A fluid drop in a Hele-Shaw cell moves due to surface tension driven potential flow. Using equations for the pressure and the Green’s function for the Laplace Equation, we can formulate an integral equation that determines the motion of the boundary of the drop. By discretizing the boundary contour and following the motion of boundary nodes, the time evolution of the drop can be determined from initial conditions. Results of a numerical simulation show the movement of a drop relaxing from coalescence and the motion of a drop undergoing electrowetting.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1957. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (v. 1, leaves 277-289).

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We study experimentally the gravity-driven bubbly flow inside a large Hele-Shaw cell. The bubbles and foam were created by a series of upside-down overturns of the half-filled cell about its horizontal axis. When the liquid flows down it entraps a large number of bubbles, which remain stable as the liquid contains surfactant molecules. The total number and sizes of these bubbles slowly asymptote to a steady state after dozens of overturns. It takes longer to reach this asymptote when the viscosity of the liquid is larger. The bubbles also become more monodisperse with more cell over-turns. The number and distribution of the bubbles in turn affects the average motion of the liquid phase, which is characterized by the downwards motion of the liquid center of mass. We use high-resolution 6k video-camera to track the trajectories of thousands of bubbles. This required the development of software codes to identify individual bubbles and follow them between video frames. Successful thresholding algorithm required a machine-learning component, which was integrated into the program. This program also needed to account for possible splitting or coalescence of adjacent bubbles. The program can also find the velocities along the trajectories. In this way we can find the vertical velocity of bubbles as a function of their sizes. The smaller bubbles are sometimes observed to move downwards against their buoyancy. This occurs when the viscous stress from the surrounding liquid phase overcomes the upwards buoyancy force. Bubbles with similar sizes were often found to be stacking together and having worm-like rising movement that is faster than their individual rising velocity. The occurrence of the bubble stacking was dependent on the distance between the bubbles, their sizes and their wakes. Clusters of tiny bubbles that are much smaller than the gap of the Hele-Shaw cell were observed to form layers which can severely hinder the overall liquid motion.

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La microfluidique à goutte a connu un essor remarquable ces dix dernières années. Pourtant, la dynamique de ces objets reste largement inexplorée et incomprise. En effet, une question aussi fondamentale que de prédire la vitesse d'une goutte poussée par une phase porteuse à vitesse imposée, est restée jusqu’à ce jour, sans réponse. Comprendre la dynamique d'une goutte suppose de caractériser les dissipations visqueuses (friction) au sein de la goutte et dans le film de lubrification. Ces dissipations visqueuses sont étroitement liées à la forme et aux propriétés physico-chimiques de l'interface séparant l'intérieur de la goutte de la phase externe. Ce manuscrit présente une caractérisation de la dynamique d’une goutte 2D en cellule de Hele-Shaw en exploitant la double mesure du film de lubrification par microscopie interférentielle et de la vitesse de la goutte. Dans un premier temps, nous étudions expérimentalement la forme adoptée par l'interface en fonction de la viscosité de la goutte et de la concentration en tensioactifs. La comparaison des topographies expérimentales mesurées avec des modèles théoriques déjà existants et un nouveau développé dans ce manuscrit, révèle que l'utilisation d'une approche purement hydrodynamique (sans effet Marangoni) pour déterminer la topographie théorique n'est en mesure de reproduire la topographie expérimentale que lorsque le système ne présente pas de tensioactif ou bien lorsque la viscosité de la goutte est suffisamment importante pour prendre le pas sur d'éventuels effets Marangoni à l'interface. Dans les autres cas, la forment de l'interface évolue en fonction de la contrainte de Marangoni qui peut s'exercer localement ou globalement à l'interface. Dans un deuxième temps, l’établissement d’un modèle théorique pour la vitesse de la goutte, basé sur la modélisation des topographies de films expérimentales mesurées, permet de retrouver quantitativement, et sans paramètre d'ajustement, les vitesses de goutte mesurées expérimentalement. / Droplet microfluidics is a growing field of research. However, the dynamics of these objects remain misunderstood. Indeed, a question as fundamental as predicting the droplet velocity while pushed by an external fluid at a given velocity is still not answered. Understanding the dynamics of a droplet requires to characterize the viscous dissipation mechanisms (friction) within the droplet and in the lubrication film. This dissipation is related to the shape and to the physicochemical properties of the interface separating the inner phase of the droplet from the outer phase. This thesis presents a characterization of the dynamics of 2D droplets in a Hele-Shaw cell, by taking advantage of the double measurement of the lubrication film by interference microscopy and of the droplet velocity. Firstly, we study experimentally the influence of the droplet viscosity and surfactant concentration on the shape of the interface. The comparison between the topographies measured experimentally with the theoretical models already existing and the new one developed in this thesis, reveals that the use of a purely hydrodynamical approach in order to derive the theoretical topography only allows to recover the experimental topography if the system is surfactant free or if the droplet viscosity is high enough to overcome the Marangoni effect at the interface. In the other cases, the shape of the interface depends on the Marangoni stress exerted either locally or globally at the interface of the droplet. In a second part, the derivation of a theoretical model for the droplet velocity, based on the modeling of the lubrication film topographies measured experimentally, allows to recover quantitatively, and without any fitting parameter, the experimental data on droplet velocities.

La digitation visqueuse est une instabilité hydrodynamique apparaissant lorsque, dans un milieu poreux, un fluide moins visqueux déplace un fluide plus visqueux. L’objectif de notre thèse est l’étude expérimentale des propriétés des motifs de digitation lorsque l'échantillon de fluide visqueux est de taille finie et lorsqu'une réaction chimique modifie la viscosité dans un milieu poreux modèle, en l’occurrence une cellule de Hele-Shaw. En particulier, notre étude a permis de quantifier la contribution de dispersion et de la digitation visqueuse à l’étalement dans l’espace d’échantillons de taille finie en fonction des paramètres expérimentaux (contraste de viscosité, vitesse de déplacement et taille de l’échantillon). Pour les fluides réactifs, nous analysons la digitation induite par une réaction A + B → C dont le produit C est plus visqueux que les réactifs A et B, ceux-ci ayant la même viscosité. Nous mettons en évidence l’effet des concentrations en réactifs, du choix du fluide vecteur et du débit d’injection sur le motif de digitation.

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Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-12-12T14:44:32Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação - Pedro Henrique Amorim Anjos.pdf: 9970150 bytes, checksum: 29bca81f576fbdecd909c0ab24d68ce5 (MD5) / Made available in DSpace on 2016-12-12T14:44:32Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação - Pedro Henrique Amorim Anjos.pdf: 9970150 bytes, checksum: 29bca81f576fbdecd909c0ab24d68ce5 (MD5) Previous issue date: 2015-02-05 / CNPQ / Consideramos o movimento da interface entre dois fluidos viscosos, imiscíveis e incompressíveis confinados em uma célula de Hele-Shaw radial. Quando o fluido de baixa viscosidade é injetado no centro da célula e desloca radialmente o fluido de alta viscosidade, a instabilidade de Saffman-Taylor entra em ação levando ao crescimento de estruturas em formato de dedos. Dependendo da natureza dos fluidos envolvidos, eles podem molhar as paredes da célula de Hele-Shaw, deixando para trás um filme molhante de espessura finita. Diante disso, investigamos a influência da camada de fluido molhante, deixada pelo fluido deslocado, na dinâmica linear e fracamente não-linear do sistema. Mais especificamente, examinamos como a instabilidade da interface e os mecanismos de formação de padrões (bifurcação e competição de dedos) são afetados pela presença da camada de filme molhante no limite de baixo número de capilaridade. Estudamos também uma variação da instabilidade de Saffman-Taylor usual induzida pela injeção: o problema do levantamento em célula de Hele-Shaw. Nossos resultados analíticos indicam que o molhamento tem um impacto significativo nos padrões não-lineares resultantes. Ele é responsável por uma atenuação na variação do comprimento dos dedos, enquanto que induz o aparecimento de estruturas que apresentam dedos pequenos e largos, provenientes do fluido não molhante, alternados por dedos pequenos e finos pertencentes ao fluido molhante. Durante o processo de levantamento, medidas adquiridas pelo teste de adesão quantificam a força adesiva de um fluido viscoso confinado entre placas paralelas. Experimentos e intensas simulações numéricas indicam que a formação de dedos afeta a força de levantamento, promovendo uma diminuição na magnitude da mesma. Concluímos este trabalho propondo um modelo analítico que forneça a força de adesão considerando não só o efeito de dedos da interface, mas também a ação do molhamento e de estresses viscosos normais. / We consider the interfacial motion between two immiscible, incompressible, viscous fluids in the confined geometry of a radial Hele-Shaw cell. When the less viscous fluid is injected at the center and drives radially the more viscous fluid, the Saffman-Taylor instability takes place leading to the growth of fingerlike shapes. Depending on the nature of the fluids involved, they can wet the walls of the Hele-Shaw cell plates, leaving behind a film of finite thickness. In this framework, we investigate the influence of a thin wetting film trailing behind the displaced fluid on the linear and weakly nonlinear dynamics of the system. More specifically, we examine how the interface instability and the pattern formation mechanisms of finger tip-splitting and finger competition are affected by the presence of such a film in the low capillary number limit. We also examined a variant of the usual injection-driven Saffman-Taylor instability: the lifting Hele-Shaw cell problem. Our analytical results indicate that wettability has a significant impact on the resulting nonlinear patterns. It restrains finger length variability while inducing the development of structures presenting short, blunt penetrating fingers of the nonwetting fluid, alternated by short, sharp fingers of the wetting fluid. During the lifting process, probe-tack measurements evaluate the adhesion strength of viscous fluids confined between parallel plates. Existing meticulous experiments and intensive numerical simulations indicate that fingering formation affects the lifting force, making it to decrease in intensity. We conclude this work by proposing an analytical model that computes the lifting adhesion force by taking into account not only the effect of interfacial fingering, but also the action of wetting, and viscous normal stresses.

The vapour extraction process, or &amp / #8216 / VAPEX&amp / #8217 / has attracted a great deal of attention in recent years as a new method of heavy oil or bitumen recovery. The VAPEX (vapour extraction) can be visualized as energy efficient recovery process for unlocking the potential of high viscosity resources trapped in bituminous and heavy oil reservoirs. A total of 20 VAPEX experiments performed with Hele-Shaw cell utilizing three different Turkish crude oils. Two different VAPEX solvents (propane and butane) were used with three different injection rates (20, 40 and 80 ml/min). Garzan, Raman and Bati Raman crude oils were used as light, medium and heavy oil. Apart from normal Dry VAPEX experiments one experiment was conducted with CO2 and another one with butane + steam as Wet VAPEX experiment. All experiments were recorded by normal video camera in order to analyze visually also. For both VAPEX solvents, oil production rates increased with injection rates for all crude oils. Instantaneous asphaltene rate for Garzan oil, showed fluctuated performance with propane solvent. Butane showed almost constant degree of asphaltene precipitation. Instantaneous asphaltene rate for Raman and Bati Raman oils gave straight line results with the injection rate of 20 ml/min for both solvent. When the injection rate increased graphs showed the same performance with Garzan oil and started to fluctuate for both solvent. For asphaltene precipitation, propane gave better results than butane in almost all injection rates for Garzan and Raman oil. In the experiments with Bati Raman oil, butane made better upgrading than propane with the injection rate 80 ml/min. With the other two rates, both solvents showed almost same performace.