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.

No description available.

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.

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.

<p>Ferrofluids are remarkable materials composed of magnetic nanoparticles dispersed in a carrier liquid. These suspensions exhibit fluid-like behavior in the absence of a magnetic field, but when exposed to a magnetic field, they can respond and deform into a variety of patterns. This responsive behavior of ferrofluids makes them an excellent material for applications such as drug delivery for targeted therapies and soft robots. In this thesis, we will focus on the interfacial dynamics of ferrofluids in Hele-Shaw cells. The three major objectives of this thesis are: understanding the pattern evolution, unraveling the underlying nonlinear dynamics, and ultimately achieving passive control of ferrofluid interfaces. First, we introduce a novel static magnetic field setup, under which a confined circular ferrofluid droplet will deform and spin steadily like a `gear’, driven by interfacial traveling waves. This study combines sharp-interface numerical simulations with weakly nonlinear theory to explain the wave propagation. Then, to better understand these interfacial traveling waves, we derive a long-wave equation for a ferrofluid thin film subject to an angled magnetic field. Interestingly, the long-wave equation derived, which is a new type of generalized Kuramoto--Sivashinsky equation (KSE), exhibits nonlinear periodic waves as dissipative solitons and reveals fascinating issues about linearly unstable but nonlinearly stable structures, such as transitions between different nonlinear periodic wave states. Next, inspired by the low-dimensional property of the KSE, we simplify the original 2D nonlocal droplet problem using the center manifold method, reducing the shape evolution to an amplitude equation (a single local ODE). We show that the formation of the rotating `gear’ arises from a Hopf bifurcation, which further inspires our work on time-dependent control. By introducing a slowly time-varying magnetic field, we propose strategies to effectively control a ferrofluid droplet's evolution into a targeted shape at a targeted time. The final chapter of this thesis concerns our ongoing research into the interfacial dynamics under the influence of a fast time-varying and rotating magnetic field, which induces a nonsymmetric viscous stress tensor in the ferrofluid, requiring the balance of the angular momentum equation. As a consequence, wave propagation on a ferrofluid interface can be now triggered by magnetic torque. A new thin-film long-wave equation is consistently derived taking magnetic torque into account.</p>

Reactive flow in porous media, leading to solid precipitation and deposition, is a fundamental process with widespread implications across various fields, such as carbonate mineralization during CO2 sequestration process. Despite the extensive research on the precipitation flow, the physical mechanisms behind the coupling between the hydrodynamics and reaction are less well-understood. This thesis investigates the complex interplay between fluid flow and a chemical reaction (A+B=C) that triggers precipitation and deposition in a Hele-Shaw cell with a gap thickness much smaller than the ones used in the past. We find that both electrostatic and hydrodynamic forces influence the onset of fingering. The results reveal that precipitation-induced fingering plays a significant role in altering mixing dynamics and precipitation rate. A model is developed, incorporating a more realistic rheology model and a first-order deposition term into an advection-diffusion-reaction framework, to comprehensively analyze the impact of critical parameters such as injection rate and initial reactant concentrations on hydrodynamic instability resulting from precipitation and deposition. Validation against experimental data demonstrates the model's capability to capture diverse precipitation patterns observed under varying experimental conditions accurately. Additionally, the results highlight the crucial role of the deposition term in accurately predicting the temporal evolution of total solid content observed in the experiments. Furthermore, the thesis explores the influence of porous media heterogeneity on calcium carbonate mineralization dynamics in a 2D radial porous system. Using a flow cell with a bimodal pore throat size distribution, the study investigates the temporal evolution of the mixing front, total precipitation amount, and spatial distribution of deposited particles under different injection rates and reactant concentrations. Findings reveal the formation of stable mixing fronts at higher injection rates, driven by the creation of large aggregates, and demonstrate enhanced precipitation in porous media dominated by advection. Conversely, in diffusion-dominated conditions, the precipitation rate transitions to scaling behaviors observed in a homogeneous media. The experimental observations elucidate the deposition of large aggregates in low-permeability regions, leading to significant alterations in cell permeability and porosity. / Thesis / Doctor of Philosophy (PhD)

[pt] Estudou-se neste trabalho o deslocamento de fluidos em meios porosos utilizando células de Hele-Shaw. Especificamente, investigou-se experimentalmente o deslocamento de um fluido não newtoniano por um newtoniano em uma célula retangular de Hele-Shaw. A instabilidade de Saffman-Taylor ou viscous fingering é um fenômeno observado quando um fluido de menor viscosidade desloca um de maior viscosidade, e a célula de Hele-Shaw é uma ferramenta conveniente para a sua observação. Esse fenômeno é muito importante em diversas aplicações, como por exemplo: recuperação secundária e terciária de petróleo, invasão de fluidos de perfuração em meios porosos, fraturamento hidráulico, processamento de polímeros, hidrologia e filtração. É vasta a literatura relativa ao estudo de fluidos newtonianos e não newtonianos deslocados por ar em células de Hele-Shaw. Entretanto, existem poucos trabalhos envolvendo deslocamentos de líquidos com viscosidades comparáveis, ou seja, razão de viscosidade diferente de zero. Apresentou-se o detalhamento do projeto de construção de uma célula de Hele-Shaw aplicável ao deslocamento de um líquido por outro líquido. A evolução da forma da interface foi analisada, através de uma câmera fotográfica, em função dos parâmetros geométricos, dinâmicos e reológicos. A partir da vetorização da forma da interface, determinou-se a eficiência do deslocamento. Sendo assim, foi definido o espectro de situações em que há formação de fingers e plugs relativos ao deslocamento de goma xantana por um óleo mineral. Não há na literatura uma convenção universal para apresentação dos resultados, logo uma contribuição original refere-se à adimensionalização proposta onde os principais parâmetros governantes são a velocidade adimensional, o número de capilaridade reológico e o índice de comportamento da goma xantana. Observou-se que para um valor constante do índice de comportamento e para um valor do número de capilaridade reológico da ordem de 10-1, a eficiência de deslocamento aumenta com a velocidade adimensional, porque a razão de viscosidade diminui. / [en] This work studied the displacement of fluids in porous media using a Hele-Shaw cell. Specifically, was investigated experimentally the displacement of a non-Newtonian fluid by a Newtonian in a rectangular Hele-Shaw cell. The Saffman-Taylor or viscous fingering instability occurs when one fluid pushes a more viscous one, and a Hele-Shaw is a convenient tool to the phenomenon observation. Applications include displacement of heavy crude oil in reservoirs, drilling fluid invasion through porous media, fracture conductivity, polymer processing, hydrology and filtration. The Saffman-Taylor instability has been extensively studied for Newtonian and non-Newtonian liquids displaced by air in a Hele-Shaw cell. However displacement flows involving two liquids of comparable viscosity (nonzero viscosity ratio) have received very little attention. It was presented the details of construction of a Hele-Shaw applicable to a liquid-liquid displacement. The evolution of the shape of the interface was analyzed through a digital camera, as a function of the geometric, dynamic and rheological parameters. From tracing the shape of the interface, was determined the displacement efficiency. Thus, it was defined the spectrum of situations in which there is formation of fingers and plugs relating to displacement of xanthan gum by a mineral oil. There is no universal convention in the literature for presenting the results so a original contribution concerns the proposed dimensionless parameters. The main parameters that govern this flow are the dimensionless flow rate, the rheological capillary number and the behavior index of xanthan gum. It was observed that for a constant value of the behavior index and for a rheological capillary number of magnitude of 10-1, the displacement efficiency increases with the dimensionless flow rate, because the viscosity ratio decreases.

La combustion pré mélangée a été depuis longtemps un domaine vaste d’étude au niveau appliqué et fondamental. Bien que la plupart des applications industrielles en combustion aient lieu dans des régimes turbulents, le passage par l’étude laminaire est indispensable pour comprendre les mécanismes fondamentaux des flammes turbulentes. Ce travail de thèse porte essentiellement sur l’étude des différentes instabilités agissant sur un front de flamme laminaire de pré mélange pour des mélanges de propane-air et méthane-air, enrichis ou non en azote. L’étude consiste à mesurer les taux de croissance des perturbations dans un brûleur d’Hele-Shaw formé par deux plaques de verre ($150\times50cm$) très rapprochées (brûleur 2D). Grâce à un système de forçage constitué par des plaques modulées spatialement avec différentes longueurs d’onde, le taux de croissance peut être mesuré même en présence du développement spontané de l’instabilité avec la longueur d’onde la plus instable. A richesse constante et pour des valeurs croissantes de la dilution en oxygène le vecteur d'onde de coupure augmente avec la vitesse de flamme qui devient plus instable. Pour des mélanges de propane ce nombre d’onde augmente également lorsqu'on augmente la richesse à vitesse constante et il diminue dans le cas des mélanges de méthane, cela est en relation avec l'évolution des effets thermodiffusifs dans chacun des cas. Une augmentation de l’épaisseur de la cellule d’Hele-Shaw, aboutit à une augmentation du taux de croissance pour les petits nombres d’onde ainsi que du nombre de Markstein, et à une diminution du taux de croissance pour les grands nombres, du fait des effets des pertes thermiques. / Premixed combustion has been the subject of extensive work, concerning both applications and fundamental aspects. Although in most practical applications combustion occurs in a turbulent environment, the study of laminar flames is important to understand the fundamental mechanisms of turbulent flame propagation. The objective of this work is to study the various instabilities acting on a laminar premixed flame for mixtures of propane-air and methane-air, enriched or not with nitrogen. it consists in measuring the linear growth rates of disturbances in a Hele-Shaw burner formed by two glass plates ($150\times50cm$) separated by a thin gap width (2D burner). Using spatially modulated plates with different wavelengths, the linear growth rate of perturbations can be measured even in the presence of the most unstable wavelength. The experimental values of the linear growth rate as a function of wavenumber are fitted by a linear dispersion relation to estimate the Markstein number and the cutoff wavenumber. For a constant equivalence ratio with increasing values of the dilution in oxygen, the cutoff wavenumber grows with the flame velocity and it is becoming more unstable. The cutoff wave number rises also when the equivalence ratio increases for propane-air mixture and decreases for methane-air mixture, in relation to the evolution of thermal diffusive effects. An enlargement in the thickness of the Hele-Shaw cell results in an increase of the growth rate for small wavenumbers thus in the Markstein number, and in a decline in the growth rate for the large wavenumbers, in relation with the effects of heat losses.

Integrated theoretical and experimental analysis is carried out in this work to investigate the fundamental failure mechanisms and flow patterns involved in the process of fluid injection into dense granular media. The experimental work is conducted with aqueous glycerin solutions, utilizing a novel setup based on a Hele-Shaw cell filled with dense dry sand. The two dimensional nature of the setup allows direct visualization and imaging analysis of the real-time fluid and grain kinematics. The experimental results reveal that the fluid flow patterns show a transition from simple radial flow to a ramified morphology while the granular media behaviors change from that of rigid porous media to localized failure that lead to development of fluid channels. Based on the failure/flow patterns, four distinct failure/flow regimes can be identified, namely, (i) a simple radial flow regime, (ii) an infiltration-dominated regime, (iii) a grain displacement-dominated regime, and (iv) a viscous fingering-dominated regime. These distinct failure/flow regimes emerge as a result of competition among various energy dissipation mechanisms, namely, viscous dissipation through infiltration, dissipation due to grain displacements, and viscous dissipation through flow in thin channels and can be classified based on the characteristic times associated with fluid injection, hydromechanical coupling and viscoelastoplasticity. The injection process is also analyzed numerically using the discrete element method (DEM) coupled with two fluid flow scheme, a fixed coarse grid scheme based on computational fluid dynamics (CFD) and a pore network modeling scheme. The numerical results from the two complementary methods reproduce phenomena consistent with the experimental observations and justify the concept of associating the displacement regimes with the partition among energy dissipation mechanisms. The research in this work, though fundamental in nature, will have direct impacts on many engineering problems in civil, environmental and petroleum engineering such as ground improvement, environmental remediation and reservoir stimulation.