FIELD OF THE INVENTION

This invention relates to a method of estimating bubble size in a froth. BACKGROUND TO THE INVENTION

Froth floatation is a process for selectively separating hydrophobic minerals from those which are hydrophilic. The process is used in several processing industries. Historically, this was first used in the mining industry, where it was one of the great enabling technologies of the 20th century. It has been described as the single most important operation used for the recovery and upgrading of ores. The development of froth flotation improved the recovery of valuable minerals such as copper- and lead-bearing minerals. Along with mechanized mining, it allowed the economic recovery of valuable metals at much lower head grades than before.

The flotation process typically takes place in an open cell and consists of the pulp phase which can be described as the 'reactor ^* and the froth phase which can be termed the 'separator ¹ . In the pulp phase, hydrophobic particles preferentially attach to rising air bubbles which form a froth at the top of the pulp and are recovered as concentrate. Sub-processes such as bubble- particle collision, attachment, detachment and entrainment dominate. These sub-processes have an overall effect of transporting particles, mostly hydrophobic particles to the froth phase. In the froth phase, the process of froth formation and transport determines the kind of sub-processes that take place. Froth phase sub-processes such as thinning of bubble films, bubble coalescence and froth drainage result in an increase in bubble sizes, particles detaching from bubbles and draining back into the pulp phase. Froth phase sub-processes may lead to cleaning/separating action if there is preferential re-attachment of the draining particles to the available bubble surface area. This cleaning action determines the overall grade and recovery of the flotation process. The initial separating action of the froth phase starts at the pulp-froth interface.

Further cleaning action may take place in the bulk of the froth phase where particles detach from bubbles mainly because of bubble coalescence. Bubble coalescence also results in a general increase of froth bubble sizes from the pulp-froth interface to the top/surface of the froth. The rate of bubble coalescence is affected by such factors as froth stability, gas rate and froth depth. At a given gas rate and froth depth, froth stability determines the rate of bubble coalescence and therefore rate of change of bubble sizes. By knowing the rate of change of bubble size, properties like froth stability and rate of bubble coalescence can be inferred. Top of the froth bubble sizes have been correlated with concentrate grade. A measure of bubble size in the froth and an understanding of the rate at which bubble sizes change within the froth phase can provide quantitative information which will assist in understanding the froth phase sub-processes, especially bubble coalescence.

An important parameter for process control of such froths is the bubble size distribution (BSD) in the pulp phase and the froth phase. Various methods for measurement of the BSD in the pulp phase have been developed. The measurement of the froth bubble size on the surface of the froth phase is done by conventional photographic or video methods. No measurement of the bubble size or the BSD in the body of the froth phase has yet been developed. SUMMARY OF THE INVENTION

In accordance with this invention there is provided a method of estimating bubble size in a froth, which method includes

applying a potential between the tip of an elongate electrode and a counter- electrode in electrical communication with the froth,

inserting the elongate electrode into the froth and measuring an electrical characteristic which distinguishes between the electrical characteristics of the liquid surface of a bubble and that of the fluid contents of a bubble,

correlating the measurements to the position of the tip of the electrode in the froth, and

estimating bubble sizes as a function of substantially similar measurements and the position of the tip of the electrode. Further features of the invention provide for the electrical characteristic to be conductivity, alternatively to be related to conductivity; for the electrical characteristic to be electrical potential; for the froth to be on the surface of a liquid body and for the counter-electrode to be in electrical communication with the liquid body.

Still further features of the invention provide for the elongate electrode to have a diameter of less than 1 mm, preferably less than 0.5 mm, more preferably about or less than 0.3 mm; for the elongate electrode to be insulated along its length and for the tip of the electrode to be exposed; and for the elongate electrode to be inserted tip first into the froth.

Yet further features of the invention provide for the electrical characteristic to be continuously measured; and for the elongate electrode to be inserted into the froth at a known velocity and in a generally upright condition.

There is further provided for bubble size estimations to be used to determine froth bubble size distribution in a froth and the rate of bubble coalescence. BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:-

Figure 1 is a simplified illustration of voltage measurements from an elongate electrode inserted into a froth;

Figure 2 is a schematic diagram of an apparatus for estimating bubble size in a froth;

Figure 3 is an elevation and detail of the elongate electrode of the apparatus in Figure 2; Figure 4 is a circuit diagram for the apparatus in Figure 2;

Figure 5 is a plot of an experimentally measured voltage signal obtained from an elongate electrode inserted into a froth; Figure 6 is a plot of a voltage signal obtained from an elongate electrode inserted into a froth of a copper sulphate solution;

Figure 7 is a derivative of the plot in Figure 6; Figure 8 is a plot of individual drop average intra-bubble impact distance (IID) as a function of height above the pulp-froth interface

Figure 9 is a plot of average IID as a function of height above the pulp-froth interface;

Figure 10 is a plot of IID distribution for two froth segments; Figure 11 is a plot of cumulative IID distribution for two froth segments;

Figure 12 is a plot of Sauter-mean bubble diameter obtained from photographs as a function of froth depth;

Figure 13 is a plot of cumulative bubble size distribution (BSD) of froth segments; and

Figure 14 is a plot of estimated bubble sizes and the Sauter-mean bubble diameters.

DETAILED DESCRIPTION WITH REFERENCE TO THE DRAWINGS

A method of estimating bubble size in a froth is provided. The froth can be the froth in a froth flotation cell. Such froth flotation cells include a pulp phase which can be equated to a liquid body containing mineral particles with a gas sparged there through to provide rising bubbles. The gas is typically air. A froth phase is present on the surface of the pulp phase or liquid body.

In accordance with the method, bubble size in the froth can be estimated by applying a potential between the tip of an elongate electrode and a counter- electrode in electrical communication with the froth. Conveniently, the counter-electrode can be in communication with the liquid body on which the froth rests. The elongate electrode is then inserted into the froth and an electrical characteristic is measured during such insertion. The electrical characteristic is selected to be one which distinguishes between the electrical characteristics of the liquid surface of a bubble and that of the fluid contents of the bubble. It will be appreciated that the contents of the bubble will be a gas which may be saturated to some extent with a liquid. The most notable characteristic which differentiates the fluid contents of the bubble liquid forming the surface of the bubble will be conductivity. The conductivity of the liquid forming the surface of the bubble will be relatively high compared to that of the gaseous contents of the bubble. It will be understood that electrical characteristics related to conductivity, such as electrical potential or voltage and resistance or current, could equally be measured. In the present embodiment, electrical potential (voltage) is measured as the elongate electrode inserted into the froth until it reaches the liquid body. The voltage measurements are correlated to the position of the tip of the electrode in the froth and the bubble size then estimated as a function of substantially similar measurements and the position of the tip of the electrode.

It will be appreciated by those skilled in the art that foams can be considered as a network of interconnected films called lamellae. Ideally, the lamellae are connected in triads and radiate 120° outward from the connection points, known as Plateau borders. The terms lamella and Plateau are used herein to denote the surfaces of bubbles where appropriate. The method of estimating bubble size can be illustrated with reference to Figure 1 , which illustrates a section through an open cell (1) containing a liquid body (2) with a froth (3) on top of the liquid body (2).

The elongate electrode (not shown) is inserted along the line A-B into the froth. A theoretical part of the voltage measurements made during insertion of the electrode into the froth is shown adjacent the illustration of the cell (1) to illustrate the voltage measurements correlated to the position of the tip of the electrode. With the tip of the elongate electrode above the froth in air, the voltage measurement is high until the tip encounters the surface of the first bubble. Thereafter, it drops extremely rapidly to a lower voltage corresponding to that of the liquid body. As the electrode moves though the surface of the bubble it encounters the gaseous interior and the voltage rises again to that of air or that corresponding to the gaseous interior of the bubble. The drop in voltage on encountering a bubble surface is very rapid, whereas the rise on moving through the bubble surface is not as rapid. This occurs as a result of viscous effects of the liquid which results in formation of a liquid bridge in contact with the insulated part of the electrode just above the non- insulated tip of the electrode which rapidly thins and breaks as the probe moves through then below the liquid surface.

(Figure 1 is a qualitative representation of the expected output signal from a conductivity probe that is connected to a resistive voltage divider circuit when the probe traverses the froth along the line A-B.) The output signal is represented as a voltage in Figure 1 , not as conductivity. The open circuit voltage was plotted as rising up to the air voltage while the probe tip passes through the air inside the bubble. When the probe hits a bubble surface the voltage drops instantaneously to the water voltage. The closed circuit voltage is a function of the relative amounts of water and air at a given position within the froth and also of the possible tendency for the probe to polarise. A decrease towards the water / pulp voltage is expected as the probe moves towards the pulp / froth interface because the amount of froth between the probe and the interface is decreasing.

The points of sharp change in voltage, or low voltage, thus occur when the elongate electrode comes into contact with the surface of a bubble and has moved from air to water. These points can be defined as points of significant impact. The distance between successive points of significant impacts defines the intra-bubble impact distance ("IID") which is related to the bubble size.

For an elongate electrode inserted through the froth at a given velocity, the time taken between successive points of significant impact and the speed at which the probe is cutting through the bubbles can be used to calculate the IID. For example, dropping the elongate electrode under the force of gravity at t=0 permits an IID to be calculated as a function of the times t and b recorded between adjacent points of significant impacts as:

IID (m) = g(t1 ² - t2 ² )

Dropping the elongate electrode into the froth phase several times, permits an average IID to be obtained which is related to the actual bubble sizes. Thus, bubble sizes can be estimated as a function of substantially similar measurements, or points of significant impact, and the position of the tip of the electrode, which can be determined as a function of the velocity at which the elongate electrode is inserted into the froth.

Referring to Figures 2 and 3, an apparatus (50) for estimating bubble sizes includes an elongate electrode (52) and a counter-electrode (54) which is inserted into a cell (56) containing a liquid body (58), or pulp phase. The elongate electrode (52) and counter-electrode (54) are operated through a measurement circuit (60) to which they are connected through cables (62, 64). The elongate electrode (52) and the cable (62) are all part of a single length of insulated wire. The wire is attached to the electrical circuit at one end and the other end is bound round a metal rod (72), in this case a steel rod, and secured to it with tape, leaving a length protruding from the bottom which forms the electrode tip (52).

The probe steel rod (72) is dropped though a ring (80), which is attached to the end of a horizontal bar (82) on vertical stand (84). The height of the horizontal bar (82) and hence the height of the ring (80) can be adjusted. A radial flange (76) is provided on the opposite end of the rod (72) and the height of the ring (80) is adjusted to trap the probe (72) at the end of its chosen travel distance so that when the electrode is dropped the flange (76) hits the ring before the probe drops too far into the column (58) and gets damaged.

As shown more clearly in Figure 3, the elongate electrode (52) is provided by a thin, insulated copper wire. The thickness of the wire is selected such that it does not cause bubbles to burst when it penetrates their surfaces. In this embodiment, the electrode is 0.3 mm in diameter. Preferably, the elongate electrode (52) will be less than 0.5 mm thick, more preferably less than 0.3 mm thick. The insulation extends along the length of the elongate electrode (52) and only its tip (68) is exposed. This is conveniently achieved by cutting diametrically through the insulated copper wire.

As shown in Figure 4, the measurement circuit (60) includes a DC power source (90), in this embodiment a 9V battery which is connected at its positive potential through a 1 Mohm resister, R _f (92) to the elongate electrode (62) and at its negative potential to the earth electrode (54) (also referred to as counter-electrode, or ground electrode). The signals from the circuit are routed to a computer (96) through a data logger (94). It will be apparent that the output voltage (Vout) depends on the resistance between the counter-electrode (ground) and the elongate electrode (Ri), the fixed resistance (R _f ) and the input voltage (V _in ) and it is calculated using the following equation:

The resistance between the elongate electrode and the ground (counter- electrode), that is froth resistance (R ₁ ), can be viewed as a variable resistor that can assume a value that ranges widely as the tip of the elongate electrode moves from bubble surface (lamella or Plateau) to the inside of a bubble. In this embodiment the data logger is an SCX1-1520 real-time interface supplied by National Instruments and has a sampling rate of up to 100 kilosamples per second (kS/s).

In use, the rod (72) is located in the ring (80) and the flange (76) raised a known distance above the upper edge of the ring (80). It is then released to drop under the force of gravity into a froth located below the ring (80). Voltage is measured as the probe drops and a typical plot of voltage measured over the time taken for the probe to drop is shown in Figure 5. The peaks in the plot represent a relatively higher voltage indicative of the tip of the elongate electrode (52) travelling through air while the troughs represent lower voltages indicative of the tip of the elongate electrode (52) encountering a bubble surface (lamella or Plateau) which has a relatively higher conductivity than air. As indicated earlier, these are denoted as points of significant impact. The differences in time between successive points of significant impact are taken as the time to travel from one bubble lamella to the next bubble lamella.

Dropping the probe vertically downwards from a known height above the surface of the froth enables the calculation of speed at which the elongate electrode (52) cuts across the froth using Newton's equation of motion. Based on such velocity calculations, the time between each significant impact can be used to estimate the IID and IID size distribution along the length of travel of the elongate electrode (52). Repeating these measurements for multiple drops provides an accurate estimate of IID distribution and average IID, which is related to the bubble size as shown below.

Experimental trials were conducted and involved generating continuous foam using a mini-flotation column and dropping the elongate electrode into the froth from a fixed height above the surface of the froth. The (13cm x 14cm x 50cm) flotation column was made from transparent Perspex to enable photographs of the foam to be taken. Air flow rate into the column was controlled by an air rotameter and bubbles were generated by a canvas sparger.

Dropping the probe vertically downwards from a known height above the froth surface enabled the calculation of the speed at which the probe cuts across the froth. Concurrently pictures of the froth were taken to enable estimation of bubble sizes from photos. A graduated ruler was fixed to the sides of the flotation cell to enable calibration during bubble size estimation. The output voltage response was recorded on a PC through a data logger SCX1-1520 supplied by National Instruments. This card has sampling rate of up to 100 kilosamples/s (kS/s) although all measurements in this embodiment were done at 40 kS/s.

Copper (II) sulphate was added to 8 litres of water in the flotation column to make 0.0075 mol/litre solution. Air flow rate to the flotation column was maintained at 8.5 1/min resulting in a froth height of 10.5 cm. The elongate electrode was dropped 10 times into the flotation column from a height of 22 cm above the surface of the froth. Concurrently, still pictures of the froth were taken.

Figure 6 shows the typical signal that was obtained after each drop when the sampling rate was set at 40 kS/second. Figure 7 is the signal derivative plotted as a function of the time. Triggering of the signal started when the tip of the elongate electrode touched the surface of the froth. Noticeable in Figure 6 are the sharp consecutive drops marking the points of significant impact. The length between two successive points defines intra-bubble impact distances (IIDs). A closed circuit voltage of 0.145volts was recorded. Because of the high ion content, bubble lamella voltages were also dropping to the closed circuit voltage. Calculating the derivative of the signal and plotting it as a function of time as shown in Figure 7 enhances the points of significant impact and enables their identification. Superimposed on Figure 7 are asterisks marking the points of significant impact. The differences in time between successive points of significant impact were taken as the time to travel from one bubble lamella (or surface) to the next bubble lamella (or surface). This was used to calculate I IDs.

A cut-off threshold value of 500 v/second was used as a basis to determine the points of significant impact. This value means that a change in voltage of 0.0125 volts in two consecutive samples can be identified as having been caused by impact with a bubble surface. This threshold value is dependent upon the conductivity of the pulp water and the sampling frequency set on the card.

Estimation of froth bubble sizes using the apparatus is based on there being a relationship between the IIDs obtained using the apparatus and the actual froth bubble sizes. The relationship is such that, if the elongate electrode is dropped several times into the froth phase and it is cutting through consecutive bubbles, the average IID per given depth below surface of the froth is related to the Sauter-mean bubble diameter provided that the electrode does not pass through vertical Plateau borders. Vertical Plateau borders are defined as those Plateau borders that are parallel to the direction of motion of the probe. If the probe passes through these Plateau borders, the IID will be an overestimate.

This can also be understood as stating that for a given froth, with fixed depth, fixed aeration and chemical conditions and at steady state, the average IID will be an over-estimate of the average size of bubbles at a certain height above the pulp-froth interface because the probe passed through a small fraction of vertical Plateau borders. To assess the variation in bubble sizes as a function of froth depth, the 10.5 cm deep froth was divided into 5 segments each 2 cm deep. For each segment and for every drop, an average IID was calculated and results are shown in Figure 8. By averaging the average IID per segment for the nine drops a global average for the nine drops per segment was then calculated and Figure 9 shows the results obtained. From Figure 9, an increase that follows a linear trend is observed in IID from the pulp-froth interface to the surface of the froth. This general increase in the average IID as a function of height above the pulp-froth interface is expected as bubble coalescence results in an increase in froth bubble sizes as a function of height above the pulp-froth interface. Although the average of many drops show this trend (Figure 9), analysis of the averages of individual drops indicated that the trend is not always linear; the average IID of a segment lower can be higher than the one above it as shown in Figure 8, but the cumulative effect of several drops always revealed the trend similar to that shown in Figure 9. The gradient of Figure 9 can also provide information regarding bubble coalescence. Its gradient shows that on average bubbles sizes are changing at 0.143 mm for every 10 mm change in froth depth, thus it can be used as well for assessing rate of bubble coalescence.

In addition to providing a global average for a segment, IID distributions (HDD) can also be obtained from the data. As an illustration, the froth was divided into two sections each 5 cm deep i.e. the first segment was 5 cm from above the pulp-froth interface and the second segment represented the remainder of the froth up to the surface. I IDs were then obtained for each segment and compared. Figure 10 shows the HDD while Figure 11 is a cumulative IID curve. Both graphs reveal that the 5-10 cm segment has a coarser IID with an IID80 (intra-bubble distance at which 80% of all IIDs are less than or equal to) of 2.75 mm when compared to 1.75 mm IID80 for the 0-5 cm segment. This agrees with known behaviour of flotation froths that bubble size distribution (BSD) near the top of the froth exhibits a coarser IID80 when compared to the IID80 of the bubbles near the pulp-froth interface.

Photographs of the froth that were taken concurrently with the measurement of froth bubble size using the method described were analysed. Measurement of bubble sizes was done manually, and the number of bubbles measured per each photograph ranged between 150 and 350 depending on the number of bubbles contained in each picture. The froth was divided into segments, each 2 cm high, a Sauter-mean bubble diameter was calculated from the bubble size distribution data in each segment and results are shown in Figure 12. The Sauter-mean bubble diameter is defined as a volume to surface mean diameter and was calculated from the equation

As expected, the Sauter-mean bubble diameter obtained showed an increase in bubble size as the height from the pulp-froth interface increases (Figure 12). The increase also followed a linear trend with a correlation coefficient of 0.972, as was obtained with the apparatus for estimating bubble size, with a rate of bubble size change of 0.119 mm/cm. The cumulative BSD obtained in each segment was plotted and results are shown in Figure 13. This plot also supports the existence of a coarser bubble size distribution in segments closer to the surface of the froth.

Figure 14 is a plot of average bubble size obtained by the method of the present invention and from analysis of photographs as a function of height above the pulp-froth interface. The average IID was found to be higher than the Sauter-mean bubble diameter for all froth segments. This result indicates that the elongate electrode may have passed through vertical Plateau borders resulting in increase in the distance between points of significant impact.

Despite the slight overestimation of bubble sizes using the apparatus, a strong relationship exists between the IID and Sauter-mean bubble size. This relationship suggests that as the average IID increases the Sauter-mean bubble diameter also increases. Comparison of the rate of change of IID and the rate of change of the Sauter-mean diameter shows a 5.6% difference. It is foreseen that the apparatus could be calibrated to adjust estimated size to empirical size measurements, should this pose a problem. It is also foreseen that all bubble size estimations will be conducted by a computer or similar automated system and that such system could provide for calibration. Adapting the apparatus to commercial use in industrial froth flotation cells will be apparent to those skilled in the art. It will be appreciated that operation of the elongate electrode can be automated to provide frequent insertion into a froth at a number of different locations, on a frequent, user determined interval and at known velocity. Model size estimates obtained from such apparatus can be used to automate control of the flotation process to achieve optimum results. It will further be appreciated that any suitable electrical characteristic which distinguishes the liquid surface or lamella of a bubble from the fluid, typically gaseous, contents thereof can be measured and the apparatus adapted accordingly if required.