The process of froth flotation relies on using air bubbles to collect desired mineral particles dispersed in aqueous media on the surface, while leaving undesirous mineral particles behind. For a particle to be collected on the surface of a bubble, the thin liquid films (or wetting films) of water formed in between must rupture. According to the Frumkin-Derjaguin isotherm, it is necessary that wetting films can rupture when the disjoining pressures are negative. However, the negative disjoining pressures are difficult to measure due to the instability and short lifetimes of the films. In the present work, two new methods of determining negative disjoining pressures have been developed. One is to use the modified thin film pressure balance (TFPB) technique, and the other is to directly determine the interaction forces using the force apparatus for deformable surfaces (FADS) developed in the present work. The former is designed to obtain spatiotemporal profiles of unstable wetting films by recording the optical interference patterns. The kinetic information derived from the spatiotemporal profiles were then used to determine the disjoining pressures using an analytical expression derived in the present work on the basis of the Reynolds lubrication theory. The technique has been used to study the effects of surface hydrophobicity, electrolyte (Al3+ ions) concentration, and bubble size on the stability of wetting films. Further, the geometric mean combining rule has been tested to see if the disjoining pressures of the wetting films can be predicted from the disjoining pressures of the colloid films formed between two hydrophobic surfaces and the disjoining pressures of the foam films formed between two air bubbles. The FADS is capable of directly measuring the interaction forces between air bubble and solid surface, and simultaneously monitoring the bubble deformation. The results were analyzed using the Reynolds lubrication theory and the extended DLVO theory to determine both the hydrodynamic and disjoining pressures. The FADS was used to study the effects of surface hydrophobicity and approach speeds. The results show that hydrophobic force is the major driving force for the bubble-particle interactions occurring in flotation. / Ph. D.

Thin liquid films (TLFs) of water are ubiquitous in daily lives as well as in many industrial processes. They can be formed between two identical phases, as in colloid films between two macroscopic surfaces and foam films between two air bubbles; and between two dissimilar phases, as in wetting films. Stability of the colloids, foams, and wetting films is determined by the surface forces in the TLFs. Depending on the nature of the surfaces involved, the stabilities can be predicted using combinations of three different forces, i.e., the van der Waals, electrical double layer (EDL), and hydrophobic forces. The objective of the present work is to study the roles of these forces in determining the stabilities of the TLFs of water confined between i) an air bubble and a hydrophobic surface and ii) an oil drop and a hydrophobic surface, with particular interest in studying the role of the hydrophobic force. The first part of the study involves the measurement of the surface forces in the TLFs confined between bitumen drops and mineral surfaces. Deformation of bitumen drops has been monitored by interferometry while it approaches a flat surface. By analyzing the spatiotemporal film profiles, both the capillary and hydrodynamic forces have been calculated using the Young-Laplace equation and the Reynolds lubrication approximation, respectively, with the surface forces being determined by subtracting the latter from the former. The results are useful for better understanding the effects of electrolyte and pH on bitumen liberation and recovery by flotation and for developing a filtration model from first principles. The second part of the study involves the surface force measurement in wetting (flotation) films. Surface forces in the TLFs of water on silica surfaces have been measured using the force apparatus for deformable surfaces (FADS) using an air bubble as a force sensor. The measurements have been conducted in the presence of various cationic surfactants such as dodecylamine hydrochloride (DAH), and alkyltrimethylammonium chloride (CnTACl), electrolytes, and polymers. The results show that film stability and hence the kinetics of film thinning can be greatly improved by the control of bubble ζ-potentials, whose role in flotation has long been neglected in flotation studies. Force measurements have also been conducted in the TLFs of water confined between oil drops and hydrophobic surfaces. Stability of this type of film plays an important role in a process of using oil drops rather than air bubbles to collect hydrophobic particles from aqueous phase. The force measurements conducted in the present work show that hydrophobic forces are much stronger in water films formed between oil drops and hydrophobic surfaces than in water films formed between air bubbles and hydrophobic surfaces, which can be attributed to the differences in the Hamaker constants involved. / Doctor of Philosophy / When two macroscopic surfaces in water are brought to a close proximity, a thin liquid film (TLF) is formed in between, with its stability being determined by the surface forces present in the film. TLFs are ubiquitous in daily lives and play a decisive role in many industrial processes such as mineral flotation, food processing, oil extraction, heat transfer, etc. In the present work, the surface forces present in wetting films have been measured by approaching an air bubble (or an oil drop) slowly toward a flat surface while monitoring the curvature changes during film thinning by interferometry and calculating the capillary forces using the Young-Laplace equations. By analyzing the results in view of the Frumkin-Derjaguin isotherm and the extended DLVO theory, it was possible to determine the changes in the van der Waals, electrical double-layer (EDL), and hydrophobic forces during film thinning. The results show that both the EDL and the long-range component of the hydrophobic force control the kinetics of film thinning and rupture while the contact angle formation is controlled by the van der Waals force and the short-range hydrophobic force. It has been found also that n-alkane drops form substantially larger contact angles than air bubbles on a hydrophobic surface due to the fact that the van der Waals force is attractive in the drop-surface interactions while the same is repulsive in the bubble-surface interactions. These observations have a profound implication in flotation, that is, oil drops can recover hydrophobic particles from an aqueous phase better than air bubbles.

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.

I started writing this thesis not only to obtain a doctoral degree, but also to compile in a particular way all the work that I have done during this time. The articles published during these years can only give a short overview of my research task. I decided to give my own perspective of the things I have learned and the results I have obtained. Some sections are directly the published articles, but some other are not and contain a significant amount of unpublished data. Even in some cases the published plots have been modified / altered to provide more insight or to maintain consistency. Historical perspectives often provide a deep understanding of the problems and have been briefly discussed in some chapters. This thesis contains theoretical and computer simulation studies to under-stand effects of spatial correlation on dynamics in several complex systems. Based on the different phenomena studied, the thesis has been divided into three major parts: I. Pair hydrophobicity, composition-dependent anomalies and structural trans-formations in aqueous binary mixtures II. Microscopic analysis of hydrophobic force law in a two dimensional (2D) water-like model system III. Diffusion of a tagged particle on a rugged energy landscape with spatial correlations The three parts have been further divided into ten chapters. In the following we provide part-wise and chapter-wise outline of the thesis. Part I consists of six chapters, where we focus on several important aqueous binary mixtures of amphiphilic molecules. To start with, Chapter 1 provides an introduction to non-ideality often encountered in aqueous binary mixtures. Here we briefly discuss the existing ideas of structural transformations associated with solvation of a foreign molecule in water, with particular emphasis on the classic “iceberg” model. Over the last decade, several investigations, especially neutron scattering and diffraction experiments, have questioned the validity of existing theories and have given rise to an alternate molecular picture involving micro aggregation of amphiphilic co-solvents in their aqueous binary mixtures. Such microheterogeneity was also supported by other experiments and simulations. In Chapter 2, we present our calculation of the separation dependence of potential of mean force (PMF) between two methane molecules in water-dimethyl sulfoxide (DMSO) mixture, using constrained molecular dynamics simulation. It helps us to understand the composition-dependence of pair hydrophobicity in this binary solvent. We find that pair hydrophobicity in the medium is surprisingly enhanced at DMSO mole fraction xDMSO ≈ 0.15, which explains several anomalous properties of this binary mixture – including the age-old mystery of DMSO being a protein stabilizer at lower concentration and protein destabilizer at higher concentration. Chapter 3 starts with discussion of non-monotonic composition dependence of several other properties in water-DMSO binary mixture, like diffusion coefficient, local composition fluctuation and fluctuations in total dipole moment of the system. All these properties exhibit weak to strong anomalies at low solute concentration. We attempt to provide a physical interpretation of such anomalies. Previous analyses often suggested occurrence of a “structural transformation” (or, microheterogeneity) in aqueous binary mixtures of amphiphilic molecules. We show that this structural transformation can be characterized and better understood under the purview of percolation theory. We define the self-aggregates of DMSO as clusters. Analysis of fractal dimension and cluster size distribution with reference to corresponding “universal” scaling exponents, combined with calculation of weight-averaged fraction of largest cluster and cluster size weight average, reveal a percolation transition of the clusters of DMSO in the anomalous concentration range. The percolation threshold appears at xDMSO ≈ 0.15. The molecular picture suggests that DMSO molecules form segregated islands or micro-aggregates at concentrations below the percolation threshold. Close to the critical concentration, DMSO molecules start forming a spanning cluster which gives rise to a bi-continuous phase (of water-rich region and DMSO-rich region) beyond the threshold of xDMSO ≈ 0.15. This percolation transition might be responsible for composition-dependent anomalies of the binary mixture in this low concentration regime. Similar phenomenon is observed for another amphiphilic molecule – ethanol, as discussed in Chapter 4. We again find composition dependent anomalies in several thermophysical properties, such as local composition fluctuation, radial distribution function of ethyl groups and self-diffusion co-efficient of ethanol. Earlier experiments often suggested distinct structural regimes in water-ethanol mixture at different concentrations. Using the statistical mechanical techniques introduced in the previous chapter, we show that ethanol clusters undergo a percolation transition in the anomalous concentration range. Despite the lack of a precise determination of the percolation threshold, estimate lies in the ethanol mole fraction range xEtOH ≈ 0.075 - 0.10. This difficulty is probably due to transient nature of the clusters (as will be discussed in Chapter 6) and finite size of the system. The scaling of ethanol cluster size distribution and the fractal behavior of ethanol clusters, however, conclusively demonstrate their “spanning” nature. To develop a unified understanding, we further study the composition-dependent anomalies and structural transformations in another amphiphilic molecule, tertiary butyl alcohol (TBA) in Chapter 5. Similar to the above-mentioned aqueous binary mixtures of DMSO and ethanol, we demonstrate here that the anomalies occur due to local structural changes involving self-aggregation of TBA molecules and percolation transition of TBA clusters at xTBA ≈ 0.05. At this percolation threshold, we observe a lambda-type divergence in the fluctuation of the size of the largest TBA cluster, reminiscent of a critical point. Interestingly, water molecules themselves exhibit a reverse percolation transition at higher TBA concentration ≈ 0.45, where large spanning water clusters now break-up into small clusters. This is accompanied by significant divergence of the fluctuations in the size of the largest water cluster. This second transition gives rise to another set of anomalies around. We conclude this part of the thesis with Chapter 6, where we introduce a novel method for understanding the stability of fluctuating clusters of DMSO, ethanol and TBA in their respective aqueous binary mixtures. We find that TBA clusters are the most stable, whereas ethanol clusters are the most transient among the three representative amphiphilic co-solvents. This correlates well with the amplitude of anomalies observed in these three binary mixtures. Part II deals with the topic of hydrophobic force law in water. In the introductory Chapter 7 of this part, we briefly discuss the concept of hydrophobicity which is believed to be of importance in understanding / explaining the initial processes involved in protein folding. We also discuss the experimental observations of Israelachvili (on the force between hydrophobic plates) and the empirical hydrophobic force law. We briefly touch upon the theoretical back-ground, including Lum-Chandler-Weeks theory. We conclude this chapter with a brief account of relevant and important in silico studies so far. In Chapter 8, we present our studies on Mercedes-Benz (MB) model – a two dimensional model system where circular disks interact with an anisotropic potential. This model was introduced by Ben-Naim and was later parametrized by Dill and co-workers to reproduce many of the anomalous properties of water. Using molecular dynamics simulation, we show that hydrophobic force law is indeed observed in MB model, with a correlation length of ξ=3.79. The simplicity of the model enables us to unravel the underlying physics that leads to this long range force between hydrophobic plates. In accordance with Lum-Chandler-Weeks theory, density fluctuation of MB particles (leading to cavitation) between the hydrophobic rods is clearly distinguishable – but it is not sufficiently long ranged, with density correlation extending only up to ζ=2.45. We find that relative orientation of MB molecules plays an important role in the origin of the hydrophobic force in long range. We define appropriate order parameters to capture the role of orientation, and briefly discuss a plausible approach of an orientation-dependent theory to explain this phenomenon. Part III consists of two chapters and focuses on the diffusion of a Brownian particle on a Gaussian random energy landscape. We articulate the rich history of the problem in the introductory Chapter 9. Despite broad applicability and historical importance of the problem, we have little knowledge about the effect of ruggedness on diffusion at a quantitative level. Every study seems to use the expression of Zwanzig [Proc. Natl. Acad. U.S.A, 85, 2029 (1988)] who derived the effective diffusion coefficient, Deff =D0 exp (-β2ε2 )for a Gaussian random surface with variance ε, but validity of the same has never been tested rigorously. In Chapter 10, we introduce two models of Gaussian random energy surface – a discrete lattice and a continuous field. Using computer simulation and theoretical analyses, we explore many different aspects of the diffusion process. We show that the elegant expression of Zwanzig can be reproduced ex-actly by Rosenfeld diffusion-entropy scaling relationship. Our simulations show that Zwanzig’s expression overestimates diffusion in the uncorrelated Gaussian random lattice – differing even by more than an order of magnitude at moderately high ruggedness (ε>3.0). The disparity originates from the presence of “three-site traps” (TST) on the landscape – which are formed by deep minima flanked by high barriers on either side. Using mean first passage time (MFPT) formalism, we derive an expression for the effective diffusion coefficient, Deff =D0 exp ( -β2ε2)[1 +erf (βε/2)]−1 in the presence of TSTs. This modified expression reproduces the simulation results accurately. Further, in presence of spatial correlation we derive a general expression, which reduces to Zwanzig’s form in the limit of infinite spatial correlation and to the above-mentioned equation in absence of correlation. The Gaussian random field has an inherent spatial correlation. Diffusion coefficient obtained from the Gaussian field – both by simulations and analytical methods – establish the effect of spatial correlation on random walk. We make special note of the fact that presence of TSTs at large ruggedness gives rise to an apparent breakdown of ergodicity of the type often encountered in glassy liquids. We characterize the same using non-Gaussian order parameter, and show that this “breakdown” scales with ruggedness following an asymptotic power law. We have discussed the scope of future work at the end of each chapter when-ever appropriate.

In the present work, novel dewatering aids and a novel centrifuge configuration were developed and applied for the purpose of dewatering fine particles. Three different types dewatering reagents were tested in different filtration and centrifugation units. These chemicals included low-HLB surfactants, naturally occurring lipids, and modified lipids. Most of these reagents are insoluble in water; therefore, they were used in solutions of appropriate solvents, such as light hydrocarbon oils and short-chain alcohols. The role of these reagents was to increase the hydrophobicity of the coal and selected mineral particles (chalcopyrite, sphalerite, galena, talc, clay, phosphate, PCC and silica) for the dewatering. In the presence of these reagents, the water contact angles on the coal samples were increased up to 90o. According to the Laplace equation, an increase in contact angle with the surfactant addition should decrease the capillary pressure in a filter cake, which should in turn increase the rate of dewatering and help reduce the cake moisture. The use of the novel dewatering aids causes a decrease in the surface tension of water and an increase in the porosity of the cake, both of which also contribute to improved dewatering. A series of batch-scale dewatering tests were conducted on a variety of the coal and mineral samples using the novel dewatering aids. The results obtained with a Buchner funnel and air pressure filters showed that cake moistures could be reduced substantially, the extent of which depends on the particle size, cake thickness, drying time, reagent dosage, conditioning time, reagent type, sample aging, water chemistry, etc. It was determined that use of the novel dewatering aids could reduce the cake formation time by a significant degree due to the increased kinetics of dewatering. At the same time, the use of the dewatering aids reduced the cake moistures by allowing the water trapped in smaller capillaries of the filter cake. It was found that final cake moistures could be reduced by 50% of what can be normally achieved without using the reagents. However, the moisture reduction becomes difficult with increasing cake thickness. This problem can be minimized by applying a mechanical vibration to the cake, spraying a short-chain alcohol on the cake and by adding a small amount of an appropriate coagulant, such as alum and CaCl2 to the coal and mineral slurries. The novel dewatering aids were also tested using several different continuous filters, including a drum filter, disc filter and horizontal belt filter (HBF). The results obtained with these continuous filtration devices were consistent with those obtained from the batch filters. Depending on the coal and mineral samples and the type of the reagent, 40 to 60% reductions in moisture were readily achieved. When using vacuum disc filters, the cake thickness increased substantially in the presence of the novel dewatering aids, which could be attributed to the increased kinetics of dewatering. A dual vacuum system was developed in the present work in order to be able to control the cake thickness, which was necessary to achieve lower cake moistures. It was based on using a lower vacuum pressure during the cake formation time, while a full vacuum pressure was used during the drying cycle time. Thus, use of the dual vacuum system allowed the disc filter to be used in conjunction with the novel dewatering aids. Its performance was similar to that of HBF, which is designed to control cake thickness and cake formation time independently. The effectiveness of using the novel dewatering aids were also tested in a full-continuous pilot plant, in which coal samples were cleaned by a flotation column before the flotation product was subjected to the disc filter. The tests were conducted with and without using novel dewatering aids. These results were consistent with those obtained from the laboratory and batch-scale tests. The novel centrifuge developed in the present work was a unit, which combined a gravity force and air pressure. The new centrifuge was based on increasing the pressure drop across the filter cake formed on the surface of the medium (centrifuge wall). This provision made it possible to take advantage of Darcy s law and improve the removal of capillary water, which should help lower the cake moisture. A series of tests were conducted on several fine coal and mineral particles and obtained more than 50% moisture reduction even at very fine particle size (2 mm x 0). Based on the test results obtained in the present work, two proof-of-concept (POC) plants have been designed. The first was for the recovery of cyclone overflows that are currently being discarded in Virginia, and the other was for the recovery of fines from a pond in southern West Virginia. The former was designed based on the results of the plant tests conducted in the present work. Cost vs. benefit analyses were conducted on the two POC plants. The results showed very favorable internal rates of return when using the novel dewatering aids. Surface chemistry studies were conducted on the coal samples based on the results obtained in the present investigation. These consisted mainly of the surface characterization of the coal samples (surface mineral composition, surface area, zeta potential, x-ray photoelectron microscopy (XPS)), acid-base interactions of the solids and liquids, dewatering kinetic tests, contact angle measurements of the coal samples and surface force measurements using AFM. In addition, carbon coating on a silica plate using palsed laser deposition (PLD) and Langmuir-Blodgett (LB) film deposition tests were conducted on the sample to better understand the surfactant adsorption and dewatering processes. The test results showed that the moisture reductions on the fine particles agree well with the surface chemistry results. / Ph. D.