mixing air with water/oil

Put some vegetable oil in a blender, and mix on high speed for "x" seconds (or minutes, if you feel so inclined)...

The foam indicates a pretty good mixture. But, that's all it is, is a mixture ~ which will naturally separate-out into the oil on bottom, air (a gas) on top.

Granted, some gas can be dissolved-into an oil (just as some is dissolved into water, including seawater). But this is not in large quantities.

Same is true for water. Mixture can easily be accomplished. But it will also undo itself in short order.

Why would such a 3some-mixture exist in an oil reservoir I am wondering?

They certainly do mix in my car when I have a water leak into the oil. I get a brown mix. If you are emulating the flow from a reservoir at rest, the water will sink to the bottom, the oil will float on the top. If the reservoir is agitated you will get a mix. Add a little soap, and they will mix into an emulsion.