For the first case (air carrying liquid droplets), it MAY be possible to use MA domain and use the trace gas part of the model to trace the liquid fraction. You'll need to fake the properties of trace gas so it doesn't impact much on the pressure and density of the air. Using the trace gas part may be easier than the water part, because there are less properties that you need to fake.
For the second case, if you are not worried about temperature change and the change of trapped gas faction during the simulation, the isothermal liquid or hydraulic (not recommended) domain allows you to have entrained air as part of the fluid properties. If you do need to track those changes, I believe you'll need a custom domain, most likely based on the thermal liquid domain. This question on modeling electrolyte may give you some ideas.
Speaking of a custom domain, the same idea may work also for the first case: tracking the concentration/fraction of liquid droplets as a "passive" scalar, on top of the existing Gas domain, which is a bit easier to handle than MA.
Good Luck and Happy Modeling!
