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Behaviour of bubble clusters in a turbulent flotation cell
Powder Technology 269 (2015) 337–344
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Behaviour of bubble clusters in a turbulent flotation cell Zhihao Chen a,1, Seher Ata b,⁎, Graeme J. Jameson a,1 a b
Centre for Multiphase Processes, University of Newcastle, Callaghan, Australia The School of Mining Engineering, University of New South Wales, Sydney 2052, Australia
a r t i c l e
i n f o
Article history: Received 28 May 2014 Received in revised form 3 September 2014 Accepted 11 September 2014 Available online 20 September 2014 Keywords: Flotation Bubble clusters Bubble size Coarse particle flotation
a b s t r a c t The rate of capture of particles decreases as the particle size increases in froth flotation. It has been postulated that the upper size range of particles that can be recovered in conventional machines could be extended by the use of bubble clusters [1]. This study is concerned with the behaviour of bubble clusters in turbulent flotation cell. The breakup and reformation of clusters and the effect of bubble size and impeller speed on the behaviour of clusters have been investigated. The apparatus used was essentially a laboratory flotation cell, agitated by a Rushton turbine. The cell was modified to allow pre-formed clusters to rise out of a fluidized bed and into the path of the rotating impeller. The events were captured using a digital camera, and the images were analysed to give the sizes of the bubbles and clusters. In the first part of the investigation, a collector was used but no frother. Under these conditions, the bubble diameter was effectively controlled by the collector concentration, and it varied considerably. It was found that the sizes of clusters decrease with increasing shear rate at low impeller speeds, and at higher speeds the clusters are broken up into bubbles and particles. In the second part, frother was used at a concentration above the critical coalescence concentration, to control the bubble size, which remained essentially constant at this concentration. The bubbles were too small to be broken by the action of the impeller, so they always remained at the same size. In this case it was found that when the impeller speed was increased, two stages of formation were observed, the fragmentation and equilibrium stages. In the fragmentation stage, at low impeller speeds, the clusters were loose and filamentous, and as the energy input increases, they rupture and re-form. In the second stage, above a critical impeller speed, dense clusters formed whose size was relatively insensitive to the energy input. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Froth flotation is one of the most important methods for separation of ore in mineral industry. The method relies on the differences in chemical and physical properties of the valuable minerals and unwanted gangue minerals. The target mineral is treated with a reagent that renders the surface of particles hydrophobic. In contact with air bubbles these hydrophobic particles attach to the bubbles and float to the surface where they are separated from the liquid. Not all the hydrophobic particles can be collected and transported to the concentrate. For a given system there is generally a size range that can be recovered. For base metals, this corresponds to 10–120 μm [13] whilst for coal, particles up to 500 μm can be floated due to its lower density. There are several reasons for declining flotation efficiency above a certain size range. Particle detachment due to stress on the bubble–particle couplet in the ⁎ Corresponding author. Tel.: +61 2 9385 7659. E-mail addresses: [email protected] (Z. Chen), [email protected] (S. Ata), [email protected] (G.J. Jameson). 1 Tel.:+61 2 4921 6181.
http://dx.doi.org/10.1016/j.powtec.2014.09.025 0032-5910/© 2014 Elsevier B.V. All rights reserved.
turbulent environment [10]; insufficient bubble buoyancy to lift the particles out of the liquid [1]; and difficulty in transferring particles from the liquid phase to the froth [6] are a few obstacles for efficient coarse particle recovery. Although the reasons for poor recovery of coarse particles have been known for some time, it appears that little has been done to try to overcome the limitations of current flotation practice. Bazin and Proulx [11] used a counter-current column cell to float phosphate ore up to 630 μm in diameter. The column was run so that no froth layer was formed, and there was always an upward flow of liquid to assist the levitation of the particles. It was found that the recoveries in the column were always larger than those in a conventional flotation cell under the same conditions. Soto and Barbery [2] proposed a reagent distribution strategy to improve the recovery of coarse particles, based on the fact that fine particles require less hydrophobicity to be floated. Instead of adding more than 70% collector in the feed to the flotation cell, the flotation tests on a Cu–Pb–Zn ore were conducted by adding 50% or less collector at the top of the bank, with further amounts being added down the bank. It was noticed that the recovery of coarse particles was improved with equivalent or less collector usage.
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The approach taken by South African researchers [12,14–16] to overcome problems related to poor coarse particle flotation was to use the froth phase as a separation medium. The work was based on the assumption that coarse particles with high hydrophobicity would rupture the froth film and therefore penetrate the froth layer under gravity and report to underflow as concentrate, whilst particles with relatively low hydrophobicity would attach to bubbles and remain in the froth. The method has applications for highly naturally hydrophobic minerals such as diamonds. The use of the froth phase as a separation medium was previously investigated by Russian researchers [8]. However, none of these approaches provides significant improvement in recovery of coarse particles. More recently it has been found that the recovery of coarse particles might be improved through the use of multiple bubbles or bubble clusters to lift the particles out of the flotation cell [1]. During experiments on the flotation of silica particles in a laboratory flotation cell, these authors observed that when the contact angle was increased by increasing the concentration of collector, bubbles became attached to other bubbles by the action of bridging particles, where more than one bubble was attached to a single particle. The practical implications for coarse particle flotation are self-evident. If a particle is too large to be lifted by a single bubble, the attachment of one or more additional bubbles may well increase its buoyancy above the level necessary to raise it in the flotation cell. Thus, the presence of such structure in flotation cell may help the flotation of coarser and heavier particles making it possible to extend the upper particle size. However, little is known about the effect of the turbulent shear in the flotation cell, as reflected in the power input or the impeller rotational speed, on the structure of the clusters, or even if clusters can form in existing equipment. In the present paper the behaviour of bubble clusters was studied at impeller speeds where solely turbulent flow applies, in purpose of understanding the entire behaviour of clusters from formation to breakup at highly turbulent conditions. 2. Experimental 2.1. Materials Silica particles (Unimin Australia Ltd, Melbourne, Australia) with diameters in the range 106 to 250 μm were used in the experiments. This size range was chosen because it includes particles that are easily floated (at the lower end of the range) together with particles that are relatively difficult to float in conventional flotation cells (at the upper end of the range). The intention was to investigate the hypothesis that the presence of the finer particles would assist in the formation of clusters that would increase the recovery of the larger particles. Before use, the particles were soaked in concentrated HCl solution and then rinsed in tap water until no change in pH could be detected. Gravel particles with a diameter of 1.7–2.0 mm were used in the base of the bed to aid the water to distribute evenly in the fluidized bed and to reduce the minimum liquid velocity that was required to fluidize the particles. Dodecylamine (Aldrich, Analytical grade) solution with various concentrations was used as surfactant and methyl isobutyl carbinol (MIBC, Merck Schuchardt OHG, 97%) as a frother. The pH of the solutions was adjusted with either NaOH (Univar, Analytical grade) or HCl (Univar, 32%) to 9. 2.2. Apparatus A schematic arrangement of the equipment is shown in Fig. 1. The equipment consists of two parts: the lower part is responsible for the generation of bubble clusters, whilst the top part is similar to a mechanical flotation cell and is used for observation of clusters. The lower part is a cylindrical column to hold the fluidized bed. It is made of perspex with diameter of 50 mm and height 350 mm. Gravel particles on the bottom were used to distribute the fluidizing water, which was controlled by a variable speed water pump. A porous glass frit was used as the bubble
Fig. 1. Schematic of equipment for formation and observation of clusters.
generator. The frit was embedded into the particle bed as shown in Fig. 1. The air flow rate is measured by a rotameter. A cylindrical neck with a diameter of 20 mm connects the two parts. The neck for the entrance of clusters is 64 mm from the front wall and 46 mm from the side wall. The top part is a rectangular mechanical flotation cell with dimensions of 150 × 150 × 270 mm, which is also made of transparent perspex, so the bubble clusters could be visually observed through the walls. Four vertical baffles with dimensions of 15 × 270 mm are mounted in the centre of each wall of the vessel. A Rushton impeller with a diameter of 50 mm and a height of 10 mm is located in the central axis of the cell. The clearance of the impeller is 50 mm. A sieve with an opening size of 45 μm was used to collect particles and separate them from the surfactant solution. The location where the clusters enter into the vessel is shown in Fig. 2. A visual technique was used to determine the size of clusters. At impeller speeds lower than 400 rpm, the clusters were viewed directly through the wall of the vessel. However, at higher impeller speed (N400 rpm), it was practically impossible to observe the individual bubble clusters in the impeller zone since significant numbers of particles and bubbles were suspended in the cell. A viewing window was built to overcome this problem. A sketch of the viewing cell is shown in Fig. 3. The viewing cell is made of two transparent acrylic sheets (300 mm high × 50 mm wide) positioned 10 mm apart with one end connected to a peristaltic pump and the lower end immersed in the cell at 10 mm above the impeller. The position of the viewing cell allows bubbles to enter the viewing chamber immediately after breakage,
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Fig. 2. Sketch of the agitated vessel, showing the location of the point at which clusters enter the vessel.
avoiding the possibility that they may subsequently re-form in a lower energy dissipation area in the vessel. The open end is slightly larger than the main body, with a dimension of 50 × 50 mm to allow more clusters to enter the viewing window. A stream of liquid containing clusters and bubbles in the impeller zone is drawn through the viewing cell by the pump at a velocity of 0.05 m/s. At this velocity, the clusters were seen to rise independently in the viewing cell. The pumping speed is low compared to the tip speed of impeller; for example, the tip speed of the impeller is 1.05 m/s at the impeller speed of 400 rpm, at which the viewing cell starts to be used. Therefore, the impact of the fluidization water on the hydrodynamics of the flotation cell is negligible. 2.3. Experimental procedure Before each run, the particles were conditioned with collector to ensure that their surface is sufficiently coated with dodecylamine (DDA).
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Two approaches were used for conditioning. In the first, the particles were mixed in a beaker using a magnetic stirrer at the desired DDA concentration for 1 h. Three concentrations were used: 1 × 10−5 M (10 g/t), 5 × 10−5 M (51 g/t) and 9 × 10−5 M (92 g/t). In the second approach, the particles were dried in an oven at 500 °C for 3 h, and then conditioned for 12 h, at concentrations of 7 × 10−5 M (72 g/t), 9 × 10−5 M, and 1.2 × 10−4 M (124 g/t). The experimental results show that both methods give similar results. The DDA concentration range was chosen based on experimental trial test. At his range, the clusters can form at the lowest DDA concentration and no precipitation was observed in DDA solution at the highest concentration. In a typical run, the column was first loaded with shallow layer of gravel, 1.7 to 2 mm in diameter, of depth 60 mm to distribute the fluidizing water. The conditioned relatively fine particles (106–250 μm, 160 g) were then added on top of the gravel and a solution containing DDA at the desired concentration was pumped into the base of the gravel bed at a flowrate of 360 mL/min. At this flowrate, the bed of fine particles is fluidized and gently mixed with a bed expansion ratio of 100%. When the liquid reaches the lip of the upper vessel, air is introduced at a rate of 10 mL/min through the porous ceramic sparger, forming small air bubbles. As they rise through the bed, the bubbles collide with the fine particles, forming clusters. At this air rate, the clusters form relatively slowly, which reduces overlapping of clusters and therefore increases the accuracy of data analysis (at higher gas rates, the concentration of clusters is so high that it is difficult experimentally to distinguish one from another). The clusters rise into the upper cell, into the turbulent zone around the impeller, where they may be broken into segments. A CCD camera (PixeLINK, Canada) coupled with a 65 mm lens was used to record images of the clusters at a frame rate of 5 frame/s. through the wall of the vessel. The images have a maximum resolution of 53 pixel/mm, corresponding to a minimum detectable limitation of 19 μm. At impeller speeds higher than 400 rpm, the concentration of bubbles and clusters in the tank was too high for the through-the-wall method to be used, so the viewing window (see Fig. 3) was used to observe the bubbles and clusters. 2.4. Analysis of data The images were analysed by Optimas imaging software (Media Cyberbetics, USA). Clusters (or bubbles) that were in focus, and which did not overlap with others, were selected. Sizing was carried out over at least four or five frames to ensure that clusters were not counted more than once. The equivalent diameter of the bubble clusters was determined by an imaging method that first computes the projected area of each cluster by tracing its perimeter. These areas were then used to calculate the diameter of an equivalent circle, which was then recorded as the equivalent cluster diameter. The cluster size is given by the number average of equivalent diameters. The size distribution of clusters is based on number distribution. Volume distribution is avoided because a few large clusters can occupy a large fraction of volume. The shape of the clusters is closely related to the cluster strength and breakage behaviour. The cluster shape can be characterized by shape factor (SF) given by 4πA/P2 where A is the area and P is the perimeter. The shape factor can take values between 0 and 1: 0 for a line and 1 for a circle.
Fig. 3. Sketch of viewing cell used for bubble clusters observation at high impeller speed.
2.4.1. Estimation of errors In this work, the mean cluster diameter (or bubble diameter) was found as the mean of a large number of samples, taken from the photographic images. It is useful to be able to specify the number of samples that must be analysed in order to be able to specify the mean diameter to within a particular accuracy, or alternatively, to estimate the likely error involved when a specified number of samples are analysed. Montgomery and Runger [9] have presented a useful method. Suppose we have a number of samples whose mean value is x, drawn from a normal distribution whose true mean value is μ. The error E ¼ jx‐μ j is to lie
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pffiffiffi within a specified range that is less than or equal to zα=2 σ = n, where σ is the standard deviation of the distribution, α is the significance level, n is the number of measurements available, and zα/2 is the number of standard deviations that will define the error. For example, in a normal distribution, 95% of the samples will lie within ∓ 1.96σ so zα/2 is equal to 1.96. The required sample size is found by choosing the number of samples n such that pffiffiffi E ¼ zα=2 σ= n
ð1Þ
Table 2 The number of samples required for various expected errors. Expected error, mm 0.01 0.02 0.05 0.07 0.08 0.09 0.10 0.2
Number of clusters
Number of bubbles
22,189 5,547 888 453 347 274 222 56
649 162 26 13 10 8 7 2
or, rearranging in terms of n: n¼
zα=2 σ 2 E
ð2Þ
During exploratory experiments, in which the mean diameter of a large number of clusters was found to be 2.5 mm, the standard deviation was 0.76 mm; similarly, for the measurement of a number of individual bubbles, the average diameter was 0.5 mm and the standard deviation was 0.13 mm. Using these values in Eq. (2), the number of samples required to achieve a specified expected error can be calculated, as shown in Table 2. For a minimum number of 350 clusters, it can be calculated that the maximum error is 0.08 mm at the 95% confidence level (3.2%). For more than 162 bubbles, the equation gives less than 0.02 mm error at the same confidence level (4%). It should be noticed that the number of samples required to achieve an error is based on an average standard deviation. However, the standard deviation varies with other experimental conditions, such as DDA concentrations and impeller speeds. Table 3 shows the number of samples counted in the experiments and associated standard deviation and error. Standard errors lower than 0.15 mm with 95% confidence level were obtained for all DDA concentrations and impeller speeds listed in the table. The error level can be reduced by increasing the number of samples analysed. The process however is very time consuming. For example, it takes more than three months to analyse 5000 cluster images, which is not practicable. To check the repeatability of each experiment, all experiments in the study were repeated at least twice. 3. Results and discussion 3.1. General observations on cluster formation Fig. 4 gives some examples of bubble clusters formed in the fluidized bed. It is seen that the clusters form in various shapes, sizes and structures. They appear to be randomly formed and some contain a considerable number of bubbles and particles. Figs. 4(a) and (b) show some clusters just after they have risen out of the fluidized bed. It was observed that clusters were not formed immediately after the introduction of air bubbles into the bed. Some bubbles were lightly loaded, but many were completely covered with particles, and were so heavy that they sat on the surface of the bed. The heavily laden bubbles only started to rise once they had obtained sufficient buoyancy either by clustering together in the bubble layer or by attaching to the lightly loaded bubbles rising out of the fluidized bed. Cluster formation in itself is no guarantee that a Table 1 The power consumption, Reynolds number and the energy dissipation rate at the impeller speeds used in the study. Impeller diameter D = 0.05 m; power number of the Rushton impeller Np = 5.5; volume of tank V = 0.006 m3. Impeller speed (rpm)
Power consumption (W)
Impeller Reynolds number
Energy dissipation rate, ε (W/kg)
250 400 550 700 850
0.12 0.51 1.32 2.73 4.89
10,417 16,667 22,917 29,167 35,417
0.021 0.085 0.22 0.45 0.81
group of bubbles may rise from the surface of the bed. Clusters can be seen in Figs. 4(a) and (b) that are heavily laden and may have nearneutral buoyancy. These remain at the surface until they can capture lightly loaded bubbles and gain positive buoyancy. Figs. 4(c) and (d) show clusters rising freely away from the bed. As clearly seen, a number of bubbles on the surface of these clusters are partially coated, and these can lend buoyancy to the cluster as a whole. 3.2. Cluster behaviour in turbulent conditions Fig. 5 shows the average bubble cluster diameter as a function of impeller speed at various DDA concentrations. As can be seen, in general the cluster size decreases with increasing impeller speed initially; however it plateaus eventually beyond the impeller speed of 550 rpm. It appears that an increase in the impeller rotational speed between 250 and 550 rpm causes a rapid drop in the size of the clusters, suggesting that larger clusters were unstable and degraded easily than the smaller ones by the impeller generated shear. Overall, the cluster size decreases approximately from 2.5 mm to 0.5 mm over the range of impeller speeds studied. Interestingly this behaviour is observed with almost all three DDA concentration used in the study. This shows that the formation and breakup of clusters are weakly dependent on the DDA concentration for the range used in the current system. Fig. 6 shows the influence of impeller speed on the behaviour of clusters at the same DDA concentration range used in Fig. 5, but in the presence of frother (MIBC) at a concentration of 80 ppm (ppm is expressed by volume i.e. μl/l). The trend in the results is similar to that shown in Fig. 5 although there are obvious differences between the two figures. The size of clusters decreases with increasing impeller speed, regardless of the DDA concentration. The change in the size is minimal beyond an impeller speed of 600 rpm, suggesting that when the bubble aggregates reach 0.6 mm in diameter, the mechanical strength of the bubble clusters is counterbalanced by the hydrodynamic force. It also appears that, the cluster size is a function of the DDA concentration at the lowest impeller speed with the largest clusters forming at the highest DDA concentration. Comparing Figs. 5 and 6, it is clear that the size of the clusters given in Fig. 6 (with frother) is much smaller than those in Fig. 5 (no frother), which is believed to be due to the different size of bubbles that form the clusters in the two systems. Fig. 7 shows the variation of bubble size as a function of DDA concentration, with no impeller involved. It is noted that no frother was present in the system so the change in the size was solely due to the presence of DDA. DDA is an ionic surfactant that can easily adsorb at the air–water interface, and reduces the surface tension, which in turn reduces the size of the bubbles. According to the figure, the bubble size decreases by 30%, as the concentration is increased from 0 to 12 × 10− 5 M. This suggests that in Fig. 5 where no frother is present, the initial bubble size formed at the base of sparger is different for each DDA concentration, which is expected to affect both cluster formation in the fluidized bed and the subsequent breakage behaviour in the impeller discharge zone. It is clear that DDA affects the size of the bubbles in the current system. To minimise this effect we measured bubble sizes in the presence of both MIBC and DDA. The results are shown in Fig. 8 where the size
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Table 3 The number of samples counted in the experiments and associated standard deviation and error. DDA: 7 × 10−5 M
DDA: 9 × 10−5 M
DDA: 1.2 × 10−4 M
Impeller speed (rpm)
Number counted
Standard dev. (mm)
Error (mm)
Number counted
Standard dev. (mm)
Error (mm)
Number counted
Standard dev. (mm)
Error (mm)
250 400 550 700 850
160 140 180 175 340
0.62 0.56 0.69 0.27 0.16
0.10 0.09 0.10 0.04 0.02
148 181 179 246 283
0.81 0.89 0.51 0.26 0.17
0.13 0.13 0.07 0.03 0.02
320 388 215 172 223
1.35 1.18 0.47 0.2 0.17
0.15 0.12 0.06 0.03 0.02
of bubbles as a function of MIBC concentrations at constant DDA concentrations at pH 9 is given. The figure shows that the bubble size decreases with increasing MIBC concentrations as expected, and then reaches its limited minimum size at all DDA concentrations. The minimum size of bubbles (around 200 μm) occurs when the concentration of MIBC exceeds 80 ppm, indicating that this is the critical coalescence concentration (CCC) of the frother. Surprisingly, the value of the CCC (determined based on the method described by [7] is in agreement with the result shown in the study of [5], although the current system contains an additional cationic surfactant. It is also interesting to observe that the CCC is essentially independent of the DDA concentration. This indicates that the bubble size at the CCC is determined primarily by the frother, and the contribution from the DDA is small.
Another factor that may affect the size of the bubbles forming the clusters in the cell is impeller speed. Once the clusters arrive into the impeller region, both the bubbles and clusters may be subjected to breakage. To investigate the influence of the impeller rotational speed on the initial bubble size, a series of experiments were carried out at impeller speeds from 0 to 850 rpm, and DDA concentrations of 0 and 1.2 × 10−4 M. The concentration of MIBC was kept at 80 ppm. The results are shown in Fig. 9. It is seen that the bubble size is approximately 200 μm at all impeller speeds for both DDA concentrations studied. This indicates that the size of bubbles is not affected by either the impeller speed or the DDA concentration and it is essentially independent of these two parameters in the current system when the frother is present. We note that as the two extreme DDA concentrations in this study were
Fig. 4. Some examples of bubble clusters formed in the fluidized bed.
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0.8
Mean Diameter of Bubbles (mm)
Mean Diameter of Clusters (mm)
3.0 -5
7 x 10 (M) -5 9 x 10 (M) -4 1.2 x 10 (M)
2.5 2.0 1.5 1.0 0.5 0.0 0
100
200
300
400
500
600
700
800
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
900
0
Impeller Speeds (rpm)
2
4
6
8
10
12
5
DDA Concentrations x 10 (M)
Fig. 5. The cluster size as a function of impeller speed in the absence of frother, at various DDA concentrations.
Fig. 7. The effect of dodecylamine concentration on bubble size. The impeller speed is zero.
tested, the result can be applied to the whole range of DDA concentration from 0 to 1.2 × 10−4 M. Revisiting Figs. 5 and 6 it may appear that there is a Critical Impeller Speed (CIS) at which there is a change in the behaviour of the bubble clusters. The presence of a CIS may be related to the two regimes that play important roles in the behaviour of bubble clusters. It may be postulated that the clusters undergo two distinct processes which are separated by a critical impeller speed in a given system: the fragmentation stage where the clusters are still exposed to breakage due to their loose, branched structure and the re-formation or collision stage in which the clusters tend to re-form due to the highly turbulent environment that promotes bubble-clusters or cluster-cluster collisions. A graph to demonstrate the existence of CIS is shown in Fig. 10 based on the Laskowski method [12], where the combined results for clusters size from our previous work [14] and the current study are given. At impeller speeds lower than the critical speed, the fragmentation of bubble clusters is predominant. In this stage, the behaviour of clusters is significantly related to the size and shape of initially formed clusters. Because the clusters are pre-generated in this study, the initial size of clusters is mainly determined by the hydrophobicity of particles, in other words, the concentration of collector. Higher DDA concentrations generate larger and branchy clusters. As the impeller speed increases, the size of the clusters reduces and becomes less sensitive to the shear rate at high impeller speeds.
When the impeller speed is increased beyond the critical speed the cluster size is determined by the balance between breakup and re-formation. The influence of the cluster size at formation is eliminated because the clusters show similar characteristics including size and shape regardless of DDA concentration. At this stage it is impossible to identify whether the clusters come from the degradation of mother clusters or re-formation due to bubble–particle, cluster–cluster or bubble–cluster collisions. However, pre-generation of clusters doesn't exist in industrial flotation cells, so the only way that clusters can form in these cells is through collision between individual bubbles and particles, to form the initial clusters, which may continue to grow until they reach an equilibrium size determined by their hydrophobicity and the turbulent conditions in the cell. This stage may be referred to as the collision stage. It is worthwhile to note that collisions may not always lead to cluster formation. It should also be noted that the CIS is more likely system-specific based on experimental conditions. [1] for example observed the CIS to be much higher than 670 rpm. However in their study, the silica particles were very small, having an average size of 7 μm. As been pointed out recently [3], fine particles can stabilize bubbles as well as foams and flotation froths. This could explain why the critical impeller speed observed by Ata and Jameson was much higher than the speed in this study. 0.8
Mean Diameter of Bubbles (mm)
Mean Diameter of Clusters (mm)
3.0 -5
2.5
7 x 10 (M) -5 9 x 10 (M) -4 1.2 x 10 (M)
2.0 1.5 1.0 0.5
0 (M) -5 1 x 10 (M) -5 5 x 10 (M) -5 7 x 10 (M) -5 9 x 10 (M) -4 1.2 x 10 (M)
0.7 0.6 0.5 0.4 0.3 0.2
0.0 0
100
200
300
400
500
600
700
800
900
Impeller Speeds (RPM) Fig. 6. The effect of impeller speed on the size of clusters with MIBC at a concentration of 80 ppm at various DDA concentrations as indicated in the legend.
0
20
40
60
80
100
120
MIBC Concentrations (ppm) Fig. 8. The bubble size as a function of MIBC concentrations at various DDA concentrations. The impeller speed is zero.
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Mean Diameter of Bubbles (mm)
0.5
0 (M) -4 1.2 x 10 (M)
0.4
0.3
0.2
0.1
0.0 0
200
400
600
800
1000
Impeller Speeds (RPM) Fig. 9. Effect of impeller speed on the bubble diameter in the presence of MIBC at a concentration of 80 ppm.
4. Conclusions The behaviour of bubble clusters has been studied in a turbulent flotation cell. The sizes of bubble clusters have been measured in the absence and presence of frother at various DDA concentrations and impeller rotation speeds. The effect of the frother has been observed through measurement of the bubble size. A critical concentration of frother (80 ppm MIBC) has been chosen for the experiments, at which the bubble size is insensitive to changes in the DDA concentration and impeller speed. It appears that the cluster size is influenced not only by the DDA concentrations but also by the bubble size. The addition of frother at a certain concentration can effectively eliminate the impact of bubble size on the behaviour of bubble clusters. In the presence of frother above the critical value the clusters have similar sizes, almost independently of the DDA concentration and impeller speed. At impeller speeds lower than the critical speed, the fragmentation of bubble clusters is predominant. Because the clusters are pre-generated in this study, the initial size of clusters is mainly determined by the hydrophobicity of particles, in other words, the concentration of collector. Higher DDA concentrations generate larger, branched clusters. As the impeller speed increases, the size of the
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clusters reduces also and becomes almost insensitive to the shear rate at high impeller speeds. When the impeller speed is increased beyond the critical speed at which the clusters are insensitive to shear rate, the clusters show similar characteristics including size and shape regardless of DDA concentration. This indicates that the influence of the cluster size at formation is eliminated. At this stage it is impossible to identify whether the clusters come from the degradation of mother clusters or re-formation due to bubble–particle, cluster–cluster or bubble–cluster collisions. However, pre-generation of clusters doesn't exist in industrial flotation cells, so the only way that clusters can form in these cells is through collision between individual bubbles and particles, to form the initial clusters that may continue to grow until they reach an equilibrium size determined by their hydrophobicity and the turbulent conditions in the cell. This stage may be referred to as the collision stage. Accordingly, the data suggest that a critical impeller speed exists, separating the behaviour of the bubble clusters into two stages. In stage one, the cluster size is governed by the fragmentation process, where filamentous branches are broken off and the clusters consolidate. In the second stage, the behaviour is determined by collisions with free particles and bubbles, until a steady state is reached where processes of cluster formation and rupture are in balance. The critical impeller speed is affected by a number of physical and chemical factors, including collector concentrations, particle size, cluster structure and so forth. The results obtained in this study can be used to provide information on the likely behaviour of clusters in industrial flotation cells. The power consumption in these cells usually lies in the range 0.5 to 5 kW/m3, and without loss of generality the range could be expressed as 0.5 to 5 W/kg to align with the units used in the present study. It is seen from Table 1, that the range of impeller speeds used in the study provides power consumptions from 0.021 W/kg (250 rpm) to 0.81 W/kg (800 rpm), indicating that only the upper speed ranges employed in the study correspond to the power consumption used in industrial cells. It appears that at the highest power inputs, the dissipation rate is sufficiently high that clusters will find themselves in the equilibrium range, rather than the fragmentation range. They will be densely packed and stable in size, and their diameters will be in the range of 500 μm to 1 mm. Acknowledgements The authors would like to acknowledge the Australia Research Council (ARC) for financial support. References
Fig. 10. The mean diameter of clusters as a function of impeller speeds at various DDA concentrations in the absence of frother. Some data points are originated from our previous publication [4].
[1] S. Ata, G.J. Jameson, The formation of bubble clusters in flotation cells, Int. J. Miner. Process. 76 (1–2) (2005) 123–139. [2] C. Bazin, M. Proulx, Distribution of reagents down a flotation bank to improve the recovery of coarse particles, Int. J. Miner. Process. 61 (1) (2001) 1–12. [3] B.P. Binks, Particles as surfactants—similarities and differences, Curr. Opin. Colloid Interface Sci. 7 (1–2) (2002) 21–41. [4] Z.H. Chen, S. Ata, G.J. Jameson, Behavior of bubble clusters in a turbulent flow, XXV International Mineral Processing Congress, Brisbane, Australia, 2010. 1773–1782. [5] Y.S. Cho, J.S. Laskowski, Effect of flotation frothers on bubble size and foam stability, Int. J. Miner. Process. 64 (2–3) (2002) 69–80. [6] M. Falutsu, G.S. Dobby, Direct measurement of froth drop back and collection zone recovery in a laboratory flotation column, Miner. Eng. 2 (3) (1989) 377–386 (1989). [7] J.S. Laskowski, Fundamental properties of flotation frothers, Proceedings of the 22nd International Mineral Processing Congress, Cape Town, South Africa, 2003, pp. 788–797, (28 September–3 October). [8] V.A. Malinovskii, N.V. Matveenko, O.M. Knaus, Y.P. Uvarov, N.N. Teterina, N.N. Boiko, Technology of froth separation and its applications, in: M.J. Jones (Ed.), Proceedings of the 10th International Mineral Processing Congress, Institution of Mining and Metallurgy, London, 1973, pp. 717–726. [9] D.C. Montgomery, G.C. Runger, Applied Statistics and Probability for Engineers, John Wiley, New York, 2007. [10] H.J. Schulze, Physicochemical Elementary Processes in Flotation, Elsevier, Amsterdam, 1984. [11] H. Soto, G. Barbery, Flotation of coarse particles in a counter-current column cell, Miner. Metall. Process. 8 (1) (1991) 16–21. [12] Ross, V.E., 1993. Separation Method and Apparatus. SA Patent 93/5367.
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[13] W.J. Trahar, A rational interpretation of the role of particle size in flotation, Int. J. Miner. Process. 8 (4) (1981) 289–327. [14] J.S.J. van Deventer, W.A. van Dyk, L. Lorenzen, The separation of coarse particles by a moving froth bed, in: P. Massacci (Ed.), The XXI International Mineral Processing Congress, 2000, (Rome, pp. 7–1 - 7–8).
[15] J.S.J. van Deventer, W.A. van Dyk, L. Lorenzen, D. Feng, The dynamic behavior of coarse particles in flotation froths: part I: model, Miner. Eng. 15 (9) (2002) 635–645. [16] W.A. van Dyk, J.S.J. van Deventer, L. Lorenzen, The dynamic behavior of coarse particles in flotation froths, in: J.A. Herbst (Ed.), The XIX International Mineral Processing Congress, 1995, pp. 99–103, (San Francisco, USA,).
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Behaviour of bubble clusters in a turbulent flotation cell Zhihao Chen a,1, Seher Ata b,⁎, Graeme J. Jameson a,1 a b
Centre for Multiphase Processes, University of Newcastle, Callaghan, Australia The School of Mining Engineering, University of New South Wales, Sydney 2052, Australia
a r t i c l e
i n f o
Article history: Received 28 May 2014 Received in revised form 3 September 2014 Accepted 11 September 2014 Available online 20 September 2014 Keywords: Flotation Bubble clusters Bubble size Coarse particle flotation
a b s t r a c t The rate of capture of particles decreases as the particle size increases in froth flotation. It has been postulated that the upper size range of particles that can be recovered in conventional machines could be extended by the use of bubble clusters [1]. This study is concerned with the behaviour of bubble clusters in turbulent flotation cell. The breakup and reformation of clusters and the effect of bubble size and impeller speed on the behaviour of clusters have been investigated. The apparatus used was essentially a laboratory flotation cell, agitated by a Rushton turbine. The cell was modified to allow pre-formed clusters to rise out of a fluidized bed and into the path of the rotating impeller. The events were captured using a digital camera, and the images were analysed to give the sizes of the bubbles and clusters. In the first part of the investigation, a collector was used but no frother. Under these conditions, the bubble diameter was effectively controlled by the collector concentration, and it varied considerably. It was found that the sizes of clusters decrease with increasing shear rate at low impeller speeds, and at higher speeds the clusters are broken up into bubbles and particles. In the second part, frother was used at a concentration above the critical coalescence concentration, to control the bubble size, which remained essentially constant at this concentration. The bubbles were too small to be broken by the action of the impeller, so they always remained at the same size. In this case it was found that when the impeller speed was increased, two stages of formation were observed, the fragmentation and equilibrium stages. In the fragmentation stage, at low impeller speeds, the clusters were loose and filamentous, and as the energy input increases, they rupture and re-form. In the second stage, above a critical impeller speed, dense clusters formed whose size was relatively insensitive to the energy input. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Froth flotation is one of the most important methods for separation of ore in mineral industry. The method relies on the differences in chemical and physical properties of the valuable minerals and unwanted gangue minerals. The target mineral is treated with a reagent that renders the surface of particles hydrophobic. In contact with air bubbles these hydrophobic particles attach to the bubbles and float to the surface where they are separated from the liquid. Not all the hydrophobic particles can be collected and transported to the concentrate. For a given system there is generally a size range that can be recovered. For base metals, this corresponds to 10–120 μm [13] whilst for coal, particles up to 500 μm can be floated due to its lower density. There are several reasons for declining flotation efficiency above a certain size range. Particle detachment due to stress on the bubble–particle couplet in the ⁎ Corresponding author. Tel.: +61 2 9385 7659. E-mail addresses: [email protected] (Z. Chen), [email protected] (S. Ata), [email protected] (G.J. Jameson). 1 Tel.:+61 2 4921 6181.
http://dx.doi.org/10.1016/j.powtec.2014.09.025 0032-5910/© 2014 Elsevier B.V. All rights reserved.
turbulent environment [10]; insufficient bubble buoyancy to lift the particles out of the liquid [1]; and difficulty in transferring particles from the liquid phase to the froth [6] are a few obstacles for efficient coarse particle recovery. Although the reasons for poor recovery of coarse particles have been known for some time, it appears that little has been done to try to overcome the limitations of current flotation practice. Bazin and Proulx [11] used a counter-current column cell to float phosphate ore up to 630 μm in diameter. The column was run so that no froth layer was formed, and there was always an upward flow of liquid to assist the levitation of the particles. It was found that the recoveries in the column were always larger than those in a conventional flotation cell under the same conditions. Soto and Barbery [2] proposed a reagent distribution strategy to improve the recovery of coarse particles, based on the fact that fine particles require less hydrophobicity to be floated. Instead of adding more than 70% collector in the feed to the flotation cell, the flotation tests on a Cu–Pb–Zn ore were conducted by adding 50% or less collector at the top of the bank, with further amounts being added down the bank. It was noticed that the recovery of coarse particles was improved with equivalent or less collector usage.
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The approach taken by South African researchers [12,14–16] to overcome problems related to poor coarse particle flotation was to use the froth phase as a separation medium. The work was based on the assumption that coarse particles with high hydrophobicity would rupture the froth film and therefore penetrate the froth layer under gravity and report to underflow as concentrate, whilst particles with relatively low hydrophobicity would attach to bubbles and remain in the froth. The method has applications for highly naturally hydrophobic minerals such as diamonds. The use of the froth phase as a separation medium was previously investigated by Russian researchers [8]. However, none of these approaches provides significant improvement in recovery of coarse particles. More recently it has been found that the recovery of coarse particles might be improved through the use of multiple bubbles or bubble clusters to lift the particles out of the flotation cell [1]. During experiments on the flotation of silica particles in a laboratory flotation cell, these authors observed that when the contact angle was increased by increasing the concentration of collector, bubbles became attached to other bubbles by the action of bridging particles, where more than one bubble was attached to a single particle. The practical implications for coarse particle flotation are self-evident. If a particle is too large to be lifted by a single bubble, the attachment of one or more additional bubbles may well increase its buoyancy above the level necessary to raise it in the flotation cell. Thus, the presence of such structure in flotation cell may help the flotation of coarser and heavier particles making it possible to extend the upper particle size. However, little is known about the effect of the turbulent shear in the flotation cell, as reflected in the power input or the impeller rotational speed, on the structure of the clusters, or even if clusters can form in existing equipment. In the present paper the behaviour of bubble clusters was studied at impeller speeds where solely turbulent flow applies, in purpose of understanding the entire behaviour of clusters from formation to breakup at highly turbulent conditions. 2. Experimental 2.1. Materials Silica particles (Unimin Australia Ltd, Melbourne, Australia) with diameters in the range 106 to 250 μm were used in the experiments. This size range was chosen because it includes particles that are easily floated (at the lower end of the range) together with particles that are relatively difficult to float in conventional flotation cells (at the upper end of the range). The intention was to investigate the hypothesis that the presence of the finer particles would assist in the formation of clusters that would increase the recovery of the larger particles. Before use, the particles were soaked in concentrated HCl solution and then rinsed in tap water until no change in pH could be detected. Gravel particles with a diameter of 1.7–2.0 mm were used in the base of the bed to aid the water to distribute evenly in the fluidized bed and to reduce the minimum liquid velocity that was required to fluidize the particles. Dodecylamine (Aldrich, Analytical grade) solution with various concentrations was used as surfactant and methyl isobutyl carbinol (MIBC, Merck Schuchardt OHG, 97%) as a frother. The pH of the solutions was adjusted with either NaOH (Univar, Analytical grade) or HCl (Univar, 32%) to 9. 2.2. Apparatus A schematic arrangement of the equipment is shown in Fig. 1. The equipment consists of two parts: the lower part is responsible for the generation of bubble clusters, whilst the top part is similar to a mechanical flotation cell and is used for observation of clusters. The lower part is a cylindrical column to hold the fluidized bed. It is made of perspex with diameter of 50 mm and height 350 mm. Gravel particles on the bottom were used to distribute the fluidizing water, which was controlled by a variable speed water pump. A porous glass frit was used as the bubble
Fig. 1. Schematic of equipment for formation and observation of clusters.
generator. The frit was embedded into the particle bed as shown in Fig. 1. The air flow rate is measured by a rotameter. A cylindrical neck with a diameter of 20 mm connects the two parts. The neck for the entrance of clusters is 64 mm from the front wall and 46 mm from the side wall. The top part is a rectangular mechanical flotation cell with dimensions of 150 × 150 × 270 mm, which is also made of transparent perspex, so the bubble clusters could be visually observed through the walls. Four vertical baffles with dimensions of 15 × 270 mm are mounted in the centre of each wall of the vessel. A Rushton impeller with a diameter of 50 mm and a height of 10 mm is located in the central axis of the cell. The clearance of the impeller is 50 mm. A sieve with an opening size of 45 μm was used to collect particles and separate them from the surfactant solution. The location where the clusters enter into the vessel is shown in Fig. 2. A visual technique was used to determine the size of clusters. At impeller speeds lower than 400 rpm, the clusters were viewed directly through the wall of the vessel. However, at higher impeller speed (N400 rpm), it was practically impossible to observe the individual bubble clusters in the impeller zone since significant numbers of particles and bubbles were suspended in the cell. A viewing window was built to overcome this problem. A sketch of the viewing cell is shown in Fig. 3. The viewing cell is made of two transparent acrylic sheets (300 mm high × 50 mm wide) positioned 10 mm apart with one end connected to a peristaltic pump and the lower end immersed in the cell at 10 mm above the impeller. The position of the viewing cell allows bubbles to enter the viewing chamber immediately after breakage,
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Fig. 2. Sketch of the agitated vessel, showing the location of the point at which clusters enter the vessel.
avoiding the possibility that they may subsequently re-form in a lower energy dissipation area in the vessel. The open end is slightly larger than the main body, with a dimension of 50 × 50 mm to allow more clusters to enter the viewing window. A stream of liquid containing clusters and bubbles in the impeller zone is drawn through the viewing cell by the pump at a velocity of 0.05 m/s. At this velocity, the clusters were seen to rise independently in the viewing cell. The pumping speed is low compared to the tip speed of impeller; for example, the tip speed of the impeller is 1.05 m/s at the impeller speed of 400 rpm, at which the viewing cell starts to be used. Therefore, the impact of the fluidization water on the hydrodynamics of the flotation cell is negligible. 2.3. Experimental procedure Before each run, the particles were conditioned with collector to ensure that their surface is sufficiently coated with dodecylamine (DDA).
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Two approaches were used for conditioning. In the first, the particles were mixed in a beaker using a magnetic stirrer at the desired DDA concentration for 1 h. Three concentrations were used: 1 × 10−5 M (10 g/t), 5 × 10−5 M (51 g/t) and 9 × 10−5 M (92 g/t). In the second approach, the particles were dried in an oven at 500 °C for 3 h, and then conditioned for 12 h, at concentrations of 7 × 10−5 M (72 g/t), 9 × 10−5 M, and 1.2 × 10−4 M (124 g/t). The experimental results show that both methods give similar results. The DDA concentration range was chosen based on experimental trial test. At his range, the clusters can form at the lowest DDA concentration and no precipitation was observed in DDA solution at the highest concentration. In a typical run, the column was first loaded with shallow layer of gravel, 1.7 to 2 mm in diameter, of depth 60 mm to distribute the fluidizing water. The conditioned relatively fine particles (106–250 μm, 160 g) were then added on top of the gravel and a solution containing DDA at the desired concentration was pumped into the base of the gravel bed at a flowrate of 360 mL/min. At this flowrate, the bed of fine particles is fluidized and gently mixed with a bed expansion ratio of 100%. When the liquid reaches the lip of the upper vessel, air is introduced at a rate of 10 mL/min through the porous ceramic sparger, forming small air bubbles. As they rise through the bed, the bubbles collide with the fine particles, forming clusters. At this air rate, the clusters form relatively slowly, which reduces overlapping of clusters and therefore increases the accuracy of data analysis (at higher gas rates, the concentration of clusters is so high that it is difficult experimentally to distinguish one from another). The clusters rise into the upper cell, into the turbulent zone around the impeller, where they may be broken into segments. A CCD camera (PixeLINK, Canada) coupled with a 65 mm lens was used to record images of the clusters at a frame rate of 5 frame/s. through the wall of the vessel. The images have a maximum resolution of 53 pixel/mm, corresponding to a minimum detectable limitation of 19 μm. At impeller speeds higher than 400 rpm, the concentration of bubbles and clusters in the tank was too high for the through-the-wall method to be used, so the viewing window (see Fig. 3) was used to observe the bubbles and clusters. 2.4. Analysis of data The images were analysed by Optimas imaging software (Media Cyberbetics, USA). Clusters (or bubbles) that were in focus, and which did not overlap with others, were selected. Sizing was carried out over at least four or five frames to ensure that clusters were not counted more than once. The equivalent diameter of the bubble clusters was determined by an imaging method that first computes the projected area of each cluster by tracing its perimeter. These areas were then used to calculate the diameter of an equivalent circle, which was then recorded as the equivalent cluster diameter. The cluster size is given by the number average of equivalent diameters. The size distribution of clusters is based on number distribution. Volume distribution is avoided because a few large clusters can occupy a large fraction of volume. The shape of the clusters is closely related to the cluster strength and breakage behaviour. The cluster shape can be characterized by shape factor (SF) given by 4πA/P2 where A is the area and P is the perimeter. The shape factor can take values between 0 and 1: 0 for a line and 1 for a circle.
Fig. 3. Sketch of viewing cell used for bubble clusters observation at high impeller speed.
2.4.1. Estimation of errors In this work, the mean cluster diameter (or bubble diameter) was found as the mean of a large number of samples, taken from the photographic images. It is useful to be able to specify the number of samples that must be analysed in order to be able to specify the mean diameter to within a particular accuracy, or alternatively, to estimate the likely error involved when a specified number of samples are analysed. Montgomery and Runger [9] have presented a useful method. Suppose we have a number of samples whose mean value is x, drawn from a normal distribution whose true mean value is μ. The error E ¼ jx‐μ j is to lie
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pffiffiffi within a specified range that is less than or equal to zα=2 σ = n, where σ is the standard deviation of the distribution, α is the significance level, n is the number of measurements available, and zα/2 is the number of standard deviations that will define the error. For example, in a normal distribution, 95% of the samples will lie within ∓ 1.96σ so zα/2 is equal to 1.96. The required sample size is found by choosing the number of samples n such that pffiffiffi E ¼ zα=2 σ= n
ð1Þ
Table 2 The number of samples required for various expected errors. Expected error, mm 0.01 0.02 0.05 0.07 0.08 0.09 0.10 0.2
Number of clusters
Number of bubbles
22,189 5,547 888 453 347 274 222 56
649 162 26 13 10 8 7 2
or, rearranging in terms of n: n¼
zα=2 σ 2 E
ð2Þ
During exploratory experiments, in which the mean diameter of a large number of clusters was found to be 2.5 mm, the standard deviation was 0.76 mm; similarly, for the measurement of a number of individual bubbles, the average diameter was 0.5 mm and the standard deviation was 0.13 mm. Using these values in Eq. (2), the number of samples required to achieve a specified expected error can be calculated, as shown in Table 2. For a minimum number of 350 clusters, it can be calculated that the maximum error is 0.08 mm at the 95% confidence level (3.2%). For more than 162 bubbles, the equation gives less than 0.02 mm error at the same confidence level (4%). It should be noticed that the number of samples required to achieve an error is based on an average standard deviation. However, the standard deviation varies with other experimental conditions, such as DDA concentrations and impeller speeds. Table 3 shows the number of samples counted in the experiments and associated standard deviation and error. Standard errors lower than 0.15 mm with 95% confidence level were obtained for all DDA concentrations and impeller speeds listed in the table. The error level can be reduced by increasing the number of samples analysed. The process however is very time consuming. For example, it takes more than three months to analyse 5000 cluster images, which is not practicable. To check the repeatability of each experiment, all experiments in the study were repeated at least twice. 3. Results and discussion 3.1. General observations on cluster formation Fig. 4 gives some examples of bubble clusters formed in the fluidized bed. It is seen that the clusters form in various shapes, sizes and structures. They appear to be randomly formed and some contain a considerable number of bubbles and particles. Figs. 4(a) and (b) show some clusters just after they have risen out of the fluidized bed. It was observed that clusters were not formed immediately after the introduction of air bubbles into the bed. Some bubbles were lightly loaded, but many were completely covered with particles, and were so heavy that they sat on the surface of the bed. The heavily laden bubbles only started to rise once they had obtained sufficient buoyancy either by clustering together in the bubble layer or by attaching to the lightly loaded bubbles rising out of the fluidized bed. Cluster formation in itself is no guarantee that a Table 1 The power consumption, Reynolds number and the energy dissipation rate at the impeller speeds used in the study. Impeller diameter D = 0.05 m; power number of the Rushton impeller Np = 5.5; volume of tank V = 0.006 m3. Impeller speed (rpm)
Power consumption (W)
Impeller Reynolds number
Energy dissipation rate, ε (W/kg)
250 400 550 700 850
0.12 0.51 1.32 2.73 4.89
10,417 16,667 22,917 29,167 35,417
0.021 0.085 0.22 0.45 0.81
group of bubbles may rise from the surface of the bed. Clusters can be seen in Figs. 4(a) and (b) that are heavily laden and may have nearneutral buoyancy. These remain at the surface until they can capture lightly loaded bubbles and gain positive buoyancy. Figs. 4(c) and (d) show clusters rising freely away from the bed. As clearly seen, a number of bubbles on the surface of these clusters are partially coated, and these can lend buoyancy to the cluster as a whole. 3.2. Cluster behaviour in turbulent conditions Fig. 5 shows the average bubble cluster diameter as a function of impeller speed at various DDA concentrations. As can be seen, in general the cluster size decreases with increasing impeller speed initially; however it plateaus eventually beyond the impeller speed of 550 rpm. It appears that an increase in the impeller rotational speed between 250 and 550 rpm causes a rapid drop in the size of the clusters, suggesting that larger clusters were unstable and degraded easily than the smaller ones by the impeller generated shear. Overall, the cluster size decreases approximately from 2.5 mm to 0.5 mm over the range of impeller speeds studied. Interestingly this behaviour is observed with almost all three DDA concentration used in the study. This shows that the formation and breakup of clusters are weakly dependent on the DDA concentration for the range used in the current system. Fig. 6 shows the influence of impeller speed on the behaviour of clusters at the same DDA concentration range used in Fig. 5, but in the presence of frother (MIBC) at a concentration of 80 ppm (ppm is expressed by volume i.e. μl/l). The trend in the results is similar to that shown in Fig. 5 although there are obvious differences between the two figures. The size of clusters decreases with increasing impeller speed, regardless of the DDA concentration. The change in the size is minimal beyond an impeller speed of 600 rpm, suggesting that when the bubble aggregates reach 0.6 mm in diameter, the mechanical strength of the bubble clusters is counterbalanced by the hydrodynamic force. It also appears that, the cluster size is a function of the DDA concentration at the lowest impeller speed with the largest clusters forming at the highest DDA concentration. Comparing Figs. 5 and 6, it is clear that the size of the clusters given in Fig. 6 (with frother) is much smaller than those in Fig. 5 (no frother), which is believed to be due to the different size of bubbles that form the clusters in the two systems. Fig. 7 shows the variation of bubble size as a function of DDA concentration, with no impeller involved. It is noted that no frother was present in the system so the change in the size was solely due to the presence of DDA. DDA is an ionic surfactant that can easily adsorb at the air–water interface, and reduces the surface tension, which in turn reduces the size of the bubbles. According to the figure, the bubble size decreases by 30%, as the concentration is increased from 0 to 12 × 10− 5 M. This suggests that in Fig. 5 where no frother is present, the initial bubble size formed at the base of sparger is different for each DDA concentration, which is expected to affect both cluster formation in the fluidized bed and the subsequent breakage behaviour in the impeller discharge zone. It is clear that DDA affects the size of the bubbles in the current system. To minimise this effect we measured bubble sizes in the presence of both MIBC and DDA. The results are shown in Fig. 8 where the size
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Table 3 The number of samples counted in the experiments and associated standard deviation and error. DDA: 7 × 10−5 M
DDA: 9 × 10−5 M
DDA: 1.2 × 10−4 M
Impeller speed (rpm)
Number counted
Standard dev. (mm)
Error (mm)
Number counted
Standard dev. (mm)
Error (mm)
Number counted
Standard dev. (mm)
Error (mm)
250 400 550 700 850
160 140 180 175 340
0.62 0.56 0.69 0.27 0.16
0.10 0.09 0.10 0.04 0.02
148 181 179 246 283
0.81 0.89 0.51 0.26 0.17
0.13 0.13 0.07 0.03 0.02
320 388 215 172 223
1.35 1.18 0.47 0.2 0.17
0.15 0.12 0.06 0.03 0.02
of bubbles as a function of MIBC concentrations at constant DDA concentrations at pH 9 is given. The figure shows that the bubble size decreases with increasing MIBC concentrations as expected, and then reaches its limited minimum size at all DDA concentrations. The minimum size of bubbles (around 200 μm) occurs when the concentration of MIBC exceeds 80 ppm, indicating that this is the critical coalescence concentration (CCC) of the frother. Surprisingly, the value of the CCC (determined based on the method described by [7] is in agreement with the result shown in the study of [5], although the current system contains an additional cationic surfactant. It is also interesting to observe that the CCC is essentially independent of the DDA concentration. This indicates that the bubble size at the CCC is determined primarily by the frother, and the contribution from the DDA is small.
Another factor that may affect the size of the bubbles forming the clusters in the cell is impeller speed. Once the clusters arrive into the impeller region, both the bubbles and clusters may be subjected to breakage. To investigate the influence of the impeller rotational speed on the initial bubble size, a series of experiments were carried out at impeller speeds from 0 to 850 rpm, and DDA concentrations of 0 and 1.2 × 10−4 M. The concentration of MIBC was kept at 80 ppm. The results are shown in Fig. 9. It is seen that the bubble size is approximately 200 μm at all impeller speeds for both DDA concentrations studied. This indicates that the size of bubbles is not affected by either the impeller speed or the DDA concentration and it is essentially independent of these two parameters in the current system when the frother is present. We note that as the two extreme DDA concentrations in this study were
Fig. 4. Some examples of bubble clusters formed in the fluidized bed.
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0.8
Mean Diameter of Bubbles (mm)
Mean Diameter of Clusters (mm)
3.0 -5
7 x 10 (M) -5 9 x 10 (M) -4 1.2 x 10 (M)
2.5 2.0 1.5 1.0 0.5 0.0 0
100
200
300
400
500
600
700
800
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
900
0
Impeller Speeds (rpm)
2
4
6
8
10
12
5
DDA Concentrations x 10 (M)
Fig. 5. The cluster size as a function of impeller speed in the absence of frother, at various DDA concentrations.
Fig. 7. The effect of dodecylamine concentration on bubble size. The impeller speed is zero.
tested, the result can be applied to the whole range of DDA concentration from 0 to 1.2 × 10−4 M. Revisiting Figs. 5 and 6 it may appear that there is a Critical Impeller Speed (CIS) at which there is a change in the behaviour of the bubble clusters. The presence of a CIS may be related to the two regimes that play important roles in the behaviour of bubble clusters. It may be postulated that the clusters undergo two distinct processes which are separated by a critical impeller speed in a given system: the fragmentation stage where the clusters are still exposed to breakage due to their loose, branched structure and the re-formation or collision stage in which the clusters tend to re-form due to the highly turbulent environment that promotes bubble-clusters or cluster-cluster collisions. A graph to demonstrate the existence of CIS is shown in Fig. 10 based on the Laskowski method [12], where the combined results for clusters size from our previous work [14] and the current study are given. At impeller speeds lower than the critical speed, the fragmentation of bubble clusters is predominant. In this stage, the behaviour of clusters is significantly related to the size and shape of initially formed clusters. Because the clusters are pre-generated in this study, the initial size of clusters is mainly determined by the hydrophobicity of particles, in other words, the concentration of collector. Higher DDA concentrations generate larger and branchy clusters. As the impeller speed increases, the size of the clusters reduces and becomes less sensitive to the shear rate at high impeller speeds.
When the impeller speed is increased beyond the critical speed the cluster size is determined by the balance between breakup and re-formation. The influence of the cluster size at formation is eliminated because the clusters show similar characteristics including size and shape regardless of DDA concentration. At this stage it is impossible to identify whether the clusters come from the degradation of mother clusters or re-formation due to bubble–particle, cluster–cluster or bubble–cluster collisions. However, pre-generation of clusters doesn't exist in industrial flotation cells, so the only way that clusters can form in these cells is through collision between individual bubbles and particles, to form the initial clusters, which may continue to grow until they reach an equilibrium size determined by their hydrophobicity and the turbulent conditions in the cell. This stage may be referred to as the collision stage. It is worthwhile to note that collisions may not always lead to cluster formation. It should also be noted that the CIS is more likely system-specific based on experimental conditions. [1] for example observed the CIS to be much higher than 670 rpm. However in their study, the silica particles were very small, having an average size of 7 μm. As been pointed out recently [3], fine particles can stabilize bubbles as well as foams and flotation froths. This could explain why the critical impeller speed observed by Ata and Jameson was much higher than the speed in this study. 0.8
Mean Diameter of Bubbles (mm)
Mean Diameter of Clusters (mm)
3.0 -5
2.5
7 x 10 (M) -5 9 x 10 (M) -4 1.2 x 10 (M)
2.0 1.5 1.0 0.5
0 (M) -5 1 x 10 (M) -5 5 x 10 (M) -5 7 x 10 (M) -5 9 x 10 (M) -4 1.2 x 10 (M)
0.7 0.6 0.5 0.4 0.3 0.2
0.0 0
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300
400
500
600
700
800
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Impeller Speeds (RPM) Fig. 6. The effect of impeller speed on the size of clusters with MIBC at a concentration of 80 ppm at various DDA concentrations as indicated in the legend.
0
20
40
60
80
100
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MIBC Concentrations (ppm) Fig. 8. The bubble size as a function of MIBC concentrations at various DDA concentrations. The impeller speed is zero.
Z. Chen et al. / Powder Technology 269 (2015) 337–344
Mean Diameter of Bubbles (mm)
0.5
0 (M) -4 1.2 x 10 (M)
0.4
0.3
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0.1
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Impeller Speeds (RPM) Fig. 9. Effect of impeller speed on the bubble diameter in the presence of MIBC at a concentration of 80 ppm.
4. Conclusions The behaviour of bubble clusters has been studied in a turbulent flotation cell. The sizes of bubble clusters have been measured in the absence and presence of frother at various DDA concentrations and impeller rotation speeds. The effect of the frother has been observed through measurement of the bubble size. A critical concentration of frother (80 ppm MIBC) has been chosen for the experiments, at which the bubble size is insensitive to changes in the DDA concentration and impeller speed. It appears that the cluster size is influenced not only by the DDA concentrations but also by the bubble size. The addition of frother at a certain concentration can effectively eliminate the impact of bubble size on the behaviour of bubble clusters. In the presence of frother above the critical value the clusters have similar sizes, almost independently of the DDA concentration and impeller speed. At impeller speeds lower than the critical speed, the fragmentation of bubble clusters is predominant. Because the clusters are pre-generated in this study, the initial size of clusters is mainly determined by the hydrophobicity of particles, in other words, the concentration of collector. Higher DDA concentrations generate larger, branched clusters. As the impeller speed increases, the size of the
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clusters reduces also and becomes almost insensitive to the shear rate at high impeller speeds. When the impeller speed is increased beyond the critical speed at which the clusters are insensitive to shear rate, the clusters show similar characteristics including size and shape regardless of DDA concentration. This indicates that the influence of the cluster size at formation is eliminated. At this stage it is impossible to identify whether the clusters come from the degradation of mother clusters or re-formation due to bubble–particle, cluster–cluster or bubble–cluster collisions. However, pre-generation of clusters doesn't exist in industrial flotation cells, so the only way that clusters can form in these cells is through collision between individual bubbles and particles, to form the initial clusters that may continue to grow until they reach an equilibrium size determined by their hydrophobicity and the turbulent conditions in the cell. This stage may be referred to as the collision stage. Accordingly, the data suggest that a critical impeller speed exists, separating the behaviour of the bubble clusters into two stages. In stage one, the cluster size is governed by the fragmentation process, where filamentous branches are broken off and the clusters consolidate. In the second stage, the behaviour is determined by collisions with free particles and bubbles, until a steady state is reached where processes of cluster formation and rupture are in balance. The critical impeller speed is affected by a number of physical and chemical factors, including collector concentrations, particle size, cluster structure and so forth. The results obtained in this study can be used to provide information on the likely behaviour of clusters in industrial flotation cells. The power consumption in these cells usually lies in the range 0.5 to 5 kW/m3, and without loss of generality the range could be expressed as 0.5 to 5 W/kg to align with the units used in the present study. It is seen from Table 1, that the range of impeller speeds used in the study provides power consumptions from 0.021 W/kg (250 rpm) to 0.81 W/kg (800 rpm), indicating that only the upper speed ranges employed in the study correspond to the power consumption used in industrial cells. It appears that at the highest power inputs, the dissipation rate is sufficiently high that clusters will find themselves in the equilibrium range, rather than the fragmentation range. They will be densely packed and stable in size, and their diameters will be in the range of 500 μm to 1 mm. Acknowledgements The authors would like to acknowledge the Australia Research Council (ARC) for financial support. References
Fig. 10. The mean diameter of clusters as a function of impeller speeds at various DDA concentrations in the absence of frother. Some data points are originated from our previous publication [4].
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