Figure A.V.1 represents a continuously operating flotation cell with retention time τ. For convenience, in this derivation it is easier to refer to the concentration of particles rather than mass, so we have a concentration C0 entering the cell with steady-state concentration C in the cell, which is also the concentration in the exit (nonfloats) as the cell is perfectly mixed.
The rate of recovery (by flotation) is then:
From the assumption of first order we can equate:
From which we deduce:
Since C/C0 is the fraction left in the cell, then the recovery is:
That is, the same as Eq. (12.28).