Hematite reverse flotation (2D)

Reverse flotation of iron ore

In reverse cationic flotation the gangue mineral, quartz, is floated into the froth and the valuable hematite (Fe₂O₃) is left behind in the cell as the product. A cationic amine collector (R-NH₃⁺) sticks to negatively charged quartz and makes it water-repellent, so it attaches to air bubbles and rises. Starch coats hematite and keeps it water-loving (a depressant).

Model equations

• Surface charge: the negative fraction of sites fneg = 1 / (1 + 10IEP − pH), with isoelectric points about 2 for quartz and about 6.5 for hematite.
• Amine ionisation: fcat = 1 / (1 + 10pH − pKa), pK_a about 10.6.
• Collector coverage (Langmuir): θ = A / (A + Kc), with A = dose × f_cat × f_neg. Starch coverage on hematite θs = S/(S + Ks) multiplies the hematite attachment by (1 − θ_s).
• First-order flotation kinetics: dm/dt = −k m, m(t) = m0 e−kt, with k = k0 θ (N/1000)0.8 G(d) + kent (impeller speed, a size window G, and entrainment of fines with the froth water).
• Fe grade = 0.699 × hematite / (hematite + silica); Fe recovery = hematite left / hematite fed.

Honest simplifications: single-stage batch cell, one size class, constant rate constants, no froth stability or water recovery model, no calcium activation, and all constants are illustrative values chosen to reproduce the usual trends (grade up and recovery down with more amine), not a calibrated plant model.

• Sweep pH on the rate graph: above the hematite isoelectric point (6.5) its surface turns negative and the amine can stick to it, so the starch has to protect it.
• Remove the starch: hematite floats too and recovery drops.
• Overdose the amine: grade rises a little but the selectivity collapses.
• Use 8 micron slimes: entrainment carries hematite into the froth.