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Initially, the food colours swirl in different patterns across and under the surface of the milk for several minutes. Note that the colours do not actually mix with each other, but continue in separate swirling patterns. The time of swirling may depend on the temperature of the milk and amount of dishwashing liquid you use. You can repeat step 6 to reactivate the swirling motion if needed. Moving the toothpick to a new spot can later result in mixing of the various colours.
The reason for the swirling motion of the food colours is caused by changes in surface tension of the milk after adding the drop of liquid dishwashing detergent. Detergent molecules have a partially charged polar end and an uncharged nonpolar end. Thus, they can bind weakly to either polar or nonpolar neighbouring molecules. When detergent is introduced into the center of the bowl, it may bind weakly to the water in the milk, decreasing its surface tension so that it flows more easily, and indirectly setting up the swirling motion.
Watch the ways in which food colouring can move through different liquids.
In plain water the drop slowly swirls and moves throughout. In salt water, the drop starts to sink and then rises. In seltzer water, the drop quickly disperses and evenly colours the liquid.
Putting food colouring in plain water does not have a dramatic effect other than that the colour becomes more pale (diluted). The gas bubbles in the seltzer water act to speed things up, like an invisible stirring spoon. The drop of food colouring is quickly broken up and carried to all parts of the liquid. Salt water is more dense than plain water. This means that anything less dense will float on the top, including the food colouring (which is a drop of coloured water).
Note: Activity adapted from multiple sources by NRC scientist Dr. Mike Day.