What does dishwasher detergent do to oil/fat?

I have a lab that is due soon that doesn't seem to be working. I finished half of it, but the second half is bothering me. I am suppose to put whole milk into a petri dish and put 4 different colors of food coloring in different spots excluding the center. After, I dip a toothpick into dishwasher detergent and touch the tip of the toothpick into the center of the petri dish. Nothing happened for me. In my first one, the oil moved away and separated when i put in the toothpick. Help~

Answer:
the detergent has emulsifiers. emulsifiers are basically substances with polar and non-polar ends. oil and fat are mostly non-polar, so it will be repelled by the non-polar ends of the emulsifiers.

rule of polarity: like signs repel each other and opposites attract

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