Yeah, "oil entering the air phase" was not the best way to put it, as it doesn't really enter it. The oil droplets coalesce with the air bubbles and thus attach to it as a lens on the bubble surface. The reason I have two transport equations, one for the amount attached to bubbles and one for the amount in the water phase is that they move at different speeds through the column. You want the oil to stick to the bubbles, such that they can be separated out faster.
Your description of flotation is correct.
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