Spontaneous Motion of a Camphor Particle with a Triangular Modification from a Circle

The spontaneous motion of a camphor particle with a slight modification from a circle is investigated. The effect of the shape on the motion is examined by the perturbation method. We introduce a slight n-mode modification from a circle, where the profile is described by r = R(1 + epsilon cos n theta) in polar coordinates. The results predict that a camphor particle with an n = 3 mode modification from a circle, i.e., a triangular modification, moves in the direction of a corner for a small particle, while it moves in the direction of a side for a large particle. The numerical simulation results well reproduce the theoretical prediction. The present study will help understand the effect of the particle shape on spontaneous motion.