How can you mix oil with water?

The method is :
Add an emulsifying agent (i.e. detergents including soap) to the mixture, and shake the mixture.

When a mixture of water, oil and detergent are shaken, the oil separates into many small drops. The detergent makes the oil cannot come together, and the mixture becomes one layer.

The above process is a physical change. Oil and water are still oil and water after emulsion. We CANNOT say that 《it is not oil anymore》.

You can mix oil with water with the following emulsification procedure, this is a kind of chemical reaction.

Emulsification is the procedure to mix two immicible liquids in the form of colloid.

Oil and water are immicible, because water is a polar compound but oil is a non-polar compound. When we mix oil with water, they will separate out from each other with the lower density one on top and the higher density one at bottom. (So, oil will be on top and water will be at bottom.) If ethanol is added, ethanol can change the situation. It is because ethanol has the non-polar hydroxyl group. It is micible with water. Also, it has the aliphatic group, that is fat-soluble. Then, ethanol serves as the agent pulling water molecules and oil molecules together.
When the mixture is shaked vigorously, the oil will be broken down into micelles. On the surface of each micelle is a layer of ethanol molecules with their hydroprobic aliphatic chain embedding in the oil micelle, but the hydrophilic hydroxyl group facing out and link with water. Then, each micelle is covered with a layer of electric charge, and the micelles would become suspending in the mass of water. This temporary equilibrium forms an unstable colloidal suspension, called a emulsion.

The following link explain the process with pictures in a very easy understand way:

http://www.newscientist.com/article.ns?id=dn3408