A first principle flotation model has been derived from the basic mechanisms involved in the bubble-particle and bubble-bubble interactions occurring in flotation. It is a kinetic model based on the premise that the energy barrier (E1) for bubble-particle interaction can be reduced by increasing the kinetic energy (Ek) for bubble-particle interaction and by increasing the hydrophobic force in wetting films. The former is controlled by energy dissipation rate (𝜀), while the latter is controlled by collector additions. The model consists of a series of analytical equations to describe bubble generation, bubble-particle collision, attachment and detachment, froth recovery, and bubble coalescence in froth phase. Unlike other flotation models that do not consider role of hydrophobic force in flotation, the first principle model developed at Virginia Tech can predict flotation recoveries and grades from the chemistry parameters such as 𝜁-potentials, surface tension (𝛾), and contact angles (𝜃) that may represent the most critical parameters to control to achieve high degrees of separation efficiencies. The objectives of the present work are to i) validate the flotation model using the experimental data published in the literature, ii) incorporate a froth model that can predict bubble coarsening due to coalescence in the absence of particles, iii) develop a computer simulator for a froth model that can predict bubble coarsening in the presence of particles, and iv) study the effects of incorporating a regrinding mill and using a stronger collector in a large copper flotation circuit. The model validation has been made using the size-by-class flotation rate constants (kij) obtained from laboratory and pilot-scale flotation tests. Model predictions are in good agreement with the experimental data. It has been found that the flotation rate constants obtained for composite particles can be normalized by those for fully liberated particles (kmax), which opens the door for minimizing the number of flotation products that need to be analyzed using a costly and time-consuming liberation analyzer. A bubble coarsening froth model has been incorporated into the flotation model to predict flotation more accurately. The model has a limitation, however, in that it cannot predict bubble-coarsening in the presence of particles. Therefore, a new computer simulator has been developed to predict the effects of particle size and particle hydrophobicity on bubble coarsening in froth phase. In addition, the first principle flotation model has been used to simulate flotation circuits that are similar to the Escondida copper flotation plant to study the effects of incorporating a re-grinding mill and using a more powerful collector to improve copper recovery. The flotation model developed from first principles is useful for predicting and diagnosing the performance of flotation plants under different circuit arrangements and chemical conditions. / Master of Science

A first-principle flotation model was derived at Virginia Tech from the basic mechanisms involved in the bubble-particle and bubble-bubble interactions occurring in a flotation cell (Yoon and Mao, 1996; Sherrell and Yoon, 2005; Do, H, 2010). The model consists of a series of analytical equations for bubble generation, bubble-particle collision, attachment, detachment, and froth phase recovery. The process of bubble-particle attachment has been modelled on the premise that bubble-particle attachment occurs when the disjoining pressure of the thin liquid in a wetting films formed between particle and bubble is negative, as was first suggested by Laskowski and Kitchener (1969). These provisions allow for the flotation model to incorporate various chemistry parameters such as zeta-potentials, contact angles, surface tension in addition to the physical and hydrodynamic parameters such as particle size, bubble size, and energy dissipation rate. In the present work, the effects of both hydrodynamic and chemistry parameters have been studied using the model-based computer simulator. A series of laboratory batch flotation experiments carried out on mono-sized glass beads validated the simulation results. The flotation feeds were characterized in terms of particle size, contact angle, and Hamaker constant, and the flotation experiments were conducted at different energy dissipation rates, gas rates, froth heights. The flotation tests were also carried out on mixtures of hydrophobic silica and hydrophilic magnetite particles, so that the grades of the flotation products can be readily determined by magnetic separation. The experimental results are in good agreement with the model predictions both in terms of grade and recovery. / Master of Science

A flotation model has been proposed that is applicable in a turbulent environment. It is the first turbulent model that takes into account hydrodynamics of the flotation cell as well as all relevant surface forces (van der Waals, electrostatic, and hydrophobic) by use of the Extended DLVO theory. The model includes probabilities for attachment, detachment, and froth recovery as well as a collision frequency. A review of the effects fluids have on the flotation process has also been given. This includes collision frequencies, attachment and detachment energies, and how the energies of the turbulent system relate to them. Flotation experiments have been conducted to verify this model. Model predictions were comparable to experimental results with similar trends. Simulations were also run that show trends and values seen in industrial flotation systems. These simulations show the many uses of the model and how it can benefit the industries that use flotation. / Ph. D.

Flotation is a process of separating particulate materials of different surface properties in a hydrodynamic environment, and is used extensively for separating different minerals from each other in the mining industry. In this process, air bubbles are introduced at the bottom of a particulate suspension (pulp), so that bubbles coated with hydrophobic particles rise to the top and form a froth phase while hydrophobic particles stay in suspension. The selectivity of the flotation process is determined by the hydrophobicity of the particulate materials involved, while the kinetics of the process is controlled by the hydrodynamic conditions and the disjoining pressures in the thin aqueous films between air bubbles and particles. In the present work, a mathematical model for the flotation process has been developed by considering both the hydrodynamic and surface chemical parameters. The model can describe the events occurring in both the pulp and froth phases of a mechanically-agitated flotation cell. The pulp-phase model is based on predicting the kinetics of bubble-particle attachment using the DLVO extended to include contributions from hydrophobic force and the theory of turbulent collision. The froth-phase model is based on predicting the rate of bubble-particle detachment by considering bubble coarsening and water recovery. The predictions from the overall flotation model are in general agreement with the results obtained in single-bubble flotation experiments and the flotation test results reported in literature. Since the model has been developed largely from first principles, it has predictive and diagnostic capabilities. / Ph. D.