I have put water and silicone oil (viscosity 100 cSt) together into a jar. Then I colored the water blue to make identifying the interfaces easier. When I shake it heavily, a kind of silicone+water "foam" builds up, which only unmixes very slowly. Even when I only shake it slightly (as for the image below), so that a few major bubbles of water enter the silicone, the bubbles won't pop back into the bulk of water for ages.
I think I remember, from doing chemistry in the past (I am not a chemist), a mixture of chloroform and water unmixes very fast, while a mixture of water and kerosene did not (i.e. performed like my recent silicone oil experiment). I first thought a lack of difference in density (because the silicone seems pretty close to 1 g/cm^3) hinders unmixing, but while chloroform has indeed much higher density than water, kerosene also has significantly lower density than water. So I think it must be something else than density. But it can't be surface tension either, can it. Because nonpolar solvents always have lower surface tension than water (lack of hydrogen bonding), don't they.
So what makes one pair of polar/nonpolar solvent unmix fast while the other builds up foam? I think that must be very important for a chemist during washing after synthesis, but I can't seem to find a suitable search term.