Spontaneous motion of an elliptic camphor particle

Abstract

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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