Spontaneous motion of a droplet evolved by resonant oscillation of a vortex pair

We studied dissipative structures in the pattern formation of self-organized flow inside a droplet and spontaneous motion of the droplet when two driving forces, mass transfer of a solute from the droplet to surrounding media and continuous supply of solution to the droplet, were applied. When solute concentration increases beyond a critical value, a jetlike flow erupts out of the droplet (eruption). A similar flow simultaneously enters the droplet (irruption), producing internal flow. The resulting internal flow develops into two vortices along the droplet surface. Each vortex moves in a circular orbit along the droplet surface by local flow due to the other vortex, while continuous solute eruptions occur out of the vortex pair. The entire droplet rotates slowly at the same velocity as the rotation of the vortex pair. The vortex pair then oscillates with rotation, inducing droplet wiggle with slow rotation. The vortex motion resembles precession accompanied by nutation of a spinning top about a fixed point. Temporal evolution of droplet motion describes a pattern of short waves superimposed on a long wave. Short waves are induced by "nutation" of the vortex pair, and the long wave by "precession." The amplitude of the short wave varies with time because of the interaction between vortices. The vortex pair acts as coupled oscillators. Resonance interaction can occur between the long wave and the envelope of short waves when the phase velocity of the long wave becomes equal to the group velocity of short waves, markedly changing droplet motion; vigorous and regular fast rotation of the droplet suddenly occurs.