When you wash an oily pan, dish soap aids in washing away the oil by surrounding the fat droplets and rinsing them away with the excess water. what similarities does this have to digestion in our bodies?

Our liver produces bile which is stored in the gall bladder and delivered to the stomach where the bile physically breaks down the fat droplets into smaller fat droplets to increase surface area to volume ratio so that enzymes can chemically break it down into simpler substances such as fatty acids and glycerol. The dish soap acts as the bile that physically breaks down the fat droplets into smaller fat droplets.