The behaviour of particles in flotation froths

Minerals Engineering, Vol. 4, Nos 7-11, pp. 959-974, 1991

0892-6875/91 $3.00 + 000 © 1991 Pergamon Press plc

Printed in Great Britain

THE BEHAVIOUR OF PARTICLES IN FLOTATION FROTHS

V.E. ROSS

De Beers Diamond Research Laboratory, PO Box 916, Johannesburg 2000, South Africa

ABSTRACT

This paper covers some developments over the past 10 years in research into the behaviour o f floating and entrained mineral particles in the froth phase of the flotation process. It focuses on the current understanding of the pulp-froth transfer of solid particles and water, and the separation and transfer processes occurring in the froth phase, in both mechanical cells and flotation columns. An analysis is also made of three methods that may be used to distinguish between the contributions made by true flotation and the entrainment of mineral particles during flotation. The observations that have been made from experimental investigations and a review of the published literature suggest that, in many cases, the froth phase is limiting the rate at which floating particles are recovered in the concentrate. Furthermore, because the region at the pulp-froth interface is instrumental in the rejection of weakly floatable valuables, gangue and water, and therefore the initial upgrading in the froth, it is suggested that future flotation research should focus largely on the development of techniques to study and quantify pulp-froth transfer processes. This will enable relationships between the froth transfer parameters and operating conditions to be established more accurately, and so assist in the simulation o f flotation networks. Importantly, emphasis should also be placed on the refinement of simulation models and their reconciliation with operating data. Keywords Mass transport, flotation, entrainment, froth INTRODUCTION

Over the past 10 years, significant progress has been made in the understanding of the behaviour of floating and entrained mineral particles in the froth phase of the flotation process. These advances have been largely due to techniques that were developed to characterize the structure and the behaviour of mineralized froths, in an attempt to overcome some of the difficulties that were experienced in the simulation of the performance of flotation networks. The principal uncertainties which have limited the usefulness of these network simulation models resulted from processes operating in the froth phase of large flotation cells (Woodburn et al. [1], King [2]), and the accent has therefore shifted towards a study of the froth phase, and the development of appropriate models, to estimate the flowsheet parameters more accurately. During the early years of mathematical modelling of the froth phase in flotation, most of the attempts were based on the two-phase model of Arbiter and Harris [3], and Harris and 959

960

V.E. Ross

Rimmer [4], who assumed that both the pulp and the froth phases are perfectly mixed. Thus, the tailings provide a representative sample of the pulp, and the concentrate a representative sample of the froth. In its present state of development the model does not take account of water flow between the two phases, or air flow, which is most probably the reason why it does not scale-up well. Although this model is a powerful but relatively simple tool which describes steady-state operation well and is the preferred choice in circuit simulations [5], it lumps all the system parameters together into rate coefficients that describe the process globally. It therefore provides little insight into the process micromechanisms, but, in the opinion of this author, was largely the cause of the stimulating research and the significant developments over the past years in the understanding of the froth phase. Studies of the froth phase have focused largely on the pulp-froth transfer of solids and water, the separation of species in the froth, and their transfer from the froth to the concentrate. Due to the complex nature of the froth phase, this work has been conducted mostly on a laboratory or pilot scale under carefully controlled conditions. Although this is probably the only way in which a more detailed, qualitative understanding of the process can be reached, it has often had little quantitative merit in terms of the operation of industrial flotation cells, where froth mobility and residence time effects can be ratedetermining. Nevertheless, valuable insight has been gained into the interactions between the sub-processes of flotation, entrainment and drainage. With the renewed interest in column flotation, originally proposed in the mid-sixties [6,7], much of the research effort has been devoted to developing this particular technology. The knowledge and consequent application of this novel flotation method have therefore grown so rapidly [8,9], and the innovations been so numerous, that today the technology is probably more advanced than that of mechanical cells. However, the first attempts at modelling the cleaning zone (i.e. the froth column) were only recently [10,1 l]; this perhaps reflects most clearly the complexity of obtaining a more detailed understanding of the flotation froth phase through experimentation and modelling. It is the aim of this review to outline some important developments in research over the past decade into the behaviour of flotation froths, both in mechanical cells and flotation columns, dealing specifically with physical factors that influence mass transport phenomena. It also endeavours to put into a clearer perspective the current understanding of the subprocesses operating in the froth phase, and to identify areas in which future research in this very important field should be directed. FROTH RESEARCH 1970-1980 The progress that has been made over the past decade in the comprehension of the complexities of the flotation froth phase, specifically in terms of fundamental experimental studies and modelling, will be put into clearer perspective if the status of research prior to the beginning of the eighties is reviewed. Since the latter is beyond the scope of this paper, only some selected aspects of the relevant research that was done in the seventies on mass transport in the froth phase are briefly described. As far as can be ascertained, the first attempt at studying the transfer of material between the pulp and the froth phase was by Watson and Grainger-Allen [12]. These authors pioneered the technique of using an equilibrium froth cell to model the rate constants that characterize pulp-froth interactions under steady-state conditions. The equilibrium cell technique was further developed by Cutting and Devenish [13], but more emphasis was being placed on studying the processes occurring within the froth phase. During this period, pioneering work was also done in studying and modelling the effects of operating conditions on entrainment. Bisshop and White [14] developed a technique to calculate the rate at which hydrophilic particles are recovered in the concentrate, by the specification of two parameters. The importance of both the liquid and the solid phases in

Behaviour of particles in flotation froths

961

determining the degree of entrainment was recognized in that the one parameter relates to the water drainage from the froth, and the other to the particle size, specific gravity, pulp density and mineral characteristics. This work has shown that 'the single most important factor in drainage from the froth, and hence particle recovery, is the residence time in the froth'. Important work on the quantification of the effects of froth height and aeration rate, and hence residence time, on flotation was done by Engelbrecht and Woodburn [15]. In a twocomponent system of pyrite and silica, a unique relationship was observed between the recovery of water and that of the components, regardless of whether froth height or aeration rate was used as a control variable. This work highlighted the relationships between the recovery of water and that of particles of various sizes and hydrophobicity, and formed the basis of later studies on flotation and entrainment. At approximately the same time, a comprehensive review of the importance of particle size in flotation and entrainment was done by Trahar and Warren [16]. Towards the end of the seventies, modelling of the froth phase had been refined to the stage where a plug-flow model of a froth was proposed by Moys [17]. This work represented the first attempt at modelling the sub-mechanisms of flotation, entrainment and drainage in the froth phase, and was based on the assumption that the rate at which particles detach from the volume of slurry ascending in the froth is proportional to their concentration in the froth. The topic of drainage was also addressed in the assumption that a constant velocity increment exists between the bubble velocity and the drainage velocity of the particles.

In essence, the work in the seventies laid the foundation not only for the modelling and simulation of the flotation froth phase, but also for many of the fundamental research studies on the behaviour of particles and water. Much pioneering work was done which greatly benefitted the research effort of the eighties. In particular, it initiated the development of techniques to quantify parameters that could be used to describe the behaviour of the various components in the froth phase mathematically, and schooled the thought for investigations into the interactions between the mechanisms operating in the froth. FROTH RESEARCH 1980-1990 Transfer into the froth phase

To date, little work has been done to quantify the transfer of floating and entrained mineral particles and water from the pulp into the froth phase. This has had an adverse effect on the development and refinement of mathematical models of the froth phase, since workers in this field have to use models of particle collection in a well-mixed pulp phase (e.g. Dobby and Finch [18], Harris [19]) to describe the input parameters of their froth models. However, work by Flynn and Woodburn [20] has shown that considerable variation could occur in the concentration of the various species in the slurry phase of a mechanical cell. In addition to these deviations from the concept of a perfectly mixed pulp, the classification of water, weakly floating and entrained particles, should be taken into account when pulpfroth transfer processes are modelled. As far as can be ascertained, no accurate method exists whereby the transfer rates of floating and entrained species into the froth phase can be measured directly. Although these rates can be calculated from the results of laboratory kinetic flotation tests, certain assumptions are still necessary to estimate the relevant mass flowrates in industrial cells. Ross [21,22] used a transfer factor, X, which describes the differential classification of entrained solids and water during flotation, to quantify the mass flowrate of floating and entrained particles into the froth phase. It has been shown [23,24] that this technique gives reliable results when applied on a laboratory scale. To estimate the flowrates in industrial cells, a representative sample of pulp that is extracted in the large-scale cell is floated in the laboratory, at the same superficial air flowrate. The laboratory test is performed in the

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presence of a shallow froth, to incorporate any possible effects of particle detachment and drainage at the p u l p - f r o t h interface in the experimental results. As a result of the variation in the concentration of solids in the slurry phase in large cells due to inadequate suspension, as well as particle size and density effects, a number of these tests normally have to be performed, and the results correlated. The major disadvantage of this method is the fact that the bubble size distribution, power input, and hence the turbulence and mixing of the pulp phases in the two types of cell are different, which obviously render the results questionable. A similar method was used by Kirjavainen [25], who proposed a specific entrainment factor P, in studying the entrainment of hydrophilic particles during flotation. It was found that the relation between the entrainment factor and the mass of individual granular particles could be described by a logarithmic equation P= 1 - Dlog(m)

(1)

where D is a constant (approximately 0.17 for pulp densities of between 2 and 20 mass percent), and m is the average mass (in nanograms) of the particle in a narrow size interval. This agrees well with the transfer factor proposed by Ross and Van Deventer [10], X = 1 - 0.429 (log d - 1)(p - 1)

(2)

where d is the diameter of the particle (in #m), and p is the density of the particle (in g/cm3). For example, for 20#m particles with a relative density of 2.7, the values for P and X are 0.72 and 0.78 respectively. Importantly, the work of Kirjavainen is in contrast with the widely accepted idea that the entrainment of gangue is decreased by decreasing the pulp density, since it showed that only the recovery of flaky material (phlogopite), and not that of granular quartz and chromite, was dependent on the pulp density. Two other methods for distinguishing between the contributions of true flotation and entrainment have been advanced (a more detailed description of these methods is given elsewhere [24]). In the method of Trahar [26], the recoveries of solids and water are measured during two batch flotation tests - one in the presence, and the other in the absence, of a collector. It is assumed that, at the same water recovery, the amount of material that was recovered by entrainment is the same. The amount of material recovered by true flotation is then calculated from the mass of solids that was recovered in the presence of the collector. The same method was recently used by Subrahmanyam and Forssberg [27] in tests on lead-zinc and copper ores in which the froth characteristics were investigated. In Warren's method [28], the recoveries of mineral particles and water obtained during tests in which the rate of froth removal and the depth of the froth are changed, are correlated. The regression line of the relationship between mineral recovery, M(t), and water recovery, W(t), after flotation time t is extrapolated to a water recovery of zero, and the intercept, F(t), on the mineral-recovery axis is interpreted as the recovery that occurs as a result of true flotation, (E(t) being the entrainment), M(t) = F(t) + E(t) = F(t) + 13 (t)W(t)

(3)

The term B(t) is also known as the 'degree of entrainment', and has been found to range from 0,72 (quartz >3,5 #m, [26]) to 0,99 (silica <12 #m, Engelbrecht and Woodburn [15]) for ultrafines. The degree of entrainment decreases with an increase in particle size, and has values that range from less than 0,1 (quartz >40 #m, [15]) to 0,03 (phosphate ore, -150+75 ~m [21 ]). A comparison of these three methods [24] has shown that the method of Trahar should ideally be applied when the frother has no collecting properties and when the feed material is fairly coarse (the hydrophobicity required for fines to float is much less than that for coarse particles). It is furthermore not particularly suitable for investigation of the effect

Behaviour of particles in flotation froths

963

of froth depth on the mass of particles that are recovered by true flotation, since very little froth is normally formed in the absence of collector. It is imperative that both tests should be conducted at the same froth depth, since work by Engelbrecht and Woodburn [15] has shown that, when the pulp contains a highly floatable component such as pyrite, the coalescence of bubbles can lead to the shedding of the valuable component when the bubbles become overloaded (this can occur in froths as shallow as 30 mm!). The accuracy of the method also depends on the drainage characteristics of entrained material, which are dependent on the structure of the froth. The method of Warren should be applied over an interval that is just long enough for the recovery of most, but not all, of the easily floatable solids, which means that the choice of a proper time interval is important (the duration of the interval will depend on the type and fineness of material that is floated). The conditions should be such that a good correlation exists between the recovery of mineral and the recovery of water over the total interval that is studied. A direct proportionality exists [15] between the recovery of gangue and the recovery of water only when the upward liquid velocity in the froth exceeds the settling velocity of the particles, which means that this method should be more suitable for fine particles. This is illustrated in Figure 1, where the three methods are compared for a relatively fine (87% -150 #m) and a coarse (85% +212 #m) gangue component of the feed material [24]. Since Warren's method involves a number of flotation tests, it is also the most time-consuming of the three methods. 50 Ross Trahar

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TIME,MIN Fig.l Calculated recoveries of particles due to true flotation, using different techniques

The method of Ross [23] is the most suitable for the study of the effect of froth depth on the rate of true flotation, and is also the least time-consuming. However, it should be applied at a pulp density that is sufficient for good mixing of the pulp phase. The variation in the froth stability, and the consequent entrainment and entrapment effects, should also be taken into account. Further important work in this field was carried out by Laplante et al. [29], who investigated the flotation rate of different size classes of silica and galena as a function of air flowrate (AFR) and frother concentration. A specially constructed flotation cell with a high cell height-to-froth surface ratio, in which two zones of different activity are formed in the pulp phase, was used for these studies. In the lower part of the cell the particles are suspended by the impeller action, whereas in the top part, which is only weakly agitated, a quiescent slurry-froth interface ensues. This results in negligible entrainment

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V.E. Ross

of material, and permitted the rate of true flotation to be studied. The flotation rate constants (FRCs) increased to a maximum and then decreased as the A F R was increased. These trends were predicted by a model which considers the effect of bubble size on both the total bubble surface area and the bubble-particle collision efficiency. As the A F R increases, the bubble area increases, which leads to an increased rate of flotation. However, the bubble size also increases, which results in a decreased collision efficiency and rate of flotation at high AFRs. Most importantly, the work showed that collision efficiency effects are also present in flotation systems where many bubbles and particles interact. Falutsu and D o b b y [30] studied the d r o p - b a c k of particles from the froth in a modified laboratory-scale flotation column which allowed direct measurement of the froth zone recovery and collection zone rate constants. Their work highlighted the very important fact that the amount of solids arriving at the p u l p - f r o t h interface is a significant parameter of the froth recovery, and that not all of the floating material entering the froth is recovered in the concentrate. In their specific column, only 60 percent of the floating particles entering the froth were recovered in the concentrate, indicating that the froth acted as the rate-limiting stage. They also observed that excessive wash water rates caused a deterioration in the recovery of particles in the froth, and concluded that the d r o p - b a c k occurred principally at the p u l p - f r o t h interface, since the froth zone recovery did not depend on the froth depth. The same observations were made by Ynchausti et al. [31 ], who reported data on the flotation of a fluorite ore from Nevada. Whereas froth depth did not have a discernible effect on the recovery, the grade increased when the froth depth was increased.

Transport in the froth phase 1. Mechanical cells

Various approaches have been taken in studying and simulating the behaviour of the froth phase. This can be attributed mainly to the fact that the behaviour and the structure of the froth are intimately related to the operating conditions, and that the complexity of modelling such a process invariably requires the simplification or generalization of concepts. For example, whereas the froth could exhibit a certain character under one set of conditions, it could behave differently under another. In the initial stages of modelling such a process, the overall rate of transfer would be described by a single constant in a simple model. Only when sufficient data is available, an analytical model can be constructed which will provide insight into the interactions between the various mechanisms that affect the overall rate of transfer, and this could lead to a more refined approach. The predictive capability of such a model will be ensured only if the interactions between the processes in the froth are taken into account. In recent years, especially, it has been realized that a better understanding of the froth phase can only be obtained if these interactions are studied in greater detail, and incorporated in mathematical models. A good example of the success that has been achieved in this respect is the 'population balance model' of Bascur and Herbst [32]. This model is applied to particles in four different states in the flotation cell, the transfer of particles in the cell between the various states being described by appropriate rate constants which are estimated according to the relevant attachment and detachment phenomena occurring within the pulp and the froth phases. The influence of important physical variables, such as aeration rate, agitation speed and frother addition, are included in the model equations. The model has been implemented successfully in the dynamic modelling of the froth. In addition to the interactions between mechanisms in the froth, the interactive effects of particles existing in a mixture of sizes and having a variety of surface characteristics influence the parameters of a froth model. For instance, the behaviour of a particular size will also influence that of other particles, and, while particles of a certain size and hydrophobicity can stabilise the froth under certain conditions, they can act as destabilisers under others (Hemmings [33,34], Dippenaar [35,36]). It is therefore important that, while the analysis of a detailed analytical model is often difficult due to the evaluation of a large

Behaviour of particles in flotation froths

965

number of model parameters, these factors should be considered when kinetic models are developed and reconciled with operating data. Most of the earlier kinetic flotation models are based on the two-phase model of Arbiter and Harris [3], which assumes that both the froth and pulp phases are perfectly mixed. However, the work carried out during the past decade by various researchers has shown that the residence time of particles in the froth is a strong function of the point at which the particle enters the froth, and hence the assumption of a perfectly mixed froth is oversimplified. A realistic model should also take into account inefficiencies such as stagnant froth zones, which do not contribute to the transfer of material from the pulp to the concentrate. Moys [37] investigated the residence time distribution of froth elements in the froth phase of large cells, and developed a two-stage 'tractable' model that predicts concentrate flowrates from a knowledge of the mass flowrate of any particular species entering the froth. Phenomena such as the development of regions of negative froth velocities (i.e. froth flowing away from the point of concentrate removal) were incorporated successfully into the model. An important conclusion from this work was that the residence time of froth in the region next to the concentrate overflow weir is normally too short to permit adequate drainage of entrained gangue material. A residence time ratio (RTR) was defined, which relates the minimum residence time of the froth to the residence time as if it is flowing in plug-flow fashion throughout the entire froth volume. He illustrated that, by inserting a deflecting plate in the froth next to the concentrate weir, the RTR could be increased, and this resulted in an unambiguous improvement in the grade of the concentrate. The work by Cutting et al. [38,39] at Warren Spring Laboratories has contributed largely to the current understanding of the behaviour of mineralized froths. They have shown that the grade and concentration of the various species in the froth is a function of the height above the pulp-froth interface, and that these profiles are influenced significantly by the rate of aeration and the removal of concentrate by means of motorized paddles. Considerable lateral variations in the structure of the froth occur in any given flotation cell. At normal aeration rates, the contours change in a fairly uniform manner with increasing height above the pulp-froth interface. At high aeration rates, however, the contribution of entrainment dominates, and the overall froth concentration increases at the expense of grade. These researchers measured concentration profiles in the froth phase of a single-discharge flotation cell, and showed that a region of negative pulp density enrichment extends from the pulp phase upwards to the froth discharge lip. This suggests that, at high aspiration levels, a strong and localized flow occurs from the lower regions of the froth to the region of froth discharge. The concentration profiles were measured by extracting froth samples, that were also analysed in terms of pulp density, grade etc., by means of a multi-point sampling lance. To characterize drainage, the total concentration of species in the froth was determined from pressure measurements using a dip tube assembly. This measurement was differentiated to produce a concentration profile up the froth column. Ross [21,22,40] interpreted concentration and grade data in the froth to study the behaviour of floating and entrained particles. This work has shown that the recovery of floatable material in the concentrate can be impaired due to the detachment of such particles from the bubble surfaces. In addition to the detachment of floating particles at the pulp-froth interface (discussed above), detachment can occur within the froth due to overloading of the bubble surfaces or the bubble films becoming too fragile to support especially coarse particles. The effects of paddle action and the turbulence prevailing in the froth in the region next to the concentrate overflow weir on the recovery of species in large-scale flotation cells were incorporated in a two-dimensional model of the froth phase [22,41,42]. As far as can be ascertained, this model is the first attempt at modelling the concentration profiles of species in the froth phase of large mechanical cells by considering the relative contributions

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of flotation, entrainment and drainage. This model takes into consideration the distribution of air over the pulp-froth interface, and uses drainage rate constants (DRCs) to describe the rates at which water, and floating and entrained particles detach from the slurry rising in the froth. Furthermore, the effect of bubble film thickness on the drainage velocities, and the consequent concentration profiles of the various species in the froth phase, are considered explicitly in the model equations. The effect of bubble film thickness on the DRCs of the various particle size fractions was considered in modelling the flotation of a pyritic sulphide ore and a phosphate ore in an equilibrium cell [43,44]. While the DRCs for entrained solids decreased significantly with increasing height in the froth, particularly for coarse particles, those of water did not change as markedly. The calculated thickness of the bubble films in the froth, as well as the drainage rate constants for the entrained solids, increased with increasing aeration rate. The effect of bubble film thickness on the entrainment of gangue material into the concentrate during flotation of fine coal was considered by Flynn and Woodburn [45]. This model clarifies the interactions between bubble loading and bubble size, and the crucial role played by the particles in establishing a 'limiting lamella thickness' (LLT), i.e. the minimum thickness a bubble film can attain before it is ruptured by hydrophobic particles in the froth. Feteris et al. [46] combined the probability model and the two-phase kinetic model of flotation to derive an expression relating the overall rate coefficient of a mineral species to the probability that it survives the cleaning action of the froth. When floating galena in a laboratory batch cell, a linear relationship was observed between the probability that a floating particle will survive the cleaning action in the froth, and the depth of the froth. However, it is surmised that this will only apply to shallow froths (Feteris used froths of between 15 and 42 m m deep) where the assumption of perfect mixing is valid, and when the rate coefficient is determined over the initial stages of batch flotation, i.e. when the froth is fairly stable and 'wet'. Work on deeper froths [17,21,30,31,40,43,44] supports a more exponential decay in the amount of floating material, the magnitude of the decay depending largely on the operating conditions. Frew and Trahar [47] investigated the flotation behaviour of particles in rougher and cleaner flotation banks. Results of surveys on several plants have shown that the flotation behaviour in cleaner banks can differ from that in roughers. The use of flotation rate constants that have been obtained solely in, for instance, a rougher stage can thus give incorrect estimates of the performance of the complete plant. These authors have also shown that batch flotation tests which reproduce roughing and cleaning conditions could be used to determine the relative performance of rougher and cleaner flotation for various size fractions. However, it should be borne in mind that the mobility of the froth in largescale flotation cells has a significant impact on the 'overall' rate constants, i.e. the constants that describe the performance of the combined froth and pulp phases. Laplante et al. [48] investigated the flotation rate of galena as a function of air flowrate and froth thickness (from 0 to 6 cm) in a specially constructed batch flotation cell in which the hydraulic entrainment of fines into the froth was prevented. The froth transport constant (FTC), which was determined from the overall rate of flotation and the rate of pulp-froth transfer, increased with an increase in the aeration rate and decreasing froth thickness. Importantly, for a froth as shallow as 5 cm, it was found that the FTC was significantly lower than the rate of pulp-froth transfer, which means that even in a batch cell the transfer processes in the froth are rate-limiting. The rate of recovery is influenced largely by the fluidity of the froth. Studies dealing with the drainage of particles and water from the froth have therefore also been concerned with the shape and characteristics of the bubbles, and the passages along which the particles drain. For instance, Kuz'kin [49] assumed an average speed of drainage, which is constant over the entire froth height. Mineral particles move downward with the streams of slurry along the Plateau borders at an increased speed relative to the average speed of drainage.

967

Behaviour of particles in flotation froths

With increasing particle size, the passage is retarded until the condition is met where the thicknesses of the particles and the bubble films are commensurate, and the particles will cease to move downward. The increased solids content will increase the viscosity of the slurry in the froth, which will result in decreased mobility. The effect of these phenomena on the drainage velocities of particles has been described mathematically and investigated experimentally by Ross [43,44]. It was found that, for coarse particles, the drainage velocities decreased significantly in the upper regions of welldrained froths (i.e. at low aeration rates) due to interactions between the particles and the walls of the Plateau borders. At higher aeration rates, the effect was not as significant, as shown in Figure 2. Results from testwork on fine particles have suggested that, unlike for the coarse particles, wall effects in the Plateau borders do not play a major role in reducing the drainage velocity in the upper regions of a deep froth. In this case, the increased viscosity of the slurry in the bubble films is affecting the drainage of particles the most. 30 Air f l o w r a t e , L/min

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Fig.2 The variation in the drainage velocity of -150+75/~m particles with increasing height in the froth The effect of froth fluidity on the performance of a flotation operation was implicitly incorporated in Bascur and Herbst's [32] dynamic model of the froth phase. The flowrate of water into the concentrate - a good indication of froth fluidity - was modelled by modifying basic relationships that were obtained from studies of flow over a weir. The fact that the kinetics of mass removal are determined not only by the mechanical design of the flotation cell, but also by the characteristics of the froth, was considered by incorporating the geometric features of the cell, as well as the average liquid holdup in the froth, into the model. The important influence of the design of the flotation cell and operating conditions on the behaviour of the froth phase was further highlighted by Meyer and Klimpel [50]. Their model, which was statistically verified by batch flotation data, couples the mechanical removal of froth by paddles with the more rapid interactions in the pulp, and clearly shows that the kinetics of mass removal are dictated not only by the dimensions and design of the flotation cell, but, more importantly, by the characteristics of the froth. It was observed that an increase in the solids content of the froth lead to a loss of froth fluidity and the rate of mass removal. These results are in accordance with observations by Cutting and Devenish [13], who showed that the progression from rougher to cleaner and recleaner flotation affected the residence time and drainage of the froth significantly.

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V.E. Ross

Work recently conducted by Ross [22] has shown that, when a dilute slurry containing a high percentage of floatable material is floated, the water that is entrained with the bubbles into the froth rapidly drains from the froth at the pulp-froth interface. Such would normally be the case in cleaner operations. The presence of floating particles increases the solids content with increasing height in the froth, leading to a loss of froth fluidity and mobility. These effects were simulated well by a computer package that was developed for the simulation of the concentration profiles of the various species in the froth phase, as shown in Figure 3.

Exp. Model [42] - -

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2. Flotation columns Modelling Yianatos et al. [51] examined the selectivity in the froth bed of two industrial flotation columns by measuring grade and percent solids profiles through the froth. A plug-flow model was used to predict the mass transport through the froth, the results of the simulation being in good agreement with experimental data.

969

Behaviour of particles in flotation froths

An analysis of the grade profiles in a relatively shallow froth of 45 cm (Figure 4) has indicated that most of the entrained material is rejected at the pulp-froth interface. The mixing action of the wash water is evident in that little further upgrading occurs within the froth. However, above the wash water input, further upgrading of especially molybdenum occurs. This is presumably due to the coalescence of bubbles and the consequent crowding of particles on the surfaces, leading to the displacement of the less hydrophobic ones. The pyrite was more floatable than chalcopyrite under the specific operating conditions, as is evident from the increase in the grade of pyrite above the wash water input. Also, the pyrite was not influenced as detrimentally by the washing action at the pulp-froth interface as was the chalcopyrite, as can be inferred from the decrease in the grade of these two species at the interface. In deeper froths, however, upgrading through the froth was more significant, which is in accordance with other investigations [30,31] in laboratory-scale columns where plug flow conditions are more closely approximated. The upgrading in deeper froths was attributed to a decreased amount of mixing due to the wash water entrance being further away from the pulp-froth interface. An important observation from this work is the fact that the effect of solid loading of the bubbles is to increase froth stability (the same observation was made by Falutsu and Dobby [30]). The detachment rate constant, describing the rate at which floating particles become detached from the bubble surfaces, decreased for a higher percentage solids in the froth, which is in accordance with results obtained by Ross [43] in the flotation of various size fractions of a pyritic sulphide ore and a phosphate ore in a deep froth. 0

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60

GRADE,%

Fig.4 Grade profiles in the froth phase of an industrial flotation column (after Yianatos et al. [51])

Carrying capacity The carrying capacity C a (expressed in g/cmZ/min) of a froth is an indication of the maximum mass flowrate of floating solids that the column is able to produce under a given set of operating conditions. It is a useful parameter to describe the efficiency of flotation since work by Espinoza-Gomez et al. [52] has shown that it is not strongly dependent on the diameter of the column. Investigations into the carrying capacity of laboratory and industrial flotation columns [52,53] have shown that, for particle densities of between 4.0 and 4.5, and ds0s of between 6 and 44 #m the following relationship is true: ME 4:7/11-V

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C a -- 0.068 (d8o pp)

(4)

where d80 is the particle size of the concentrate (the 80 percent passing size in #m), and pp the density of the particle (in g/cm3). This means that the carrying capacity of froths can be expected to decrease if the particle size is decreased. First principles suggest that, in addition to particle size and density, the carrying capacity is also a function of the bubble size, the superficial air flowrate and the particle size distribution. For example, at a superficial air flowrate of 3 cm/sec, a bubble size of 3 mm, a 100% particle packing density on the bubble surfaces, and an average particle size d = 0.3d80 [53], the carrying capacity is C a = 0.063da0Pp,Which correlates well with that exhibited by the testwork. Carrying capacity is an important operating parameter, since it is also influenced by the aeration rate and the bubble size. Therefore, it has a direct implication in terms of the design of column flotation circuits, and could also influence decisions regarding the operation of column cells. If, for example, a column is operated at its maximum capacity, a decrease in the particle size or an increase in the feed grade will result in a loss of valuable mineral to the tailings. In such a case, a further scavenging stage will be necessary for the recovery of these particles. Espinoza-Gomez et al. [53] made a very important observation in that the carrying capacity decreased for a particular stream when the feed rate was increased. In that case, the percent solids in the slurry was used as the variable to control the feed rate. A possible explanation for the observed effect is the fact that bubble size increases with an increased pulp density (O'Connor et al. [54]), and hence would have resulted in a decreased bubble surface area and carrying capacity. The same could happen when the temperature is reduced, such as during winter months. Obviously, these results have far-reaching implications in the control of column flotation circuits and should be investigated further. Unlike the situation in mechanical cells, froth fluidity does not seem to influence the performance of flotation columns significantly. This is probably the result of the wash water that is introduced to eliminate the entrainment of fines into the concentrate, which 'loosens' up the froth structure. Furthermore, because of the high length-to-diameter ratio of column cells, the distance that elements of froth have to traverse in a horizontal direction towards the concentrate lip is much smaller than in conventional cells of similar volume. Therefore, the radial variation in the ratio of solids to water, and hence the mobility of the froth, would be negligible in comparison with conventional mechanical flotation cells. CONCLUSIONS AND RECOMMENDATIONS Extensive research has been done over the past years on the transport mechanisms of floating and entrained mineral particles and water in the froth phase of the flotation process. This work originated mainly from difficulties that were experienced in the scaleup of flotation cells and the simulation of flotation circuits, due to an inadequate characterization of froth effects on the efficiency of flotation. Although the progress in research has been relatively slow due to the complexity and the diversity of the topic, today we have a much improved understanding of the way in which the various sub-processes operating in the froth, and the interactions between these processes, influence the structure and the behaviour of the froth phase. In an increasing measure, emphasis is being placed on the development and testing of analytical models, and it is believed that this would assist in the refinement of simpler mathematical models that are preferable for the simulation of flotation networks. However, much work is still needed in various areas, such as the estimation of model parameters, the application of different models and techniques in an industrial environment, and the reconciliation of simulation models with operating data. The following general observations, as well as conclusions that were drawn from experimental investigations and a literature survey, are of particular relevance to this review:

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1. An analysis has been made of three methods that may be used to determine the relative contributions of true flotation and entrainment of mineral particles during batch flotation tests. It has been shown that any particular method should be decided upon and applied only after careful consideration of the relevant operating conditions. Laboratory-scale testwork has shown that differing results could be obtained when the various methods are applied under the same operating conditions. 2. While some degree of mixing occurs in flotation froths, the assumption of a perfectly mixed froth phase is not valid. In flotation columns, where wash water is introduced countercurrently to the bubble flow, most of the weakly-floatable material and gangue is rejected in a region around the pulp-froth interface. Therefore, since little upgrading is normally observed with further height in the froth, the cleaning zone can be modelled by considering it as two layers of perfect mixing (the one next to the interface and the other comprising the remainder of the froth volume), with plug flow transport occurring between the layers. The relative size of these layers will depend on the operating conditions and the structure of the froth. For instance, if little or no wash water is used, mass transport in the froth phase could be described adequately by a plug-flow model. In such a situation, the two well-mixed regions of primary and secondary cleaning would be replaced by one in which a more gradual upgrading occurs. In large mechanical cells, such as is widely used in the modern flotation industry, the residence time of the mineral particles is a strong function of their point of entry into the froth. Therefore, the pulp density, the mobility of the froth, and the grade and concentration of the particles depend not only on the height above the pulp-froth interface, but also on the position at which an element of slurry enters the froth. This means that the efficient removal of concentrate is of great importance if the operation of such cells is to be optimized. Thus, for modelling purposes, the transport of solids and water could be described by plug-flow conditions along a bubble streamline. Depending on the operating conditions, various degrees of mixing could be included in the model to account for the processes occurring in the region next to the concentrate overflow weir. 3. Only once sufficient knowledge of the interactions between the sub-processes occurring within the froth is obtained, will it be possible to analyse the behaviour of the froth phase in such detail that meaningful development and refinement of two-phase models can be accomplished. It is therefore imperative that measuring techniques should be developed, and laboratory-scale techniques be modified to such an extent, that they can be applied in analytical research into the performance of industrial-scale flotation cells and columns. The advantage of the two-phase model over analytical models is its simplicity and applicability in circuit simulation, but it should be supported by a more 'detailed' knowledge of the process to account for deviations from a specific set of operating conditions. This is summarized well in the words of Harris [5]: "In a process as complex as flotation, lumped parameter methods might provide applicable results at a relatively early stage, but only analytical models can provide insight into the process". 4. In probably most cases, the froth phase is limiting the rate at which floating particles are recovered in the concentrate. While the mobility of the froth is relatively unimportant in flotation columns where the wash water 'loosens' the froth that is rising vertically upwards, it can exert a major influence on both the grade and recovery of the concentrate in large mechanical cells. When flotation columns are used in cleaner operations, the bubble surface area that is available for flotation is a critical factor since it can limit the rate of concentrate production. Since the region next to the pulp-froth interface plays a principal part in the rejection of weakly-floating valuables, non-valuables and water, future research studies should focus largely on quantifying the transfer of floating and entrained solids and water from the pulp into the froth phase. This would enable the sub-processes operating in the froth, such as the flotation, entrainment, and drainage of particles, to be studied in greater detail. It would also allow more accurate relationships to be established between the froth transfer

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parameters and the operating conditions, and therefore greatly assist in the simulation of flotation networks. Finally, with the rapid depletion of rich ore bodies, it has become increasingly important to fine-tune flotation cells according to the properties of the feed material. In this respect, it is envisaged that the use of computer control systems, especially knowledge-based systems (KBS), will grow rapidly in the next decade. Although a KBS, based on operator input, could function efficiently in a qualitative supervisory capacity, it is believed that only analytical models can provide quantitative estimates of the effect of control actions on grade and recovery over a wide range of operating conditions. It is therefore essential to bridge the present gap which exists between such technology and its useful application, i.e. the absence of refined analytical models and techniques on which a quantitative KBS can be based. It will require a united effort of research and development scientists and engineers to ensure that the necessary structures and techniques for the characterization and simulation of the flotation process are developed, refined and applied. ACKNOWLEDGEMENTS This paper is published by permission of the Director of Research, De Beers Industrial Diamond Division (Pty) Ltd. REFERENCES

.

.

3. 4. 5. 6. 7. 8. . 10. 11. 12. 13. 14. 15.

Woodburn E.T., Kropholler H.W., Green J.C.A. & Cramer L.A. The utility and limitations of mathematical modelling in the prediction of the properties of flotation networks. In: M.C. Fuerstenau (ed.), Flotation. A.M. Gaudin Memorial Vol. 2., AIME New York, 638 (1976). King R.P., Simulation of flotation plants. Trans. Soc. Min. Eng., AIME, 258, 286 (1975). Arbiter N., & Harris C.C., Flotation Kinetics. In: D.W. Fuerstenau (ed.), Froth Flotation, AIME, New York, 215 (1962). Harris C.C., & Rimmer H.W., Study of a two-phase model of the flotation process. Trans. Inst. Min. Metall. C75, 153 (1966). Harris C.C., Multiphase models of flotation machine behaviour. Int. J. Miner. Process. 5, 107 (1978). Wheeler D.A., Big flotation column mill tested. Eng. Min. J, 88 (1966). Boutin P. & Wheeler D.A., Column flotation. World Mining, 47 (1967). Yianatos J.B. A review of column flotation modelling and technology. Report: Mineral Processing, University of Queensland, Dept. of Mining and Metallurgical Engineering, June (1987). Lane G.S. & Dunne R.C., Column flotation: An Australian perspective. AuslMM Kalgoorlie Branch, Equipment in the minerals industry: Exploration, Mining and Processing Conference, Kalgoorlie, Western Australia (1987). Ross V.E. & Van Deventer J.S.J., Mass transport in flotation column froths. Column Flotation '88. Proceedings of an Inter. Symp. on Column Flotation (K.V.S. Sastry, ed.), A.I.M.E., Phoenix, Arizona, 81 (1988). Yianatos J.B., Finch J.A. & Laplante A.R., Selectivity in column flotation froths. Int. J. Miner. Process. 23,279 (1988). Watson D. & Grainger-Allen T.J.N., Study of froth flotation by use of a steady-state technique. Trans. Inst. Min. Metall. C82, 103 (1973). Cutting G.W. & Devenish M., A steady-state model of flotation froth structures. In: AIME Annual Meeting, New York, N.Y., Preprint 75-B-56 (1975). Bisshop J.P & White M.E., Study of particle entrainment in flotation froths. Proc. I.M.M. 85, 191 (1976). Engelbrecht J.A. & Woodburn E.T., The effects of froth height, aeration rate and gas precipitation on flotation. J.S. Aft. Inst. Min. Metall., 125 (1975).

Behaviour of particles in flotation froths

16. 17. 18. 19. 20. 21. 22. 23. 2~.

25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.

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Trahar W.J. & Warren L.J., The floatability of very fine particles - a review. Int. J. Miner. Process. 3, 103 (1976). Moys M.H., A study of a plug-flow model for flotation froth behaviour. Int. J. Miner. Process. 5, 21 (1978). Dobby G.S. & Finch J . A . , Particle size dependence in flotation derived from a fundamental model of the capture process. S M E - A I M E Annual Meeting, New York, Preprint 85 - 124 (1985). Harris C.C., Impeller speed, air, and power requirements in flotation machine scaleup. Int. J. Miner. Process. 1, 51 (1974). Flynn S.A. & Woodburn E.T., A froth model for the selective separation of ultrafine coal from mineral in a dispersed air flotation cell. Draft paper, April (1985). Ross V.E., Mass transport in flotation froths. Ph.D. Thesis, University of Stellenbosch, South Africa (1988). Ross V.E., A study of the froth phase in large-scale pyrite flotation cells. To be published in Int. J. Miner. Process., 30, (1991). Ross V.E., Flotation and entrainment of mineral particles during the flotation process. Minerals Engng. 3 (3), 245 (1990). Ross V.E., Determination of the contributions of true flotation and entrainment during the flotation process. Proceedings of an Int. Colloquium: Developments in Froth Flotation. Gordon's Bay, South Africa. South African Institute of Mining and Metallurgy (1989). Kirjavainen V.M., Application of a probability model for the entrainment of hydrophilic particles in froth flotation. Int. J. Miner. Process. 27, 63 (1989). Trahar W.J., A rational interpretation of the role of particle size in flotation, bzt. J. Miner. Process. 8, 289 (1981). Subrahmanyam T.V. & Forssberg E., Froth characteristics and grade-recovery relationships in the flotation of lead-zinc and copper ores. Minerals Engng 1 (1), 41 (1988). Warren L.J., Determination of the contributions of true flotation and entrainment in batch flotation tests. Int. J. Miner. Process. 14, 33 (1985). Laplante A.R., Toguri J.M. & Smith H.W., The effect of air flow rate on the kinetics of flotation. I) The transfer of material from the slurry to the froth. Int. J. Miner. Process. 11,203 (1983a). Falutsu M. & Dobby G.S., Direct measurement of froth drop back and collection zone recovery in a laboratory flotation column. Minerals Engng 2, 377 (1989). Ynchausti R.A., McKay J.D. & Foot D.G., Column flotation parameters - their effects. Column Flotation '88. Proceedings of an Inter. Symp. on Column Flotation (K.V.S. Sastry, ed.), A.I.M.E., Phoenix, Arizona, 157 (1988). Bascur O.A. & Herbst J.A., Dynamic modelling of a flotation cell with a view toward automatic control. CIM X I V Int. Miner. Process. Congr., III-11.1, Oct. 17-23, Toronto, Canada, (1982). Hemmings C.E., An alternative viewpoint on flotation behaviour of ultrafine particles. Trans. Inst. Min. Metall. Sect. C89, 113 (1980). Hemmings C.E., On the significance of flotation froth liquid lamella thickness. Trans. Inst. Min. Metall. Sect. C90, 96 (1981). Dippenaar A., The destabilization of froth by solids. 1. The mechanism of film rupture. Int. J. Miner. Process. 9, 1 (1982). Dippenaar A., The destabilization of froth by solids. 2. The rate-determining step. Int. J. Miner. Process. 9, 15 (1982). Moys M.H., Residence time distributions and mass transport in the froth phase of the flotation process. Int. J. Miner. Process. 13, 117 (1984). Cutting G.W., Watson D., Whitehead A. & Barber S.P., Froth structure in continuous flotation cells: Relation to the prediction of plant performance from laboratory data using process models. Int. J. Miner. Process. 7, 347 (1981). Cutting G.W., Barber S.P. & Newton S., Effects of froth structure and mobility on performance and simulation of continuously operated flotation cells. Int. J. Miner. Process. 16, 43 (1986). Ross V.E., Interpretation of froth data to study the detachment of floating particles in flotation froths. Minerals Engng. 3 (50), 525 (1990).

974

41.

42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54.

V.E. Ross

Ross V.E. & Van Deventer J.S.J., A computer model to predict froth behaviour in the scale-up of flotation cells. APCOM '87. Proceedings o f the 20th Inter. Symp. on the Application of Computers and Mathematics in the Mineral Industries. Volume 2: Metallurgy. Johannesburg, SAIMM, 73 (1987). Ross V.E., A model for the froth phase in large flotation cells. Unpublished paper (1990). Ross V.E., An investigation of sub-processes in equilibrium froths: (I) The mechanisms of detachment and drainage. To be published in Int. J. Miner. Process., (1991). Ross V.E., An investigation of sub-processes in equilibrium froths: (II) The influence of operating conditions. To be published in Int. J. Miner. Process., (1991). Flynn S.A. & Woodburn E.T., A froth ultra-fine model for the selective separation of ultra-fine coal from mineral in a dispersed air flotation cell. Powder Technol. 49 (2), 127 (1987). Feteris S.M., Frew J.A. & Jowett A., Modelling the effect of froth depth in flotation. Int. J. Miner. Process. 20, 121 (1987). Frew J.A. & Trahar W.J., Roughing and cleaning flotation behaviour and the realistic simulation of complete plant performance, h~t. J. Miner. Process. 9, 101 (1982). Laplante A.R., Toguri J.M. & Smith H.W., The effect of air flow rate on the kinetics of flotation. II) The transfer of material from the froth over the cell lip. Int. J. Miner. Process. 11,221 (1983b). Kuz'kin A.S., Characteristics of passage of particles of various sizes into the flotation froth product. Tsvetnye Metally 24(4), 102 (1983). Meyer W.C. & Klimpel R.R., Rate limitations in froth flotation. SME Preprint 82-35, S M E - A I M E Annual Meeting, Dallas, Texas, Feb. 14-18 (1982). Yianatos J.B., Finch J.A. & Laplante A.R., Selectivity in column flotation froths. Int. J. Miner. Process. 23,279 (1988). Espinosa-Gomez R., Finch J.A., Yianatos J.B. & Dobby G.S., Column carrying capacity: particle size and density effects. Minerals Engng 1 (1), 77 (1988). Espinoza-Gomez R., Yianatos J.B., Finch J. & Johnson N.W., Carrying capacity limitations in flotation columns. Column Flotation '88. Proceedings of an Inter. Symp. on Column Flotation (K.V.S. Sastry, ed.), AIME, Phoenix, Arizona, 143 (1988). O'Connor C.T., Randall E.W. & Goodall C.M., Measurement of the effects of physical and chemical variables on bubble size. Int. J. Miner. Process 28 (1/2), 139 (1990).