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.

by Ho Wing Kin. / Thesis submitted in: July 1997. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 89-92). / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- The Euler-Lagrange Equation for Capillary Surfaces --- p.6 / Chapter 1.2 --- The Capillary Tube --- p.12 / Chapter 2 --- Comparison Principles --- p.16 / Chapter 2.1 --- The General Comparison Principle --- p.16 / Chapter 2.2 --- Applications --- p.24 / Chapter 3 --- Existence Criteria --- p.30 / Chapter 3.1 --- Necessary Conditions --- p.31 / Chapter 3.2 --- Sufficient Conditions --- p.35 / Chapter 4 --- Uniqueness --- p.53 / Chapter 4.1 --- General Bounded Domains Case --- p.53 / Chapter 4.2 --- Infinite Strip Case --- p.56 / Chapter 5 --- Gradient Estimate of Surfaces of Constant Mean Curvature --- p.66 / Chapter 5.1 --- The Gradient Estimate --- p.67 / Chapter 5.2 --- Behavior as R→ 1 --- p.70 / Chapter 5.3 --- Existence of the Comparison Surfaces --- p.76 / Chapter 5.4 --- Ro is Best Possible --- p.82 / Appendix Mean Curvature --- p.85

"A series of one dimensional horizontal infiltration experiments were performed to investigate the predictive capabilities of the Kao and Hunt model. By modifying pristine laboratory apparatus, a reasonable range of soil temperatures was achieved. Experiments were run at approximately 5°C, 20°C, and 35°C. Distilled water was used as an infiltrating liquid and silica powder was used as soil. The infiltrating liquid was dispensed into the column at zero pressure head. The results of the experiments show that the model is adaptable to a range of temperature conditions by modifying terms for the liquid effects of the model, viscosity and surface tension. Experimental data and model predictions differed by 30 percent at most. Although the change in the rate of infiltration across the range of temperatures is perceivable, it is small in comparison to the effects caused by heterogeneity encountered in nature. "

Ce mémoire de thèse a été consacrée à étudier expérimentalement la perméabilité relative au gaz et à l’eau des matériaux cimentaires partiellement saturés, et à simuler numériquement le transfert d’eau dans le béton. La perméabilité relative d’un mortier de référence et d’un béton utilisé dans un centre de stockage de déchets radioactifs a été mesurée. Une méthode de mesurer la perméabilité relative à l’eau de deux bétons CEM I et CEM V, qui seront utilisés dans un stockage profond, a été proposée. Mais les quantités d’eau mis en jeu n’ont pas permis d’exploiter cette approche. Ceci indique la prépondérance de la capillarité sur la perméation lors du processus de saturation du matériau. On a ensuite mesuré la sorption capillaire de deux bétons CEM I et CEM V. A la même saturation en eau, la perméabilité relative au gaz de l’échantillon pré-traité par l’imbibition capillaire est moins grande que celle de l’échantillon pré-traité par adsorption sous humidité relative. Un double-modèle de rétention a été proposé qui peut bien modéliser l’isotherme de sorption des bétons CEM I et CEM V. La perméabilité relative au gaz et à l’eau est déduite. L’hystérésis de l’isotherme de sorption entraîne l’hystérésis de la perméabilité relative à l’eau tandis que la perméabilité relative au gaz n’a pas d’hystérésis remarquable. Avec le double-modèle de rétention et les courbes de la perméabilité relative à l’eau, on a pu simuler le processus de sorption sous humidité relative en utilisant une propre perméabilité intrinsèque à l’eau qui est dans le domaine de valeurs mesurées tandis que on n’a pas réussi à simuler l’imbibition capillaire à cause de la cinétique différente / This dissertation was devoted to study gas and water relative permeability and transfer of water in partially saturated cementitious materials. The gas relative permeability of a reference mortar and a concrete, which is used in the low and intermediate level waste storage center in Soulaines, has been measured. A method to measure water relative permeability of two concretes CEM I and CEM V, which will be used in the building of a underground disposal, has been proposed. But the difficulty of isolating the part due to the permeation in the unsaturated flow shows that the flow of capillarity is predominant in unsaturated flow. The capillary adsorption of concretes CEM I and CEM V has been measured. At the same level of water saturation, the gas relative permeability of sample pre-treated by capillary adsorption is less than that of sample pre-treated by adsorption in relative humidity. A double retention model has been proposed and it can describe the sorption isotherm of two concretes CEM I and CEM V. The curves of gas and water relative permeability are deducted. The hysteresis of sorption leads to the hysteresis of water relative permeability while there is not notable hysteresis of gas relative permeability. With double-retention model and water relative permeability expression, we can simulate sorption process under relative humidity by using a proper value of water intrinsic permeability which is in the domain of measured values

Graduation date: 1994

This thesis covers two topics. The first subject involves tests run on a ultralite reflux tube supplied by Battelle Pacific Northwest Laboratories (PNL). The second topic involves tests to determine the relative wicking rates of several different fabrics. The ultralite reflux tube supplied by PNL was constructed of copper and Nextel 312. It had a 10 mil thick copper evaporator and a 10 mil thick copper condenser end cap. The bulk of the condenser was 2 mil thick copper covered by a one inch diameter Nextel 312 woven hose. A life test was run within the Heat Pipe Test Facility, a chamber used to simulate low earth orbit. The life test lasted for over 800 hours, during which time the reflux tube operated steadily with no drop in performance. At the end of the test the reflux tube was removed and observed. The only noticeable change was a slight discoloration of the Nextel 312 used to cover the condenser. This discoloration was consistent with previously observed phenomenon. The second topic, fabric wicking rate studies were done as a follow up study to the dry uptake tests previously conducted at Oregon State University. The purpose of the tests were to get a relative feel for the ability of different fabrics to wick water. This was achieved using a drop test in which the fabrics were laid out on a bridge connecting two containers. One of the containers was elevated above the other. The fabrics were allowed to wick water from the upper container to the lower container and the rate at which this was accomplished was measured. The fabrics were all able to move significant amounts of water. The stiffer fabrics seemed to perform better. The major transport mechanism was transport between fabric layers and the fabric and the bridge. / Graduation date: 1993

The capillary surface $u(x,y)$ near a cusp region satisfies the boundary value problem: \begin{eqnarray} \nabla \cdot \frac{\nabla u}{\sqrt{1+\left|\nabla u \right|^2}}&=&\kappa u \qquad \textrm{in }\left\{(x,y): 0<x,f_2(x)<y<f_1(x)\right\}\,, \label{0.1}\\ \nu \cdot \frac{\nabla u}{\sqrt{1+\left|\nabla u \right|^2}}&=& \cos \gamma_1 \qquad \textrm{on } y=f_1(x)\,,\\ \nu \cdot \frac{\nabla u}{\sqrt{1+\left|\nabla u \right|^2}}&=& \cos \gamma_2 \qquad \textrm{on } y=f_2(x)\,, \label{0.3} \end{eqnarray} where $\lim_{x\rightarrow 0}f_1(x),f_2(x)=0$, $\lim_{x\rightarrow 0}f'_1(x),f'_2(x)=0$. It is shown that the capillary surface is unbounded at the cusp and satisfies $u(x,y)=O\left(\frac{1}{f_1(x)-f_2(x)}\right)$, even for types of cusp not investigated previously (e.g. exponential cusps). By using a tangent cylinder coordinate system, we show that the exact solution $v(x,y)$ of the boundary value problem: \begin{eqnarray} \nabla \cdot \frac{\nabla v}{\left|\nabla v \right|}&=&\kappa v \qquad \textrm{in }\left\{(x,y): 0<x,f_2(x)<y<f_1(x)\right\}\,,\\ \nu \cdot \frac{\nabla v}{\left|\nabla v \right|}&=& \cos \gamma_1 \qquad \textrm{on } y=f_1(x)\,,\\ \nu \cdot \frac{\nabla v}{\left|\nabla v \right|}&=& \cos \gamma_2 \qquad \textrm{on } y=f_2(x)\,, \end{eqnarray} exhibits sixth order asymptotic accuracy to the capillary equations~\eqref{0.1}$-$\eqref{0.3} near a circular cusp. Finally, we show that the solution is bounded and can be defined to be continuous at a symmetric cusp ($f_1(x)=-f_2(x)$) with the supplementary contact angles ($\gamma_2=\pi-\gamma_1$). Also it is shown that the solution surface is of the order $O\left(f_1(x)\right)$, and moreover, the formal asymptotic series for a symmetric circular cusp region is derived.

The capillary surface $u(x,y)$ near a cusp region satisfies the boundary value problem: \begin{eqnarray} \nabla \cdot \frac{\nabla u}{\sqrt{1+\left|\nabla u \right|^2}}&=&\kappa u \qquad \textrm{in }\left\{(x,y): 0<x,f_2(x)<y<f_1(x)\right\}\,, \label{0.1}\\ \nu \cdot \frac{\nabla u}{\sqrt{1+\left|\nabla u \right|^2}}&=& \cos \gamma_1 \qquad \textrm{on } y=f_1(x)\,,\\ \nu \cdot \frac{\nabla u}{\sqrt{1+\left|\nabla u \right|^2}}&=& \cos \gamma_2 \qquad \textrm{on } y=f_2(x)\,, \label{0.3} \end{eqnarray} where $\lim_{x\rightarrow 0}f_1(x),f_2(x)=0$, $\lim_{x\rightarrow 0}f'_1(x),f'_2(x)=0$. It is shown that the capillary surface is unbounded at the cusp and satisfies $u(x,y)=O\left(\frac{1}{f_1(x)-f_2(x)}\right)$, even for types of cusp not investigated previously (e.g. exponential cusps). By using a tangent cylinder coordinate system, we show that the exact solution $v(x,y)$ of the boundary value problem: \begin{eqnarray} \nabla \cdot \frac{\nabla v}{\left|\nabla v \right|}&=&\kappa v \qquad \textrm{in }\left\{(x,y): 0<x,f_2(x)<y<f_1(x)\right\}\,,\\ \nu \cdot \frac{\nabla v}{\left|\nabla v \right|}&=& \cos \gamma_1 \qquad \textrm{on } y=f_1(x)\,,\\ \nu \cdot \frac{\nabla v}{\left|\nabla v \right|}&=& \cos \gamma_2 \qquad \textrm{on } y=f_2(x)\,, \end{eqnarray} exhibits sixth order asymptotic accuracy to the capillary equations~\eqref{0.1}$-$\eqref{0.3} near a circular cusp. Finally, we show that the solution is bounded and can be defined to be continuous at a symmetric cusp ($f_1(x)=-f_2(x)$) with the supplementary contact angles ($\gamma_2=\pi-\gamma_1$). Also it is shown that the solution surface is of the order $O\left(f_1(x)\right)$, and moreover, the formal asymptotic series for a symmetric circular cusp region is derived.

Placée sous le signe de la fragmentation liquide, cette thèse met l'emphase sur une série d'étapes pouvant, d'un film suspendu, mener à une assemblée de gouttes : déstabilisation, rupture puis fragmentation. Elle prend appui sur des expériences originales, analysées à l'aide de modèles à la portée générale. En guise de prologue, capillarité, cisaillement et viscosité sont discutées à travers l'étude de la déstabilisation Marangoni d'un filament d'huile visqueuse déposé à la surface de l'eau. La mise en mouvement du filament, pilotée par une différence de tensions de surface, produit une cascade critique auto-similaire, accélérée jusqu'à la dilution complète de l'huile, miscible à l'eau. Sur un film, l'effet Marangoni créé par un déficit localisé de tension de surface, dont le support (la température ou un soluté) diffuse, engendre sa déstabilisation, étudiée au deuxième chapitre. L'analyse linéaire exhibe une échelle de temps inertielle basée sur le cisaillement surfacique, sur laquelle s'établit un écoulement interstitiel, caractérisé expérimentalement. Le scénario introduit un nombre de Péclet, critère pour la rupture spontanée des films épais. Les conséquences sur la stabilité finale du film sont explorées au troisième chapitre, avec la revue des possibles régularisations. La dynamique de rupture est interprétée en termes de choc. Enfin, suivant la rupture d'un film en divers points, la collision de cylindres liquides est isolée en tant que mécanisme individuel de fragmentation. L'analyse détaillée de l'impact révèle la transition entre deux régimes, vers des gouttes de plus en plus fines / This thesis deals primarily with liquid films fragmentation. It consists, thanks to quantitative and original experiments, in the transformation of a free suspended film into a collection of droplets: destabilization, rupture, and fragmentation.In a prologue, notions of capillarity, momentum transfer and viscosity are introduced by the Marangoni-driven destabilization of a thin thread of viscous oil on water. The difference of surface tension feeds an accelerated, critical, self-similar cascade which ends up with the complete dilution of oil into water. When applied to a free film, the Marangoni effect driven by a localized deficit of surface tension, whose carrier (temperature or a solute) is diffusing into the liquid, destabilizes it (chapter two). The linear instability analysis points out the crucial role of an inertial timescale based on the surface shear stress. Experiments validate the prediction of an interstitial flow, which digs out the film in the case of a surface tension deficit. These observations offer new insights into a long-standing problem, namely the spontaneous nucleation of holes on planar liquid films.The third chapter investigates the consequences of the linear instability, as far as the film final stability is concerned, reviewing possible regularizations. The rupture dynamics is described within the framework of shocks. In the final chapter, the collision of liquid cylinders is identified as an individual mechanism for liquid fragmentation. The impact dynamics is analyzed, leading to two principal fragmentation regimes. The onset to the splashing one, which produces fine and fast droplets, is described

No description available.