statistical mechanics - Homemade salad dressing separates into layers after it sits for a while. Why doesn't this violate the 2nd law of thermodynamics?

The oil, vinegar and other liquids in homemade salad dressing separate into layers after sitting for a while, making the mixture become more organized as time evolves. Why doesn't this violate the 2nd law of thermodynamics?

I assume that the answer is that since the separation is due to gravity, the effect is due to an external force and so the system isn't closed which is necessary for the 2nd law, but I'm not sure.

If that's the answer, then what happens if I consider the whole system include the salad dressing, gravitational field and whatever mass is generating the gravitational field? The entropy of the salad dressing seems to decrease and so the entropy of some other component of this system must be increasing, but it's hard to see what this other component would be.

Answer

The separation does not violate the 2nd law of thermodynamics, because the oil and water phases being separate is a lower energy state.

The water molecules strongly interact with each other, forming hydrogen bonds. The protons of water are shared between two oxygen atoms of two different water molecules, forming a constantly changing network of molecules. Water molecules do not have strong intermolecular interactions with oil molecules.

The more the two phrases are mixed, the more water molecules are at an interface surface. The water molecules at an interface surface can not fully participate in intermolecular interactions with other water molecules, so this is a higher energy state.

For a process to spontaneously occur, the Gibbs free energy (G) must decrease.

$\Delta G = \Delta H-T\Delta S$

So entropy (S) is only part of the consideration. Enthalpy (H) and temperature (T) must also be considered. In this case the decrease in enthalpy (H) due to energy of intermolecular interactions makes up for the decrease in entropy (S). The process is an exothermic process.

Even absent gravity, it is still thermodynamically favorable for the phases to separate, to minimize the interfacial surface area, just like a spherical drop of water being the lowest energy state absent gravity.

I would predict that absent any gravity, the lowest energy state of the salad dressing would be a sphere of water phase surrounded by a spherical shell of oil phase.