  The collective motion of chemically active particles at an air-liquid
interface is studied theoretically as a dynamic self-organization problem.
Based on a physical consideration, we propose a minimal model for
self-propelled particles by combining hydrodynamic interaction, capillary
interaction, driving force by Marangoni effect, and Marangoni flow. Our model
has successfully captured the features of chemically active particles, that
represent dynamic self-organized states such as crystalline, worm-like,
liquid-like and spreading states.
