Theoretical study on the translation and rotation of an elliptic camphor particle

The spontaneous motion of an elliptic camphor particle floating on water is studied theoretically and experimentally. Considering a mathematical model for the motion of an elliptic camphor particle in a two-dimensional space, we first investigate the asymptotic solutions with numerical computation. We then introduce a small parameter ε into the definition of the particle shape, which represents an elliptic deformation from a circular shape and, by means of perturbation theory, we analytically calculate the travelling solution to within O ( ε ) . The results show that short-axis-directed travelling solutions primarily bifurcate from stationary solutions and that long-axis-directed ones are secondary which means that elliptic camphor particles are easier to move in the short-axis direction. Furthermore, we show that rotating solutions bifurcate from stationary solutions and that the bifurcation point changes with O ( ε 2 ) , which suggests that elliptic camphor disks easily exhibit translational motion, rather than rotational, within the small deformation. Finally, our theoretical suggestions are confirmed by an experiment.