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Surfactant flooding in carbonate matrix acidizing treatment has been widely used for changing the wettability of the rock and to achieve low IFT values. Optimizing the type of surfactant and concentration for the specific oil field is very important in order to avoid formation damage and to reduce the treatment cost. We built an experimental procedure for screening the right surfactant to alter the wettability and aid in acidizing of Pekisko formation, Canada, which is strongly oil-wet and has high viscosity oil. Five surfactants were tested out of which three are cationic, one amphoteric and the other one was a fluoro-surfactant. Measurements were made of interfacial tension with different surfactant types/concentrations in brine with the oil and xylene, critical micelle concentration of each surfactant, solubility characteristics of the surfactants, compatibility of the chemical additives, wettability of the core after treating with surfactants, and core flooding in the laboratory to simulate matrix acidizing. From the results obtained we noted that the fluoro-surfactant can cause formation damage due to precipitation in the brine. So the compatibility of every chemical additive should be tested first. The use of xylene as a pre-flush solution lowered the CMC and hence reduced the cost of the surfactant treatment. Aromox, an amine based surfactant was best suited for matrix acidizing treatment of the Pekisko formation.

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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.

Contact angle behavior controls the spreading, sticking, or movement of fluid droplets on top of solid substrates, and the immiscible displacement of mixed fluids in porous media. Therefore, it influences applications such as oil recovery, CO2 geological storage, water transport in unsaturated soils, and DNAPL soil remediation techniques. The attraction forces and geometrical-molecular arrangement at the atomic scale define the strength of the interfacial tension that changes in response to changes in temperature, pressure, or the fluid composition within the system. Contact line behavior such as contact line pinning or depinning, microscale roughness, and changes in interfacial tensions influence advancing and receding contact angles. This study consists of a comprehensive database of published advancing and receding contact angles to understand the underlying mechanisms of contact line pinning and depinning and the implications of these phenomena on advancing and receding contact angles. Calcite experiments that investigate advancing and receding contact angle measurements as a function of ionic concentration complement the published literature. Critical results include: an advancing contact angle trend with calcite as a function of ionic concentration, a point of minimum contact angle hysteresis when brine concentrations are close to 0.1 M, and that contact angle behavior depends on cation type and the calcite surface anisotropy. Contact line pinning prevents flow and increases contact angle hysteresis. An analysis of the database suggests that the wide range of contact angle hysteresis of calcite and quartz with water results both from hydrogen bonds and microscale roughness at the surface which leads to pinned contact lines. The Jamin effect reduces significantly in calcite when the resultant injection brines have an ionic concentration close to 0.1 M. Thus, the pressure difference required to displace a non-wetting fluid for a wetting fluid reduces, and leads to enhanced recovery of trapped oil, gas or DNAPL.

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.