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Froth flotation is the largest tonnage separation process worldwide and is used for paper deinking, water purification and, particularly, mineral separation. One of the key aspects of the performance of flotation cells is the behaviour of the liquid within the froth, as it is crucial to the purity of the product and a major influence on the overall recovery. Nonlinearities in models for liquid motion in the froth make them complex to solve and existing numerical solutions have been in two dimensions at most. In order to predict the performance of industrial flotation cell designs, a three-dimensional solution for these equations is desirable. Moreover, the understanding of the process would be enhanced if a transient model were used to predict the dynamics of foam drainage. In this work, the equations for the liquid drainage have been rearranged in order to make them analogous to a compressible version of the Navier-Stokes equations, coupled to an equation of state. A model for predicting the movement of the flowing foam has also been developed, which is able to solve for the foam velocity in two and three dimensions. This has allowed the transient behaviour of liquid in flotation foams to be modelled using Fluidity, a general purpose finite element method code that allows simulations to be carried out on unstructured adaptive meshes. This is an important feature for improving the computational cost of modelling these systems, as there are boundary layers present in the process, whose size is independent of the scale of the flotation system being modelled. These models have allowed, for the first time, to carry out numerical investigations of drainage for arbitrary flotation tank geometries in up to three dimensions, and have been verified against analytical solutions and compared to laboratory scale experiments with satisfactory agreement.

Over the past decade, decision makers in the mining and mineral processing industry have had to deal with multiple challenges such as varying metal prices, depleting resource quality, and complying with stricter environmental regulations. Besides, the mining and mineral processing industry also needs to consider the use of renewable energy in order to comply with strict environmental regulations. In addition, since the use of renewable energy has costs associated to the additional equipment installation and maintenance, optimizing the equipment selection to minimise energy costs is of vital importance. Therefore, decision makers in the sector often face problems that involve multidisciplinary knowledge that take into account technical, social, economic and environmental aspects. Multiple Criteria Decision Making (MCDM), which is a part of operations research, has become extremely useful to overcome a variety of decision making problems in mining and mineral processing. Although a very large number of MCDM methods have been developed, the effectiveness of these methods still depends on the objective of the decision making process (i.e. selection, sorting, ranking, description) and the nature of the problem. An exhaustive literature review on the applications and trends of MCDM for the selection problem in mining and mineral processing has been conducted in this work. The literature review indicates that conventional MCDM methods have been frequently criticised on several drawbacks including its inability to quantify the uncertainty in data and information, the occurrence of the rank reversal phenomenon, and its difficulty in aggregating several judgements and preferences from multiple decision makers including related uncertainty on their judgements or preferences, as well as the robustness of MCDM methods in dealing with non-homogenous data (i.e. quantitative and qualitative). This thesis presents the development of four new MCDM methods and their application to the selection problem (i.e. determining the best option from a set) in mining and mineral processing by taking into account the role of uncertainties in the decision making process. This work mainly demonstrates the value of applying the concept of constrained fuzzy arithmetic in fuzzy extension of conventional MCDM methods when the input data that need to be analysed are difficult to define precisely. In order to showcase the capability of the developed methods, three case studies on the selection problem in the mining industry were conducted. Furthermore, the robustness of the developed methods are shown by conducting sensitivity analyses and comparing their results to those obtained from existing methods.

Surface tension is one of the most important physical properties that determines the behaviour of bubbles. While the effect of nanoparticles and surfactants on the surface tension of bubbles have been widely studied, the role of microparticles has not received too much attention. In this work, the effect of silica microparticles on the surface tension and the behaviour of bubbles was explored, both for bubbles at rest and during dynamic processes such as pinch-off, oscillation and coalescence. The influence of microparticles on the shape and surface tension of static bub- bles grown from a submerged nozzle was investigated first using a modified sessile bubble method. The results show that particles were in static equilibrium at the static bubble, without any change in bubble surface tension. In addition, it was found that the presence of particles at the bubble interface led to a change in the bubble contour, similar to the effect of the changes in surface tension for uncoated bubbles, which explains why classical sessile bubble tensiometry overestimated the surface tension of particle-laden bubbles. Secondly, the influence of microparticles on the surface tension and shape defor- mation during and immediately after pinch-off was investigated. It was found that microparticles at the deforming air-liquid interfaces generated surface pressure and reduced surface tension of the interfaces, leading to a hindered shape deformation compared to that of uncoated bubbles. Moreover, it was found that changing bubble surface coverage has noticeable effect on the surface pressure after pinch-off, while not during pinch-off. In addition, increasing particle contact angle and particle size both led to an increase in the surface pressure during pinch-off. Experiments on bub- ble oscillations were conducted, harmonic analysis shows the presence of particles at bubble surfaces decreased the damping rate of the dominant harmonic signifi- cantly while having a minor influence on the oscillation frequency during the shape oscillation of the bubbles. Lastly, the influence of microparticles on the surface tension and the neck growth dynamics during the early stage of bubble coalescence was studied. Results show that the particles at the bubble surface hindered the neck growth dynamics due to the generation of the surface pressure by particle interactions. The existence of the surface pressure lead to a lower surface tension compared to that of the uncoated bubbles, with coarser particles generating higher surface pressure and correspond- ing to lower surface tension. This thesis provided a systematic study of the behaviour of particle-laden bub- bles using high-speed photography, macrophotography and image analysis tech- niques. This work contributes to fundamental understanding of the surface tension of particle-laden interfaces both on and off equilibrium.

Froth flotation is the most important mineral concentration process. Over the last few decades, throughput has increased due to flotation equipment becoming exponentially larger. Small improvements in performance, therefore, significantly impact the economic revenue and sustainability of the process. The optimisation of flotation has thus been extensively studied, resulting in several improvements, especially in operating conditions, and important advances in our understanding of flotation. Publications on flotation equipment designs and their impact on flotation phenomena, however, are scarce and flotation tank design has, to a large extent, remained in-house know-how of manufacturing companies. Currently, flotation tank design tends to focus mainly on pulp zone parameters without considering its effect on the froth zone, despite the importance of froth stability in flotation performance. Moreover, while most new designs are studied using computational fluid dynamics models, these are typically validated with one- or two-phase systems, which oversimplify flotation phenomena. To solve these problems, large experimental datasets quantifying the effects of design variables on flotation phenomena are required. This thesis fills these and other gaps identified in the literature, by studying the effects of different impeller-stator designs on flotation phenomena. A continuously overflowing laboratory-scale flotation tank was used to study two different impeller designs, a Rushton turbine and a rotor, both with and without a stator. Bubble size distribution was measured for two- and three-phase systems, froth stability was quantified using air recovery, and flotation performance was assessed. Furthermore, a scaled-down bench-scale flotation cell was used to study the effect of these impeller-stators on the hydrodynamics of the flotation system, using Positron Emission Particle Tracking, which determines the motion of radioactive particle tracers, representative of hydrophobic and hydrophilic particles. Results show that the effect of the stator is predominant over the effect of impeller design. This thesis quantifies, for the first time in the literature, stator-induced bubble size reduction, caused by changes in bubble size distribution. Similarly, it shows for the first time that stators enhance froth stability and drastically change the hydrodynamics of the system by altering flow patterns and particle speed. All these effects improve flotation performance, markedly increasing metallurgical recovery. The information presented herein allows for a better understanding of physical phenomena within a flotation tank. Moreover, these datasets represent an important contribution to the validation and improvement of three-phase computational fluid dynamics models and will be valuable for the design of pilot- and industrial-scale test work.

There is a huge potential to optimise the froth flotation industry as even small improvements in the extraction of metals from the mineral ores can translate to a substantially higher revenue. Typically, laboratory studies into froth flotation involve batch tests where the system does not operate at steady-state, making it difficult to directly apply results to industrial systems. In this work, a continuously overflowing flotation cell, which does operate at steady state, has been used to investigate the effects of different operating conditions on flotation performance. This work used two experimental systems which are more comparable to industrial systems than previous studies using the same bench scale flotation cell. The first system investigated in this thesis used a copper tailings ore. The effects of varying the particle size distribution on the flotation performance and froth stability were investigated. For the first time, a direct comparison between two measures of stability was made, and both measures showed an optimum in froth stability with an intermediate particle size distribution. This optimal particle size distribution also resulted in an improved copper recovery which has important implications for the reprocessing of tailings material via froth flotation. The second system investigated used a synthetic magnetite-silica ore. This ore allows more control over the system, whilst still providing a good proxy for industrial flotation. This system was used to investigate the effects that inserting two retrofit design modifications (horizontal meshes) into the cell had on flotation performance. These meshes were designed to provide a more quiescent environment at the pulp-froth interface (PFI) and reduce particle detachment. The "basic mesh" shifted the grade-recovery curve to an improved grade, while the "blocked mesh" resulted in a significant improvement in recovery and a reduction in entrained magnetite. Positron emission particle tracking (PEPT), a technique that tracks the movement of radioactive tracer particles, was used to investigate the mechanisms that resulted in the improved flotation performance when using the meshes. PEPT experiments were performed with different tracer types and tracer sizes. It was shown that the presence of the mesh reduced the presence of swirl at the pulp-froth interface, and formed a secondary, more quiescent, pulp zone with a shallower froth. In some cases, a mixing loop formed in this secondary pulp zone which promoted the reattachment of detached valuable mineral. It was also shown that both meshes improved the flotation of the coarsest tracer size indicating that the meshes can be used to improve the recovery of coarse particles. For the first time, a continuous bench scale flotation cell has been used to investigate the relationship between design modifications, particle size and the flotation performance. This was done using two different ores, both more complex than what has previously been investigated in similar equipment. These experiments also utilised PEPT to further the understanding of the effect that design modifications have on the flotation performance of different types of particle. The results of this work have two primary applications to improving the flotation of both fine and coarse particles for improving the sustainability of the minerals processing industry. The first application relates to fine particle flotation by finding an optimal feed particle size distribution. This will enhance the ability to reprocess tailings material by froth flotation and therefore improve the sustainability of the industry. The second application relates to coarse particle flotation by using a simple retrofit design modification to increase the floatability of these particles. This will improve sustainability within minerals processing by reducing the comminution requirements and therefore energy consumption. There is, however, more work needed to investigate these modifications further to ensure they are applicable at an industrial scale.

The use of mini-hydrocyclones (e.g. 10 mm in diameter) for the separation of par-ticles in the micron range is of growing interest in industry. However, these hydro-cyclones are typically limited to conventional shapes or restricted to specific outletsizes, which can lead to sub-optimal performance. Mini-hydrocyclones exhibit abypass fraction that is larger than the water recovery, resulting in a high particlerecovery to the underflow, as well as low water recovery, which is convenient fordewatering processes. However, this larger bypass fraction can be a disadvantagewhen the purpose of the hydrocyclone is particle classification, because of the largeamount of fine particles that are misplaced in the underflow. Therefore, a deeperunderstanding of the mini-hydrocyclones performance is needed. The aim of this thesis is to present a method for the optimisation of mini-hydrocyclonedesign. The method consists of designing and 3D printing mini-hydrocyclones, car-rying out Computational Fluid Dynamics (CFD) simulations, and performing ex-perimental tests. 3D printed mini-hydrocyclones were tested and the effect thatchanges in vortex finder and spigot diameters have on separation performance wasstudied. A CFD model was implemented and validated with experimental data formini-hydrocyclones applied to dewatering and classification processes. Lastly, noveldesign of hydrocyclones (i.e. with parabolic walls) were studied in a full factorialand Central Composite Rotatable (CCRD) designs. The first outcome of this thesis is the application of the 3D printing technologyfor practical and rapid prototyping of mini-hydrocyclones. The second outcome isthe implementation of a validated CFD model to predict the performance of mini-hydrocyclone for dewatering and particle classification processes. The third outcomeis the combination of 3D printing technology and the CFD model to evaluate hydro-cyclones with parabolic walls. This thesis demonstrates the potential of 3D printing,CFD modelling and robust experimental testwork to improve the understanding ofmini-hydrocyclones performance in dewatering and classification processes.

Bubble-particle aggregates play a dominant role in separation processes such as froth flotation. Previous studies on individual rising bubble motion have mainly focused on gas-liquid two-phase systems and there has been no systematic investigation on the influence of particles on the rising behavior of particle-laden bubbles. In this project, clear visualization of the behavior of bubble-particle aggregates is achieved by using capillaries to generate bubbles of controlled size in a transparent experimental rig, which are released after attachment of particles is achieved. The pendant drop model was used and fitted to the edge points of the bubbles to calculate their particle surface coverage. High-speed photography and image analysis techniques were used to record and analyze the hydrodynamics of rising bubbles in terms of velocity and aspect ratio. The influence of particle coverage and particle size on the behavior of rising bubbles was studied. In addition, the buoyancy force, drag force as well as the mass force on the particles and bubbles were calculated and interpreted. Results show that with the increase of particle coverage or attached particle size, the aspect ratio oscillation patterns of the rising bubbles are similar and the high frequency oscillation periods do not change significantly. This indicates that the capillary wave caused by surface tension does not change, it is the hydrodynamic force that differentiates bubble motion. With the increase of particle size or coverage, the rising bubbles show a lower velocity as well as a damped aspect ratio oscillation. Particles attached on the bubbles decrease the bubble acceleration, and this acceleration is inversely correlated to the bubble aspect ratio and its change. The highest rising velocities correspond to the lowest aspect ratios and vice versa, independently of the particle size or coverage. A particle drag modification factor, which quantifies the drag influence of particles on bubble velocity, was identified from force analysis. A modified drag coefficient for uncoated and particle-laden bubbles was introduced, which allows, for the first time, to predict the behavior of rising particle-laden bubbles in gas-liquid-solid systems. The results and interpretation produced a quantitative description of the behavior of rising particle-laden bubbles and the development of correlations that can be used to inform the modelling of industrial applications such as pulp phase phenomena in froth flotation.

Froth flotation is a physico-chemical technique used to separate the constituents of a mixed mineral slurry by their relative surface hydrophobicity. In order to do so economically, it is necessary to treat large volumes of material in ever-larger and more efficient tanks. The efficiency and efficacy of such tanks can be enhanced through mechanical modifications designed to improve froth handling, increase the likelihood of bubble-particle interactions in the pulp, and increase the residence time of suspended solids in the tank. However, design modifications suggested by computational modelling or bench-scale experiments often do not realise performance improvements at pilot and plant-scale because of imperfect scale-up from bench-scale, and differences in the type and intensity of the sub-processes affecting performance at different scales. The first outcome of this thesis is an intermediate, laboratory-scale froth flotation circuit that more closely resembles continuously-operated pilot-scale equipment, but which is better instrumented and controlled. This work describes not only the laboratory-scale system, but also detailed regression models of its behaviour and performance based on extensive monitoring and instrumentation. The resultant performance models provide a baseline against which to test design modifications, and the resultant behaviour models inform the design of such modifications. The second outcome of this thesis, a performance-enhancing design modification, was prompted by the discovery that minimising the variability of the pulp-froth interface leads to an increase in both indicative grade and recovery. The resultant tank modification was a horizontal mesh inserted into the pulp below the pulp-froth interface, designed to isolate it from the turbulent region around the impeller. The mesh pore size and thickness, and the position at which it was installed in the tank, were taken as design variables to be optimised by the genetic algorithm method. The result is a grade-recovery curve corresponding to an optimal mesh pore size of 123.4 +/- 3.1 mm. From this curve it was found that increasing the mesh thickness from 33 mm to 47 mm yields a maximum improvement in the recovery of 18.9% without compromising the grade, and increasing the depth of the mesh from 200 mm to 250 mm below the pulp-froth interface yields a maximum improvement in the grade of 3.2% without compromising the recovery. This grade-recovery curve, and the insights gained during the process of design and refinement, provides the rationale for a proposed program of mesh tests at pilot-scale.

An efficient numerical framework for the macroscale simulation of three-phase polydispersed flows is presented in this thesis. The primary focus of this research is on modelling the polydispersity in multiphase flows ensuring the tractability of the solution framework. Fluidity, an open-source adaptive-mesh finite element code, has been used for solving the coupled equations efficiently. Froth flotation is one of the most widely used mineral processing operations. The multiphase, turbulent and polydispersed nature of flow in the pulp phase in froth flotation makes it all the more challenging to model this process. Considering that two of the three phases in froth flotation are polydispersed, modelling this polydispersity is particularly important for an accurate prediction of the overall process. The direct quadrature method of moments (DQMOM) is implemented in the Fluidity code to solve the population balance equation (PBE) for modelling the polydispersity of the gas bubbles. The PBE is coupled to the Eulerian--Eulerian flow equations for the liquid and gas phases. Polydispersed solids are modelled using separate transport equations for the free and attached mineral particles for each size class. The PBE has been solved using DQMOM in a finite element framework for the first time in this work. The behaviour of various finite element and control volume discretisation schemes in the solution of the PBE is analysed. Rigorous verification and benchmarking is presented along with model validation on turbulent gravity-driven flow in a bubble column. This research also establishes the importance of modelling the polydispersity of solids in flotation columns, which is undertaken for the first time, for an accurate prediction of the flotation rate. The application of fully-unstructured anisotropic mesh adaptivity to the polydispersed framework is also analysed for the first time. Significant improvement in the solution efficiency is reported through its use.

Froth flotation is an established method of separating mineral from its associated ore. Although there has been many years of research and development, there remains much room for development. A 4 L bench-scale, continuously overflowing and recycling single species flotation system was developed for this work. It was used to investigate the effect of particle size and retrofit designs on air recovery, a measure of froth stability, as well as the solid and liquid flowrates of the system. Particle size had an effect on air recovery and flotation performance. An increase in solids flowrate corresponded with a decrease in the particle size in the concentrate. When air recovery was below 50 %, the peak in solids flowrate corresponded with the peak in air recovery. The addition of a retrofit design, a horizontal mesh of varying hole-size and thickness, was tested at a range of superficial gas velocities in a three-way full factorial trial. It was shown that a mesh of 30 mm hole-size and 40 mm thickness resulted in a statistically significant improvement in solids flowrate to the concentrate, when compared with the unmodified base case. Position Emission Particle Tracking (PEPT) provided an opportunity to make qualitative and quantitative assessments of particle behaviour within the pulp and froth. PEPT data indicated that in the unmodified base case, swirl from the pulp continued in the lower froth, a behaviour never observed before. Variation in mesh hole-size lead to visible changes in tracer trajectories, and an increase in mesh thickness resulted in both tracers entering the froth more frequently. This work has developed a novel experimental system capable of determining the effects of a range of operational and design parameters on air recovery and flotation performance, and has corroborated and justified the trends seen through statistical analysis and novel imaging techniques.