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Register a new userInterface dynamics under nonequilibrium conditions: from a self-propelled droplet to dynamic pattern evolution
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In this article, we describe the instability of a contact line under nonequilibrium conditions mainly based on the results of our recent studies. Two experimental examples are presented: the self-propelled motion of a liquid droplet and spontaneous dynamic pattern formation. For the self-propelled motion of a droplet, we introduce an experiment in which a droplet of aniline sitting on an aqueous layer moves spontaneously at an air-water interface. The spontaneous symmetry breaking of Marangoni-driven spreading causes regular motion. In a circular Petri dish, the droplet exhibits either beeline motion or circular motion. On the other hand, we show the emergence of a dynamic labyrinthine pattern caused by dewetting of a metastable thin film from the air-water interface. The contact line between the organic phase and aqueous phase forms a unique spatio-temporal pattern characterized as a dynamic labyrinthine. Motion of the contact line is controlled by diffusion processes. We propose a theoretical model to interpret essential aspects of the observed dynamic behavior.
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The transport of small quantities of liquid on a solid surface is inhibited by the resistance to motion caused by the contact between the liquid and the solid. To overcome such resistance, motion can be externally driven through gradients in electric fields, but these all inconveniently involve the input of external energy. Alternatively, gradients in physical shape and wettability - the conical shape of cactus spines to create self-propelled motion. However, such self-propelled motion to date has limited success in overcoming the inherent resistance to motion of the liquid contact with the solid. Here we propose a simple solution in the form of shaped-liquid surface, where solid topographic structures at one length scale provides the base for a smaller length-scale liquid conformal layer. This dual-length scale render possible slippery surfaces with superhydrophobic properties. Combined to an heterogeneous topography, it provides a gradient in liquid-on-liquid wettability with minimal resistance to motion and long range directional self-propelled droplet transport. Moreover, the liquid-liquid contact enables impacting droplets to be captured and transported, even when the substrate is inverted. These design principles are highly beneficial for droplet transport in microfluidics, self-cleaning surfaces, fog harvesting and in heat transfer.
We report the generation of directed self-propelled motion of a droplet of aniline oil with a velocity on the order of centimeters per second on an aqueous phase. It is found that, depending on the initial conditions, the droplet shows either circular or beeline motion in a circular Petri dish. The motion of a droplet depends on volume of the droplet and concentration of solution. The velocity decreases when volume of the droplet and concentration of solution increase. Such unique motion is discussed in terms of Marangoni-driven spreading under chemical nonequilibrium. The simulation reproduces the mode of motion in a circular Petri dish.
We study the dynamic wetting of a self-propelled viscous droplet using the time-dependent lubrication equation on a conical-shaped substrate for different cone radii, cone angles and slip lengths. The droplet velocity is found to increase with the cone angle and the slip length, but decrease with the cone radius. We show that a film is formed at the receding part of the droplet, much like the classical Landau-Levich-Derjaguin (LLD) film. The film thickness $h_f$ is found to decrease with the slip length $lambda$. By using the approach of matching asymptotic profiles in the film region and the quasi-static droplet, we obtain the same film thickness as the results from the lubrication approach for all slip lengths. We identify two scaling laws for the asymptotic regimes: $h_fh_o sim Ca^{2/3}$ for $lambdall h_f$ and $h_f h^{3}_osim (Ca/lambda)^2$ for $lambdagg h_f$, here $1/h_o$ is a characteristic length at the receding contact line and $Ca$ is the capillary number. We compare the position and the shape of the droplet predicted from our continuum theory with molecular dynamics simulations, which are in close agreement. Our results show that manipulating the droplet size, the cone angle and the slip length provides different schemes for guiding droplet motion and coating the substrate with a film.
We consider self-propelled droplets which are driven by internal flow. Tracer particles, which are advected by the flow, in general follow chaotic trajectories, even though the motion of the autonomous swimmer is completely regular. The flow is mixing, and for P{e}clet and Batchelor numbers, which are realized e.g. in eucaryotic cells, advective mixing can substantially accelerate and even dominate transport by diffusion.
To understand the behavior of composite fluid particles such as nucleated cells and double-emulsions in flow, we study a finite-size particle encapsulated in a deforming droplet under shear flow as a model system. In addition to its concentric particle-droplet configuration, we numerically explore other eccentric and time-periodic equilibrium solutions, which emerge spontaneously via supercritical pitchfork and Hopf bifurcations. We present the loci of these solutions around the codimenstion-two point. We adopt a dynamical system approach to model and characterize the coupled behavior of the two bifurcations. By exploring the flow fields and hydrodynamic forces in detail, we identify the role of hydrodynamic particle-droplet interaction which gives rise to these bifurcations.
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