9.1 Froth Flotation Chemistry, Reagents & Cell Kinetics

Froth flotation is the most widely utilized physical-chemical mineral concentration technology for fine-grained sulfide ores, industrial minerals, and coal. The process exploits differences in surface wettability between valuable minerals and unwanted gangue, selective attachment of air bubbles to hydrophobic mineral surfaces, and their buoyed elevation into a stable froth layer for collection.

Surface Chemistry, Contact Angle & Young Equation

The fundamental prerequisite for mineral attachment to an air bubble is the creation of a hydrophobic (water-repellent) mineral surface. When a three-phase contact line forms between a solid mineral particle, a liquid aqueous pulp, and a gaseous air bubble, the interfacial tensions at equilibrium satisfy Young's equation:

$\gamma_{SV} = \gamma_{SL} + \gamma_{LV} \cos \theta$

Where:

• $\gamma_{SV}$ is the solid-vapor interfacial surface energy ($\text{J/m}^2$ or $\text{N/m}$),
• $\gamma_{SL}$ is the solid-liquid interfacial surface energy ($\text{J/m}^2$),
• $\gamma_{LV}$ is the liquid-vapor interfacial surface tension ($\text{J/m}^2$),
• $\theta$ is the contact angle measured through the aqueous liquid phase.

Re-arranging for the contact angle yields:

$\cos \theta = \frac{\gamma_{SV} - \gamma_{SL}}{\gamma_{LV}}$

Combining the interfacial balance with the change in surface free energy gives the Young-Dupré work for attaching a gas bubble to the mineral in water, when $\theta$ is measured through the aqueous phase:

$W_A = \gamma_{LV} (1 - \cos \theta)$

At $\theta = 0^\circ$, water completely wets the hydrophilic mineral and $W_A=0$, so stable bubble attachment is not favored. As a collector makes the surface more hydrophobic, the contact angle and attachment work increase. Contact angle is therefore useful evidence of wettability, but actual recovery also requires collision, attachment, and survival against detachment in the cell hydrodynamics.

Flotation Reagents & Chemical Functionality

Naturally occurring minerals—with few exceptions like talc, graphite, and native sulfur—are naturally hydrophilic. Selective flotation relies on precise chemical conditioning using four main classes of flotation reagents:

1. Collectors

Collectors are heteropolar organic compounds featuring a polar, charged head group that selectively adsorbs onto specific mineral crystal faces and a non-polar hydrocarbon tail pointing outward into the solution. This arrangement renders the mineral surface hydrophobic.

• Xanthates (O-alkyldithiocarbonates): The primary collectors for sulfide minerals (chalcopyrite $\text{CuFeS}_2$, galena $\text{PbS}$, pyrite $\text{FeS}_2$). Common industrial xanthates include Sodium Isopropyl Xanthate (SIPX) and Potassium Amyl Xanthate (PAX). Longer hydrocarbon chains (such as amyl xanthate) impart stronger hydrophobicity but lower chemical selectivity than shorter chains (such as ethyl or isopropyl xanthate).
• Dithiophosphates & Thionocarbamates: Secondary collectors utilized for selective copper-gold flotation in complex ores, operating effectively at lower pH levels or in high-tarnished sulfide pulps.

2. Frothers

Frothers are non-ionic surface-active organic compounds (surfactants) that concentrate at the liquid-gas interface. They reduce pulp surface tension, prevent bubble coalescence, control bubble size distribution ($1.0 - 2.5 \text{ mm}$ diameter), and stabilize a free-draining froth column.

• Common frothers include Methyl Isobutyl Carbinol (MIBC), pine oil (terpineol), and polyglycol ethers.

3. Depressants

Depressants are organic or inorganic reagents that selectively increase the hydrophilicity of unwanted minerals, preventing collector adsorption or bubble attachment.

• Cyanide ($\text{NaCN}$): Depresses pyrite ($\text{FeS}_2$) and sphalerite ($\text{ZnS}$) during copper mineral flotation by forming soluble iron and zinc cyanide complexes.
• Lime ($\text{Ca(OH)}_2$): Elevates pulp pH ($\text{pH } 10.0 - 11.5$), precipitating hydrophilic ferric hydroxide ($\text{Fe(OH)}_3$) films on pyrite surfaces to suppress pyrite flotation.
• Sodium Silicate ($\text{Na}_2\text{SiO}_3$): Acts as a gangue depressant and slime dispersant, keeping fine silicate clays suspended.
• Sodium Hydrosulfide ($\text{NaHS}$): Used as a strong reducing depressant for copper sulfides during copper-molybdenite ($\text{Cu-Mo}$) separation, allowing molybdenite ($\text{MoS}_2$, naturally hydrophobic) to float into the concentrate while chalcopyrite is depressed.

4. Activators

Activators are chemical compounds that modify mineral surfaces to allow collector adsorption on minerals that otherwise resist collector attachment.

• Copper Sulfate ($\text{CuSO}_4$): The classic activator for sphalerite ($\text{ZnS}$). Unactivated sphalerite reacts poorly with xanthates. $\text{Cu}^{2+}$ ions displace $\text{Zn}^{2+}$ ions on the crystal lattice to form a thin surface layer of copper sulfide (covellite-like, $\text{CuS}$), which readily adsorbs xanthate collectors.

Flotation Circuit Configuration

Industrial flotation plants arrange flotation cells in sequential stages to maximize both mineral recovery and concentrate grade:

1. Roughers: Receive primary ground slurry from the grinding circuit. The main objective is maximizing overall valuable mineral recovery, producing an intermediate rougher concentrate and a final or intermediate tailing.
2. Scavengers: Treat rougher tailings to recover remaining valuable particles, unliberated middlings, or slow-floating mineral grains. Scavenger concentrate is typically recycled back to the regrind mill or rougher feed.
3. Cleaners: Re-float the rougher and scavenger concentrates through multi-stage cleaner cells (Cleaner 1, Cleaner 2, Cleaner 3) with wash water or specific depressants to eliminate entrained fine gangue and produce market-grade final concentrate.

Flotation Cell Technologies: Mechanical vs. Column Cells

• Mechanical Flotation Cells: Utilize a submerged motor-driven rotor-stator impeller that provides intense mechanical agitation to keep heavy mineral particles in suspension while shearing ingested air into fine bubbles. Mechanical cells offer high throughput and strong agitation for coarse particle suspension.
• Column Flotation Cells: Tall cylindrical or rectangular vessels ($10 - 15 \text{ m}$ high) with no internal moving parts. Compressed gas spargers inject micro-bubbles at the base, while wash water is sprayed from the top down through a deep froth layer ($1.0 - 2.0 \text{ m}$). Counter-current wash water flushes entrained fine gangue back down into the slurry, producing exceptional concentrate grades. Columns are widely installed in final cleaner stages.

Flotation Kinetics & Rate Constant Modeling

Flotation recovery proceeds as a pseudo-first-order rate process proportional to valuable mineral concentration in the pulp. A commonly used simple first-order kinetic model expresses fractional recovery ($R$) over retention time ($t$):

$R = R_{\max} \left( 1 - e^{-k t} \right)$

Where:

• $R$ is the fractional recovery of the valuable mineral at time $t$,
• $R_{\max}$ is the ultimate achievable recovery at infinite retention time,
• $k$ is the flotation rate constant ($\text{min}^{-1}$), influenced by particle size, collector concentration, bubble surface area flux, and cell hydrodynamics,
• $t$ is the pulp retention time ($\text{min}$) within the flotation stage.

Optimizing flotation circuits requires balancing retention time ($t$) and rate constant ($k$) against energy input and reagent consumption.