A theoretical and experimental study on the unidirectional motion of a camphor disk

Nagayama, Masaharu; Nakata, Satoshi; Doi, Yukie; Hayashima, Yuko

doi:10.1016/j.physd.2004.02.003

Cited by 122 publications

(177 citation statements)

References 29 publications

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“…The motion caused by the spontaneous symmetry breaking is described in terms of bifurcations. It has been shown that the mathematical model based on the reaction-diffusion system in which the camphor surface concentration is coupled with the Newtonian equation for motion of the camphor particle reproduces such spontaneous symmetry breaking, which can be described as the pitchfork bifurcation [20,27].…”

Section: Introductionmentioning

confidence: 99%

Relationship between the size of a camphor-driven rotor and its angular velocity

et al. 2017

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We consider a rotor made of two camphor disks glued below the ends of a plastic stripe. The disks are floating on a water surface and the plastic stripe does not touch the surface. The system can rotate around a vertical axis located at the center of the stripe. The disks dissipate camphor molecules. The driving momentum comes from the nonuniformity of surface tension resulting from inhomogeneous surface concentration of camphor molecules around the disks. We investigate the stationary angular velocity as a function of rotor radius ℓ. For large ℓ the angular velocity decreases for increasing ℓ. At a specific value of ℓ the angular velocity reaches its maximum and, for short ℓ it rapidly decreases. Such behaviour is confirmed by a simple numerical model. The model also predicts that there is a critical rotor size below which it does not rotate. Within the introduced model we analyze the type of this bifurcation.

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Section: Introductionmentioning

confidence: 99%

Relationship between the size of a camphor-driven rotor and its angular velocity

et al. 2017

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“…19 Although it was possible to reproduce and analyze the experimental results for the motion of a camphor disk by use of their model, the same approach is not applicable to the motion of droplets due to the rigid body assumption of the disk. In particular, droplet shape deformations are not negligible, since the coupling between the shape and motion plays an important role in the self-motion of the droplet as has been reported in previous works.…”

Section: Introductionmentioning

confidence: 99%

Mathematical model for self-propelled droplets driven by interfacial tension

Nagai

Tachibana

Tobe

et al. 2016

The Journal of Chemical Physics

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Articles you may be interested inNumerical study on the effects of non-dimensional parameters on drop-on-demand droplet formation dynamics and printability range in the up-scaled model Phys. Fluids 24, 082103 (2012) We propose a model for the spontaneous motion of a droplet induced by inhomogeneity in interfacial tension. The model is derived from a variation of the Lagrangian of the system and we use a time-discretized Morse flow scheme to perform its numerical simulations. Our model can naturally simulate the dynamics of a single droplet, as well as that of multiple droplets, where the volume of each droplet is conserved. We reproduced the ballistic motion and fission of a droplet, and the collision of two droplets was also examined numerically. C 2016 AIP Publishing LLC. [http://dx

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“…We note that the present analysis is done for the camphor-water system, but it can be easily adapted to other systems in which surface tension is the driving force of the droplet, such as a water-alcohol system [21], or an aniline droplet [22]. The model equation is derived based on previous works [14,15,23]. First, we describe the shape of the camphor particle.…”

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“…In such a case, motion in a certain direction at a constant velocity is stabilized and realized. Consequently, the profile of the surface concentration becomes asymmetric [14][15][16]. This camphor-water system has attracted attention since it exhibits interesting and complicated phenomena such as collective motion [17][18][19] and jamming [20] in spite of its simple setup.…”

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Spontaneous motion of an elliptic camphor particle

2013

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The coupling between deformation and motion in a self-propelled system has attracted broader interest. In the present study, we consider an elliptic camphor particle for investigating the effect of particle shape on spontaneous motion. It is concluded that the symmetric spatial distribution of camphor molecules at the water surface becomes unstable first in the direction of a short axis, which induces the camphor disk motion in this direction. Experimental results also support the theoretical analysis. From the present results, we suggest that when an elliptic particle supplies surface-active molecules to the water surface, the particle can exhibit translational motion only in the short-axis direction. Spontaneous motion in nonequilibrium systems has long attracted the interest of scientists because it is related to the motion of living organisms. In particular, the coupling between deformation and spontaneous motion has been actively investigated and several important and interesting studies, both experimental and theoretical, have been reported. For example, Ohta et al. proposed a generic model for the coupling between deformation and spontaneous motion by analyzing such coupling from the viewpoint of the bifurcation theory of dynamical systems [1][2][3]. Teramoto et al. studied the coupling between deformation and motion in pulse propagation in a reaction-diffusion system [4]. In experiments, cell motion is analyzed in relation to cell shape [5][6][7], and mathematical models have also been proposed for such cell deformation [8,9].For investigating the coupling between motion and deformation, one approach is to decouple them; i.e., we consider the effect of particle shape on motion. For this purpose, we chose a camphor-water system, in which a camphor particle exhibits spontaneous motion but not deformation. The camphor-water system was first reported in the 19th century [10,11]. As a camphor particle is placed on pure water, it exhibits spontaneous motion. The mechanism of the motion is briefly described as follows [12,13]: Camphor molecules escape from the camphor particle to the water surface. Since camphor has a surface activity, the camphor molecules at the water surface reduce the surface tension. It should be noted that the camphor molecules sublimate to the air, so that the profile of the surface concentration of camphor molecules at the water surface can reach a steady state. If the camphor particle is circular and does not move, the profile of the surface concentration of camphor molecules should be symmetric with respect to the center of the camphor particle. However, it is known that such a steady state can become unstable by an infinitesimal fluctuation. In such a case, motion in a certain direction at a constant velocity is stabilized and realized. Consequently, the profile of * Corresponding author: kitahata@physics.s.chiba-u.ac.jp the surface concentration becomes asymmetric [14][15][16]. This camphor-water system has attracted attention since it exhibits interesting and complicated phenomena ...

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A theoretical and experimental study on the unidirectional motion of a camphor disk

Cited by 122 publications

References 29 publications

Relationship between the size of a camphor-driven rotor and its angular velocity

Relationship between the size of a camphor-driven rotor and its angular velocity

Mathematical model for self-propelled droplets driven by interfacial tension

Spontaneous motion of an elliptic camphor particle

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