It only floats on water because it has nowhere else to go. Can’t go down, can’t go up, and going to the side is just more water. So all the oil just huddles together. But if it’s already on your hand, it will happily stick to it, because your skin doesn’t repel oil.
As to why water doesn’t displace it away, water doesn’t just *displace* oil. When you wash your hands, what water is actually doing is sticking to things like dirt and grime. Then it drags it away down the sink as they’re all washed away. Water doesn’t really want to stick to oil, and so we use soap, which is like a mediator between oil and water. Water sticks to soap, soap sticks to oil, and the 3 friends get washed down the sink all as one.
Its why we were instructed as kids to use soap. Those bubbles arent just there to say you’re clean. Those bubbles are a result of surfactants sticking to oils and lifting dirt, and when you rinse with water your mitts are clean. But sometimes even the surfactants need help, in which case you could use pumiced soap. (Mechanics will know lava soap, or the Go Orange stuff)
Water molecules are polar, meaning that there are slightly positivly charged parts and slightly negatively charged parts in a water molecule and those attract each other. In oils on the other hand all charge is distributed pretty evenly through the molecule. That means there is no bonding whatsoever happing between oil and water and therefore the water doesn’t take the oil with it when you wash your hands without soap.
Soap molecules have polar and non polar parts so they can act as a sort of bridge and bind oil and water together.
The reason why oil floats on water is because the bonds between water molecules are strong enough to push out any oil molecules between them
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