Wetting of a substance has been widely investigated since it has many applications to many different fields. Wetting principles can be applied to better select cleans for front end of line (FEOL) and back end of line (BEOL) cleaning processes. These principles can also be used to help determine processes that best repel water from a semiconductor device. It is known that the value of the dielectric constant in an insulator increases when water is absorbed. These contact angle experiments will determine which processes can eliminate water absorption. Wetting is measured by the contact angle between a solid and a liquid. It is known that roughness plays a crucial role on the wetting of a substance. Different surface groups also affect the wetting of a surface. In this work, it was investigated how wetting was affected by different solid surfaces with different chemistries and different roughness. Four different materials were used: silicon; thermally grown silicon dioxide on silicon; chemically vapor deposited (CVD) silicon dioxide on silicon made from tetraethyl orthosilicate (TEOS); and organosilicate glass (OSG) on silicon. The contact angle of each of the samples was measured using a goniometer. The roughness of the samples was measured by atomic force microscopy (AFM). The chemistry of each of the samples were characterized by using X-ray photoelectron spectroscopy (XPS) and grazing angle total attenuated total reflection Fourier transform infrared spectroscopy (FTIR/GATR). Also, the contact angle was measured at the micro scale by using an environmental scanning electron microscope (ESEM).

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The contact angle defined by Young's equation depends on the ratio between solid and liquid surface energies. Young's contact angle is constant for a given system, and cannot explain the stability of fluid droplets in capillary tubes. Within this framework, large variations in contact angle and explained aassuming surface roughness, heterogeneity or contamination. This research explores the static and dynamic behavior of fluid droplets within capillary tubes and the variations in contact angle among interacting menisci. Various cases are considered including wetting and non-wetting gluids, droplets in inclined capillary tubes or subjected to a pressure difference, within one-dimensional and three-dimensional capillary systems, and under static or dynamic conditions (either harmonic fluid pressure or tube oscillation). The research approach is based on complementary analytical modeling (total energy formulation) and experimental techniques (microscopic observations). The evolution of meniscus curvatures and droplet displacements are studied in all cases. Analytical and experimental results show that droplets can be stable within capillary tubes even under the influence of an external force, the resulting contact angles are not constant, and bariations from Young's contact angle aare extensively justified as menisci interaction. Menisci introduce stiffness, therefore two immiscible Newtonian fluids behave as a Maxwellian fluid, and droplets can exhibit resonance or relaxation spectral features.

Bloodstain pattern analysis has been used in criminal investigations for more than 100 years. It provides valuable information about the events that took place prior to the formation of bloodstains at a crime scene. Forensic scientists use empirical laws to make a deduction from bloodstains, but the validity of these conclusions has been challenged in courts due to a lack of understanding of the underlying fluid mechanics. With this motivation, this thesis illustrates how mathematical modeling and numerical simulation can help gain insight into the spreading of blood droplets which eventually leads to the formation of a bloodstain. Understanding the fluid mechanics of droplet spreading and sliding has been accomplished with the help of the lubrication approximation which simplifies the Navier-Stokes equations to a more tractable form, i.e. a coupled set of non-linear partial differential equations. The resulting highly non-linear coupled set of equations is discretized using Finite-Difference. The resulting algebraic system is solved via an efficient Multigrid algorithm. These equations are modified to understand the effects of contact angle hysteresis, fluid rheology and absorptive properties of substrates on sliding dynamics. Variations in the inclination of the substrate cause the droplets to attain different advancing and receding contact angles as they slide down the incline under gravitational pull. This work explores a new way to introduce contact angle hysteresis in the numerical simulation to predict the different phases of a sliding droplet. Experiments of fluid droplet spreading/sliding on inclined surfaces have been performed to measure the terminal sliding velocity. A simplified hysteresis model has been proposed. This model automatically locates the section of the contact line which is advancing and the section which is receding which enables the application of the contact angles for the advancing and receding fronts and therefore takes into account contact angle hysteresis. A simplified analytical model is also suggested for droplets moving down the incline with near circular footprints. With the inclusion of the contact angle hysteresis, simulation results were brought in closer agreement with the experimental ones and the results from both were compared with the results from the analytical model. Blood is a shear-thinning fluid. One of the main objectives of this study is to investigate numerically the effect on the spreading and/or sliding of non-Newtonian fluid droplets on surfaces. To achieve this, the effect of rheology on the leveling of thin fluid films on horizontal solid substrates is first investigated as a preliminary investigation since this problem does not involve a contact line and is therefore more tractable. A mathematical model based on the lubrication approximation which defines non-Newtonian rheology using a power-law model is presented. Results for the leveling of sinusoidal perturbations of the fluid film highlight important differences between the leveling of shear-thinning and shear-thickening fluids. Namely, the onset of leveling occurs earlier for the shear-thinning fluid than for the shear-thickening one. However, the rate of leveling is higher for the shear-thickening fluid than the shear-thinning one. An important aspect of this part of the work is the verification of the numerical implementation using the Method of Manufactured Solutions (MMS). This leveling study also highlights differences between the leveling of two-dimensional and three-dimensional perturbations. This verified numerical formulation is then used to study the effects of rheology on the spreading/sliding of droplets. Results for the spreading of fully wetting droplets on a horizontal substrate show that, for all other quantities being equal, an increase of the flow index leads to a more rapid wetting. It also shows that, even for non-Newtonian fluids, the droplet velocity asymptotes to a constant value when sliding down an inclined substrate. This terminal velocity is strongly dependent on the rheological parameters and as it is reached, the droplets travel with a visibly constant profile. Finally, the numerical simulations revealed the formation of a tail at the rear of the droplet as it slides down the incline plane in the case of shear-thickening fluids. Finally, a more complex dynamics of fluid being absorbed in a porous substrate as it slides/spreads is considered. A mathematical model based on the lubrication approximation which defines the absorptive property of a substrate using a Darcy’s model is presented. This numerical model is verified with the help of comparison between the analytical and numerical solutions for the absorption of thin film on horizontal porous substrates. Results show that physical properties of the substrates, i.e. permeability, porosity, capillary pressure and equilibrium contact angle affect the rate of absorption of the fluid. Adding inclination to the problem, introduces the gravitational pull in the absorption dynamics. This directly shows its effects on the footprints formed inside the porous substrates. The following papers, based on sections of this thesis, have appeared or been accepted for publication: - Ahmed, G., Sellier, M., Lee, Y., Jermy, M., and Taylor, M. (2013). Modeling the spreading and sliding of power-law droplets. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 432:2–7. - Ahmed, G., Sellier, M., Lee, Y., Jermy, M., and Taylor, M. (2014). Rheological effects on the leveling dynamics of thin fluid films. Accepted for publication in the International Journal of Numerical Methods for Heat and Fluid Flow. - Ahmed, G., Sellier, M., Jermy, M., and Taylor, M. (2014). Modelling the effects of contact angle hysteresis on sliding of droplets on inclined surfaces. Submitted for peer review in The European Journal of Mechanics - B/Fluids.

Capillarity is a physical phenomenon that acts as a driving force in the displacement of one fluid by another within a porous medium. This mechanism operates on the micro and nanoscale, and is responsible for countless observable events. This can include applications such as absorption in various hygiene products, self-cleaning surfaces such as water beading up and rolling off a specially-coated windshield, anti-icing, and water management in fuel cells, among many others. The most significant research into capillarity has occurred within the last century or so. Traditional formulations for fluid absorption include the Lucas–Washburn model for porous media, which is a 1-D model that reduces a porous medium to a series of capillary tubes of some educated equivalent radius. The Richards equation allows for modeling fluid saturation as a function of time and space, but requires additional information on capillary pressure as a function of saturation (pc(S)) in order to solve for absorption. In both approaches, the surface can only possess one fluid affinity. This thesis focuses on developing capillary models necessary for predicting fluid absorption and repulsion in fibrous media. Some of the work entails utilizing approximations based on pore space available to the fluid, which allows for capillary pressure simulation in media with arbitrary fiber orientation. This thesis also presents models for tracking the fluid interface in fibrous media and coatings with simpler geometries such as horizontally and vertically aligned fibers and orthogonal fiber layers. This method hinges on solving for the true fluid interface shape between the fibers based on the balance of forces across it, ensuring the accurate location and total content of fluid in the medium, and therefore accurate pc(S). Using this approach also allows, for the first time, fibers of different fluid affinities to exist in the same structure, to examine their combined influence on fluid behavior. The models in this thesis focus mainly on absorbent fabrics and superhydrophobic coatings, but can be easily expanded for use in other applications such as water filtration from fuel, fluid transport and storage in microchannels, polymer impregnation in fiber-reinforced composite materials, among countless others.

Polystyrene (PS) fiber mats incorporating iron (Fe) particles were fabricated by electrospinning and the hydrophobicity of the resulting magnetic fabrics was investigated with and without an applied magnetic field. The results show that the hydrophobicity (as measured using water droplet contact angle) increases in the presence of a magnetic field and the hysterisis in the advancing/receding contact angle (a measure of the stickiness of the surface) decreases in the presence of a magnetic field. It is also shown that the contact angle and hysterises increase with decreasing fiber diameter and mat thickness.

The interest in superhydrophobic coatings have increased exponentially in the recentdecades due to their potential and versatility in their applications. The use forsuperhydrophobic surfaces range from water repellent fabric, to self cleaning surfacesand numerous applications in industry. In this project the durability of 6 differentsuperhydrophobic coatings have been examined. The durability was tested bydropping sand on the surfaces from a set hight of 10 cm and a flow of 40 g/min. Thesurfaces were mounted on a 45° angle. The surfaces were abraded for 30 seconds ata time and the static, receding, and advancing contact angles along with the roll-ofangle was measured. Five of the surfaces were built up with nano particles and onewas sand blasted and anodized to create a superhydrophobic structure. The surfacesthat withstood the most abrasion was the surface that had been calcined to improveadhesion and the surface that had been sand blasted and anodized. Measurementsshowed that the roll-off angle and the receding contact angle were the two bestindicators of the deterioration of a surface, while the static contact angle and theadvancing contact angle varied little with abrasion. The project was done at thecompany Technical Research Institute of Sweden (SP) at their chemistry, surfaces andmaterials department in Stockholm. All coatings and equipment was supplied by SP.

"The temperature dependence of the contact angle of water on graphite, silicon and gold was investigated under various conditions to test the Sharp-Kink Approximation. Despite correctly predicting the contact angle at room temperature, the ideal Sharp-Kink Approximation was not found to accurately describe the contact angle's temperature dependence. The discrepancies from the predicted contact angle were characterized in terms of a correction H(T) to the liquid-solid surface tension. H(T) was found to be linear in temperature and decreasing, and is consistent with electrostatic charge effects."

Este trabalho aborda a molhabilidade de apatita por água em temperatura ambiente (20-25°C) objetivando contribuir para um melhor entendimento de seu comportamento em sistemas de flotação. Água, devido às fortes forças atrativas entre suas moléculas, não espalha completamente sobre sólidos de baixa energia como apatita pré-tratada com surfatantes aniônicos de cadeia longa. Este comportamento é explorado por engenheiros de processamento mineral para separar apatita de minerais de ganga via flotação aniônica direta em circuitos industriais ao redor do mundo. Nesta tese, a molhabilidade de apatita (tratada ou não com oleato de sódio-NaOl em pH=10,5) foi caracterizada pelo ângulo de contato de avanço da água (TETAa), trabalho de adesão (Wa) da água sobre apatita e coeficiente de espalhamento (S) de água sobre o sólido. Medidas diretas de TETAa sobre os planos frontal (010) e basal (001) de um cristal de apatita bem definido proveniente de Ipirá- BA (apatita-Ipirá) foram executadas pelo Método da Bolha Cativa (MBC), enquanto determinações indiretas de TETAa foram realizadas pelo Método da Ascensão Capilar (MAC) através da percolação de líquidos (água e/ou metanol) através de leitos partículas de apatita-Ipirá ou apatita-Cajati (proveniente de Cajati-SP). No MAC, o uso de hexano foi adequado para determinar a magnitude da constante de empacotamento (c) para partículas de apatita de baixa molhabilidade (TETAa>>0°), enquanto que a água se mostrou mais apropriada para ser usada na determinação da constante c para partículas de apatita não tratadas com surfatantes (TETAa~0o). Ensaios de microflotação foram conduzidos com apatita-Ipirá em pH=10,5 e com NaOl (0-75mg/L) enquanto ensaios de flotação gama foram executados com minério de fosfato proveniente de Cajati-SP previamente tratado com amido (37,5mg/L) e alquil sarcosinato de sódio-Berol®867 (25mg/L) em pH=10,6. Os resultados das medidas de TETAa e dos ensaios de microflotação indicaram uma relação de causa-efeito entre a concentração de NaOl (0-75mg/L), molhabilidade de apatita-Ipirá e sua resposta à microflotação: as maiores recuperações foram obtidas com as maiores concentrações do coletor NaOl, maiores valores de TETAa, menores valores de Wa e valores mais negativos de S. Os valores de TETAa diretamente medidos sobre as faces de um cristal de apatita-Ipirá pelo MBC mostrou que NaOl adsorve preferencialmente sobre o plano (010) comparado ao plano (001). Além disso, a tensão superficial crítica de molhabilidade (GAMAc) da apatita-Ipirá, pré-tratada com 75mg/L de NaOl, foi de 30,2erg/cm2 para o plano (001) versus 29,6erg/cm2 para o plano (010). Após serem condicionadas com reagentes de flotação (amido=37,5mg/L e Berol®867=25mg/L em pH=10,6) e flotadas em estágio rougher, partículas de apatita-Cajati exibiram TETAa=64.2°±1.1°. O valor de GAMAc, determinado via experimentos de flotação gama foi GAMAc~34,5erg/cm2; enquanto GAMAc determinado por diagramas cosTETA x GAMALV foi de GAMAc~33,9erg/cm2. Os resultados de flotação gama com o minério de fosfato de Cajati mostrou um platô de máxima recuperação de apatita (95-98%) quando 52,7erg/cm2<GAMALV<72,9erg/cm2. Ao contrário da apatita, a recuperação dos minerais de ganga (silicatos e carbonatos) foi estritamente ascendente com o aumento de GAMALV. A maior Eficiência de Separação apatita/ganga (E.S. = recuperação de apatita menos a recuperação de ganga) foi obtida em GAMALV=50,5erg/cm2 para apatita/silicatos e em GAMALV=51,4erg/cm2 para apatita/carbonatos. Os resultados dos experimentos de flotação gama indicaram que, no circuito industrial de Cajati-SP, GAMALV pode ser modulada pela dosagem do coletor, e sua magnitude pode guiar engenheiros na tomada de decisões a respeito da dosagem de coletor que promova a maior seletividade de separação apatita/ganga. Entretanto, a falta de instrumentos apropriados para realizar medidas on-line confiáveis de GAMALV tem impedido a execução destas medidas em circuitos industriais. Deste modo, decisões a respeito da dosagem do coletor feitas pelos engenheiros continuam a ser baseadas em uma abordagem empírica ao invés de científica. / This work approaches the wetting of apatite by water at room temperature (20-25°C) aiming at to contribute towards a better understanding of its behavior in flotation systems. Water, because of its powerful attractive forces, does not readily spread over the surface of low energy solids as apatite pre-treated with anionic long chain surfactants. This behavior is exploited by mineral processing engineers to separate apatite from gangue minerals via direct anionic flotation in industrial plants around the world. In this thesis, the wettability of apatite (treated or not with sodium oleate- NaOl at pH=10.5) was characterized by the advancing water contact angle (TETAa), work of adhesion (Wa) of water to apatite and the spreading coefficient (S) of water over the solid. Direct measurements of TETAa on either frontal-(010) or basal-(001) planes of a well formed apatite crystal from Ipirá-BA (apatite-Ipirá) were carried out via Captive Bubble (CB) method, whereas indirect determinations of TETAa were accomplished via Capillary Rise (CR) method by means of percolation of liquids (water and/or methanol) through particle beds of apatite-Ipirá and apatite-Cajati (from Cajati-SP). At CR method, the use of hexane was adequate to determine the magnitude of packing constant (c) for apatite particles of low wettability (TETAa>>0o), whereas water proved to be more appropriate to be used in the determination constant c for apatite particles non-treated with surfactants (TETAa~0o). Microflotation tests were conducted with apatite-Ipirá at pH=10.5 with NaOl (0-75mg/L) whereas gamma flotation tests were carried out with phosphate ore from Cajati-SP previously treated with starch (37.5mg/L) and sodium alkyl sarcosinate-Berol®867 (25mg/L) at pH=10.6. Results from measurements of TETAa and microflotation experiments indicated a cause-effect relationship between concentration of NaOl (0-75mg/L), wettability of apatite-Ipirá and its microflotation response: the highest recoveries were yielded at higher concentration of collector NaOl, higher values of TETAa, lower values of Wa and more negative the values of S. Values of TETAa directly measured on the faces of a crystal of apatite-Ipirá by CB method showed that NaOl adsorbs preferentially onto (010) plane compared to (001) plane. Moreover, the critical surface tension of wettability (GAMAc) of apatite-Ipirá, pre-treated with 75mg/L of NaOl, was 30.2erg/cm2 for (001)-plane versus 29.6erg/cm2 for (010)-plane. After being conditioned with flotation reagents (starch=37.5mg/L and Berol®867=25mg/L at pH=10.6) and floated at rougher stage, particles of apatite-Cajati exhibited TETAa=64.2o±1.1o. The value of GAMAc, determined via gamma flotation experiments was GAMAc~34.5erg/cm2; whereas GAMAc determined by cosTETA x GAMALV plots was GAMAc~33.9erg/cm2. Results from gamma flotation experiments with phosphate ore from Cajati showed a plateau of maximum apatite recovery (95-98%) when 52.7erg/cm2<GAMALV<72.9erg/cm2. Unlike apatite, the recovery of gangue minerals (silicates and carbonates) was strictly ascending when GAMALV was increased. The highest Efficiency of Separation apatite/gangue (E.S. = recovery of apatite minus recovery of gangue) was attained at GAMALV=50.5erg/cm2 for apatite/silicates and at GAMALV=51.4erg/cm2 for apatite/carbonates. The results from gamma flotation experiments indicate that, at the industrial plant of Cajati-SP, GAMALV can be modulated by collector dosage, and its magnitude can provide guidance to practitioners to make decision on collector dosage to achieve a desired value of GAMALV which promotes the best selectivity of the separation apatite/gangue. Notwithstanding, the lack of suitable instruments to accomplish on-line reliable measurements of GAMALV has been hindering the implementation of those measurements at industrial circuits. This way, decisions on collector dosage made by practitioners continue to be based rather on empirical than on scientific approach.

Graphite and graphene electrodes are used to study two electrochemical processes: the decoration of these electrodes with Au metallic nanoparticles through the use of electrodeposition, and electrowetting, the potential-dependent change in hydrophobicity of a surface. Electrodeposition provides a useful route to electrode functionalisation, in particular to combine the enhanced properties of metallic nanoparticles with the advantageous features of carbon materials. A combination of cyclic voltammetry, chronoamperometry, and both ex situ and in situ atomic force microscopy are used to deduce the mechanism of Au electrodeposition on graphite and graphene. Notably, the mechanism of Au nanoparticle formation cannot be deduced from simple voltammetry alone, and the spontaneous formation of Au within the timescale of the electrodeposition experiment is confirmed. Electrowetting is a uniquely responsive method to manipulate the wetting properties of an electrode. However, a dielectric coating is commonly required to protect the surface from electrolysis, which in turn further increases the potentials needed to perform electrowetting. In contrast to this, here it is shown that bare graphite and graphene electrodes support electrowetting without the disadvantages of a dielectric coating, allowing an unprecedented combination of performance and efficiency. Furthermore, the ideal behaviour this system demonstrates is implemented as a platform to study electrowetting itself. The influence of electrolyte composition, surface defects and electrode-blocking dielectric-like films are investigated to determine the factors that impede electrowetting, a key step to understanding the phenomenon that is normally hindered by the use of the dielectric.