What would happen if I where to mix water and oil in a vacuum in microgravity where the temperatures were low enough so that the oil and water remain liquids also, the mixture is not inside of a container. I would expect the water and oil two separate into two blobs, but wouldn't the London dispersion forces hold the two blobs together?
An experiment similar to this was carried out using a free-fall drop shaft to provide the microgravity environment in Japan in 2000.
From the abstract of the publication$^1$:
An experimental study was performed to obtain the detailed information needed to provide a deep understanding of the combustion process and the secondary atomization of an oil-in-water emulsion droplet. The oil-in-water emulsion, which consisted of n-hexadecane as a base fuel, distilled water, and a trace of surfactant was tested. Photographic observation and temperature measurements were made of the suspended emulsion droplet during the heating-up and combustion processes under microgravity. The primary attention was toward the phase separation in the droplet, and the time histories of droplet temperature and the amount of water in the droplet, during the period of time prior to disruptive microexplosion. The results showed that the separation of the base fuel and water as well as their agglomeration and coalescence occurred with the lapse of time. The increase in the droplet temperature resulted in phase separation, and the formation of a single water droplet enveloped by a shell of the base fuel, prior to the microexplosion.
Interestingly, the phase separation was attributed to the increase in droplet temperature. It's my guess that the heating increased the rate of separation, but that given time the final result of "the formation of a single water droplet enveloped by a shell of the base fuel" would have taken place, and I think this would be the result of the situation described in the question; that van der Waals forces between the oil and water would prevent them from separating into two separate balls of liquid. The stronger hydrogen bonds of water were likely the reason for water forming on the inside of the droplet, and I would expect the same to happen in the case described in the question.
Based on the results of the drop-shaft microgravity experiment described above, I would expect similar results for an experiment as described in the question. There should be an inner ball of water held together by hydrogen bonding, surrounded by an oil shell held together, and to the surface of the water, by the weaker van der Waals forces.
1) "Water-coalescence in an oil-in-water emulsion droplet burning under microgravity", Proceedings of the Combustion Institute, Volume 28, Issue 1, 2000, Pages 985-990.
Your reasoning, that there are still London dispersion forces between the oil and the water, is correct. However the contact area will either be small, because you still have to deform the ideal spherical phase boundaries of each phase, or the phase with higher surface tension will surround itself with the other phase (core-shell droplet, see other answer). It depends on the relative values of the surface/interfacial tensions.
(It does not work in vaccuum, though. The water will boil until it freezes. Just use a big enough container filled with air instead.)