Now, once you've done that, get a Q-Tip, dip it in dish detergent, and dip the Q-Tip in the dish.
Or, even better, just add the detergent directly.
No drinking the milk afterward. You added detergent to it, you sick puppy. Ew.
Here's what's going on, according to about.com, because they explain it better than I can:
When you introduce detergent to the milk, several things happen at once. The detergent lowers the surface tension of the liquid so that the food coloring is free to flow throughout the milk. The detergent reacts with the protein in the milk, altering the shape of those molecules and setting them in motion. The reaction between the detergent and the fat forms micelles, which is how detergent helps to lift grease off of dirty dishes. As the micelles form, the pigments in the food coloring get pushed around. Eventually equilibrium is reached, but the swirling of the colors continues for quite a while before stopping.