Spontaneous change in trajectory patterns of a self-propelled oil droplet at the air-surfactant solution interface.

Trajectory-pattern formation of a self-propelled oil droplet floating on the surface of a surfactant solution in a circular dish is studied both experimentally and by simulation. The Marangoni effect induced by the dissolution of oil in the solution drives the droplet's motion. The trajectories spontaneously organize into several patterns including circular, knot-forming, back-and-forth, and irregular ones. They are either global patterns, whose center corresponds to the dish center, or other local patterns. Our simple model consisting of three forces, the driving force, the viscous resistance, and the repulsion from the boundary, successfully reproduces the global trajectory patterns including the power spectrum of the droplet speed.