FLOTATION
A. V. Nguyen, University of Newcastle, New South
Wales, Australia &
2007 Elsevier Ltd. All rights reserved.
Introduction Main Features of Flotation and the Froth Flotation Process
Flotation is a process of separation and concentration of one kind of particulate particles from another by their their selec selectiv tivee attach attachmen mentt onto onto the fluid–l fluid–liqu iquid id interf interface aces. s. Froth Froth flotati flotation on and film (skin) (skin) flotatio flotation n are the best examples of flotation taking place on the gas–liquid interface. Film flotation occurs on a free water surface. Particles are gently fed onto the free surfac surface, e, allowi allowing ng the separ separatio ation n of hydrop hydrophob hobic ic (water-repelling) particles, which attach to the free surfac surface, e, from from nonfloa nonfloatab table le hydrop hydrophil hilic ic (water (water-at -at-tracting) particles, which sink into the liquid. In froth flotation, hydrophobic particles are separated by attaching themselves to rising air bubbles to form a particle-rich froth on the suspension sur1. The particle suspension is face as shown in Figure 1. usually usually first conditioned conditioned with the appropriat appropriatee reagents and then agitated to disperse the particles in the flotation cell. Air is drawn in or sometimes fed into
Air Skimmer Particle Froth
Pulp
Entrained particles
Bubble Baffle
Rotor Figure 1
Stator
Schematic of froth flotation where hydrophobic particles are separated by attaching to rising air bubbles to form a particle-rich froth on the surface. (Reproduced with permission from Nguyen AV and Schulze HJ (2004) Colloidal Science of Flotation . New York: Marcel Dekker.)
the cell near the impeller to create fine bubbles for collecting particles. The froth contains inter-bubble water (in the plateau plateau borders), borders), hydrophobic hydrophobic partiparticles cles,, and and a smal smalll frac fracti tion on of hydr hydrop ophi hilic lic gang gangue ue particles, which get into the froth by entrainment. Further separation between the hydrophobic and entrained hydrophilic particles in the froth phase occurs by the gravity drainage of water back to the pulp. The removal of hydrophilic particles from the froth phase can be improved using wash water added into the froth, which is common in column flotation. The top layer of the froth containing mainly hydrophobic particles is removed by skimming and overflow flow to the the conc concen entr trat atee laun launde derr. Hydr Hydrop ophi hili licc 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 is the only one technique that has significant nificant industrial industrial applications applications and is described described in this encyclopedia. For simplicity, froth flotation will be referred to henceforth as flotation.
Industrial Applications of Flotation
Flotation has been used by mineral and chemical engineers for the separation and concentration of aqueous suspensions or solutions of a variety of minerals, coal, coal, precipitat precipitates, es, inorganic inorganic waste constituent constituents, s, effluents, and even microorganisms and proteins. It is estimated that more than two billion tons of various ores ores and and coal coal are are annu annual ally ly trea treate ted d by flota flotatio tion n worl worldw dwid ide. e. This This figur figure, e, whic which h repr repres esen ents ts abou aboutt 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 that produces large amounts of fine coal particles ticles.. The scope scope of flotatio flotation n techno technolog logy y has been been expanded into many other areas, such as deinking of wastepaper for recycling, water treatment, and separation of plastics. Today flotation deinking annually contri contribute butess about about 130 million millionss tons tons of recov recovere ered d paper to the worldwide paper production. This figure corresponds to about 50% of the annual papermaking capacity.
2
I / FLOTATIO FLOTATION N
Mineral flotation flotation Flotation is widely used to separate valuable minerals from the rock and fine coal particles from clay, silt, shale, and other ash-producing matter. It is usually preceded by crushing and finely grinding the ore to liberate valuable particles in a host rock, and may be followed by metallurgical processes. One of the earliest flotation applications was in the recovery of sphalerite (ZnS) minerals from finel finely y grou ground nd ores ores at Brok Broken en Hill Hill in Austr Austral alia ia 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, edited by D. W. Fuerstenau (see Further Reading), 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 tation.. At presen presentt metall metallic ic and indust industria riall concen concen-trates trates recov recovere ered d by flotati flotation on contin continue ue to increa increase. se. Tabl ablee 1 shows shows the curren currentt annual annual produc productio tion n of some some princi principal pal metall metallic ic and indust industria riall minera minerals, ls, 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 from tar sands by Syncrude which is the world’s 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 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 (below 500 mm) are recovered by flotati flotation. on. Hydroc Hydrocarb arbon on oils, oils, such such as kerose kerosene, ne, B
Table 1
pine oil, and diesel, are used in many coal flotation plants to increase increase the floatability floatability of naturally naturally hydrophobic coal particles. Only a small quantity of methyl isobutyl carbinol (MIBC) (50–100 g per tonne of of material) is used as frother (and collector) in coal flotation. Wastepaper astepaper deinking deinking Flotat Flotation ion has been used used to remove ink particles in wastepaper recycling and is simi simila larr to mine minera rall flota flotatio tion n in many many aspe aspects cts.. Air Air bubbles are used to collect and separate hydrophobic ink ink part partic icle less from from the the pulp pulp of fiber fiberss comp compris risin ing g mostly cellulose. The nonfloated fibers form the deinked inked produc productt of the operat operation ion.. Select Selectivi ivity ty is not critical to flotation deinking but ink recovery is important. The feature of the flotation chemistry is the dual role of the surfactants used as the liberation agent to remove ink from the surface and as the collector to render the librated 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 and diet diethy hyle lene ne tria triami mine ne penta penta acet acetic ic acid acid as the the complexing complexing agent for heavy heavy metals. metals. The The flota flotatio tion n dein deinki king ng mark market et has has grow grown n exextremel tremely y rapidl rapidly y since since 1980. 1980. At prese present, nt, there there are more more than than 600 major major deinki deinking ng system systemss operat operating ing 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 Germ Ge rman an news newspr prin intt pape paperr is made made from from dein deinke ked d wastepaper. Water treatment In water treatment, two flotation techniques commonly used include electrolytic and dissolved air flotation. Electrolytic flotation involves the generation of hydrogen and oxygen bubbles between electrodes. Electric power is supplied at low potential (5–10 V). The energy energy consumption depends depends on the pulp conductivity and the distance between
Annual production of principal metals and mineral concentrates (millions of metric tons) for 2000–2004
Metals (in concentrates) Copper Lead Zinc Mineral concentrates Potash (K2O equivalent) Iron ore Phosphate rock (P2O5 content)
Australia
Canada
China
0.74 0.70 1.35
0.61 0.14 0.97
0.57 0.64 1.63
0.13 0.06 0.06
0.75 0.47 0.81
10.86 3.03 8.61
— 140.04 1.14
8.66 23.03 0.57
0.40 165.53 14.83
— 27.12 1.87
1.20 39.15 22.95
27.10 894.33 88.29
Reproduced with permission from Minerals Yearbook, US Geological Survey, 2006.
South Africa
USA
Total world
I / FLOTATION
the electrodes. The bubbles formed in electrolytic flotation are smaller than 40 mm 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 and 30 m 3 h À 1. In dissolved air flotation, the bubbles are produced by controlling the pressure of water saturated with air. Three main processes of dissolved air flotation include vacuum flotation, microflotation, 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 microflotation, the entire volume of water is subjected to increased pressure by passing the water down and up a shaft approximately 10 m deep or by passing the water through a special mixing-aeration system. In pressurized flotation, which is the most widely used technique at present, air is dissolved in water by applying high pressure. The bubble size depends on the applied pressure but is typically between 20 and 100 mm. Flocculation is often used in flotation applications. The collection and removal of fragile flocs by flotation presents the difficulty of dissolved air flotation. The bubble–floc agglomerates are created by a number of mechanisms, including entrapment of bubbles within a network of flocs, growth of bubbles from nuclei within the flocs, and particle and floc attachment onto bubbles by collision, which is very significant to the flotation process. Flotation of 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 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 À 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
3
treatment techniques for rendering the plastic surface hydrophilic also have potential application. Complex chemistry of many plastics can be a problem in 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 how flotation works, many aspects of flotation have to be considered. The most important aspects can be grouped into the following: *
*
*
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 described briefly.
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.
4
I / FLOTATION
Engineering aspects - Bubble generation - Particle dispersion - Cell design
Flotation
Physical aspects - Hydrophobicity and floatability - Bubble−particle interactions - Froth drainage - Flotation kinetics Figure 2
Aspects needed for a fuller understanding of how flotation works.
Air wa
wm
Mineral Contact angle between an air bubble and a mineral surface in water. Figure 3
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
þ gwa cos y ¼ gma ;
cos y
¼ gma gÀ gwm ½1 wa
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 rgwa . The bubble–particle interaction is often described in terms of the change in the free energy (the work of
À
¼
À
þ
¼À
ma
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 equation [1], giving Dg gwa(1 cos y). In flotation, surfactants are used to control Dg by changing all the components, gwa, gma, and gmw, of the interfacial energies, and hence the contact angle. The Gibbs equation for surfactant adsorption can be used to describe the change in Dg as a function of surfactant concentration. In Figure 4 strong correlations between the contact angle and the flotation recovery, adsorption density of surfactants, and zeta potential are shown.
¼
Water
gwm
Chemical aspects - Mineral surface chemistry - Reagent chemistry - Mineral−reagent interaction
À
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 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.
I / FLOTATION
5
40 20 0 V m , −20 l a i t n e −40 t o p a −60 t e Z
−80 −100 −120
100 y r e v o c e r e g a r e v o c e c a f r u s e l g n a t c a t n o C
Flotation recovery, % 80
Surface coverage, % of monolayer
60
40 Contact angle, degrees
20
0
0
2
4
6
8
10
12
14
pH Flotation of quartz with 4 10 À 5 molL À 1 dodecyl ammonium acetate (positively charged in water) versus contact angle, adsorption density, and zeta (surface) potential. (Reproduced with permission from Fuerstenau MC, Miller JD and Kuhn MC (1985) Chemistry of Flotation . New York: Society of Mining Engineers of the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.)
Â
Figure 4
Mineral Air
Air
Mineral Water
Sessile drop technique
Sessile bubble technique Figure 5
Air
Water
Measurement techniques of contact angles on a mineral surface.
Water Wilhelmy plate technique
6
I / FLOTATION
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 gwa. 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, D p 2gwa cosy=r, is the driving force for a Poiseuille-type flow rate, d pr2 h =dt pr4 D p= 8mh . The Washburn equation is obtained, giving cos y 2mh2 = tr gwa . The
¼
ð
Þ ¼
ð Þ
¼
ð
Þ
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 crosssectional area of the tube and e the void fraction of particles, and d the liquid density. Finally, one obtains m2 t gwa d2 cos y=m rS2 e2 =2 . Typical experimental data shown in Figure 7 confirm the theoretical dependence of m on t . The slope of log(m) versus log(t ) can be used to determine the contact angle. In practice, the last term of the theoretical dependence of m2 on t is usually not known, but it can be determined using a second liquid, such as cyclohexane, which fully wets the particles ( 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. The principle is show in Figure 8. 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
¼
Â
¼
¼ð
Þð
Þ p
ffiffi
¼
Pipette
Solids bed
Porous plug
h
Solution
Equipment with an electronic balance for measuring the liquid mass penetrated into a particle bed as a function of time in the Washburn theory of contact angle on particles. Figure 6
I / FLOTATION
7
6
) 4 g ( s s a M
2
0
0
50
100
150
200
250
Time (s)
¼
Figure 7
Measured (points) mass of water penetrated into silica beads (y 421) versus time. Theoretical curve (line) describing the Washburn equation agrees with the experimental data within the width of the line.
Colloidal sphere
+ Water
Cantilever spring
Bubble C e c r o 0 F
A B D
Detachment force
E
d
−
0
Position
Figure 8
AFM principle of the measurement of contact angles on a colloidal particle. (Reproduced with permission from Preuss M and Butt H-J (1998) Measuring the contact angle of individual colloidal particles. Journal of Colloid and Interface Science 208: 468– 477.)
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 yrec 1 d =Rparticle and F detachment 2pRparticle gaw sin2 yadv =2 . Detachment force and distance, d , can be measured with AFM to determine the receding and advancing contact angles.
ð
Þ¼
¼ À ð
Þ
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 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 the gas flow and
8
I / FLOTATION
Froth layer
Path of floated particles Ground joint
Concentrate stem
Magnetic stirring bar Porous frit Gas inlet
Collected concentrate Stopper
Ralston−Allen 1916 test tube for flotation
Hallimond−Ewer 1952 flotation tube
Magnetic stirrer
Hallimond−Fuerstenau 1955 flotation tube
Figure 9
Test tubes used to determine the particle floatability. (Reproduced from Fuerstenau DW (1999) The froth flotation century. In: Parekh BK and Miller JD (eds) Advances in Flotation Technology , pp. 3–21. Littleton, CO: Society for Mining, Metallurgy, and Exploration, Inc.)
stirring rates constant and varying the amount of * electrostatic double-layer force due to the intercollector, for example, the floatability of the mineral action between diffuse layers of electrolytes conparticles responded to the collector can be evaluated. centrated at the electrically charged surfaces of Many other techniques have also been used, includparticles and bubbles in water, and * ing the ‘bubble-pickup’ technique, which consists of non-Derjaguin–Landau–Verwey–Overbeek pressing a captive bubble against a bed of particles (DLVO) forces. and then counting or weighing the load of particles attached to the bubble. However, the Hallimond The van der Waals and double-layer forces are tubes usually give the best reproducibility. fairly well investigated, both theoretically and experimentally. They form the basis of the DLVO theBubble–Particle Interactions ory of colloidal stability and are referred to as DLVO Since contact angle and work of adhesion are the forces. The hydrophobic attraction between hydrothermodynamic variables, they only describe the phobic surfaces in water, which is one of many other overall free-energy change occurring before and after non-DLVO forces, is the most relevant to flotation. The van der Waals force, F vdW, can be determined the bubble–particle contact. To examine the intermediate stages of the bubble–particle interaction using the macroscopic (Hamaker) and/or the microwith an intervening liquid film, we need to know the scopic (Lifshitz) theories. For bubble–particle intersurface force interaction between a bubble and a actions, the most recent expression derived from the particle in water and the dynamics of bubble–particle combined Hamaker–Lifshitz theory gives interactions. 2Rp Rb dEvdW d A F vdW Surface forces Wetting films between a bubble and dr dr 6 r2 Rp Rb 2 a solid surface, and the associated molecular forces 2Rp Rb have been investigated since the 1930s. Briefly, sumr2 Rp Rb 2 mation of all the interactions among atoms, ions, and molecules constituting the particle, bubble, and r2 Rp Rb 2 intervening liquid film gives a force acting between ln 2 2 2 r R R p b the bubble and particle surfaces, known as the surface force, which is proportional to the particle and bubble surface area (radius), and inversely propor- where EvdW is the van der Waals interaction energy. tional to the (shortest) inter-surface separation dis- The inter-center bubble–particle distance, r, is related tance. Surface force has a number of components to the shortest separation distance, H , between their with different molecular origins, which include surfaces by r H Rp Rb, where Rb and Rp are the bubble and particle radii, respectively. The * van der Waals force due to the dipolar (electroHamaker–Lifshitz function, A, is also a function of dynamic) interactions among atoms and mole- H due to the electromagnetic retardation and is cules, defined as A A0 1 2kH eÀ2kH Ax H , where k
À
¼
("
Àð þ Þ
þ Àð À Þ þ ÀÀ ðð þÀ ÞÞ
¼ þ þ
¼ ð þ
Þ
þ ð Þ
#)
½
I / FLOTATION
is the Debye constant (defined later). The zero-frequency, A0, and nonzero frequency, Ax, terms are described by A0
¼ 3k4BT
Ax H
N
m
m 1
ð Þ ¼ À 0:235_o Â
(
79 80 81 80
X À& ¼
n2p
3
À 1:887 n2p À 1
m
þ
e e
n2p
þ 1:887ÞÀ1=2
)
where q 1.185, kB 1.381 10 À 23 J K À 1 is the Boltzmann constant, T the absolute temperature, e the static dielectric constant of the mineral particle, 1.05459 10 À 34 Jsrad À 1 is the Planck constant _ divided by 2p, n p the particle refractive index, o 2 1016 rads À 1, and lp a modified London wavelength accounting for the retardation effect, defined as lp nm 9:499= n2p 1:887. If e is not known, the first-order approximation, A0 0.75kBT , can be used since the m-infinite sum for 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 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 (o50 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 on 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 ( r50– 60 mV), the Hogg–Healy–Fuerstenau approximation
¼
¼ ¼ Â
¼
þ
where zp and zb are the particle and bubble surface (zeta) potentials, e0 8.854 10 À 19 C2 J À 1 m À 1 is the permittivity of the vacuum, er the dielectric constant (relative permittivity) of the medium ( er 80 for water), and k the Debye constant (reciprocal length) described by
q ffiffi ffi ffiþffi ffi ffi ffi ffi ffi ffi ffi
¼
Â
¼
k2
Â
Â
ð Þ¼
¼
ð Þ À z2p À z2b ½3 ð ÞÀ1
Rp Rb 2zp zb exp kH 2per e0 k Rp Rb exp 2kH
¼
ð À ½1 þ ðH =5:59Þq1=q ½1 þ ðH =lp Þq1=q 0:588
for the double-layer force, F edl, at constant surface potentials gives F edl
À'
9
¼
nX
z2i e2 N A 1000ci = er e0 kB T
ð
o
Þ
where e 1.602 10 À 19 C is the charge of a proton, ci the molar (mol L À 1) concentration of electrolyte ions of type i in the bulk solution with the valence zi, and N A 6.022 1023 molecules mol À 1 the Avogadro number. If the condition of constant surface charge density is considered, the double-layer force can be determined as F edl
¼
¼
Â
¼
Â
ð Þ þ z2p þ z2b ½4 ð ÞÀ1
Rp Rb 2zp zb exp kH 2per e0 k Rp Rb exp 2kH
þ
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. The hydrophobic (non-DLVO) force is not predictable at present and the following empirical expression can be used: F hydrophobic
¼À
Rp Rb K exp Rp Rb
þ
H
À l
½5
where K is a force constant, and l 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 (see Further Reading). Sometimes, the doubleexponential function with two force constants and two decay lengths are used to describe the longranged 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 conditions.) B
10
I / FLOTATION
Summing the double layer, van der Waals and hydrophobic interaction forces give a good approximation of the total surface force, F s, between a bubble and a particle, described by F s
¼ F vdW þ F edl þ F hydrophobic
½6
From the above equation, 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 intersurface 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. 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 the particle motion can be divided into *
*
*
Volume forces such as particle weight, buoyancy, and inertial forces, which are proportional to the particle volume and 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 intersurface separation distance. Hydrodynamic forces due to the resistance of liquid films between the surfaces. These microhydrodynamic forces also depend on the intersurface separation distance.
Summing up the governing forces gives the following equation of motion of particles: 4pR3p rp dV 3 dt
¼
4pR3p rl dW 3 dt 3 4pRp rp
þ
4pR3p rl d V W 6 dt
ð À Þ À Fd À ð À rl Þ g þ F ½7 s 3
where V and W are the velocities of particle and liquid, relative to the bubble; rp and rl the particle and liquid densities; t is the reference time; g the acceleration due to gravity; Fd the steady drag force with inclusion of corrections for the microhydrodynamic
0.2 Hydrophobic force parameters: K = 0.5 mN m −1 = 12.85 nm 0.1 )
1
−
m N n ( e c r o F
0 0
20
40
60
80
H (nm)
100
van der Waals force −0.1
Hydrophobic force Double layer force (CPI) Net force
−0.2
(a) 0.2
Hydrophobic force parameters: K = 1.5 mN m −1 = 5 nm
0.1 )
1
−
m N n ( e c r o F
0 0
20
40
60
80
100
H (nm)
van der Waals force −0.1
Hydrophobic force Double layer force (CPI) Net force
−0.2
(b) 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 mm, R p 1.475 mm, zb 62mV, À1 zp 19mV, n p 1.59, k 0.042 nm , T 201C; (b) R b 23.1 mm, R p 1.475 mm, zb 25mV, zp 4mV, n p 1.59, k 0.042 nm À 1, T 201C. Strong attractive surface force in (b) causes the particle attachment to the air bubbles, as experimentally observed. Figure 10
¼À ¼ ¼
¼
¼ ¼ ¼
¼ ¼ ¼À ¼
¼À ¼ ¼À
interactions with liquid films; and Fs describes the surface forces acting between the bubble and particle surfaces. The variables in boldface 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. It is difficult to solve eqn [7] analytically. Simple approximate solutions can be obtained by considering different physical nature of the forces and scaling
I / FLOTATION
R c
y
Particle trajectory
Particle grazing trajectory
F d
F b
H
Bubble
U
r
F g
F s
c x
Bubble
Figure 11
Grazing trajectories of particles around a rising bubble define the particles within the path of the bubble rise to be collected. The inset 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.
11
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. 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 j 51.81, a non-DLVO attractive (hydrophobic) force with K 1.5mNm À 1 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
¼
75
¼
¼
75
DLVO forces + non-DLVO attractive force 50
50
25
25
) m μ (
) m μ (
y
y
0
0 0
25
−25
50
−25
Only DLVO forces
Only DLVO forces
DLVO forces + non-DLVO attractive force
Without surface forces Without surface forces −50
x
(μm)
−50
0
25 x
50
(μm)
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
12
I / FLOTATION
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 on the right diagram in Figure 12, the predicted outgoing trajectories are significantly influenced by the surface forces. Specifically, to match the experimental trajectory, hydrophobic attractive force has to be included in eqn [6] for the model predictions. Froth Drainage
The use of froth in flotation is twofold. First, froth is used to convey the mineral-laden bubbles from the froth–pulp interface to the concentrate launder. Second, 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 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 compli-
cated 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 rise to the following expression for the superficial liquid recovery rate J l: J l
rl gA ¼ J g 1 Àel e À 150 el m
½8
l
where J g is the superficial gas velocity, el the liquid fraction, m and rl are the liquid viscosity and density, g the acceleration due to gravity, and A 3 p=2 r2 the cross-sectional area of the PB with radius r, where r 1:734Rb el 1 el 1=3 = 1 0:765e0l :409 . The first term in eqn [8] describes the influence of the gas momentum, and 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
¼
¼ ðp À Þ
ffiffi
p ð À Þ ð þ
ffiffi ffi
Þ
Polyhedral bubbles (Dry froth) Bubble Water
Bubble Packed bubble bed
Bubble
Bubble
Froth
Expanded bubble bed (Wet froth)
Pulp Figure 13
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 AV and Schulze HJ (2004) Colloidal Science of Flotation . New York: Marcel Dekker.)
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E pR2b h C q= 4pR3b =3 . The mass balance then gives
ð
25
Þ ð ð
ÞÞ
dN dt
20
¼ ÀE pR2bh C 4pRq3=3
À Á
½9
b
where N is the total number of particles in the cell with volume V c. The left-hand side of eqn [9] describes the rate of the decrease 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
) % ( a 15 c i l i s f o y r e v o 10 c e R
¼
ð À Þ
dC dt
¼ ÀkC
½10
where k is the rate constant of flotation described by
5
k 0
13
0
10
20
30
40
Recovery of water (%) Recovery of entrained silica gangue at different size fractions: 12 mm ( ); 23.3–32.3 mm ( ); and 46 mm (m). (Reproduced with permission from Nguyen AV and Schulze HJ (2004) Colloidal Science of Flotation . New York: Marcel Dekker.) Figure 14
À
Â
þ
4R 3E b 1 À e g
À Á
q V c =h
¼ 4 13EÀ e
À Á g
J g Rb
¼ 4 1ESÀbe ½11
À Á g
with J g being the superficial gas velocity and Sb 3 J g =Rb the bubble surface area flux. Eqn [10] can be integrated to give R t
ð Þ ¼ 1 À expðÀkt Þ
¼
½12
C 0 C t =C 0 is the flotation rewhere R t covery. Eqns [10] and [12] describe flotation kinetics of the first order. Deviation 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 (see Further Reading). 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 flotaFlotation Kinetics tion recovery under steady-state condition can be As the bubbles rise in the flotation cell they collect determined by eqn [12], giving R 1 exp kt . particles with a collection efficiency, E, and carry For flotation running under the condition of perfect them out of the cell. The total number of particles mixing one obtains R kt= 1 kt . For flotation collected and removed from the cell by a bubble as operating between the plug-flow and perfect mixing air rises through the suspension, with the particle regimes, the recovery also depends on the particle concentration C , in the cell of depth h is E pR2b h C . dispersion in the cell in a more complicated way. If the gas volumetric flow rate is q, the number of Mixing often has a detrimental effect upon recovery. bubbles formed per unit time is q= 4pR3b =3 . The rate For example, for t 5min and k 0.5 min À 1, the of removal of particles from the cell is then equal to recovery in plug-flow regime is 92%, while recovery 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.
ð Þ f ð Þ À ð Þg ð Þ
¼
ð
ð
Þ
¼ À ð þ Þ
Þ
¼
¼
ðÀ Þ
14
I / FLOTATION
1 Impeller mechanism
)
1
n 0.8 i m 1 ( t n a 0.6 t s n o c e t 0.4 a r n o i t a t o 0.2 l F
Pipsa
0
50
−
Chile-X Outokumpu Dorr-Oliver
100
150
200
250
−1
Bubble surface area flux (1 s ) 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 AV and Schulze HJ (2004) Colloidal Science of Flotation . New York: Marcel Dekker.) Figure 15
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 (see Further Reading).
Chemical Aspects of Flotation Surface Chemistry of Minerals in Water
Minerals with nonpolar surface characteristics Only a few mineral surfaces, such as graphite, coal, sulfur, talc (Mg3Si4O10(OH)2), and molybdenite (MoS2), are not readily wetted by water. These minerals are composed of covalent molecules held together by van der Waals (nonpolar) forces which produce special crystal lattice structures with nonpolar 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 nonpolar 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 901. 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, MIBC is used as
both collector and frother, and kerosene or diesel can be used to increase the coal floatability. Similarly, graphite, which sometimes occurs as a gangue mineral in sulfide ores, can be removed by flotation with MIBC and hydrocarbon oils. Some auriferous ores contain a significant amount of carbonaceous materials, which can be floated with oil and frother, and burned to recover any combined gold. Bitumen in tar sands is one of the significant fuel minerals. This insoluble liquid oil is inherently hydrophobic and is presently recovered by a hot-water flotation process. The hydrophobicity and floatability of bitumen are reduced by clay minerals (e.g., montmorillonite in presence of Ca2 þ ) in the oil sands. A number of man-made particles also have 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) Sulfide minerals (e.g., galena PbS, sphalerite ZnS, chalcopyrite CuFeS 2, pyrite FeS2, and chalcocite Cu2S)
I / FLOTATION
*
*
*
Insoluble minerals (e.g., oxides, silicates, chromates, and vanadates of many multivalent metals) Sparingly soluble minerals (e.g., carbonates, phosphates, and calcite CaF 2) Soluble salt minerals (e.g., halite NaCl, sylvite KCl, trona Na3(HCO3)(CO3) 2H2O, and borax Na2B4O7 10H2O).
Á
Á
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, and 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 Al2O3, 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. 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 low solubility although each has theoretically a definite ionic solubility product in water. However, the surface of sulfide minerals is usually unstable in the presence of water and oxygen, catalyzing the sulfide surface oxidation. The oxidation is very slow in dry air. In water, the oxidation of sulfide minerals is very intensive, following electrochemical reactions similar to the corrosion of metals and semiconductors (a few sulfides are intrinsically semiconductors). Oxidation of sulfide minerals can proceed through successive steps producing various sulfur products, from elementary sulfur, through different intermediate sulfur oxides such as S 2O23 À (thiosulfate) and S 4O26 À (tetrathionate), to sulfate, SO24 À . 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.
Á
15
Many sulfide minerals possess natural hydrophobicity and floatability to a varying extent. Molybdenite, stibnite, realgar (AsS), and orpiment (As2S3) are naturally hydrophobic. The natural hydrophobicity of these sulfide minerals is related to their special crystal structures as discussed earlier. A number of sulfide minerals can be floated without the use of any collector under some special conditions. This collectorless flotation is due to self-induced hydrophobicity of the sulfide minerals, acquired by surface reaction with atmospheric oxygen and water. For instance, clean galena (PbS) free of oxidation products is known to be floatable without treatment with xanthate or any surfactant. The collectorless flotation of sulfide minerals can be due to the oxidation of S2 À 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 metaldeficient sulfides, which are hydrophobic. The formation of polysulfide or metal-deficient species is common at pH48, while elemental sulfur occurs at pHo6. The ease of collectorless flotation follows the order chalcopyrite4galena4sphalerite. 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 À ions with the metal cations inserted into the crystal interstices (silica, SiO 2, is a special case, in that the Si–O bond is tetrahedrally arranged around each silicon atom, Si 4 þ , which is regarded as semicovalent). 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 edl. The ionic surfaces of the oxide minerals are amphoteric and can take up either a proton or an OH À ion depending on the pH, which can become either positively 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 B
