Bubble size is considered to be one of the most important parameters affecting the performance of froth flotation cells. However, monitoring, controlling and predicting bubble size is a very challenging task. This dissertation presents results obtained from a comprehensive pilot- and industrial-scale experimental investigation of gas dispersion performance of two commercially available flotation cells. To facilitate this investigation, a continuous pilot-scale flotation system was developed and tested. The results of the hydrodynamic and metallurgical testing conducted on the pilot-scale flotation circuit are presented. In addition, an assessment of the impact of two commercially available rotor/stator mechanism designs on bubble generation was performed under non-coalescing conditions. Based on obtained results, the mechanisms of gas dispersion throughout the flotation cell and gas cavity formation behind the impeller blades have been presented and discussed. A new in-situ optical bubble sampling method was also developed as part of this investigation. The new system allowed an accurate estimation of local bubble sizes and determination of overall gas dispersion patterns within the cell. The new method was compared to the existing ex-situ bubble sampling method commonly used in industry. Two image analysis techniques were also evaluated, i.e., a template matching BubbleSEdit technique and the edge detection Northern Eclipse technique. Significant variations in bubble size as a function of the sampling method, sampling location, operating condition, machine type and image analysis method were observed. Generally, bubbles observed with the in-situ sampling method appeared to be larger than bubbles recorded with the ex-situ method. Furthermore, the mean bubble size determined by the Northern Eclipse bubble sizing method was smaller than the BubbleSEdit value. The experimental tests also revealed that sampling location had a strong effect on measured local mean bubble size and bubble size distribution in both vertical and horizontal directions. In addition, aeration rate was found to have a profound impact on the gas dispersion pattern in the cell and on local bubble size. Agitation rate also had a significant effect on bubble size, although the degree of impact strongly depended on the agitation level, chemical conditions in the cell and the machine type. / Ph. D.

Field assessments were performed to establish the performance capabilities of a new flotation technology for fine coal upgrading, known as StackCell flotation. Flotation release analysis was performed on all samples to determine the amount of hydrophilic material present in the streams around the flotation cell. Data from this work supported recommendations from the equipment manufacturer that the wash water distribution system should be changed to a drip pan and that the design of the slurry-air distributor from the mixing chamber should be altered. The experimental data showed that as froth depth, rotor speed, and wash water rate changed, the performance of the cell followed expected trends with respect to product quality, but diverged from expected trends with respect to carbon recovery and yield. Other work performed includes the development of a new carbon partitioning test, which uses a blender to provide a high shear environment and uses oil to partition the slurry into a carbon rich oil phase and an ash rich pulp phase. This test is capable of producing results comparable to those of a traditional release analysis. Lastly, a spreadsheet program was developed that can aid users in designing drip pans. This program is capable of producing custom designs or unit cell designs. A study of the effect that plate thickness has on flow rate was performed in order to develop a model for flow through an orifice plate. The results of this work showed that plate thickness has little to no effect on the flow rate. / Master of Science

Froth Flotation is an industrial separation process commonly used in the primary enrichment of run-of-mine mineral material. Over the past 100 years, much of the process's development has come from empirical evolution, rather than fundamental understanding. While many of the governing sub-processes are still poorly understood, the primary influential factors lie within the chemical, equipment, and operational variables unique to each flotation system. This investigation focuses on the phenomenological investigation of the equipment variables, particularly the rotor design, at the laboratory scale. During this study, several small-scale flotation systems were developed, including various rotor and stator designs, tank sizes, and flow conditions. Experimental techniques were also developed to identify operational performance in four criteria: power consumption, gas dispersion, operational robustness, and flotation kinetics. Evaluation of the various rotors was conducted in two campaigns: (1) an exploratory campaign which featured 14 rotors in limited operational conditions (2) a detailed campaign which featured three rotors in an exhaustive set of conditions. The results show that different rotors exhibited varying degrees of performance when judged by the aforementioned performance criteria. In general, excessive fluid pumping leads to an increase range of stable operation at the expense of greater power consumption. However, this increased power consumption does not necessarily correspond to increased flotation performance, as the data generally confirms the linearly proportional relationship of flotation rate and bubble surface area flux. Consequently, enhanced flotation kinetics can be achieved by rotors which disperse high rates of gas while retaining a small bubble size. / Master of Science

The collisions frequency of dispersed phases (particles, droplets, bubbles) in a turbulent carrier phase is a fundamental quantity that is needed for modeling multiphase flows with applications to chemical processes, minerals flotation, food science, and many other industries. In this dissertation, numerical simulations are performed to determine collisions frequency of bi-dispersed particles (solid particles and bubbles) in homogeneous isotropic turbulence. Both direct numerical simulations (DNS) and Large Eddy simulations (LES) are conducted to determine velocity fluctuations of the carrier phase. The DNS results are used to validate existing theoretical models as well as the LES results. The dissertation also presents a CFD-based flotation model for predicting the pulp recovery rate in froth flotation machines. In the direct numerical simulations work, particles and bubbles suspended in homogeneous isotropic turbulence are tracked and their collisions frequency is determined as a function of particle Stokes number. The effects of the dispersed phases on the carrier phase are neglected. Particles and bubbles of sizes on the order of Kolmogorov length scale are treated as point masses. Equations of motion of dispersed phases are integrated simultaneously with the equations of the carrier phase using the same time stepping scheme. In addition to Stokes drag, the pressure gradient in the carrier phase and added-mass forces are also included. The collision model used here allows overlap of particles and bubbles. Collisions kernel, radial relative velocity, and radial distribution function found by DNS are compared to theoretical models over a range of particle Stokes number. In general, good agreement between DNS and recent theoretical models is obtained for radial relative velocity for both particle-particle and particle-bubble collisions. The DNS results show that around Stokes number of unity particles of the same group undergo expected preferential concentration while particles and bubbles are segregated. The segregation behavior of particles and bubbles leads to a radial distribution function that is less than one. Existing theoretical models do not account for effects of this segregation behavior of particles and bubbles on the radial distribution function. In the large-eddy simulations efforts, the dissertation addresses the importance of the subgrid fluctuations on the collisions frequency and investigates techniques for predicting those fluctuations. The cases studied are of particles-particles and particles-bubbles collisions at Reynolds number Re_λ = 96. A study is conducted first by neglecting the effects of subgrid velocity fluctuations on particles and bubbles motions. It is found that around Stokes number of unity solid particles of the same group undergo the well known preferential concentration as observed in the DNS. Effects of pressure gradient on the particles are negligible due to their small sizes. Bubbles as a low inertia particles are very sensitive to subgrid velocity and acceleration fields where the effects of pressure gradient in the carrier phase are dominant. However, particle-bubble radial distribution functions from LES are not as low as that from DNS. To account for the effects of subgrid field on the dispersion of particles and bubbles, a new multifractal methodology has been developed to construct a subgrid vorticity field from the resolved vorticity field in frame work of LES. A Poisson's solver is used to obtain the subgrid velocity field from the subgrid vorticity field. Accounting for the subgrid velocity fluctuations (but neglecting pressure gradient) produced minor changes in the radial distribution function for particle-particle and particle-bubble collisions. We conclude from this study that for accurate particle tracking in LES the subgrid velocity fluctuations must be dynamically realizable field (temporally and spatially correlated with the large scale motion). Adding random SGS velocity fluctuations is not enough to capture the correct radial distribution functions of dispersed phases especially for bubbles-particles collisions where the pressure gradient term ( or acceleration Du_f′/Dt) is responsible for particle-bubble segregation around particle Stokes number near one. A CFD-based model for minerals flotation machines has been developed in this dissertation. The objective of flotation models is to predict the recovery rate of minerals from a flotation cell. The developed model advances the state-of-the-art of pulp recovery rate prediction by incorporating validated theoretical collisions frequency models and detailed hydrodynamics from two-phase flow simulations. Spatial distributions of dissipation rate and air volume fraction are determined by the two-phase hydrodynamic simulations. Knowing these parameters throughout the machine is essential in understanding the effectiveness of different components of flotation machine (rotor, stator or disperser, jets) on the flotation efficiency. The developed model not only predicts the average pulp recovery rate but also it indicates regions of high/low recovery rates. The CFD-based flotation model presented here can be used to determine the dependence of recovery rate constant at any locality within the pulp based on particle diameter, particle specfic gravity, contact angle, and surface tension. / Ph. D.