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The Limits of Fine and Coarse Particle Flotation Carlos de F. Gontijo, Daniel Fornasiero and John Ralston* Ian Wark Research Institute, University of South Australia, Mawson Lakes Campus, Mawson Lakes, Adelaide, SA 5095, Australia The flotation behaviour of quartz particles was studied over the particle size range from 0.5 µm to 1000 µm and for advancing water contact angles between 0º and 83º. Flotation was performed in a column and in a Rushton turbine cell. Particle contact angle th
   VOLUME 85, OCTOBER 2007 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING 739 INTRODUCTION F roth flotation is a process designed to separate hydropho-bic particles selectively in an aqueous medium, in which gas bubbles are dispersed. Hydrophobic particles selectively attach to the gas bubbles, forming aggregates. If the aggregate density is lower than the medium density the aggregates float to the top of the separation cell, where they overflow into a launder (Schulze, 1993; Shergold, 1984). The flotation of mineral sulphides and oxides, for example, operates most efficiently when the particle diameter is between 10 and 150 µ m (Shergold, 1984). Coarse and fine particles are often not recovered during the flotation process, or are recovered poorly.Flotation is achieved in part by increasing the hydrophobicity of the particles (Lucassen-Reynders and Lucassen, 1984). The degree of hydrophobicity can be expressed by the contact angle, the angle at the three-phase line of contact between the mineral, The Limits of Fine and Coarse Particle Flotation Carlos de F. Gontijo, Daniel Fornasiero and John Ralston * Ian Wark Research Institute, University of South Australia, Mawson Lakes Campus, Mawson Lakes, Adelaide, SA 5095, Australia the aqueous phase and the air bubble (Gaudin, 1957). It is accepted that the higher the contact angle of a mineral surface, the more readily it is wetted by air, and is thus more hydropho-bic (Lucassen-Reynders and Lucassen, 1984; Gaudin, 1957). Particle hydrophobicity or contact angle is dependent on the type and distribution of species present on the mineral surface (Crawford et al., 1987). Generally, the mineral particle surface may be covered with hydrophobic (e.g. collector, polysulphide) and hydrophilic species (oxide, hydroxide, and sulphate) as well as with different mineral phases, as found in composite particles (Prestidge and Ralston, 1995). Recovery decreases with increas-ing particle size because of detachment and decreases at small particle sizes due to inefficient collision (Dai et al., 2000). The flotation behaviour of quartz particles was studied over the particle size range from 0.5 µ m to 1000 µ m and for advancing water contact angles between 0º and 83º. Flotation was performed in a column and in a Rushton turbine cell. Particle contact angle threshold values, below which the particles could not be floated, were identified for the particle size range 0.5–1000 µ m, under different hydrodynamic conditions. The  flotation response of the particles, either in a column or in a mechanically agitated cell with a similar bubble size, was comparable. Turbulence plays a role, as does bubble-particle aggregate velocity and bubble size. The stability of the bubble-particle aggregate controls the maximum  floatable particle size of coarse particles. For fine particles, the flotation limit is dictated by the energy required to rupture the intervening liquid  film between the particle and bubble. Flotation of very fine and large particles is facilitated with small bubbles and high contact angles. These results greatly extend our earlier observations and theoretical predictions. On a étudié le comportement de flottation de particules de quartz pour des tailles de particules comprises entre 0,5 µm et 1000 µm et des angles de contact de l’eau de 0º et 83º. La flottation a été réalisée dans une colonne et dans une cellule munie d’une turbine Rushton. Les valeurs de seuils des angles de contact, en dessous desquels les particules ne pouvaient pas flotter, ont été identifiées pour une gamme de particules de 0,5-1000 µm, dans différentes conditions hydrodynamiques. La réponse de flottation, dans une colonne ou dans une cellule agitée mécaniquement avec une taille de bulles similaire, est comparable. La turbulence exerce une influence, tout comme la vitesse des agrégats de bulles et de particules et la taille des bulles. La flottation des particules très fines et des particules larges est facilitée avec des bulles petites et des angles de contact élevés. Ces résultats élargissent de façon importante nos observations et prédictions théoriques antérieures. Keywords: coarse particle flotation, detachment, stability, critical contact angle, kinetic theory of flotation * Author to whom correspondence may be addressed.  E-mail address:   740 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING VOLUME 85, OCTOBER 2007 There is an upper size limit for floatable particles (Schulze, 1984; Glembotskii et al., 1963). The balance of forces acting on the particle and bubble will determine the aggregate stability. Coarse particles, whether they are of one type or composite, can be detached from the bubble surface (Crawford and Ralston, 1988). After attachment, two conditions are necessary for flotation: aggregate stability and buoyancy (Wark, 1933). Consider a spherical particle at the liquid/gas interface as shown in Figure 1. In the following analysis r b  is the bubble radius, r p  is the particle radius, r o  is the radius of the three-phase contact line, a  is the acceleration in the external field of flow, υ b  is the bubble velocity, υ p  is the particle velocity, ρ p  is the particle density, ρ l  the liquid density, γ  LV  is the liquid-vapour surface tension, ρ  is the gravitational acceleration, and z o  and ω  are defined in Figure 1. According to Huh and Scriven (1969) and Schulze (1993, 1977) the forces acting on a spherical particle at a static liquid/gas interface can be described by the following equations:ã the force of gravity;  Frg   gpp = 43 3 p ρ  (1)ã the static buoyancy force of the immersed part;  Frg  bpl = − ( )  + ( ) pρ ω ω 312 32 coscos (2)ã the hydrostatic pressure of the liquid of height z o  above the contact area;  Frgzrgz hydlpl = =  ( ) p ρ p ω ρ 020220 sin (3)ã the capillary force on the three-phase line;  Fr  cap = + ( ) 2 p γ ω ω q sinsin (4)ã the capillary pressure in the bubble acting on the contact area of the particle;  FrPr r rg   pbpbbl = ≈ −      p p ω γ ρ 0222 22sin (5)Additional detaching forces, for instance represented by the acceleration provided by a mechanical impeller, can be accounted for as the product of the particle mass and the acceleration in the external flow field:  Fra app = 43 3 p ρ  (6)Huh and Scriven (1969) developed a numerical solution that can be used to calculate z o , whilst approximate solutions have also been proposed (James, 1974):  zr  gr  oplp LV  =+ ( )           − sinsinlnsincos. ω fρ ωγ  f 4105 22 88   (7)where f  = ω  + q  – p  (in degrees) (8)The capillary force, the buoyancy force of the immersed part and the hydrostatic pressure all contribute to the particle attach-ment at the gas/liquid interface, whilst the force of gravity, the capillary pressure and the additional external acceleration act to detach the particle. The sum of all the forces dictates whether or not the particle detaches from the liquid/gas interface or remains attached, Σ    F = F   g   + F  b  + F  hyd  + F  ca  + F   p  + F  a  (9)The maximum floatable particle size can be calculated by solving Equation (9) numerically. Schulze assumed that when d p   <<  d b  the effect of the capillary pressure of the gas bubble was negligible (Schulze, 1984; Schulze, 1977). Neglecting the hydrostatic term and considering that the static buoyancy of the immersed part of the particle is approximately equal to the buoyancy for the whole sphere (Equation (10)) Schulze derived an approximate solution to calculate the upper floatable particle size (Equation (9)),  Frg  bpl ≈ 43 3 p ρ  (10)Equating Equation (4) and Equation (10) with Equation (1) and Equation (6), one obtains, d ga  pg  p max, sinsin()() = ++ 232 γ ω ω qρ ρ∆  (11)where d pmax,g  is the maximum size of the particle that can stay attached to the liquid/gas interface, under static conditions. Schulze (1977) showed that the energy necessary for detach-ment, E d  is  EFdh dhh eqcrit  =  ( ) ∫   Σ  (12)where h eq  is the equilibrium position of the particle at the liquid/gas interface, h crit is the maximum displacement of the particle before detachment and ∑  F is the summation of all the forces acting on the particle (Equation (9)). Schulze (1977) found that in a freely moving system, as in flotation, particles could only be loaded up to the maximum attachment force, ∑  F max , which occurs when: ω q≈ − 1802º (13) Figure 1 . Spherical particle located at the liquid/gas interface (Schulze, 1977, 1984, 1993; Huh and Scriven, 1969). r  p  is the particle radius, r  o  is the radius of the three-phase contact line, h is the immersion depth of the particle, H is the height of the spherical cap above the meniscus; z o  is the height of the meniscus above the three-phase line (deformation of the liquid meniscus at the solid surface), q  is the particle contact angle, Φ  is the polar angle, i.e., the angle between the surface tension direction (the tangent of the meniscus at the three-phase line) and the horizontal, ω  is the central angle at the particle, i e., the angle between the surface tension direction and the vertical downwards, γ  LV   is the liquid-gas surface tension.     VOLUME 85, OCTOBER 2007 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING 741 0.4–5 µ m A90–150 µ m B150–250 µ m C50–1000 µ m DA small quantity of very coarse particles, up to 3.5 mm in diameter, was prepared for the bubble pick-up experiments.The quartz particles were cleaned with hot aqua regia  for 2 h and then rinsed with high-purity water until the pH became neutral. They were then exposed to a hot concentrated NaOH solution to remove organic contamination and again rinsed with high-purity water until the pH became neutral. Trimethylchlorosilane (TMCS) solutions were used for particle methylation (Crawford et al., 1987). Since TMCS reacts with water, the methylation reaction was performed in a glove box under a dry nitrogen atmosphere. Phosphorus pentoxide was used as a drying agent. To prepare the required volume of solutions, TMCS was delivered using a micro-syringe and diluted in cyclohexane. The quartz samples were weighed into a reactor flask and then heated in a clean oven at 110 º C overnight to remove the physisorbed water. The TMCS solution was placed in the reactor flask for the silylation process. Using different TMCS concentrations and reaction times, different particle contact angles were obtained. The quartz particles were then allowed to settle and rinsed with cyclohexane. The cyclohexane was removed and the flask containing the particles was transferred to a clean oven to dry overnight at 110°C. The measurements of contact angle on the particles used in the flotation experiments were carried out using the Washburn, sessile-drop, tape and film techniques (e.g. Bröckel and Löffler, 1991; Crawford et al., 1987). All glassware was cleaned and methylated before use, using the same procedure as for the particles.The additional acceleration, a , depends on the structure and the intensity of the turbulent flow field, thus on the turbulent energy dissipation, ε , in a given volume of the flotation cell (Schulze, 1993). Schulze assumed that aggregates, the dimensions of which correspond to those of the turbulent vortices, are moved mainly by the centrifugal acceleration in the vortex. If r v  is the radius of the vortex in the turbulent eddies and V  2  is its root mean square velocity, then aV r r  vv ≈ = 22313 19./ // ε  (14)For aggregates, where the particle size is smaller than the bubble size, the vortex radius should be set equal to the aggregate radius. Hence, a   ≈  1.9 ε   2/3 /(r b + r p ) 1/3  (15)Hui (2001) derived an expression for the average acceleration of the attached particle, as a function of the mean energy dissipa-tion in the flotation cell, when the turbulent eddies and the particle have similar size. arr  bp   =+ ( ) 235 2313 . // ε  (16)where ε – is the average energy dissipation in the flotation cell.The existence of a critical contact angle, necessary for the flotation of fine particles, was first proposed by Scheludko et al. (1976). The kinetic energy of fine particles must be larger than the energy needed to disrupt the intervening liquid film and form a three-phase contact line, enabling bubble-particle attach-ment to occur. When these energies are in balance, the minimum particle diameter, d p(min) , is given by d-  pbLVpfr    (min) cos /  - = ( ) ( )  2 321 2 13 τυ γ ρ ρ q  (17)where τ  is the solid-liquid-vapour three-phase contact line tension, and q r  is the receding particle contact angle. During the process of bubble-particle attachment, the three-phase contact line expands and the liquid front recedes, so that a receding water contact angle is used in Equation (17). The Scheludko et al. (1976) approach has not been validated to date, due to the lack of experimental data for very fine particles and the paucity of reliable line tension determinations (Amirfazli and Neumann, 2004).The purpose of this present study is to explore the limits of flotation for extremely fine and coarse particles under very differ-ent hydrodynamic conditions and particle hydrophobicities. EXPERIMENTAL SECTION Flotation experiments were performed in a microflotation column and in a Rushton turbine cell. Analytical grade reagents were used throughout the experiments. High purity water, with conductivity ≤  0.8 µ S, pH 5.6, γ   = 72.8 mNm –1  at 20ºC was used in the microflotation experiments. Flotation in the Rushton turbine cell was performed using deionized water. Experiments were performed at 25ºC. The particles used in the experiments were pure, crystalline quartz (Sigma and G. Bottley Pty Ltd., London). Particles were prepared by grinding, sieving and sedimentation, as necessary, in the following size fractions: Figure 2 . Apparatus for captive bubble pick-up experiments. A bubble, generated using a syringe, was held at the end of the needle. It was pressed against particles with known water advancing contact angle for 5 s and then raised by a motor at a constant velocity. The experiments were recorded using a high-speed camera.     742 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING VOLUME 85, OCTOBER 2007 The experimental apparatus for the bubble pick-up experi-ment consists of a syringe linked to a precision motor, enabling the syringe to move vertically downwards or upwards at constant velocity (Figure 2). Particles were placed into a vial with a transparent wall, containing high-purity water. Using the motor-driven syringe, a bubble was pressed against a particle for attachment to the bubble. After this the syringe was driven upwards at constant velocity. In these experiments a slow (20 µ m/s) and a fast (200 µ m/s) velocity were used. Experiments were repeated at least six times for each velocity. It is important to note that there is an initial acceleration before constant velocity is achieved. Using a microscope and a high-speed camera, images of the experiment were recorded. Particle and bubble sizes were measured using the images. Diagnostic single bubble capture experiments were also performed for Figure 3 . Maximum size of quartz particle (d pmax,g ) that could be raised by a captive bubble in high purity water as a function of the particle water advancing contact angle for various bubble sizes (d b ) and rising velocities (  ν b ) of (  ) d b  = 1.8 mm,  ν b  = 20 µm/s; ( ♦ ) d b  = 1 mm,  ν b  = 20 µm/s; ( ∆ ) db = 1 mm,  ν b  = 20 µm/s). The lines were calculated using Equation (11), with the external acceleration, a  as a  fitting parameter. The external acceleration used are respectively, (1) a = 0 ms –2 ; (2) a = 0.5 ms –2 ; (3) a = 7.2 ms –2 ; (4) a = 14.6 ms –2  (particle density ( ρ p ) = 2650 kg/m 3 ; surface tension ( γ  LV  ) = 72.8 mNm –1 ). Figure 4 . Quartz (sample B) recovery after 8 min of flotation obtained in a flotation column as a function of particle size and advancing water contact angle of (  ) 25º; ( ○ ) 49º; ( ■ ) 51º, (  ) 52º; ( ∆ ) 57º; (  ): 62º ( γ   = 72.8 mNm -1 ; ρ p  = 2650 kg/m 3 ; d 50  = 153 ± 4 µm; d b  = 0.8 ± 0.7 mm; magnetic stirrer rotational speed = 547 ± 4 rpm; Re  f   = 1573; gas flow rate = 4.3 ± 0.4 cm 3 /min) Figure 5 . Quartz (sample C) recovery after 8 min of flotation obtained in a flotation column as a function of particle size and advancing water contact angle of (  ) 21º, ( ■ ) 42º, (  ) 58º; (  ) 59º; ( ∆ ) 69º; ( ○ ) 74º ( γ   = 72.8 mNm -1 ; ρ p  = 2650 kg/m 3 ; d 50  = 262 ± 10 µm; d b  = 0.9 ± 0.7 mm; magnetic stirrer rotational speed = 560 ± 10 rpm; Re  f   = 1582; gas  flow rate = 4.6 ± 0.4 cm 3 /min) Figure 6 . Quartz recovery after 8 min of flotation obtained in a Rushton turbine cell as a function of particle size and advancing water contact angle of ( ◊ ) 40º; ( ▲ ) 57º; ( ○ ) 75º; ( ■ ) 83º ( ρ p  = 2650 kg/m 3 ; d 50  = 353 ± 8 µ m; [DF250] = 20 mg/l; d b  = 0.7 ± 0.3 mm; rotational speed = 650 ± 4 rpm, turbulent energy dissipation = 6.46 m 2 /s 3 ; Re  f   = 26063; gas  flow rate = 4.5 l/min) sample A using procedures that we have described elsewhere (Dai et al., 1998).Column flotation was performed in a modified Hallimond tube (Crawford and Ralston, 1988; Blake and Ralston, 1985). A porous steel plate was used to generate a swarm of bubbles at the bottom of the tube. A glass magnetic stirrer was used to suspend the particles (Crawford and Ralston, 1988; Blake and Ralston, 1985). For each flotation experiment, 1 g of quartz was placed in the cell. The column was then assembled and filled with high purity water (the total volume was 200 cm 3 ). The quartz particles were then conditioned for one minute. The agitation was adjusted to a rotation speed that was just enough to suspend the particles. At the beginning of flotation the solid concentration of the suspension was approximately 27 wt.%. Images of the bubbles were recorded and the bubble size was analyzed using ImageJ software. Flotation under turbulent conditions was performed using a 2.25 L Rushton turbine cell, agitated by an overhead motor with variable speed capacity (Duan et al., 2003). The impeller speed was adjusted and confirmed independently using an optical tachometer. For each experiment 100 gram of particles was placed in the cell and conditioned for 1 min with 8 x 10 –5  M polypropylene glycol (MW 25º). The solid concentration in the cell was approximately
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