What causes an emulsion to be stable or unstable? The other day I made a salad dressing based on oil and vinegar. To my understanding, there is a positive energy associated with the surface between the oil and vinegar. The most stable state is also the state of minimum energy, hence the mixture tends to separate into two layers, minimizing the total surface energy of the mixture.
Now, adding mustard had the effect of stabilizing the emulsion. The salad dressing didn't separate nearly so much or so quickly. This makes me wonder:
In general, what causes an emulsion to be stable?
For stable emulsions, why don't the two liquids completely mix together?
Are there emulsions that are unstable energetically, but tend to separate so slowly that they appear stable? If so, what causes them, and how do these differ from stable emulsions?
 A: With the exception of some microemulsions an emulsion is always thermodynamically unstable. That is because the interfacial tension is always greater than zero so it always costs energy to increase the interfacial area.
Emulsions exist only because they are kinetically stable. If you calculate the energy as two emulsion droplets approach and merge it will look something like this:

At intermediate distances between the drops the energy goes up, and this creates a repulsive force that keeps the droplets apart.
The barrier can have many causes. For example emulsions in water are often charged - typically the droplets carry a negative charge. The droplets then repel each other due to this electrostatic repulsion. Another common phenomenon is steric stabilisation where the droplets have some large floppy polymer adsorbed at the surface. Your system is one of the rarer cases because it is a Pickering emulsion. The mustard particles adsorb at the oil water interface and they create the barrier that stops the droplets from merging.
