[Cwm9]

Suppose I compress CO2 and N2 at 35 bar at 0c.

I'd expect the CO2 to liquify and the N2 to be supercritical.

Does the supercritical fluid sit on top of the liquid since it is of lower density?

[Enthalpy]

Instead of "supercritical", you can say "gas" for N₂.

35bar and 0°C is a boiling condition for CO₂. At equilibrium, you would have a partial pressure of 35bar CO₂ vapour in the gas phase, to which a partial pressure of N₂ gas adds, so equilibrium is impossible.

The out-of-equilibrium proportions depend on the process and are more difficult to determine. If for instance CO₂ is fully liquefied at 35bar and 0°C and you add N₂ at 35bar and 0°C too, then liquid CO₂ will stay at the bottom and gaseous N₂ on the top, but CO₂ evaporates slowly (without boiling if the pressure exceeds the liquid-vapour equilibrium pressure) and the total pressure rises above 35bar, for instance towards 70bar if the volume is constant.

"Superfluid" has a different meaning.