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Spontaneous Oscillations and Synchronization of Active Droplets on Water Surface via Marangoni Convection Yong-Jun Chen, Koichiro Sadakane, Hiroki Sakuta, Chenggui Yao, and Kenichi Yoshikawa Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b03061 • Publication Date (Web): 09 Oct 2017 Downloaded from http://pubs.acs.org on October 10, 2017
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Spontaneous Oscillations and Synchronization of Active Droplets on Water Surface via Marangoni Convection Yong-Jun Chen*,†,‡, Koichiro Sadakane‡, Hiroki Sakuta‡, Chenggui Yao§, Kenichi Yoshikawa*,‡
†
Department of Physics, Shaoxing University, Shaoxing, Zhejiang Province, 312000, China ‡
§
Faculty of Life and Medical Sciences, Doshisha University, Kyotanabe, Kyoto 610-394, Japan
Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang Province, 312000, China
KEYWORDS: Oscillation, Synchronization, Surfactant, Marangoni effect, Droplet.
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ABSTRACT: Shape-oscillations and synchronization are intriguing phenomenon in many biological and physical systems. Here, we report the rhythmic mechanical oscillations and synchronization of aniline oil droplets on a water phase, which is induced by Marangoni convection during transfer of the solute. The repetitive increase and decrease in the surface concentration in the vicinity of the contact line leads to the oscillations of droplets through an imbalance in surface tensions. The nature of the oscillations depends on the diameter of the droplet, the depth of the bulk aqueous phase, and the concentration of the aqueous phase. A numerical simulation reproduces the essential behaviors of active oscillations of a droplet. Droplets sense each other through a surface tension gradient and advection, and hydrodynamic coupling in the bulk solution induces the synchronization of droplet oscillations.
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INTRODUCTION Shape-oscillations and self-motion are ubiquitous features of biological cells [1-3]. During mechanical motion, the cell remodels its cytoskeleton, where chemical energy is transduced to mechanical energy [1-3]. Inanimate droplets that exhibit autonomous agitation have attracted considerable attention as a real-world model of chemical machinery and can exhibit locomotion and/or oscillations [4, 5]. The self-propulsion and oscillations of droplets are generated by chemical reactions [6-8], surfactant transfer [9-12], surface graft [13], geometric asymmetry [14], a concentration gradient [15, 16], a temperature gradient [17], a continuous reactant flow [18] and so on. The imbalance of surface forces and the asymmetry of surface properties deviate the system from an equilibrium state and cause the mechanical motion [4, 5]. The spontaneous agitation of single droplet has been well studied by many authors [4, 5]. For example, we described the self-propelled motion of a droplet induced by Marangoni-driven spreading [9], Sumino et al. presented a self-running droplet that consumed surfactant on a glass surface [7], Pimienta et al. observed the complex agitation of a dichloromethane droplet [9], Sugawara and coworkers demonstrated self-propelled oil droplets in an aqueous phase [6, 12], and Lv et al. used a substrate curvature gradient to drive a droplet [14]. However, there have been few observations of the collective behavior of self-agitating droplets because of the difficulty of controlling the droplets and the unclear nature of the interaction between them. In this article, we demonstrate the spontaneous oscillations and synchronization of active droplets on an air-water interface. The periodical oscillations of surface tension and coupling via inter-droplet spreading and Marangoni convection lead to the spontaneous oscillations and robust global rhythm of droplets. These oscillating droplets can serve as a simple but useful model for studying the deformation of biological objects and the synchronization of oscillators.
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EXPERIMENT The experiment was performed using aniline oil ( ρ a = 1.020g/ml at 20℃, 99.0%). Ultra-pure water was used as the aqueous phase in beakers with various diameters. The depth of water in the beaker was from several to 10 centimeters. A drop of aniline with a diameter above 2cm was situated on the air-aqueous surface. A small amount of aniline spontaneously dissolved to lower the surface tension, which allowed the droplet to sit on the aqueous phase stably at a fixed position. The droplet began to oscillate after the aniline oil spread over the contact area for several tens of seconds. To observe the nature of the interaction and synchronization among the oscillating droplets, droplets were placed at certain desired positions using pipettes. The selfagitation of the droplets was recorded with a video camera (Sony HDR-CX370V) and analyzed with image-analysis software (Image J). The oscillations of surface pressure were monitored using a USI FSD-220 controller with a Wilhelmy balance as a surface-pressure sensor. The distance between the plate and the edge of the droplet was 1.0 cm during surface pressure measurement. The experiments were carried out at room temperature (18±2℃).
RESULTS Oscillation of a single droplet. Figure 1 exemplifies the periodical oscillations of an aniline oil droplet on an aqueous phase. The droplet undergoes repeated cycles of contraction and expansion (Fig. 1(a)). The temporal change in the radius of the droplet from the top view is shown in Fig. 1(b). The radius exhibits a maximum contraction of several millimeters. During the recoil and spreading of the droplet, the height of the droplet also changes periodically, as shown in the side view of the droplet in Fig.
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d (mm)
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(b) Time
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T(s)
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(d)
d (mm) Figure 1. Oscillations of a droplet. (a) Oscillations of a droplet (top view). The time interval is 0.05s. The size of the image is 25mm×25mm. The inset shows oscillations of the diameter. The depth of the aqueous phase is 7.0cm. (b) Spatial-temporal evolution of the self-pulsations of the droplet. Upper: top view (Movie 1), lower: side view (Movie 2). The size of the images is 25mm×25mm and 10mm×30mm, respectively. The scale bars for time are 2.0s. (c) Dependence of periodicity on the depth of the aqueous phase. The concentration is 0.5vol%. (d) Dependence
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of periodicity on the initial concentration of the aqueous phase. The depth of the aqueous phase is 7.0cm. The period of oscillations changes with the size of the droplet (d: diameter of the droplet, cf. Movie 1-size). The diameter of the beaker used in the experiments is 4.7cm.
1(b). The typical period of the droplet oscillations is from one second to over 10 seconds, depending on the parameters. The period of oscillations is mainly related to the diameter of the droplet, the depth of the aqueous phase, the concentration of the aqueous phase, and the size of the beaker (Fig. 1(c) and (d)). The period of oscillations decreases with a decrease in the droplet size. The depth of the aqueous phase in the beaker critically influences the oscillations. A shallower depth of the aqueous phase leads to a greater period of oscillations (Fig. 1(c)). When the depth is relatively shallow (h
