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The limits of fine and coarse particle flotation.


Froth flotation is a process designed to separate hydrophobic 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 [micro]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 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 hydrophobic (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 increasing particle size because of detachment and decreases at small particle sizes due to inefficient collision (Dai et al., 2000).

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.sub.b] is the bubble radius, [r.sub.p] is the particle radius, [r.sub.o] is the radius of the three-phase contact line, a is the acceleration in the external field of flow, [[upsilon].sub.b] is the bubble velocity, [[upsilon].sub.p] is the particle velocity, [[rho].sub.p] is the particle density, [[rho].sub.l] the liquid density, [[gamma].sub.LV] is the liquid-vapour surface tension, [rho] is the gravitational acceleration, and [z.sub.o] and [omega] 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:

* the force of gravity;

[F.sub.g] = 4/3 [pi][r.sup.3.sub.p][[rho].sub.p.sup.g] (1)

* the static buoyancy force of the immersed part;

[F.sub.b] = [pi]/3 [r.sup.3.sub.p [[rho].sub.t]g[(1- cos[omega]).sup.2] (2 + cos [omega]) (2)

* the hydrostatic pressure of the liquid of height [z.sub.o] above the contact area;

[F.sub.hyd] = [pi][r.sup.2.sub.0][[rho].sub.t] g [z.sub.0] = [pi][r.sup.2.sub.p] ([sin.sup.2][omega])[[rho].sub.t] g [z.sub.0] (3)

* the capillary force on the three-phase line;

[] = 2[pi][r.sub.p] [gamma] sin [omega] sin ([omega] + [theta] (4)

* the capillary pressure in the bubble acting on the contact area of the particle;

[F.sub.p] = [pi][r.sup.2.sub.0][P.sub.b][approximately equal to][pi][r.sup.2.sub.p] [sin.sup.2] [omega] (2[gamma]/[r.sub.b] - 2[r.sub.b] [[rho].sub.t] g) (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:

[F.sub.a] = 4/3[pi][r.sup.3.sub.p][[rho].sub.p]a (6)

Huh and Scriven (1969) developed a numerical solution that can be used to calculate [z.sub.o], whilst approximate solutions have also been proposed (James, 1974):

[z.sub.o] - [r.sub.p] sin [omega] sin [phi] [ln(4/[square root of [[rho].sub.t] g [r.sup.2.sub.p] [sin.sup.2] [omega]/[[gamma].sub.LV] (1 + COS [phi])) - 0.58] (7)

where [phi] = [omega] + [theta] - [pi] (in degrees) (8)

The capillary force, the buoyancy force of the immersed part and the hydrostatic pressure all contribute to the particle attachment 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,

[summation] F = [F.sub.g] + [F.sub.b] + [F.sub.hyd] + [] + [F.sub.p] + [F.sub.a] (9)

The maximum floatable particle size can be calculated by solving Equation (9) numerically. Schulze assumed that when [d.sub.p] < < [d.sub.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)),

[F.sub.b] [approximately equal to] 4/3 [pi][r.sup.3.sub.p] [[rho].sub.t] g (10)

Equating Equation (4) and Equation (10) with Equation (1) and Equation (6), one obtains,

[d.sub.pmax,g] = 2 [square root of 3 [gamma] sin [omega] sin ([omega + [theta]) / 2([DELTA] [rho] g + [[rho].sub.p] a (11)

where [d.sub.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 detachment, [E.sub.d] is


where [h.sub.eq] is the equilibrium position of the particle at the liquid/gas interface, [h.sub.crit] is the maximum displacement of the particle before detachment and [SIGMA] 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, [summation] [F.sub.max], which occurs when:

[omega] [approximately equal to] 180[degrees] - [theta]/2 (13)


The additional acceleration, a, depends on the structure and the intensity of the turbulent flow field, thus on the turbulent energy dissipation, ?, 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.sub.v] is the radius of the vortex in the turbulent eddies and [absolute value of [bar.[v.sup.2]]] is its root mean square velocity, then

a [approximately equal to] [bar.V.sup.2]]/ [r.sub.v] = 1.9 [[epsilon].sup.2/3 / [r.sub.v.sup.1/3] (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 [approximately equal to] 1.9[[epsilon].sup.2/3 / [([r.sub.b] + [r.sub.p]).sup.1/3] (15)

Hui (2001) derived an expression for the average acceleration of the attached particle, as a function of the mean energy dissipation in the flotation cell, when the turbulent eddies and the particle have similar size.

a = 23.5 [bar.[[epsilon].sup.2/3]] / ([r.sub.b] + [r.sub.p]).sup.1/3] (16)

where [bar.[epsilon]] 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 attachment to occur. When these energies are in balance, the minimum particle diameter, [d.sub.p(min)], is given by

[d.sub.p(min)] = 2 [[3[[tau].sup.2]/[[upsilon].sup.2.sub.b] [[gamma].sub.LV] ([[rho].sub.p] - [[rho].sub.f]) (1 - cos [[theta].sub.r])].sup.1/3] (17)

where [tau] is the solid-liquid-vapour three-phase contact line tension, and [[theta].sub.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 different hydrodynamic conditions and particle hydrophobicities.


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 [less than or equal to] 0.8 [micro] S, pH 5.6, [gamma] = 72.8 [mNm.sup.-1] at 20[degrees]C was used in the microflotation experiments. Flotation in the Rushton turbine cell was performed using deionized water. Experiments were performed at 25[degrees]C.

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:
0.4-5 [micro]m A
90-150 [micro]m B
150-250 [micro]m C
50-1000 [micro]m D

A 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[degrees]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[degrees]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. Brockel and Loffler, 1991; Crawford et al., 1987). All glassware was cleaned and methylated before use, using the same procedure as for the particles.


The experimental apparatus for the bubble pick-up experiment 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 [micro]m/s) and a fast (200 [micro]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 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.sup.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.sup.-5] M polypropylene glycol (MW 25[degrees]). The solid concentration in the cell was approximately 4.3 wt.%. The cell specifications are given in Table 1 (Pyke et al., 2003).




Coarse Particle Behaviour

Figure 3 shows the results of the maximum size of particles that could be raised by a captive bubble as a function of particle contact angle, in the absence of turbulence, when the hydrodynamic and acceleration forces are minimized ([d.sub.pmax,g]). The predominant forces are the gravitational and capillary forces. The maximum particle size that can be raised is different from the maximum floatable particle size, as we will see below--the former is obtained under static conditions whilst the latter of course reflects a dynamic state. The results indicate that a higher contact angle is required to raise particles with a larger particle size. For example a 3.4 mm particle can only be raised by a 1.8 mm bubble, at a constant rising velocity of 20 [micro]m/s, if the particle advancing water contact angle is at least 80[degrees]. The size of the particles that can be raised decreases with decreasing bubble diameter. Rising velocity is also important and the size of the particle that can be raised decreases when the rising velocity increases. Equation (11) shows that [d.sub.pmax,g] depends on the particle contact angle, the surface tension of the solution and on the external acceleration. Three variables were explored in the bubble pick-up experiments, the particle contact angle, the rising velocity (external acceleration), and the bubble volume. Using Equation (11), an acceptable fit with the experimental data is obtained in Figure 3 for a bubble diameter of 1.8 mm, with a zero value of the acceleration. Acceleration occurs when the bubble is raised from its stationary position to a finite velocity. The lines in Figure 3 were calculated using Equation (11), with the external acceleration, a, as a fitting parameter. Curve 4 has the highest rising velocity and acceleration. 1 mm diameter bubbles can raise quartz particles with an 80[degrees] contact angle up to 2.4 mm in diameter, whereas 1.8 mm diameter bubbles can raise 3.4 mm diameter particles, the theoretical maximum particle size with a contact angle of 80[degrees] that remains attached to a bubble (Schulze, 1984, 1977).



The results of flotation in the column for quartz samples B and C are shown in Figures 4 and 5 and in the Rushton turbine cell in Figure 6. Flotation recovery increases as the particle contact angle increases and 100% recovery was obtained for the 83[degrees] particles in the Rushton turbine cell and for particles with contact angles above 59[degrees] in the column. In the flotation column the agitation was set to the minimum value required to disperse and suspend the particles. Particles larger than 550 ?m were not fully suspended and their flotation behaviour could not be determined. In the Rushton turbine cell, particles up to 1000 [micro]m were suspended at rotational speeds equal or higher than 500 rpm. It is quite remarkable that these very large particles could be floated readily in the Rushton turbine cell in spite of the turbulent environment. For 83[degrees] particles, 90% recovery was obtained after 1.5 min of flotation. When the recovery versus contact angle for each particle size is considered (examples are given in Figures 7, 8 and 9) it is observed that there is a critical contact angle, below which flotation does not occur. This effect was first reported by Blake and Ralston (1985) and confirmed by Crawford and Ralston (1988). In this previous work, a rather monodisperse suspension was used, whereas in the present study the suspension is quite polydisperse. For this reason, the present recovery curves have a sigmoid shape, instead of showing a sharp cut-off value.



To determine the critical contact angle the recovery curves in Figures 7 to 9 were described by a sigmoid function of recovery at 8 min of flotation versus the water advancing contact angle. The point where the tangent at the inflexion point intercepts the horizontal axis determines the critical contact angle. The critical contact angle/particle size threshold values obtained for flotation are shown in Figure 10. A flotation domain is evident in Figure 10, within which flotation occurs, outside of which there is no flotation. For comparison the results obtained by Crawford and Ralston (1988) are also shown. The critical contact angle/ particle size threshold for flotation was affected by the particle size distribution of the quartz feed sample, as shown in Figure 10. The critical contact angle required for flotation is smaller for the sample with coarse particles, sample C.

The aggregate stability is controlled by the energy required to detach the particle from the bubble and the kinetic energy of the particle. The kinetic energy may come from the bubble velocity and from turbulent stresses exerted on the bubble/particle aggregate as the aggregate collides with other bubbles and aggregates or when the aggregate is moved by turbulent vortices. The kinetic energy of the particle can be represented by:

KE = [pi]/12 [d.sup.3.sub.p] [[rho].sub.p] [[upsilon].sup.2.sub.p] (18)

Detachment will occur when the kinetic energy of the particle (Equation (18)) equals the detachment energy (Equation (12)). It is possible to calculate the maximum floatable particle size by plotting the detachment energy as a function of the particle size and overlaying the plot of the kinetic energy for a given value of [v.sub.b]. For a given contact angle, both curves intersect each other, defining a critical particle size, [d.sub.pmax,K]. Figure 11 shows the detachment energy, solved numerically for 1 mm bubbles and the kinetic energy for different bubble velocities. The results are in agreement with the values calculated by Schulze (1984). Particles larger than the critical size detach, imposing a kinetic limit to flotation. The dependence of [d.sub.pmax,K] on [theta] is also shown in Figure 10 for [v.sub.b] = 1, 5, 10, 20, and 30 cm/s. In this calculation [[rho].sub.p] = 2650 kg/[m.sup.3] and [gamma] = 72.0 x [10.sup.-3] N/m. Figure 10 shows that the experimental threshold values or critical particle size as a function of contact angle are much smaller than predicted under static conditions ([d.sub.pmax,g]). The threshold values experimentally determined for sample B in column flotation correspond to the dependence of [d.sub.pmax,K] for [v.sub.b] = 30 cm/s, for particles up to 150 [micro]m, as found originally by Crawford and Ralston (1988).

We now focus on the different behaviour between quartz samples B and C in column flotation. For particles larger than 150 [micro]m in sample B, the threshold values shift towards the theoretical predictions of [d.sub.pmax,K] for smaller bubble velocities, reaching the calculated curve for 10 cm/s. For sample C, the threshold values lie between the theoretical predictions for [v.sub.b] = 5 cm/s and [v.sub.b] = 10 cm/s. This seemingly odd behaviour may be caused by bubble loading. King et al. (1974) and King (2001) reported that the bubble load is proportional to the square of the particle diameter and that the bubble velocity decreases with increasing bubble load. This observation may explain why the critical contact angle/particle size curve changes with the particle size distribution of the sample, for the kinetic energy decreases for a heavily loaded bubble. Since the kinetic energy of the bubble-particle aggregate also decreases for small bubbles, this suggests that small bubbles can improve coarse particle flotation.

The critical contact angle/particle size relationship for flotation in the Rushton turbine cell falls between the results for samples B and C obtained in a flotation column using similar bubble diameters. Large particles could be floated in the Rushton turbine cell, in spite of the much higher turbulence, since the maximum size of particle that could float is determined by the velocity of the bubble-particle aggregate as well as the corresponding detachment forces. We have demonstrated that turbulence alone does not prevent coarse particle flotation. Bubble size and loading also have a strong influence on the flotation of coarse particles.

Fine Particle Behaviour

The critical contact angle for quartz particles with a diameter less than 5 [micro]m to float was determined using single bubble, bubble swarm (flotation column) and Rushton turbine cell flotation experiments. For 1 [micro]m diameter particles, the experimental data for single bubble and bubble swarm experiments are shown in Figure 12 as a function of advancing water contact angle. Data for the Rushton turbine cell are shown in Figure 13. Figure 12 and Figure 13 show a similar critical contact angle for flotation of approximately 55 to 60[degrees], independent of the flotation conditions. This self-consistency is quite remarkable.




Overall the results show that the advancing water contact angle of fine quartz particles (0.5 to 5 [micro]m in diameter) has to be 55 to 60[degrees] or above for these particles to float. The increase in recovery is very sharp for particles with contact angles between 50 and 60[degrees] but plateaus above 60[degrees].

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). To compare Scheludko's model with the experimental data, receding water contact angles were obtained using the equilibrium capillary pressure technique applied to particles with heterogeneous surfaces (Stevens, 2006; Crawford et al., 1987; Cassie, 1948). A receding contact angle of 50[degrees] was obtained with this technique for particles with an advancing contact angle of 60[degrees].

Figures 12 and 13 show that the critical advancing water contact angle for the flotation of fine quartz particles (0.5-5 [micro]m) is around 60[degrees]. There is very little difference between the critical contact angles required to float these very small particles. The range is within experimental error, thus one point is shown. This critical contact angle is compared in Figure 10 with that calculated using the Scheludko's model (Equation (17)) along with Crawford and Ralston's (Crawford and Ralston, 1988) experimental data for critical contact angles for flotation. A line tension of -3 x [10.sup.-10] Nm for a bubble is taken from the data of Yang et al. (2003) and bubble velocities (10-30 cm/s) are taken from experimental measurements in the Hallimond tube and the Rushton turbine flotation cell (Miettinen, 2007). [d.sub.p(min)] values between 0.9 to 1.4 [micro]m are calculated using Equation (17). The agreement between the Scheludko model and the experimental data for the 0.5-5 [micro]m diameter particles is satisfactory.


The detachment process controls the maximum floatable particle size for coarse particles. If the particle kinetic energy exceeds the energy required to detach it from the gas-liquid interface, the particle detaches, defining a kinetic limit for flotation. For fine particles, the critical water receding contact angle required for flotation is defined by the energy required to rupture the intervening thin liquid film between particle and bubble. The flotation response of coarse or fine particles was similar either in a column or in a mechanically agitated cell, for a similar bubble size. Flotation of very large and very fine particles is possible, provided that they have high contact angles with smaller bubbles enhancing the process. This information may be incorporated into flotation models and has major implications for flotation practice.


Financial support from the Australian Research Council through the Special Research Centre Linkage Scheme and from AMIRA International is gratefully acknowledged. We thank Nicolas Hugonnet from L'Ecole superieure de chimie physique electronique de Lyon (CPE Lyon) for his valuable assistance in the bubble attachment experiments.

Manuscript received March 19, 2007; accepted for publication May 25, 2007.


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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

* Author to whom correspondence may be addressed. E-mail address:
Table 1. Rushton turbine flotation cell specifications

Tank specifications Impeller specifications

Volume = 2.25 litre 6 blade Rushton turbine
Diameter = 144 mm Diameter = 48 mm
Height:diameter = 1:1 Width:height:diameter = 5:4:20
Baffle:diameter = 1:10
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Author:Gontijo, Carlos de F.; Fornasiero, Daniel; Ralston, John
Publication:Canadian Journal of Chemical Engineering
Date:Oct 1, 2007
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