THE USE OF THE FROTH SURFACE LAMELLAE BURST RATE AS A FLOTATION FROTH STABILITY MEASUREMENT S. H. Morar 1,* , D. J. Bradshaw 2 , M. C. Harris 1

1

Center for Minerals Research, University of Cape Town Julius Kruttschnitt Mineral Research Centre, University of Queensland *Corresponding author: [email protected] 2

ABSTRACT Much research has been performed on the effect of froth stability on flotation performance. Generally, stable froths result in high recoveries at low grade, and conversely, unstable froths result in low recoveries at higher grade.

However, to manage the performance of a flotation cell using froth stability, a robust measure of froth stability is required. Currently, the established froth stability measurement techniques are either taken in the absence of hydrophobic solids, difficult to measure within an industrial environment or are empirical in their nature. In addition, an understanding of the factors that affect the measure of froth stability is necessary to provide a meaningful interpretation of the stability measure to model performance.

The stability of the froth is typically reflected by a number of attributes visible on the froth surface, such as the size of surface lamellae, reflecting the extent of coalescence, or the rate at which the surface lamellae burst, reflecting a lamella failure rate. Thus, this paper presents a machine vision technique developed to measure the rate at which lamellae on the froth surface burst, which may be a more practical measure of froth stability for an industrial environment.

1

The effect that factors such as bubble size and solids loading have on the burst rate is investigated and the potential of using this stability measurement for the management of a flotation bank is discussed with respect to flotation performance control.

Keywords: Flotation froths, Froth flotation

2

INTRODUCTION It is widely recognised that froth stability is a key driver of flotation selectivity and recovery (Subrahmanyam and Forssberg, 1988, Ventura-Medina, 2003, Hatfield, 2006, Hadler and Cilliers, 2009). However, owing to the non-linearity of mechanisms occurring within the froth as well as the dominant mechanistic effects changing across different conditions, it is not well understood. The effect operating variables have on both froth stability behaviour and their relationship to flotation performance is not clearly established for wide ranging conditions.

Extensive work has been performed in two-phase foam systems to characterise the effect of surfactants on bubble size, foam stability and water recovery (Bikerman, 1973, Malysa et.al., 1981). This work has shown that stability within a two-phase froth is well characterised by the nature and concentration of the surfactant, along with the air rate. It is clear that the understanding of mechanisms that relate to two-phase foam stability is relatively well understood and authors have demonstrated models that are able to predict factors such as liquid content and water recovery under different conditions (Neethling and Cilliers, 2003, Neethling et. al., 2003, Stevenson, 2007).

However, the understanding of three-phase froths is much less advanced. Studies on the effect of solids hydrophobicity have shown that not only can solid particles stabilize the froth, high loadings and highly hydrophobic solids can override the effect of solution stabilising effects within the froth. Therefore, two-phase foam stability work is inadequate as a means of understanding three-phase froth stability behaviour, as solution effects are easily overwhelmed by solid effects.

A number of froth stability measurement devices have been developed for industrial three-phase froths systems. Many of these measurement devices are intrusive, such as the column, acoustic or electrical impedance measurements. The only non-intrusive froth stability measurements developed to date are based upon machine vision.

3

Barbian et. al. (2005) and Zanin et. al. (2009) developed froth stability measurement devices using a column inserted into a flotation cell. These devices measure the rise rate of the froth surface, and the device developed by Zanin et. al. also measures the froth half-life, thereby measuring differential froth stability as a function of froth height. This information can be used to determine the effect of changing froth height on the froth stability, which would be useful as an on-line measurement (Hadler and Cilliers (2009)) and in on-line froth phase modelling. However, this relationship to froth height is largely dependent on the geometry of the froth column and may not linearly scale up to the entire flotation cell. Machine vision could be used to obtain similar data, but the operating conditions would have to be stepped, by taking measurements at different froth depths, disrupting the process.

However, column based measurements are intrusive to the process as they disrupt the flow of the froth and decrease the flotation cell’s efficiency. The column system also takes up more physical area relative to a machine vision approach and thus is not practical in smaller flotation cells. Finally, a flotation cell is a hostile environment to any equipment with moving parts. The maintenance requirements of a column based instrument are likely to be frequent and awkward.

Ventura-Medina et al. (2003) developed a measure related to froth stability incorporating some machine vision measurements. Their method is based upon the recovery of air to the concentrate launder relative to the amount of air added into the flotation cell. This measurement also relates to froth transport factors. The air recovery measure depends on two key parameters. The first requires either the measurement of the amount of air flowing into the cell (Qa) discounting the air lost to the tails, or the superficial gas velocity (Jg) through the flotation cell. The air flowing into the cell is usually measured as air input into forced aerated mechanical flotation cells. The superficial gas velocity is usually measured using a probe inserted through the froth into the pulp.

The second parameter is the volumetric flow rate of the froth recovered to the launder. This can be determined by measuring the height of the froth flowing over the weir (hfroth,weir), which can either 4

be measured manually or using a range meter located above the start of the launder, the length of the weir (lweir) and the velocity of the top surface of the froth (vf), measured using a machine vision method.

Thus, air recovery, as defined by Ventura-Medina et al. (2003) can be determined using (1).

(1)

This measure utilises the volume of the froth recovered, without accounting for the volume occupied by the water and solids within the froth. While air takes up the majority of the volume, the proportion of the air making up the froth varies with the state of the froth. Generally, froths with small bubbles are comprised of more water than froths with large bubbles.

Comparisons between the air recovery measure and column based measurements have shown conflicting results. Where work performed by Ventura-Medina et. al. (2003) showed no relationship between the two methods on a copper system, while work performed by Barbian et. al. (2005) showed a relationship between the two measurements in a platinum system.

Froth stability measurements based purely on machine vision techniques were proposed by Hyotyniemi et. al. (2000), de Jager et. al. (2005) and Hatfield (2006). These studies all used methods which involved the comparison of consecutive video frames. Their methods measure the correlation and disparity between the consecutive frames.

The disadvantage of this approach is that the machine vision algorithms output measurements which do not relate directly to a physical aspect of the froth. Thus, these measurements are difficult to interpret and perform non-linearly with respect to differences in froth structure.

5

A burst rate measurement would solve these problems by simply detecting and counting bubble burst events. The burst events represent a physical process occurring to the froth structure. The signal of each event is not skewed by bubble size or any other froth structural effects.

BURST RATE METHOD Typically, a bubble that bursts on the froth surface reveals a number of smaller bubbles below it. Thus, the identification of bursting bubbles is possible by analysing the output of aligned (de Jager et. al., 2005, Hatfield, 2006) and segmented images (Wright, 1997, Forbes and de Jager, 2004, 2006) to identify regions, or bubbles, which are replaced by multiple smaller regions, or bubbles in a consecutive frame.

The algorithm to perform this detection of burst bubbles is illustrated in Figure 1, and described below:

1. Segment consecutive images in a video sequence using the texture watershed technique. 2. Determine the displacement between the consecutive images using a single block match. 3. Align the labelled image outputs from the watershed segmentation with one another. 4. Determine the centroid of each region in both of the output images. 5. Determine the intersection of bubbles between consecutive frames. 6. For each bubble in the first frame: a. Determine whether the centroids of the bubbles in the second frame are within a radius, r, specified relative to the size of the selected bubble in the first frame. b. If the ratio of the bubble size from the first frame relative to the average area of the intersecting bubbles is greater than a threshold, t, the selected bubble in the first frame has burst. 6

i. Fit an ellipse around the selected bubble in the first frame. ii. Rotate the ellipse around its long axis to approximate the volume of the selected bubble in the first frame.

Figure 1: Flow-sheet illustrating the algorithm used to detect the burst bubble and determine the volume of air lost due to a bubble burst event on the froth surface.

This algorithm outputs both the number, size and volume information of bubbles bursting per pair of frames analysed. Typically, bubble size related information is reported in decile intervals of the cumulative bubble size distribution. Thus, the number of that bubbles burst per decile can be divided by the bubble count in each decile to determine the fraction of bubbles that burst per framepair interval as a function of bubble size. To determine the fraction of bubbles that burst rate per second, the video frame-rate needs to be considered. Figure 2 illustrates this process.

7

Figure 2: Determining the burst rate as a function of bubble size from the number of bubbles present, number of burst bubbles determined and using the frame rate (25 frames per second).

Bubble burst events occur at non-regular intervals. Thus, air loss on the froth surface follows a nonuniform cyclic pattern. As a result, it is more appropriate to analyse air loss data using the cumulative sum of the number of bubbles burst, or air lost on the froth surface, where the gradient of the cumulative sum is used to determine a measure across a period of time.

8

EXPERIMENTAL METHODOLOGY Two experimental systems were considered. Copper and platinum flotation systems were chosen, to represent slow and fast floating material respectively. The copper test work was performed in industrial flotation cells at NorthParkes Mine in New South Wales, Australia. This plant processes an ore, where the majority of the copper mineralisation occurs in bornite (Cu5FeS4) and chalcopyrite (CuFeS2). The platinum test work was performed on the pilot plant at Anglo Platinum Divisional Metallurgical Laboratories in Rustenburg, South Africa. The ore used in this study was obtained from the Merensky reef in the Bushveld complex. Merensky reef is feldspathic pyroxenite and shows a large variation in mineralogy, both on a small and large scale. It also contains talc which is a problematic gangue mineral. The PGM’s are finely disseminated and associated in solid solution with the sulphide minerals which are predominantly pentlandite, chalcopyrite and pyrrhotite.

Within these systems, a number of measurements were performed in the first and third cells of the rougher bank, to represent the presence of high and low amounts of floatable material present within the pulp respectively.

Machine vision measurements were taken. These consisted of 20 minutes of video footage across each test. This footage was analysed using the SmartFroth machine vision system (Sweet et.al., 2000) and software implementing the new measurements described in this work. Measurements of the superficial gas velocity were obtained using the JKMRC superficial gas velocity probe (Gorain et.al., 1996) and Anglo Platinum bubble sizer (Taute and Mc Clelland, 2006) in the copper and platinum systems respectively. Solids loading measurements were obtained using a gravimetric method (Sadr-Kazemi and Cilliers, 2000). These measurements were then used to calibrate a machine vision method (Morar, 2010), from which the solids loading was determined as a function of bubble size.

In both systems, experiments were performed where the operating conditions were modified between high and low conditions. In the copper system the frother concentration, froth depth and 9

air rate to each cell were modified for each experiment, while in the platinum system the frother concentration, frother type (Senmin XP200 and XP250), froth depth and presence of activator (CuSO4) were modified for each experiment.

RESULTS AND DISCUSSION Method validation This measurement was validated using a comparison of the algorithm’s output to manually segmented images of bursting bubbles. These manually segmented images were used in the same way that the algorithm determines the volume of air lost. Thus, this validation tests both the ability of the algorithm to detect burst bubbles and the accuracy of the segmentation of these bubbles.

Images from copper and platinum froth systems were used to validate this measurement. Within both systems, video clips of 10 seconds in duration were selected. Each sample video was taken in the first rougher. The manual segmentation was performed by ‘painting’ the area occupied by each burst bubble onto an image overlaid on the froth. The volume of air released from the bursting bubble is approximated by subsequently fitting an ellipse to the painted area and rotating the ellipse around its long axis, which is the same method that the algorithm uses.

A comparison of the identification of a burst bubble using manual segmentation and the algorithm, for a single burst event, is shown in Figure 3. Figure 3(a) shows that a bubble has burst in the second frame. Thus, this bubble is manually segmented, as shown in Figure 3(b). The corresponding bubble region from the segmentation algorithm is shown in Figure 3(c).

Using these two measurements on a series of images, the volume of air lost, as determined by the algorithm, can be compared to a more accurate measurement of the volume of air lost over time. This comparison can be use to validate the use of the algorithm as a relative measure and calibrate it to an absolute value. 10

Figure 3: An example of a bubble bursting in two consecutive frames shown in (a), where the burst bubble has been identified in (b) by manual segmentation and (c) using the automatic air loss algorithm (in a copper froth).

Results from individual tests show that the volume of air lost determined by the algorithm is less than that determined manually. However, the intensity of air loss determined by the algorithm correlates with the air loss determined from the manual segmentation.

The results of this comparison across all of the tested conditions are shown in Figure 4, where the average rate of air loss across the ten second clips is determined using the automatic algorithm and manually segmented measures.

11

(a) Copper froth

(b) Platinum froth

Figure 4: Comparison between the air loss measurements determined by the automatic algorithm and as determined by manually segmented images for (a) copper and (b) platinum froth data set.

These results show that an element of bias exists between the manually and automatically segmented regions. This bias has been attributed to a few factors.

Firstly, regions may be over-segmented. Larger bubbles are prone to over-segmentation at their boundary, which may be as a result of a filtering artefact, due to the low-pass filter currently implemented in pre-processing, before the segmentation algorithm. With larger bubbles, the segmentation line in the current watershed algorithm tends to be on the inside of the bubble’s border, thus resulting in a smaller elliptical fit for the bubble. The significance of this effect on bubble volume increases with bubble size.

This phenomenon can be observed in Figure 5, where the burst bubble can be observed to have been over segmented in the darker shadowed regions of the bubble.

12

Figure 5: An example of a bubble that bursts (a), showing over-segmentation along the top border and into multiple regions (b), both leading to an under-estimation of the amount of air lost.

Secondly, larger bubbles are prone to over-segmentation. However, this may occur due to an uneven surface lamella, or multiple highlights, which tend to occur further apart on larger bubbles. Here, the segmentation may result in a single bubble being segmented into two regions, where both of these regions are identified as having ‘burst’. In this case, the total volume of air lost determined from these regions would be lower than if the bubble had been correctly segmented into a single region.

13

This phenomenon can be observed in Figure 5, where the burst bubble can be observed to be oversegmented into four distinct regions.

Another factor that may result in a measurement error may be due to the mis-identification of a burst bubble, due to the over-segmentation of the bubble in a consecutive frame. However, this would lead to an over-estimation in the amount of air lost, which is not determined to be the cases shown in Figure 4. This problem can be mitigated by a comparison of the current frame’s segmentation with the previous and future frames after its consecutive frame. This was implemented in the air loss measurement and minimised the scenarios where an over-estimation of the air lost occurs.

The bias due to the mechanisms described above has been shown to be consistent across all of the different conditions investigated. Based upon this evidence, the bias can be corrected and accounted for using a calibration factor that has been shown to be independent of the operating conditions tested.

Comparing burst rate to air recovery Ventura-Medina et al. (2003) developed a measure related to froth stability based upon the recovery of air to the concentrate launder relative to the amount of air added into the flotation cell. This air recovery measurement was only obtained in the copper system. By considering the measured air recovery and the amount of air entering the cell, the results of this air recovery measurement can be compared to the measurement of air loss through the froth surface.

The amount of air entering the froth was calibrated using a measurement of the superficial gas velocity. The height of the froth overflowing the launder was measured manually with a measuring tape. The froth velocity was measured using the velocity measurement output from the SmartFroth machine vision system.

14

Figure 6 shows a comparison between the rates of air lost through the froth surface measured using the machine vision method from which the burst rate is determined, and the air lost through the froth surface calculated by using the measured alpha value and the average superficial gas velocity through the flotation cell. These results show that the average air loss measured using the machine vision method tends to underestimate the average air loss across the entire surface when compared to the air loss determined using the alpha value. This occurs owing to volume of air lost determined using the alpha value considering the air loss across the entire froth surface. The air loss estimated using the machine vision method is only able to estimate the air loss in the vicinity of the camera.

Figure 6: Comparison between the air loss measurement by the developed algorithm and the air loss measurement calculated using the measurement of air recovery and the superficial gas velocity for the copper data set.

Other factors that may explain the variation between these two measurements are that the velocity measured may not be representative of the velocity of the froth overflowing the launder. Lower layers of the froth may be travelling over the launder slower than the froth surface, resulting in an under-estimation of velocity and thus alpha value. In addition, the froth accelerates as it moves to

15

the launder, which means that the average velocity of the froth in view of the camera is less than the velocity of the froth at the launder, resulting in an over-estimation of velocity and thus alpha value.

The machine vision measurement of air lost through the froth surface is more sensitive to changes near the launder, while the air recovery method is sensitive to the average air loss across the entire froth surface. However, the difference between these two regions appears to decrease further down the bank, where the machine vision measurement underestimated the average air loss fewer times.

The broader range of air loss measurements obtained from the machine vision measurement as compared to the air recovery measurement implies that the air loss near the launder is more sensitive to the cell operating conditions than the overall air loss across the entire cell surface.

Incorporating bubble size and solids loading Froth stability is known to be affected by the solids loading and quality or hydrophobicity of the solids present on the bubble lamellae. Ata (2003) determined that while an increase in particle hydrophobicity stabilises the froth, highly hydrophobic particles are less effective at stabilising the froth than particles of intermediate hydrophobicity.

Within the experiments performed, both of these factors have been either measured or varied. A machine vision based solids loading measurement has been developed (Morar, 2010), which requires calibration to a gravimetric loading measurement (Sadr-Kazemi and Cilliers, 2000). The machine vision measurement outputs the solids loading as a function of bubble size, as related to each decile within a cumulative bubble size distribution. The effect of hydrophobicity can be inferred by the consideration of the two different systems used, and the location of measurements within the flotation bank. Floatable solids from the copper system are expected to be highly hydrophobic, while the floatable solids present in the platinum system are expected to be moderately hydrophobic. In addition, the solids recovered in the first rougher are fast floating, while the solids recovered in the third rougher are slow floating.

16

The effect of bubble size on the burst rate is illustrated in Figure 2. Here it can be seen that larger bubbles burst more readily. Therefore, bubble size on the froth surface will strongly affect the bursting rate of bubbles. This occurs owing to interactions between the drainage of liquid from the lamellae and the surface tension required to stabilise larger bubbles.

An empirical power-law model (Equation 2) has been fitted to model the effect of solids loading (φ) and bubble size (db) on the bubble burst rate (ζ).

(2) Table 1: Results of the model fit to explain the effect of bubble size and solids loading on burst rate.

Cell a b c R2 of fit Rougher 1 6.63E+4 2.27 1.91 0.885 Rougher 3 1.62 2.89 -1.95 0.960 Platinum Rougher 1 2.01 2.49 -2.97 0.940 Rougher 3 7.77E+7 5.02 -0.389 0.980 System Copper

The results of this model fit are shown in Table 1, and plotted in Figure 7. These results show the effect that bubble size and solids loading have on burst rate. The model fits the experimental data well for the small and intermediate bubble sizes. However, the model fit at the larger bubble sizes shows larger amounts of variation. A number of sources of error may explain this variability, including ore feed variability (particularly in the first rougher of the industrial system), errors in bubble segmentation (known to increase with bubble size) and the solids loading measurement and calibration. Despite this variability, the effect that the solids loading and bubble size have on the burst rate is apparent.

In the first rougher of the copper system (Figure 7a) an increase in solids loading can be seen to increase the burst rate, whereas in the third rougher of the copper and both roughers in the platinum systems, an increase in solids loading results in a decrease in the burst rate. Ata et. al. (2003) showed that highly hydrophobic particles tend to destabilise the froth when compared to 17

moderately hydrophobic particles. The floatable particles in the first rougher of the copper system are fast floating, and are considered highly hydrophobic. The results shown in Figure 7(a) support this finding, as an increased burst rate results in a less stable froth.

(a) Copper rougher 1

(b) Copper rougher 3

(c) Platinum rougher 1

(d) Platinum rougher 3

Figure 7: Results showing the effect that bubble size and solids loading have on the burst rate of bubbles on the froth surface in the copper and platinum systems in the first and third rougher. The red points are the measured data. The plotted surfaces represent the model fitted to the measured data. The solid lines between the plotted surface and the red points represent the residuals between the model fit and the data. The dashed lines connecting points on the plotted surfaces represent measurements obtained at the same operating conditions across different bubble sizes.

As bubble size increases the burst rate tends to increase. The significance of this relationship is greater than that of the effect of solids loading, which can be determined from the model coefficients in Table 1. In addition, within the platinum system, the burst rate and solids loading can be attributed to limit the size that bubbles are able to attain. At lower solids loadings, smaller

18

bubbles are present, which tend to burst at a marginally lower rate than conditions of higher solids loadings where larger bubbles able to remain stable. This trend is less clear in the copper system, and may be due to effects of highly hydrophobic particles, or variation in the ore feed.

These findings show that the development of both the burst rate and solids loading measurements are able to augment the bubble size information obtained on the froth surface to characterise the stability of the froth. These measurements have been shown to be sensitive to variations in operating conditions, however this sensitivity is constrained within a region that can be easily modelled. Thus, these measurements have the potential to provide information that may be useful in the management of a flotation bank.

Froth stability has been shown to be sensitive to the quality of particles attached on bubble lamellae (Dippenaar, 1982, Ata et. al., 2003). Thus, these measurements may have the potential to infer the grade of particles that reach the froth surface. Combining the information down the bank may result in a system that can detect changes to head grade, as this model relationship has been demonstrated to remain consistent across operating conditions. However, further work linking the mineralogy of the solid particles reaching the froth surface and their effect on froth stability is required to develop this relationship.

CONCLUSIONS A new machine vision measurement has been developed to measure the burst rate of bubbles on the froth surface. This measurement has been proposed as a measure that characterises the stability of the froth. The stability behaviour measured by this measurement has been shown to be constrained to a simple model of the bubble size and solids loading present on the froth surface. The nature of this model has been shown to change when the floatability and concentration of available solids changes within a bank. Therefore, this measurement shows promise for applications in online flotation bank management and froth recovery prediction. 19

REFERENCES Ata, S., Nafis, A., Jameson, G.J., 2003. A study of bubble coalescence in flotation froths. International Journal of Mineral Processing 72, pp. 255-266.

Barbian, N., Hadler, K., Ventura-Medina, E., Cilliers, J., 2005. The froth stability column: linking froth stability and flotation performance. Minerals Engineering 18, 317–324.

Barbian, N., Hadler, K., Cilliers, J.J., 2005. The froth stability column – Measuring froth stability at an industrial scale. In: Proceedings of the Centenary of Flotation Symposium, Brisbane, pp. 315-319.

Bikerman, J., 1973. Foams. Springer-Verlag, New York.

de Jager, G., Hatfield, D., Bradshaw, D., Francis, J., Morar, S., 2005. A method and a control system for extracting valuable minerals from mined ore, “SmartFroth”. South African Patent 2005/04232.

Dippenaar, A., 1982. The destabilisation of froths by solids: I The mechanism of film rupture. International Journal of Mineral Processing 9, 1–14.

Forbes, G., de Jager, G., 2004. Texture measures for improved watershed segmentation of froth images. In: Proceedings of the Twelfth Annual Symposium of the Pattern of South Africa.

Forbes, G., de Jager, G., 2006. A method of determining the size distribution of bubbles in the froth and a froth flotation process, “SmartFroth 5”. Adams & Adams Patent Attorneys Pretoria A&A REF: 2006/01520.

Gorain, B., Franzidis, J., Manlapig, E., 1996. Studies on impeller type, impeller speed and air flow rate in an industrial cell. Part 3: Effect on superficial gas velocity. Minerals Engineering 9, 639–654.

Hadler, K., Cilliers, J., 2009. The relationship between the peak in air recovery and flotation performance. Minerals Engineering 22, 451–455.

20

Hatfield, D., 2006. The implications of froth structure and surface appearance for flotation performance. PhD thesis, University of Cape Town. Malysa, K., Pawlikowska-Czubak, J., Pomianowski, A., 1978. Proceedings of the VIIth International Congress of Surface Active Substances (Moscow 1976). Vol. 3. Moscow, Chapter: 4. Frothing properties of solutions and their influence on the floatability, pp. 513–520.

Morar, S.H., 2010. The use of machine vision to describe and evaluate froth phase behaviour and performance in mineral flotation systems. PhD thesis, University of Cape Town.

Neethling, S., Cilliers, J., 2003. Modelling flotation froths. International Journal of Mineral Processing 72, 267–287.

Neethling, S., Lee, H., Cilliers, J., 2003. Simple relationships for predicting the recovery of liquid from flowing foams and froths. Minerals Engineering 16, 1123–1130.

Sadr-Kazemi, N., Cilliers, J., 2000. Technical note: A technique for measuring flotation bubble shell thickness and concentration. Minerals Engineering 13, 773–776.

Stevenson, P., 2007. Hydrodynamic theory of rising foam. Minerals Engineering 20, 282–289.

Subrahmanyam, T., Forssberg, E., 1988. Froth stability, particle entrainment and drainage in flotation - A review. International Journal of Mineral Processing 23, 33–53.

Sweet, C., Bradshaw, D., Cilliers, J., Wright, B., de Jager, G., Francis, J., 2000. The extraction of valuable minerals from mined ore.“SmartFroth”. South African Patent 2000/7079.

Taute, J., Mc Clelland, A., 2006. Introduction to the Anglo Platinum bubble sizer. Presented at the SAIMM Conference, Cape Town.

21

Ventura-Medina, E., Barbian, N., Cilliers, J., 2003. Froth stability and flotation performance. In: Proceedings of XXII International Mineral Processing Congress. Cape Town, South Africa, pp. 937– 945.

Wright, B., 1997. An investigation into the use of the watershed transform for the real-time segmentation of flotation froth images. MSc thesis, University of Cape Town.

Zanin, M., Wightman, E., Grano, S., Franzidis, J.-P., 2009. Quantifying contributions to froth stability in porphyry copper plants. International Journal of Mineral Processing 91, 19–27.

22