[Physics] Mix of oil and water under pressure

liquid-statepressurewater

I'm not a physicist so please ignore my ignorance. I'm wondering what would happen if:
Imagine a mug with hollow handle. Now, one half of that mug is filled with water, another half with oil (of some kind). If i seal that mug and apply a lot of pressure on top (where the opening is), taking into account oil and water have different characteristics would oil start flowing through handle and back to the surface or simply nothing would happen?

EDIT:
Basically, my idea was without high temperatures – would high pressure cause oil to perhaps heat a bit, expand a bit and start flowing through handle to the bottom of the mug (literally, a mug shaped container) and then back to the surface? Would a high static pressure be enough to create a motion of oil through the water taking into account different properties (and possibly different reactions to pressure) of those different liquids?

Best Answer

EDIT

This is not an answer suitable for the question above, but I will leave it here for reference in case anybody else reads the question incorrectly, as I did.

END EDIT

Under standard conditions, hydrocarbons and water do not mix; however, at high temperatures and high pressures near the critical point of water, they freely mix. You need a lot of pressure

Oil and water are not miscible but can form emulsions in which tiny droplets of one component are dispersed in the other. Milk and face creams, are examples of oil/water emulsions.

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Image Source: Wikipedia Critical Point of Water

When water is heated under pressure it reaches its critical point at 374 °C and 22.1 MPa. (3191 psi) At this point there is no longer a difference between the liquid and gas phases. The water no longer dissociates and no clusters of water molecules can form. At this point, the properties of the water are like those of an oil and the two can be freely mixed together.

I don't fully follow your mug description, but whereever water flows, this mixture should flow also.

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