Froth flotation
Froth flotation is a selective process for separating minerals from gangue by using surfactants and wetting agents. The selective separation of the minerals makes processing complex (that is, mixed) ores economically feasible. The flotation process is used for the separation of a large range of sulfides, carbonates and oxides prior to further refinement. Phosphates and coal are also processed by flotation technology.
The flotation process is also widely used in industrial waste water treatment plants, where it is applied to remove fats, oil, grease and suspended solids from waste water. These units are called Dissolved air flotation (DAF) units. In particular, dissolved air flotation units are used in removing oil from the wastewater effluents of oil refineries, petrochemical and chemical plants, natural gas processing plants and similar industrial facilities.

# History
William Haynes in 1869 patented a process for separating sulfide and gangue minerals using oil and called it bulk-oil flotation. The modern froth flotation process was invented in 1901 by C.V Potter in Australia and in 1902 by G.D Delprat in Holland. In the early times, only naturally occurring chemicals such as fatty acids and oils were used as flotation reagents in a large quantity. Since then, the process has been adapted to apply to a wide variety of materials to be separated, and additional collector agents, including surfactants and synthetic compounds have been adopted for various applications.

# Principle of operation
Froth flotation commences by comminution (that is, crushing/grinding), which is used to increase the surface area of the ore for subsequent processing and break the rocks into the desired mineral and gangue, which then has to be separated from the desired mineral. The ore is ground into a fine powder. The desired mineral is rendered hydrophobic by the addition of a surfactant or collector chemical. The particular chemical depends on the mineral is being refined. As an example, pine oil is used to extract copper (see copper extraction). This slurry (more properly called the pulp) of hydrophobic mineral-bearing ore and hydrophilic gangue is then introduced to a water bath which is aerated, creating bubbles. The hydrophobic grains of mineral-bearing ore escape the water by attaching to the air bubbles, which rise to the surface, forming a foam or a scum (more properly called a froth). The froth is removed and the concentrated mineral is further refined.

# Science of flotation
To be effective on a given ore slurry, the surfactants are chosen based upon their selective wetting of the types of particles to be separated.  A good surfactant candidate will completely wet one of the types of particles, while partially wetting the other type, which allows bubbles to attach to them and lift them into a froth.  The wetting activity of a surfactant on a particle can be quantitated by measuring the contact angles that the liquid/bubble interface makes with it. For complete wetting the contact angle is zero.
Another consideration, especially important for heavy particles, is to balance the weight of the particle with the surfactant adhesion and buoyant forces of the bubbles that would lift it.
For typical values of metal densities and surface tensions, if the bubbles are larger than the ore particles, and the particles are or less that 1 mm radius, then particles will rise into the froth layer if:
where \scriptstyle R is the radius of the particles, \scriptstyle \bar{\gamma} is the average surface tension between the three pairs of phases (particle, flotation solution, air), \scriptstyle \rho is the mass density of the particles, and \scriptstyle g is the acceleration of gravity (9.81 m/s2).
For particles larger than the bubbles, they too can rise into the froth, each buoyed by a swarm of bubbles, under similar conditions as those expressed in the inequality.

# Flotation equipment
Flotation can be performed in mechanically agitated cells or tanks, in tall flotation columns and in several other units including the Jameson cell.
Mechanical cells use a large mixer and diffuser mechanism at the bottom of the mixing tank to introduce air and provide mixing action.  Flotation columns use air spargers to introduce air at the bottom of a tall column while introducing slurry above.  The countercurrent motion of the slurry flowing down and the air flowing up provides mixing action.  Mechanical cells generally have a higher throughput rate, but produce material that is of lower quality, while flotation columns generally have a low throughput rate but produce higher quality material.
Mechanical flotation cell used for mineral concentration.  Numbered triangles show direction of stream flow.  A mixture of ore and water called pulp  enters the cell from a conditioner, and flows to the bottom of the cell.  Air  or sometimes nitrogen is passed down a vertical impeller where shearing forces break the air stream into small bubbles.  The mineral concentrate froth is collected from the top of the cell , while the pulp  flows to another cell.
The Jameson cell uses neither impellers nor spargers, instead combining the slurry with air in a downcomer where high shear gives excellent bubble particle contacting.
In dissolved air flotation (DAF), which is used in wastewater treatment, air is dissolved into the flotation solution under high pressure. When the solution is released into the flotation chamber, the reduced pressure causes much of the dissolved air to come out of solution to form bubbles in the same way that dissolved carbon dioxide forms bubbles when a beer bottle is opened.

# Mechanics of flotation
The following steps are followed:
- Grinding to liberate the mineral particles
- Reagent conditioning to achieve hydrophobic surface charges on the desired particles
- Collection and upward transport by bubbles in an intimate contact with air or nitrogen
- Formation of a stable froth on the surface of the flotation cell
- Separation of the mineral laden froth from the bath (flotation cell)
Simple flotation circuit for mineral concentration.  Numbered triangles show direction of stream flow,  Various flotation reagents are added to a mixture of ore and water (called pulp) in a conditioning tank.  The flow rate and tank size are designed to give the minerals enough time to be activated.  The conditioner pulp  is fed to a bank of rougher cells which remove most of the desired minerals as a concentrate.  The rougher pulp  passes to a bank of scavenger cells where additional reagents may be added.  The scavenger cell froth  is usually returned to the rougher cells for additional treatment, but in some cases may be sent to special cleaner cells.  The scavenger pulp is usually barren enough to be discarded as tails.  More complex flotation circuits have several sets of cleaner and re-cleaner cells, and intermediate re-grinding of pulp or concentrate.

# Chemicals of flotation

## Collectors

## Frothers

## Modifiers
pH modifiers such as:
- Lime CaO
- Soda ash Na2CO3
- Caustic soda NaOH
- Acid H2SO4, HCl
Cationic modifiers:
- Ba2+, Ca2+, Cu+, Pb2+, Zn2+, Ag+
Anionic modifiers:
- SiO32-, PO43-, CN-, CO32-, S2-
Organic modifers:
- Dextrin, starch, glue, CMC

# Specific ore applications