An alcohol (pentanol) droplet exhibits spontaneous motion on an aqueous solution, driven by a solutal Marangoni effect. We found that the droplets mode of motion is controlled by its volume. A droplet with a volume of less than 0.1 microl shows irregular translational motion, whereas intermediate-sized droplets of 0.1-200 microl show vectorial motion. When the volume is above 300 microl, the droplet splits into smaller drops. These experimental results regarding mode selection are interpreted in terms of the wave-number selection depending on the droplet volume.

The development of self-propelled motors that mimic biological motors is an important challenge for the transport of either themselves or some material in a small space, since biological systems exhibit high autonomy and various types of responses, such as taxis and swarming. In this perspective, we review non-living systems that behave like living matter. We especially focus on nonlinearity to enhance autonomy and the response of the system, since characteristic nonlinear phenomena, such as oscillation, synchronization, pattern formation, bifurcation, and hysteresis, are coupled to self-motion of which driving force is the difference in the interfacial tension. Mathematical modelling based on reaction-diffusion equations and equations of motion as well as physicochemical analysis from the point of view of the molecular structure are also important for the design of non-living motors that mimic living motors.

We theoretically derive the amplitude equations for a self-propelled droplet driven by Marangoni flow. As advective flow driven by surface tension gradient is enhanced, the stationary state becomes unstable and the droplet starts to move. The velocity of the droplet is determined from a cubic nonlinear term in the amplitude equations. The obtained critical point and the characteristic velocity are well supported by numerical simulations.

The generation of convective flow by a chemical wave was studied experimentally on a mm-sized droplet of Belousov-Zhabotinsky ͑BZ͒ reaction medium. A propagating chemical wave causes a transient increase in interfacial tension, and this local change in interfacial tension induces convection. The observed flow profile was reproduced with a numerical simulation by introducing the transient increase in interfacial tension to a modified Navier-Stokes equation coupled with a chemical kinetic equation; a modified Oregonator. We also observed the periodic motion of a BZ droplet floating on an oil phase. Such periodic motion is attributed to the rhythmic change in interfacial tension. The observed periodic convective motion coupled with a chemical reaction is discussed in relation to chemo-mechanical energy transduction under isothermal conditions.