Soap molecules consist of a hydrophilic (“water-loving”) end and a hydrophobic (“water-fearing”) end. Water molecules are polar molecules that can dissolve other polar molecules. Fat (and oil) molecules are nonpolar molecules, so they cannot dissolve in water.
Milk is a mixture of water, fat, vitamins and minerals. When soap is added to the milk, it helps to separate the water and fat in the milk. When soap is mixed in with the fat and water, the hydrophobic end of the soap molecule breaks up the nonpolar fat molecules, and the hydrophilic end of the soap molecule links up with the polar water molecules. Now that the soap is connecting the fat and water, the nonpolar fat molecules can be carried by the polar water molecules.
As the soap molecules connect to the fat molecules, the molecules of the food coloring get pushed around everywhere resulting in an explosion of color! As the majority of soap molecules attach to the fat molecules and the soap spreads throughout the milk, the color explosion will slow and eventually stop. Add more soap and see if there are more fat molecules that haven’t attached to soap – if there are unattached fat molecules still, the color explosion will begin again.