The results show that the self-driving speed of a water droplet can reach ∼80 m s−1 driven by the Young–Laplace pressure difference. The rule of energy change during the droplet self-driving process indicates that the potential energy of the droplet and the interaction energy between the droplet and the GNC undergo cooperation and competition successively, resulting in the droplet first speeding up and then slowing down to a steady moving state. A larger droplet can extend the high-speed stage, which is beneficial to long-distance self-driving of droplets in a water-harvesting process. Continuum theory in the self-driving of a droplet at a microscale is used to describe the steady moving process, in order to further understand the rule in GNC-based water transport. The findings will open a broad range of novel perspectives for spontaneous droplet transport and water harvesting by graphene-covered functional surfaces.