The role of turbulence on the bubble-particle collision – An experimental study with particle tracking methods

Die Analyse von Kollisionen zwischen Partikeln und Blasen in einer turbulenten Strömung ist ein grundlegendes Problem von hoher technologischer Relevanz, z. B. für die Abtrennung wertvoller Mineralpartikel durch Schaumflotation. Dieser Relevanz steht ein Defizit an experimentellen Daten und Erkenntnissen über den Kollisionsprozess gegenüber. Ein Hauptproblem ist die geringe Anzahl der verfügbaren Messtechniken zur direkten Beobachtung der Kollisionen zwischen Partikeln und Blasen. Daher besteht das Ziel dieser Dissertation darin, neue Methoden zu entwickeln, um die Wechselwirkung zwischen Blasen und Partikeln unter definierten hydrodynamischen Bedingungen zu messen. Diese Methoden beruhen auf der Verfolgung von einzelnen Partikeln mit 4D Particle Tracking Velocimetry (PTV) und Positron Emission Particle Tracking (PEPT), um die Lagrangeschen Partikeltrajektorien in der Nähe einer Blase zu bestimmen und die kollidierenden Partikel zu klassifizieren. In zwei Versuchsaufbauten werden diese Messmethoden angewandt, um die Wechselwirkung zwischen Blasen und Partikeln in turbulenten Strömungen zu untersuchen. In einer Blasensäule wird die Turbulenz im Nachlauf einer frei aufsteigenden Blasenkette erzeugt, während in einem Wasserkanal die Turbulenz durch die Umströmung eines Gitters produziert wird. In beiden Fällen wird das vorhandene turbulente Strömungsfeld um die Blasen mittels Tomographic Particle Image Velocimetry (TPIV) charakterisiert. Zunächst wird der Einfluss des Blasennachlaufs auf die Blasen-Partikel-Kollision für beide Versuchsaufbauten mit dem 4D-PTV-Verfahren analysiert. Es wird gezeigt, dass in beiden Versuchsanordnungen die Kollision von feinen Partikeln nicht nur an der Vorderseite, sondern auch an der Hinterseite der Blase stattfindet. Diese Ergebnisse werden mit der gemessenen turbulenten kinetischen Energie und der Dissipationsrate um die Blase korreliert. Anschließend werden die experimentell ermittelte turbulente kinetische Energie und Dissipationsrate genutzt, um die Kollisionsfrequenz vorherzusagen. Dafür werden bestehende Modelle angewendet und deren Vorhersagen den experimentellen Ergebnissen gegenübergestellt. Weiterhin wird der Wasserkanal genutzt, um den Einfluss der turbulenten Flüssigkeitsströmung auf die Kollision zwischen einer stagnierenden Blase und den Modellpartikeln zu verdeutlichen. Neben der Untersuchung in einer verdünnten Feststoffsuspension wird auch die Blasen-Partikel-Wechselwirkung in einer dichten Strömung mit dem PEPT-Verfahren untersucht. Das PEPT-Verfahren hat das Potenzial, Suspensionen mit einem hohen Feststoffanteil zu messen, was mit optischen Trackingverfahren, wie 4D-PTV, nicht möglich ist. Für den Nachweis einzelner Partikel mit dem PEPT-Verfahren wurden radioaktive Tracerpartikel entwickelt, welche repräsentativ für die Modellpartikeln sind. Die Trajektorien der markierten Partikel werden verwendet, um die durchschnittliche Partikelverteilung im turbulenten Feld zu bestimmen und die Blasen-Partikel-Wechselwirkung zu beschreiben. Insgesamt bieten die entwickelten Methoden eine Möglichkeit die Kollision zwischen Partikeln und Blasen in einer turbulenten Strömung direkt zu untersuchen. Die gewonnenen experimentellen Daten ermöglichen es, bestehende Kollisionsmodelle zu überprüfen und das Verständnis über die Rolle von Turbulenzen in der Schaumflotation zu verbessern.The analysis of collisions between particles and bubbles in a turbulent flow is a fundamental problem of high technological relevance, e.g. for the separation of valuable mineral particles by froth flotation. That relevance contrasts with an apparent lack of experimental data and insights into this collision process. A major issue is the limitation of available measurement techniques to directly observe the collisions between particles and bubbles. In this dissertation, novel methodologies are developed to measure the interaction between bubbles and particles under defined hydrodynamic conditions. These methodologies comprise particle tracking techniques such as 4D PTV and PEPT to triangulate the Lagrangian particle trajectories in the vicinity of a bubble and classify those which are colliding. In two experimental setups, these techniques are applied to investigate the bubble-particle interaction in turbulent flows. In a bubble column, turbulence is generated in the wake of a freely rising bubble chain, whereas in a water channel, a fluid passing through grid produces a turbulent flow upstream of a stagnant bubble. Accordingly, the turbulent flow field around these bubbles is characterized by TPIV. Firstly, the influence of the bubble wake on the bubble-particle collision is analyzed for both experimental setups with 4D PTV. It is shown that the collision of fluorescent fine particles take place not only at the leading edge but also at the trailing edge of the bubble, independently of the experimental setup. These findings are correlated with the measured TKE and dissipation rates around the bubble and in the bubble wake. Subsequently, the experimental TKE and dissipation rates are applied to existing models for collision frequency, and their predictions are discussed. Secondly, the impact of the turbulent liquid flow on the collision between a stagnant bubble and model particles is studied for a range of turbulent length scales. Besides the investigation in a dilute solid suspension, the bubble-particle interaction is also examined in a dense flow with PEPT. PEPT has the potential to measure suspensions with a high solid fraction, which could not be achieved with optical particle tracking methods. For the detection of individual particles with PEPT, radioactive tracer particles were designed to represent the bulk particles. The trajectories of the labeled particles are used to determine the average particle distribution in the turbulent field and describe the bubble-particle interactions. Overall, the developed methodologies in this dissertation provide a framework to investigate directly the collision between particles and bubble in a turbulent flow. The gained experimental validation data allows to verify existing collision models and to advance our understanding of the role of turbulence in froth flotation

Flotation in a novel oscillatory baffled column

Includes abstract.Includes bibliographical references (p. 200-212).This thesis presents an evaluation of an Oscillatory Baffled Column as a novel flotation device and as a research tool for investigating the role which hydrodynamics play in promoting particle-bubble contacting. The cell differs from a conventional cell design in that bubble generation is decoupled from the power input. This allows the hydrodynamic environment to be optimised for effective particlebubble contacting. The design also incorporates a novel mechanism of agitation which provides a more even distribution of shear rate than would be obtained in a stirred system and allows considerably more variation of the power input to the cell. Based on these properties it is hypothesised that the OBC would provide an effective hydrodynamic environment for fine particle flotation, particularly in highly viscous, non-Newtonian slurries. It is also hypothesised that the development of such a cell technology will facilitate an improved understanding of the role which hydrodynamics play in promoting particle-bubble contacting. To investigate these hypotheses, the OBC was first characterised in terms of key flotation parameters, such as bubble size, gas hold-up and mixing. The cell was then flotation tested on quartz, in order to benchmark the study against previous studies on hydrodynamics and particle-bubble contacting in stirred systems. Finally, the OBC was tested in application to a highly viscous, non-Newtonian nickel ore slimes slurry which is difficult to treat using conventional cell technologies. This study gave context to the potential future role of OBC technology in the minerals processing industry. The results of this thesis clearly show that the OBC is a promising novel technology for the treatment of fine mineral slurries. The cell has been demonstrated to significantly improve flotation kinetics by a factor of between 1.4 and 1.6 relative to a standard column. Optimal flotation conditions were obtained at power dissipations as low as 10 W/m3. The advantages of the OBC as a novel device include its ability to decouple bubble generation and particle-bubble contacting, its even distribution of shear rate in the cell as well as the additional fluctuating fluid motion produced under oscillatory flow. Furthermore, the flotation kinetics in the cell were shown to be unaffected by slurry rheology indicating the cell is best suited to niche application in the processing of ore types exhibiting highly viscous non-Newtonian behaviour

Submicron gas bubbles in water

Gas bubbles smaller than 1 micrometre in water, commonly referred to as nanobubbles, is a growing field of research and innovation. Applications range from medical imaging and drug delivery to mining industry and environmental remediation. Despite much activity, important questions remain – which are the mechanisms that allow small gas bubbles to be stable against dissolution and are stable nanobubbles really as common and easily generated as is often claimed?This work demonstrates that several common nanobubble generation methods can generate particle agglomerates or oil droplets which can be mistaken for bubbles, whereas stable nano- and microbubbles are less easy to generate than commonly believed. The results further suggest that stable bubbles are normally stable due to a shell of surface-active organic compounds, whereas other proposed stability mechanisms are less likely. An unexpected finding was that sorbitan surfactant stabilized air nanobubbles can form long-lived bubble agglomerates.Holographic Nanoparticle Tracking Analysis (H-NTA) is demonstrated as a powerful new method to detect and differentiate between bubbles and particles in the same dispersion. As H-NTA determines the refractive index of tracked objects, bubbles will differ very significantly from solid particles or oil droplets. The method also enables detection of different populations of particles, agglomerates and oil droplets in the same dispersion

Effect of interface contamination on particle–bubble collision

This study focuses on the impact of the interface contamination on the collision efficiency between bubbles and inertial particles. The bubble's surface mobility has been integrated into the collision modelling by using the hydrodynamics stagnant-cap model, in which the clean angle O clean is used to characterise the interface contamination level. Direct numerical simulations have been performed for various bubble's Reynolds numbers (1≤Reb≤100), particle to bubble size ratio (0:001≤rp/rb≤0:02) and particle's Stokes numbers (0:001 O crit, the contact point of the "grazing trajectory" can only be situated on the mobile interface, while for O clean < O crit, the contact point may be on both mobile and immobile part of the interface and only the positive inertial effect is observed. A simple model has been proposed that makes possible the description of collision efficiency for clean or contaminated bubbles

Mass Transfer in Multiphase Systems and its Applications

This book covers a number of developing topics in mass transfer processes in multiphase systems for a variety of applications. The book effectively blends theoretical, numerical, modeling and experimental aspects of mass transfer in multiphase systems that are usually encountered in many research areas such as chemical, reactor, environmental and petroleum engineering. From biological and chemical reactors to paper and wood industry and all the way to thin film, the 31 chapters of this book serve as an important reference for any researcher or engineer working in the field of mass transfer and related topics

Computational fluid dynamics and experimental study of the hydrodynamics of a bubble column and an air-water jet-stirred cell

A large number of flows encountered in nature and in many industrial processes areintrinsically multiphase flows. The efficiency and the effectiveness of multiphase flow processes strongly depend on the ability to model the fluid flow behaviour. Thus, a robust and accurate description of multiphase flow can lead to an increase in performance, a reduction in cost, and an improvement in safety for engineering systems. In recent years, Computational Fluid Dynamics (CFD) has become an indispensable predictive tool for gathering information to be used for design and optimization for fluid systems. In this thesis the hydrodynamics of two bubbly flow systems, a bubble column and a waterjet-agitated flotation cell (Hydrojet cell), were studied by means of numerical simulations. In order to validate the bubble column CFD simulations Particle Image Velocimetry (PIV) was used. An experimental investigation about bubble size distribution (BSD) along a water jet was carried out by means of image analysis. Because of high gas fraction and high velocity of the air/water streams used to agitate the Hydrojet cell, with the available equipment, no experimental measurements could be done to evaluate the velocity field of the cell. The thesis consists of three parts: theoretical part, bubble column study and Hydrojet cell study. In the theoretical part, first, a summary of fluid dynamics principles and an overview of the principal issues related to multiphase flow modelling were presented. Then a brief introduction to PIV and its application to two phase bubbly flow were given. Finally a review of the principle of the flotation process and its modelling were done in order to highlight the reasons for the low recovery of fine particles. Then the potentialities offered by the use of waterjets to fine particles flotation were presented. In the second part experimental and numerical studies of a bubble column were presented. PIV technique was used to determine the velocity field of a laboratory bubble column. A separation method for multiphase PIV was developed and tested. By means of the proposed method, the acquired mixed-fluid images were processed to obtain two sets of single phase images before PIV analysis. The velocity field was determined using a multi-pass crosscorrelation. Following three-dimensional time-dependent CFD simulations of a lab-scale bubble column were presented. The simulations were carried out using the Euler - Euler approach. Two different multiphase turbulence models, Shear Stress Transport (SST) and Large Eddy Simulation (LES), were tested, and different interfacial closure models reported in the literature were examined. When LES were used to model the turbulence instead of the SST model, much better agreement with the experimental data was found, provided that the drag, lift and virtual mass forces were taken into account. In the third part a preliminary experimental study, carried out in a rectangular flat cell, was presented. It was carried out to investigate the size distribution of bubbles generated by a moderate pressure water jet, by means of image analysis. This study showed the ability of water jets at moderate pressure to break an air stream into small bubbles. Increasing the pressure of the pump, smaller and more uniform bubbles were obtained. Then three-dimensional CFD simulations of the Hydrojet cell are presented. The Hydrojet cell, due to the exceeding computational burden, was simulated as a two-phase (gas-liquid) system, although actually it is a three-phase (gas-liquid-solid) system. Also in this case simulations were carried out using the Euler - Euler approach. The turbulence of the liquid phase was modelled with the SST model. The single reference frame technique was used to describe the movement of the waterjet lance. To achieve a homogeneous aeration in the region near the inlets different inlet velocity and rotational speed were tested. The results gave useful indications about the role of the four principal operating parameters: nozzles diameter, velocity of rotation of the lance, speed of the water jets and then pressure of the pump and inlet air flow rate. What emerges is the need of high rotational speed of the waterjet lance in order to ensure an uniform gas distribution within the mixing zone. This is not possible with the current apparatus. Thus in order to make the system suitable to produce an appropriate environment for the full development of the flotation process it is necessary to modify the system

Computational fluid dynamics and experimental study of the hydrodynamics of a bubble column and an air-water jet-stirred cell

A large number of flows encountered in nature and in many industrial processes areintrinsically multiphase flows. The efficiency and the effectiveness of multiphase flow processes strongly depend on the ability to model the fluid flow behaviour. Thus, a robust and accurate description of multiphase flow can lead to an increase in performance, a reduction in cost, and an improvement in safety for engineering systems. In recent years, Computational Fluid Dynamics (CFD) has become an indispensable predictive tool for gathering information to be used for design and optimization for fluid systems. In this thesis the hydrodynamics of two bubbly flow systems, a bubble column and a waterjet-agitated flotation cell (Hydrojet cell), were studied by means of numerical simulations. In order to validate the bubble column CFD simulations Particle Image Velocimetry (PIV) was used. An experimental investigation about bubble size distribution (BSD) along a water jet was carried out by means of image analysis. Because of high gas fraction and high velocity of the air/water streams used to agitate the Hydrojet cell, with the available equipment, no experimental measurements could be done to evaluate the velocity field of the cell. The thesis consists of three parts: theoretical part, bubble column study and Hydrojet cell study. In the theoretical part, first, a summary of fluid dynamics principles and an overview of the principal issues related to multiphase flow modelling were presented. Then a brief introduction to PIV and its application to two phase bubbly flow were given. Finally a review of the principle of the flotation process and its modelling were done in order to highlight the reasons for the low recovery of fine particles. Then the potentialities offered by the use of waterjets to fine particles flotation were presented. In the second part experimental and numerical studies of a bubble column were presented. PIV technique was used to determine the velocity field of a laboratory bubble column. A separation method for multiphase PIV was developed and tested. By means of the proposed method, the acquired mixed-fluid images were processed to obtain two sets of single phase images before PIV analysis. The velocity field was determined using a multi-pass crosscorrelation. Following three-dimensional time-dependent CFD simulations of a lab-scale bubble column were presented. The simulations were carried out using the Euler - Euler approach. Two different multiphase turbulence models, Shear Stress Transport (SST) and Large Eddy Simulation (LES), were tested, and different interfacial closure models reported in the literature were examined. When LES were used to model the turbulence instead of the SST model, much better agreement with the experimental data was found, provided that the drag, lift and virtual mass forces were taken into account. In the third part a preliminary experimental study, carried out in a rectangular flat cell, was presented. It was carried out to investigate the size distribution of bubbles generated by a moderate pressure water jet, by means of image analysis. This study showed the ability of water jets at moderate pressure to break an air stream into small bubbles. Increasing the pressure of the pump, smaller and more uniform bubbles were obtained. Then three-dimensional CFD simulations of the Hydrojet cell are presented. The Hydrojet cell, due to the exceeding computational burden, was simulated as a two-phase (gas-liquid) system, although actually it is a three-phase (gas-liquid-solid) system. Also in this case simulations were carried out using the Euler - Euler approach. The turbulence of the liquid phase was modelled with the SST model. The single reference frame technique was used to describe the movement of the waterjet lance. To achieve a homogeneous aeration in the region near the inlets different inlet velocity and rotational speed were tested. The results gave useful indications about the role of the four principal operating parameters: nozzles diameter, velocity of rotation of the lance, speed of the water jets and then pressure of the pump and inlet air flow rate. What emerges is the need of high rotational speed of the waterjet lance in order to ensure an uniform gas distribution within the mixing zone. This is not possible with the current apparatus. Thus in order to make the system suitable to produce an appropriate environment for the full development of the flotation process it is necessary to modify the system

Topical scientific researches into resource-saving technologies of mineral mining and processing

Table of contents Preface . 5 Malanchuk Z.R., Soroka V.S., Lahodniuk O.A., Marchuk M.M. Physical-mechanical and technological features of amber extraction in the Rivne-Volyn region of Ukraine . 6 Moshynskyi, V.S., Korniyenko V.Ya., Khrystyuk A.O., Solvar L.M. Research of energy effective parameters of the process of hydro mechanical extraction of amber from sandy deposits . 24 Mohamed Tafsir Diallo, Mamadou Oury Fatoumata Diallo Tidal Park – Modeling and Control Strategy . 38 Savina N.B., Malanchuk L.O., Ignatiuk I.Z., Moshchych S.Z. Institutional basis and trends of management of the use of the subsoil in Ukraine . 51 Dedelyanova Kr.Y. Column flotation machine – innovative aeration, vibra-tory – acoustic and technological researches . 60 Makarenko V.D., Manhura A.M., Lartseva I.I., Manhura S.I. Magnetic field on asphalt, resin, paraffin and salt deposits 79 Krzysztof Tomiczek The problem of beds stability in the conditions of undermining higher deposited beds in the context of selected analytical solutions . 95 Safonyk A.P., Koziar M.M., Martyniuk P.M., Fylypchuk V.L. Management of pollution - purification system for mining plants . 117 Marinela Panayotova, Vladko Panayotov Recent developments in the flotation of sulfide ores of base metals - bioflotation . 130 Remez N., Dychko A., Bronytskyi V., Kraychuk S. Simulation of shock waves from explosion of mixture explosive charges . 149 Melodi M.M. Akande V.O. Analysis of productivity and technical efficiency in granite aggregate production in selected quarries in south-western, Nigeria . 166 Doroshenko Ya.V., Karpash O.M., Rybitskyi I.V. Investigation of dispersed contaminates influence on the hydraulic energy consumption of elements of gas pipeline systems with complex geometry . 182 Skipochka S.I., Krukovskyi O.P., Krukovska V.V., Palamarchuk T.A. Features of methane emission in coal mines at high speed longwall face advance 208 Daouda Keita, Valery Pozdnyakov Statistical analysis of experimental data on the indices of operation of the loading units of the bauxite compa-ny of Guinea (CBG) . 226 Yevhenii Malanchuk, Sergiy Stets, Ruslan Zhomyruk, Andriy Stets Modeling of the process of mining of zeolite-smectite tuffs by hydro-well method . 244 Samusia V. I., Kyrychenko Y. О., Cheberiachko I. M., Trofymova, O. P. Development of experimental methods to study heterogenic flows in the context of hydraulic hoisting design . 260 Makarenko V.D., Kharchenko M.O., Manhura A.M., Petrash O.V. Magnetic treatment of production fluid with high content of asphalt-resin-paraffin deposits . 268 Kovshun N.E., Ignatiuk I.Z., Moshchych S.Z. Malanchuk L.O. Innovative model of development of fuel and energy complex of Ukraine 279 Bondarenko А.O., Ostapchuk O.V. Design and implementation of a jet pump dredge . 296 Sotskov V.O., Dereviahina N.I. Research of dependencies of stope stress-strain state change under various conditions of partial stowing of developed space . 305 Sakhno S., Liulchenko Y., Chyrva T., Pischikova O. Determination of bear-ing capacity and calculation of the gain of the damaged span of a railway overpass by the finite element method . 326 Melodi М.М., Ojulari M.K. Oluwafemi V.I. Economic and environmental impacts of artisanal gold mining on near-by community of Sauka-Kahuta, Nigeria . 340 Kruchkov A.I., Besarabets Y.J., Yevtieieva L.I. Energy saving modes of excavators type power shovel . 353 Hryhorash M.V., Kuzminskyi V.P., Ovchinnikova O.V., Kukhar V.Yu. Energy saving through quality of technical water: new types of mechanical screen filters for various links of water treatment . 369 Didenko M. The modeling of the interaction of rock mass and compliant lining while it is expanded . 394 Makarenko V.D., Liashenko A.V. Complex approach to research and selection of hydrocarbon solvents for asphaltene-resin-paraffin-hydrate deposits control . 408 Mykhailovska O.V., Zotsenko M.L. Investigation of the oscillations amplitudes bases and foundations of the forming machine . 417 Inkin O.V., Puhach A.M., Dereviahina N.I. Physical-chemical and technological parameters of improving profitability of underground coal burning . 42

The effect of energy input on flotation kinetics

SYNOPSIS Energy/power input in a flotation cell is an important parameter which, if optimised, can increase the flotation rate. The optimum energy/power input within a flotation cell is still a matter of conjecture and there is a need for a better understanding of the effect of energy input on flotation kinetics. This study investigates the effect of energy/power input on flotation kinetics in an oscillating grid flotation cell (OGC). The OGC decouples the processes of solid suspension and bubble generation as well as producing relatively isotropic and homogeneous turbulence with zero mean flow. Due to this, oscillating grids provide a potentially ideal environment for investigating the effects of energy input on flotation kinetics, which cannot be achieved in a mechanical flotation cell. The first objective of this thesis was to determine the effect of energy/power input on the flotation kinetics of sulphide minerals (galena, pyrite & pentlandite) and oxide minerals (apatite & hematite) in a laboratory scale oscillating grid flotation cell. The second objective was to compare the results from the laboratory OGC to comparative studies in the flotation literature and to fundamental models for particle-bubble contacting. The third objective was to determine whether the experimental results from the laboratory OGC are consistent with those from a pilot-scale OGC operating on a platinum ore. Galena, pyrite, pentlandite (-150 μm), apatite (-650 μm) and hematite (-75 μm) were floated in the laboratory OGC at energy inputs from 0.1 to 5.0 W/kg, using 0.13, 0.24, 0.58 and 0.82 mm bubble sizes (d₁₀), and at three collector dosages. Platinum ore (-75 μm) was floated in the pilot-scale OGC at energy inputs from 0 to 2.5 W/kg, using 0.71 and 1.47 mm bubble sizes (d₁₀). The effect of energy input on flotation kinetics was interpreted through trends in experimental flotation rate constants, simulated flotation rate constants and attachment-detachment flotation rate constants. Here, simulated flotation rate constants were calculated using a literature fundamental model for flotation in turbulent systems. This model is based on suitable expressions for the collision frequency, collision efficiency, attachment efficiency and stability efficiency, Attachment-detachment flotation rate constants were calculated using a kinetic model which allows for the two separate processes of bubble-particle collision/attachment and detachment. This model is based on kinetic expressions using empirical correlations for the attachment and detachment rate constants. Experimental flotation results show that the effect of energy input on the flotation rate is strongly dependent on the particle size and particle density and less dependent on bubble size and contact angle. Flotation rates generally increase with increasing particle size, decreasing bubble size and increasing contact angle, as is commonly found in the literature. Increasing energy input generally leads to an increase in the flotation rate for fine particles, an optimum flotation rate for intermediate particles and a decrease in the flotation rate for coarse particles. The optimum in the flotation rate for minerals with higher density is at a lower energy input than that for lower density minerals. The changes (increases/decreases) in the flotation rate with increasing energy input are very large for most of the conditions, indicating that this is an important parameter in flotation. Pilot scale results generally support the trends observed in the laboratory OGC. These findings are attributed to the effect of energy/power input on bubble-particle collection which is a balance between two competing effects, those of bubble-particle collision/attachment and those of bubble-particle detachment. Increasing energy input generally leads to significant increases in the flotation rate of fine particles, due to increased bubble-particle collision/attachment. Increasing energy input generally leads to an optimum flotation rate for intermediate particles, due to a combination of increased bubble-particle collision/attachment and detachment. For coarse particles, increasing energy input leads to significant increases in bubble-particle detachment. The relationship between the flotation rate and energy input is often described as k ɛᴺ, in the absence of significant bubble-particle detachment. The typical values of N are in the range of 0.44-0.75 for theoretical studies and 0.7-1 for experimental studies. The values of N found in the current study are in the range of 0.7-1, which suggests that bubbleparticle collision/attachment has a stronger dependence on energy input than theory suggests. Simulated flotation results for fine particles compare well to the experimental data in terms of both trends and magnitude. This suggest that the turbulent collision model used is appropriate for fine particles. For intermediate particles there are differences between the simulated flotation rate constants and the experimental data, primarily in terms of trends. For coarse particles there are very large differences between simulated flotation rate constants and the experimental data. This is attributed to under prediction of the collision frequency/efficiency and incorrect prediction of the stability efficiency. Here, the stability efficiency is considered to be under predicted at low energy inputs and over predicted at high energy inputs. This suggests that the stability efficiency has a much stronger dependence on energy input than theory suggests. Attachment-detachment results show that the attachment rate constant has a stronger dependence on energy input than theory suggest, supporting finding from the experimental results and simulated results for coarser particles. In addition, the detachment rate constant has a much stronger dependence on energy input than theory suggests, supporting findings from both the experimental and simulated results. Based on the objectives of this study and literature reviewed, the following hypotheses were made at the outset 1) Increasing energy/power input will increase the rate of flotation of fine particles but will result in an optimum for intermediate and coarse particles. The position of this optimum will depend on the particle density, bubble size and contact angle. 2) Fundamental models based on the RMS turbulent velocity will be appropriate for describing flotation kinetics as turbulence in the oscillating grid cell is relatively homogeneous and isotropic and 3) Trends in flotation results for a laboratory and pilot-scale oscillating grid flotation cell will be comparable as the distribution of turbulence in OGCs at equivalent specific power inputs is scale independent. Hypothesis 1 was found to be valid for both fine and intermediate particles, but for coarse particles increasing energy input resulted in sharp decreases in the flotation rate. In addition, the increase in the flotation rate with increasing energy input was found to be more dependent on the particle size and particle density than the bubble size and contact angle. Hypothesis 2 was found to be valid for fine particles but not for intermediate or coarse particles. Here, it was found that the processes of bubble-particle collision/attachment and detachment have a stronger dependence on energy input than theory suggests. Hypothesis 3 was supported by general trends in results for the laboratory and pilot-scale oscillating grid flotation cells, but was not convincingly demonstrated

The use of machine vision to describe and evaluate froth phase behaviour and performance in mineral flotation systems

Includes synopsis.Includes bibliographical references (leaves 179-190).Within froth flotation, it is widely acknowledged that froth stability affects flotation performance. As a result, it is expected that through the effective management of froth stability, it would be possible to both control and optimise a flotation cell and bank. However, for this to be possible, the relationships between the operating conditions, froth stability behaviour and flotation performance attributes need to be well understood. In addition, froth stability would need to be measured using a robust method suitable for on-line operation. Within the literature, no robust methods are available to measure either the concentration of solids on the froth surface, or froth stability in a manner suitable for on-line operation. Thus, two novel non-intrusive machine vision measurements have been developed in this work to quantify these attributes