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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.

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.

Surface force measurements previously conducted with thiolated gold surfaces showed a decrease in excess film entropy (£GSf), suggesting that hydrophobic force originates from changes in the structure of the medium (water) confined between hydrophobic surfaces. As a follow-up to the previous study, surface force measurements have been conducted using an atomic force microscope (AFM) with hydrophobic silica surfaces at temperatures in the range of 10 to 40¢XC. The silica sphere and silica plate were treated by both chemisorption of octadecyltrichlorosilane (OTS) and physical adsorption of octadecyltrimethylammonium chloride (C18TACl). A thermodynamic analysis of the results show similar results for both of the samples, that both ""Sf and excess film enthalpy ("Hf) become more negative with decreasing thickness of the water layer between the hydrophobic surfaces and decreasing temperature. |"Hf | > |T"Sf| represents a necessary condition for the excess free energy change ("Gf ) to be negative and the hydrophobic interaction to be attractive. Thus, the results obtained with both the silylated and C18TACl-adosrbed silica surfaces in the present work and the thiolated gold suefaces reported before show hydrophobic forces originate from structural changes in the medium. Thermodynamic analysis of SFA force measurements obtained at various temperatures revealed that "Sf were much more negative in the shorter hydrophobic force ranges than in the longer ranges, indicating a more significant degree of structuring in the water film when the two hydrophobic surfaces are closer together. It is believed that the water molecules in the thin liquid films (TLFs) of water form clusters as a means to reduce their free energy when they cannot form H-bonds to neighboring hydrophobic surfaces. Dissolved gas molecules should enhance the stability of structured cluster due to the van der Waals force between the entrapped gas molecules and the surrounding water molecules1, which may enhance the strength of the hydrophobic force. Weaker long-range attractive forces detected in degassed water than in air-equilibrated water was found in the present work by means of AFM force measurements, supporting the effect of dissolved gas on the structuring of water. At last, temperature effects on hydrophobic interactions measured in ethanol and the thermodynamic analysis revealed similar results as those found in water, indicating that the hydrophobic force originates from H-bond propagated structuring in the mediums. / Ph. D.

Hydrophobic interaction plays an important role in biology, daily lives, and a variety of industrial processes such as flotation. While the mechanisms of hydrophobic interactions at molecular scale, as in self-assembly and micellization, is relatively well understood, the mechanisms of macroscopic hydrophobic interactions have been controversial. It is, therefore, the objective of the present work to study the mechanisms of interactions between macroscopic hydrophobic surfaces in H-bonding liquids, including water, ethanol, and water-ethanol mixtures. The first part of the present study involves the measurement of the hydrophobic forces in the thin liquid films (TLFs) confined between two identical hydrophobic surfaces of contact angle 95.3o using an atomic force microscope (AFM). The measurements are conducted in pure water, pure ethanol, and ethanol-water mixtures of varying mole fractions. The results show that strong attractive forces, not considered in the classical DLVO theory, are present in the colloid films formed with all of the H-bonding liquids tested. When an H-bonding liquid is confined between two hydrophobic surfaces, the vicinal liquid molecules form clusters in the TLFs and give rise to an attractive force. The cluster formation is a way to minimize free energy for the molecules denied of H-bonding with the substrates. Thus, solvophobic forces are the result of the antipathy between the CH2- and CH3-coated surface and H-bonding liquid confined in the film. A thermodynamic analysis of the solvophobic forces measured at different temperatures support this mechanism, in which solvophobic interactions entail decreases in the excess film enthalpy and entropy. The former represents the energy gained by building clusters, while the latter represents loss of entropy due to structure building. Thus, hydrophobic interaction may be a subset of solvophobic interaction. The solvophobic forces are strongest in pure water and pure ethanol, and decrease when one is added to the other. Adding a very small amount of ethanol to water sharply reduced the solvophobic force due to the adsorption of the former with an inverse orientation. An exposure of the OH-group toward the aqueous phase decreases the antipathy between the surface and H-bonding liquid and hence causes the hydrophobic (or solvophobic) forces to decrease. The second part of the study involves the measurement of the hydrophobic forces in the wetting films of water using the force apparatus for deformable surfaces (FADS). This new instrument recently developed at Virginia Tech is designed to monitor the deformation of bubbles to determine the surface forces in wetting films. In effect, an air bubble is used a force sensor. The measurements have been conducted with gold, chalcopyrite, and galena as substrates. The results obtained with all three minerals show that hydrophobic force increases with increasing water contact angle, suggesting that hydrophobic forces are inherent properties of hydrophobic surfaces rather than created from artifacts such as preexisting nanobubbles and/or cavitation. A utility of the intrinsic relationship between hydrophobic force and contact angle is to predict flotation kinetics from the hydrophobicity of the minerals of interest. / Ph. D.

In general, the stability of suspension can be studied using two methods. <i>One</i> is to directly measure the forces between two interacting surfaces in media. <i>The other</i> is to study the interfacial surface free energies of the particles in suspension. Direct surface force measurements were conducted between silica surfaces in octadecyltrimetylammonium chloride (C₁₈TACl) solutions using an Atomic Force Microscope (AFM). The results showed that the hydrophobic force existed in both air-saturated and degassed C₁₈TACl solutions. The attraction decreased with NaCl addition, and was the strongest at the point of charge neutralization (p.c.n.) of silica substrate. The force measurement results obtained in C_nTACl solutions showed that the attractions decayed exponentially and became the maximum at the p.c.n.'s. The decay lengths (<i>D</i>) increased with surfactant chain length. The measured forces were fitted to a charged-patch model of Miklavic <i>et al</i>. (1994) with rather large patch sizes. It was also found that the decay length decreased linearly with the effective concentration of the CH2/CH3 groups raised to the power of -1/2. This finding is in line with the model of Eriksson <i>et al</i>. (1989). It suggested that the long-range attractions are hydrophobic forces originating from the changes in water structure across a hydrophobic surface-solution interface. For the TiO₂/water/TiO₂ system, the Hamaker constant was found to be 4±1×10^-20 J. The force curves obtained in the TiO₂/C_nTACl system showed a repulsion-attraction-repulsion transition with increasing surfactant concentration. The long-range attraction observed between TiO₂ surfaces in C_nTACl solutions reached maximum at the p.c.n., and the decay length increased with chain length. In present work, the thin-layer wicking technique was used to determine the surface free energy (γ_s) and its components of talc samples. The results showed that the basal surfaces of talc are weakly basic while the edge surfaces are acidic. The effect of chemicals on the surface free energies of talc was systemically studied. The results showed that CMC (carboxymethyl cellulose sodium salt) and EO/PO (ethylene oxide/propylene oxide) co-polymers made talc surface hydrophilic by increasing the surface free energies, especially γ^LW and γ^-. SOPA (sodium polyacrylate) increased greatly the zeta-potentials instead of the surface free energies. / Ph. D.