2013 Froth Flotation

Froth Flotation

AV Nguyen, The University of Queensland, Brisbane, QLD, Australia

2013 Elsevier Inc. All rights reserved.

Introduction 1Main Features of Flotation and the Froth Flotation Process 1Industrial Applications of Flotation 2Mineral flotation 2Wastepaper deinking 3Water treatment 3Flotation of plastics 3Flotation Science and Technology 4Physical Aspects of Flotation 4Particle Hydrophobicity and Floatability 4Young equation, contact angle, and Gibbs free energy of bubble-particle contact 4Measurement of contact angle 5Measurement of particle floatability 7Bubble-Particle Interactions 8Surface forces 8Dynamics of bubble-particle interaction 10Froth Drainage 12Flotation Kinetics 12Chemical Aspects of Flotation 14Surface Chemistry of Minerals in Water 14Minerals with non-polar surface characteristics 14Minerals with polar surface characteristics 14Chemistry of Flotation Reagents 17Collectors 17Non-ionizing collectors 17Ionizing collectors 18Regulators 18Frothers 18Mineral-Reagent Interactions and Flotation 19Sulfide minerals and thio collectors 19Insoluble oxide and silicates 20Sparingly soluble minerals 21Soluble salt minerals 21Non-polar collectors and non-polar minerals 23Engineering Aspects of Flotation 23Bubble Generation and Particle Dispersion 23Flotation Cells and Circuits 25Flotation of Fine and Coarse Particles 25References 26Introduction

Main Features of Flotation and the Froth Flotation Process

Flotation is a process of separation and concentration of one kind of particulate particles from another by their selective attachment

onto the fluid-liquid interfaces. Froth flotation and film (skin) flotation are the best examples of flotation taking place on the gas

liquid interface. Film flotation occurs on a free water surface. Particles are gently fed onto the free surface, allowing the separation of

hydrophobic (water-repelling) particles, which attach to the free surface, from non-floatable hydrophilic (water-attracting)

particles, which sink into the liquid.Change History: June 2013. AV Nguyen updated title to Froth Flotation to better reflect the content. Updated Section and Tables 1 and 4. Replaced the

previous links to different chapters by in-text citations. Added the reference section.

Reference Module in Chemistry, Molecular Sciences and Chemical Engineering http://dx.doi.org/10.1016/B978-0-12-409547-2.04401-2 1

http://dx.doi.org/10.1016/B978-0-12-409547-2.04401-2

Figure 1 Schematic of froth flotation where hydrophobic particles are separated by attaching to rising air bubbles to form a particle-rich froth onthe surface. Reproduced with permission from Nguyen, A. V. and Schulze, H. J. (2004). Colloidal science of flotation. New York: Marcel Dekker.

2 Froth FlotationIn froth flotation hydrophobic particles are separated by attaching themselves to rising air bubbles to form a particle-rich froth

on the suspension surface as shown in Figure 1. The particle suspension is usually first conditioned with the appropriate reagents

and then agitated to disperse the particles in the flotation cell. Air is drawn in or sometimes fed into the cell near the impeller to

create fine bubbles for collecting particles. The froth contains inter-bubble water (in the Plateau borders), hydrophobic particles,

and a small fraction of hydrophilic gangue particles which get into the froth by entrainment. Further separation between the

hydrophobic and entrained hydrophilic particles in the froth phase occurs by the gravity drainage of water back to the pulp. The

removal of hydrophilic particles from the froth phase can be improved using wash water added into the froth, which is common in

column flotation. The top layer of the froth containing mainly hydrophobic particles is removed by skimming and overflow to the

concentrate launder. Hydrophilic particles do not attach to air bubbles and settle to the bottom of the cell to be discharged

as tailings.

Small bubbles used in froth flotation produce very high (specific) area (per unit volume of liquid) of the gasliquid interface

available for particle attachment and are the most efficient for separation. This is the main reason why of the known flotation

techniques, froth flotation is the only one technique that has significant industrial applications and is described in this chapter. For

simplicity, froth flotation will be referred to henceforth as flotation.Industrial Applications of Flotation

Flotation has been used by mineral and chemical engineers for the separation and concentration of aqueous suspensions or

solutions of a variety of minerals, coal, precipitates, inorganic waste constituents, effluents, and even microorganisms and proteins.

It is estimated that more than two billion tons of various ores and coal are annually treated by flotation worldwide. This figure,

which represents about 85% of ores mined annually, is likely to increase in the future with the depletion of high-grade ore deposits.

Coal flotation has also significantly increased due to the increased mechanization of mining methods which produces large

amounts of fine coal particles.1 The scope of flotation technology has been expanded into many other areas, such as deinking of

wastepaper for recycling, water treatment, and separation of plastics. Today flotation deinking annually contributes about 130

million tons of recovered paper to the worldwide paper production. This figure corresponds to about 50% of the annual

papermaking capacity.2Mineral flotationFlotation is widely used to separate valuable minerals from the rock and fine coal particles from clay, silt, shale and other ash-

producing matter. It is usually preceded by crushing and grinding the ore to liberate valuable particles in a host rock, and may be

followed by metallurgical processes. One of the earliest flotation applications was in the recovery of sphalerite (ZnS) minerals from

finely ground ores at Broken Hill in Australia in 1905. The first flotation plant in the United States, the Timber Butte Mill at Basin,

Montana, began operation in 1911. The volume to commemorate the 50th anniversary of froth flotation3 shows very clearly how

the vast national mineral development of the United States, Canada, Australia, Africa, and many other countries began with the

introduction of flotation. A good account on history of the flotation development and industrial applications can be found in the

recent book published by the Australasian Institute of Mining and Metallurgy.4 At present metallic and industrial concentrates

recovered by flotation continue to increase. Table 1 shows the current annual production of some principal metallic and industrial

minerals, which have dominantly been recovered by flotation. The percentage of iron ores recovered by flotation may not be as

high as those of the base metals since the iron ores are principally concentrated by magnetic separation methods.

Table 1 does not contain mineral fuels and related materials such as coal and tar sands which are being increasingly treated by

flotation. In 2005, about 13% (90 million barrels) of petroleum needs in Canada were produced from tar sands by Syncrudewhich is the world largest producer of light sweet crude oil from oil sands and operates the largest oil sand mines and bitumen

extraction plants. Oil sand deposits in Alberta, Canada contain approximately 1.7 trillion barrels of bitumen, of which more than

Table 1 Annual production of principal metals and mineral concentrates (million metric tons) for 20102011

Australia Canada Chile China USA World

Metals (in concentrates)Copper 0.86 0.52 3.33 1.16 1.09 12.70Lead 0.62 0.06 0.00 2.35 0.34 4.70Zinc 1.51 0.61 0.04 4.31 0.77 12.80

Mineral concentratesPotash (K2O equivalent) 11.0 3.7 1.0 36.4Phosphate rock (P2O5 content) 0.6 0.3 24.0 8.2 60.9Iron ore (metal content) 277.0 21.0 7.7 412.0 11.1 1390.0

Source : Minerals Yearbook, US Geological Survey, 2013, with permission from USGS.

Froth Flotation 3175 billion are recoverable with the current technology, and 315 billion barrels are ultimately recoverable with technological

advances of flotation (Alberta Energy and Utilities Board).

Fine coal particles (under 500 microns) are recovered by flotation. Hydrocarbon oils, such as kerosene, pine oil and diesel, are

used in many coal flotation plants to increase the floatability of naturally hydrophobic coal particles. Only a small quantity of

methyl isobutyl carbinol (50100 g per ton of material) is used as frother (and collector) in coal flotation.1

Wastepaper deinkingFlotation has been used to remove ink particles in wastepaper recycling and is similar to mineral flotation in many aspects. Air

bubbles are used to collect and separate hydrophobic ink particles from the pulp of fibers comprising mostly cellulose. The non-

floated fibers form the deinked product of the operation. Selectivity is not critical to flotation deinking but ink recovery

is important.

The feature of the flotation chemistry is the dual role of the surfactants used as the liberation agent to remove ink from the

surface and as the collector to render the liberated ink particles strongly hydrophobic. The standard reagent regime includes soap

(e.g., sodium stearate), sodium silicate to disperse the particles, hydrogen peroxide as the bleaching reagent, and diethylene

triamine penta acetic acid as the complexing agent for heavy metals.

The flotation deinking market has grown extremely rapidly since 1980. At present, there are more than 600 major deinking

systems operating worldwide. The deinked pulp is used in the production of four main paper grades: newsprint, tissue, printing and

writing grade in North America (36%), Europe (33%) and Japan (16%). Today 100% of German newsprint paper is made from

deinked wastepaper.

Water treatmentIn water treatment, two flotation techniques commonly used include electrolytic flotation5 and dissolved air flotation.6 Electrolytic

flotation involves the generation of hydrogen and oxygen bubbles between electrodes. Electric power is supplied at low potential

(5 to 10 V). The energy consumption depends on the pulp conductivity and the distance between the electrodes. The bubbles

formed in electrolytic flotation are smaller than 40 mm in diameter which are efficient for floating small particles. Since the bubblegeneration does not involve turbulence, the technique is also attractive for fragile flocs. The electrolytic flotation has mainly been

used for small plants with capacity between 20 to 30 m3 h1.In dissolved air flotation the bubbles are produced by controlling pressure of water saturated with air. Three main processes of

dissolved air flotation include vacuum flotation, micro-flotation, and pressurized flotation. In vacuum flotation, the wastewater is

saturated with air at atmospheric pressure. A vacuum is then applied to the flotation tank to produce small bubbles. This process

has been used in the paper industry to recover the process water. Because of the expensive equipment required to maintain the

vacuum, the flotation process has been replaced by pressurized flotation. In micro-flotation, the entire volume of water is subjected

to increased pressure by passing the water down and up a shaft approximately 10 m deep or by passing the water through a special

mixing-aeration system. In pressurized flotation, which is the most widely used technique at present, air is dissolved in water by

applying high pressure. The bubble size depends on the applied pressure but is typically between 20 and 100 mm.Flocculation is often used in flotation applications. The collection and removal of fragile flocs by flotation presents the difficulty

of dissolved air flotation. The bubble-floc agglomerates are created by a number of mechanisms, including entrapment of bubbles

within a network of flocs, growth of bubbles from nuclei within the flocs, and particle and floc attachment onto bubbles by

collision, which is very significant to the flotation process.

Flotation of plasticsPlastic components such as polyvinyl chloride (PVC) can be separated from solid wastes by flotation. Plastics flotation utilizes the

differences in the surface energy of different plastics. A number of flotation methods and surface treatment have been examined,

including selective hydrophobization or hydrophilization of plastic surfaces by chemical reagents and physical processing such as

corona discharge or radiation, and gamma flotation carried out in a liquid with a specifically chosen surface tension. Some plastics

4 Froth Flotationdo not float in the liquid with the chosen surface tension, while some other plastics float. The critical surface tension to wet plastics

is between 25 and 40 mN m1. Experiments have shown that selective hydrophilization of plastic surfaces by the adsorption ofhydrophilic substances can be very efficient for many plastics. The plasma treatment techniques for rendering the plastic surface

hydrophilic also have potential application. Complex chemistry of many plastics can be a problem of the flotation separation.

Several commercialized flotation processes have been developed for separating plastic waste particles. The separation of

polypropylene from polyethylene was successfully developed by Mitsui Mining and Smelting (Japan). Flotation separation of

vinyl flakes from polyethylene terephthalate was commercialized by Recovery Processes International (USA). In Europe, pilot plant

processes for separating the plastic wastes by flotation have also been carried out by DaimlerBenz (Germany).Flotation Science and Technology

For a better understanding of how flotation works, many aspects of flotation have to be considered. Themost important aspects can

be grouped into

Physical aspects: particle hydrophobicity and floatability, bubble-particle interactions, froth drainage, and flotation kinetics. Chemical aspects: surface chemistry of mineral and gangue particles, chemistry of flotation reagents, and mineral-

reagent interactions.

Engineering aspects: bubble generation, particle dispersion, and cell design and circuits.

Successful flotation separations also depend on the interactions between the physical, chemical, and mechanical engineering

aspects. A triangular representation (Figure 2) of the three elements of flotation science and technology is often used to illustrate

their mutual interaction.

There are many other significant areas for research, notably the mineralogical, economic, and environmental aspects. However,

these aspects are outside the scope of this chapter. In the following, the three major groups of flotation aspects will be

briefly described.Physical Aspects of Flotation

Particle Hydrophobicity and Floatability

Surface properties of particles and air bubbles are central to flotation and can be described in terms of particle surface hydropho-

bicity and surface forces. The surface hydrophobicity is normally measured by the contact angle against water, surfactant solutions

or other liquids. Forces between surfaces will be described in the next section.Young equation, contact angle, and Gibbs free energy of bubble-particle contactThe ability of mineral particles to displace water and to attach to air bubbles can be described by contact angle (Figure 3).

Minimizing the Gibbs free energy of the bubble-surface system at equilibrium yields the Young equation relating the three

interfacial free energies, g, and the contact angle, y, by

gwm gwa cos y gma cos y gma gwm

gwa [1]

If the contact angle approaches zero, the mineral-air contact is replaced by the mineral-water contact, resulting in no flotation.

For flotation to occur, a mineral-air interface must be created with the simultaneous destruction of waterair and mineralwater

interfaces of equal area. Thus for bubble-mineral particle attachment to take place, the contact angle must be finite and eqn [1] gives

gmagwmgwa.Figure 2 Aspects needed for a fuller understanding of how flotation works.

Figure 3 Contact angle between an air bubble and a mineral surface in water. Courtesy of Dr Ryan McCabe.

Figure 4 Flotation of quartz with 4105 mole/L dodecyl ammonium acetate (positively charged in water) versus contact angle, adsorptiondensity and zeta (surface) potential. Reproduced with permission from Fuerstenau, M.C., Miller, J., D. and Kuhn, M.C., 1985. Chemistry of Flotation.New York: Society of Mining Engineers of the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Courtesy of Dr Melanie OByrne.

Froth Flotation 5The bubble-particle interaction is often described in terms of the change in the free energy (the work of adhesion), Dg, of thesystem due to the bubble-mineral contact as: Dg energy after contact energy before contact gma(gwmgwa). For flotation tooccur, the equation shows that Dg must be negative. In fact, the more negative the free energy Dg, the greater the probability ofparticle-bubble attachment. Dg between an air bubble and a particle can be described in terms of the contact angle described by theYoung eqn [1], giving Dggwa(1cos y). In flotation surfactants are used to control Dg by changing all the components, gwa, gma,and gmw, of the interfacial energies, and hence the contact angle. The Gibbs equation for surfactant adsorption can be used todescribe the change in Dg as a function of surfactant concentration. Shown in Figure 4 are strong correlations between the contactangle and the flotation recovery, adsorption density of surfactants, and zeta potential.

Measurement of contact angleThe simplest but less accurate way to determine the contact angle involves direct measurement of the contact angle between

the mineral surface and the meniscus of a sessile bubble or a sessile drop or a two-dimensional meniscus around a surface of the

6 Froth Flotationmineral Wilhelmy plate (Figure 5). Commercial contact angle goniometers employ a microscope objective to view the angle

directly. More sophisticated approaches involve the use of CCD cameras to obtain digital images of the gasliquid interface. The

images are then digitized to obtain the gasliquid interface profile, which can be used to fit the Young-Laplace equation to

determine the contact angle and the surface tension.

The mineral plate in the Wilhelmy plate technique can also be suspended from a balance for measuring the vertical component

of the wetting force acting on the wetting perimeter, which is balanced by the vertical component of the surface tension force.

Knowing the wetting perimeter and the surface tension, the cosine of contact angle can be calculated from the measured force. This

method is also suitable for studying the dynamic contact angle versus wetting velocity.

If the mineral in question is available as a powder, it may be compressed into a cake with a planar surface, which can be used to

measure contact angle with one of the techniques described above. To obtain reliable results the cake should be consolidated and

should not re-disperse upon contact with liquid, which is a problem for less hydrophobic particles.

Another procedure used in coal and mineral flotation is based on the liquid penetration into the porous bed of particles

(Figure 6) and the Washburn equation. The particles are placed into a small glass tube with the bottom end being closed off with a

glass wool or a porous disk. The tube is then placed vertically in a beaker containing the test liquid with viscosity m and surfacetension gwa. As the liquid penetrates into the particle bed by the capillary suction, the position of the wetting interface, h, can bedetermined from the mass, m, of the penetrated liquid as a function of time t. The particle bed is regarded as a bundle at capillaries

of amean radius r, then the Laplace pressure, Dp2gwacos y/r, is the driving force for a Poiseuille-type flow rate, d(pr2h)/dtpr4Dp/(8mh). The Washburn equation is obtained, giving, cos y2mh2/(trgwa). The position h of the wetting interface is related to themass, m, of the penetrated liquid by mvolumedensityhSed, where S is the cross-sectional area of the tube and e is the voidfraction of particles and d is the liquid density. Finally, one obtains m2 t gwad

2 cos ym

rS2e2

2. Typical experimental data shown

in Figure 7 confirms the theoretical dependence of m onffiffit

p. The slope of log(m) versus log(t) can be used to determine the contactFigure 5 Measurement techniques of contact angles on a mineral surface. Courtesy of Dr Philippe Estrade.

Figure 6 Equipment with an electronic balance for measuring the liquid mass penetrated into a particle bed as a function time in the Washburn theoryof contact angle on particles.

Figure 7 Measured (points) mass of water penetrated into silica beads (y42) versus time. Theoretical curve (line) describing the Washburnequation agrees with the experimental data within the width of the line.

Figure 8 AFM principle of the measurement of contact angles on a colloidal particle. Reproduced with permission from Preuss, M. and Butt, H.-J.(1998). Measuring the contact angle of individual colloidal particles. J. Colloid Interface Sci. 208: 468477.

Froth Flotation 7angle. In practice, the last term of the theoretical dependence of m2 on t is usually not known, but it can be determined using a

second liquid, such as cyclohexane, which fully wets the particles (y0).Recently, contact angle on individual colloidal particles can be measured with atomic force microscopy (AFM). The particle can

be glued to the AFM microfabricated cantilever. The particle is then pressed against an air bubble and the force recorded. Figure 8

shows the principle. It relates the force to the height of the particle with respect to the bubble. In the sketch other forces apart from

capillary ones are ignored and the sphere is assumed partly wetted by the liquid. At a large distance (position A), the cantilever is

not deflected. This is the reference for the force. The particle is then brought downward. After touching the bubble, the particle is

spontaneously drawn down, forming a (receding) contact angle (see jump line B in the picture). Pressing the particle further down

(arrow C) makes the three-phase contact line shift over the particle. The process is now reversed (arrow D) until eventually the

particle is drawn off the interface (jump line E). On the way up, the contact angle is advancing. It can be shown that cos yrec1d/Rparticle and F(detachment)2pRparticlegaw sin 2(yadv/2). Detachment force and distance, d, can be measured with AFM to determinethe receding and advancing contact angles.Measurement of particle floatabilityThe actual flotation of mineral particles depends on a large number of interacting variables. For better understanding many aspects

of the unit operation of flotation, and in particular the surface chemistry that is so critical in obtaining selective separation, a

laboratory flotation device is needed in which chemical and mechanical variables can be closely controlled. Such a device, known

as the test tube or the Hallimond (and the modified Hallimond) tube, is shown in Figure 9. The mineral of interest is first

conditioned in the absence of air with the reagents to be studied, and the solution-mineral suspension is poured into the tube so

that the mineral settles onto the sintered glass disk at the base of the tube. A small magnetic stirrer is used to insure uniform mixing

of the particles with the incoming gas bubbles. A controlled volume of nitrogen (or other gas) is passed at a controlled rate through

the sintered glass disk and into the agitated bed of mineral. The bubbles rise with their load of particles and since no frother is used

Figure 9 Test tubes used to determine the particle floatability. Reproduced from Fuerstenau, D.W. (1999). The froth flotation century. In B.K. Parekhand J. Miller, D. (Eds.). Advances in Flotation Technology. pp 321. Littleton, CO, USA: Society for Mining, Metallurgy, and Exploration, Inc.

8 Froth Flotationthe bubbles burst at the water surface. The mineral concentrate so formed then drops back into the side arm and can be recovered

at the end of an experiment, weighed, and compared with the weight of unfloatedmineral. By keeping the gas flow and stirring rates

constant and varying the amount of collector, for example, the floatability of the mineral particles responded to the collector can

be evaluated. Many other techniques have also been used, including the bubble-pickup technique which consists of pressing

a captive bubble against a bed of particles and then counting or weighing the load of particles attached to the bubble. However, the

Hallimond tubes usually give the best reproducibility.Bubble-Particle Interactions

Since contact angle and work of adhesion are the thermodynamic variables, they only describe the overall free energy change

occurring before and after the bubble-particle contact. To examine the intermediate stages of the bubble-particle interaction with an

intervening liquid film we need to know the surface force interaction between a bubble and a particle in water and the dynamics of

bubble-particle interactions.Surface forcesWetting films between a bubble and a solid surface, and the associated molecular forces have been investigated since the 1930s.

Briefly, summation of all the interactions among atoms, ions and molecules constituting the particle, bubble, and intervening

liquid film gives a force acting between the bubble and particle surfaces, known as the surface force, which is proportional to the

particle and bubble surface area (radius), and inversely proportional to the (shortest) inter-surface separation distance. Surface

force has a number of components with different molecular origins, which include

van der Waals force due to electrodynamic (electromagnetic) interactions among atoms and molecules, Electrostatic double layer force due to the interaction between diffuse layers of electrolytes concentrated at the electrically

charged surfaces of particles and bubbles in water, and

Non-DLVO forces.

The van der Waals and double layer forces are fairly well investigated, both theoretically and experimentally. They form the basis of

the DLVO (Derjaguin-Landau-Verwey-Overbeek) theory of colloid stability and are referred to as DLVO forces. The hydrophobic

attraction between hydrophobic surfaces in water which is one of many other non-DLVO forces is the most relevant to flotation.

The van der Waals force, FvdW, can be determined using the macroscopic (Hamaker) and/or the microscopic (Lifshitz) theories.

For bubble-particle interactions, the most recent expression derived from the combined HamakerLifshitz theory gives

FvdW dEvdWdr

ddr

A

6

2RpRb

r2 Rp Rb 2 2RpRb

r2 Rp Rb 2 ln r2 Rp Rb

2r2 Rp Rb

2" #( )

[2]

where EvdW is the van der Waals interaction energy. The inter-center bubble-particle distance, r is related to the shortest separation

distance,H, between their surfaces by rHRpRb, where Rb and Rp are the bubble and particle radii, respectively. The HamakerLifshitz function, A, is also a function of H due to the electromagnetic retardation and is defined as AA0(12kH)e2kHAx(H),where k is the Debye constant (defined later). The zero-frequency, A0, and non-zero frequency, Ax, terms are described by

A0 3kBT4

X1m1

m379

81

80 e80 e

m

Froth Flotation 9Ax H 0:235o n2p 1:887n2p 1

0:588

1 H=5:59 q 1=q n2p 1:887

1=21 H=lp

qh i1=q8>:

9>=>;

where q1.185, kB1.3811023 J K1 is the Boltzmann constant, T is the absolute temperature, e is the static dielectric constantof the mineral particle, 1.054591034 J s rad1 is the Planck constant divided by 2p, np is the particle refractive index,o21016rad/s, and lp is a modified London wavelength accounting for the retardation effect, defined aslp nm 9:499=

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffin2p 1:887

q. If e is not known, the first-order approximation, A00.75 kBT, can be used since the m-infinite

sum for most minerals is approximately equal to 1. The van derWaals interaction depends on the electromagnetic nature of mineral

particles through their refractive index which is the only one parameter required in eqn [2]. It can usually be found in the literature

on mineralogy. Both the van der Waals force and energy predicted by eqn [2] are positive at small separation distance (

Figure 10 van der Waals, double-layer (constant potential interaction, CPI) and hydrophobic interaction forces between a latex particle and an airbubble as a function of inter-surface separation distance, H. The bubble and particle parameters include (a) Rb20.9 mm, Rp1.475 mm, zb62 mV,zp19 mV, np1.59, k0.042 nm1, T20 C; (b) Rb23.1 mm, Rp1.475 mm, zb25 mV, zp4 mV, np1.59, k0.042 nm1,T20 C. Strong attractive surface force in Figure 10(b) causes the particle attachment to the air bubbles, as experimentally observed.

Figure 11 Grazing trajectories of particles around a rising bubble define the particles within the path of the bubble rise to be collected. The insertshows possible forces on a particle at the bubble surface, including the particle weight, Fg, buoyancy, Fb, drag force, Fd, surface forces, Fs, andinertial forces.

10 Froth FlotationDynamics of bubble-particle interactionThe collection of particles by rising air bubbles in flotation can be predicted by determining the motion of particles in the path of

the bubble rise. The analysis is based on the dynamic equations of bubble-particle interaction. Specifically, the equation for particle

motion around the bubble is solved for the trajectories of particles as shown in Figure 11. Different forces affecting particle motion

can be divided into three groups:

Volume forces such as particle weight, buoyancy, and inertial forces which are proportional to the particle volume andmass, butare independent of the inter-surface separation distance.

Surface forces such as those described in the previous section. These forces depend on the inter-surface separation distance. Hydrodynamic forces due to the resistance of liquid films between the surfaces. These microhydrodynamic forces also depend

on the inter-surface separation distance.

Figure 12 Comparison between the experimental particle trajectory (points) and the model predictions by eqn [7]. The experimental data are describedin the caption to Figure 10.

Froth Flotation 11Summing up the governing forces gives the following equation of motion of particles

4pRp3rp3

dV!

dt 4pRp

3rl3

dW!

dt 4pRp

3rl6

d V! W!

dt

F!d 4pRp3 rp rl

3

g! F!s [7]

where V!andW

!are the velocities of particle and liquid, relative to the bubble; rp and rl are the particle and liquid densities; t is the

reference time; g is the acceleration due to gravity; F!

d is the steady drag force with inclusion of corrections for the microhydrody-

namic interactions with liquid films; and F!

s describes the surface forces acting between the bubble and particle surfaces. The arrow

over the scalar variables in eqn [7] and elsewhere in this paper describes the vectors. eqn [7] can have additional forces, including

the capillary forces significant for the particle motion with a contact angle with the bubble surface.

Equation [7] is difficult to solve analytically. Simple approximate solutions can be obtained by considering different physical

natures of the forces and scaling their magnitudes as a function of the inter-surface distance. The common approach is to consider

three major bubble-particle interactions, including collision, attachment, and detachment interactions.7

Alternatively, the particle collection can be determined by directly solving eqn [7] with inclusion of all significant forces,

including microhydrodynamic resistance corrections and surface forces. Two examples are shown in Figure 12 to demonstrate the

influence of surface forces on particle attachment. In the case of attachment of the latex particle, the zeta potentials of the particle

and bubble surfaces are low, and the repulsion between the surfaces and the force barrier are significantly reduced as shown in

Figure 10. However, all of the model trajectory predictions without surface forces or with only DLVO forces do not result in particle

attachment. For the attachment to occur at 51.8, a non-DLVO attractive (hydrophobic) force with K1.5 mN m1 andl5 nm must be included in the force balance described by eqn [6]. In the second case, the particle did not attach to the bubbleand left the surface after some contact time. All of the predicted trajectories, with and without surface forces, agree with the

incoming part of the experimental trajectory. In contrast to the incoming trajectory shown in the right diagram of Figure 12, the

predicted outgoing trajectories are significantly influenced by the surface forces. Specifically, in order to match the experimental

trajectory, hydrophobic attractive force has to be included in eqn [6] for the model predictions.

12 Froth FlotationFroth Drainage

The use of froth in flotation is twofold. Firstly, froth is used to convey themineral laden bubbles from the froth-pulp interface to the

concentrate launder. Secondly, froth is used to remove entrained hydrophilic particles by the gravity drainage of water back to

the pulp (Figure 13). The froth cleaning process can be improved by applying spraying (wash) water upon the surface or inside the

upper layer of the froth. The spraying increases the volume of water draining through the froth which dilutes the mineral content of

the pulp between the bubbles so that the froth contains fewer entrained particles. The use of wash water is now common in

flotation. Despite intensive theoretical and experimental studies accurate prediction for water drainage in flotation remains a

challenge, not only because flotation froth is a complex dynamic system containing gas, liquid and solid phases but also because

the water flow in the froth phase is governed by the motion of air bubbles with complicated interfacial properties produced by the

adsorbed surfactants and attached particles.

The starting point of modern description of foam and froth drainage is the so-called drainage equation, which describes the

balance among gravitational and capillary forces, and momentum of gas motion and liquid flow in the Plateau borders (the liquid

channel) in the froth phase. The standard drainage theory considers the Poiseuille flow in the Plateau borders with zero velocity at

the gasliquid interface. If the liquid content does not significantly change over the froth height, the effect of capillary force can be

neglected, giving to the following expression for the superficial liquid recovery rate, Jl,

Jl Jg el1 el

rlgAel150m

[8]

In eqn [8], Jg is the superficial gas velocity, el is the liquid fraction, m and rl are the liquid viscosity and density, g is the acceleration

due to gravity, and A ffiffiffi3p p=2 r2 is the cross-sectional area of the PB with radius r, where r Rb 1:734ffiffiffiffiel

p1 el 1=3

1 0:765el0:409 .The first term in eqn [8] describes the influence of the gas momentum. The second term describes the gravity drainage, which

has been derived by considering the rigid (solid-like) gasliquid interface. Deviation from the assumption of the rigid gasliquid

interface in flotation is real and can be due to a number of effects, including the low (but finite) interfacial shear and dilational

viscosities of the adsorbed surfactants. Consequently, the numerical factor of 150 in the gravity drainage term in eqn [8] can be

different, depending on many interfacial phenomena such as Gibbs-Marangoni flow, surface tension gradient, and interfacial

diffusion and viscosities. At present there are a few extensions of the standard drainage equation to wet froth drainage, indicating

that many real foam and froth systems are still far from being satisfactorily described.

The effect of the water recovery and drainage on the recovery of gangue particles has been investigated experimentally. Figure 14

shows typical experimental data for the recovery of gangue particles by entrainment as a function of the water recovery. Satisfactory

theoretical prediction for the dependence is still missing.Flotation Kinetics

As the bubbles rise in the flotation cell they collect particles with a collection efficiency, E, and carry them out of the cell. The total

number of particles collected and removed from the cell by a bubble as air rises through the suspension, with the particle

concentration C, in the cell of depth h is E pRb2h C. If the gas volumetric flow rate is q, the number of bubbles formed perunit time is q= 4pRb3=3 . The rate of removal of particles from the cell is then equal to E pRb2h C q4pRb3=3. The mass balancethen givesFigure 13 Draining froth layer formed on the pulp surface (left), producing dry foam on the top and wet foam at the bottom (middle). Gangueparticles drop back to the pulp with the draining water (right). Reproduced with permission from Nguyen, A. V. and Schulze, H. J. (2004). Colloidalscience of flotation. New York: Marcel Dekker.

Figure 14 Recovery of entrained silica gangue at different size fractions: 12 mm (); 23.332.3 mm (); and 46 mm (). Reproduced withpermission from Nguyen, A. V. and Schulze, H. J. (2004). Colloidal science of flotation. New York: Marcel Dekker.

Froth Flotation 13dN

dt E pRb2h

C q4pRb3=3

[9]

whereN is the total number of particles in the cell with the volume Vc. The left hand side of eqn [9] describes the rate of the decrease

in the particle number in the cell. Substitution of the expression NCVc(1 eg), where eg is the gas holdup, into eqn [9] andrearranging gives

dC

dt k C [10]

In eqn [10], k is the rate constant of flotation being described by

k 3E4Rb 1 eg

qVc=h

3E4 1 eg Jg

Rb ESb

4 1 eg [11]

where Jg is the superficial gas velocity and Sb3Jg/Rb is the bubble surface area flux. Equation [10] can be integrated to giveR t 1 exp kt [12]

where R(t){C(0)C(t)}/C(0) is the flotation recovery. eqns [10] and [12] describe flotation kinetics of the first order. Deviationfrom the first order kinetics may be due to a number of factors, including mixing, heterogeneity of the particle floatability,

distribution of particle size and bubble size, etc., which results in distribution of the flotation rate constant. Effect of these factors on

flotation kinetics has been reviewed in the book by AV Nguyen and HJ Schulze.7 Nevertheless, eqns [10] and [12] have been shown

to be a good approximation for the actual flotation process in many cases. In particular, the linear correlation between k and Sb has

been confirmed in practice (Figure 15).

The above theory is applied to transient flotation processes, including the batch-wise processes taking place in the laboratory

flotation machines. For flotation processes operating under steady state condition, the flotation time is determined by the particle

residence time, t. In the plug-flow regime, the flotation recovery under steady state condition can be determined by eqn [12], givingR1exp(kt). For flotation running under the condition of perfect mixing one obtains Rkt/(1kt). For flotation operatingbetween the plug-flow and perfect mixing regimes, the recovery also depends on the particle dispersion in the cell in a more

complicated way. Mixing often has a detrimental effect upon recovery. For example, for t5 minutes and k0.5 minute1, therecovery in plug flow regime is 92%, while recovery in perfectly mixed flow is only 71%. Predicting the flotation rate constant,

specifically, the collection efficiency has been central to flotation theory. The efficiency can be modeled from the first principle and

the collision, attachment, and detachment interactions between bubbles and particles. A full review is available in the book by AV

Nguyen and Schulze.7

Figure 15 Flotation rate constant versus bubble surface area flux measured in a 2.8 m3 cell and with four different impellers. Reproduced withpermission from Nguyen, A. V. and Schulze, H. J. (2004). Colloidal science of flotation. New York: Marcel Dekker.

14 Froth FlotationChemical Aspects of Flotation

Surface Chemistry of Minerals in Water

Minerals with non-polar surface characteristicsOnly a few mineral surfaces are not readily wetted by water, like graphite, coal, sulfur, talc (Mg3Si4O10(OH)2), and molybdenite

(MoS2). These minerals are composed of covalent molecules held together by van der Waals (non-polar) forces which produce

special crystal lattice structures with non-polar surfaces. Examples of the special crystal lattice structures include (1) the layered

structure in graphite andmolybdenite, (2) the open sheet structure in talc with the van derWaals bonding between oxygen atoms of

the neighboring sheets, and (3) the structures with fracture and/or cleavage surfaces forming without interatomic bonds (stibnite,

Sb2S3, or sulfur). The non-polar surfaces do not readily attach to the water dipoles, and in consequence are hydrophobic and have

high natural floatability with contact angles between 60 and 90 degrees. Although it is possible to float these minerals without the

use of chemical reagents, it is universal to increase their hydrophobicity by the addition of hydrocarbon oils or frothing agents.

In coal flotation, methyl isobutyl carbinol is used as both collector and frother, and kerosene or diesel can be used to increase the

coal floatability.

Similarly, graphite, which sometimes occurs as a gangue mineral in sulfide ores, can be removed by flotation with MIBC and

hydrocarbon oils. Some auriferous ores contain a significant amount of carbonaceous materials which can be floated with oil and

frother, and burned to recover any combined gold.

Bitumen in tar sands is one of the significant fuel minerals. This insoluble liquid oil is inherently hydrophobic and is presently

recovered by a hot water flotation process. The hydrophobicity and floatability of bitumen are reduced by clay minerals (e.g.,

montmorillonite in presence of Ca2) in the oil sands. A number of man-made particles have also inherent hydrophobic surfaces.They include ink particles and many plastic materials.Minerals with polar surface characteristicsThe vast majority of minerals have strong covalent or ionic surface bonding and exhibit high free energy at their polar surface. These

surfaces react strongly with polar water molecules, rendering the minerals naturally hydrophilic in varying degrees. Chemical

treatment with reagents is required to make them floatable. According to the properties of the mineral-water interfaces important to

flotation, this polar group of minerals is subdivided into

Native metals (elemental minerals, e.g., copper, silver, gold and platinum, etc.) Sulfide minerals (e.g., galena PbS, sphalerite ZnS, chalcopyrite CuFeS2, pyrite FeS2, chalcocite Cu2S, etc.) Insoluble minerals (e.g., oxides, silicates, chromates, and vanadates of many multivalent metals, etc.) Sparingly soluble minerals (e.g., carbonates, phosphates, calcite CaF2, etc.) Soluble salt minerals (e.g., halite NaCl, sylvite KCl, trona Na3(HCO3)(CO3).2H2O, borax Na2B4O7.10H2O, etc.).

The degree of polarity of these minerals generally increases from sulfides, through sulfates to carbonates, phosphates, halides, etc.,

then to oxides, hydroxides, and, finally to silicates and quartz. Many of these minerals such as sulfides, oxides, and carbonates

contain the heavy metals (Cu, Pb, Zn, Sn, Mn, Fe) and are usually concentrated for the recovery of the metals. Many other minerals

such as Ca-phosphates (hydroxylapatite, fluorapatite, and chlorapatite, Ca5(PO4)3(OH, F, Cl)), barite (BaSO4), gypsum

(CaSO4.2H2O), micas, quartz, corundum A12O3, rutile TiO2, and potash (impure form of potassium carbonate, K2CO3) are the

major sources of raw materials for the chemical industries and fertilizers for agriculture.

Froth Flotation 15The native metals with polar surface characteristics are occasionally associated with the sulfides of copper, lead, and iron. They

have internally strongly covalently bonded atoms and are insoluble per se. However, at the surface these structures present

unsaturated atoms (and broken bonds) which are chemically reactive with oxygen in the atmosphere. Even gold is believed to

carry chemisorbed oxygen. Of course, the detailed interaction of these surfaces with water has to be studied case by case.

Sulfide minerals are predominantly covalently bounded and are of low solubility although each has theoretically a definite ionic

solubility product in water. However, the surface of sulfide minerals is usually unstable in the presence of water and oxygen,

catalyzing the sulfide surface oxidation. The oxidation is very slow in dry air. In water, the oxidation of sulfide minerals is very

intensive, following electrochemical reactions similar to the corrosion of metals and semiconductors (a few sulfides are intrinsically

semiconductors). Oxidation of sulfide minerals can proceed through successive steps producing various sulfur products, from

elementary sulfur, through different intermediate sulfur oxides such as S2O32 (thiosulfate) and S4O6

2 (tetrathionate), to sulfate,SO4

2. Modern electrochemical and spectroscopic methods have been used to investigate the mechanisms of oxidation of sulfideminerals and their reactions with flotation reagents. The problems are complicated but of fascinating interest to

flotation researchers.

Many sulfide minerals possess natural hydrophobicity and floatability in varying extent. Molybdenite, stibnite, realgar (AsS),

and orpiment (As2S3) are naturally hydrophobic. The natural hydrophobicity of these sulfide minerals is related to their special

crystal structures as discussed earlier. A number of sulfide minerals can be floated without the use of any collector under some

special conditions. This collectorless flotation is due to self-induced hydrophobicity of the sulfide minerals, acquired by surface

reaction with atmospheric oxygen and water. For instance, clean galena (PbS) free of oxidation products is known to be floatable

without treatment with xanthate or any surfactant. The collectorless flotation of sulfide minerals can be due to the oxidation of S2

to form elemental sulfur on the mineral surface, such as in the collectorless flotation of galena. The electrochemical oxidation of

sulfur is controlled by redox potential which can be changed by applied potential. For galena, the applied potential is 0 mV(versus standard hydrogen electrode SHE). The elemental sulfur can further react with metal sulfide forming polysulfide species

or metal deficient sulfides, which are hydrophobic. The formation of polysulfide or metal deficient species is common at pH>8,

while elemental sulfur occurs at pHgalena> sphalerite.

Industrial applications of collectorless flotation are few. However, self-induced hydrophobicity and collectorless floatability of

sulfide minerals can have inadvertent effect on the selective flotation of minerals from complex ores as with nickel ores bearing

pyrrhotite and chalcopyrite, whose collectorless flotation can be suppressed by maintaining a negative potential.

Many simple and complex oxide minerals are ionic crystals which are composed of close-packed O2 ions with the metalcations inserted in the crystal interstices (silica, SiO2, is a special case, in that the SiO bond is tetrahedrally arranged around each

silicon atom, Si4, which is regarded as semi-covalent). These oxide minerals are usually not intensively soluble in water sinceinsoluble species (e.g., hydroxides) are formed on the surface and prevents further dissolution. However, the surface charge can

arise at the mineral-water interface due to an excess of the lattice ions, allowing adsorption and/or exchange with ions in the bulk

solution to establish the electrical double layer. The ionic surfaces of the oxide minerals are amphoteric and can take up either a

proton or an OH ion depending on the pH, which can become either positively charged or negatively charged. This aspect of thesurface chemistry of oxide minerals and many other minerals of limited solubility has been considerably investigated by

electrokinetic studies. Every amphoteric mineral has one particular pH at which the potential is zero because the density of positive

sites is equal to the density of negative sites. This is the so-called point of zero charge (PZC) or isoelectric point (IEP). Some authors

make a fine distinction between PZC and IEP but the two should be the same if no specifically adsorbed species are present. There is

an experimental fact that the PZC ofminerals is rather variable, from sample to sample. Nevertheless, the PZC is a useful property of

minerals for flotation engineering and technology. The mineral surfaces are negatively charged in the pH range above the PZC,

while they are positively charged in the pH range below the PZC. For these minerals, flotation is possible with both negatively and

positively charged collectors depending on pH. Some typical, approximate data for the PZC are shown in Table 2.

Silica presents an interesting oxide. Natural silica is strongly hydrophilic, due to the contribution of hydrogen bonding between

water and silanol groups. Silica can become dehydrated, and consequently hydrophobic, if it is heated to about 450 C to removethe hydrated water. The hydrophobicity is due to the formation of SiOSi bond structure which does not readily react with water.

Silicates and aluminosilicates (e.g., zircon ZrSiO4; pyroxene X2Si2O6 where XNa, Li, Mg, Ca, Mn, Fe, Ti, Al and micas) are thecombined oxides but differ from the simple oxides in the network structures with oxygen linked through Si and/or Al atoms, which

can be partially replaced by magnesium and iron. The SiOSi structures are intrinsically insoluble and stable to hydrolytic

breakdown. Cation exchange and preferential leaching out of bases (Na, Li, Mg, Ca, Mn, Fe, Ti, Al) are the dominant features of

surface chemistry of silicate minerals. Silicate minerals generally acquire negatively charged surfaces in water.

Sparingly soluble (salt-type or semi-soluble) minerals include carbonates (magnesite MgCO3, dolomite CaCO3.MgCO3, calcite

CaCO3), phosphates (apatite), sulfates (barite, gypsum), tungstates (scheelite CaWO4), and some halide minerals (fluorite, CaF2).

These minerals are characterized by their low ionic binding and moderate solubility in water, which is lower than those of salt

minerals like halite and sylvite, but higher than those of most oxides and silicates. The extent of the mineral dissolution depends onTable 2 Typical, approximate pH ranges of the PZC of some minerals

Minerals SiO2 Al2O3 Fe2O3 TiO2 Graphite Dolomite

pH of PZC 23 7.59.0 58 56 2.2 1112

Table 3 Solubility and surface tension of saturated salt solutions and soluble minerals

Salt solution/soluble mineral Solubility (mol L1) Surface tension (mN m1) Sign of surface charge

Halite, NaCl 5.2 81.18 PositiveNaF 1.0 73.68 PositiveSylvite, KCl 4.1 78.20 NegativeCsI 4.2 53.9 PositiveKI 6.8 78.51 PositiveSchoenite, K2SO4.MgSO4.6H2O 0.8 Not available Negative, pH210Kainite, KCl.MgSO4.3H2O 1.5 Not available NegativeCarnalite, KCl.MgCl.6H2O 2.4 Not available Not availableNa2CO3 2.3 77.15 Not availableNaHCO3 1.1 73.44 Not available

Table 4 Correlation of the wettability of alkali halides salts with water structure

16 Froth Flotationthe solubility product of the mineral and type and concentration of chemicals in solution. The dissolved species can undergo

further reactions like hydrolysis, complexation, adsorption, and precipitation at the mineral surface or in the bulk solution. The

interfacial properties and flotation response of sparingly soluble minerals strongly depend on the mineral-solution equilibrium

which is also affected by pH and atmospheric CO2. For example, in the case of calcite and dolomite, carbonate and metal ions are

first formed by dissociation and then undergo hydrolysis, forming different species depending on pH. For calcite-water systems

open to atmospheric CO2, carbonate and bicarbonate are dominant in the alkaline pH range, while Ca2 dominates in the acidic

pH range. Since calcium is important in calcite flotation, the species distribution and the possible role of CO2 on flotation are

critical to the flotation research. The same principle of species analysis also applies to phosphates and other sparingly soluble

minerals. The species of one mineral can also influence interfacial properties and floatability of the other minerals in their mixture.

For example, under certain conditions apatite can be converted to calcite by dissolved ions.

Soluble salt minerals have to be floated from their saturated brine solutions. Important aspects of the flotation chemistry of

soluble salt minerals include solubility, surface charge, thermal stability of crystal hydrates, and interfacial water structure.

Solubility and surface tension of some saturated salt solutions at room temperature are shown in Table 3. Flotation of salts of

high solubility is difficult due to the effect of high viscosity. Flotation of salts of low solubility is influenced by surface charge. Some

salt minerals form crystal hydrates and are stable only in certain temperature regions. Flotation is most effective when the salt is in

its stable crystal form. If the salt is unstable with respect to hydration or dehydration, flotation will be difficult in the unstable state.

Examples include Na2SO4 only floated above 32Cwhere the anhydrous state is stable. Na2SO4.10H2O is only floated below 32 C

where the hydrated state is stable. Species of soluble minerals can influence the structure of water. In particular, small ions, which

increase the solution viscosity are kosmotropic (water structure making) ions, while the larger ions which increase the fluidity of

water are chaotropic (structure breaking) (see Table 4). The interfacial water at the salt crystal surface of structure making ions is

strongly hydrogen bonded and collector adsorption may not occur and the salt will not acquire a hydrophobic surface state needed

for flotation. On this principal, halides of Li and Na, and fluorides of K, Rb and Cs are structure making salts, and are not readily

floatable with most collectors. The effect of surface hydration can also be offset by the collector hydrocarbon chain with strong

hydrophobicity. The overall collector-mineral interaction and adsorption are determined by the balance between the surface charge

interaction, the van der Waals interaction and the solvent structure effects. Therefore, some structure making salts (for example,

Froth Flotation 17NaCl) can be floated (using caprylic acid), while some structure breaking salts (for example, KCl) cannot be floated (using

caprylic acid).Chemistry of Flotation Reagents

Numerous inorganic and organic reagents (surfactants) are employed in flotation for controlling the characteristics of interfaces.

According to their functionality, flotation reagents are classified into collectors, regulators and frothers.

CollectorsThese flotation reagents preferentially adsorb at the solidliquid interface, making the surface of wanted minerals water repellent

and facilitating bubble-particle attachment. They are classified based on composition and whether they exist as cations, anions or

molecular species in water. Therefore, collector molecules may be ionizing compounds, which dissociate into ions in water, or non-

ionizing (non-polar) compounds, which are practically insoluble, and render the minerals water-repellent by covering its surface

with a thin film. Ionizing collectors have a complex asymmetric molecular structure, which comprises a functional polar head

group and a non-polar hydrocarbon chain (Figure 16). In general, the polar group is the portion of the collector molecule that

reacts with water and adsorbs on the mineral surface, while the hydrocarbon chain having the water-repellent properties extends to

the solution and thereby provides hydrophobicity to the mineral surface (Figure 16). Typical industrial flotation collectors are

summarized in Figure 17.

Non-ionizing collectorsThese collectors do not contain polar functional groups and cannot chemically adsorb to the mineral surface. These compounds

are hydrocarbon liquids of petroleum origin and their adsorption is due to the intermolecular van der Waals forces. The collectors

are primarily used in the flotation of naturally hydrophobic minerals, such as coal, graphite, sulfur, and molybdenite, which haveFigure 16 Adsorption of a polar collector at mineral-water interface.

Figure 17 Typical industrial flotation collectors. R represents different hydrocarbon chains (and hydrogen atoms in cationic collectors).

18 Froth Flotationinsufficient hydrophobicity for the strong and fast attachment to bubbles. They are also used in combination with heteropolar

collectors for coarse particle flotation of copper sulfides and phosphate minerals (to reduce consumption of xanthate and fatty acid,

and to strengthen the attachment).

Ionizing collectorsThese collectors are widely used in flotation and can be conveniently divided into two classes: (1) Thio-collectors, represented by

alkyl xanthates, dithiocarbonates, thionocarbamates, mercaptobenzothiozole, etc. The non-polar tails of these collectors are

relatively short alkyl hydrocarbon chains (ethyl to hexyl) or occasionally cyclic hydrocarbon rings like phenyl or cyclohexyl are

used. (2) Nonthio-collectors, represented by alkyl carboxylates, alkyl sulfates, amines and substitute amines, etc. The alkyl chains of

these collectors usually change from lauryl to octadecyl or oleyl. The most important properties of the thio and nonthio-collectors

in aqueous solution include solubility, oxidation and micellization (Table 5).

Micelles form because the hydrocarbon chain is nonionic in nature, and a mutual incompatibility between polar water

molecules and nonpolar hydrocarbon chains exists. When a certain concentration of surfactant ions is reached in solution, termed

the critical micelle concentration, CMC, the hydrocarbon chains associate into aggregates or micelles and come out of solution. The

CMC of flotation collectors is of the order of 1 mmol l1. Micelles cannot be seen by eye, but their presence can be noted by theirability to scatter light when a beam is passed through the solution. Micellization assumes an important role in flotation systems.

If the concentration of collectors added to a solution exceeds the CMC, micellization occurs and the concentration of collectors

available for mineral adsorption is greatly reduced.

RegulatorsA number of inorganic reagents and are used to control flotation by regulating the solution chemistry. The regulators can be

classified into activators, depressants, dispersants and pHmodifiers. Activators can alter the chemical species at the mineral surface

which enhance collector adsorption. Activators are generally soluble salts. Examples of flotation activators include copper and lead

sulfates used to increase the floatability of sphalerite, and sodium sulfide or hydrosulfide used to create a sulfide compound on the

surface of oxidized minerals which can be floated with xanthates. Depressants are used to increase the selectivity of flotation by

rendering certain minerals hydrophilic, thus preventing their flotation. Cyanides and polymers are the best examples of depressants

used in flotation. Cyanides can dissolve and remove stable xanthate salts from the surface of sulfide minerals. Polymers can adsorb

to hydrophobic surfaces, making them hydrophilic. pH modifiers play an important, though very complex, role in flotation,

specifically in selectivity of complex ore separation which is dependent on a delicate balance between reagent concentrations and

pH. Flotation is often carried out in an alkaline medium since most collectors, including xanthates, are stable under these

conditions and corrosion of cells, pipes, etc., is minimized. Alkalinity is controlled by lime and sodium carbonate (soda ash).

Sulfuric or sulfurous acids are used when a decrease in pH is required.

FrothersThese reagents are water-soluble organic reagents that preferentially absorb at the gasliquid interface, helping the production of

small bubbles and a transient stable froth. They are heteropolar molecules (Table 6), with a polar group to provide solubility in

water, and a nonpolar hydrocarbon group for the adsorption.

Frothers are similar to the ionic collectors in many aspects, to the extent that many collectors such as oleates are also powerful

frothers. These powerful frothers produce very stable froths which cannot allow efficient transport of the flotation products to

further processing. Froth build-ups on the surfaces of thickeners and excessive frothing of flotation cells are problems at many

mineral processing plants. A good frother should have negligible collecting power and should produce a transient stable froth

required for transporting the floated minerals to the concentrate launder. The most effective polar groups of frothers include

hydroxyl (OH), carboxyl (COOH), carbonyl (CO), amine group (NH2) and sulfur group (OSO2OH-SO2OH).Alcohols and related compounds like glycol ethers are the most widely used frothers, largely because of their inability to adsorb

on mineral particles, i.e., to act as collectors. Aromatic alcohols from natural sources, such as pine oil or cresylic acid, have been

used extensively. Synthetic frothers are now widely used and have the controlled composition, which assists in maintaining theTable 5 Important characteristics of ionizing collectors in solutions

Thio collectors (thiols & thiolates) Nonthio collectors

Highly soluble in water Less soluble in waterDo not form micelles in water Form micelles in waterAre highly susceptible to oxidation Have no susceptibility to oxidation; stable with time and temperatureDo not significantly decrease surface tension of theirsolutions

Can significantly decrease surface tension of their solutions

React readily with heavy metal ions, producinghydrophobic precipitates on the mineral surface

Carboxylates have high affinity toward metal ions (calcium), giving hydrophobicprecipitates, similar to thio collectors. Other nonthio collectors do not readily react withinorganic ions

Table 6 Typical flotation frothers

Frothers Chemical formula

Polypropylene glycol ether

Methyl isobutyl carbinol (MIBC)

Terpinol (pine oil)

Xylenol (creslic acid)

Froth Flotation 19plant stability. Methyl isobutyl carbinol and the polypropylene glycol ethers are in this category under various commercial names.

Frothers based on polyglycols are also commonly used in various blends with alcohols and polyglycol ethers which provide special

frothers for flotation circuits. The alcohol groups provide a selective but often brittle froth which allows good control and product

transportation. The glycol ethers are stronger than the alcohol groups. The polyglycols are the strongest frothers used in flotation.

Non-alcohol frorhers include acids and amines. The carboxyl acids are also powerful collectors but the collecting and frothing

properties in one reagent may reduce flotation selectivity. Frothers with amine or sulfur groups also have weak collector properties.

Surface-inactive frothers include a few special reagents, such as diacetone alcohol and ethyl acetal, which behave like frothers in

the solidliquid-air systems but not in the two-phase liquid-air systems. Molecules of these reagents have two polar groups and are

readily soluble in water. They adsorb on solid surfaces but do not significantly change their hydrophobicity. During the bubble-

particle interaction in the froth phase the adsorbed molecules of the surface inactive frother can change their molecular orientation

and produce a sufficiently stable three-phase froth. The surface inactive reagents do not reduce surface tension and maintain the

magnitude of the capillary forces needed for strong bubble-particle attachment in flotation.Mineral-Reagent Interactions and Flotation

Sulfide minerals and thio collectorsSulfide minerals are floated using mostly xanthates, dithiophosphates, and other thio compounds as collectors. The mineral-

collector interactions and the selectivity in separating individual sulfide minerals from each other and from the rest of the

nonsulfide particles can be controlled by a careful adjustment of pH and oxidizing, reducing, and complexing additives. Figure 18

shows typical effect of pH and collector concentration on sulfide flotation. There is a critical pH value below which any given

sulfide mineral will float, and above which it will not float. This critical pH of sulfide flotation is different from the critical pH of the

PZC for flotation of nonsulfide minerals.

Interactions between sulfides and thio collectors have been explained by electrochemistry or ion exchange. Electrochemical

reactions lead to chemisorption of xanthates and formation of dixanthogen, which is the most hydrophobic of xanthate species.

Chemisorption occurs with most sulfide minerals when the surface has not been subject to oxidation by oxygen. The electron

transfer from xanthate to the mineral surface takes place during chemisorption, which may catalyze further chemical

reactions producing stable surface compounds of the metal xanthates with a varying degree of hydrophobicity, e.g.,

Hg2X>CuX>PbX2>ZnX2. The solubility of metal xanthate species is in the reverse order but the solubility of chemisorbed

xanthate species is lower than that of the corresponding precipitated metal xanthate.

Figure 19 shows strong influence of the electrochemical potential on sulfide flotation recovery. The active surface entities for

chalcocite and bornite are metal xanthates, dixanthogen for pyrite, metal xanthate for initial flotation of chalcopyrite and

dixanthogen for full flotation.

Ion exchange is dominant when the sulfide surface has been oxidized to produce a film of sulfoxyl ions like sulfite or thiosulfate.

The ionic species are then exchanged for xanthate or other collector anions. The critical pH curves in Figure 18 have been

interpreted by ion exchange giving constant ratio of concentrations of the xanthate ion to OH. The ion exchange hypothesishas been supported by thermochemical studies.

Figure 18 Flotation domain of pyrite, galena and chalcopyrite as a function of pH and concentration of sodium diethyl dithiophosphate. Keys:F flotation and NFNo flotation. Reproduced with permission from Sutherland, K. L. and Wark, I. W. (1955). Principles of Flotation.Melbourne: Australasian Institute of Mining and Metallurgy.

Figure 19 Flotation recovery versus pulp potential for chalcocite (Cu2S), bornite (Cu5FeS4), chalcopyrite (CuFeS2), and pyrite (FeS2). Ethyl xanthatewas 0.0144 mmol L1 for chalcocite and 0.02 mmol L1 for the other minerals. Reproduced and modified from Fuerstenau, D.W. (1999). The frothflotation century. In B.K. Parekh and J. Miller, D. (Eds.). Advances in Flotation Technology. pp 321. Littleton, CO, USA: Society for Mining,Metallurgy, and Exploration.

20 Froth FlotationInsoluble oxide and silicatesInsoluble oxide and silicate minerals are floatable with both anionic and cationic collectors. The mineral-collector interaction and

flotation determined by electrical properties of the mineral surface, electrical charge of the collector, molecular weight of the

collector, solubility of the minerals, and stability of metal-collector salts. Depending on the properties, the collector may adsorb

either by electrostatic interaction with the surface (physical adsorption) or by specific chemical interaction with surface species

(chemical adsorption).

Physical adsorption of many collectors occurs by electrostatic interaction with oxide and silicate surfaces. When these collectors

are used, knowledge of the point of zero charge (PZC) of the minerals in question must be known as discussed earlier. Flotation by

physical adsorption has been studied with hematite, alumina, corundum, quartz, etc. However, if the PZCs are very low, such as in

the case of quartz with the PZC being at pH1.8, anionic collectors are not adsorbed in sufficient amount below the PZC to resultin flotation since these species must compete with anions present (from pH adjustment) in concentrations greater than

1102 mol L1. The physical adsorption of collectors changes the surface charge and the PZC by forming hemi-micelles whichnowadays can be determined by atomic force microscopy. The collector concentration at the PZC gives the rapid rise in the flotation

recovery. Fluoride ion is widely used to activate flotation of silicates. The fluosilicate complex and its adsorption at metal sites on

the mineral are significant. Note that quartz has nometal ion site and is depressed by fluoride ion. Inorganic cations and ions act as

Figure 20 Flotation of chromite versus pH and oleate concentration. Reproduced with permission from Fuerstenau, M.C., Miller, J., D. and Kuhn, M.C.(1985). Chemistry of Flotation. New York: Society of Mining Engineers of the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.

Froth Flotation 21depressors in flotation of oxides and silicate with cationic and anionic collectors. Macromolecules (starches, dextrin, tannin) also

act as depressors. With very insoluble oxides and silicates such as hematite, sufficient conditioning time must be allowed for surface

conditions to stabilize both before and after collector adsorption. Temperature also has significant effects on flotation by

physical adsorption.

Chemisorption of high molecular weight collectors on oxides and silicates involve the hydrolysis of cations comprising these

minerals. The hydroxy complexes thus formed are very surface active; they adsorb strongly on mineral surfaces and reverse the sign

of the zeta potential if their concentration is sufficiently high. Therefore, flotation by chemisorption may have one peak with

anionic collectors or two peaks with cationic collectors as shown in Figure 20.

Sparingly soluble mineralsThese minerals can readily be separated from oxides and silicates, but they are extremely difficult to separate from each other

because of the great similarity in their surface chemical and physical properties. Both anionic and cationic collectors as used for

oxide and silicate flotation are used with the semi-soluble minerals. The mechanism of adsorption is complex and not well

understood; however, it has been shown that chemisorption as well as physical adsorption can occur. Improved selectivity can be

obtained by the controlled application of both inorganic and organic modifiers. Polyvalent cations and inorganic anions affect the

physical adsorption of collector on semi-soluble minerals in the same way as oxides and silicates. The selectivity, however, is not

significantly changed. Sodium silicate (water glass) is commonly used as a depressant for calcite; it has the added advantage that it

also acts as a depressant for silica if present. However, sodium silicate will depress all calciumminerals to some extent. The addition

of aluminum ions improves selectivity by reducing the depressant action of sodium silicate on calcium salts other than calcite (e.g.,

fluorite or scheelite). Other anions are also used to improve selectivity, but to a lesser extent. Macromolecules have been used for

many years to improve selectivity between the semi-soluble minerals, but understanding of the mechanisms involved is limited.

Starch, tannin, and quebracho are all used for calcite depression, but different mechanisms are believed to be involved.

Soluble salt mineralsFlotation of these minerals differ from other non-metallic flotation systems, in that ionic strengths on the order of 5 mol L1 aretypically encountered, such as in the processing of potash. Under these conditions, the zeta potential is approximately zero. The

electrical double layer is essentially thin (about one ion in thickness), and the solubility of collectors is limited. A number of

mechanisms have been proposed for the collector adsorption in soluble mineral flotation and it is thought that more than one

must be operative.

Under the conditions of ionic strengths, the electrical double-layer interactions between particles and between a bubble and a

particle do not control the flotation process. However, the surface charge can be important in the mineral-collector interaction and

adsorption in the flotation process, which can be identified in the flotation systems of negatively charged KCl and positively

charged NaCl with positively charged dodecyl ammonium hydrochloride (DAH) and negatively charged caprylic acid (Figure 21).

In the case of halite, NaCl, flotation is not achieved with amines under any circumstances. On the other hand, good recovery is

obtained with carboxylate collectors after the particular sodium carboxylate has precipitated. Sylvite does not respond to flotation

with a 10-carbon carboxylate as collector, but complete flotation is affected with a 10-carbon sulfonate below the solubility limit of

potassium decyl sulfonate. The surface charge-collector colloid adsorption cannot explain the floatability of KCl with both

positively (DAH) and negatively charged (SDS) collectors. The inability of NaCl to float with oppositely (negatively) charged

Figure 21 Flotation of sylvite (KCl) and halite (NaCl) versus concentration of dodecyl ammonium hydrochloride (DAH), sodium dodecylsulfonate (SDS) and caprylic acid collectors. Reproduced with permission from Fuerstenau, M.C., Miller, J., D. and Kuhn, M.C. (1985). Chemistryof Flotation. New York: Society of Mining Engineers of the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.

Froth Flotation 23sodium dodecyl sulfate cannot be explained by the surface charge effect. The solvent-structure making and breaking effects have to

be considered to explain the flotation response of the structure breaking KCl and structure making NaCl with SDS.Non-polar collectors and non-polar mineralsNon-ionizing collectors are not soluble in water and have to be emulsified into fine droplets for adsorption onto the mineral

surfaces (Figure 22). Emulsification can be achieved by intensive mechanical mixing, using ultrasonic devices, and can be

enhanced in presence of ionizing surfactants.

Optimum droplet size of non-polar collectors for flotation is between 1 to 10 mm. Larger droplets lead to higher consumption.Smaller droplets are difficult to adsorb onto the mineral surface since the droplets are carried away from the particles by the liquid

stream. The kinetics of the spreading of liquid hydrocarbons over the surface of minerals is also dependent on the droplet size.

Small droplets also increase the spreading of nonpolar collectors on the mineral surface.

Important physical and physicochemical properties of nonpolar collectors include: (1) viscosity, which influences the collector

spreading on the mineral surface and emulsification. The viscosity of nonpolar collectors is between 10 and 400 mPa s. (2) Surface

tension, which influences the capillary force of the bubble-collector-mineral aggregate against detaching forces due to gravity and

turbulence as can be seen from Figure 23.

Experiments show that the viscosity of oily collectors increases the flotation recovery and size of floatable particles. Highly

viscous oils (200 mPa s or above) should be used for the flotation of coarse coals and coal of slightly hydrophobic or oxygen-

containing minerals. For more hydrophobic and smaller mineral particles, low-viscosity oils can be more effective.

Non-polar commercial oils usually decrease the stability of the flotation froths by bridging mechanism. For each class of

frothing agent there is suitable nonpolar collector which exerts the most favorable influence. This influence depends on the

composition of the oil, the presence of surface-active compounds, and the fact that the collector can interact with the frothing agent

on the surface of the bubbles and in the bulk of the pulp liquid.Engineering Aspects of Flotation

Bubble Generation and Particle Dispersion

Small bubbles with high specific surface area are needed for efficient bubble-particle attachment. Solid particles have also to be well

suspended and dispersed for efficient collection by air bubbles. The production of small air bubbles and particle dispersion are

usually carried out by turbulence generated by intensive mixing. The particle suspension is controlled by macroturbulence, while

the production of air bubbles and bubble-particle aggregates are governed by microturbulence. The reagent preconditioning can

also be achieved by turbulence. The high intensity conditioning (HIC) generated by turbulent shear is used to improve flotation of

fine particles by the mechanisms of shear coagulation and surface cleaning.

The dispersion of solid particles into the state of suspension requires a minimum turbulent velocity to counterbalance the

particle settling. The so-called one-second criterion is usually used to experimentally characterize the state of suspension: The

suspension is well dispersed if individual particles do not remain settled at the bottom of the vessel for longer than 1 s. The 1 s-

criterion is widely used to establish the relationship between the specific power input and the parameters of the systems, which

generate turbulence, such as the rotational speeds of impellers. The minimum specific power input in flotation may be smaller than

the minimum specific power input required to disperse non-gassed suspensions.Figure 22 Formation of a non-polar collector layer between a bubble and a particle.

Figure 23 Action of nonpolar collector layer against disruptive forces.

24 Froth FlotationExperiments show that the air dispersion into small bubbles in flotation machines occurs in the regions on the downstream side

of the impeller elements (blades, bars, fingers etc.). The peripheral speeds of the impellers in the industrial scale are typically about

6 to 9 m s1 but still too low for cavitations in the liquid phase to occur. Therefore, the air dispersion in flotation is not due to thecavitation phenomenon in pure liquid, which requires the pressure behind the impeller elements to be dropped below the vapor

pressure. However, as air is usually drawn into the impeller zone through the draft tube, the air-loaded cavities in the downstream

regions are formed, independently of whether or not a self-aerating system is given or air is blown into the cell. Diagram 1 in

Figure 24 refers to flow without air supply: vortex streets, found with flows around obstructions form behind the impeller element.

Diagram 2 describes flow at a low rate of air introduced into liquid: bubbles form in the low-pressure regions behind the impeller

element by turbulent stresses. The precipitation of dissolved air and the microbubble formation by the pressure drop and the

turbulent fluctuations can be expected. Finally, diagram 3 shows flow at developing air-loaded cavities: at a high rate of the

introduced air the liquid breaks away at the edges of the impeller elements. An air-loaded cavity forms and extends into the flow

direction. This cavity is dispersed into bubbles at its end by turbulent eddies. A further increase in the airflow rate causes the cavity

elongation and the pulsation of the gasliquid interface.

In general, air bubbles and particles can suppress turbulence. Therefore, only a fraction of the power input is available for

generating turbulence in the pulp. The relative motion between the particles and the liquid phase consumes the other portion of the

power input. This phenomenon depends on both the volume fraction and the size of particles: the finer the particle and the higher

the particle concentration, the more the turbulence is suppressed. In the case of particles with the same size as the smallest eddies,

the dissipation rate of the two-phase turbulence is equal to the dissipation rate of the pure liquid plus the dissipation rate due to the

relative particle motion. This rule, however, does not apply to fine particles smaller than the smallest eddies. These fine particles can

follow the liquid fluctuation instantly, but the surface force interaction between particles occurring in the turbulent flow may result

in the particles aggregating or dispersing, which changes the rheological properties of the liquid phase. As fine particles have strong

influence on the turbulence, they may reduce the efficiency of the air dispersion into bubbles and the bubble-particle interaction.

These negative effects can be limited in different ways, such as, by increasing the specific power input, reducing the particle

concentration, and desliming the feed or dispersing the fine particle fraction using surfactants.

In addition to turbulent pressure fluctuation, air can also be split into bubbles by applying shear. The gasliquid interface in

flotation cells are subjected to external forces, which act in such a way that causes the bubble deformation and splitting. Balancing

the splitting pressure and capillary pressure gives the critical Weber number,We, which can be experimentally determined and used

to calculate the bubble size in flotation. One defines We splitting pressure/capillary pressure 2duc2Rb/s, where uc is somecharacteristic velocity causing the splitting. For splitting due to shear stress, uc2GRb where G is the shear rate. In the case ofturbulent dispersion, the turbulent fluctuation of pressure is the main contributor to the kinetic energy responsible for the bubble

break-up. The critical Weber number is obviously a function of the local flow pattern responsible for the bubble deformation. For a

simple plunging shear,We4.7. For gas bubble break-up due to a water jet plunging into a pool of water,We1.3. For air bubblessplitting due to a water jet plunging into a confined downcomer used in the Jameson flotation cell, We1.2.Figure 24 Illustration of the cavitation-analogous phenomena and the air dispersion into bubbles from air pockets behind the impeller element.Reproduced with permission from Nguyen, A. V. and Schulze, H. J. (2004). Colloidal science of flotation. New York, N.Y.: Marcel Dekker.

Froth Flotation 25Flotation Cells and Circuits

In the plants, flotation takes place in circuits, in which the flotation cells are arranged into banks of cells to obtain the desired final

recovery and grade. If the recovery of minerals in individual cells is R, then overall recovery of the first cell is R, and the fractional

feed entering the second cell is 1R. The overall recovery of minerals in the second cell is, therefore, R (1R). In the i-th cell, the

overall recovery is R(1R)i1. The total recovery of a bank of N cells is equal to Rbank XNi1

R 1 R i1 1 1 R N . This

equation shows that the total recovery of a bank increases with the number of cells, approaching unity in the limit as N!1. Thisideal bank recovery of unity is hardly approached in practice. Instead, the arrangement of cells in series leads to the situation where

mixing in the bank effectively approaches the ideal plug flow, resulting in better flotation kinetics, as can be seen from the following

analysis. It can be started with the worst case in which mixing in each cell of the bank is perfect, giving Rkti/(1kti), where ti isthe mean particle residence time in the i-th cell and k is the flotation rate constant. It can be established that the particle residence

time in the bank approaches the residence time of plug flows as the number of cells increases, despite the particle residence time

distribution in individual cells following the residence time distribution of perfect mixing. As a result, in the limit of a high number

of cells, the particle mean residence time, t, in the bank of N cells is determined by ttiN. Finally, the total recovery of the bank isequal to Rbank1(1kt/N)N. In the limit as N!1, one obtains Rbank 1 lim N!1 1 kt=N N 1 exp kt . Thisequation describes the flotation kinetics under the steady condition of plug flow in the cell. Arranging flotation cells into a bank of

cell in series increases the overall flotation kinetics in a bank of cells, approaching the limit of flotation kinetics under the plug

flow condition.

The improvements in flotation cells have been developed with both mechanical and pneumatic cells. Features of new

mechanical cells include the giant volume designed to process high tonnage of low-grade ores which has been driven by the

economic benefits. The volume of single mechanical cells now can be as large as 500 m3. Column flotation is now a matured

technique with applications extended beyond the boundary of mineral flotation. Developments in flotation cell technology

include the bubble generator systems using inline mixers in the Microcel technology developed at Virginia Tech (Blacksburg,

Virginia, USA) and the inline cavitation tube spargers commercialized by Eriez (Erie, PA, USA), and the Jameson cell technology

developed at the University of Newcastle (Newcastle, Australia).Flotation of Fine and Coarse Particles

Typical dependence of the flotation recovery on particle size is shown in Figure 25. The recovery of minerals by flotation is most

successful in the 10200 mm size range. Major problems in flotation are the relatively poor response in many cases of fine andcoarse particle fractions. The recovery suffers a decline for both small and large particles. The reasons for the drop off in recovery

and flotation rate for the fine and the coarse ends of the particle size distribution are different. The relatively slow flotation rate of

fine particles is generally attributed to the decrease in efficiency of the particle-bubble collision and attachment. The very poor

recovery of coarse particles is thought to be due to disruption of particle-bubble aggregates in excessively tur