Self-motion of an oil droplet: a simple physicochemical model of active Brownian motion

The self-motion of an oil droplet in an aqueous phase on a glass surface is reported. The aqueous phase contains a cationic surfactant, which tends to be adsorbed onto the glass surface. The oil droplet contains potassium iodide and iodine, which prefers to make an ion pair with the cationic surfactant. Since the ion pair is soluble in the oil droplet, dissolution of the surfactant into the oil droplet is promoted, i.e., the system is far from equilibrium with regard to surfactant concentration. The oil droplet is self-driven in a reactive manner by the spatial gradient of the glass surface tension. We discuss the intrinsic nature of this self-motion by developing a simple mathematical model that incorporates adsorption and desorption of the surfactant on the glass surface. Using this mathematical model we were able to construct an equation of motion that reproduces the observed self-motion of an oil droplet. This equation describes active Brownian motion. Theoretical considerations were used to predict the generation of the regular mode of oil-droplet motion, which was subsequently confirmed by experiments.