WATER OVERFLOW RATE AND BUBBLE SURFACE AREA FLUX IN FLOTATION

Transcription

1 WATER OVERFLOW RATE AND BUBBLE SURFACE AREA FLUX IN FLOTATION Student: Wei Zhang Supervisor: James A. Finch Department of Mining and Materials Engineering McGill University Montreal, Canada August 2009 A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements of the degree of Master of Engineering Wei Zhang, 2009

2 ABSTRACT One of the most important factors that determines the concentrate grade in flotation is water recovery. Water recovery is influenced by frother through control of bubble size and possibly a frother-related chemical effect. A frother mass balance approach is presented for determining an equivalent water film thickness associated with bubble surface area flux exiting via the froth overflow to represent the chemistry effect. A closed loop mini flotation cell setup is used to achieve steady state in continuous tests. Four frothers are evaluated to reveal the dependence of water overflow velocity (J wo ) on frother type and concentration. Using Total Organic Carbon analysis, frother partitioning between overflow and underflow is measured, showing a remarkable preferential distribution to the overflow at low frother dosage. From surface tension measurements the Gibbs excess adsorption density (Г) is estimated and used in the mass balance approach to estimate bubble surface area flux to overflow (S bo ). Estimations from this approach are compared with bubble surface area flux into and on top of froth obtained from bubble size data using image analysis. A correlation is shown between J wo and S bo permitting an equivalent water film thickness carried by the bubble into the overflow (δ O ) to be estimated. The δ O reflects the frother type: a stronger frother creates a larger δ O and a weaker frother creates a smaller δ O. Possible implications in flotation are discussed. ii

3 RÉSUMÉ Dans les machines de flottation, le recouvrement d eau est l un des facteurs les plus importants dans la détermination de la teneur en minerai du concentré. Le recouvrement d eau est influencé par l agent moussant qui contrôle la taille des bulles et interagit possiblement d un point de vue chimique. Afin de mettre en évidence le caractère chimique de cette interaction, une approche basée sur le bilan massique de l agent moussant est présentée. Celle-ci vise plus précisément à déterminer l épaisseur moyenne du film d eau associé à l aire de surface du flux de bulles empruntant comme voie de sortie la partie supérieure de la mousse. Une cellule de mini flottation dotée d un circuit en boucle est utilisée afin d atteindre un d état d équilibre stable lors des tests en continu. Quatre agents moussants font l objet d études afin de comprendre la relation existant entre la vélocité du flux d eau sortant (J wo ) et le type et/ou la concentration d agent moussant. Avec la méthode d analyse du Carbone Organique Total, il est possible de mesurer la répartition de l agent moussant entre la partie supérieure et la partie inferieure de la mousse. Lorsque la concentration en agent moussant est faible, on remarque que l agent moussant se concentre préférentiellement dans la partie supérieure de la mousse. A partir de mesures de tension superficielle, l excès de la densité d adsorption de Gibbs (Г) est évalué et inclus dans le bilan massique afin d estimer l aire de surface du flux de bulle dans la partie supérieure de la mousse (S bo ). Ces estimations sont comparées avec les aires de surface des flux de bulles au centre et dans la partie supérieure de la mousse, obtenues à l aide de la iii

4 technique d analyse d images. Une corrélation obtenue, entre J wo et (δ O ) permet d estimer une épaisseur équivalente de film d eau transporté par la bulle dans la partie supérieure. Des épaisseurs comparables de film d eau transporté par la bulle dans la partie supérieure de la mousse δ O sont obtenues. Le δ O est caractéristique du type d agent moussant : dans le cas d un fort agent moussant, δ O est épais alors que dans le cas d un faible agent moussant, δ O est fin. De possibles conséquences engendrées en matière de flottation font l objet d une discussion. iv

5 ACKNOWLEDGEMENTS Foremost and importantly, I would like to express my most sincere gratitude to my supervisor and promoter Prof. James A. Finch, for his constant efforts, encouragements and support during the course of this research project. His enthusiasm, kindness, patience and gentleness during these last two years are deeply appreciated and became an invaluable treasure of my life. I wish to appreciate Mr. Nesset for his support and advice in the submission of this thesis. I wish to thank Dr. Mirnezami, Dr. Gomez and Mr. Uddin for providing critical guidance and insights throughout the project. The fruitful discussions with Dr. Rao are also acknowledged. I would like to extend my gratitude to James Shockley and Dr. Kolahdoozan for their dedicated cooperation in beginning this research. Special thanks to Frank Rosenblum and Ray Langlois for assistance in developing and setting up the apparatus. I would like to acknowledge other colleagues in the mineral processing group at McGill University for their selfless help and constructive suggestions and comments. I appreciate Dr. Barnabe and Cecile for the assistance in translating the abstract of this thesis. I would also like to thank Ranjan Roy and Andrew Golsztajn for easy access to the Chem. Eng. laboratory facilities and their assistance in the experiments during the study. v

6 TABLE OF CONTENTS ABSTRACT...II RÉSUMÉ... III ACKNOWLEDGEMENTS...V TABLE OF CONTENTS... VI LIST OF FIGURES...VIII LIST OF TABLES...X CHAPTER INTRODUCTION GENERAL BACKGROUND OBJECTIVES AND ORGANIZATION OF THESIS Objectives of thesis Organization of thesis REFERENCES...6 CHAPTER LITERATURE REVIEW AND THEORETICAL CONSIDERATIONS GAS DISPERSION/HYDRODYNAMIC PARAMETERS Superficial Gas Velocity Bubble Size Bubble Surface Area Flux Gas holdup Hydrodynamic hierarchies in froth zone WATER TRANSPORT INTO FROTH WATER RECOVERY/OVERFLOW RATE FROTHERS Frother types Effect of frothers on bubble size and bubble film thickness Effect of frothers on water overflow rate Effect of frothers on surface tension Frother partitioning REFERENCES...38 CHAPTER EXPERIMENTAL WATER OVERFLOW RATE FROTHER TYPE AND ANALYSIS SURFACE TENSION BUBBLE SIZE REFERENCES...52 CHAPTER RESULTS VALIDATION Reproducibility...54 vi

7 4.1.2 Number of bubbles sampled Water flow balance Frother mass balance Comparing surface tension for two water types WATER OVERFLOW RATE FROTHER PARTITIONING BUBBLE SIZE SURFACE TENSION AND ADSORPTION DENSITY BUBBLE SURFACE AREA FLUX From bubble size data From frother mass balance OVERFLOW GAS HOLDUP ESTIMATION EQUIVALENT WATER LAYER THICKNESS REFERENCES...70 CHAPTER DISCUSSION REFERENCES...77 CHAPTER CONCLUSIONS AND FUTURE WORK CONCLUSIONS FUTURE WORK REFERENCES...82 APPENDICES APPENDIX I: EXPERIMENTAL DATA APPENDIX II: BUBBLE SURFACE AREA FLUX ANALYSIS APPENDIX III: 5.5L MINI-CELL GEOMETRICAL DETAILS vii

8 LIST OF FIGURES Figure 1.1: Schematic of a mechanical flotation cell apparatus and a simplified diagram of the process..2 Figure 1.2: Bubble interaction with hydrophobic particles (black) and hydrophilic particles (grey) in the pulp zone...3 Figure 2.1: Bubble surface area flux schematic derivation diagram 13 Figure 2.2: S b as function of J g and D b, 3-D surface plot (Adapted from Vera et al., 1999)..15 Figure 2.3: Schematic hydrodynamic hierarchy and associated notation...19 Figure 2.4: Schematic of the water transport mechanism into froth: rising bubble with an equivalent water layer thickness...21 Figure 2.5: Gas holdup vs. gas velocity, generated by drift flux model 24 Figure 2.6: Water recovery vs. Gangue recovery (Adapted from Trahar et al., 1981).26 Figure 2.7: Schematic of the Plateau border at the junction of three bubbles in the froth 27 Figure 2.8: Frother alignment at the bubble surface and the formation of the bound and free layers (After Gélinas and Finch, 2005) 30 Figure 2.9: The general bubble size-concentration model (Adapted from Nesset et al., 2007).. 33 Figure 2.10: Surface tension of aqueous solutions of MIBC, DF250-A and DF250-C (20 C) (After from Hernandez-Aguilar et al., 2006) Figure 3.1: Setup for continuous closed loop testing on air-water system...49 Figure 3.2: Details of 5.5L mini-mechanical flotation cell Figure 3.3: Bubble size distribution measurements: into froth and top of froth.52 Figure 4.1: Bubble size (D 32 ) as a function of the number of bubbles counted: (a) Into froth; (b) Top of froth (example using DF250 7 ppm).56 viii

9 Figure 4.2: Validation test - overflow, underflow and combined (computed) feed mass flow rate and comparison to set feed flow rate (2300 g/min).57 Figure 4.3: Validation test - mass balance on frother showing calculated feed concentration compares well with system concentration.58 Figure 4.4: Water overflow velocity (primary y-axis) and recovery (secondary y-axis) as a function of system frother concentration Figure 4.5: Frother partitioning to overflow and underflow as a function of system concentration: a F150; b DF250; c FX160-05; d MIBC...60 Figure 4.6: a) Sauter mean bubble size into froth (D bi ) as a function of frother system concentration; b) Example images MIBC (top) and F150 (bottom) both at 50 ppm.61 Figure 4.7: a) Sauter mean bubble size on top of froth (D bt ) as a function of frother system concentration (including minimum D bi for reference); b) Example images: MIBC (top) and F150 (bottom) both at 50 ppm.62 Figure 4.8: Surface tension vs. natural logarithm of concentration; slope yields Gibbs adsorption excess, Γ using Eq Figure 4.9: Bubble surface area flux as a function of frother concentration (a F250; b DF250; c FX160-05; d MIBC)...65 Figure 4.10: Comparing gas holdup in overflow vs. concentration for the four frothers.67 Figure 4.11: Bubble surface area flux as a function of gas holdup in overflow.68 Figure 4.12: Superficial water overflow velocity (J wo ) vs. bubble surface area flux to overflow (S bo ) Figure 4.13: Superficial water overflow velocity (J wo ) vs. bubble surface area flux recovery (S bo /S bi ).70 Figure 6.1: Schematic diagram of flotation column continuous loop testing.. 81 Figure AIII-1.1: General Arrangement Drawing..91 Figure AIII-1.2: Section A Sectional View Figure AIII-1.3: Section B Sectional View Figure AIII-1.4: Section C Vertical View 1.94 Figure AIII-1.5: Section D Vertical View ix

10 LIST OF TABLES Table 3.1: Frothers used in the study.. 50 Table 4.1: 95% CI for selected measurements.. 55 Table 4.2: Surface tension for the two water types...58 Table 4.3: Estimated Gibbs adsorption excess from Figure Table 4.4: Estimated minimum S bo and bubble equivalent film thickness in overflow..69 Table AI-1.1: Flottec Table AI-1.2: DowFroth Table AI-1.3: FX Table AI-1.4: MIBC.85 Table AI-2.1: Flottec Table AI-2.2: DowFroth Table AI-2.3: FX Table AI-2.4: MIBC...86 Table AI-3: Frother Concentration vs. Surface Tension 86 Table AI-4.1: Flottec Table AI-4.2: DowFroth Table AI-4.3: FX Table AI-4.4: MIBC 88 Table AII-1.1: Flottec Table AII-1.2: DowFroth Table AII-1.3: FX Table AII-1.4: MIBC.90 x

11 CHAPTER 1 INTRODUCTION In this chapter a general overview of flotation is presented. The focus is on mechanical flotation cells, chemical and physical fundamentals, the role of chemical reagents, gas dispersion and water transport by rising bubbles. 1.1 GENERAL BACKGROUND Froth flotation, or simply flotation, has been used since early last century to separate minerals at least 100 different minerals, including all the world s copper, nickel, zinc, lead and cobalt are processed by flotation today [Wills, 2006]. The challenge is to recover minerals from ever poorer grade and more mineralogically complex ores. Flotation has also been applied to many non-mineral areas such as water purification and ink removal from recycled paper [Rao and Leja, 2004]. Flotation depends on complex physico-chemistry phenomena which occur at the liquidgas-solid interfaces. Although most of the principles are well established, a general model is difficult to create, due to the variety of sub-processes that combine to give the overall result. The flotation vessel is referred to as a machine or cell. Most are mechanically agitated cells, ranging in volume up to 300 m 3 [Yanez et al., 2009]. Separation in a mechanical cell can be described, in a simplified manner, as a two-step process [Yianatos, 2003] 1

12 collection of particles in the pulp and transfer through the froth, as shown in Figure 1.1. Concentrate Concentrate (bubble exit) Froth Zone Froth Zone Pulp Zone Bubble Recirculation Drainage Entrainment Tailings Impeller (rotor) Tailings Pulp Zone Feed Air Reagents Figure 1.1: Schematic of a mechanical flotation cell apparatus and a simplified diagram of the process The first step is achieved by injecting air into the cell which is dispersed by the impeller as bubbles throughout the volume of the cell through a combination of shearing, pumping and distribution (diffuser) actions. Minerals selectively attach to the air bubbles aided by chemical reagents called collectors that adsorb on the surface of the minerals to make them hydrophobic (Figure 1.2). Generally, collectors are hetero-polar organic compounds which have two parts: one is ionic through which the reagent reacts with (adsorbs at) the mineral surface and the other is a hydrocarbon chain that confers the hydrophobic property to the mineral. After collection the bubble-particle aggregate rises to reach the pulp-froth interface. The aggregate joins the froth, which comprises the second step. Excess liquid drains and the froth carries the particles to the overflow. The hydrophilic particles remain in the pulp, to form the non-float stream. Generally, the overflow 2

13 contains the valuable component and the non-float stream contains the gangue referred to, respectively, as concentrate and tailings [Booth and Freyberger, 1962]. Air Ascending bubble Hydrophobic particle Hydrophobic particle Hydrophilic particle Ascending bubble Hydrophilic particle Figure 1.2: Bubble interaction with hydrophobic particles (black) and hydrophilic particles (grey) in the pulp zone It is considered that the efficiency of collision between particles and bubbles limits the flotation of fine particles (e.g. < 50 µm); while in the case of coarse particles (e.g. >50 µm) detachment is considered the limiting mechanism. Both are dependent on bubble size prior to other factors [Tao, 2004]. It is evident that bubbles play a fundamental role in the flotation process. The ability to control the size distribution of bubbles in a flotation cell appears to be highly attractive. A specific class of surface active surfactants, termed frothers, are used in flotation to help produce small bubbles ( mm) and stabilise the froth [Harris, 1976; Cho and Laskowski, 2002]. Compared to collectors, frother molecules are usually non-ionic. They possess 3

14 hydrophilic groups (e.g. O, OH) and a hydrophobic hydrocarbon chain. Recent studies suggest that above a critical concentration (the CCC) frothers prevent bubble coalescence which is believed to be the main mechanism responsible for small bubble formation [Cho and Laskowski, 2002]. There are two main classes of frother commercially available: alcohol-based and polyglycol-based. Alcohols, chain length 5 to 7, which are slightly soluble in water, are the most common (e.g. MIBC). The other frother class, which are derivatives of polyglycol and polyglycol ethers that are completely miscible in water, with molecular weight ranging between 80 g/mol to 600 g/mol; among the best known are Dow Froth 250 and Flottec 150. Water overflow is an important component in the flotation process. It controls recovery of fine gangue by a process known as entrainment and consequently influences concentrate grade [Lynch et al., 1981; Trahar, 1981; Smith and Warren, 1989]. Water is transported, as a surface film and in the trailing wake of ascending bubbles, from the pulp zone into the froth zone. The water is transported through the froth, predominantly in the Plateau borders, to the overflow. Water overflow rate shows a sensitive response to system variables, including gas (air) rate and bubble size. Flotation performance is measured by the rate of mineral recovery, purity of the concentrate (i.e. grade), and fraction of the valuable mineral reporting to the concentrate (i.e. recovery). Flotation efficiency is controlled by the combination of surface chemical and hydrodynamic variables [Ahmed and Jameson, 1985; Dobby and Finch, 1986; Yoon and Luttrel, 1989; Fuerstenau, 1999]. As the interaction between these variables and the resulting performance is not fully understood, the study of key parameters such as 4

15 superficial gas velocity, bubble diameter, gas hold-up and bubble surface area flux is essential. The full understanding of how these parameters relate to each other and how they affect flotation performance has not only scientific importance, but could provide new tools to design more efficient flotation systems. 1.2 OBJECTIVES AND ORGANIZATION OF THESIS Objectives of thesis Frother influences water overflow rate through control of bubble size and possibly a chemical effect. The focusing objective of the thesis is to de-couple these two contributions to try to quantify the chemistry effect. This is to be accomplished by the following specific objectives: i. Measuring overflow rate versus concentration for frothers with a range in strength. ii. Measuring bubble size into froth (i.e. in pulp zone) and on top of froth at a known air rate to provide estimates of bubble surface area flux to overflow, S bo. iii. Estimating S bo using a frother mass balance approach. iv. Relating S bo to the water overflow rate, J WO. v. Trying to quantify the chemistry effect as an equivalent water layer thickness, δ Organization of thesis Chapter 1 overviews the flotation process and introduces the project objectives. Chapter 2 presents the literature review which is divided into three parts: hydrodynamic parameters, water overflow rate and frother chemistry. Chapter 3 describes the experimental set-up, procedure and measurement techniques. Test results, observations and sensitivity analysis 5

16 are given in Chapter 4. Chapter 5 discusses the results, providing mechanistic arguments and quantitative interpretation of the frother mass balance approach to estimate S bo. Chapter 6 covers the conclusions, with future works explored. 1.3 REFERENCES Ahmed N. and Jameson G. J., The Effect of Bubble Size on the Rate of Flotation of Fine Particles, International Journal of Mineral Processing, Vol.14, No. 3, pp Araya R., Engineering master student, Department of Mining and Materials Engineering, McGill University, personal communication. Booth, R.B. and Freyberger, W.L., Froths and Frothing Agents, In: Fuerstenau, D.W. (Ed.), Froth Flotation. AIME, New York, NY, pp Cho Y. S. and Laskowski J. S., Effect of Flotation Frothers on Bubble Size and Foam Stability, International Journal of Mineral Processing, Vol. 64, No. 2-3, pp Dobby G. S. and Finch J. A., Particle Collection in Columns - Gas Rate and Bubble Size Effects, Canadian Metallurgical Quarterly, Vol. 25, No. 1, pp Fuerstenau D.W., Advances in Flotation Technology, Proceedings of Symposium of Advances in Flotation Technology held at the SME Annual Meeting, Edited by Parekh B.K. and Miller J.D., Society for Mining Metallurgy and Exploration, Littleton, Colorado, pp Harris C. C., Flotation Machines, in Flotation, A. M. Gaudin Memorial volume, Vol. 2, M. C. Fuerstenau, Ed., AIME, New York, pp Lynch A. J., Johnson N. J., Manlapig E. V. and Thorne C. G., Mineral and Coal Flotation Circuits, Elsevier, Amsterdam. Quinn J., Exploring the Effects of Salts on Gas Dispersion and Froth Properties in Flotation Systems, Master s Thesis, McGill University, Montreal, Canada. Rao S. R and Leja J., Surface Chemistry of Froth Flotation, 2 nd Edition, Vol. 1, Kluwer Academic Publishers, New York. Smith, P. G. and Warren L. J., Entrainment of particles into flotation froths. Frothing in flotation I, Edited by Laskowski, J.S Gordon and Breach Science Publishers, New York, pp

17 Tao D., Role of Bubble Size in Flotation of Coarse and Fine Particles - a Review, Separation Science and Technology 39 (4), pp Trahar W. J., A Rational Interpretation of the Role of Particle Size in Flotation, International Journal of Mineral Processing, Vol. 8, No. 4, pp Wills B. A. and Napier-Munn T. J., Mineral Processing Technology, 7 th Edition, Published by Oxford, pp Yanez A., Pedro M., Coddou F., Elgueta H., Ortiz J. M., Perez C., Cortes G., Finch J. A., Gomez C. and Morales P., Gas Dispersion Characterization of TallCell 300 at Chuquicamata Concentrator, to be presented 48 th Conference of Metallurgists, Sudbury. Yianatos, J. B., Design, Modeling and Control of Flotation Equipment, In: Lorenzen, Bradshaw, D.J. (Eds.), proceedings of the XXII International mineral processing Congress, Cape Town, South Africa, pp Yoon R. H. and Luttrel H. H., The Effect of Bubble Size on Fine Particle Flotation, Frothing in flotation: A volume in honour of Jan Leja. Edited by J.S. Laskowski, pp

18 CHAPTER TWO LITERATURE REVIEW AND THEORETICAL CONSIDERATIONS As a conceptual aid to understanding, a flotation cell can be considered as a combination of pulp and froth zones. Initial work perhaps focused on particle collection in the pulp zone leading, for example, to diagnostic procedures [Trahar, 1981] and semi-quantitative models [Duan et al., 2003]. Recent work has raised the possibility that flotation performance can be predicted by modeling the froth [Neethling et al., 2003; Stevenson et al., 2003]. One outcome of the froth modeling work, which inspired the work in this thesis, is the dependence of water overflow rate on process variables. 2.1 GAS DISPERSION/HYDRODYNAMIC PARAMETERS In this section a description of some gas dispersion properties will be presented. Gas dispersion includes the following four variables: gas hold-up (E g ), bubble size (D b ), superficial gas velocity (J g ) and bubble surface area flux (S b ). Starting in the 90s, pioneering work on gas dispersion measurements in industrial cells was undertaken by various groups [Gorain et al., 1995, 1996, 1997; Tavera et al., 1996; Gomez and Finch, 2002; Deglon et al., 2000; Torrealba-Vargas et al., 2004; Hernandez- Aguilar et al., 2004, Finch et al., 2006]. This research has realized that optimizing gas dispersion parameters can produce metallurgical gains [Cooper et al., 2004; Gorain, 2005; Hernandez-Aguilar, 2009]. Sophisticated gas dispersion measurements techniques 8

19 and instruments have been developed by McGill University s mineral process group led by Prof. Finch over the last 2 decades [Gomez and Finch, 2002; 2007]. Heiskanen and co-workers have developed and employed similar gas dispersion instruments [Grau and Heiskanen, 2003], as have Yianatos and co-workers [Yianatos et al., 2001] Superficial Gas Velocity Superficial gas velocity, J g, is defined as the volume of air introduced into the cell, Q g, divided by the effective cross-sectional area of the cell, A cell. Q g J g = (2.1) Acell This is often expressed simply as gas velocity or gas rate with units cm/s. Typical range of J g in flotation cells is between 0.5 to 2.0 cm/s depending on factors such as bubble size and slurry rheology [Finch and Dobby, 1990]. Low J g may result in low recoveries because of limited overflow (removal) rate; high J g may induce boiling of the froth bed which reduces recoveries. Flotation operators use J g as a parameter to optimize flotation, although J g alone does not complete the picture. The superficial gas velocity in the pulp zone impacts the froth zone behaviour. Neethling et al. (2003) introduced superficial gas velocity to the overflow, J go, and air recovery, α, the fraction of air overflowing the lip of a flotation cell in unbroken bubbles calculated, respectively, as follows: 9

20 and, J go v h l froth lip lip = (2.2) J A cell go α = (2.3) J g where v froth is the velocity of overflowing froth, h lip is the depth of the froth above the lip and l lip is the lip length of the cell. The air recovery indicates froth stability: for a stable froth the value of α should be relatively high, i.e. more than 50%, suggesting little air (1- α) escapes the froth by bubble bursting on the surface. To measure the overflowing froth velocity, point-to-point timing of the flow of bubbles over a known distance on an image of the froth top captured by a camera is used. This has proved reliable under a wide range of plant conditions. Less certain is how uniform this flow is, and thus the reliability of h lip and l lip. Further theoretical development and experimental validation techniques are required Bubble Size In flotation hydrophobic particles are collected and transported by bubbles from the pulp to froth zone. The efficiency of the process is dependent on the size of the bubbles [Pryor 1965; Ahmed and Jameson, 1985; Dobby and Finch, 1986; Yoon and Luttrell, 1986; Miller and Ye, 1987]. Therefore, the ability to control the generation of bubbles in order to produce an optimum size range in a flotation cell is attractive. Towards this purpose, bubble size measurements in industrial flotation cells have to be made. 10

21 As single metrics, bubble size distribution is often expressed by two means, D 10 (number mean) and D 32 (Sauter mean) derived by the following: i= n Di = i= 1 D10 (2.4 a) i= n n i= 1 i= n i= 1 i 3 Di = i= 1 D32 i (2.4 b) = n D 2 i where D i is equivalent spherical bubble diameter and n is total number of bubbles. For each bubble, the maximum and minimum diameter (D max and D min ) are computed by the software and D i is obtained from [Hernandez-Aguilar et al., 2005]: 3 2 D b = D max Dmin (2.5) The Sauter mean is the diameter giving the same interfacial (i.e. surface) area to volume ratio as the distribution. The Sauter mean diameter is the appropriate metric for calculating the bubble surface area flux (S b ). Typical range of bubble size is ca mm in the pulp zone [Gorain et al., 1995; Nesset et al., 2007]. Coalescence is considered the mechanism which reduces air dispersion efficiency [Harris, 1976]. The bubble size distribution depends on the balance between coalescence and breakup [Gorain et al., 1995; Grau and Laskowski, 2005; Kracht and Finch, 2009]. There are many factors that influence bubble size including superficial gas velocity, frother type and concentration, bubble generation device and operating pressure. An empirical relationship [Dobby and 11

22 Finch, 1986] gave the Sauter mean bubble size as a function of superficial gas velocity as follows: n D32 C J g = (2.6) where C and n are empirical parameters. More recently [Finch et al., 2008] this relationship was modified to: D = D + C J (2.7) g where D 0 and C 1 are empirical parameters. Several researchers [Woodburn et al., 1994; Aldrich et al., 1997; Sadr-Kazemi and Cilliers, 1997] have suggested that the froth zone controls the performance of a cell. This implies there is a close relationship between the bubble size distribution in the pulp and froth zones [Aldrich and Feng, 2000]. The bubble size distributions can be measured by use of capillary [Randall et al., 1989] and sampling-for-imaging techniques [Hernandez- Aguilar et al., 2004]. The results from Aldrich and Feng [2000] showed the mean bubble size in the pulp is smaller than in the froth, and the different rates of retardation in bubble coalescence associated with different frother type and concentration affect the bubble size in both the pulp and froth zones. Cilliers [2007] derived an expression to calculate number of bubble coalescence events in the froth: DbT 3ln( ) DbI Number of Coalescence Events = (2.8) ln 2 12

23 where D bt is the Sauter mean bubble diameter on the top surface of the froth and, D bi represents the Sauter mean bubble size entering ( into ) the froth. Cilliers pointed out that a bubble typically coalesces ca. 15 times while passing through the froth some three coalescence events every second. Although the expression does not include system variables (e.g. gas rate, chemistry effect, water entrainment, etc.) and it has not been rigorously tested, it has established a mathematical skeleton for future experimental investigations Bubble Surface Area Flux Bubble surface area flux, S b, is formally defined as the surface area of bubbles per unit cross-sectional area of flotation cell per unit time [Xu et al., 1991; Finch et al., 1999]. The S b is the available bubble area for transporting particles to the froth zone. From Figure 2.1, Eq. 2.9 can be derived: here S is the average surface area per bubble and n corresponds to the number of bubbles per second passing through cell area A. Figure 2.1: Bubble surface area flux schematic derivation diagram From Figure 2.1, by inspection, 13

24 S b n S = (2.9) A where, assuming spherical bubbles, S is: 2 S = Π D b (2.10) and the number of bubbles can be expressed as: Q n = (2.11) Π 6 g 3 Db Substituting Eq and 2.11 into Eq. 2.9 gives: S b = Q 6 g D b A (2.12) From Eq. 2.1 and Eq can be derived the common expression for calculating S b from J g and D b : S b J g = 6 (2.13) D b where D b is usually given by the Sauter mean bubble diameter (D 32 ) [Finch and Dobby, 1990]. Although S b cannot be measured directly, researchers have shown that water recovery [Xu et al., 1991] and solids recovery [Luttrell and Yoon, 1992; Gorain et al., 1997; Finch et al., 1999; Deglon et al., 2000; Hernandez et al., 2001; Comley et al., 2007] is dependent on the bubble surface area flux in the pulp. The S b is a property of the 14

25 dispersed gas which combines the effect of superficial gas velocity J g and mean bubble size D b. Depending on hydrodynamic conditions and cell type, there is a range in S b (Figure 2.2). Figure 2.2: S b as function of J g and D b, 3-D surface plot (Adapted from Vera et al., 1999) Figure 2.2 is a plot of S b as a function of J g and D b. The parameter ranges are typical: superficial gas velocity, cm/s; Sauter mean bubble size, mm. Combining the two parameters, the S b surface is given. Figure 2.2 indicates S b can extend up to 80 s -1, supported by the current data base [Power et al., 2000; Nesset et al., 2006]. Xu et al. [1991] suggested a maximum S b in air-water system of ca. 160 s -1. Usually industrial cells can handle greater superficial gas velocity than laboratory cells and therefore offer a wider S b range: s -1, compared to 5-30 s -1 [Vera et al., 1999]. The results for the McGill 5.5 L lab flotation cell used in this thesis ranged, as will be shown, 15

26 from a low of 10 s -1 to a high of 80 s -1, i.e., overlapping the industrial flotation cell range because of the cell s specific geometry. In flotation, bubbles enter the froth phase and carry the hydrophobic mineral particles to the overflow, thus effecting the separation. However, some of the bubbles coalesce in the froth and burst on the surface. The overflow superficial gas velocity and the overflow bubble size combined as the bubble surface area flux to the overflow are key variables that control the solids and water overflow rate. Neethling et al. [2003] suggested an approach to determine the bubble surface area flux to the overflow (i.e. S bo ) by measuring J go (Eq. 2.2) and D bt, the mean bubble size on the top of the froth. It is difficult to carry out measurements of S bo by this approach. There are two problems: One is the measurement of J go as air recovery is required (refer to section 2.1.1); the second problem is the measured bubble size on the top of froth (D bt ) is not same as the bubble size in the overflow (D bo ). The video clips included by Neethling et al. [2003] indicate that the large bubbles observed on the top froth accompany smaller bubbles underneath and most of the collected froth (i.e. overflow) is made up of bubbles flowing from under the top froth layer (i.e. D bo is smaller than D bt ). Ireland and Jameson [2007] make the same point. A new approach will be demonstrated here to estimate bubble surface area flux in overflow by using a frother mass balance. It remains widely held that overflow rate is dependent on the S b in the pulp zone. Estrada- Ruiz and Perez-Garibay [2009] demonstrated that the mass overflow rate of solids, and inferred water overflow rate, was less than that estimated in their model with full air 16

27 recovery; i.e. solid and water overflow rates are affected by air recovery α, or more explicitly, the S bo Gas holdup The gas holdup (E g ) in a liquid (or slurry) is defined as the contained volumetric fraction of gas: Vbubbles E g = 100% (2.14) V + V bubbles liquid Gas holdup is influenced by gas flow rate and frother concentration and type. The gas flow rate has a direct effect, and measuring E g as a function of J g can be used to define the effective operating range of a flotation machine as well as troubleshoot for operational and maintenance problems [Dahlke et al., 2001; Dahlke et al., 2005]. Frother concentration influences E g by controlling bubble size and hence bubble rise velocity. Azgomi et al. [2007] showed that frother type had an effect on gas holdup in addition to its role in controlling bubble size. This was later traced to an effect of frother type on bubble rise velocity [Rafiei and Finch, 2009]. To explore the relationship between water transport and chemical effects (i.e. frother type and concentration), Moyo et al. [2007] used E g versus water overflow rate to characterize frother type. Moyo [2005] attempted to correlate overflow rate with S b but failed because S b was essentially constant for the conditions used (concentration > CCC); what was needed was S bo. 17

28 2.1.5 Hydrodynamic hierarchies in froth zone In flotation, froth building is a combination of two factors, chemical (i.e. adding frother) and physical (i.e. introducing and mixing gas into the liquid). Froth properties depend on hydrodynamic parameters and the level of water entrainment. Before expanding on this, a brief introduction to our understanding of flotation froths is worthwhile, especially in terms of the hydrodynamic properties which help distinguish three hierarchies: into froth, on top of froth, and into overflow (Figure 2.3). 1) Into froth: Figure 2.3 shows the movement of air, and associated nomenclature starting in the pulp and reaching the overflow. Hydrodynamic conditions in the pulp represent those into the froth, distinguished by the subscript I. Gas velocity generally written as J g would now be J gi. The hydrodynamic conditions lead to a certain rate of water entrainment into the froth, here given on a superficial basis (i.e. per unit area of cell), J WI. 2) Top of froth Bubbles coalesce as they rise through the froth; therefore bubbles are larger at the top surface than those entering. In addition, bubbles on the top can burst. Together these processes mean D bt > D bi, where subscript T represents top of froth. Converting to bubble surface area flux, then S bt < S bi. A complication here is what gas velocity to use; since some bubbles burst it could be argued that J gt < J gi, the difference being the air loss (i.e. 1- α). 3) Into overflow: 18

29 As discussed, the top of the froth is not the same as the froth that overflows. It is evident (using subscript O for into overflow ) that J go < J gi ; in fact J go = α J gi, which suggests it is measurable but uncertainty still remains with D bo. A direct measure of D bo seems unlikely. It is a contribution of this thesis that rather than trying to measure J go and D bo, a direct estimate of S bo is attempted using a frother mass balance approach. Superficial velocity of entrained water into froth: J wi J g Water overflow rate: J wo On top surface of froth: J gt, E gt, D bt, S bt Into the overflow: J go, E go, D bo, S bo Superficial feed velocity: J wf Into froth (interface of pulp/froth): J gi, E gi, D bi, S bi Superficial water underflow velocity: J wu Figure 2.3: Schematic hydrodynamic hierarchy and associated notation 2.2 WATER TRANSPORT INTO FROTH In flotation, water transport by bubbles produces non-selective particle entrainment which influences the grade of float product. As Figure 2.3 suggests, water transport can be considered a two-step process: 1 - transfer of water from the upper surface of pulp zone to the lower boundary of froth zone; 2 - water transfer through the froth to the overflow. These two steps are not independent. This section concerns the first step (section 2.3 will address the second step), where the superficial water flow rate into froth is notated as J wi. 19

30 The J wi is related to the S bi and possibly frother type. When the rising bubbles enter the froth from the pulp, water is carried both as a film on the surface and as a trailing wake (Figure 2.4). The wake is the main source of water entering the froth [Gaudin 1957; Yianatos, et al., 1986; George et al., 2004]. Researchers [Mika and Fuerstenau, 1969; Bascur and Herbst, 1982; Finch et al., 2006] have given a description of the transported water which can be divided into two categories a boundary layer (hydration) water which does not drain, and a free water layer which does drain. By using IR spectroscopy, Finch et al. [2006] demonstrated a layer of bound water that is associated with a frother-stabilised bubble. Reported thickness of the bound water layer was 1.1 µm for the frother F150, 0.6 µm for DF250, and <0.16 µm for MIBC. However, this water entrainment mechanism was argued to by Smith and Warren [1989] based on: i. It is only within a limited range of hydrodynamic conditions that the development of bubble wake would take place and such occurrence is unlikely to be found at the base of every froth column. ii. It is not likely to find a wake inside the froth considering the close-packed structure of bubbles. iii. The thickness of the bubble boundary film is unknown in the froth. Instead Smith and Warren [1989] proposed a mechanism they named bubble swarm effect where water is mechanically pushed into the froth by ascending swarms of bubbles. Bubbles will continually rise through the froth pushing water ahead of them, and finally out into the overflow. 20

31 To simplify modeling the water flow rate into froth (i.e. J wi ), it can be assumed that an equivalent water layer exists to represent the total volume of bound and wake water per bubble, as demonstrated in Figure 2.4 [Bascur and Herbst, 1982; Xu, et al., 1991]. Therefore J wo becomes a function of bubble surface area flux multiplied by this equivalent water boundary layer thickness (δ Ι ): JwI = SbI δ I (2.15) film bubble bubble diameter, D b rising bubble wake equivalent water layer thickness, δ I Figure 2.4: Schematic of the water transport mechanism into froth: rising bubble with an equivalent water layer thickness Xu et al. [1991] introduced S b for the purpose of quantifying the rate with which water is carried into the froth and showed that the volume of water did vary with S b. The S b in the pulp zone can be determined. Bascur and Herbst [1982] attempted to estimate δ I using Levich s [1962] boundary layer thickness correlations: 21

32 Db ν 2 δ I = U sb 0.5 (2.16) where ν represents the kinematic viscosity and U sb corresponds to the bubble rise velocity. For Reb >> 1 (Re b = bubble Reynolds number), the boundary layer thickness is small compared to the bubble radius [Levich, 1962]. Hydration effects at the bubblewater interface and agitation conditions in the slurry were considered to control the magnitude of the boundary layer [Bascur and Herbst, 1982]. A method to estimate J wi can be based on the water wake volume, since this represents the bulk of the water being transported. From numerical analysis, George et al. [2004] correlated the wake volume carried by an ascending bubble (Vol w ) with the bubble volume (Vol b ) and the bubble Reynolds number (Re b ): Volw = Vol b Reb Reb 400 (2.17) Since water carrying rate into froth J wi can be defined as: J wi nvol A w = (2.18) where n is the number of bubbles per unit time, then: 22

33 J Q = Vol g wi b Reb AVol b 20 Reb 400 (2.19) Eq is further simplified as: JwI = JgI Reb Reb 400 (2.20) Eq shows J wi correlates with superficial gas velocity into froth and the Reynolds number. Therefore in the applicable Re b range for flotation-size bubbles (i.e. 20 Re b 400), an increase in J wi occurs when J gi increases; the range of J wi /J gi is between and 2 for flotation-related conditions [Finch, 2007]. A third approach to estimate J wi is to apply drift flux analysis (Details on drift flux analysis can be found in the literature [Molerus, 1993; Wallis, 1969; Finch, 2007].). To predict J wi, the drift flux model can be expressed as: J wi 2 [ U bt Eg (1 Eg ) Jg ](1 Eg ) = (2.21) E g where U bt represents bubble terminal velocity (that of a single bubble). U bt is a function of bubble size (i.e. D 32 ) in the pulp. Since D 32 is typically less than 1.5 mm, an expression for U bt is [Finch, 2007]: lnu = 1.23ln D (2.22) bt 32 23

34 By applying Eq and 2.22, J wi can be determined if E g and D b are known; however, in the cell used in this thesis E g could not be measured. As a first approximation, to predict the E g -J g relationship, conditions were assumed as in water-only and batch operation (i.e. J wi = 0), which means Eq can be rewritten as: J U E E 2 g = bt g(1 g) (2.23) By applying Eq. 2.23, two solutions are obtained: one describes conditions in the pulp zone and the other conditions in the froth zone, as shown in Figure 2.5: Froth zone Eg (%) Pulp zone Jg (cm/s) Figure 2.5: Gas holdup vs. gas velocity, generated by drift flux model Figure 2.5 shows that as J g is increased, E g increases in the pulp zone and decreases in the froth zone. The result for the pulp zone is as expected. For the froth zone, physically this result means that a volumetric increment in gas rate (higher J g ) carries a larger volumetric 24

35 increment of water into the froth. Since all the experiments in this thesis were run at a constant gas velocity J g = cm/s into the froth (dashed line in Figure 2.5), E g in the froth is predicted to be in the range ca. 85 to 95%. 2.3 WATER RECOVERY/OVERFLOW RATE The last section considered water transport into and through the froth; this section concerns the water carried to the overflow. The behaviour of gangue particles is influenced by the water overflow rate, the recovery mechanism being termed entrainment. The relationship between water recovery and recovery of several minerals was studied by Bishop and White [1976] who showed entrained particle recovery increased with increasing water recovery, no matter the hydrophobicity of the mineral. The trend is illustrated in Figure 2.6 [Trahar, 1981], which indicates a linear relationship between -5µm quartz (hydrophilic) recovery and water recovery over varying pulp density (16 27 %) and frother concentration (2.5 6 ppm). Although Trahar did not describe the relationships for larger particles, Figure 2.6 clearly shows that the entrained gangue recovery is directly proportional to water recovery. Others [e.g., Jowett, 1966; Vanangamudi and Rao, 1989] have shown similar results. 25

36 Figure 2.6: Water recovery vs. Gangue recovery (Adapted from Trahar et al., 1981) In JKSimFloat [Alford, 1990], a commercial computer software package for flotation modelling and simulation, the water overflow rate J wo, is expressed as a power function of the concentrate solids flow rate F s : J wo = a F (2.24) b s where a and b are empirically fitted parameters dependent on cell type and operating conditions. Water recovery is the fraction of total water entering the flotation cell that reports to overflow; in other words, it is the ratio of water overflow velocity to feed velocity, J wo /J wf. 26

37 Only a certain fraction of the water entering the froth phase reports to the overflow; the rest returns to the pulp phase via drainage and bubble coalescence and bursting. This means that J wo < J wi. Water overflow rate is influenced by many factors including bubble size, gas rate, froth depth and frother type and most importantly the presence of solids [Engelbrecht and Woodburn, 1975; Clift et al., 1978; Subrahmanyam and Forssberg, 1988; Melo and Laskowski, 2006; Finch et al., 2006]. Neethling et al. [2003] described that bubbles in the froth are surrounded by thin lamellae (the bound layer). When three (or more) bubbles meet in the froth phase, a reservoir (Plateau border region) is formed at the intersection of the bubbles (Figure 2.7). Most of the water in a froth is contained in the Plateau border region with only a small fraction residing in the lamellae. Film Plateau Border Figure 2.7: Schematic of the Plateau border at the junction of three bubbles in the froth Cilliers and co-workers [Neethling et al., 2000; Neethling and Cilliers, 2002; Neethling et al., 2003] have proposed fundamental models to predict water overflow from flowing foam (two-phase froth). Their analysis takes into account foam drainage and resulted in 27

38 two relationships [Neethling et al., 2003] depending on air recovery, α. Writing in terms of the current symbols these relationships are: J wo 1 J = ( )(1 α ) α α < 0.5 (50%) (2.25) k D 2 g 2 bt J wo = J α 0.5 (50%) (2.26) 2 1 g 2 k DbO where constant k represents the balance between gravity and viscosity, expressed as: ρ g k = 3C pb μ (2.27) where ρ, µ, g is liquid density (g/cm 3 ), kinetic viscosity (g/cm*s) and the gravitational constant (cm/s 2 ), respectively, and C pb is the viscous drag coefficient in the Plateau border. To balance the units, the unit of constant k is cm -1 *s -1. In Eq. 2.25, α is air recovery, which was introduced in section An α < 0.5 represents unstable, shallow froth, which creates an overflow rate that depends closely on α (since more than 50% of the air in froth bubbles is lost to bursting before overflowing). When the froth becomes stable, α > 0.5, bubble coalescence and bursting can be neglected in the portion of the froth above the overflow lip, and the water overflow rate becomes independent of α. Note that the bubble size to calculate J wo is the mean bubble size flowing over the lip. 28

39 Regardless of α, both relationships show J wo varies with J 2 g which is supported by some work [Neethling et al., 2003; Stevenson, 2006] but not others [Quinn, 2006]. An experimental difficulty is that varying J g also varies D bi and likely influences D bo. Further investigations are required. Το use the water overflow rate models, some technical developments are still required since α, the constant k and mean bubble size in overflow (D bo ) can not be measured readily. Furthermore, interestingly no effect of frother type or concentration is directly included in the relationships, their impact apparently residing solely in their effect on D bo. To reach the overflow, water needs to survive the drainage process. Although the bulk of water is carried into the overflow via the Plateau borders, this can be still considered as an equivalent water film with a thickness on the bubble in the overflow of δ O. The approach of Bascur and Herbst (1982) described in Eq can thus be modified as: JwO = SbO δo (2.28) To meet the challenge, S bo is required which cannot be directly measured. Finch et al. [2006] suggested the relationship between S bo and J wo does offer a simple empirical approach with the advantage that δ O can accommodate chemical effects (i.e., frother type and concentration), which will be introduced in the next section. 29

40 2.4 FROTHERS The significance of frother in controlling hydrodynamic properties and consequently flotation efficiency has long been recognized and summarized in various reviews [Harris, 1976; Ahmed and Jameson, 1985; Dobby and Finch, 1986; Yoon and Luttrell, 1986; Fuerstanau, 1999]. The role of frother is to facilitate air dispersion into fine bubbles, to aid particle collection, and to stabilize the froth phase to enable the collected particles to reach the overflow [Zieminski et al., 1967; Klimpel and Isherwood, 1991; Laskowski, 1998]. Frothers are surface active reagents or surfactants that consist of a polar (hydrophilic) and non-polar (hydrophobic) parts. The non-polar part is a hydrocarbon chain and the polar part is typically OH. At the bubble surface (air-water interface), the hydrocarbon chain orients to the air side and the polar group to the water side (Figure 2.8). Bubble stability against coalescence is enhanced by strong polar-group/water-dipole interaction (hydration) at the air-liquid interface, which produces the bound layer. Frother: Hydrophilic end Free layer Frother: Hydrophobic end Air Bound layer Air-water interface (bubble surface) 30

41 Figure 2.8: Frother alignment at the bubble surface and the formation of the bound and free layers (After Gélinas and Finch, 2005) Frother types There are two types of frothers commonly used in the flotation industry today, alcohols and polyglycols [Klimpel and Isherwood, 1991; Laskowski, 1998]: i. Alcohol type frothers: These frothers are generally considered as weak frothers having low surface activity (i.e. do not reduce surface tension very much). The surface activity of alcohol frothers increases with increasing chain length, with maximum occurring around six to seven carbon atoms. Alcohol frothers produce froths that are relatively shallow and dry (carry less water) [Cytec, 2002] and have low persistence [Azgomi et al., 2009]. MIBC is the most well-known frother in this group. ii. Polyglycol type frothers: These frothers form a large class with varying molecular structure and molecular weight. When the molecular weight increases, water recovery increases. These frothers tend to produce relatively deep and wet froth, and hence more stable and persistent froths [Azgomi et al., 2009]. Flottec 150 (F150) and Dowfroth 250 (DF250) are among the best-known examples in this group. iii. Blended frothers: this is becoming popular in flotation practice, apparently enhancing performance [Cappuccitti and Finch, 2008]. The purpose for blending is to allow flotation operators to select various ratios of frother to achieve a target metallurgical performance. Elmahdy and Finch [2009] suggest blending offers some independence over the two- 31

42 frother functions, bubble size reduction and froth stabilization. They reported alcohols blended with a small amount of polyglycol (e.g. 1 ppm) can create this outcome Effect of frothers on bubble size and bubble film thickness In aiding production of small bubbles, it is believed that frothers act by preventing the coalescence [Harris, 1976; Metso Minerals, 2002; Cho and Laskowski, 2002]. The continued addition of frother has a diminishing effect resulting in the bubble size reaching a limiting value at a certain concentration. Although the mechanism by which frothers retard coalescence is still debated, new evidence (Grau et al, 2005, Gélinas and Finch, 2005) suggests that they might bind water molecules to the bubble by means of hydrogen bonding, thus making it more difficult for the water to drain between approaching bubbles. Several other researchers [Laskowski, 1998; Wang and Yoon, 2008] infer this also by reference to bubble hydration by frothers. The work of Cho and Laskowski [2002] suggested that bubble coalescence is completely prevented at a certain frother concentration, the Critical Coalescence Concentration, CCC, which they argued, was a property of the frother (i.e. was independent of machine type). At frother concentrations below the CCC the bubble size is a strong function of concentration, while, at concentrations exceeding the CCC, coalescence is suppressed and bubble size is determined by the initial air mass break-up process. These is evidence that bubble size continuous to decrease above CCC [Azgomi et al., 2007] but the CCC concept remains very useful although the values are difficult to establish using the geometric method of Laskowski et al. [2003]. Nesset et al. [2007] fitted bubble size (D 32 ) versus concentration using a three-parameter exponential model and introduced the 32

43 CCC95, the frother concentration for which 95% of the ultimate decrease in D 32 has been achieved, which is readily calculated from the model. The three-parameter model is: D 32=D 0+aExp(-b*C) (2.29) where C is frother concentration and D 0 refers to the limiting bubble size while a and b are fitted constants. Eq can be subsequently modified as, D 32=D 0+aExp(-b*C/CCC95) (2.30) to provide a general model, Figure 2.8 showing that all frothers follow this common trend Jg=0.5 cm/s Jg=1 cm/s Model D32 (mm) Normalized Frother Concentration (C/CCC95) Figure 2.9: The general bubble size-concentration model (Adapted from Nesset et al., 2007) A static bubble generation technique was employed by Gélinas and Finch [2005] to measure film thickness on bubbles blown in different frother solutions. The bubble 33

44 appeared to have a dual water layer surface, an inner layer bound due to H-bonding with adsorbed frother and an outer layer of free water (Figure 2.8). The results showed that the polyglycol frother (F150) had a thicker bound layer (ca. 1 µm) than MIBC (ca µm) Effect of frothers on water overflow rate It is generally understood that the type of frother influences water transport, and thus influences water overflow rate [Cytec, 2002]. Transport is influenced by the bubble size or more precisely the bubble surface area flux, and possibly the nature of the frother itself [Moyo et al., 2007; Nguyen et al., 2003; Melo and Laskowski, 2006]. It is widely accepted that alcohol-based frothers (e.g. MIBC) generate dry froths and polyglycoltype frothers (e.g. DF250) create wet froths [Cytec, 2002]. To determine the role of frother chemistry in water transport, it must be de-coupled from other factors such as the frother effect on bubble size, and the role of solid particles. Moyo et al. [2007] demonstrated a method to characterize frothers using water overflow rate versus gas holdup at frother concentrations in excess of the CCC, in which case, it was assumed, all frother types yield the same concentration-independent bubble size and bubble surface area flux into the froth. As noted the actual need is S b into overflow, S bo, for which no method of estimation was available to Moyo et al. [2007]. There are only a few studies comparing two- and three-phase systems. Rahal et al. [2001] built an empirical model that showed water recovery was independent of frother type and concentration. Melo and Laskowski [2006] studied how frother type affected water recovery in coal flotation systems. They demonstrated that two alcohol frothers (Diacetone and MIBC) gave lower water recoveries in two-phase (air-water) tests than 34

45 polyglycol frothers (e.g. DF1012) but higher water recovery in the presence of coal particles. This probably reflects different levels of frother interaction with coal (i.e. adsorption of frother). A similar finding was demonstrated by Gredelj et al. [2009]. The complication of the presence of the solid particles in flotation hydrophobic solids particles can change the stress state at the air-water interface and hydrophilic particles can modify the rheology of the interstitial fluid within the froth [Stevenson et al., 2003] means two phase systems remain a necessary precursor to gain insight into the frother effect on water overflow rate. Based on the approach of Bascur and Herbst [1982] (Eq. 2.16), Eq was proposed. It can be considered that an equivalent water layer thickness (δ O ) accompanies the overflowing bubble surface area flux (S bo ) and represents the frother chemistry effect on water overflow rate. The problem is determination of S bo. This thesis demonstrates a way to accomplish this task. To start we need to consider the surface tension-frother concentration relationship Effect of frothers on surface tension According to thermodynamics, matter seeks to be in a low-energy state, and bonding reduces chemical energy. This is the drive for bubble coalescence which reduces the surface area and hence energy of the system [Leja, 1982; Rao and Leja, 2004]. A common thought is that adding frother lowers surface tension, hence reducing the free energy, and the probability of coalescence [Wang and Yoon, 2008]. However, tests indicate that surface tension has no direct role to play as the decrease with most frothers 35

46 at the concentrations used in flotation is too small to be considered a factor [Sweet et al., 1997]. The relationship between surface tension and frother concentration can be described by the Langmuir-Szyszkowski equation [Adamson, 1990]: ( kc) γ = γ0 Γ RTln 1+ (2.30) where γ 0 is the surface tension of water, Γ is the frother adsorption density, k is the equilibrium constant and c is the frother concentration. An example of surface tension data as a function of solution concentration for three frothers MIBC, DF250-A and DF250-C determined using the Wilhelmy plate method is shown in Figure 2.10 [Hernandez-Aguilar et al., 2006]. The Langmuir-Szyszkowski equation (Eq. 2.30) was used to fit and interpolate surface tension values. 36

47 Figure 2.10: Surface tension of aqueous solutions of MIBC, DF250-A and DF250-C (20 C) (After from Hernandez-Aguilar et al., 2006) The Gibbs surface excess (adsorption density) Γ (mol/m 2 ), can be calculated from the the Gibbs adsorption isotherm [Hiemenz and Rajagopalan, 1997]: 1 γ Γ= (2.31) RT ln c where R and T are gas constant and absolute temperature, respectively. Eq shows that surfactant adsorption density can be measured by the slope of the plot γ versus the natural logarithm of frother concentration. If γ ln c is negative, Γ is positive and an excess of the frother is present in the surface, i.e. the solute is surface active and is said to positively adsorb at the interface. This is the case for frothers. If the slope is positive, there is a deficiency of solute at the surface which is said to be negatively adsorbed; this is the case for many salts. These relationships, in association with dynamic (time-dependent) surface tension data, have been used to estimate surface coverage of frother on bubbles as they enter the froth zone and overflow [Comley et al., 2002; Tan et al., 2005] Frother partitioning Frother adsorbs on the bubble surface and thus transfers to the froth and releases to the water as bubbles burst. Measuring frother distribution between pulp, froth and overflow has potential diagnostic value [Zangooi et al., 2009]. 37

48 A colormetric technique for measuring frother concentration was introduced by Gélinas and Finch [2005]. Using this technique, for instance, significant concentration of F150 into the overflow was detected at one operation [Gélinas and Finch, 2007], up to 100 ppm compared to ca. 1 ppm in the pulp. Though the magnitude of the distribution was a surprise, the observation follows expectation: frother is surface active and adsorbs on bubbles and is thus transported to the froth and to the overflow. The observation at that particular plant explained evident frother enrichment in downstream cleaner banks which made them difficult to operate. The colorimetric technique is specific to frothers and therefore is well suited to plant studies. It is, however, fairly time consuming. Total Organic Carbon (TOC) analysis offers an alternative when only one organic is involved [Hadler et al., 2004]. This method proved suited to the current needs. 2.5 REFERENCES Adamson, A. W., Physical Chemistry, 5 th Edition, Wiley Publication, New York. Ahmed, N. and Jameson, G. J., The Effect of Bubble Size on the Rate of Flotation of Fine Particles, International Journal of Mineral Processing, Vol. 14, No. 3, pp Aldrich C., Moolman D. W., Harris M. C., Bunkell S.-J. and Theron D. A., Relationship between Froth Structure and Recoveries and Grades in the Batch Flotation of Sulphide Ores, Minerals Engineering, Vol. 10, No. 11, pp Aldrich C. and Feng D., The Effect of Frothers on Bubble Size Distributions in Flotation Pulp Phases and Surface Froths, Minerals Engineering, Vol. 13, No , pp Alford, R. A., An Improved Model for Design of Industrial Column Flotation Circuits in Sulphide Applications, In: P.M.J. Gary, Editor, Sulphide Deposits Their Origin and Processing, IMM, London. 38

49 Azgomi F, Gomez C. O. and Finch J. A., Correspondence of Gas Holdup and Bubble Size in Presence of Different Frothers, International Journal of Mineral Processing, Vol. 83, No. 1-2, pp Azgomi F, Gomez C. O. and Finch J. A., Frother Persistence: A Measure Using Gas Holdup, Minerals Engineering, Vol. 22, No. 9-10, pp Bascur O. A. and Herbst J. A., Dynamic Modeling of a Flotation Cell with a View toward Automatic Control, in: Proc. 14th Int. Miner. Proc. Congr., Toronto, pp Bishop J. P. and White M. E., A Study of Particle Entrainment in Flotation Froths, in: Transactions of IMM 89, pp Cappuccitti F. and Finch J. A., Development of New Frothers through Hydrodynamic Characterization, Minerals Engineering, Vol. 21, No , pp Cilliers J. J., Column flotation, Section II: the Froth in Column Flotation, In: Fuerstenau, M.C., Jameson, G., Yoon, R.-H. (Eds.), Froth Flotation A Century of Innovation, pp Cho Y. S. and Laskowski J. S., Effect of Flotation Frothers on Bubble Size and Foam Stability, International Journal of Mineral Processing, Vol. 64, No. 2-3, pp Clift R., Grace J. R. and Weber M. E., Bubbles, Drops and Particles, Academic Press, New York. Comley B. A., Harris P.J., Bradshaw D.J. and Harris M.C., Frother Characterisation Using Dynamic Surface Tension Measurements, International Journal of Mineral Processing, Vol. 64, pp Comley B. A., Vera M. A. and Franzidis J.-P., Interpretation of the Effect of Frother Type and Concentration on Flotation Performance in an OK3 Cell, Mineral and Metallurgical Processing, Vol. 24, No. 4, pp Cooper M., Scott D., Dahlke R., Gomez C. O. and Finch J. A., Impact of Air Distribution Profile on Banks in a Zn Cleaning Circuit, CIM Bulletin, Vol. 97, No. 1083, pp Cytec Mining Chemicals Handbook, 2002, pp Dahlke R., Scott D., Leroux D., Gomez C.O. and Finch J. A., Trouble Shooting Flotation Cell Operation Using Gas Velocity Measurements, In: Proceedings-33rd Annual Meeting of the Canadian Mineral Processors (division of CIM), January 23 25, pp

50 Dahlke R., Gomez C. and Finch J. A., Operating Range of a Flotation Cell Determined from Gas Holdup vs. Gas Rate, Minerals Engineering, Vol. 18, No. 9, pp Deglon D. A., Egya-Mensah D. and Franzidis J. P., Review of Hydrodynamics and Gas Dispersion in Flotation Cells on South African Platinum Concentrators, Minerals Engineering, Vol. 13, No. 3, pp Dobby G. S. and Finch J. A., Particle Collection in Columns - Gas Rate and Bubble Size Effects, Canadian Metallurgy Quarterly, Vol. 25 No. 1, pp Duan J., Fornasiero D. and Ralston J., Calculation of the Flotation Rate Constant of Chalcopyrite Particles in an Ore, International Journal of Mineral Processing, Vol. 72, No. 1-4, pp Elmahdy A. M. and Finch J. A., Effect of Frother Blends on Hydrodynamic Properties, to be presented 48 th Conference of Metallurgists, Sudbury. Engelbrecht J. A. and Woodburn E. T., The Effects of Froth Height, Aeration Rate and Gas Precipitation on Flotation, Journal of the South African Institute of Mining & Metallurgy, Vol. 76, pp Estrada-Ruiz R. H. and Perez-Garibay R., Evaluation of Models for Air Recovery in a Laboratory Column, Minerals Engineering, available online. Finch J. A. and Dobby G. S., Column Flotation, Pergamon Press, New York. Finch J. A., Gomez C. O., Hardie C., Leichtle G., Filippone R. and Leroux D., Bubble Surface Area Flux: a Parameter to Characterise Flotation Cells, in Proceedings of the 31 st Canadian Mineral Processors Conference, Ottawa, pp Finch J. A. Gélinas S. and Moyo P., Frother-related Research at McGill University, Minerals Engineering, Vol. 19, pp Finch J. A., Column flotation, Section I: the Collection Zone, In: Fuerstenau, M.C., Jameson, G., Yoon, R.-H. (Eds.), Froth Flotation A Century of Innovation. Finch J. A., Nesset J. E. and Acuña C., Role of Frother on Bubble Production and Behaviour in Flotation, Minerals Engineering, Vol. 21, No , pp Fuerstenau D.W., Advances in Flotation Technology, Proceedings of Symposium of Advances in Flotation Technology held at the SME Annual Meeting, Edited by Parekh B.K. and Miller J.D., Society for Mining Metallurgy and Exploration, Littleton, Colorado, pp Gaudin A. M., Flotation, McGraw-Hill, New York, Chapter 11, pp

51 Gélinas S., Finch J. A. and Gouet-Kaplan M, Comparative Real-time Characterization of Frother Bubble Thin Films, Journal of Colloid and Interface Science, Vol. 291, No. 1, pp Gélinas S and Finch J.A., Colorimetric Determination of Common Industrial Frothers, Minerals Engineering, Vol. 18, No. 2, pp George P., Nguyen A. V. and Jameson G.J., Assessment of True Flotation and Entrainment in the Flotation of Submicron Particles by Fine Bubbles, Minerals Engineering Vol. 17, pp Gomez C. O. and Finch J. A., Gas Dispersion Measurements in Flotation Machines, CIM Bulletin, Vol. 95, No. 1066, pp Gomez C. O., Cortés-López F. and Finch J. A., Industrial Testing of a Gas Holdup Sensor for Flotation Systems, Minerals Engineering, Vol. 16, No. 6, pp Gomez C. O. and Finch J. A., Gas Dispersion Measurements in Flotation Cells, International Journal of Mineral Processing, Vol. 84, No. 1-4, pp Gorain B.K., Franzidis J.P. and Manlapig E.V., Studies on Impeller Type, Impeller Speed and Air Flow Rate in an Industrial Scale Flotation Cell. Part 1: Effect on Bubble Size Distribution, Minerals Engineering, Vol. 8, No. 6, pp Gorain B.K., Franzidis J.P. and Manlapig E.V., Studies on Impeller Type, Impeller Speed and Air Flow Rate in an Industrial Scale Flotation Cell. Part 2: Effect on Gas Holdup, Minerals Engineering, Vol. 8, No. 12, pp Gorain B.K., Franzidis J.P. and Manlapig E.V., Studies on Impeller Type, Impeller Speed and Air Flow Rate in an Industrial Scale Flotation Cell. Part 3: Effect on Superficial Gas Velocity, Minerals Engineering, Vol. 9, No. 6, pp Gorain B.K., Franzidis J.P. and Manlapig E.V., Studies on Impeller Type, Impeller Speed and Air Flow Rate in an Industrial Scale Flotation Cell. Part 4: Effect of Bubble Surface Area Flux on Flotation Performance, Minerals Engineering, Vol. 10, pp Gorain B. K., Optimization of Flotation Circuits with Large Flotation Cells, Centenary of Flotation Symposium, Brisbane, pp Grau R. A. and Heiskanen K., Gas Dispersion Measurements in a Flotation Cell, Minerals Engineering, Vol. 16, pp Grau R. A., Laskowski J. S. and Heiskanen K., Effect of Frothers on Bubble Size, International Journal of Mineral Processing, Vol. 76, No. 4, pp

52 Gredelj S., Zanin M. and Grano S. R., Selective Flotation of Carbon in the Pb Zn Carbonaceous Sulphide Ores of Century Mine, Zinifex, Minerals Engineering, Vol. 22, No. 3, pp Hadler K., Aktas Z. and Cilliers J. J., The Effects of Frother and Collector Distribution on Flotation Performance, Minerals Engineering, Vol. 18, No. 2, pp Harris, C. C., Flotation Machines in Flotation, in: A.M.Gaudin Memorial Volume, Vol 2, Chapter 27, pp Hernandez H., Gomez C. O. and Finch J. A., A Test of Flotation Rate Constant vs. Bubble Surface Area Flux Relationship in Flotation, in Interactions in Mineral Processing. Edited by Finch J. A., Rao S. R. and Huang L., pp Hernandez-Aguilar J. R., Coleman R. G., Gomez C. O. and Finch J. A., A Comparison between Capillary and Imaging Techniques for Sizing Bubbles in Flotation Systems ; Minerals Engineering, Vo. 17, pp Hernandez-Aguilar J. R., Rao S. R. and Finch J. A., Testing the k S b Relationship at the Microscale, Minerals Engineering, Vol. 18, No. 6, pp Hernandez-Aguilar J. R., Cunningham R., Finch J. A., A Test of the Tate equation to Predict Bubble Size at an Orifice in the Presence of Frother, International Journal of Mineral Processing, Vol. 79, No. 2, pp Hernandez-Aguilar J., Gas Dispersion Studies at Highland Valley Copper, to be presented 48 th Conference of Metallurgists, Sudbury. Hiemenz P. C. and Rajagopalan R., Principles of Colloid and Surface Chemistry, 3 rd Edition, Marcel Dekker Inc., New York. Ireland P. M. and Jameson G. J., Liquid Transport in a Multi-layer Froth, J. Colloid and Interface Science 314, pp Jowett A., British Chemical Engineering, Vol. 2, pp Klimpel R. and Isherwood S., Some Industrial Implications of Changing Frother Chemical Structure, International Journal of Mineral Processing, Vol. 33, pp Kracht W and Finch J. A., Bubble Break-up and the Role of Frother and Salt, International Journal of Mineral Processing, Vol. 92, No. 3-4, pp Laskowski, J. S., Frothers and Flotation in Frothing in Flotation II, Edited by Laskowski, J. S. and Woodburn, E. T., Chapter 1, pp

53 Laskowski J. S., Tlhone T., Williams P. and Ding K., Fundamental Properties of the Polyoxypropylene Alkyl Ether Flotation Frothers, International Journal of Mineral Processing, Vol. 72, No. 1-4, pp Leja J., Surface Chemistry of Froth Flotation, Plenum Press, New York. Levich, V.G., Physicochemical Hydrodynamics, Translated by Scripta Technica Inc. Engelwood Cliffs, N.J.: Prentice-Hall, Chapter 8, pp Luttrell G. and Yoon R., A Hydrodynamic Model for Bubble Particle Attachment, Journal of Colloid and Interface Science, Vol. 154, No. 1, pp Lynch A. J., Johnson N. J., Manlapig E. V. and Thorne C. G., Mineral and Coal Flotation Circuits, Elsevier, Amsterdam. Melo F. and Laskowski J. S., Fundamental Properties of Flotation Frothers and Their Effect on Flotation, Minerals Engineering, Vol. 19, No. 6-8, pp Metso Minerals CBT (Computer Based Training), Mill Operator Training Package. Flotation Module. Formerly Brenda Process Technology CBT (Computer Based Training) (1996). Miller J. D. and Ye Y., The Significance of Bubble/Particle Contact Time in the Analysis of Flotation Phenomena - the Effect of Bubble Size and Motion, in: presented at 116th Ann. SME/AIME Meeting. Mika T. S. and Fuerstenau D. W., A Microscopic Model of the Flotation Process, in: Proc. 8th Int. Miner. Proc. Congr., Leningrad, pp Molerus O., Principle of Flow in Disperse Systems, Chapman and Hall, New York. Moyo P., Characterization of Frothers by Water Carrying Rate, master s thesis, Department of Mining and Materials Engineering, McGill University. Moyo P., Gomez C. O. and Finch, J. A., Characterizing Frothers Using Water Carrying Rate, Canadian Metallurgical Quarterly, Vol. 46, No. 3, pp Neethling S. J., Cilliers J. J. and Woodburn E. T., The Prediction of the Water Distribution in a Flowing Foam. Chem. Eng. Sci. Vol. 55, pp Neethling S. J. and Cilliers J. J., The Entrainment of Gangue into a Flotation Froth, International Journal of Mineral Processing, Vol. 64 No. 2 3, pp

54 Neethling S. J., Lee H. T. and Cilliers J. J., Simple Relationships for Predicting the Recovery of Liquid from Flowing Foams and Froths, Minerals Engineering, Vol. 16, No. 11, pp Nesset J. E., Hernandez-Aguilar J. R., Acuna C., Gomez C. O. and Finch J. A., Some Gas Dispersion Characteristics of Mechanical Flotation Machines, Minerals Engineering, Vol. 19, No. 6-8, pp Nesset, J. E., Finch, J. A., Gomez, C.O., Operating variables affecting the bubble size in forced-air mechanical flotation machines. In: Proceedings AusIMM 9th Mill Operators Conference, Fremantle, Australia, pp Nguyen A. V., Harvey P. A. and Jameson G. J., Influence of Gas Flow Rate and Frothers on Water Recovery in a Froth Column, Minerals Engineering, Vol. 16, No. 11, pp Power A., Franzidis J. P. and Manlapig E. V., The Characterization of Hydrodynamic Conditions in Industrial Flotation Cells, in: AusIMM Seventh Mill Operators Conference, Kalgoorlie, Australia, pp Pryor E. J., Mineral Processing, 3 rd Edn (Geneva: Elsevier), pp Quinn J., Exploring the Effects of Salts on Gas Dispersion and Froth Properties in Flotation Systems, Master s Thesis, McGill University, Montreal, Canada. Rafiei A and Finch J. A., A Comparison of Bubble Rise Velocity Profile of Two Surfactants to Explain Gas Holdup Data, to be presented 48 th Conference of Metallurgists, Sudbury. Rahal K., Manlaping E. and Franzidis J.-P., Effect of Frother Type and Concentration on the Water Recovery and Entrainment Recovery Relationship, Mineral & Metallurgical Processing, Vol. 18, No. 3, pp Randall E. W., Goodall C. M., Fairlamb P. M., Dold P. L. and O'Connor C. T., A Method for Measuring the Sizes of Bubbles in Two- and Three-phase Systems, Journal of Physics Engineering Science Instruments, Vol. 22, pp Rao, S. R. and Leja J., Surface Chemistry of Froth Flotation, 2 nd Edition, Kluwer Academic Publication, New York. Sadr-Kazemi N. and Cilliers J. J., An Image Processing Algorithm for Measurement of Flotation Froth Bubble Size and Shape Distributions, Minerals Engineering, Vol. 10, No. 10, pp

55 Smith, P. G. and Warren L. J., Entrainment of particles into flotation froths. Frothing in flotation I, Edited by Laskowski, J.S Gordon and Breach Science Publishers, New York, pp Stevenson P., Stevanov C. and Jameson G. J., Liquid Overflow from a Column of Rising Aqueous Froth, Minerals Engineering, Vol. 16, No. 11, pp Stevenson P., The Wetness of a Rising Foam, Ind. Eng. Chem. Res. 45, pp Subrahmanyam T.V. and Forssberg E., Frother Performance in Flotation of Cu and Pb-Zn Ores, Mineral Processing and Extractive Metallurgy, Vol. 97, pp Sweet C., Hoogstraten J. V., Harris M. C. and Laskowski J. S., The Effect of Frothers on Bubble Size and Frothability of Aqueous Solutions, In: Finch J. A. and Holubec I., Editors, Processing of Complex Ores - Proc. 2 nd UBC-McGill Symposium, CIM, Montreal, pp Tan S. N., Fornasiero D., Sedev R. and Ralston J., Marangoni Effects in Aqueous Polypropylene Glycol Foams, Journal of Colloid and Interface Science, Vol. 286, pp Tavera F. J., Gomez C. O. and Finch J. A., Novel Gas Hold-up Probe and Application in Flotation Columns, Trans. Instn. Min. Met., Vol. 105, pp. C99-C104. Torrealba-Vargas J. A., Gomez C. O. and Finch J. A., Continuous Air Rate Measurement in Flotation Cells: Steps towards Gas Distribution Management, Minerals Engineering, Vol. 17, pp Trahar W. J., A Rational Interpretation of the Role of Particle Size in Flotation, International Journal of Mineral Processing, Vol. 8, No. 4, pp Vanangamudi M. and Rao T. C., A Model for the Prediction of Fines Recovery in Batch Coal Flotation, Minerals Engineering, Vol. 2, No. 2, pp Vera M. A., Franzidis J-P. and Manlapig E. V., The JKMRC High Bubble Surface Area Flux Flotation Cell, Minerals Engineering, Vol. 12, No. 5, pp Wallis G. B., One-Dimensional Two-Phase Flow, McGraw-Hill, New York. Wang L., Yong R.-H., Effects of Surface Forces and Film Elasticity on Foam Stability, International Journal of Mineral Processing, Vol. 85, No. 4, 31 pp Woodburn E. T., Austin L. G. and Stockton J. B., A Froth Based Flotation Kinetic Model, Transactions of the Institute of Chemical Engineers, Vol. 72, pp

56 Xu M., Finch J. A. and Uribe-Salas A., Maximum Gas and Bubble Surface Area Rates in Flotation Columns, International Journal of Mineral Processing, Vol. 32, pp Yianatos J. B., Finch J. A. and Laplante, A. R., Holdup profile and bubble size distribution of flotation froths. Canadian Metallurgical Quarterly 25 (1): Yianatos J. B., Bergh L., Condori P. and Aguilera J., Hydrodynamic and Metallurgical Characterization of Industrial Flotation Banks for Control Purposes ; Minerals Engineering, Vol. 14 No. 9, pp Yoon R. H. and Luttrell G. H., The Effect of Bubble Size on Fine Coal Flotation, Coal Preparation, Vol. 2, pp Zangooi A. and Finch J. A., Frother Analysis in Industrial Flotation Cells, to be presented 48 th Conference of Metallurgists, Sudbury. Zhang W., Nesset, J. E. and Finch J. A., Water Recovery and Bubble Surface Area Flux, to be presented 48 th Conference of Metallurgists, Sudbury. Zieminski S., Caron M. and Blackmore R., Behaviour of Air Bubbles in Dilute Aqueous Solutions, I&EC Fundam., Vol. 6, No. 2, pp

57 CHAPTER 3 EXPERIMENTAL A mini, mechanically agitated flotation cell setup was used in closed cycle to establish steady state in continuous tests to determine water overflow rate as a function of frother type and concentration. Bubble size in the pulp, i.e. entering the froth (D bi ), and on top of froth (D bt ) were measured using imaging techniques in order to calculate S bi and S bt. From frother analysis data, a novel frother mass balance approach was used to estimate bubble surface area flux into the overflow (i.e. S bo ). The work is on the air-water system as a prelude to using the approach under actual flotation (i.e. with solids) conditions. 3.1 WATER OVERFLOW RATE The setup is based on the rig designed at the Noranda Technology Centre for continuous small-scale on-site testing [Shink et al., 1992]. The arrangement comprised the mini-cell, holding tank, conditioning tank and feed flow regulator tank configured in a closed loop to achieve steady state (Figure 3.1). The cell (Figure 3.2) is 5.5 L and the volume of the entire setup is 56 L (details related to cell geometry are in Appendix III). Gas (air) to the cell is injected via a flow meter down the impeller shaft. A stator surrounds the Agitair type impeller to dampen rotational movement of the aerated pulp. A control box to manipulate the various stirrers, the cell impeller and gas flow rate was constructed. Water is held in the holding tank and pumped into the feed flow regulator, which allows a calibrated flow into the conditioning tank while the remainder returns to the holding tank. 47

58 The conditioning tank is mixed (stirrer at 1000 rpm). Flow from the conditioning tank is feed to the cell. The position of an opening (2 cm x 6 cm) on the underflow (tailings) discharge pipe (Figure 3.2) regulates water rate to underflow and hence controls froth depth (level) in the cell. Cell overflow and underflow were recombined and pumped to the holding tank to complete the closed loop. The pump was used to ensure a flow above the minimum to maintain the target feed flow rate set at the regulator tank. Samples of both cell products were taken to measure flow rate and frother concentration; all unused sample was returned to the holding tank. Frother was added to concentration and mixed by circulating between conditioning and holding tanks for 15 minutes prior to initiating a test. This concentration is referred to as system concentration to distinguish from frother concentration determined analytically. Unless otherwise stated, operating conditions were feed flow 2300 g/min (i.e. retention time in cell ca. 2 min), impeller speed 1250 rpm, air flow rate 4200 cm 3 /min and froth depth 1 cm. For analysis it is convenient to use superficial flow velocities. Based on the area of the cell at the froth depth used, 96.8 cm 2, the superficial feed (water) velocity J F = cm/s and the air velocity J g = cm/s. The air velocity in the impeller region (where the area is cm 2 ) is J g = cm/s, which is at the low end of the operating range for flotation cells [Vera et al., 1999; Gomez and Finch, 2002]. Selected conditions were repeated at random to establish precision; and the error bars reported, unless otherwise stated, are the 95% confidence interval. 48

59 Figure 3.1: Setup for continuous closed loop testing on air-water system Air input Feed, i.e. conditioning tank output Shaft Impeller Froth discharge box Tailings discharge pipe The opening location in tailings pipe Impeller and diffuser Figure 3.2: Details of 5.5L mini-mechanical flotation cell 49

60 3.2 FROTHER TYPE AND ANALYSIS Table 1 identifies the four commercial frothers used, F150, DF250, FX and MIBC. These were selected to give a wide range in water recovery based on their known hydrodynamic characteristics [Cappuccitti et al., 2009]. Solutions were prepared with Montréal tap water equilibrated to room temperature (20±2 o C). Options explored for frother analysis included colorimetry [Gélinas and Finch, 2005], surface tension (following an observation by Grau and Laskowski [2006]) but the most convenient proved to be Total Organic Carbon (TOC), as employed by Hadler et al. [2005]. Given only one organic is added, frother, TOC gave accurate concentration readings after allowing for background TOC in the tap water. The instrument was a Dohrmanns DC 80 (TELEDYNE Instruments Company, U.S.). Table 3.1: Frothers used in the study Trade Name Mol Wt (g/mol) Chemical Formula Supplier MIBC 102 CH 3 CHCH 3 CH(OH)CH 3 Flottec DF CH 3 (C 3 H 6 O) 4 OH Dow Chemical FX CH 3 CH 2 CH 2 (C 3 H 6 O) 2.5 OH Flottec F H-(C 3 H 6 O) 7 -OH Flottec 3.3 SURFACE TENSION Surface tension as a function of concentration was used to estimate frother concentration on the bubble surface (adsorption density) by solving the Gibbs adsorption isotherm for a water-air interface. The Wilhelmy Plate method was used (Krauss K-12 Tensiometer). Some solutions were made with distilled water, but most work employed Montréal tap 50

61 water. Readings were taken after 3 minutes to approximate equilibrium. Each experiment was repeated at least three times and the mean and 95% confidence interval is quoted. 3.4 BUBBLE SIZE Bubble size distribution was determined both below the froth (i.e. bubble size into froth, D bi ) and on top of the froth (D bt ). Below the froth, the McGill Bubble Size Analyzer (MBSA) was used with some bubbles counted. MBSA employs a sampling tube to collect and direct bubbles to the viewing chamber (Figure 3.3). Details on the method are in Gomez and Finch [2007]. The recommended protocol was followed which included: using frother in the sampling/viewer assembly to reduce bubble coalescence [Zhang et al., 2009] and locating the tip of the sampling tube close to the water-froth interface, to minimize the effect of the turbulence on the measurements [Grau and Heiskanen, 2003]. The bubble size distribution on top of the froth was measured using a digital camera (Canon DC-40) mounted on a braced support with the lens 10 cm from the froth surface (Figure 3.3). Lighting was a single 100 W bulb next to the camera. Twenty images per run were captured and transferred to a computer and approximately 1200~1500 bubbles counted. Analysis used PhotoImact 8.0 software. The relative standard deviation on the Sauter mean bubble size was less than 3% for both into froth and top of froth cases. 51

62 Digital Camera Viewing Chamber Light Digital Camera Figure 3.3: Bubble size distribution measurements: into froth and top of froth 3.5 REFERENCES Cappuccitti F., Finch J. A., Nesset J. E. and Zhang W., Characterization of Frothers and its Role in Flotation Optimization, SME Annual Meeting, Denver, preprint Gélinas S. and Finch J. A., Colorimetric Determination of Common Industrial Frothers, Minerals Engineering, Vol. 18, No. 2, pp Gomez C. O. and Finch J. A., Gas Dispersion Measurements in Flotation Machines, CIM Bulletin 95 (1066), pp Gomez C. O. and Finch J. A., Gas Dispersion Measurements in Flotation Cells, International Journal of Minerals Engineering, Vol. 84, No. 1-4, pp Grau, R. A., Heiskanen, K., Gas Dispersion Measurements in a Flotation Cell, Minerals Engineering, Vol. 16, No. 11, pp Grau R.A. and Laskowski J. S., Role of Frothers in Bubble Generation and Coalescence in a Mechanical Flotation Cell, Canadian Journal of Chemical Engineering, Vol. 84, pp

63 Hadler K., Aktas Z. and Cilliers J. J., The Effects of Frother and Collector Distribution on Flotation Performance, Minerals Engineering, Vol. 18, No. 2, pp Shink D., Rosenblum R., Kim J. Y. and Stowe K. G., Development of Small Scale Flotation Cells and Its Application in Milling Operations, Proc. 24 th Annual Meeting of CMP, Ottawa. Vera M. A., Franzidis J-P. and Manlapig E.V., The JKMRC High Bubble Surface Area Flux Flotation Cell, Minerals Engineering, Vol. 12, No. 5, pp Zhang W., Kolahdoozan M., Nesset J. E. and Finch J. A., Use of Frother with Sampling-for-imaging Bubble Sizing Technique, Minerals Engineering, Vol. 22, No. 5, pp

64 CHAPTER 4 RESULTS 4.1 VALIDATION Reproducibility A minimum of 3 tests for each condition was used. Sample standard deviation (s) was calculated by the following: s = N i= 1 xi x N 1 2 (4.1) where x i, x and N are the individual measurements, the average and number of measurements, respectively. The relative standard deviation, often more informative, was calculated as below: 100 s Relative Standard Deviation = (4.2) x When several data sets have the same sources of indeterminate error (i.e. the same type of measurement but different means) the standard deviation of the individual data sets may be pooled to more accurately determine the standard deviation of the analysis method. The pooled standard deviation (s pooled ) was calculated by the following: 54

65 s pooled = N N2 x x + x x i 1 j 2 i= 1 j= 1 N1+ N2 1 (4.3) From this the 95% confidence interval (CI) was computed as follows: s pooled 95% CI =± 1.96 (4.4) N The error bars shown in the graphs in the thesis correspond to the 95% CI. The 95% CI for selected conditions are listed in Table 4.1. DF250 concentration (ppm) Table 4.1: 95% CI for selected measurements Concentration by Surface TOC (ppm) tension Water overflow rate (g/min) Sauter mean bubble size into froth D bi (mm) Sauter mean bubble size on top of froth D bt (mm) (mn/m) 5 ±10.5 ±0.07 ±0.24 ±0.08 ± ±11.2 ±0.04 ±0.21 ±0.06 ± ±13.6 ±0.05 ±0.16 ±0.04 ± ±9.41 ±0.04 ±0.13 ±0.05 ± ±8.65 ±0.03 ±0.19 ±0.03 ± Number of bubbles sampled The minimum number of bubbles to accurately determined the Sauter mean bubble size (D 32 ) depends on the distribution. Irani and Callis [1963] recommended that the number of bubbles measured should be large enough so that the results no longer change. This concept is shown in Figure 4.1 (a) and (b). The figures show that to obtain a consistent and therefore accurate bubble size, a minimum of ca and 1000 bubbles should be counted for the into froth and top of froth experiments, respectively. In this thesis, the number of the bubbles sized was always larger than the number inferred from Figure 55

66 4.1 i.e bubbles measured compared with minimum 3000 for into froth, and bubbles versus minimum 1000 in the top of froth experiments. Sauter mean bubble size (mm) and standard deviation Min. requirement Stdev Number of bubbles sized D32 (a) Sauter mean bubble size (mm) and standard deviation Min. requirement D32 Stdev Number of bubbles sized (b) Figure 4.1: Bubble size (D 32 ) as a function of the number of bubbles counted: (a) Into froth; (b) Top of froth (example using DF250 7 ppm) 56

67 4.1.3 Water flow balance Figure 4.2 shows water mass flow data as a function of frother system concentration for three full repeat tests. Reliability is established by noting that the relative standard deviation was ca. 2% (resulting in too small a 95% confidence interval to indicate on the plot), and showing that the back-calculated feed rate (sum of overflow and underflow) was constant and equal to that set (2300 g/min). Figure 4.2: Validation test - overflow, underflow and combined (computed) feed mass flow rate and comparison to set feed flow rate (2300 g/min) Frother mass balance Figure 4.3 establishes the validity of the TOC measurement showing that the backcalculated ( measured ) feed concentration compares well to the system concentration. Precision was poorest for MIBC likely due to high volatility [Azgomi et al., 2009] but the back-calculated values remained within 5% of the known (i.e. an estimated 5% MIBC was volatilized). 57

68 Figure 4.3: Validation test - mass balance on frother showing calculated feed concentration compares well with system concentration Comparing surface tension for two water types Table 4.2 compares surface tension measurements using Montréal Tap (MT) water vs. de-ionized (DI) water with other conditions constant. The table shows that the difference in surface tension between the waters is negligible, from 0.13 to 0.43 although that in deionized water is always greater than in Montréal Tap water. As a consequence, all subsequent work used Montréal Tap water. Table 4.2: Surface tension for the two water types DF250 concentration Surface tension (avg.) (mn/m) (ppm) De-ionized water Montreal tap water Difference (DI-MT)

69 4.2 WATER OVERFLOW RATE Figure 4.4 shows the results for the four frothers, with superficial water overflow velocity (J wo ) on the primary axis and percentage recovery (= J wo /J wf ) on the secondary axis. The pattern for all four is similar: a minimum concentration to achieve overflow followed by a rapid rise then a slower steady increase, although MIBC may arguably not have reached this condition. For F150 and DF250, water recovery reaches more than 20%. Figure 4.4: Water overflow velocity (primary y-axis) and recovery (secondary y- axis) as a function of system frother concentration 4.3 FROTHER PARTITIONING Figure 4.5 shows frother concentration in the overflow was consistently higher than in the underflow which illustrates the preferential transport of frother into the froth resulting from adsorption onto bubbles. Assuming perfect mixing the underflow concentration is that within the cell below the froth (bubbly zone). All the frothers showed the same trend, including the notable enrichment in overflow low system concentration, i.e. concentration just exceeding the minimum for overflow. The case for F150 was tracked to ca. 1 ppm 59

70 system concentration by sampling the froth directly (as no overflow was achieved below ca. 3 ppm) and reached 160 ppm compared to 1 ppm in the underflow. Measured F150 Concentration (ppm) 160 a) F F150 System Comcemtration (ppm) Measured DF250 Concentration (ppm) b) DF DF250 System Concentration (ppm) Measured FX Concentration (ppm) c) FX FX System Concentration (ppm) Measured MIBC Concentration (ppm) d) MIBC MIBC System Concentration (ppm) Figure 4.5: Frother partitioning to overflow and underflow as a function of system concentration: a F150; b DF250; c FX160-05; d MIBC The observation of strong frother partitioning at low system concentration is qualitatively explained by low system concentrations giving dry froths and thus the water overflowing is rich in frother carried by the bubbles and released upon bubble bursting. 4.4 BUBBLE SIZE The bubble size (Sauter mean diameter) in the bubbly zone, i.e. into the froth (D bi ), follows the recognized trend (Figure 4.6) [Cho and Laskowski, 2002]: a rapid decrease to a common near-constant size, ca. 0.5 mm, equated with reaching the critical coalescence 60

71 concentration (CCC). This small mean size is compatible with the low J g at the impeller (J g =0.227 cm/s) [Nesset et al., 2007]. The relative frother strength is also as anticipated, F150 having the lowest CCC, MIBC the highest [Nesset et al., 2006]. a) MIBC - 50 ppm b) 2.5 mm F ppm 2.5 mm Figure 4.6: a) Sauter mean bubble size into froth (D bi ) as a function of frother system concentration; b) Example images MIBC (top) and F150 (bottom) both at 50 ppm Mean bubble size on top of the froth (D bt ) shows a similar trend to D bi (Figure 4.7), but the minimum size reached is now a function of frother chemistry, F150 holding the smallest size, ca. 1.2 mm, and MIBC yielding the largest, ca. 1.8 mm. The increase in size relative to the minimum D bi (included for reference) reflects coalescence in the froth that is frother dependent, as the accompanying images further illustrate. 61

72 a) MIBC - 50 ppm b) 0.8 mm F ppm 0.8 mm Figure 4.7: a) Sauter mean bubble size on top of froth (D bt ) as a function of frother system concentration (including minimum D bi for reference); b) Example images: MIBC (top) and F150 (bottom) both at 50 ppm 4.5 SURFACE TENSION AND ADSORPTION DENSITY The concentration of frother per unit area on the bubble surface, or adsorption density Γ, is estimated from the Gibbs adsorption isotherm: γ Γ= RT ln c (4.5) where Γ is in moles/m 2, γ surface tension (N/m 2 ), R the gas constant, T temperature (K), and c concentration (mol/l). Given the form of Eq. 4.5 the appropriate plot is γ vs. ln c (Figure 4.8). As a first approximation trends are treated as linear over a limited concentration range [Hiemenz and Rajagopalan, 1997] and this average Γ (in mmol/m 2 ) 62

73 is reported in Table 4.3. The linear fit to the data has a least-squares R 2 value greater than 0.9 for all cases. MIBC FX F150 DF250 Figure 4.8: Surface tension vs. natural logarithm of concentration; slope yields Gibbs adsorption excess, Γ using Eq. 4.5 Table 4.3: Estimated Gibbs adsorption excess from Figure 4.8 Frother Type Adsorption Density R 2 Value (mmol/m 2 ) MIBC 2.184E FX E DF E F E BUBBLE SURFACE AREA FLUX From bubble size data The bubble size data can be converted into bubble surface area flux, BSAF. Figure 4.9 gives the results for BASF into froth (S bi = 6J gi /D bi ) and through top of froth (S bt = 6J gi /D bt ). The S bi can be related to water entering the froth [Bascur and Herbst, 1982; Xu et al., 1991] but S bt is not necessarily related to water reporting to overflow. There are two issues: 1, the overflowing bubbles derive not just from the top layer observed but 63

74 from a number of layers below that depend on froth height above the overflow lip and these sizes are not measurable; and 2, not all J gi overflows as some air is lost when bubbles burst. An alternative approach was found to directly estimate bubble surface area flux to overflow (S bo ) using a frother mass balance on the froth exiting the cell From frother mass balance There are two mechanisms by which frother enters the overflow: adsorbed on bubbles and in the entrained water (i.e. water carried in lamellae and Plateau borders). Expressed as a mass balance on a per unit area of cell basis, this is: SbO Γ + JE CE = JwO C (4.6) O where S bo Г is the mass rate of frother carried on the bubble surface, J E C E is the mass rate of frother in the entrained water and J wo C O is the mass rate to overflow. Since the first term represents no water volume then J E = J wo and assuming perfect mixing C E = C U ; consequently Eq. 4.6 can be rewritten as: SbO Γ + JwO CU = JwO CO (4.7) where all the parameters except S bo are known (measured). 64

75 Sb (1/s) S bi S bo S bt a) F150 b) DF250 Sb (1/s) S bi 70 S bo S bt F-150 System Concentration (ppm) DF250 System Concentration (ppm) Sb (1/s) c) FX d) MIBC FX System Concentration (ppm) S bi S bo S bt S bo 80 S 70 bi S 20 bt MIBC System Concentration (ppm) Figure 4.9: Bubble surface area flux as a function of frother concentration (a F250; b DF250; c FX160-05; d MIBC) Sb (1/s) Figure 4.9 includes the S bi, S bt and S bo results (the error bars are estimates of 95% CI from propagation of error rules). The S bo trend lies between S bi and S bt in all but a couple of high concentrations of MIBC. This agreeably reflects both the enlargement due to coalescence of bubbles as they journey through froth (i.e. D bi is less than D bo hence S bi should be larger than S bo ) and the fact that many bubbles smaller than D bt will overflow from the layers underneath the surface (i.e. D bt is larger than D bo and hence S bt should be less than S bo ). In addition, since J go = αj gi due to bubble bursting, then again, S bo should be greater than S bt. 65

76 4.7 OVERFLOW GAS HOLDUP ESTIMATION According to the literature [Finch and Dobby, 1990; Estrada-Ruiz and Perez-Garibay, 2009], gas holdup can be estimated as a function of superficial water velocity and superficial gas velocity. The relationship can be applied in the overflow, assuming air recovery is 100% (this considers that the bulk of the overflowing bubbles come from the layers below the top surface of froth, i.e. represent unburst bubbles). Under this assumption gas holdup in the overflow (E go ) can be estimated as: E go = J g J g + J wo (4.8) Figure 4.10 shows the estimated gas holdup in overflow (E go ) vs. concentration for the four tested frothers. It can be seen that at low concentrations, E go reaches more than 99%, i.e. a dry froth situation. As frother concentration is increased there is a decline in E go ; weaker frothers (e.g. MIBC) show a relatively slow decrease compared with stronger frothers (e.g. F150) which again implies that polyglycol frothers result in a more water transport. The range of E go (i.e. 89% 99%) is reasonable according to the predicted results from the drift flux model (Figure 2.5). 66

77 EgO (%) MIBC FX DF250 F Frother System Concentration (ppm) Figure 4.10: Comparing gas holdup in overflow vs. concentration for the four frothers 100 MIBC 80 DF250 FX SbO (1/s) F EgO (%) Figure 4.11: Bubble surface area flux as a function of gas holdup in overflow 67

78 Figure 4.11 explores a relationship between E go and S bo. Clearly, E go and S bo do not relate directly. Finch et al. [2000] and Massinaei et al. [2009] proposed a linear relationship between E g and S b in the pulp zone (bubbly zone). Compared to this previous research, Figure 4.11 demonstrates an inverse (E go increases as S bo decreases) and nonlinear relationship. 4.8 EQUIVALENT WATER LAYER THICKNESS Applying the Bascur and Herbst [1982] approach to the overflow gave Eq. 2.28: J = S * δ (2.28) wo bo O where δ O represents the water carried per unit of bubble surface area flux to overflow. The relationship is tested in Figure The result suggests two regimes (regime 1 and 2 representing low and high S bo, respectively), each approximated by a linear dependence (MIBC may not have reached the upper S bo region). For present purposes consider the regime at the lower S bo values, which is closer to the range of frother addition in practice. It is evident that there is an intercept, representing a minimum S bo before any overflow occurs (S min bo ). Incremental increases in air rate result in gradual froth build up, then sufficient to flow over the lip. For each frother type, the S bo min is obtained by extrapolation (Table 4.4) and Eq is then re-written as, J wo min ( S bo S bo ) δ O = (4.9) 68

79 Table 4.4 gives estimates of S bo min and δ O ; the ranking in δ O reflects the observed frother type effect on water overflow rate. Regime 2 Regime 1 Figure 4.12: Superficial water overflow velocity (J wo ) vs. bubble surface area flux to overflow (S bo ) Table 4.4: Estimated minimum S bo and bubble equivalent film thickness in overflow Frother Type S min bo (s -1 ) δ O (µm) F (± 0.11) DF (± 0.07) FX (± 0.20) MIBC (± 0.23) Neethling et al. [2003] introduced the concept of air recovery which holds promise in modeling and optimizing flotation [Smith et al., 2009]. By analogy, the ratio S bo /S bi is bubble surface area flux recovery and a case can be made that this may relate more closely to flotation performance. To explore, Figure 4.13 presents S bo /S bi vs. J wo for each frother type, showing consistent linear correlations. The implication of this observation is under review. 69

80 Figure 4.13: Superficial water overflow velocity (J wo ) vs. bubble surface area flux recovery (S bo /S bi ) 4.9 REFERENCES Azgomi F., Gomez C. O. and Finch J. A., Frother persistence: A Measure Using Gas Holdup, Minerals Engineering, Vol. 22, No. 9-10, pp Bascur O. A. and Herbst J. A., Dynamic Modeling of a Flotation Cell with a View toward Automatic Control, In: Proc. 14th Int. Miner. Proc. Congress, Toronto, pp Cho Y. S. and Laskwski J. S., Effect of Flotation Frothers on Bubble Size and Foam Stability, International Journal of Mineral Processing, Vol. 64, No. 2-3, pp Estrada-Ruiz R. H. and Pérez-Garibay R., Evaluation of Models for Air Recovery in a Laboratory Flotation Column, Minerals Engineering, 2009 (available online). Finch J. A. and Dobby G. S., Column Flotation, Pergamon Press, New York. Finch J. A., Xiao J., Hardie C. and Gomez C., Gas Dispersion Properties: Bubble Surface Area Flux and Gas Holdup, Minerals Engineering, Vol. 13, No. 14, pp Finch J. A. Gelinas S. and Moyo P., Frother-related Research at McGill University, Minerals Engineering, Vol. 19, pp Hiemenz P. C. and Rajagopalan R., Principles of Colloid and Surface Chemistry, 3 rd Edition, Marcel Dekker Inc., New York. 70

81 Irani R. R. and Callis C. F., Particle Size: Measurement, Interpretation, and Application, John Wiley Express, New York. Massinaei M., Kolahdoozan M., Noaparast M., Oliazadeh M., Yianatos J., Shamsadini R. and Yarahmadi M., Hydrodynamic and Kinetic Characterization of Industrial Columns in Rougher Circuit, Minerals Engineering, Vol. 22, No. 4, pp Moyo P., Gomez C. O., Finch J. A., Characterizing Frothers Using Water Carrying Rate, Canadian Metallurgical Quarterly, Vol. 46, No. 3, pp Neethling S. J., Lee H. T. and Cilliers J. J., Simple Relationships for Predicting the Recovery of Liquid from Flowing Foams and Froths, Minerals Engineering, Vol. 16, No. 11, pp Nesset J. E., Hernandez-Aguilar J. R., Acuña C., Gomez C. O. and Finch J. A., Some Gas Dispersion Characteristics of Mechanical Flotation Machines, Minerals Engineering, Vol. 19, No. 6-8, pp Nesset, J. E., Finch, J. A., Gomez, C.O., Operating variables affecting the bubble size in forced-air mechanical flotation machines. In: Proceedings AusIMM 9th Mill Operators Conference, Fremantle, Australia, pp Smith C., Hadler K. and Cilliers J., The Total Air Addition and the Air Profile for a Flotation Bank, to be presented 48 th Conference of Metallurgists, Sudbury. Xu M., Finch J. A. and Uribe-Salas A., Maximum Gas and Bubble Surface Rates in Flotation Columns, International Journal of Mineral Processing, Vol. 32, No. 3-4, pp

82 CHAPTER 5 DISCUSSION In this study, the effect of frother type on water overflow rate was quantitatively analyzed. To achieve overflow it was necessary to go to concentrations above typical flotation practice (with solids), even when a froth depth of only 1 cm was used. This is common in air-water studies but this system needs to be understood before the effect of particles can be incorporated. The impact of frother is due to two actions: increasing bubble surface area flux by reducing bubble size, and an apparent chemistry effect altering the bubble s ability to transport water. Taking the standpoint that the rate at which water overflows is related the rate the water enters the froth, we start by considering D bi (Figure 4.6). It is evident that above ppm (Figure 4.9), while water overflow continues to increase and is different for each frother, D bi and hence S bi is constant and independent of frother type; thus as such, an effect of bubble size is ruled out and chemistry appears to be a factor. More closely related to the overflow than D bi is D bt. Here bubble size is a function of frother type (Figure 4.7); for instance, F150 retaining a smaller size than MIBC. This difference between frothers reflects their differing abilities to resist coalescence in the froth. However, the difference in bubble size does not appear sufficient to account for the difference in overflow rate. Consider the 50 ppm case: D bt ~ 1.7 mm for MIBC and

83 mm for F150, a ratio of ~ 1.5, while the water overflow velocity increased ~ 3.4-fold (to from 0.025). Even taking a square function on the bubble size [Neethling et al., 2003] the ratio is only ~ 2.2, again apparently not enough to account for the difference in water overflow between the two frothers. Once more it appears that a chemistry effect is at play. The most direct link would be to consider bubble size in the overflow [Neethling et al., 2003]. This is not readily measurable. The alternative approach was to exploit the partition of frother between underflow and overflow to establish a mass balance on the exiting froth and estimate S bo without need of D bo data. The partitioning of frother (Figure 4.5) reflects that frother adsorbs on the bubble. Hence, it is transported preferentially to the froth and deposited in the overflow water when the bubbles burst. This phenomenon allowed the mass balance approach, but it was initially surprising the extent of preferential concentration in the overflow at low dosage. The observation is due to the fact that low addition of frother gives dry froth and the frother carried on the bubble surface dominates the concentration in the overflow water (i.e. there is little entrained water to dilute the concentration). This effect has potential ramifications for frother use in practice. The speculation that the excess F150 concentration in cleaner cells (~ 50 ppm) compared to rougher cells (< 1 ppm) noted at one operation [Gélinas and Finch, 2007] was due to frother concentrating in the rougher froth (feed to the cleaners) is substantiated by the present work, for example. 73

84 In order to perform the mass balance, frother adsorption density Г is required. This was estimated (Table 4.2) from surface tension vs. concentration data (Figure 4.8) using the Gibbs adsorption excess isotherm. The data were interpreted as a constant Г over the concentration range used. Applying the mass balance concept involves some assumptions. The calculation implies bubbles have reached equilibrium with the contacting solution and that a bubble rising through the bubbly zone and then through the froth retains the adsorption density associated with the equilibrium value as measured at a static water-air interface. Others have made the same tacit assumption [Tan et al., 2005]. To date, there seems to be no alternative way to estimate Г. A related assumption is that the appropriate concentration in solving the Gibbs isotherm for the bubble in the overflow is the system concentration. However, in this case, the difference from the solution (i.e. underflow) concentration is minor and can be reasonably ignored. This assumption of equilibrium being retained in the froth means the inter-bubble water has the same concentration as in the zone below, which on the basis of perfect mixing is the same as measured in the underflow. There is no doubt that frother is concentrated in the froth but a distinction between that carried on the bubble surface, that contributes the added concentration, and that the inter-bubble water represents water entrained from the solution below, appears tenable. Provided that no water volume is represented by the bubble surface, it finally means that the rate of entrained water into the overflow J E is equal to the measured overflow rate J wo (Eq. 4.6 and 4.7). 74

85 As a result one can determine the bubble surface area flux to overflow S bo without need of D bo. The S bo values predominantly lie between S bi and S bt (Figure 4.9), which offers credence to the approach. The S bo was plotted against J wo (Figure 4.12) to test the notion that the rate of water transport is determined by the bubble surface area flux, as suggested by Bascur and Herbst (1982) and Xu et al. (1991). There is an objection to this: since S bo is derived using J wo in the mass balance, subsequent correlation between S bo and J wo may be compromised. Accepting this possibility, using the lower S bo range, corresponding closer to frother concentration in practice, the equivalent film thickness δ O was calculated. The calculation of δ O represents a blackbox approach. No suggestion is made that water is carried as a uniform layer surrounding a bubble either below in the bubbly zone or in the froth. The notion of δ O offers an empirical parameter to describe the frother chemistry effect on water recovery and separates that effect from bubble size reduction. As such it is finding use, for example in the JKSimFloat modeling scheme [Harris, 2007]. The δ O values do follow the known order in which frothers transport water. Direct measurements of film thickness on bubbles blown in air show a similar ranking of frother type as found here (e.g. F150 > MIBC) but with thicknesses is of the order of 1 μm and less (F150 ~ 1100nm, MIBC < 160 nm) [Finch et al., 2006]. It can be argued that a bubble blown in air roughly corresponds to a bubble on the froth surface in the current experiments. If one takes the measured film thickness as the lamellae thickness associated with bubbles in the froth then the values of δ O indicate the bulk of the water is carried in the Plateau borders, as is known [Neethling et al., 2003; Nguyen and Schulze, 2004]. 75

86 A phenomenalogical approach to incorporate frother chemistry can be considered. It can be included in the proportionality constant in the water transport model of Neethling et al. [2003]. (Interesting, in terms of the terminology in this thesis the model shows a dependence on the square of S bo.) The frother effect can be simulated by surface viscosity in the Nguyen and Schulze [2004] froth model which shows surface viscosity strongly influences water flow in the Plateau borders. The problem now moves to measuring that parameter [Stevenson, 2005] if it is not to remain a calibrated value. Stevenson [2006] has recently proposed a froth model with two adjustable parameters that are claimed to apply to the surfactant (frother) type. The present froth is too shallow to measure some of the necessary properties, e.g. gas holdup, to use drift flux analysis which offers a promising approach [Ireland and Jameson, 2007]. Ultimately the chemistry effect has to be related to the frother structure and the interaction with water for a fundamental explanation to emerge [Finch et al., 2006]. At this stage, it is difficult to explain the two regimes in Figure 12. A tentative interpretation is offered: in regime 1 (i.e. lower portion of J wo vs. S bo ) bubble size in the overflow D bo is still varying, thus there is both a bubble size and frother-related (chemistry) effect contributing to J wo ; in regime 2 (i.e. higher portion) D bo is no longer varying (concentration above CCC for overflow) and thus water overflow is dominated by the chemistry effect. Further analysis is required. Another blackbox approach was applied by Moyo et al. [2007]. Using gas holdup they concluded there was a frother chemistry effect controlling water overflow. Their studies showed that water to overflow was correlated against gas hold-up in the bubbly zone (i.e. 76

87 below the froth). Moyo [2007] failed to find a connection with bubble surface are flux (S bi in current terminology) because the frother concentrations used all exceeded the CCC and so bubble size and thus S bi was constant. One can now say that it is S bo that was needed. The correlation with gas hold-up nevertheless suggests a connection between what enters the froth and what exits the froth. An approach is to consider the ratio S bo / S bi, i.e. the bubble surface area flux recovery (Figure 4.13). One can observe that the increase in J wo as frother dosage is increased beyond the CCC is because the ratio S bo / S bi is increasing. BSAF recovery has analogies to air recovery, a factor that is finding increasing application [Barbian et al., 2007; Cilliers, 2007; Smith et al., 2009]. Modifying the present system to avoid the change in cross-section in the cell would facilitate further investigations along the lines. While the air-water system is a necessary starting point, others have noted that the presence of solids can dominate over frother type [Melo and Laskowski, 2006; Gredelj et al., 2009; Kuan and Finch, 2009]. In most conditions solids promote froth stability but in some others they cause collapse. In principle the measurements here can be executed in the presence of solids, even on an industrial cell substituting the frother analysis procedure of Gélinas and Finch [2005] for TOC (although estimating Г under plant conditions may pose a challenge). One aim would be to investigate the particle/frother/water interaction controlling water (and solids) overflow. 5.1 REFERENCES Barbian N., Cilliers J. J., Morar S. H. and Bradshaw D.J., Froth Imaging, Air Recovery and Bubble Loading to Describe Flotation Bank Performance, International Journal of Mineral Processing, Vol. 84, No. 1-4, pp

88 Bascur O. A. and Herbst J. A., Dynamic Modeling of a Flotation Cell with a View toward Automatic Control, In: Proc. 14th Int. Miner. Proc. Congress, Toronto, pp Cilliers J. J., Column flotation, Section II: the Froth in Column Flotation, In: Fuerstenau, M.C., Jameson, G., Yoon, R.-H. (Eds.), Froth Flotation A Century of Innovation, pp Finch J. A., Gélinas S. and Moyo P., Frother-related research at McGill University, Minerals Engineering, Vol. 19, No. 6-8, pp Gélinas S. and Finch J. A., Colorimetric Determination of Common Industrial Frothers, Minerals Engineering, Vol. 18, No. 2, pp Gélinas S. and Finch J. A., Frother Analysis: Some Plant Experiences, Minerals Engineering, Vol. 20, No. 14, pp Gredelj S., Zanin M. and Grano S. R., Selective Flotation of Carbon in the Pb Zn Carbonaceous Sulphide Ores of Century Mine, Zinifex, Minerals Engineering, Vol. 22, No. 3, pp Harris M., Personal communication to Professor Finch J. A.. Ireland P. M. and Jameson G. J., Liquid Transport in a Multi-layer Froth, J. Colloid and Interface Science 314, pp Kuan S. H. and Finch J. A., The Effect of Solids on Gas Holdup, Bubble Size and Water Overflow Rate in Flotation, to be presented 4 th International Flotation Conference (Flotation 09), Cape Town, South Africa. Melo F. and Laskowski J. S., Fundamental Properties of Flotation Frothers and Their Effect on Flotation, Minerals Engineering, Vol. 19, No. 6-8, pp Moyo P., Gomez C. O. and Finch J. A., Characterizing Frothers Using Water Carrying Rate, Canadian Metallurgical Quarterly, Vol. 46, No. 3, pp Neethling S. J., Lee H. T. and Cilliers J. J., Simple Relationships for Predicting the Recovery of Liquid from Flowing Foams and Froths, Minerals Engineering, Vol. 16, No. 11, pp Nguyen A. V. and Schulze H. J., Colloid Science in Flotation, Marcel Dekker Inc., New York, pp Smith C., Hadler K. and Ciliers J., The Total Air Addition and the Air Profile for a Flotation Bank, to be presented 48 th Conference of Metallurgists, Sudbury. 78

89 Stevenson P., Remarks on the Shear Viscosity of Surfaces Stabilized with Soluble Surfactants, Journal of Colloid and Interface Science, Vol. 290, pp Stevenson P., The Wetness of a Rising Foam, Ind. Eng. Chem. Res. 45, pp Tan S. N., Fornasiero D., Sedev R. and Ralston J., Marangoni Effects in Aqueous Polypropylene Glycol Foams, Journal of Colloid and Interface Science, Vol. 286, pp Xu M., Finch J. A. and Uribe-Salas A., Maximum Gas and Bubble Surface Rates in Flotation Columns, International Journal of Mineral Processing, Vol. 32, No. 3-4, pp

90 CHAPTER 6 CONCLUSIONS AND FUTURE WORK 6.1 CONCLUSIONS In this study, water recovery for four commercial frothers covering a wide range in structure and molecular weight was measured at steady state in a closed loop mini-cell setup. Image analysis was employed to measure bubble size into and on top of froth. Frother concentration was measured by TOC and frother partitioning between overflow and underflow determined. Estimating the Gibbs adsorption excess on the bubble in the overflow from surface tension-concentration data coupled with the frother partitioning permitted a frother mass balance approach to estimate bubble surface area flux to overflow (S bo ). It was found that the water overflow rate has an approximate linear relationship to S bo, and an equivalent water film thickness was used to quantify the frother chemistry effect. The concept of bubble surface area flux recovery is introduced. BSAF recovery along with air recovery provide new tools to analyze and model flotation performance. 6.2 FUTURE WORK To verify the current findings, a setup that allows more flexibility is required. It is proposed to apply the approach in a continuous flotation column initially in a two-phase (air-water) system, then with three-phase. A column permits froth depth and gas rate to 80

91 be varied over a wider range than the mini-cell. In Figure 7.1 a possible arrangement is explored. Frother solution is fed into the column at a constant air rate. Water with residual frother at concentration C U underflows from the column at flow rate J wu. Froth overflows and bubbles collapse, giving water overflow rate J wo at concentration C O. The bubble swarm is assumed to keep the solution well mixed and entrained water into the froth is presumed to have the same concentration as the bulk water. Knowing (measuring) the adsorption density (Γ), the mass balance on the frother leaving the froth phase of the column can be established using Eq Figure 6.1: Schematic diagram of flotation column continuous loop testing It has to be conceded that the two phase system results may not be directly relevant to airwater-solids systems. The possibility of using talc (i.e. hydrophobic) and silica (i.e. 81