Dynamic oscillatory cluster ordering of self-propelled droplets

We report here a peculiar dynamically ordered state of clustering droplets of a mixture of organic solvent. There droplets are driven by the solutal Marangoni effect on the surface of aqueous surfactant solution. They form temporal ring clusters which start collapsing immediately after its formation. This process is repeated for more than several hours with the period of 5--20 minutes. We propose an inhomogeneous force model to phenomenologically understand the basic mechanism of this dynamics, where the forces acting on each particle are controlled differently. This droplet system offers a simple, non-biological experimental model for the study of complex dynamical states realized by a group of self-propelled particles.