Froth Flotation☆ AV Nguyen, The University of Queensland, Brisbane, QLD, Australia ã 2013
Elsevier Inc. All rights reserved.
Introduction Main Features of Flotation and the Froth Flotation Process Industrial Applications of Flotation Mineral flotation Wastepaper deinking Water treatment Flotation of plastics Flotation Science and Technology Physical Aspects of Flotation Particle Hydrophobicity and Floatability Young equation, contact angle, and Gibbs free energy of bubble-particle contact Measurement of contact angle Measurement of particle floatability Bubble-Particle Interactions Surface forces Dynamics of bubble-particle interaction Froth Drainage Flotation Kinetics Chemical Aspects of Flotation Surface Chemistry of Minerals in Water Minerals with non-polar surface characteristics Minerals with polar surface characteristics Chemistry of Flotation Reagents Collectors Non-ionizing collectors Ionizing collectors Regulators Frothers Mineral-Reagent Interactions and Flotation Sulfide minerals and thio collectors Insoluble oxide and silicates Sparingly soluble minerals Soluble salt minerals Non-polar collectors and non-polar minerals Engineering Aspects of Flotation Bubble Generation and Particle Dispersion Flotation Cells and Circuits Flotation of Fine and Coarse Particles References
1 1 2 2 3 3 3 4 4 4 4 5 7 8 8 10 12 12 14 14 14 14 17 17 17 18 18 18 19 19 20 21 21 23 23 23 25 25 26
Introduction Main Features of Flotation and the Froth Flotation Process Flotat Flotation ion is a proces processs of separa separatio tion n and concen concentra tratio tion n of one kind kind of partic particula ulate te partic particles les from from anothe anotherr by their their select selective ive attach attachmen ment t onto the fluid-liquid interfaces. Froth flotation and film (skin) flotation are the best examples of flotation taking place on the gas– liquid liquid interf interface ace.. Film Film flotat flotation ion occurs occurs on a free free water water surfac surface. e. Partic Particles les are gently gently fed onto onto thefree surfac surface, e, allowi allowing ng the separa separatio tion n of hydrophobic hydrophobic (water-re (water-repelli pelling) ng) particles, particles, which attach attach to the free surface, surface, from non-floata non-floatable ble hydrophilic hydrophilic (water-at (water-attract tracting) ing) particles, which sink into the liquid.
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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
2
Froth Flotation
Schematic of froth flotation where where hydrophobic particles particles are separated by attaching to rising air bubbles to form a particle-ric particle-rich h froth on Figure 1 Schematic the surface. Reproduced Reproduced with permission permission from Nguyen, A. V. and Schulze, H. J. (2004). Colloidal (2004). Colloidal science of flotation. flotation . New York: Marcel Dekker.
In 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 wash water added into the froth, which is common 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 gas–liquid 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 flotation is the only one technique that has significant industrial applications 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 solutions of a variety variety of minerals, coal, precipitate precipitates, s, inorganic waste constitu constituents, ents, effluents, effluents, and even microorgan microorganisms isms and proteins. 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 million tons of recovered recovered paper to the worldwide worldwide paper production. production. This figure figure correspond correspondss to about 50% of the annual 2 papermaking capacity.
Mineral flotation Flotation is widely used to separate valuable minerals from the rock and fine coal particles from clay, silt, shale and other ashproducing matter. It is usually preceded by crushing and grinding the ore to liberate valuable particles in a host rock, and may be followed followed by metallurgic metallurgical al processes. processes. One of the earliest earliest flotation flotation applicati applications ons was in the recovery recovery of sphalerite sphalerite (ZnS) minerals 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 flotation 3 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 developme nt and industrial applications can be found in the recent recent book published published by the Australasian Australasian Institute of Mining Mining and Metallurgy. 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 petroleum needs in Canada Canada were produced produced from tar sands by Syncrude which 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
3
Froth Flotation
Table 1
Annual production of principal metals and mineral concentrates (million metric tons) for 2010–2011
Metals (in concentrates) Copper Lead Zinc Mineral concentrates Potash (K2O equivalent) Phosphate rock (P2O5 content) Iron ore (metal content)
Australia
Canada
Chile
0.86 0.62 1.51
0.52 0.06 0.61
3.33 0.00 0.04
– 0.6 277.0
11.0 0.3 21.0
– – 7.7
China
1.16 2.35 4.31 3.7 24.0 412.0
USA
1.09 0.34 0.77 1.0 8.2 11.1
World
12.70 4.70 12.80 36.4 60.9 1 390.0
Source : Minerals Yearbook, US Geological Survey, 2013, with permission from USGS.
175 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. Onl y a small quantity of methyl isobutyl carbinol (50–100 g per ton of material) is used as frother (and collector) in coal flotation. 1
Wastepaper deinking Flotation 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 nonfloated 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 i nk 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 treatment In 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 m m in diameter which are efficient for floating small particles. Since the bubble generation 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 m 3 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 m m. 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 plastics Plastic 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 Flotation
do 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 m 1. Experiments have shown that selective hydrophilization of plastic surfaces by the adsorption of hydrophilic 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 Daimler–Benz (Germany).
Flotation Science and Technology For a better understanding of howflotation 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 hydrophobicity 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 contact The 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
wa cos y
þg
¼g
ma
∴
cos y
¼ g g g ma
wm
wa
[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 water–air and mineral–water interfaces of equal area. Thus for bubble-mineral particle attachment to take place, the contact angle must be finite and eqn[1] gives gma gwm gwa.
Figure 2
Aspects needed for a fuller understanding of how flotation works.
Froth Flotation
Figure 3
5
Contact angle between an air bubble and a mineral surface in water. Courtesy of Dr Ryan McCabe.
Flotation of quartz with 4 105 mole/L dodecyl ammonium acetate (positively charged in water) versus contact angle, adsorption density 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 O’Byrne. Figure 4
The bubble-particle interaction is often described in terms of the change in the free energy (the work of adhesion), Dg , of the system due to the bubble-mineral contact as: Dg energy after contact – energy before contact gma (gwm gwa). For flotation to occur, the equation shows that Dg must be negative. In fact, the more negative the free energy Dg , the greater the probability of particle-bubble attachment. Dg between an air bubble and a particle can be described in terms of the contact angle described by the Young eqn [1], giving Dg gwa(1 cos y ). In flotation surfactants are used to control Dg by changing all the components, gwa, gma, and g mw, of the interfacial energies, and hence the contact angle. The Gibbs equation for surfactant adsorption can be used to describe the change in Dg as a function of surfactant concentration. Shown in Figure 4 are strong correlations between the contact angle and the flotation recovery, adsorption density of surfactants, and zeta potential.
¼
¼
¼
þ
Measurement of contact angle The 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 Flotation
mineral 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 gas–liquid interface. The images are then digitized to obtain the gas–liquid 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 surface tension g wa. As the liquid penetrates into the particle bed by the capillary suction, the position of the wetting interface, h , can be determined 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 a mean radius r , then the Laplace pressure, Dp 2gwa cos y /r , is thedriving force for a Poiseuille-type flow rate, d(pr 2h)/dt pr 4Dp / (8mh). The Washburn equation is obtained, giving, cos y 2mh2 /(tr gwa). The position h of the wetting interface is related to the mass, m , of the penetrated liquid by m volume density hSed, where S is the cross-sectional area of the tube and e is the void g d2 cos y rS2 e2 fraction of particles and d is the liquid density. Finally, one obtains m2 t wa . Typical experimental data shown 2 m in Figure 7 confirms the theoretical dependence of m on t . The slope of log( m) versus log(t ) can be used to determine the contact
¼
¼
¼
¼ ¼
p
¼
ffiffi
Figure 5
Measurement techniques of contact angles on a mineral surface. Courtesy of Dr Philippe Estrade.
Equipment with an electronic balance for measuring the liquid mass penetrated into a particle bed as a function time in the Washburn theory of contact angle on particles. Figure 6
Froth Flotation
Measured (points) mass of water penetrated into silica beads (y equation agrees with the experimental data within the width of the line. Figure 7
7
¼ 42 ) versus time. Theoretical curve (line) describing the Washburn
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 : 468–477. Figure 8
angle. In practice, the last term of the theoretical dependence of m 2 on t is usually not known, but it can be determined using a second liquid, such as cyclohexane, which fully wets the particles ( y 0). 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 y rec 1 d / Rparticle and F (detachment) 2pRparticlegaw sin 2 (yadv /2). Detachment force and distance, d, can be measured with AFM to determine the receding and advancing contact angles.
¼
¼
¼
Measurement of particle floatability The 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
8
Froth Flotation
Test tubes used to determine the particle floatability. Reproduced from Fuerstenau, D.W. (1999). The froth flotation century. In B.K. Parekh and J. Miller, D. (Eds.). Advances in Flotation Technology . pp 3–21. Littleton, CO, USA: Society for Mining, Metallurgy, and Exploration, Inc. Figure 9
the 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 unfloated mineral. By keeping thegas 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 forces Wetting 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, F vdW , 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 Hamaker–Lifshitz theory gives
F vdW
dEvdW dr
¼
("
2Rp Rb
d A dr 6 r 2
Rp
þR
b
2 þ
r 2
2 þ ln 2 R r
2Rp Rb r 2
Rp
b
Rp Rp
þR R
b b
2
#)
[2]
2
where E vdW 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 r H Rp Rb, where Rb and Rp are the bubble and particle radii, respectively. The Hamaker– Lifshitz function, A, is also a function of H due to the electromagnetic retardation and is defined as A A0(1 2kH )e2kH Ax(H ), where k is the Debye constant (defined later). The zero-frequency, A 0, and non-zero frequency, A x, terms are described by
¼ þ þ
¼
¼
A0
3kB T 1 3 79 80 m 4 m¼1 81 80
X
m
e þe
þ
þ
Froth Flotation
Ax H
ð Þ ¼ 0:235ħo
n2p
1:887 n2 1 p
8>< >: þ ð
0:588
1=2
þ 9>= ; Þ h þ i >
H =5:59
1
9
q 1=q
n2p
1:887
1
H =lp
q 1=q
where q 1.185, kB 1.381 1023 J K 1 is the Boltzmann constant, T is the absolute temperature, e is the static dielectric constant of the mineral particle, 1.05459 1034 J s rad1 is the Planck constant divided by 2 p, np is the particle refractive index, o 2 1016rad/s, and lp is a modified London wavelength accounting for the retardation effect, defined as 9:499= n2p 1:887. If e is not known, the first-order approximation, A0 0.75 kBT , can be used since the m -infinite lp nm sumfor most minerals is approximately equal to 1. The van der Waals 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 (<50 nm) and negative at longer distance, meaning that the interaction is repulsive and attractive at short and long distances. This feature of the Lifshitz theory based on quantum mechanics is one of the important subtleties of modern development and is beyond the scope of the classical Hamaker theory. The particle and bubble surfaces are electrostatically charged in water, forming the electrical double layers (edl). The diffuse layers of the double layers at the particle and bubble surfaces overlap at close approach, giving a repulsive or attractive force. The determination of the edl force depends on the charging mechanism during the overlapping of the diffuse layers. The double-layer interactions at constant surface potential and constant surface charge are usually considered. The actual double-layer interaction occurs between the two limits. The edl interaction force is determined based on the Poisson-Boltzmann equation, which describes the electrostatic potential in an ionic solution as a function of position relative to the particle and bubble surfaces, and has been found to be accurate down to separations of a few nanometers. For low surface (zeta) potentials ( 50 to 60 mV), the Hogg-HealyFuerstenau approximation for the double-layer force, F edl, at constant surface potentials gives
¼
¼
¼ ½ ¼
¼
q ffiffi ffi þffi ffi ffi ffi ffi ffi ffi ffi ffi
¼
ð Þ z2 z2 [3] ð Þ1 where z and z are the particle and bubble surface (zeta) potentials, e ¼ 8.854 10 C /J m is the permittivity of the vacuum, e is the dielectric constant (relative permittivity) of the medium ( e ¼ 80 for water). k is the Debye constant (reciprocal length) described by k ¼ { z e N 1000c /(ee k T )}, where e ¼ 1.602 10 C is the charge of a proton, c is the molar (mol/l) concentration of electrolyte ions of type i in the bulk solution with the valence z , and N ¼ 6.022 10 molecules/mole is the ¼ 2pe e0k RRþRR
F edl
p
p b
r
p
b
2zp zb exp kH exp 2kH
b
p
b
19
2
1
r
0
r
2
P
2 2
i
19
A
i
0
B
i
23
i
A
Avogadro number. If the condition of constant surface charge density is considered, the double-layer force can be determined as
¼ 2pee0 k RRþRR p b
F edl
p
ð Þ þ z2 þ z2 exp ð2kH Þ 1
2zp zb exp kH
b
p
b
[4]
When contact time between the surfaces is short, the assumption of constant surface charge is appropriate, although the surface charging mechanism also depends on dissociation or adsorption/desorption of surfactants and functional groups. Hydrophobic (non-DLVO) force is not predictable at present and the following empirical expression can be used Rp Rb K exp Rp Rb
¼
F hydrophobic
þ
H l
[5]
where K is a force constants, and l is the decay length of the hydrophobic force. These parameters are determined from force measurements obtained using a surface force apparatus or an atomic force microscope. The available data for these parameters are reviewed in the book by AV Nguyen and HJ Schulze. 7 Sometimes, the double exponential function with two force constants and two decay lengths are used to describe the long-ranged hydrophobic interaction. The exponential dependence in eqn[5] has no real physical basis – it only describes a difference between DLVO and experimental data for surface forces. Indeed, the double exponential reflects the presence of surface nanobubbles of dissolved gases preferably accumulated at hydrophobic surfaces in water (There is 20 mL of dissolved gases contained in 1 L of water under normal condition). Summing the double-layer, van der Waals and hydrophobic interaction forces gives a good approximation of the total surface force, F s, between a bubble and a particle, described by
F s
¼ F þ F þ F vdW
edl
hydrophobic
[6]
From eqn [6], several different types of the total surface force versus separation distance can be constructed which have similar features to the celebrated DLVO curves (Figure 10). As in the classical cases, the total surface interaction force or energy curve shows a primary minimum at close inter-surface separation distances and a primary maximum with a repulsive (positive) force or energy. The repulsive energy maximum can be the energetic barrier, which has to be overcome by the bubble-particle relative motion or collision interaction.
10
Froth Flotation
van der Waals, double-layer (constant potential interaction, CPI) and hydrophobic interaction forces between a latex particle and an air bubble as a function of inter-surface separation distance, H . The bubble and particle parameters include (a) R b 20.9 m m, R p 1.475 m m, z b 62 mV, 19 mV, n p 1.59, k 0.042 nm1, T 20 C; (b) R b 23.1 m m, R p 1.475 m m, z b 25 mV, z p 4 mV, n p 1.59, k 0.042 nm1, z p T 20 C. Strong attractive surface force in Figure 10(b) causes the particle attachment to the air bubbles, as experimentally observed. Figure 10
¼ ¼
¼
¼
¼
¼
¼
¼
¼ ¼
¼
¼
¼
¼
Grazing trajectories of particles around a rising bubble define the particles within the path of the bubble rise to be collected. The insert shows possible forces on a particle at the bubble surface, including the particle weight, F g, buoyancy, F b, drag force, F d , surface forces, F s, and inertial forces. Figure 11
Dynamics of bubble-particle interaction The 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 theparticle volumeand mass, but • •
are 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.
Froth Flotation
11
Comparison between the experimental particle trajectory (points) and the model predictions by eqn [7]. The experimental data are described in the caption to Figure 10 . Figure 12
Summing up the governing forces gives the following equation of motion of particles 3
!
4pRp rp dV 3 dt
!
¼ 4pR3
p
3
!
rl dW
dt
! !
4pRp rl d V W 6 dt 3
!
F þ d
!
4pRp 3 rp 3
rl
g
þ!F
[7]
s
!
where V and W 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 microhydrodynamic 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 K 1.5 mN m1 and l 5 nm must be included in the force balance described by eqn [6]. In the second case, the particle did not attach to the bubble and 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.
¼
¼
¼
12
Froth Flotation
Froth Drainage The use of froth in flotation is twofold. Firstly, froth is used to convey the mineral 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 gas–liquid 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, J l, gAe ¼ J 1 e e r150 m
J l
g
l
l
l
[8]
l
In eqn [8], J g is the superficial gas velocity, e l is the liquid fraction, m and rl are the liquid viscosity and density, g is the acceleration
p ð Þ þ
1:734 el 1 el 1=3 due to gravity, and A 3 p=2 r is the cross-sectional area of the PB with radius r , where r Rb . 1 0:765el 0:409 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) gas–liquid interface. Deviation from the assumption of the rigid gas–liquid 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.
ffiffi ¼ p
2
¼
ffiffi ffi
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 pRb 2 h concentration C , in the cell of depth h is E C. If the gas volumetric flow rate is q , the number of bubbles formed per 3 unit time is q= 4 pRb =3 . The rate of removal of particles from the cell is then equal to E C 4pRqb 3 =3. The mass balance pRb 2 h then gives
ð
Þ
ð
Þ
ð
Þ
Draining froth layer formed on the pulp surface (left), producing dry foam on the top and wet foam at the bottom (middle). Gangue particles drop back to the pulp with the draining water (right). Reproduced with permission from Nguyen, A. V. and Schulze, H. J. (2004). Colloidal science of flotation. New York: Marcel Dekker. Figure 13
13
Froth Flotation
Recovery of entrained silica gangue at different size fractions: 12 m m ( •); 23.3 32.3 m m ( ); and 46 m m ( ▲). Reproduced with permission from Nguyen, A. V. and Schulze, H. J. (2004). Colloidal science of flotation. New York: Marcel Dekker. Figure 14
d N dt
¼ E
pRb 2 h
C
þ
4pRq 3 =3
[9]
b
where N is the total number of particles in the cell with the volume V c. The lefthand sideof eqn [9] describes the rate of thedecrease in the particle number in the cell. Substitution of the expression N CV c(1 e g ), where e g is the gas holdup, into eqn [9] and rearranging gives
¼
dC dt
¼ k C
[10]
In eqn [10], k is the rate constant of flotation being described by
4R 31E e V q=h ¼ 4 13E e J R ¼ 4 1ES e [11] where J is the superficial gas velocity and S ¼ 3 J /R is the bubble surface area flux. Equation [10] can be integrated to give Rðt Þ ¼ 1 exp ðkt Þ [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. Deviation g
k
b
g
b
g
g
b
c
g
b
b
g
from 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], giving R 1 exp( kt). For flotation running under the condition of perfect mixing one obtains R kt /(1 kt). For flotation operating between 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 t 5 minutes and k 0.5 minute1, the recovery 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
¼
¼
¼
þ
¼
14
Froth Flotation
Flotation rate constant versus bubble surface area flux measured in a 2.8 m3 cell and with four different impellers. Reproduced with permission from Nguyen, A. V. and Schulze, H. J. (2004). Colloidal science of flotation. New York: Marcel Dekker. Figure 15
Chemical Aspects of Flotation Surface Chemistry of Minerals in Water Minerals with non-polar surface characteristics Only a few mineral surfaces are not readily wetted by water, like graphite, coal, sulfur, talc (Mg 3Si4O10(OH)2), and molybdenite (MoS 2). 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 and molybdenite, (2)the open sheet structure in talc with the van der Waals 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 Ca2þ) 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 characteristics The 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, K 2CO3) are the major sources of raw materials for the chemical industries and fertilizers for agriculture.
Froth Flotation
15
The 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 lowsolubility although each has theoreticallya 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 fewsulfides 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 S 2O32 (thiosulfate) and S4O62 (tetrathionate), to sulfate, SO42. Modern electrochemical and spectroscopic methods have been used to investigate the mechanisms of oxidation of sulfide minerals 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 S 2 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 pH< 6. The ease of collectorless flotation follows the order chalcopyrite > galena> 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 metal cations inserted in the crystal interstices (silica, SiO2, is a special case, in that the Si–O bond is tetrahedrally arranged around each silicon atom, Si4þ, which is regarded as semi-covalent). These oxide minerals are usually not intensively soluble in water since insoluble 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 the surface 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 of minerals 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 remove the hydrated water. The hydrophobicity is due to the formation of Si–O–Si bond structure which does not readily react with water. Silicates and aluminosilicates (e.g., zircon ZrSiO4; pyroxene X 2Si2O6 where X Na, Li, Mg, Ca, Mn, Fe, Ti, Al and micas) are the combined 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 on
¼
Table 2
Typical, approximate pH ranges of the PZC of some minerals
Minerals
SiO 2
Al 2O 3
Fe 2O 3
TiO 2
pH of PZC
2–3
7.5–9.0
5–8
5–6
Graphite
Dolomite
2.2
11–12
16
Table 3
Froth Flotation
Solubility and surface tension of saturated salt solutions and soluble minerals
Salt solution/soluble mineral
Solubility (mol L1 )
Surface tension (mN m 1 )
Sign of surface ch arge
Halite, NaCl NaF Sylvite, KCl CsI KI Schoenite, K2SO4.MgSO4.6H2O Kainite, KCl.MgSO4.3H2O Carnalite, KCl.MgCl.6H2O Na2CO3 NaHCO3
5.2 1.0 4.1 4.2 6.8 0.8 1.5 2.4 2.3 1.1
81.18 73.68 78.20 53.9 78.51 Not available Not available Not available 77.15 73.44
Positive Positive Negative Positive Positive Negative, pH 2–10 Negative Not available Not available Not available
Table 4
¼
Correlation of the wettability of alkali halides salts with water structure
the 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 Ca 2þ dominates in the acidic pH range. Since calcium is important in calcite flotation, the species distribution and the possible role of CO 2 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 32 C where 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
17
NaCl) 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.
Collectors These flotation reagents preferentially adsorb at the solid–liquid 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 nonionizing (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 collectors These 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 have
Figure 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 Flotation
insufficient 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 (toreduce consumption of xanthate and fatty acid, and to strengthen the attachment).
Ionizing collectors These 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 l 1. Micelles cannot be seen by eye, but their presence can be noted by their ability 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. Regulators A 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 pH modifiers. 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 thebest 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. Frothers These reagents are water-soluble organic reagents that preferentially absorb at the gas–liquid 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 (–OSO 2OH-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 the
¼
Table 5
Important characteristics of ionizing collectors in solutions
Thio collectors (thiols & thiolates)
Nonthio collectors
Highly soluble in water Do not form micelles in water Are highly susceptible to oxidation Do not significantly decrease surface tension of their solutions React readily with heavy metal ions, producing hydrophobic precipitates on the mineral surface
Less soluble in water Form micelles in water Have no susceptibility to oxidation; stable with time and temperature Can significantly decrease surface tension of their solutions Carboxylates have high affinity toward metal ions (calcium), giving hydrophobic precipitates, similar to thio collectors. Other nonthio collectors do not readily react with inorganic ions
Froth Flotation
Table 6
19
Typical flotation frothers
Frothers
Chemical formula
Polypropylene glycol ether
Methyl isobutyl carbinol (MIBC)
Terpinol (pine oil)
Xylenol (creslic acid)
plant 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 solid–liquid-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 bubbleparticle 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 collectors Sulfide minerals are floated using mostly xanthates, dithiophosphates, and other thio compounds as collectors. The mineralcollector 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., Hg 2 X > CuX > PbX 2 > ZnX 2. 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 hypothesis has been supported by thermochemical studies.
20
Froth Flotation
Flotation domain of pyrite, galena and chalcopyrite as a function of pH and concentration of sodium diethyl dithiophosphate. Keys: F flotation and NF No flotation. Reproduced with permission from Sutherland, K. L. and Wark, I. W. (1955). Principles of Flotation. Melbourne: Australasian Institute of Mining and Metallurgy. Figure 18
¼
¼
Flotation recovery versus pulp potential for chalcocite (Cu2S), bornite (Cu5FeS4), chalcopyrite (CuFeS2), and pyrite (FeS2). Ethyl xanthate was 0.0144 mmol L1 for chalcocite and 0.02 mmol L 1 for the other minerals. Reproduced and modified from Fuerstenau, D.W. (1999). The froth flotation century. In B.K. Parekh and J. Miller, D. (Eds.). Advances in Flotation Technology . pp 3–21. Littleton, CO, USA: Society for Mining, Metallurgy, and Exploration. Figure 19
Insoluble oxide and silicates Insoluble 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 PZC’s are very low, such as in the case of quartz with the PZC being at pH 1.8, anionic collectors are not adsorbed in sufficient amount below the PZC to result in flotation since these species must compete with anions present (from pH adjustment) in concentrations greater than 1 102 mol L 1. The physical adsorption of collectors changes the surface charge and the PZC by forming hemi-micelles which nowadays can be determined by atomic force microscopy. Thecollector concentration at the PZC gives the rapid risein theflotation 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 no metal ion site and is depressed by fluoride ion. Inorganic cations and ions act as
¼
Froth Flotation
21
Flotation of chromite versus pH a nd 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. Figure 20
depressors 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 minerals These 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 calcium minerals 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 minerals Flotation of these minerals differ from other non-metallic flotation systems, in that ionic strengths on the order of 5 mol L 1 are typically 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
Flotation of sylvite (KCl) and halite (NaCl) versus concentration of dodecyl ammonium hydrochloride (DAH), sodium dodecyl sulfonate (SDS) and caprylic acid collectors. 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. Figure 21
Froth Flotation
23
sodium 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 minerals Non-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 m m. 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 oxygencontaining 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 scriterion 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 maybe 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 Flotation
Experiments 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 s 1 but still too low for cavitations in the liquid phase to occur. Therefore, the air dispersion in flotation is not due to the cavitation 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 gas–liquid interface. In general, air bubbles and particles can suppress turbulence. Therefore, only a fraction of the power input is available for generating turbulence in thepulp. The relative motion between theparticles and the liquid phase consumes theother 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 gas–liquid 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 2duc 2Rb /s, where uc is some characteristic velocity causing the splitting. For splitting due to shear stress, uc 2GRb where G is the shear rate. In the case of turbulent 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, We 4.7. For gas bubble break-up due to a water jet plunging into a pool of water, We 1.3. For air bubbles splitting due to a water jet plunging into a confined downcomer used in the Jameson flotation cell, We 1.2.
¼
¼
¼
¼
¼
¼
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. Figure 24
Froth Flotation
25
Flotation 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 1 R. The overall recovery of minerals in the second cell is, therefore, R (1 R). In the i -th cell, the
N
overall recovery is R(1 R)i1. The total recovery of a bank of N cells is equal to Rbank
i 1
X ð Þ ¼
¼
R1
N
ð1 RÞ . This ¼1 equation shows that the total recovery of a bank increases with the number of cells, approaching unity in the limit as N !1. This
R
1
i
ideal 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 R kt /(1 kti), where ti is i the 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 t ti N . Finally, the total recovery of the bank is equal to Rbank 1 (1 kt / N ) N . In the limit as N , one obtains Rbank 1 lim N !1 1 kt= N N 1 exp kt . This equation 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 m 3. 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).
¼
¼ þ
!1
¼
¼
ð þ
þ
Þ ¼
ð Þ
™
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 10–200 m m size range. Major problems in flotation are the relatively poor response in many cases of fine and coarse 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 turbulent zones in flotation cells, leading to the increase in efficiency of the particle-bubble detachment.
Typical dependence of the flotation recovery on the particle size and hydrophobicity. Reproduced with permission from Nguyen, A. V. and Schulze, H. J. (2004). Colloidal science of flotation. New York: Marcel Dekker. Figure 25
26
Froth Flotation
Zones of best performance for fine and coarse particle flotation. Reproduced with permission from Nguyen, A. V. and Schulze, H. J. (2004). Colloidal science of flotation. New York, N.Y.: Marcel Dekker. Figure 26
It appears that flotation kinetics depend on a balance among the collision, attachment and detachment processes which are strong functions of the particle size, density and hydrophobicity, the bubble size and the turbulent kinetic energy. The particle physical properties are the input into the flotation system and are, therefore, difficult to manipulate, but the latter are the manipulated variables, which define the best flotation cell design and operating conditions for a given particle size distribution. The existence of an optimum field of operation for various particle sizes has been appreciated. For fine particles an increased rotational speed of rotor above the minimum (1 s–criterion) value required for particle suspension often results in an increased recovery. On the other hand, the recovery of coarse particles has a maximum at the minimum suspension speed of rotor, and decreases with further agitation. Therefore, the optimum hydrodynamic conditions for fine and coarse particles are different. Fine particle flotation is controlled by the bubble-particle collision and attachment processes and should be operated at higher power-input, which produces smaller bubbles at moderate to high agitation. Coarse particle flotation is controlled by the bubble-particle detachment process and requires a turbulence intensity which just ensures the complete suspension of all particles. For coarse or high-density particles the advantage of using smaller bubbles is reduced and a high turbulence is detrimental. The requirements of the different particle sizes are schematically shown in Figure 26. These requirements need not necessarily involve different cell designs for fine and coarse particles, but the bubble size is, to some extent, controlled by the impeller design and the mechanical entrainment of fine particles can be reduced by a proper baffle system. With flotation feeds containing a wide range of particle sizes, it is unlikely that a single flotation cell can be devised to give optimum recovery over the whole particle size range. The feed should be split into fine and coarse particles so that they can be handled separately in the flotation circuits. Fine particles should be floated with moderate to high agitation, whereas the coarse fraction would respond best to a stirring speed just above the minimum speed for complete suspension. Alternatively, a wide bubble size distribution can be generated to float particles of a size distribution at high rates of recovery. There is also a very pronounced chemical effect on the relationship between particle size and floatability. Both the reagent regime and the hydrodynamic conditions are equally important in flotation and should be optimized in parallel. In the past, the hydrodynamic conditions were often neglected in the flotation research. Regarding the reagent regime, the chemical conditions for fine and coarse particle flotation are different. It is not easy to optimize the reagent regime for both fine and coarse particles in the one flotation cell.
References 1. Laskowski, J. S. Coal Flotation and Fine Coal Utilisation; Elsevier: Amsterdam, 2001. 2. Dorris, G.; Ben, Y.; Ricard, M. Prog. Pap. Recycl. 2011, 20, 3–42. 3. Fuerstenau, D. W., Ed.; Froth Flotation: 50th Anniversary Volume ; AIME: New York, 1962. 4. Lynch, A. J.; Harbort, G. J.; Nelson, M. G. History of Flotation; Australasian Institute of Mining and Metallurgy: Burwood, Australia, 2010. 5. Matis, K. A.; Peleka, E. N. Sep. Sci. Technol. 2010, 45, (16), 2465–2474. 6. Shammas, N. K. Handbook of Environmental Engineering ; Flotation Technology; 2010; Vol. 12; pp 327–345. Humana Press/Springer, New York. 7. Nguyen, A. V.; Schulze, H. J. 2004. Colloidal Science of Flotation, New York, N.Y.: Marcel Dekker.
