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.

In this study we use PDMS thin films to fabricate of multi-domain surface. PDMS gets the characteristic of good physical properties and chemical, not only low surface free energy, flexible, also has low toxicity, low cost and can protect our environment. We used the DI water that was dropped on the PDMS thin film surface and became stable to explore the wettability of the surface, and we had a discussion about when liquid crystal dropped on the PDMS thin film surface. Then we also observe the phenomenon that was liquid crystal will shift a little distance and we used the optical image to analyze our device.

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.

Possibilities for increasing the upper limit of floatable particle sizs in the froth flotation process have been examined since the early beginnings of mineral flotation. The economic implications of such an incresae are far ranging; from decreased grinding costs and increased recoveries to simplified flow-sheet design and increased throughput, all leading to increased revenue. Bubble-particle detachment has been studied to better understand the factors influencing the strength of attachment and the energies involved. Direct measurements of bubble particle detachment were performed using a hanging balance apparatus (KSV Sigma 70 tensiometer) and using a submerged hydrophobic plate in water. Three experiments were used; direct force measurement of bubble-particle detachment, detachment force and energy of a bubble from a submerged hydrophobic plate, and detachment force and energy of a cetyltrimethylammonium bromide coated silica sphere from a flat bubble. Octadecyltrichlorosilane was used as a hydrophobic coating in the first two experimental methods. These experiments were recorded with a CCD camera to identify the detachment processes involved. Energies for both methods were calculated and divided into the two main steps of the detachment process: Three-Phase-Contact pinning and three phase contact line sliding. The first step represents the energy barrier which must be overcome before detachment can begin. It is directly related to contact angle hysteresis. Detachment occurs during the second step, where the solid-vapor interface is replaced by solid-liquid and liquid-vapor. This step corresponds to the work of adhesion. The effects of surface tension, contact angle and hysteresis were well demonstrated with the three experimental methods. Good correlation was found between theoretical work of adhesion and measured energies. / Master of Science

Capillarity is often exploited in self-cleaning, drag reducing and fluid absorption/storage (sanitary products) purposes just to name a few. Formulating the underlying physics of capillarity helps future design and development of optimized structures. This work reports on developing computational models to quantify the capillary pressure and capillary forces on the fibrous surfaces. To this end, the current study utilizes a novel mass-spring-damper approach to incorporate the mechanical properties of the fibers in generating virtual fibrous structures that can best represent fibrous membranes. Such virtual fibrous structures are then subjected to a pressure estimation model, developed for the first time in this work, to estimate the liquid entry pressure (LEP) for a hydrophobic fibrous membrane. As for accurate prediction (and not just estimation) of the capillary pressure, this work also presents an energy minimization method, implemented in the Surface Evolver code, for tracking the air–water interface intrusion in a hydrophobic fibrous membrane comprised of orthogonally oriented fibers. This novel interface tracking algorithm is used to investigate the effects of the membrane’s microstructure and wetting properties on its resistance to water intrusion (i.e., LEP). The simulation method developed in this work is computationally affordable and it is accurate in its predictions of the air–water interface shape and position inside the membrane as a function of pressure. Application of the simulation method in studying effects of fiber diameter or contact angle heterogeneity on water intrusion pressure is reported for demonstration purposes. Capillary forces between fibrous surfaces are also studied experimentally and numerically via the liquid bridge between two parallel plates coated with electrospun fibers. In the experiment, a droplet was placed on one of the polystyrene- or polyurethane-coated plates and then compressed, stretched, or sheared using the other plate and the force was measured using a sensitive scale. In the simulation, the liquid bridge was mathematically defined for the Surface Evolver finite element code to predict its 3-D shape and resistance to normal and shearing forces, respectively, in presence of the contact angle hysteresis effect. Despite the inherent non-uniformity of the fibrous surfaces used in the experiments and the simplifying assumptions considered for the simulations, reasonable agreement was observed between the experiments and simulations. Results reveal that both normal and shear force on the plates increase by increasing the liquid volume, or decreasing the spacing between the plates.

This thesis highlights generic aspects of contact angle hysteresis and stick-slip motion,encountered in most practical wetting situations.First, we study the scaling relation between the heterogeneity strength and the amplitudeof the contact angle hysteresis it induces in the model configuration of a chemicallyheterogeneous microchannel. A key parameter which determines the qualitativefeatures is the heterogeneity wavelength. In particular, we identify a near-thresholdbehavior where the quadratic scaling between the heterogeneity amplitude and the resultinghysteresis, already known for a dilute system of wetting defects, is explainedby the closeness to the threshold, and a macroscopic limit without observable stick-slipwhere this scaling is linear.In the second part, we adapt the description to the configuration of a meniscusaround a wavy fibre. This adaptation brings the generic results of the first part in thereach of experiments. A comparison with experiments is achieved at the level of theindividual topography-induced jumps.In the third part, we expand the formulation to treat the quasi-steady interface shapecontact line dynamics and study how the the presence of stick-slip motion at the observableor unobservable scale modifies the scaling relation between the contact linevelocity and contact angle. We recover the known result that the scaling exponent dependson the nature of the externally controlled parameter, identify the causes of thisdependency in the corresponding static limits, and predict the disappearance of this dependencyabove a critical velocity which decreases with the heterogeneity wavelength.Finally, we show trough examples how the modelling framework which permitscapturing contact angle hysteresis and stick-slip motion in a minimalistic way can beadopted to treat configurations with a finite amount of contact points, or the 3D problemof a drop with a deformed contact line. We discuss the arising configuration-specificeffects, also in configurations of biomimetic interest. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

In this work, we develop an interface-preserving level-set method in the finite-element framework for interfacial flows with moving contact lines. In our method, the contact line is advected naturally by the flow field. Contact angle hysteresis can be easily implemented without explicit calculation of the contact angle or the contact line velocity, and meshindependent results can be obtained following a simple computational strategy. We have implemented the method in three dimensions and provide numerical studies that compare well with analytical solutions to verify our algorithm. We first develop a high-order numerical method for interface-preserving level-set reinitialization. Within the interface cells, the gradient of the level set function is determined by a weighted local projection scheme and the missing additive constant is determined such that the position of the zero level set is preserved. For the non-interface cells, we compute the gradient of the level set function by solving a Hamilton-Jacobi equation as a conservation law system using the discontinuous Galerkin method. This follows the work by Hu and Shu [SIAM J. Sci. Comput. 21 (1999) 660-690]. The missing constant for these cells is recovered using the continuity of the level set function while taking into account the characteristics. To treat highly distorted initial conditions, we develop a hybrid numerical flux that combines the Lax-Friedrichs flux and a penalty flux. Our method is accurate for non-trivial test cases and handles singularities away from the interface very well. When derivative singularities are present on the interface, a second-derivative limiter is designed to suppress the oscillations. At least (N + 1)th order accuracy in the interface cells and Nth order accuracy in the whole domain are observed for smooth solutions when Nth degree polynomials are used. Two dimensional test cases are presented to demonstrate superior properties such as accuracy, long-term stability, interface-preserving capability, and easy treatment of contact lines. We then develop a level-set method in the finite-element framework. The contact line singularity is removed by the slip boundary condition proposed by Ren and E [Phys. Fluids, vol. 19, p. 022101, 2007], which has two friction coefficients: βN that controls the slip between the bulk fluids and the solid wall and βCL that controls the deviation of the microscopic dynamic contact angle from the static one. The predicted contact line dynamics from our method matches the Cox theory very well. We further find that the same slip length in the Cox theory can be reproduced by different combinations of (βN; βCL). This combination leads to a computational strategy for mesh-independent results that can match the experiments. There is no need to impose the contact angle condition geometrically, and the dynamic contact angle automatically emerges as part of the numerical solution. With a little modification, our method can also be used to compute contact angle hysteresis, where the tendency of contact line motion is readily available from the level-set function. Different test cases, including code validation and mesh-convergence study, are provided to demonstrate the efficiency and capability of our method. Lastly, we extend our method to three-dimensional simulations, where an extension equation is solved on the wall boundary to obtain the boundary condition for level-set reinitializaiton with contact lines. Reinitialization of ellipsoidal interfaces is presented to show the accuracy and stability of our method. In addition, simulations of a drop on an inclined wall are presented that are in agreement with theoretical results. / Doctor of Philosophy / When a liquid droplet is sliding along a solid surface, a moving contact line is formed at the intersection of the three phases: liquid, air and solid. This work develops a numerical method to study problems with moving contact lines. The partial differential equations describing the problem are solved by finite element methods. Our numerical method is validated against experiments and theories. Furthermore, we have implemented our method in three-dimensional problems.

This thesis is devoted to several aspects of geometry and morphology in wetting problems and hard sphere packings. First, we propose a new method to simulate wetting and slip on nanostructured substrates: a phase field model associated with a dynamical density theory approach. We showed omniphobicity, meaning repellency, no matter the chemical properties of the liquid on monovalued surfaces, i.e. surfaces without overhangs, which is in contradiction with the macroscopic Cassie-Baxter-Wenzel theory, can produce so-called We checked systematically the impact of the surface parameters on omniphobic repellency, and we show that the key ingredient are line tensions, which emerge from needle shaped surface structures. Geometrical effects have also an important influence on glassy or jammed systems, for example amorphous hard sphere systems in infinite pressure limit. Such hard sphere packings got stuck in a so-called jammed phase, and we shall demonstrate that the local structure in such systems is universal, i.e. independent of the protocol of the generation. For this, robust order parameters - so-called Minkowski tensors - are developed, which overcome robustness deficiencies of widely used order parameters. This leads to a unifying picture of local order parameters, based on geometrical principles. Furthermore, we find with the Minkowski tensor analysis crystallization in jammed sphere packs at the random closed packing point

Cette thèse porte sur différents aspects géométriques et morphologiques concernant des problèmes de mouillage et d'empilement de sphères. Nous proposons tout d'abord une nouvelle méthode de simulation pour étudier le mouillage et le glissement d'un liquide sur une surface nanostructurée: un modèle de champ de phase en lien avec la théorie de la fonctionnelle de la densité dynamique. Nous étudions grâce à cette méthode la possibilité de transformer une surface quelconque en surface omniphobe (c'est à dire qui repousse tous les liquides). Nous montrons que contrairement à la théorie classique de Cassie-Baxter-Wenzel, il est possible d'inverser la mouillabilité d'une surface en la texturant, et nous montrons qu'une surface monovaluée, i.e. sans constrictions, peut produire un comportement omniphobe c'est à dire repousser tous les liquides grâce à un effet de pointe. La géométrie a également un effet considérable dans les milieux vitreux ou bloqués. Les empilements aléatoires de sphères conduisent par exemple à des état bloqués ("jamming") et nous montrons que la structure locale de ces systèmes est universelle, c'est à dire indépendante de la méthode de préparation. Pour cela, nous introduisons des paramètres d'ordre - les tenseurs de Minkowski - qui suppriment les problèmes de robustesse qu'ont les paramètres d'ordre utilisés classiquement. Ces nouveaux paramètres d'ordre conduisent à une vision unifiée, basée sur des principes géométriques. Enfin, nous montrons grâce aux tenseurs de Minkowski que les empilements de sphères se mettent à cristalliser au delà du point d'empilement aléatoire le plus dense ("random close packing") / This thesis is devoted to several aspects of geometry and morphology in wetting problems and hard sphere packings. First, we propose a new method to simulate wetting and slip on nanostructured substrates: a phase field model associated with a dynamical density theory approach. We showed omniphobicity, meaning repellency, no matter the chemical properties of the liquid on monovalued surfaces, i.e. surfaces without overhangs, which is in contradiction with the macroscopic Cassie-Baxter-Wenzel theory, can produce so-called We checked systematically the impact of the surface parameters on omniphobic repellency, and we show that the key ingredient are line tensions, which emerge from needle shaped surface structures. Geometrical effects have also an important influence on glassy or jammed systems, for example amorphous hard sphere systems in infinite pressure limit. Such hard sphere packings got stuck in a so-called jammed phase, and we shall demonstrate that the local structure in such systems is universal, i.e. independent of the protocol of the generation. For this, robust order parameters - so-called Minkowski tensors - are developed, which overcome robustness deficiencies of widely used order parameters. This leads to a unifying picture of local order parameters, based on geometrical principles. Furthermore, we find with the Minkowski tensor analysis crystallization in jammed sphere packs at the random closed packing point

<p>  </p> <p>Water scarcity is a global problem impacting a majority of the world population. A significant proportion of the global population is deprived of clean drinking water, an impact felt by the rural as well as urban population. Saltwater desalination provides an attractive option to produce clean water. Some technologies to generate potable water include reverse osmosis (RO), multi-stage flash distillation (MSF), vapor compression distillation and multi-effect distillation (MED). Distillation plants such as those in MED often have falling-film evaporators operating at low energy conversion efficiency and hence distillation is performed over multiple stages (or effects). Porous materials can be utilized as evaporators in such plants with the objective of leveraging their superior efficiency. This can potentially decrease the number of effects over which distillation occurs. However, evaporation of high-salinity salt solution eventually results in salt precipitation which can cause fouling and induce structural damages, especially if the precipitates appear within the porous medium. Crystallization-induced structural damages are also of significant concern to building materials and for their role in weathering of historical monuments. It is thus crucial to understand the mechanisms governing salt precipitation in a porous medium.</p> <p>Transport of solute in such a medium is either driven by flow of the solution (advection) or by concentration gradients (diffusion). The dynamics of solute transport is further complicated due to the involvement of a reaction term accounting for any salt precipitation. The relative strengths of these driving forces determine the solute transport behavior during an evaporation-driven process. The wide-scale applications of solute transport and its complicated nature warrant investigation, both experimental and theoretical, of the dependence of solute transport and the subsequent precipitation on the operating conditions and the properties of the porous medium.</p> <p>This dissertation first focuses on developing a novel modeling framework for evaluating the transient behavior of the solute mass fraction profile within the domain of a one-dimensional porous medium, and extending its capability to predict the formation of salt precipitate in the medium.  Experimental investigations are then performed to study the formation of precipitate on sintered porous copper wicks of different particle-size compositions, and developing a mechanistic understanding of the governing principles.</p> <p>A numerical modeling framework is developed to analyze evaporation-driven solute transport. Transient advection-diffusion equations govern the salt mass fraction profile of the solution inside the porous medium. These governing equations are solved to obtain the solute mass fraction profile within the porous medium as well as the effloresced salt crust. Further accounting for precipitation allows a study of the formation and growth of efflorescence and subflorescence. Crystallization experiments are performed by allowing a NaCl solution to evaporate from a porous medium of copper particles and the subflorescence trends predicted by the model are validated. The modeling framework offers a comprehensive tool for predicting the spatio-temporal solute mass fraction profiles and subsequent precipitation in a porous medium.</p> <p>The dependence of efflorescence pattern on the properties of a porous medium is also investigated. Efflorescence patterns are visually observed and characterized on sintered copper particle wicks with spatially unimodal and bimodal compositions of different particle sizes. Efflorescence is found to form earlier and spread readily over a wick made from smaller particles, owing to their lower porosity, while it is limited to certain areas of the surface for wicks composed of the larger particles. A scaling analysis explains the observed efflorescence patterns in the bimodal wicks caused by particle size-induced non-uniform porosity and permeability. The non-uniformity reduces the advective flux in a high-permeability region by diverting flow towards a low-permeability region. This reduction in advective flux manifests as an exclusion distance surrounding a crystallization site where efflorescence is not expected to occur. The dependence of this exclusion distance on the porosity and permeability of the porous medium and the operating conditions is investigated. A large exclusion distance associated with the regions with bigger particles in the bimodal wicks explains preferential efflorescence over the regions with smaller particles. This novel scaling analysis coupled with the introduction of the exclusion distance provides guidelines for designing heterogeneous porous media that can localize efflorescence.</p> <p>Additionally, droplet interactions with microstructured superhydrophobic surfaces as well as soft surfaces were investigated during the course of this dissertation, separate from the above investigations. These investigations involve the interplay of surface energies with electrical or elastic energies and are studied both experimentally and through theoretical models, and therefore are retained as additional chapters in the thesis as being of relevant interest.  Electrowetting experiments are performed on superhydrophobic surfaces with re-entrant structures to study their resilience to the Cassie-to-Wenzel transition. The deformation of soft surfaces caused by forces exerted by microscale droplets is studied and the resulting interaction between multiple droplets is explored. </p>