In this thesis, we develop a physical understanding of the effects of viscosity and geometry on the dynamics of interfacial flows in drops and bubbles. We first consider the coalescence of pairs of conical water droplets surrounded by air. Droplet pairs can form cones under the influence of an electric field and have been observed to coalesce or recoil depending on the angle of this cone. With high resolution numerical simulations we show the coalescence and non-coalescence of these drop pairs is negligibly affected by the electric field and can be understood through a purely hydrodynamic process. The coalescence and recoil dynamics are shown to be self similar, demonstrating that for these conical droplet pairs viscosity has a negligible effect on the observed behavior. We generalize this result to the coalescence and recoil of droplets with different cone angles, and focus on droplets coalescing with a liquid bath and flat substrate. From the simulations of these droplets with different cone angles, an equivalent angle is found that describes the coalescence and recoil behavior for all water cones of any cone angle. While viscosity is found to negligibly affect the coalescence of conical water drops, it plays a key role in regulating the coalescence process of bursting gas bubbles. When these gas bubbles burst, a narrow liquid jet is formed that can break up into tiny liquid jet drops. Through consideration of the effects of viscosity, we show that these jet drops can be over an order of magnitude smaller than previously thought. Here, viscosity plays a key role in balancing surface tension and inertial forces and determining the size of the jet drops. Finally, we investigate the drainage of surfactant free, ultra-viscous bubbles where surface tension serves only to set the initial shape of the bubble. We use interferometry to find the thickness profiles of draining bubble films up to the point the of rupture. A theoretical film drainage model considering the balance of viscous and gravitational stresses is developed and numerically computed. The numerical results are found to be consistent with the experimentally obtained thickness profiles. In this work we provide insight into the role of viscosity in the outlined interfacial flows. The results of this thesis will advance the understanding of drop production in clouds, the marine climate, and the degassing of glass melts.

The goal of this study is to quantify the transient performance of microfabricated superhydrophobic surfaces when used in underwater applications. A mathematical framework is developed and used to predict the stability, longevity, and drag reduction benefits of submerged superhydrophobic surfaces with two- or three-dimensional micro-textures. In addition, a novel design is proposed to improve the drag-reduction benefits of lubricant-infused surfaces, by placing a layer of trapped air underneath the lubricant layer. The new design is referred to as lubricant–infused surfaces with trapped air, and it is designed to eliminate the long-lasting longevity problem of submerged superhydrophobic surfaces. The effectiveness of liquid-infused surface with trapped air design was examined via numerical simulation, and it was found to outperform its liquid-infused surface counterpart by about 37%.

This thesis presents an axisymmetric numerical model to simulate interfacial flows near a sharp corner, where contact line pinning occurs. The method has been used to analyze drop imbibition into a capillary. To evaluate the performance of the numerical method, for a liquid drop initially placed partially within a capillary, a thermodynamic model has also been developed, to predict equilibrium states. The first part of this thesis presents an axisymmetric VoF algorithm to simulate interfacial flows near a sharp corner. (1) A new method to exactly calculate the normals and curvatures of any circle with a radius as small as the grid size is presented. This method is a hybrid least squares height function technique which fits a discretized osculating circle to a curve, from which interface normals and curvature can be evaluated. (2) A novel technique for applying the contact angle boundary condition has been devised, based on the definition of an osculating circle near a solid phase. (3) A new flux volume construction technique is presented, which can be applied to any split advection scheme. Unlike the traditional approach where the flux volumes are assumed rectangular, the new flux volumes can be either trapezoidal or triangular. The new technique improves the accuracy and consistency of the advection scheme. (4) Explicit PLIC reconstruction expressions for axisymmetric coordinates have been derived. (5) Finally, a numerical treatment of VoF for contact line motion near a sharp corner is presented, base on the idea of contact line pinning and an edge contact angle. The second part of the thesis is on the imbibition of a drop into an open capillary. A thermodynamic analysis based on minimization of an interfacial surface energy function is presented to predict equilibrium configurations of drops. Based on the drop size compared to the hole size, the equilibrium contact angle, and the geometry of the capillary, the drop can be totally imbibed by the capillary, or may not wet the capillary at all. The thesis concludes with application of the numerical scheme to the same problem, to examine the dynamics of wetting or dewetting of a capillary. All of the simulations yield results that correspond to the equilibrium states predicted by the thermodynamic analysis, but offer additional insight on contact line motion and interface deformation near the capillary edge.

This thesis presents an axisymmetric numerical model to simulate interfacial flows near a sharp corner, where contact line pinning occurs. The method has been used to analyze drop imbibition into a capillary. To evaluate the performance of the numerical method, for a liquid drop initially placed partially within a capillary, a thermodynamic model has also been developed, to predict equilibrium states. The first part of this thesis presents an axisymmetric VoF algorithm to simulate interfacial flows near a sharp corner. (1) A new method to exactly calculate the normals and curvatures of any circle with a radius as small as the grid size is presented. This method is a hybrid least squares height function technique which fits a discretized osculating circle to a curve, from which interface normals and curvature can be evaluated. (2) A novel technique for applying the contact angle boundary condition has been devised, based on the definition of an osculating circle near a solid phase. (3) A new flux volume construction technique is presented, which can be applied to any split advection scheme. Unlike the traditional approach where the flux volumes are assumed rectangular, the new flux volumes can be either trapezoidal or triangular. The new technique improves the accuracy and consistency of the advection scheme. (4) Explicit PLIC reconstruction expressions for axisymmetric coordinates have been derived. (5) Finally, a numerical treatment of VoF for contact line motion near a sharp corner is presented, base on the idea of contact line pinning and an edge contact angle. The second part of the thesis is on the imbibition of a drop into an open capillary. A thermodynamic analysis based on minimization of an interfacial surface energy function is presented to predict equilibrium configurations of drops. Based on the drop size compared to the hole size, the equilibrium contact angle, and the geometry of the capillary, the drop can be totally imbibed by the capillary, or may not wet the capillary at all. The thesis concludes with application of the numerical scheme to the same problem, to examine the dynamics of wetting or dewetting of a capillary. All of the simulations yield results that correspond to the equilibrium states predicted by the thermodynamic analysis, but offer additional insight on contact line motion and interface deformation near the capillary edge.

This thesis addresses aspects of the transport of bubbles and capsules (a thin elastic membrane enclosing a viscous fluid) by means of a viscous flow in complex vessel geometries. It focusses on two related themes: (i) the trapping of air bubbles in a sudden streamwise tube expansion and (ii) the extreme deformation of bubbles and capsules in a localised tube constriction. Air bubbles of different volumes were trapped in a tube with a square cross-section, which contains a sudden streamwise expansion in tube width. The liquid filling the tube was driven by constant volume-flux flow, and experiments were performed in both millimetric and micrometric tubes to identify the range of flow rates for which bubbles could get trapped. The gradients in surface energy generated by the broadening of the bubble into the expansion depend strongly on bubble volume and the expansion length. It is shown that in order for a trapped bubble to release from the expansion, the work of the pressure forces due to flow past the bubble must exceed the change in surface energy required to squeeze into the narrower channel. This criterion for trapping was verified by direct pressure measurements and a capillary static model, which uses three-dimensional Surface Evolver calculations. The extreme deformation of bubbles and capsules was investigated using a localised constriction of the tube width. Both bubbles and capsules were shown to adopt highly contorted configurations and exhibit broadly similar features over a wide range of flow rates, suggesting that the deformation was primarily imposed by the geometry through viscous shear forces. However, bubbles and capsules also display distinguishing features. Bubbles can breakup and exhibit thinning of the rear of the bubble at a critical flow rate, which is associated with a divergence of the rear tip speed and curvature. In contrast, the capsule membrane can wrinkle and fold, and the membrane thickness imposes the value of the maximum curvature locally available to the capsule.

Cette thèse concerne l'étude de la dynamique d'impacts de gouttes, dans des situations de friction réduite entre le substrat solide et la goutte liquide. Cette diminution de friction s'est faite au moyen d'un film d'air inséré entre le liquide et le solide. Il existe plusieurs stratégies permettant l'existence de ce film d'air : la première est d'utiliser le phénomène de caléfaction, ou effet Leidenfrost : un liquide approché d'une surface chauffée au delà d'une température critique s'évapore suffisamment rapidement pour pouvoir léviter sur sa propre vapeur, et ainsi être isolé de la surface solide. Dans certaines conditions, les surfaces super-hydrophobes micro-texturées permettent au liquide de rester dans un état "fakir", c'est à dire de n'être en contact qu'avec le sommet de micro-piliers, le reste du liquide demeurant au dessus d'un coussin d'air. Enfin, il a également été constaté que l'écoulement d'air engendré par le mouvement d'une surface solide peut induire une force de portance sur une goutte, et ainsi lui permettre de léviter au dessus de cette surface / In this thesis we study the dynamic of drop impacts, in situations of low friction between the liquid and the solid surface. This low friction can be obtained thanks to an air cushion trapped between the liquid and the solid, which can be achieved by several ways. The first one is the Leidenfrost effect : when a liquid is moved close to a hot surface, the evaparation rate can be sufficient make liquid levitate on its own vapour. In certain conditions, onto micro-patterned super-hydrophobic surfaces, a drop can be in a "fakir" state, which means that the contact is limited to the top of micro-pillars, the rest of the liquid is at the top of an air cushion. Finally, we also observed that the air flow due to a moving surface can generate a lift force which can permit the levitation of the drop

Dans de nombreuses applications aérospatiales, on peut trouver des films liquides cisaillés, c'est-à-dire une fine couche liquide qui ruisselle sur une paroi entrainée par le gaz. Par exemple, une couche de liquide peut se développer sur la voilure des avions, givrer et dégrader les performances. Des vagues peuvent se développer à l'interface liquide-gaz, et l'analyse correcte de ces instabilités devient très importante pour modéliser ce phénomène physique. En effet, la présence d'instabilités modifie les échanges liquide-gaz, notamment les transferts de masse et chaleur. Le but de cette thèse est de développer une technique permettant de coupler la phase gazeuse afin de reproduire les interactions à l'interface. La couche de liquide étant beaucoup plus mince que celle du gaz, une approche intégrale sur l'épaisseur est utilisée pour la modélisation. Enfin, deux cas d'un écoulement diphasique se développant dans une conduite confinée et dans une conduite plus large sont étudiés. les résultats sont ensuite comparés à des autres méthodes de référence, plus coûteuses en temps de calcul. / In many aerospace applications one can find liquid films sheared by a gas flow. In example, these liquid sheets can develop on aircraft wings, freeze and then destroy the aerodynamics performances. Waves can develop at the liquid-gas interface, and the correct analysis of such instabilities becomes very important to model this physical phenomenon. Indeed, instabilities mdify liquid-gas exchanges, such as mass and heat transfers. The aim of the present work consists in developing a technique to couple the liquid phase to the gas phase in order to reproduce the interactions at the interface. Since the liquid layer is much thinner then the gas, anintegral approach is used for modeling. Finally, two cases of a two-phase flow developing in a strictly confined channel and in a large channel are studied. Results are then compared to other reference methods which are more expensive in terms of computational cost.

Cette thèse expérimentale porte sur des impacts de gouttes en caléfaction, aussi appelée régime Leidenfrost. Dans ce cas, la goutte est isolée thermiquement et mécaniquement du substrat surchauffé par une fine couche de vapeur. On s'affranchit ainsi de la friction visqueuse. Les substrats présentent des textures micrométriques localisées. On retrouve un régime autosimilaire d'étalement aux temps courts. On caractérise des régimes de recouvrement d'un défaut ponctuel par la goutte. Ces régimes sont dictés par l'épaisseur de lamelle par rapport à celle du défaut. Les défauts génèrent des excroissances dans leur sillage dont la dynamique peut être approchée selon deux modèles inertio-capillaires ; l'un valable aux temps courts, l'autre aux temps plus longs. En présence de plusieurs défauts, on fragmente la lamelle depuis plusieurs sites selon le ratio entre largeur des défauts et épaisseur de la lamelle. On simule par un algorithme de pavage le motif final sur lequel le fluide se concentre à la fin de la fragmentation. Grâce à des rugosités plus complexes on peut canaliser l'étalement de la goutte. On exacerbe alors l'étalement maximal dans l'axe des canaux. On peut aussi inhiber l'étalement par des textures circulaires. Les rugosités affectent le temps avant rebond de la goutte. On exhibe une dépendance générale unique entre temps avant rebond et étalement maximal. La dépendance est valable lorsque les textures exacerbent l’étalement, aussi bien que lorsqu’elles l’inhibent / The presented work deals with drop impacts in Leidenfrost regime. In such a case, the drop is thermally and mechanically isolated from the overheated substrate by a thin vapor layer. Viscous friction can therefore be neglected. The substrates are shaped with localized micrometric textures. We rediscover a self-similar spreading regime at short times. We characterize covering regimes of a single defect by the drop. Those regimes are driven by the ratio between lamella thickness and defect thickness. Defects give rise to excrescences in their wake, whose dynamic can be approached by two inertial-capillary recoil models. One is valid at short times and the other at longer times. In the case of several defects, we break up the lamella from different sites according to the ratio between defect width and lamella thickness. We numerically predict, with a tessellation algorithm, the pattern on which the fluid is localized at the end of the fragmentation. Through more complex textures, we can channel the drop spreading. The spreading is increased in the directions of the channels. One can also inhibit the spreading with circular textures. The textures affect the time before drop rebound. We exhibit a general and unique dependency between time before rebound and maximal spreading. This dependency is valid when textures increase the spreading as well as when they inhibit it

<div>Free surface flows where the shape of the interface separating two fluids is unknown <i>apriori</i> are an important area of interest in fluid dynamics. The study of free surface flows such as the breakup and coalescence of drops, and thinning and rupture of films lends itself to a diverse range of industrial applications, such as inkjet printing, crop spraying, foam and emulsion stability, and nanolithography, and helps develop an understanding of natural phenomena such as sea spray generation in oceans, or the dynamics of tear films in our eyes. In free surface flows, singularities are commonly observed in nite time, such as when the radius of a thread goes to zero upon pinchoff or when the thickness of a film becomes zero upon rupture. Dynamics in the vicinity of singularities usually lack a length scale and exhibit self-similarity. In such cases, universal scaling laws that govern the temporal behavior of measurable physical quantities such as the thickness of a lm can be determined from asymptotic analysis and veried by high-resolution experiments and numerical simulations. These scaling laws provide deep insight into the underlying physics, and help delineate the regions of parameter space in which certain forces are dominant, while others are negligible. While the majority of previous works on singularities in free-surface flows deal with Newtonian fluids, many fluids in daily use and industry exhibit non-Newtonian rheology, such as polymer-laden, emulsion, foam, and suspension flows.</div><div><br></div><div><div>The primary goal of this thesis is to investigate the thinning and rupture of thin films of non-Newtonian fluids exhibiting deformation-rate-thinning (power-law) rheology due to attractive intermolecular van der Waals forces. This is accomplished by means of intermediate asymptotic analysis and numerical simulations which utilize a robust Arbitrary Eulerian-Lagrangian (ALE) method that employs the Galerkin/Finite-Element Method for spatial discretization. For thinning of sheets of power-law fluids, a signicant finding is the discovery of a previously undiscovered scaling regime where capillary, viscous and van der Waals forces due to attraction between the surfaces of the sheet, are in balance. For thinning of supported thin films, the breakdown of the lubrication approximation used almost exclusively in the past to study such systems, is shown to occur for films of power-law fluids through theory and conrmed by two dimensional simulations. The universality of scaling laws determined for rupture of supported films is shown by studying the impact of a bubble immersed in a power-law fluid with a solid wall.</div></div><div><br></div><div><div>Emulsions, which are ne dispersions of drops of one liquid in another immiscible liquid, are commonly encountered in a variety of industries such as food, oil and gas, pharmaceuticals, and chemicals. Stability over a specied time frame is desirable in some applications, such as the shelf life of food products, while rapid separation into its constituent phases is required in others, such as when separating out brine from crude oil. The timescale over which coalescence of two drops of the dispersed phase occurs is crucial in determining emulsion stability. The drainage of a thin film of the outer liquid that forms between the two drops is often the rate limiting step in this process. In this thesis, numerical simulations are used to decode the role played by fluid inertia in causing drop rebound, and the subsequent increase in drainage times, when two drops immersed in a second liquid are brought together due to a compressional flow imposed on the outer liquid. Additionally, the influence of the presence of insoluble surfactants at the drop interface is studied. It is shown that insoluble surfactants cause a dramatic increase in drainage times by two means, by causing drop rebound for small surfactant concentrations, and by partially immobilizing the interface for large surfactant concentrations.</div></div>