What’s going on

• Milk is mostly water, but it also contains tiny droplets of fat and suspended proteins. The surface of the milk has surface tension, created by the attraction between water molecules. This surface tension keeps the food coloring drops from spreading on their own.
• Dish soap is a surfactant, meaning it changes surface tension. When soap touches the milk, it lowers the surface tension locally. Areas of higher surface tension pull liquid away from areas of lower surface tension, creating rapid surface flow. This flow, driven by surface tension differences, causes the initial burst of color.
• Soap molecules also have two ends: one that is attracted to water (hydrophilic) and one that is attracted to fat (hydrophobic). The hydrophobic ends attach to the fat droplets in the milk. As the soap spreads and surrounds these fat droplets, it breaks them apart and disperses them. The movement of fat droplets and surrounding liquid further drives the swirling motion.
• The food coloring does not cause the motion. It acts as a tracer, making the fluid movement visible.
• The motion slows and eventually stops once the soap has spread throughout the milk, surface tension becomes more uniform, and most fat droplets are coated by soap. Adding soap to a new location creates a new surface tension difference and restarts the motion.