A first-order rate model
Metallurgists often describe a flotation cell like a chemical reaction: in each minute a fixed fraction of the floatable mineral is captured. That gives recovery R = 1 minus e to the power of minus k times t, where k is the rate constant and t is the time the slurry spends in the cell.
Here k rises in proportion to the air rate, a simplified stand-in for the bubble surface area flowing through the cell. Real k values depend on particle size, chemistry and bubble size, and also plateau because recovery never quite reaches 100 percent.
Recovery versus grade
Pushing recovery too hard drags along waste particles trapped in the froth, lowering the grade of the concentrate. Plants run banks of cells in series, with rougher, scavenger and cleaner stages, to balance the two.