If one mixes two distinct ideal gases above the Earth's surface, one with a higher molecular mass than the other, then at equilibrium, their number density gradients will be such that at low heights, the density of the heavier gas will dominate while higher up, the density of the lighter gas will dominate. This is something I know how to show using stat mech + chemical potential etc.
I would think that for liquids, the situation is different in the sense that the liquid with higher molecular mass would completely separate from the liquid with lower molecular mass. I suspect this because I've seen this happen with liquids in the real world, but is this always the case? If not, then what assumptions must hold about the liquids? Does surface tension play a role in all of this? Ultimately, is there a stat mech explanation for this?