Between two neighboring air bubbles in a froth (or foam), a thin liquid film (TLF) is formed. As the bubbles rise upwards, the TLFs thin initially due to the capillary pressure created by curvature changes. As the film thicknesses (H) reach approximately 200 nm, the disjoining pressure created by surface forces in the films also begins to control the film drainage rate and affect the waves motions at the air/water interfaces. If the disjoining pressure is negative, both the film drainage and the capillary wave motion accelerate. When the TLF thins to a critical film thickness (Hcr), the amplitude of the wave motion grows suddenly and the two air/water interfaces touch each other, causing the TLF to rupture and bubbles to coalesce. In the present work, a new model that can predict Hcr has been developed by considering the film drainage due to both viscous film thinning and capillary wave motion. Based on the Hcr model, bubble-coarsening in a dynamic foam has been predicted by deriving the geometric relation between the thickness of the lamella film, which controls bubble-coalescence rate, and the Plateau border area, which controls liquid drainage rate. Furthermore, a model for predicting bubble-coarsening in froth (3-phase foam) has been developed by developing a film drainage model quantifying the effect of particles on pc. The parameter pc is affected by the number of particles and the local capillary pressure around particles, which in turn vary with the hydrophobicity and size of the particles in the film. Assuming that films rupture at free films, the pc corrected for the particles in lamella films has been used to determine the critical rupture time (tcr), at which the film thickness reaches Hcr, using the Reynolds equation. Assuming that the number of bubbles decrease exponentially with froth height, and knowing that bubbles coalesce when film drains to a thickness Hcr, a bubble coarsening model has been developed. The model predictions are in agreement with the experimental data obtained using particle of varying hydrophobicity and size. / Ph. D.

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