Collective Behaviour of Self-propelled Objects on a Water Surface
A variety of self-propelled objects has been developed. As an example of self-propelled objects, we can point to a surfactant solid/droplet moving on water and an oil/water droplet swimming in an aqueous/oil medium with a surfactant. These self-propelled objects have recently acquired functionalities, such as chemotaxis, phototaxis, gathering specific materials, maze solving, and so on. In addition to such functionalities, multi-object systems have also shown characteristic behaviours, such as clustering, aligned moving direction and spatiotemporal patterns. Such characteristic behaviours are called ‘collective motion’, which has been investigated in the field of biophysics and statistical physics theoretically and experimentally. The development of self-propelled objects in the field of physical chemistry provides a novel approach to the investigation of collective motion. In contrast to biological systems, the physicochemical conditions affecting self-propelled objects can be artificially controlled. Thus, it is one of the most promising systems for investigating collective motion. In this chapter, we present an introduction to the collective motion of self-propelled objects moving on water and the fundamental mathematical approaches.