Magic Milk Experiment

Milk is made up of minerals, proteins and fats. When the dish soap enters the milk,  the fat begins to break up. The soap molecules run around and try to attach to the fat molecules in the milk.
The fat and proteins are super sensitive to changes in the milk and so when the dishwashing liquid is added a chemical reaction occurs. The soap and fat work  to join together, which causes the movement.
Normally this process would be invisible to you, but the food coloring helps you to see all of the movement taking place.