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Role of frothers in bubble generation and coalescence in a mechanical flotation cell.

Two frothers covering a very broad range from weak and selective (DF-200) to powerful (DF-1012) flotation performance were chosen to test the effect of frothers on bubble generation and bubble coalescence in a laboratory scale flotation cell. In two-phase, gas-liquid systems, the experiments showed that the frothers affect both the bubble breaking process and the coalescence of bubbles. While the DF-200 frother, characterized by much larger critical coalescence concentration (CCC) values than DF-1012, has the ability to produce finer bubbles at concentrations exceeding the CCC value, the bubbles generated in the DF-1012 solutions at concentrations exceeding CCC are much larger.

On a retenu deux agents moussants couvrant une vaste gamme, allant d'une performance de flottation faible et selective (DF-200) a puissante (DF-1012), afin de tester l'effet des agents moussants sur la production et la coalescence des bulles dans une cellule de flottation a l'echelle de laboratoire. Dans des systemes gaz-liquide diphasiques, les experiences montrent que les agents moussants influent a la fois sur le processus de rupture des bulles et la coalescence des bulles. Alors que l'agent moussant DF-200, qui se caracterise par des valeurs de concentration de coalescence critique (CCC) beaucoup plus grandes que pour le DF-1012, a la capacite de produire des bulles fines a des concentrations excedant la CCC, les bulles produites dans les solutions de DF-1012 a des concentrations excedant la CCC sont beaucoup plus larges.

Keywords: flotation, flotation frothers, bubble size, critical coalescence concentration, surface tension

Frothers play a fundamental role in the flotation process. According to the Schulman-Leja penetration theory (Leja and Schulman, 1954; Leja, 1956/1957), frother molecules are preferentially adsorbed at the water/air interface, and their interaction with the collector molecules adsorbed on mineral particles in the moment of the particle-to-bubble attachment is a vital step in the attachment process. Because frothers adsorb at the air/liquid interface they enhance gas dispersion into fine bubbles and stabilize the froth. The role of the froth in a flotation process is to act as a separating medium to segregate valuable mineral particles from gangue (Booth and Freyberger, 1962). Frother agents also enhance dramatically gas dispersion in flotation machines and reduce the size of the bubbles. Ahmed and Jameson (1985) found that bubble size has a strong influence on the rate of removal of the particles (flotation rate constant k). Yoon (2000) derived from first principles that the first order kinetic constant varies as [d.sub.v.sup.-3] ([d.sub.v] is the volume based bubble size) at quiescent conditions. However, under turbulent conditions, as in the case of mechanical cells, it is known that the flotation rate constant is less influenced by the bubble size (Heiskanen, 2000). Gorain et al. (1998) recently concluded that the overall flotation rate constant k is strongly correlated with the average bubble surface area flux in the cell [S.sub.b] = 6Jg/[d.sub.32] (where Jg is the superficial gas velocity and [d.sub.32] is the Sauter mean bubble diameter), which in turn is inversely related to the bubble size. Frother agents also affect the shape and the rising velocity of bubbles. Bubbles become more spherical in the presence of frother agents (Bogdanov, 1950; Fuerstenau and Wayman, 1958). The terminal velocity of a bubble in a liquid is dramatically reduced by increasing the concentration of frother. Sam et al. (1996) and Krasowska et al. (2004) demonstrated that this improves the probability of bubble-particle attachment.

Laskowski and his co-workers (Cho and Laskowski, 2002a, b; Laskowski et al. 2003; Laskowski, 2003) have shown that frothers can be characterized using two parameters: the critical coalescence concentration (CCC) and the Dynamic Foamabilty Index (DFI), examples of which are shown in Table 1. They showed that frothers reduce bubble size by preventing bubbles from coalescing. With increasing frother concentration, the degree of bubble coalescence decreases and at a particular frother concentration (CCC) the coalescence of bubbles is entirely prevented. The CCC values for several frothing agents have been determined using the University of Cape Town (UCT) Bubble Size Analyzer.

Grau et al. (2005) measured bubble size with the use of the Helsinki University of Technology (HUT) Bubble Size Analyzer and recently verified the validity of the CCC values obtained with the UCT technique. The experiments were carried out at different frother concentrations using three commercial Dow frothers: DF-200, DF-250 and DF-1012 ("polyglycol frothers"). Although both methods provided rather similar CCC values for the three tested frothers, they also revealed import differences. The main conclusions can be summarized as follows:

1. The bubble size measurements carried out using the HUT bubble size analyzer in a fifty [dm.sup.3] Outokumpu lab flotation cell and the UCT bubble size meter in a one [dm.sup.3] Open-Top Leeds flotation cell gave practically the same CCC values for three Dow frothers (DF-200, DF-250 and DF-1012).

2. Almost identical CCC values obtained when using different equipment, operating at different conditions, confirmed that the CCC values can be treated as material constants for frothers.

3. While the obtained experimental bubble size-frother concentration curves showed the same trends irrespective of the method used to size bubbles, the bubble sizes measured at frother concentrations exceeding the CCC values were much larger when the HUT method was utilized, especially for DF-250 and DF-1012.

In this project, a set of experiments was designed to examine the source of differences in the measured bubble sizes. The commercial frothers DF-1012 and DF-200 were selected for the experimental work. According to the DFI-CCC diagram published by Laskowski et al. (2003), the DF-200 frother can be considered to be weaker than DF-1012.

EXPERIMENTAL

Flotation Cell

An Outokumpu cylindrical flotation cell with a volume of 265 [dm.sup.3] (65 cm in diameter and 80 cm high) was used throughout. The cell is made of Plexiglas. Two types of commercial rotor/stator mechanisms manufactured by Outokumpu, Multi-Mix and Free-Flow (rotor diameter 15 cm) were used in the tests. The rotational speed of the rotor is controlled by a variable speed drive and is measured using a digital tachometer. In the Outokumpu cell, air is introduced through a hollow shaft. The air flow rate is continuously measured using a calibrated rotameter. The cylindrical cell is enclosed in a Plexiglas open-top box that is filled with water during the experiments to make visualization of the flow and gas dispersion conditions in the cell possible. A special launder made also of Plexiglas is designed to collect the foam overflowing the lip of the cell. This cell is designed to carry out mainly gas-liquid (two-phase system) experiments.

Only aqueous solutions of two commercial Dow frothers were utilized: DF-200 and DF-1012 (Table 1). The solutions were prepared using municipal tap water. All the experiments were run at room temperature. The temperature in the cell was continuously monitored.

Bubble Size Equipment

Bubble size was measured with the Helsinki University of Technology's (HUT) new Bubble Size Analyzer (BSA). This technique (from now on referred to as HUT BSA) is based on the apparatus developed by Jameson and Allum (1984) for sizing bubbles in industrial scale flotation cells. The technique was also adopted by Chen et al. (2001) and later improved by Hernandez-Aguilar et al. (2003). Recently Ata and Jameson (2005) used a similar apparatus to observe bubble-solid clusters formed in a 12 [dm.sup.3] mechanically agitated flotation cell. Earlier designs of the HUT BSA and their operation have been described in detail by Grau and Heiskanen (2002, 2003). The apparatus comprises of a viewing chamber connected to a sampler tube of adaptable length. The sampler tube has an internal diameter of 2 cm and is made of a transparent Plexiglas (Figure1). The lower end of the sampling tube is connected to a pinch valve. The viewing chamber is made of two sloped glass window sheets (20 x 15 cm and 20[degrees] angle) and PVC. The apparatus is filled with an aqueous solution of a frother (see Table 1) by using a peristaltic pump. The lower end of the sampling probe is immersed in the flotation cell, below the froth/liquid interface. As the pinch valve is opened, a swarm of bubbles rises through the sampling tube and reaches the viewing chamber. The bubbles rise up against the inner surface of the glass window as a single layer. The bubbles are then exposed to a video camera. As the bubbles reach the top of the chamber and burst, the excess air is removed using a second peristaltic pump, so that a controlled level of water is maintained in the chamber. Since, the water level does not change during bubble sampling, a down-flow of water in the sampling tube and inlet is prevented.

[FIGURE 1 OMITTED]

An inclined viewing chamber as suggested by Hernandez-Aguilar et al. (2004) reduces the probability of bubbles overlapping, so that the number of miscounted bubbles decreases. The inclined viewing chamber allows better setting of the focus plane. A JAI CV-M10 camera fitted with AF Micro Nikkor 60mm f/2.8D macro lens is used to capture images of a swarm of bubbles. The shutter speed of the camera was set at 1/2000 s. A Light Emitting Diode (LED) Backlight, with a high light output is used to expose the contour of the bubbles in the swarm. A rather shallow depth of field is set for the measurements. Images of the swarm of bubbles crossing the field of view (about 12 x 16 mm) are grabbed and then recorded on the hard disk of a personal computer at a fixed sampling rate.

Image Analysis

The series of captured images is processed off-line using Matrox Inspector (Matrox Electronic Systems) combined with in-house software (a Visual Basic Application). The captured images are digitized as greyscale images (8-bit = 256 intensity levels or shades) with a resolution of 768 x 576 pixels (square pixels). In order to size the bubbles, they are separated (segmented) from the background by converting the images into binary images (black and white). Each image is segmented by defining a threshold intensity, which ranges from 180 to 190. The same threshold intensity is set for the whole series of images by the experimenter, based on the quality of the images. For each bubble, its maximum and minimum diameter are computed by evaluating the Feret diameter of the bubble at a specified number of angles. Evaluation at 22 different angles was found to give accurate results. The bubble volume equivalent diameter ([d.sub.v]) is calculated using the maximum Feret diameter ([F.sub.max]) and the minimum Feret diameter ([F.sub.min]) as indicated in Equation (1), by assuming that the bubble is axisymmetric (Raymond and Rosant, 2000):

[d.sub.v] = [cube root of ([F.sup.2.sub.max][F.sub.min])] (1)

The Feret diameter depends upon the selected threshold value. In terms of the number of pixels, as the threshold intensity is increased the Feret diameter increases (Leifer et al., 2003). The dimension of a single pixel is calibrated by imaging an object of a known size: in this study, a syringe needle with external diameter of 0.710 mm. The calibration image is also converted into a binary image using the same threshold intensity, so accurate dimensions are assigned to each pixel in the image (about 21 ?m). Along with the Feret diameters, Matrox Inspector computes the compactness of a bubble, which is given by:

compactness = [p.sup.2]/4[pi]A (2)

where p is the perimeter of the projected bubble, and A is the projected area of the bubble. A circle has a minimum compactness value of 1. The bubble compactness factor is used as a criterion to identify clusters of bubbles or touching bubbles that could not be separated into single bubbles despite the fact that a separating algorithm (subroutine in Matrox Inspector) is applied to each image to split touching bubbles or bubbles in clusters. Often the algorithm failed to efficiently split each cluster. Thus, the compactness was found to be useful for identifying clusters and over-segmented objects or blobs in an image. A blob in an image with a compactness exceeding 1.25 is identified as possible cluster or over-segmented object and is therefore excluded from the results.

The bubble volume equivalent diameters ([d.sub.v]) computed from each image are stored automatically in an Excel workbook. It is in the workbook where the Sauter mean bubble diameter ([d.sub.32]) and the mean number diameter ([d.sub.10], see Equation (3)) of the sample are calculated, along with other parameters associated with the bubble size distribution. The Sauter mean bubble diameter is defined as the volume-to-surface mean, as described by Equation (4). The diameters are reported under standard temperature (298 K) and pressure (101 325 Pa) conditions.

[d.sub.10] = [N.summation over (i=1)][d.sub.vi]/N (3)

[d.sub.32] = [N.summation over (i=1)][d.sup.3.sub.vi]/[N.summation over (i=1)][d.sup.2.sub.vi] (4)

Monodisperse distributions of glass microspheres (NIST traceable monodisperse standards), manufactured by Whitehouse Scientific (England), are used to validate the image analysis method. The glass spheres are dropped into an inverted viewing chamber filled with water, mimicking a swarm of bubbles. The microspheres slide down the inner surface of the glass window. Although glass microspheres are rigid objects, which behave differently than gas bubbles, they can be used to study the impact of different parameters on image analysis and processing errors.

Preliminary results for different size classes are shown in Table 2. The same methodology used for gas bubbles was applied to the images of the glass microspheres. The relative errors shown in Table 2 were computed using Equation (5), where [d.sub.10HUT] is the number mean diameter calculated using the HUT BSA and [d.sub.10spheres] is the certified mean size.

error = [d.sub.10HUT] - [d.sub.10spheres]/[d.sub.10spheres] (5)

Sampling Location

Since a larger flotation cell is used in these tests, preliminary experiments were conducted in order to determine an adequate location for sampling bubbles. The lower end of the sampling probe was placed at different axial locations in the cell, as shown schematically in Figure 2. The impeller speed was set at 700 rpm, and the air flow rate was set at 99 [dm.sup.3]/min (Jg = 0.5 cm/s) and 197 [dm.sup.3]/min (Jg=1.0 cm/s). Non-coalescing conditions were established in the cell by using frothers at concentrations well above the CCC points see Table 1 or Laskowski et al. (2003). The variation of bubble diameter ([d.sub.32]) with sampling location is shown in Table 3. It was found that the HUT bubble size analyzer detected larger bubbles as the lower end of the sampling probe was placed at deeper locations in the cell, see Table 1. An explanation for this finding might be that the sampling probe only collects rising bubbles, and in the neighbourhood of the rotor/stator mechanism fine bubbles are not necessarily rising; they instead follow the flow lines. Therefore at locations 2 and 3, the bubble size measurements appear to be biased toward larger bubbles. At location 1, which is often referred to as the separation zone, the bubble population can be expected to travel upward. It could be expected that bubble size measured at locations near to the froth/liquid interface under non-coalescing conditions, is identical to that measured in the rotor/stator zone. In the preliminary experiments (with results shown in Table 3), DF-200 was used with only the Free-Flow mechanism shown in Figure 3 and DF-1012 was used with only the Multi-Mix mechanism shown in the same Figure. Similar behaviour is likely using other combinations of frothers and mechanisms.

[FIGURES 2-3 OMITTED]

The radial location of the lower end of the sampling probe was not modified throughout the experimental work. In the tests conducted in the 265 [dm.sup.3] Outokumpu flotation cell, Rudolphy et al. (2005) found that the Multi-Mix and Free-Flow rotor/slator mechanisms shown in Figure 3 produce rather uniform air distributions along the radial direction of the cell at impeller speeds higher than 500 rpm and aeration rates below 197 [dm.sup.3]/min. The tests were carried out at different frother concentrations. These findings indicate that under non-coalescing conditions a representative sample of the bubble population in the cell can be collected at any radial location near the froth/liquid- interface.

Methods

The experiments were carried out in a batch mode. The level of liquid in the cell was set equal to the diameter of the cell (65 cm), so a total volume of 215 [dm.sup.3] of tap water was added to the cell. In the frother tests, the hydrodynamic conditions in the cell were altered by modifying the aeration rate and impeller speed. The impeller speed was set at 600 rpm (tip speed of 4.7 m/s) and 900 rpm (tip speed of 7.1 m/s) and the air flow rate was set at 99 [dm.sup.3]/min (Jg = 0.5 cm/s) and 197 [dm.sup.3]/min (Jg = 1.0 cm/s) in the cell. The required volume of frother was added from a stock solution (around 10 g/[dm.sup.3]). Owing to the large volume of water used in the experiments, the cell was refilled with fresh water only if the temperature of the water exceeded 25[degrees]C. At temperatures below 25[degrees]C, only the volume of water required to change the frother concentration was added. The bubble viewer was filled with the same frother solution prepared in the cell.

Bubbles were sampled from the cell, once the foam reached a stable level in the cell. However, in some of the experiments, the foam flowed over the lip of the cell. As the foam overflowed the lip of the cell, it was discharged into the launder, and collected in a small vessel. The aqueous solution was recirculated back to the cell with a peristaltic pump and is re-injected through a port in the sidewall near the bottom of the cell. The location of the inlet was chosen to avoid disturbances to the prevailing hydrodynamic conditions in the cell. The recirculation flow rate was chosen so that steady-state conditions were achieved in the cell. The cell is operated with a maximum possible froth depth of 15 cm without considering air holdup. Foam overflow was observed mostly at high concentrations of frother, high air flow rates and high impeller speeds.

Bubbles were sampled exclusively from location 1 (see Figure 2) near the froth/liquid interface in the separation zone of the cell. A sampler tube 70 cm in length was used. Images of the swarm of bubbles were captured once steady state flow was achieved. In general, bubbles were sampled for several minutes before initiating the recording process. Two or more duplicate measurements were made for each condition. On average, more than 5000 bubbles were analyzed. In general, 500 images were captured and analyzed in each run; however, at low frother concentrations the number of images was increased so that a relatively large number of bubbles were sized. The images were captured at a fixed rate of either 1 s or 2 s intervals. Therefore, the image acquisition process was at least 8.5 min in duration. Surface tension was measured dynamically using a commercial maximum bubble pressure tensiometer [KSV BPA-800P].

RESULTS

The effect of two different frothers on bubble size under varying aeration conditions is shown in Figures 4 through 7. These experimental data can clearly be fitted as two linear regions with the intersection between the two giving the critical coalescence concentration (CCC). Figures 4 and 6 clearly show that in the non-coalescing region, the bubble size depends on the aeration rate when frother DF-1012 is used. Conversely, the effect of aeration rate in this region is negligible when DF-200 is used, as shown in Figures 5 and 7. This is again shown in Figure 8. Figures 4 and 5 include experimental data measured in a 50 [dm.sup.3] Outokumpu flotation cell (Grau et al., 2005). The narrow bands in these figures illustrate the range over which the critical coalescence concentration varies. Figures 6 and 7 include the location for each of the CCC values, which are indicated using arrows. The CCC values determined graphically are listed in Tables 4 and 5 for different hydrodynamic conditions in the flotation cell.

[FIGURES 4-8 OMITTED]

The rationale for determining the CCC in this way is described below. A linear equation is fitted to the bubble size-frother concentration curve at low concentrations using Microsoft Excel. A second linear equation is then fitted to the horizontal part of the curve that occurs at higher frother concentrations. Each linear equation is fitted to a minimum of three points. It was not always clear whether points close to the inflection of the bubble size-concentration curves should be assigned to the high- or low-slope lines. Therefore, the change in the slope of the steeper line induced by adding a point near the intersection was determined with a large change in slope indicating that the point in question is part of the low-slope line. The curves for the DF-200 frother are not linear over the entire low concentration range, so only the linear portion that meets the horizontal asymptote is used to determine the CCC point in each case (see Grau et al., 2005).

The Sauter mean bubble diameter, [d.sub.32], and the mean bubble diameter, [d.sub.10], are not very sensitive to the hydrodynamic conditions, particularly at low aeration rates. The maximum stable diameter [d.sub.90], which is defined as the bubble diameter such that 90% of the total gas volume is in bubbles of smaller diameter (see Figure 9), shows quite clearly the effect of the impeller speed on the bubble size, especially for the DF-1012 frother (Figure 10). As Figure 11 demonstrates, DF-1012 frother is much more surface active than DF-200. The dynamic surface tension isotherms for three Dow frothers are shown in Figure 11. Samples of the foam and solutions were taken as bubble size was measured. The solution was sampled by pumping a small amount of liquid from the zone close to the impeller. Results obtained with the DF-250 frother are also included in Figure 11, since this frother has been used in previous experimental tests (Laskowski et al., 2003; Grau et al., 2005).

[FIGURES 9-11 OMITTED]

DISCUSSION

All the bubble size versus frother concentration curves show the same patterns and agree very well with previous publications. The curves can be fitted with two linear segments with the intersection giving the CCC value. The curves in the region where the frother concentration is less than the CCC show the effect of frother on bubble coalescence. It is also evident that the size of the bubbles in the region where the frother concentration is greater than the CCC may be very different. This is the size of the bubbles produced by the rotor/stator mechanism and as Figure 8 demonstrates the size of these bubbles increases with increasing aeration rate. Figure 10 indicates that the size of largest bubbles in the non-coalescing frother concentration range also depends on the type of frother. These bubbles are larger for the DF-1012 frother than for the DF-200. As Figure 11 reveals, DF-1012 is much more surface active than DF-200. The foam generated in the aqueous solution of DF-200 is in equilibrium with the solution and the DF-200 concentrations are practically identical in the solution and in the foam (Figure 11). This trend is very different for DF-1012. Because of its surface activity, DF-1012 accumulates in the foam and its concentration in the foam quickly becomes much greater than in the solution.

Critical Coalescence Concentration

As Figures 4 through 7 shows, the CCC values for the frothers tested here do not seem to be substantially influenced by the hydrodynamic conditions prevailing in the flotation machine. As shown in Figures 6 and 7, the CCC values for the DF-1012 frother varied within a narrow range between 0.017 and 0.020 mmol/ [dm.sup.3]; for the DF-200 frother, the CCC values varied between 0.65 and 0.73 mmol/[dm.sup.3] (See Tables 4, 5 and 6). It is noteworthy that while the CCC values obtained for the DF-1012 frother seem to increase slightly with increasing aeration rate in the flotation cell, the CCC values obtained for the DF-200 were not affected by the changes in aeration conditions in the cell (Tables 4 and 5). This behaviour may be attributed to the frother depletion from the solution and its accumulation in the foam. As shown in Figure 11, the dynamic surface tension-bubble life time isotherms exhibit large differences for the two frothers tested here. For the less surface active frother, the dynamic surface tension data obtained from the collected samples of the foam and solution are almost identical, indicating that the foam and solution (liquid phase) were in equilibrium. For the more surface-active agents, large deviations between the surface tension-bubble life time isotherms are observed, which is an indicator that the frothing agents accumulated in the foam. The rate of accumulation of the frother in the foam and the amount accumulated may be correlated with the gas dispersion conditions, and particularly with the bubble surface area flux in the flotation cell, the surface activity of the frothing agent and its rate of adsorption.

Bubble Coalescence

Sagert et al. (1976) studied coalescence of bubble pairs generated on two adjacent capillary tubes in solutions of various alcohols. They showed that the measured coalescence time versus concentration curves obtained for various aliphatic alcohols correlate well with the surface tension--concentration relationships for these alcohols (Figure 12). Drogaris and Weiland (1983) further confirmed the relationship between the measured coalescence time and change in surface tension. These measurements were carried out under static conditions, which are very different from the dynamic conditions in the cell. However, if these coalescence time measurements have the same meaning under dynamic conditions then it is obvious that the coalescence under dynamic conditions can take place only if the time of contact between two colliding bubbles is longer than the coalescence time. By extrapolating the relationship between the coalescence time and concentration obtained for different alcohols by Sagert et al. (1976) to polyglycols (Dowfrothers), it could be expected that for a given concentration the coalescence time for DF-1012 would be much greater than for DF-200 (Figure 12). With increasing frother concentration the coalescence time increases; therefore, the number of bubbles coalescing decreases. As a result, a decrease in bubble size is observed (Figures 4 through 7). At concentrations exceeding the CCC values of each frother, the coalescence time might be longer than the time of contact, thus preventing bubbles from coalescing.

[FIGURE 12 OMITTED]

Critical coalescence times were calculated from the coalescence time-concentration curves (Drogaris and Weiland, 1983) by using the CCC values for n-butanol, n-pentanol, and nhexanol solutions given by Cho and Laskowski (2002a). It was found that the critical coalescence times fall within a narrow range between 0.05 and 0.1 s, indicating that the average contact between two colliding bubbles in a flotation cell is shorter than 0.1 s. This provides a time scale for the dynamic events occurring in a flotation cell.

It is usually assumed that bubble coalescene is a binary event, and that the mechanism of coalescence is based on drainage, thinning and rupture of the liquid film between two colliding or adjacent bubbles (Marrucci, 1969). The thinning or deformation of the film between two colliding bubbles can be regarded as a highly dynamic process. When a thin film of a solution of a surface-active agent is stretched or deformed, surface elasticity forces arise because of variations in surface tension. As bubble coalescence in the liquid phase is strongly retarded or prevented in the presence of frothing agents, the bubbles reach the surface of the liquid and form foam. Flotation foams are very unstable systems: after gas bubbling is stopped they collapse quickly (Malysa, 1992). Foam stability is generally explained by surface elasticity forces. The surface tension of a foam film (bubble-liquid surface) is higher than its static value during dilation and lower during compression. This variation in surface tension provides a restoring force that counteracts the disturbances (Kitchener and Cooper, 1959; Harris, 1982). This is known as the Marangoni effect:

E = d[gamma]/d ln([A.sub.B]) or E = [A.sub.B] d[gamma]/d[A.sub.B] (6)

Malysa et al. (1981), using a pulsating bubble technique, determined the Marangoni dilational modulus of n-octanol solutions (Figure.13). The Marangoni dilational modulus is defined as the change in surface tension (d[gamma]) with respect to the relative change in surface area deformation. A general definition of surface elasticity forces (modulus of elasticity) is given in Equation (6). The Marangoni dilational modulus refers to the so-called insoluble behaviour of the adsorption layer; that is to say, its values of the surface elasticity forces are the greatest that can be induced when frequencies of the interface disturbances are much higher than kinetics of adsorption-desorption processes. With increasing concentration of the surface-active agent, the Marangoni dilational modulus was found to increase, reaching values comparable to the equilibrium surface tension. This finding indicates that low concentrations of a surface-active agent might drastically modify the surface elasticity of a bubble. The Marangoni elasticity is believed to be greater in presence of more surface-active agents. Hence, it could be expected that this elasticity would be much greater in the presence of the DF-1012 frother than in the presence of the DF-200 frother at any given concentration. This seems to be the main reason why the molar CCC value of the DF-200 frother is almost four times higher than the CCC value of the DF-1012 frother (Table 6). It can also be concluded that at any frother concentration exceeding its CCC value, the film between colliding bubbles becomes elastic enough to resist rupture.

[FIGURE 13 OMITTED]

Bubble Breakup

Bubble generation in a mechanically agitated cell has been shown to occur in the zone close to the rotor/stator mechanism. Grainger-Allen (1970) observed that air cavities formed at the rear face of impeller blades in laboratory mechanical flotation cells. At low aeration rates, aerated cavities behind the blades of the Outokumpu rotor have been observed with the use of a high speed camera. The aerated cavities showed a high rotational speed, resembling the clinging cavities described by Bruijn et al. (1974). The main mechanism of bubble generation seems to be the shedding of bubbles from the tail of the rotating cavities (Grainger-Allen 1970; Van't Riet and Smith, 1973). The primary bubbles generated by the action of the aerated cavities may be further broken up in the region near the rotor/stator because of the highly turbulent conditions in this zone. The bubble size measured at concentrations exceeding the CCC values (non-coalescing conditions) is that generated by the rotor/stator mechanism at the hydrodynamic conditions prevailing in the cell. It is clear from Figures 4 through 7 that the type of frother has an effect on the size of the bubbles produced in the neighbourhood of the rotor/stator. Under non-coalescing conditions in the cell, the size of the bubbles produced by the mechanisms increased sharply with increasing aeration rate in the presence of the DF-1012 frother (Figure 8). In the presence of the DF-200 frother, only a moderate increase was observed. This result suggests that frothers may affect bubble generation differently. These differences become even more evident as the maximum stable bubble diameter ([d.sub.90]) is plotted against impeller speed (Figure 10). It is usually assumed that there is a maximum bubble diameter above which no stable bubble can exist in a turbulent flow. It is also obvious from Figure 10 that the Sauter mean bubble diameter ([d.sub.32]) and the number mean diameter ([d.sub.10]) did not reveal adequately the differences between the bubble size distributions produced in the presence of different frothers.

As shown in Figure 9, the value of [d.sub.90] is calculated by fitting the upper-limit distribution to the experimental data (ASTM E799-92, 1996). The corresponding [d.sub.10] (Equation 3) and [d.sub.32] (Equation 4) of the distribution are also included in the same figure. The upper-limit distribution has been found to describe satisfactorily bubble size distributions in laboratory scale flotation cells (Grau and Heiskanen, 2005). Other investigators have taken different cut-off sizes in the cumulative bubble size distribution as a measure of the maximum stable bubble size ([d.sub.max]). Deglon et al. (1998) and Takahashi et al. (1992) adopted the ([d.sub.95]) criterion (95% bubble size based on the cumulative bubble size distribution) as the maximum stable bubble diameter, while Hinze (1955) chose the 95% drop size from the cumulative volume distribution, as the maximum stable drop for a liquid-liquid dispersion. In this paper, the [d.sub.90] value was selected as the adequate measure to represent the maximum stable bubble diameter ([d.sub.max]) in a flotation cell.

Figure 10 reveals an interesting pattern: more surface active agent produced larger stable maximum bubble diameters. This finding seems to be contrary to the commonly accepted belief that reducing the surface tension of the liquid decreases the bubble size. The correlation for the maximum stable diameter for drops in locally isotropic turbulent fluids derived by Hinze (1955) has been adapted to model bubble breakup in stirred tanks (Calderbank, 1958; Parthasarathy et al., 1991). Parthasarathy and Ahmed (1994) obtained the following relationship for estimating the maximum stable bubble diameter in stirred vessels at low gas velocities and under non-coalescing conditions (concentration of 50 ppm of MIBC, see Table 1):

[d.sub.max] = C [[gamma].sup.3/5]/[(P/V).sup.2/5] [[rho].sup.1/5] (7)

where [gamma] is the equilibrium surface tension,[rho] is the density of the continuous phase, P/V is the power input per unit of volume and C is a constant. Although, this relationship, based on the theoretical model for liquid-liquid dispersions, predicts a reduction in the maximum stable diameter with decreasing surface tension, the real effect of the surface tension on the bubble breakup was not studied by the authors. Walter and Blanch (1986) studied the effect of several surfactants on bubble breakup in a turbulent pipe flow. They found that long hydrocarbon chain surfactants produce larger stable bubbles than short chain surfactants in solutions with similar surface tensions. In the presence of Dow frothers the following trend has been observed: at concentrations exceeding the CCC value, the maximum stable bubble diameter increased with increasing chain length of the frother molecule. The DF-1012 frother was found to produce larger stable bubbles than DF-250 and DF-200 (Figure 14, Grau et al., 2005). This trend seems to be more evident at higher aeration rates in the cell (Figure 8). At low aeration rates in the non-coalescing region, no large differences in the Sauter mean bubble diameters produced were observed. A similar pattern was observed previously by Laskowski et al. (2003). These results might suggest that in some cases the Sauter mean diameter is not a suitable parameter to reveal differences in bubble size distributions, particularly at the coarse end of the distribution, as depicted in Figure 10.

[FIGURE 14 OMITTED]

The reason why DF-1012 produced more stable bubbles than the other Dow frothers can be also found in the surface elasticity of adsorption layer of the bubbles. As bubbles are exposed to rapid deformation of their interface during the breakage process, it is likely that elasticity forces arise that withstand the disruptive forces. Indeed, Walter and Blanch (1986) modified Equation (7) by introducing the effect of surface elasticity on the breakage process as described by Equation (8):

[d.sub.max] = C [([gamma] + E).sup.3/5]/[(P/V).sup.2/5] [[rho].sup.1/5] (8)

where E is a dilational elasticity or dilational modulus (see Figure 13).

Elasticity forces have also been found to play an important role in drop breakup in liquid-liquid dispersions. Janssen et al. (1994a; b) concluded that the equilibrium surface tension could not explain the magnitude of the interfacial restoring forces arising during the deformation of an isolated single drop in the presence of surface-active agents in a Couette device. They defined an effective surface tension as described by Equation (9), which accounts for the net effect of the presence of surface-active agents:

[[gamma].sub.effective] = [gamma] + [beta]E (9)

In Equation (9) E is the elasticity modulus, which represents the dynamic component of the effective surface tension, [gamma] is the equilibrium surface tension and [beta] is a constant.

It seems that frothing agents endow bubbles with elastic properties, which arise during rapid deformation of the bubble interface. It is likely that in a turbulent flow, as in the zone close to the rotor/stator in a flotation cell, the distribution of a surfactant around the surface of a bubble is far from being uniform owing to the motion of the bubble. It is commonly accepted that the accumulation of surfactants at the gas/liquid interface of a rising bubble reduces the mobility of its interface, which results in a reduction in the rising velocity (Levich, 1962). According to Krzan and Malysa (2002) the concentration of surfactant at the interface of a rising bubble varies drastically. At the leading pole of the bubble (adsorption point) there is a low concentration of surfactant, while at the rear pole (desorption point) there is a high concentration of surfactant. The rotor/ stator neighbourhood is the zone where bubbles are broken up and high rates of collision between bubbles can be expected. A rapid deformation of a bubble will lead to even larger variation in frother concentration across the interface, resulting in local zones with high and low frother concentrations. The gradient in surface density of the surfactant leads to variations in surface tension, which might be an important factor stabilizing the bubble against coalescence and breakup. The distribution of the surfactant at the gas/liquid interface of a bubble is influenced by the surface activity of the surfactant, rate of transport to the surface, surface transport mechanisms, concentration of the frothing agent in the solution, motion of the bubble and physical properties of the liquid. It can be expected that long hydrocarbon chain frothers would show a lower rate of adsorption and lower ability to migrate along the surface of the bubble than shorter chain frothers.

CONCLUSIONS

The following conclusions can be drawn from this project: 1. The shape of the experimental bubble size-frother concentration curves agree very well with early publications. The curves are clearly divided into two regions by the critical coalescence concentration (CCC): the coalescing region and the non-coalescing region. The CCC value for each tested frother was found to vary within a narrow range. The size of the bubbles measured in the non-coalescing region is the size produced in the rotor/stator zone of the cell. In the presence of DF-1012, the aeration conditions in the cell were found to affect substantially the size of the bubbles produced over the non-coalescing range, while in the presence of DF-200, the effect of the hydrodynamic conditions in the cell was fairly small.

2. The tested frothers appear to affect both bubble coalescence and bubble breakup processes. The CCC values obtained experimentally for the less surface active frother (DF-200) were higher than those obtained for the DF-1012 frother, which is a more surface-active frother. The DF-200 frother was found to produce finer stable bubbles in the non-coalescing concentration range than the more surface-active frother (DF-1012).

NOMENCLATURE

A projected area of a bubble ([mm.sup.2])

[A.sub.B] surface area of a bubble ([m.sup.2])

C dimensionless empirical constant

CCC critical coalescence concentration (mol/[dm.sup.3])

DFI dynamic foamability index (s? [dm.sup.3]/mol)

[d.sub.v] bubble volume equivalent diameter (mm)

[d.sub.10] linear (arithmetic) mean bubble diameter (mm)

[d.sub.10spheres] mean size of glass spheres (mm)

[d.sub.10HUT] mean size of glass spheres determined by the HUT BSA (mm)

[d.sub.32] Sauter mean bubble diameter (mm)

[d.sub.90] bubble diameter such that 90% of the total gas volume is in bubbles of smaller diameter (mm)

[d.sub.max] maximum stable bubble diameter (mm)

E modulus of elasticity (N/m)

[F.sub.max] maximum Feret diameter (mm)

[F.sub.min] minimum Feret diameter (mm)

Jg superficial gas velocity (cm/s)

p perimeter of the projected bubble

TS impeller tip speed (m/s)

P/V power input per unit volume (W/[m.sup.3])

Greek Symbols

[beta] dimensionless constant

[gamma] surface tension (N/m)

[[gamma].sub.effective] effective surface tension (N/m)

[rho] density of the liquid phase (kg/[m.sup.3])

ACKNOWLEDGEMENTS

The authors are grateful to Outokumpu Technology for their financial support to conduct this research. This paper was mainly written during a visit to the Department of Chemical Engineering, University of Cape Town, which was made possible thanks to the travel grant awarded to Rodrigo Grau by the Outokumpu Oy Foundation. The assistance of Dee Bradshaw of the University of Cape Town in organizing the visit is gratefully acknowledged.

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Manuscript received June 21, 2005; revised manuscript received September 15, 2005; accepted for publication February 2, 2006.

Rodrigo A. Grau (1) and Janusz S. Laskowski (2) *

(1.) Helsinki University of Technology, Helsinki, Finland

(2.) The University of British Columbia, Vancouver, BC, Canada

* Author to whom correspondence may be addressed. E-mail address: jsl@apsc.ubc.ca
Table 1. Different operating conditions for all experiments

Common name Chemical formula Molecular weight

([dagger])[(PO).sub.1] C[H.sub.3][(O[C.sub.3] 90.12
 [H.sub.6]).sub.1]OH
[(PO).sub.2] C[H.sub.3][(O[C.sub.3] 148.12
 [H.sub.6]).sub.2]OH
([double dagger])DF-200 C[H.sub.3][(O[C.sub.3] 206.29
 [H.sub.6]).sub.3]OH
DF-250 C[H.sub.3][(O[C.sub.3] 264.37
 [H.sub.6]).sub.4]OH
DF-1012 C[H.sub.3](O[C.sub.3] 397.95
 [H.sub.6])6.3OH
MIBC C[H.sub.3]CHC[H.sub.2] 102.18
 CH(OH)C[H.sub.3]

 CCC * DFI
Common name ppm (s x [dm.sup.3]/mol)

([dagger])[(PO).sub.1] 46.8 5,700
[(PO).sub.2] 25.1 35,000
([double dagger])DF-200 17.3 196,000
DF-250 9.1 208,000
DF-1012 6.6 267,000
MIBC 11.2 34,000

* The CCC values have been published by Grau et al. (2005). The values
shown here are the maximum CCC values measured.

([dagger])PO is the acronym of polypropylene group, -O[C.sub.3]
[H.sub.6].

([double dagger])The acronym DF stands for the trade name Dowfroth.

Table 2. Validation of the HUT BSA using glass microspheres

[d.sub.10spheres] [d.sub.10HUT]
([micro]m) monodisperse ([micro]m) measured Relative
glass microspheres using HUT BSA errors

405.9 +/-8.7 429 5.7%

589 +/-8 618 4.9%

774 +/-3 752 -2.80%

978 +/-7 988 0.99%

1917 +/-11 1955 1.94%

Table 3. Effect of the sampling location on bubble size, impeller speed
700 rpm

 DF-200 25 ppm/ DF-200 25 ppm/
Frother/mechanism Free-Flow Free-Flow

Gas velocity Jg=0.5 cm/s Jg=1.0 cm/s
Sampling location [d.sub.32] (mm) [d.sub.32] (mm)
Location 1 0.68 0.79
Location 2 0.72 0.85
Location 3 0.79 0.93

 DF-1012 15 ppm/ DF-1012 15 ppm/
Frother/mechanism Multi-Mix Multi-Mix

Gas velocity Jg=1.0 cm/s Jg=0.5 cm/s
Sampling location [d.sub.32] (mm) [d.sub.32] (mm)
Location 1 0.96 0.67
Location 2 1.09 0.72
Location 3 1.38 0.87

Table 4. CCC values for the DF-1012 frother

Frother: DF-1012 CCC, Jg=0.5 cm/s CCC, Jg=1.0 cm/s

 Multi-Mix

 mmol/ mmol/
Impeller speed (rpm) [dm.sup.3] ppm [dm.sup.3] ppm

600 rpm 0.017 6.8 0.019 7.6
900 rpm 0.018 7.2 0.018 7.2

 Free-Flow

 mmol/ mmol/
Impeller speed (rpm) [dm.sup.3] ppm [dm.sup.3] ppm

600 rpm 0.017 6.8 0.020 8.0
900 rpm 0.017 6.8 0.020 8.0
CCC average 0.017 6.8 0.019 7.6

Table 5. CCC values for the DF-200 frother

Frother: DF-200 CCC, Jg=0.5 cm/s CCC, Jg=1.0 cm/s

 Multi-Mix

 mmol/ mmol/
Impeller speed (rpm) [dm.sup.3] ppm [dm.sup.3] ppm

600 rpm 0.073 15.1 0.065 13.4
900 rpm 0.070 14.4 0.066 13.6

 Free-Flow

 mmol/ mmol/
Impeller speed (rpm) [dm.sup.3] ppm [dm.sup.3] ppm

600 rpm 0.067 13.8 0.071 14.6
900 rpm 0.073 15.1 0.071 14.6
CCC average 0.071 14.6 0.068 14.1

Table 6. CCC mean values

 CCC mean STDEV CCC mean STDEV
Frother mmol/[dm.sup.3] mmol/[dm.sup.3] ppm ppm

DF-200 0.070 0.003 14.4 0.62
DF-1012 0.018 0.001 7.16 0.40
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Date:Apr 1, 2006
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