After tackling the phrase "comparing apples and oranges" a couple weeks ago, a co-worker suggested I take a look at "mixing like oil and water." O.K. Here goes:
The phrase, as we know, is applied to any two things that don't get along together. And it's not a bad analogy; oil and water won't immediately mix. Water molecules are polar and one end has a slight negative charge, the other a slight positive charge. Those charges let the molecules form hydrogen bonds and attach to other molecules that are polar, including other water molecules. Oil molecules, however, are non-polar, and they can't form hydrogen bonds. If you put oil and water in a container, the water molecules will bunch up together and the oil molecules will bunch up together, forming two distinct layers.
To get around the propensity of oil and water molecules to only pal around with each other, you'll have to make an emulsion, dispersing one of the liquids in the other. It's possible to create an unstable emulsion through vigorous shaking or mixing; an example would be an oil-and-water vinaigrette, which separates if left too long on the table. To get a stable emulsion, you'll have to add an emulsifier.
An emulsifier is a molecule that has a hydrophobic (non-polar) end and a hydrophilic end. The molecules of the emulsifier will surround tiny droplets of oil, attaching the hydrophobic ends to it and leaving the hydrophilic ends exposed so the now-surrounded oil can easily mix among the water molecules. Common food emulsions are stable vinaigrettes that contain mustard and mayonnaise, which uses the molecule lecithin from egg yolks as the emulsifier.
Oil and water will mix, you see, they just need a little help.