Wills' Mineral Processing Technology, 8th Edition

Appendix V

Derivation of Fully Mixed Recovery Equation (Chapter 12, Equation 12.28)

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.

Figure A.V.1 Continuous operating cell; perfectly mixed, first-order kinetics.

The rate of recovery (by flotation) is then:

$\frac{\mathrm{d}R}{\mathrm{d}t}=\frac{C_0-C}{\tau }$

From the assumption of first order we can equate:

$\frac{C_0-}{}$