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The science
Froth flotation kinetics
Each flotation cell is a perfectly mixed tank. A mineral with flotation rate constant k is removed to the froth at a rate k m, so for one cell V dm/dt = Q (min - m) - k V m. In steady state N cells in series recover R = 1 - (1 + k τ)-N where τ = Vcell/Q is the residence time per cell. The page integrates the cell chain explicitly in time and checks it against this closed form.
Selective Pb-Zn circuit
SEDEX (sedimentary-exhalative) Zn-Pb ores are processed by floating galena first, then activating and floating sphalerite. Concentrate grade is the metal mass over concentrate mass: Zn grade = 0.671 · mZnS / (mZnS + mgangue,entrained). Raising collector dose increases k = kmax D/(D + D50) and recovery but lets more gangue through, giving the classic grade-recovery trade-off curve.
Liberation and grinding
Finer grinding frees (liberates) the minerals: here L = 1/(1 + (P80/150 µm)3) (illustrative). Grinding energy follows Bond's law W = 10 Wi (1/√P80 - 1/√F80) with Wi = 12 kWh/t.
Honest simplifications: generic SEDEX-style numbers, not a specific mine. Entrainment is a constant fraction of froth water recovery, the liberation curve and the rate constants are illustrative, there are no cleaner stages or recycle streams, and the 3D page's arcade tonnage counters are replaced by this mass balance.
What to try
- Sweep the collector dose and watch the operating point slide along the grade-recovery curve.
- Coarse grind: energy drops but liberation and recovery fall.
- "Dirty froth": high water recovery entrains gangue and the concentrate grade collapses.
- "Overloaded circuit": high feed shortens residence time per cell and recovery drops.