The extended DLVO theory was used to develop a flotation model by considering both hydrodynamic and surface forces involved in the process. A stream function was used to estimate the kinetic energies for thinning the water films between bubbles and particles, which were compared with the energy barriers, created by surface forces, to determine the probability of adhesion. A general expression for the probability of detachment was derived from similar mechanism for chemical reaction, and the kinetic energy for detachment was estimated with French and Wilson's model. The hydrophobic force parameter (K132) calculated from the rate constants of single bubble flotation tests showed that, K132 for bubble-particle interaction were close to the geometric means of K131 for particle-particle interactions and K232 for bubble-bubble interaction, indicating that the combining rules developed for dispersion forces may be useful for hydrophobic forces. The model was used to predict flotation results as functions of several important parameters such as contact angle, double-layer potentials, particle size, bubble size, etc. The predictions were consistent with experience, and could be explained in view of the various subprocesses considered in the model development. Furthermore, the model suggested optimum conditions for achieving the maximum separation efficiency. The extended DLVO theory was also used to determine the hydrophobic force between two oil/solution interfaces from the equilibrium film thicknesses of dodecylammonium chloride (RNH3Cl) solutions obtained using Thin Film Balance (TFB) technique. The results showed that, the oil droplets were inherently hydrophobic, and the hydrophobic force played an important role in the stability of emulsions. This force decreased with increasing surfactant concentration, and also changed with pH and the addition of electrolyte. The interfacial area occupied by molecules indicated that, the dodecane molecules might present between two surfactant ions at interface, thus the hydrophobicity of oil/solution interface was less sensitive to the addition of the surfactant than that of air/solution interface. Thermodynamic analysis suggested that, there might exist a relationship between the interfacial hydrophobicity and the interfacial tension. / Ph. D.

Flotation is regarded as the best available separation method for the recovery of valuable minerals such as chalcopyrite (CuFeS2), sphalerite (ZnS), etc., from mined ores. Practically all metals humans use today are produced by flotation. The process relies on controlling the stability of the thin liquid films (TLFs) of water formed between minerals and air bubbles (wetting film), air bubbles (foam film), and mineral particles (colloid films). In flotation, a desired mineral is rendered hydrophobic by surfactant coating as a means to destabilize the TLFs, so that they can be attached to the hydrophobic air bubbles. A TLF ruptures when the disjoining pressure (or surface forces per unit area) of the film becomes negative, i.e., Π < 0. Thermodynamically, a wetting film can rupture when the contact angle (θ) of a mineral surface is larger than zero. It would, therefore, be reasonable to consider the roles of the surface forces to better understand the fundamental mechanisms involved in flotation. The surface forces considered in the present work included the electric double layer (EDL), van der Waals (vdW), and attractive hydrophobic (HP) forces. A flotation model has been developed by using the hydrophobic force as a kinetic parameter, which made it possible to track the fates of mineral particles of different of size, surface liberation, and contact angle to predict both recovery and grades for the first time. The model has been validated against the plant survey data obtained from an operating copper flotation plant. The simulation results obtained using the first principles model have been utilized to address the limitations of current flotation practices. One such limitation is the presence of slow-floating target minerals present in the cleaner-scavenger tails (CST) that are routinely recycled back to the rougher flotation bank as circulating loads (CLs) to allow longer retention times for the slow-floating particles for additional recovery. The simulation results show also that opening a flotation circuit by treating the CST streams separately in an advanced circuit can substantially improve the plant performance. One of the major limitations of flotation is that the coarse particles in a feed stream are difficult to recover due to the low hydrophobicity associated with poor surface liberation. A new flotation model developed in the present work suggests various ways to address the problem. One is to increase the hydrophobicity of the composite (poorly liberated) particles using the Super Collectors that can increase the contact angles to 150 -170o. Simulation results obtained using the model developed in the present work show significant financial benefits of using Super Collectors. Flotation is controlled by surface forces as noted above. As particle size becomes larger than 150 µm, however, the gravitational force comes into the picture and can override the surface forces. A new flotation cell has been developed to mitigate the effects of the extraneous force by decreasing the effective specific gravity (SG) by attaching air bubbles to facilitate levitation and by creating a pulsation to allow particles to move according to SGs independent of particle size, which should help increase the upper particle size limit of flotation. Surface forces in foam and oil-in-water emulsion films have been measured at different temperatures to determine the changes in thermodynamic properties of the thin liquid films (TLFs) of water confined between two bubbles and two oil drops. The results show that the films are destabilized by the attractive hydrophobic forces created during the course of building H-bonded structures in confined spaces, which entails decreases in enthalpy (H < 0) and entropy (TS < 0), the second term representing the thermodynamic cost of building the structures. / Doctor of Philosophy / Flotation is a kinetic process designed to separate valuable minerals from mined ores. This process depends on several hydrodynamic and surface chemistry parameters making it hard to model. A U.S. patent was awarded to Sulman and Picard in 1905 for using air bubbles to selectively collect hydrophobic particles from the aqueous phase, leaving hydrophilic particles behind. Since then, the separation process known as flotation has been used to produce practically all metals humans use. Many investigators developed flotation models using hydrodynamic parameters, e.g., particle size, bubble size, energy dissipation rate, etc., but without a reference to particle hydrophobicity. Therefore, the models were successful in predicting recoveries but not product grades. Derjaguin and Dukhin (1961) were the first to model flotation using surface forces but without due consideration of the role of hydrophobic force in flotation. Therefore, it also failed to predict product grades. In the current work, a new flotation model has been developed using the hydrophobic force as a kinetic parameter. This approach made it possible to predict both recoveries and grades for the first time. The model has been reduced to a simple form mimicking the Arrhenius equation so that it can be used to delineate the different conditions required for optimizing coarse and fine particle flotation. The model has been derived by considering the surface forces in the thin liquid films (TLFs) of water confined between bubbles, and bubbles and particles. It has been found that the hydrophobic force plays a decisive role in destabilizing a wetting film and inducing bubble-particle attachment. The surface forces measured in the present work show that the hydrophobic interactions in macroscopic scales are controlled by enthalpy rather than entropy, which is contrary to the nanoscale hydrophobic interactions. The model has been validated against a full-scale plant operation and demonstrated predictive capabilities. The simulation results have been analyzed to determine the limitations of the current flotation practices. It was found that coarse particle flotation is difficult either due to the presence of composite particles reducing the particle contact angle or due to their poor hydrodynamic properties. Utilizing the insights from the model, various methods of alleviating these limitations have been developed and presented in the current work. References Derjaguin, B.V., Dukhin, S.S., 1961. Theory of flotation of small and medium-size particles. Inst. Min. Metall. 241–267. Sulman, H.L., and Kirkpatrick-Picard (1905). U.S. Patent No. 793,808.