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Cummings, Linda Jane. "Free boundary models in viscous flow." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339364.
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Jackson, Michael. "Interfacial instability analysis of viscous flows in a Hele-Shaw channel." Thesis, Queensland University of Technology, 2021. https://eprints.qut.edu.au/212417/1/Michael_Jackson_Thesis.pdf.
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When a less viscous fluid displaces a more viscous fluid inside a quasi-two-dimensional channel, the interface separating the two fluids can become highly unstable and perturbed. By assuming that the more viscous fluid is finite in volume, this thesis uses analytical and computational methods to investigate the effect of two fluid interfaces. The results could have implication in fields such as oil extraction, geology, and advanced manufacturing.
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Azzopardi, Charles-Louis. "Dispositifs microfluidiques pour l’injection de fluides à travers un réseau de gouttes : application biocapteur." Thesis, Bourgogne Franche-Comté, 2018. http://www.theses.fr/2018UBFCD020/document.
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La microfluidique, domaine de recherche qui a émergé il y a juste 20 ans, a permis de réduire les dimensions des dispositifs d’analyse biologique ouvrant la porte au concept de « laboratoire-sur-puce » (lab-on-chip). Les succès de cette approche sont déjà nombreux, depuis l’analyse du génome en passant par la réduction du coût des analyses médicales. L’utilisation de gouttes comme enceinte réactionnelle au sein de ces dispositifs est une évolution récente qui permet de réduire encore le volume des échantillons biologiques et d’augmenter la vitesse d’analyse en parallélisant les mesures.Notre équipe développe des capteurs acoustiques dédiés à la détection d’analytes biologiques en milieu liquide. Ce type de capteur a pour principal défaut de ne permettre qu’une mesure contraignant au remplacement de l’interface de biodétection pour une réutilisation éventuelle du capteur. Dès lors, ils utilisent majoritairement une chambre de détection tout ou partie jetable, même si quelques travaux de recherche ont pu montrer la régénération d’un capteur par traitement chimique.Nous proposons ici de s’affranchir des étapes lourdes de remplacement ou de traitement de l’interface de détection qui conduisent entre chaque mesure au démontage du dispositif de détection. Nous employons dans ce cas les gouttes non plus comme enceinte réactionnelle mais comme interface de détection mobile. Elles ont ainsi le potentiel d’être générées et fonctionnalisées directement dans le dispositif pour détecter un analyte spécifique et peuvent être simplement évacuées afin de régénérer l’interface pour effectuer une mesure différente.Les travaux présentés dans cette thèse visent plus particulièrement la capture sur gouttes fonctionnalisées dans ce type de capteur innovant. Ils exposent le développement, incluant la fabrication et la caractérisation, de ces dispositifs microfluidiques ainsi que le montage d’un banc de test expérimental dédié. Ce sujet est suivi de deux projets ancillaires de développement de dispositifs microfluidiques liés aux capteurs acoustiques et à l’utilisation de gouttes. Le premier vise à homogénéiser les vitesses d’écoulements dans une chambre réactionnelle. Le second exploite les propriétés de génération de gouttes pour réaliser un condensateur à capacité variable<br>Since two decades the research on microfluidics systems allowed creating devices for biological detection with regular improvement in compactness, functionality integration and quantity of biological sample, leading to the concept of lab-on-chip. This approach has resulted in dramatic changes in the biomedical field, for example, opening the possibility to perform genomic analysis or improving the medical analysis cost. Using droplet as reaction chamber is a recent evolution that leads to a decrease in biological sample volume and an increase in analysis speed by multiplexing.Our team develops acoustical sensors dedicated to detect biomarker of interest in liquids. The principal weakness of theses sensors lies in their need for replacement of the biodetection interface for performing a new measurement. Accordingly, they use a detection chamber partially or totally disposable. However, few research works showed reusability of sensor by regenerating the bioreceptor layer on the detection interface by chemical treatment.We are proposing to avoid the replacement or the chemical treatment of the detection interface that requires dismounting the device between measurements. We are using here droplets, not as reaction chambers but as movable detection interface. They can be generated and configured directly inside the device to detect a specific biomarker. Then, droplets can be easily evacuated and replaced through the device, which allows to chain measurement of various configurations without dismounting it.The research work conducted in this thesis focuses on the fluidic aspects of this innovative sensor. They show development, including realization and characterization, of theses microfluidic devices and its dedicated characterization setup. This project is followed by two ancillary works about development of microfluidic devices for acoustical sensors and droplets systems. The first one is aiming at the homogenization of the flow velocity inside a reaction chamber. The second one is exploiting property of droplet generation for the realization of a variable capacitance capacitor
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Brown, Sarah Marie. "A Numerical Scheme for Mullins-Sekerka Flow in Three Space Dimensions." BYU ScholarsArchive, 2004. https://scholarsarchive.byu.edu/etd/136.
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The Mullins-Sekerka problem, also called two-sided Hele-Shaw flow, arises in modeling a binary material with two stable concentration phases. A coarsening process occurs, and large particles grow while smaller particles eventually dissolve. Single particles become spherical. This process is described by evolving harmonic functions within the two phases with the moving interface driven by the jump in the normal derivatives of the harmonic functions at the interface. The harmonic functions are continuous across the interface, taking on values equal to the mean curvature of the interface. This dissertation reformulates the three-dimensional problem as one on the two-dimensional interface by using boundary integrals. A semi-implicit scheme to solve the free boundary problem numerically is implemented. Numerical analysis tasks include discretizing surfaces, overcoming node bunching, and dealing with topology change in a toroidal particle. A particle (node)-cluster technique is developed with the aim of alleviating excessive run time caused by filling the dense matrix used in solving a system of linear equations.
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ANJOS, Pedro Henrique Amorim. "Efeitos de molhamento nas instabilidades hidrodinâmicas e em forças adesivas em fluidos confinados." Universidade Federal de Pernambuco, 2015. https://repositorio.ufpe.br/handle/123456789/18074.
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Previous issue date: 2015-02-05<br>CNPQ<br>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.<br>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.
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Maes, RENAUD POL. "Etude expérimentale de la digitation visqueuse de fluides miscibles en cellule de Hele-Shaw." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/216585.
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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, 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.<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished
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Beauvier, Edouard. "Propagation d'un front de réaction-diffusion dans un écoulement cellulaire multi-échelle." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4728/document.
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La propagation d'un front de réaction-diffusion est étudiée expérimentalement dans un écoulement cellulaire multiéchelle. Le front est produit par réaction autocatalytique en solution. L'écoulement est réalisé en géométrie de Hele-Shaw par électroconvection, son caractère multiéchelle étant réalisé par l'action combinée de deux nappes d'aimants d'échelles différentes. La géométrie du front et sa vitesse moyenne de propagation sont déterminées pour une large gamme d'intensité des vortex de chaque échelle. Elles sont confortées par une simulation numérique de l'avancée du domaine brulé dans le domaine frais. L'effet de la nature multiéchelle de l'écoulement sur la vitesse moyenne du front est compris par une méthode de renormalisation dont la validation est fournie par l'obtention d'un courbe maitresse pour l'ensemble des données<br>The propagation of a reaction-diffusion front is experimentally studied in a multi-scale cellular flow. The front is produced by an autocatalytic chemical reaction in an aqueous solution. The flow is generated by electroconvection and its multi-scale nature is induced by overlaying magnets of different scales. This enables an independent tune of the flow intensity at each scale. The geometry and the mean velocity of the front have been determined over a large range of scale intensities. These features are confirmed by a numerical simulation based on a burnt and fresh domain dynamics, the burnt domain expanding across the fresh one. The effect of the multi-scale nature of the flow on the mean front velocity is recovered by a renormalisation method validated by a collapse of the data onto a single curve
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Morrow, Liam Christopher. "A numerical investigation of Darcy-type moving boundary problems." Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/204264/1/Liam_Morrow_Thesis.pdf.
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We investigate the development of interfacial instabilities and singularities that occur in solutions to Darcy-type moving boundary problems. We present a robust numerical scheme which can easily be adapted to a wide range of problems that, to date, have not yet been solved. Using this scheme, we provide insight into how perturbing the geometry of a Hele-Shaw cell can be used to control the development of interfacial patterns. Further, we consider how different physical effects influence the development of a singularity due to an air bubble contracting to a point or breaking up into multiple bubbles.
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Kreyenberg, Philipp Johannes [Verfasser], and Kurt [Akademischer Betreuer] Roth. "Flow Field Estimation of Active Solute Transport – Information Transfer from Synthetic Data to Hele-Shaw Cell Experiments Using Convolutional Neural Networks / Philipp Johannes Kreyenberg ; Betreuer: Kurt Roth." Heidelberg : Universitätsbibliothek Heidelberg, 2019. http://d-nb.info/1200021592/34.
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Burgess, Don Edward. "Topics in Hele-Shaw flows /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487682558443754.
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Jonsson, Karl. "Multiple Phase Hele-Shaw Flows." Thesis, KTH, Matematik (Avd.), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-139321.
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A one phase Hele-Shaw flow, described by a domain D(t) (t represents time) in the plane is the flow of a liquid injected at a constant rate in the separation between two narrowly separated parallel planes. This thesis deals with the formulation and proof of existence for a multiple phase Hele-Shaw flow in arbitrary dimension R^n exhibiting separation of the phases. A smooth version of the problem, depending on a small parameter epsilon, has been considered. Solutions to this smooth problem approximate the multiple-phase Hele-Shaw flow. We show that the smooth problem has a solution using a variational technique with functions u=u(t;eps) in the Sobolev space H_0^1 describing the Hele-Shaw flow with D(t)=support(u(t;eps)). As we let the parameter epsilon tend to zero we get that the solutions u(t;eps) converges weakly to a family of functions u(t) in the same Sobolev space which describe the desired Hele-Shaw flow. Furthermore the phases represented by the components of u(t) are separated in the sense that the overlap of any two distinct phases has vanishing n-dimensional Lebesgue measure. We also touch upon a formulation of the multiple phase Hele-Shaw flow which would, beyond separation of the phases, provide freezing of the intersecting boundary of two phases. This formulation of the problem tries to incorporate memory in to the system via means of an integration over previous states.
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Zhang, Fengshou. "Pattern formation in fluid injection into dense granular media." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/43716.
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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.
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Malaikah, Khalid R. "Laplacian Growth: Interfacial Evolution in a Hele-Shaw Cell." Ohio University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1367417377.
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Mostefai, Mohamed Sadek. "Déduction rigoureuse de l'équation de Reynolds à partir d'un système modélisant l'écoulement à faible épaisseur d'un fluide micropolaire, et étude de deux problèmes à frontière libre : Hele-Shaw généralisé et Stephan à deux phases pour un fluide non newtonien." Saint-Etienne, 1997. http://www.theses.fr/1997STET4019.
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Dans le chapitre 1, on considère le modèle micropolaire de Navier-Stokes avec conditions de bords de type Dirichlet non homogènes en dimension deux. On donnera un résultat d'existence d'une solution faible en utilisant le théorème du point fixe de Leray-Schauder, puis on prouvera l'unicité de la solution faible du problème sous certaines hypothèses. On établiera une justification mathématique de l’équation de Reynolds généralisé à partir de ce modèle là. On étudiera ensuite la forme de l'équation de Reynolds suivant le choix de la viscosité et des données initiales. Dans le chapitre 2, nous considérons le modèle de Hele-Shaw généralisé dans une cellule laminaire, qui consiste à injecter du fluide, avec un débit non constant w 0, à travers un trou de frontière 1, situé sur l'une des deux surfaces ; et à tenir compte que l'une des surfaces a une géométrie quelconque et animée d'un mouvement relatif vertical. En introduisant un changement de variable de type Baiocchi, le problème initial se ramène à l'étude d'une inéquation variationnelle avec terme de Volterra. L'existence d'une solution pour cette dernière est donnée par le théorème du point fixe de Banach. Des résultats de régularité en espace pour la solution seront prouvés en introduisant un problème pénalisé et en utilisant la méthode de Rothe (semi-discrétisation en temps), puis on montrera que la dérivée par rapport à t de la solution de l'inéquation variationnelle est dans l#(0, t, h#2()), ce dernier résultat nous permet de revenir au problème initial. Dans le chapitre 3, on considère un problème de Stefan à deux phases avec convection. Le problème est gouverné par un système couple non linéaire, comprenant la loi de Darcy pour un fluide non newtonien et l'équation d'équilibre d'énergie avec second membre dans l#1. Pour prouver l'existence de solutions du problème faible on introduira une famille de solutions approchées (#, p#), > 0, définies sur le domaine entier , en insérant une fonction de pénalité convenable dans l'équation de pression. On considère ensuite séparement les problèmes en # et p#, respectivement, et en utilisant le principe de point fixe de Schauder, on montre l'existence de couples solutions (#, p#) du problème approché, pour tout > 0. En faisant tendre vers zéro, on montre que les solutions du problème approché convergent vers une limite (, p) qui est une solution faible du problème variationnel. On montre aussi que la fonction est continue d'où le domaine où > 0 est un ensemble ouvert, et l'interface des deux phases est définie a posteriori comme l'ensemble de niveau = 0. On établira, enfin, quelques relations entre les solutions faibles et classiques, dans le cas d’une courbe assez régulière
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VARGES, PRISCILLA RIBEIRO. "LIQUID-LIQUID DISPLACEMENT FLOWS IN A HELE-SHAW CELL INCLUDING NON-NEWTONIAN EFFECTS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2010. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=16992@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>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.<br>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.
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AZEVEDO, PATRICIA EMIDIO DE. "LIQUID-LIQUID DISPLACEMENT FLOWS IN A HELE-SHAW CELL INCLUDING NON-NEWTONIAN EFFECTS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=26868@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>A perfuração de poços de petróleo, principalmente em ambientes offshore, é
uma operação que demanda um custo muito elevado, portanto a minimização de
problemas e danos ao reservatório produtor é muito importante. O projeto de um
fluido de perfuração que garanta a mínima invasão na rocha reservatório é um tópico
fundamental, como consequência a indústria petrolífera tem investido em estudos
com o intuito de evitar que este problema ocorra. Sendo assim, nesse trabalho
estudou-se o escoamento de fluidos em um meio poroso ideal, a célula de Hele-Shaw.
Para realizar esse trabalho foram utilizados dois fluidos não newtonianos: uma
solução aquosa de um polímero flexível, a poliacrilamida; e uma solução aquosa de
um polímero rígido, a goma xantana. Esses fluidos não newtonianos representaram
o fluido de perfuração, já o papel do petróleo presente na rocha reservatório foi
desempenhado pelo óleo mineral. A partir desse experimento é possível observar a
instabilidade de Saffman-Taylor ou viscous fingers, que é um fenômeno observado
quando um fluido de menor viscosidade desloca outro de maior viscosidade. Esse
fenômeno é muito importante em diversas aplicações, tais como: invasão de fluido
de perfuração em meios porosos (caso que será estudado), recuperação secundária e
terciária de petróleo, fraturamento hidráulico, processamento de polímeros,
hidrologia e filtração. O experimento consiste em analisar a evolução da interface
entre os dois fluidos através de uma câmera filmadora. A partir das imagens é
determinada qualitativamente a eficiência do deslocamento. Com o conjunto de
imagens é possível observar também em quais parâmetros dinâmicos e reológicos
ocorre a transição fingers (interface instável) para plug (interface estável), e viceversa.
Também foram realizados testes reológicos nos quais foi possível conhecer o
comportamento dos fluidos não newtonianos utilizados. Com base nos dados
coletados observou-se que tanto para a poliacrilamida quanto para a goma xantana a
transição ocorre a uma taxa de cisalhamento adimensional próxima de 3.<br>The drilling of oil wells, particularly in offshore environments, is an operation
which demands a high cost, thus, the minimization of problems and damage to the
producing reservoir is very important. The design of a drilling fluid that ensures
minimum invasion into the reservoir rock is a major topic, consequently the oil
industry has invested in research in order to prevent this problem from occurring.
Therefore, this research studied the displacement of fluids in an ideal porous medium,
a Hele-Shaw cell. To accomplish this task, the following two non-Newtonian fluids
were used: an aqueous solution of a flexible polymer, polyacrylamide; and the other
an aqueous solution of a rigid polymer, xanthan gum. Such non-Newtonian fluids
represent the drilling fluid, while the function of oil present in the reservoir rock was
represented by mineral oil. From this experiment it is possible to observe the
Saffman-Taylor instability or viscous fingers, which is a phenomenon observed when
a low viscosity fluid displaces a higher viscosity fluid. This phenomenon is very
important in many applications, such as drilling fluid invasion in porous media,
secondary and tertiary oil recovery, hydraulic fracturing, polymer processing,
hydrology and filtration. The experiment consists in analyzing the evolution of the
interface between two fluids through a digital camera, and determining the
displacement efficiency qualitatively from the imagens. With the set of images is
possible to observe in which dynamic and rheological parameters the transition from
fingers (unstable interface) to plug (stable interface) occurs, and vice versa. Also,
rheological tests were performed in which it was possible to know the behavior of
non-Newtonian fluids used in the study. From the data collected it was observed that
both the polyacrylamide and for xanthan gum transition occurs near the
dimensionless shear rate of 3.
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Wenzel, Michael [Verfasser]. "Classical solutions for stabilized periodic Hele-Shaw flows with a free surface / Michael Wenzel." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2013. http://d-nb.info/104735263X/34.
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Trieu, Hung Truong. "Études théorique et expérimentale du transport de fluides miscibles en cellule Hele-Shaw." Thesis, Vandoeuvre-les-Nancy, INPL, 2011. http://www.theses.fr/2011INPL027N/document.
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Dans cette thèse, nous avons étudié expérimentalement, numériquement et théoriquement la sédimentation d’un soluté en cellule de Hele-Shaw, modèle analogue de milieu poreux, avec un écoulement zonal horizontal. Une cellule, alimentée par deux grands réservoirs assurant un écoulement zonal uniforme, a été réalisée au laboratoire. La vitesse a été mesurée par PIV. L’injection d’une solution saline dans cet écoulement permet de visualiser la propagation du panache de pollution, et de mesurer le champ de concentration par LIF. Trois configurations typiques ont été observées : panache sans digitation (« stable »), avec une seule digitation (« faiblement instable »), et avec de nombreuses digitations (« fortement instable »). L’influence du contraste de densité, de la vitesse zonale, et du débit d’injection sur la stabilité du panache a été analysée. Ces résultats ont été comparés à des simulations numériques sous COMSOL Multiphysics®. Les champs de concentration simulés sont en accord quantitatif avec les champs expérimentaux. Ces simulations ont de plus permis d’étudier l’influence de l’anisotropie du tenseur de dispersion sur la stabilité du panache. Une étude théorique linéaire, effectuée à partir d’un écoulement de base unidirectionnel et quasi-stationnaire, est venue compléter ces résultats. Elle montre que le panache est toujours convectivement instable pour les valeurs des paramètres considérées, et permet de retrouver et de quantifier les principaux résultats mis en évidence lors des études expérimentale et numérique, comme l’effet stabilisant de la dispersivité longitudinale ou l’effet déstabilisant du contraste de densité<br>This thesis is an experimental and numerical investigation of solute transport and sedimentation in a Hele-Shaw cell with zonal flow. A vertical cell joining two large tanks has been built to provide a uniform horizontal flow, the velocity of which has been measured by using PIV. The concentration field of a solute injected in this flow has been measured by using LIF. Three typical plume configurations have been observed: without digitations (“stable”), with a single digitation (“weakly unstable”), and with various digitations appearing at the lower interface (“unstable plume”). The influence of density contrast, zonal flow and solute flow rate on the appearance of the various configurations has been investigated. These results have been compared to numerical simulations using the COMSOL Multiphysics® software. The numerical concentration fields are in qualitative agreement with the experimental ones. In addition, these simulations allowed us to investigate the effect of the anisotropy of the dispersion tensor on the occurrence of unstable configurations. A linear stability analysis based on a uniform parallel flow superposed to a quasi-steady horizontal layer of solute has been performed. It shows that the plume is convectively unstable for the parameters considered here, and confirms the various behaviors observed in both the experimental and the numerical analyses, like the stabilizing effect of the longitudinal dispersivity or the destabilizing effect of the solute concentration
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Jonsson, Karl. "Two Problems in non-linear PDE’s with Phase Transitions." Licentiate thesis, KTH, Matematik (Avd.), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-223562.
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This thesis is in the field of non-linear partial differential equations (PDE), focusing on problems which show some type of phase-transition. A single phase Hele-Shaw flow models a Newtoninan fluid which is being injected in the space between two narrowly separated parallel planes. The time evolution of the space that the fluid occupies can be modelled by a semi-linear PDE. This is a problem within the field of free boundary problems. In the multi-phase problem we consider the time-evolution of a system of phases which interact according to the principle that the joint boundary which emerges when two phases meet is fixed for all future times. The problem is handled by introducing a parameterized equation which is regularized and penalized. The penalization is non-local in time and tracks the history of the system, penalizing the joint support of two different phases in space-time. The main result in the first paper is the existence theory of a weak solution to the parameterized equations in a Bochner space using the implicit function theorem. The family of solutions to the parameterized problem is uniformly bounded allowing us to extract a weakly convergent subsequence for the case when the penalization tends to infinity. The second problem deals with a parameterized highly oscillatory quasi-linear elliptic equation in divergence form. As the regularization parameter tends to zero the equation gets a jump in the conductivity which occur at the level set of a locally periodic function, the obstacle. As the oscillations in the problem data increases the solution to the equation experiences high frequency jumps in the conductivity, resulting in the corresponding solutions showing an effective global behaviour. The global behavior is related to the so called homogenized solution. We show that the parameterized equation has a weak solution in a Sobolev space and derive bounds on the solutions used in the analysis for the case when the regularization is lost. Surprisingly, the limiting problem in this case includes an extra term describing the interaction between the solution and the obstacle, not appearing in the case when obstacle is the zero level-set. The oscillatory nature of the problem makes standard numerical algorithms computationally expensive, since the global domain needs to be resolved on the micro scale. We develop a multi scale method for this problem based on the heterogeneous multiscale method (HMM) framework and using a finite element (FE) approach to capture the macroscopic variations of the solutions at a significantly lower cost. We numerically investigate the effect of the obstacle on the homogenized solution, finding empirical proof that certain choices of obstacles make the limiting problem have a form structurally different from that of the parameterized problem.<br><p>QC 20180222</p>
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Schafroth, Dario. "Influence of non monotonic viscosity profiles on the stability of miscible displacement flows in a Hele-Shaw cell." Zürich : ETH, Eidgenössische Technische Hochschule Zürich, Institut of Fluid Dynamics, 2006. http://e-collection.ethbib.ethz.ch/show?type=dipl&nr=232.
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Callens, Natacha. "Développement, étude expérimentale et visualisation par holographie digitale de mini-séparateurs fluidiques (STEP-SPLITT) en vue de la séparation d'objets de taille micrométrique." Doctoral thesis, Universite Libre de Bruxelles, 2005. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210976.
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Cette thèse expérimentale s’inscrit dans le domaine des sciences séparatives et se base sur la technique de SPLITT (SPLIT-flow Thin fractionation). Son objectif consiste en l’étude des mécanismes qui sont à l’origine de la séparation, en continu et sans membrane, d’objets de taille micrométrique dans des mini-séparateurs fluidiques (Step-SPLITT). Les expériences menées, en laboratoire et lors de vols paraboliques, ont révélé le couplage complexe comme l’influence des effets hydrodynamiques et du champ gravitationnel sur la migration transverse des espèces en écoulement. Des visualisations tridimensionnelles par holographie digitale ont corroboré nos résultats et dévoilé des comportements inattendus. Les capacités séparatives des Step-SPLITT ont rendu possible l’analyse et la séparation d’objets biologiques et biomimétiques. Enfin, cette étude complétée par une modélisation tridimensionnelle de l’écoulement nous a permis de mettre au point un nouveau prototype de séparateur.<p><p>This experimental thesis belongs to the field of separative sciences and is based on the SPLITT technique (SPLIT-flow Thin fractionation). The objective is to study the mechanisms that are at the origin of continuous and membraneless separation of micron-size species in mini fluidic separators (Step-SPLITT). Experiments undertaken in laboratory and during parabolic flights revealed the complex coupling of the hydrodynamic effects and the gravitational field influencing the transverse migration of the flowing species. Three-dimensional visualizations performed by digital holography confirmed our results and disclosed unexpected behaviours. The separation capacities of Step-SPLITT made the analysis and the separation of biological and biomimetic species possible. In addition this study in conjunction with a three-dimensional flow modelling enabled us to develop a new prototype of separator.<br>Doctorat en sciences appliquées<br>info:eu-repo/semantics/nonPublished
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Pauné, i. Xuriguera Eduard. "Interface Dynamics in Two-dimensional Viscous Flows." Doctoral thesis, Universitat de Barcelona, 2002. http://hdl.handle.net/10803/1584.
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The subject of this thesis is viscous fingering in Hele-Shaw cells, or Hele-Shaw flows. We look for insights into the fundamental mechanisms<br/>underlying the physics of interface dynamics, which we hope will exhibit some degree of universality. The aim is twofold: on the one hand we focus on the role of surface tension and viscosity contrast in the dynamics of fingering patterns. On the other hand we introduce a modification of the original problem and study the effects of a inhomogeneous gap between the<br/>plates of a Hele-Shaw cell.<br/><br/>A dynamical systems approach to competition of Saffman-Taylor (ST) fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the ODE sets associated to the exact solutions of the problem without surface tension. A general proof of the existence of finite-time singularities for broad classes of solutions is given. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic. Hyperbolicity (saddle-point structure) of multifinger fixed points is argued to be essential to the physically correct qualitative<br/>description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic Dynamical Solvability Scenario for interfacial pattern selection.<br/><br/>We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques developed by Tanveer and Siegel, and numerical computation, following the numerical scheme of Hou, Lowengrub, and<br/>Shelley. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact<br/>(non-singular) zero-surface tension solutions. The effect is present even when the zero surface tension solution has asymptotic behavior consistent with selection theory. Such singular effects therefore cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow.<br/><br/>Finger competition with arbitrary viscosity contrast (or Atwood ratio) is<br/>studied by means of numerical computation. Two different types of dynamics<br/>are observed, depending on the value of the viscosity contrast an the<br/>initial condition. One of them exhibits finger competition and ends up in<br/>the ST finger. In opposition, the second dynamics does not exhibit finger<br/>competition and the long time dynamics seems attracted to bubble shaped<br/>solutions. An initial condition appropriate to study the ST finger basin<br/>of attraction is identified, and used to characterize its dependence on<br/>the viscosity contrast, obtaining that its size decreases for decreasing<br/>viscosity contrast, being very small for zero viscosity contrast. The ST<br/>finger is not the universal attractor for arbitrary viscosity contrast. An<br/>alternative class of attractors is identified as the set of Taylor-Saffman<br/>bubble solutions, and one important implication of this result is that the<br/>interface is strongly attracted to finite time pinchoff.<br/><br/>A nonlocal interface equation is derived for two-phase fluid flow, with<br/>arbitrary wettability and viscosity contrast c, in a model porous medium defined as a Hele-Shaw cell with random gap b. Fluctuations of both capillary and viscous pressure are explicitly related to the microscopic quenched disorder, yielding conserved, non-conserved and power-law correlated noise terms. Two length scales are identified that control the possible scaling regimes and which depend on capillary number Ca as l sub 1 = b sub zero (c Ca)(superindex -1/2) and l sub 2 = b sub zero/Ca. Exponents for forced fluid invasion are obtained from numerical simulation and compared with recent experiments,obtaining good partial agreement.
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Laborde, Maxime. "Systèmes de particules en interaction, approche par flot de gradient dans l'espace de Wasserstein." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLED014/document.
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Depuis l’article fondateur de Jordan, Kinderlehrer et Otto en 1998, il est bien connu qu’une large classe d’équations paraboliques peuvent être vues comme des flots de gradient dans l’espace de Wasserstein. Le but de cette thèse est d’étendre cette théorie à certaines équations et systèmes qui n’ont pas exactement une structure de flot de gradient. Les interactions étudiées sont de différentes natures. Le premier chapitre traite des systèmes avec des interactions non locales dans la dérive. Nous étudions ensuite des systèmes de diffusions croisées s’appliquant aux modèles de congestion pour plusieurs populations. Un autre modèle étudié est celui où le couplage se trouve dans le terme de réaction comme les systèmes proie-prédateur avec diffusion ou encore les modèles de croissance tumorale. Nous étudierons enfin des systèmes de type nouveau où l’interaction est donnée par un problème de transport multi-marges. Une grande partie de ces problèmes est illustrée de simulations numériques<br>Since 1998 and the seminal work of Jordan, Kinderlehrer and Otto, it is well known that a large class of parabolic equations can be seen as gradient flows in the Wasserstein space. This thesis is devoted to extensions of this theory to equations and systems which do not have exactly a gradient flow structure. We study different kind of couplings. First, we treat the case of nonlocal interactions in the drift. Then, we study cross diffusion systems which model congestion for several species. We are also interested in reaction-diffusion systems as diffusive prey-predator systems or tumor growth models. Finally, we introduce a new class of systems where the interaction is given by a multi-marginal transport problem. In many cases, we give numerical simulations to illustrate our theorical results
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Chang, Sha. "Hele-Shaw Flow Near Cusp Singularities." Thesis, 2013. https://thesis.library.caltech.edu/7252/1/Chang-Sha-2013.pdf.
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This thesis discusses the radial version of the Hele-Shaw problem. Different from the channel version, traveling-wave solutions do not exist in this version. Under algebraic potentials, in the case that the droplets expand, in finite time, cusps will appear on the boundary and classical solutions may not exist afterwards. Physicists have suggested that for (2p+1,2)-cusps, that near cusp singularities of Hele-Shaw flow, after scaling X, Y by some powers of time t respectively, the main part of Y(X, t) is a one-parameter family and does not depend on time t. They have also suggested that the solutions of the Hele-Shaw problem are connected with dispersionless KdV (dKdV) hierarchy. In this study, we rigorously proved that this is the case for (3,2)-cusps when the droplets are simply connected and the external potentials are algebraic. We gave exact solutions and showed that the main parts of the exact solutions are some special solutions of the dispersionless string equation. More over, borrowed from the physical paper$\cite{Teo}$ with a little more details, we showed the arguments of how these special solutions are related to dKdV hierarchy.
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Shu-Shian, Chen, and 陳書嫻. "Numerical Simulation of an Immiscible Lifting Hele-Shaw Flow." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/38d2w4.
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碩士<br>國立交通大學<br>機械工程系所<br>106<br>The LOCA coating machine uses stress to force two plates where OCR material is placed between close-fitting. The glue optimal pattern spreads close to its base plate and no glue should excess the plate boundary. The processes mimic the problems of compressing Hele-Shaw flows. Accordingly, we assume that the inner flow pattern formed from the pulled plate is same as the original figure which upper plate pushed down. In this study, we use computer simulation method to find out that how the viscosity ratio, the initial aspect ratio, the lifting plate velocity and the surface tension induce the optimization of glue pattern. As the result of interfacial instability, less viscous fluid displaces another fluid of higher viscosity while the height increasing. Four sides of the rectangle will rapidly shrink inward. On the contrary, the pattern will appear four fingers on the corner of the rectangle.
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Lee, Bo-Heng, and 李伯亨. "The Effects of Crack Infiltration and Hele-Shaw Modeling the Seepage Flow." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/uv56bg.
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博士<br>國立中央大學<br>土木工程研究所<br>97<br>This study explores the 2-D transient seepage flow and steady flow from cracks into different porous media, including both coarse material and fine material. The Crack Apparatus of Hele-Shaw Model is chosen to analyze the configuration of wetting front in the coarse material. Due to the effect of gravity on the flow condition, the wetting front in the coarse material is more elongated than that of the fine material. The limited width of wetting front is approaching a constant value in the coarse material. On the other hand, the effect of capillary causes the wetting front in the fine sand expands continuously as time increases. In this paper, a Green-Ampt type of conceptual model is proposed to describe the propagating process of the wetting front in different materials. The time-dependent wetting front and the corresponding wetted area are obtained in this study, which are beneficial for examining the leaky contaminant transport from cracks into different porous media or for the analysis of the slope stability problems.
The second topic of this study is development and validation of an analytical solution for the flow through horizontal and sloping bed. The parameter, B, shown in the analytical solution of horizontal bed increases with the increasing ratio of width to upstream level. The Hele–Shaw model is employed to examine the phreatic surface and exit point of seepage flow by adjusting gap width and fluids density. Aluminum powders were used to as tracking particles inside the gap and the flow visualization was performed. Both horizontal and sloping bed, the phreatic (free) surfaces and exit points are in good agreement between experimental data and the analytical solution. The assumption of a parabolic piezometric head was verified by experimental data. In the horizontal bed, the ratio of down-upstream water depth is large than 0.9 and the ratio of upstream depth -width is less than 0.1, the solution based on Dupuit model is close to the analytical solution.
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Rezanezhad, Fereidoun [Verfasser]. "Experimental study of fingering flow in porous hele shaw cells / presented by Fereidoun Rezanezhad." 2007. http://d-nb.info/984517863/34.
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Al, Brahim Ahmed. "Experimental study on the viscosity effects on the bubbly flow dynamics inside a large Hele-Shaw cell." Thesis, 2018. http://hdl.handle.net/10754/629182.
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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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Mei-YuChen and 陳眉羽. "Study on Flow Instabilities on the Miscible Magnetic Fluid Interface in the Rotating Hele-Shaw Cell." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/29403570718640549572.
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碩士<br>國立成功大學<br>航空太空工程學系碩博士班<br>100<br>In this study, the interfacial instabilities of miscible magnetic fluids and diesel were theoretically and experimentally studied in a rotating Hele-Shaw cell. First, the dimensional analysis was used to understand the relation magnetic force, viscous force, centrifugal force, pressure force and Coriolis force. In addition, it could assist in experimental design.
Two kinds of the flow field were studied, the open Hele-Shaw cell and the closed Hele-Shaw cell. The labyrinthine fingering phenomena of the miscible magnetic fluid interface on a perpendicular magnetic field were investigated. First, the interface of miscible magnetic fluids and diesel became more unstable when the rotating speed and the consequent centrifugal force were increased without magnetic field applied.
Three ferrofluids were used in this study. To compare the results, the gyration radius will be grown fast with ferrofluid EMG905. The first reason was that the initial susceptibility and particle concentration for EMG905 were higher than that for the other two ferrofluids. So the diffusion and magnetic effects for EMG905 will be the most obvious one. The second reason was that the density difference between EMG905 and the diesel was the highest, so the Rayleigh-Taylor instability will increase for the centrifugal force.
In the first part, the subject focused on the labyrinthine fingering phenomena of the interface in an open Hele-Shaw cell. Experimental results showed that the gyration radius will be grown fast with increasing the rotating speed in the same magnetic field. Under the same rotating speed condition, the gyration radius will be grown fast with higher magnetic field in the first stage. And in the later stage, there will be some differences between the developments of gyration radius with different magnetic fields. For lower magnetic field, the growth will be demonstrated by the centrifugal force. For higher magnetic field, the viscosity will be increased because of the perpendicular magnetic field, and the viscous force will stabilize the interface.
The second part of this study focused on the experiment in a closed Hele-Shaw cell. For the closed flow field, it can be regard as a solid-body rotation and there will produce an opposite pressure force, which can help to stabilize the interface. Experimental results showed that the growth of gyration radius will be fast in an open Hele-Shaw cell. By doing so, the appearance of the opposite pressure force can be proved.
At last, the experimental results also showed that the growth of gyration radius will be fast in an open Hele-Shaw cell with higher gap. So, the three-dimensional effect played an important role in miscible magnetic fluids and diesel.
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Wang, Li-Chieh, and 王立杰. "Studies on Flow Instabilities on the Miscible Fluid Interface in a Hele-Shaw Cell—Injection and Lifting." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/x4zg84.
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博士<br>國立交通大學<br>機械工程系所<br>102<br>Viscous fingering is an interfacial fluid flow instability that occurs when less viscous fluid displaces another more viscous one in a Hele-Shaw cell or porous media, leading to the formation of finger-like pattern at the interface of both fluids. The interfacial evolution of multiphase flows will severely impact on the quality of production and efficiency in a variety of practical application of industrial process. Most frequent example of this instability is that of oil recovery for which viscous fingering takes place when an aqueous solution displaces more viscous oil in underground reservoirs, leading to the formation of nontrivial fingerlike structure and reduce the efficiency of the displacement process. Another particularly
interesting variation of the classic radial flow is the investigation of fingering instabilities in Hele-Shaw cells presenting variable gap spacing. This is also a very important issue in many industrial areas including adhesion, lubrication, and colloidal hydrodynamics. In this dissertation, we carried out the highly accurate simulation to investigate the interfacial evolution in two scenarios－radial injection-driven miscible flow and lifting radial Hele-Shaw flow, both with the monotonic and nonmonotonic viscosity profile. So, the thesis consists of two parts:
Part 1 focus on radial injection-driven miscible flow in a Hele-Shaw cell and covers three major topics. To begin with, we perform numerical experiments in a wide range to study the dispersion relation on both the Péclet number and the parameters of the viscosity profile. A monotonic viscosity-concentration relation of exponential type (concave) by other scholars is assumed, and a linear and reverse (convex) monotonic viscosity profiles and nonmonotonic one are also discussed. Results of this study
show that as the overall viscosity contrast held constant, nonmonotonic viscosity profile lead to a more stable flow than that of monotonic one, and there are no significant differences in different viscosity profiles. However, if the nonmonotonic viscosity profile crosses the convex monotonic viscosity profile, the nonmonotonic feature enhances the prominence of interfacial instability. Then, a great variety of morphological behaviors is systematically introduced. In general, the nonmonotonic feature enhances
the prominence of interfacial instability. Formation of dual vortex pairs and “reverse fingering”, where the fingers spread farther in the backward than in the forward direction are observed, which are not present in monotonic
viscosity profile. Finally, we have carried out a parameter study to understand the effects of nonmonotonicity on the stability of the injection flow.
In part 2, discussions start with the investigation of the influence of lifting scenario and the perturbation set. Contrast to the injection-driven miscible flow in radial Hele-Shaw cells which leads to the formation of morphing flow phenomenon of finger tip-splitting and side-branch events are plentiful if the injection rate is constant with time. More complicated flow are present for time-dependent gap flow which results in different kinds of patterns, and leads to intricate morphologies if the cell’s gap width
grows exponentially with time. Recent studies show that the growing of intricate patterns due to lifting can be ntrolled by properly adjusting the
time-dependent gap width. Moreover, we found the exponential lifting case will cause the flow more unstable than the variant lifting situation. We also deduce higher Péclet number and viscous contrast (A in monotonic viscosity profile and μm in nonmonotonic one) demonstrate more vigorous fingering. The sensitivity of the system to changes in the initial conditions and perturbation set is also discussed. Next, the effects of four viscosity profiles as stated in part 1 have been investigated. Unlike injection flow,the stability of three monotonic viscosity profiles are always in the series of concave, linear and convex. However, as injection flow, if the nonmonotonic viscosity profile crosses the convex curve will enhances the
prominence of interfacial instability. Finally, we have carried out a parameter study to understand the effects of nonmonotonicity viscosity profile on the stability of the lifting flow.
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Li-KueiChen and 陳力魁. "Study on Flow Instabilities on the Miscible Magnetic Fluid Interface in a Hele-Shaw Cell –Stationary and Rotating." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/08438886445186839086.
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Yan, Pei-Yu, and 顏佩俞. "Radial Hele-Shaw Flows in a Heterogeneous Porous Medium." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/50297738415480547969.
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碩士<br>國立交通大學<br>機械工程系所<br>103<br>In this study, we successfully use high-order numerical scheme and diffuse-interface method based on Darcy-Cahn-Hilliard model to simulate miscible and immiscible injection flows with constant and linear injection rate in various heterogeneous porous media. It can be applied to analyze the process whereby carbon dioxide is injected into an oil reservoir. We optimize the injection process by reducing the extent of fingering instability and hence increase oil recovery efficiency. Direct qualitative and quantitative comparisons regarding the pattern formations in different fluid miscibility conditions are presented in details. With the presences of heterogeneity, active secondary phenomena such as finger competition, side-branching, and tip-splitting are triggered. Prominences of fingering instability are quantitatively evaluated by the channeling and interfacial lengths. The channeling lengths show strong and monotonic dependences on the heterogeneous variances. In addition, the regime of slower growth of interfacial length at later times which was experimentally observed in homogeneous miscible injection is universally verified in heterogeneous porous media. Furthermore, we can successfully optimize the injection process by analyzing the channeling effects and fingering instabilities.
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Huang, Chi-wen, and 黃琦雯. "Numerical Simulations of Radial Flows on a Rotating Hele-Shaw Cell." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/59925264052841313966.
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碩士<br>雲林科技大學<br>機械工程系碩士班<br>96<br>In this work, we have revisited the immiscible radial fingering problem in Hele-Shaw cells, now considering that the fluids are miscible. In addition to injection, the confined system can be subjected to rotation, so that centrifugal and Coriolis forces may affect the evolution of the diffusing interface in a nontrivial manner. This complex pattern formation problem is examined in detail through intensive numerical simulations. Our numerical experiments reveal that, when fingering is initiated between miscible fluids, the lack of surface tension at the moving interface results in patterns which are much richer in detail and gross structure. In fact, we have observed dramatic changes in pattern morphology as the main control parameters of the problem are varied. Depending on the balance among injection, suction, diffusion, and rotational effects a gallery of pattern-forming structures is obtained, ranging through fragmented, cog wheel, pinwheel shaped, spiny, and clover-like patterns. In addition to unveiling a wide variety of shapes, we have verified that the miscible patterns can be made to resemble the more familiar morphologies of their immiscible counterparts (i.e., typical fanlike patterns for outward flow, and a characteristic hierarchy of screened-off fingers for inward flow) by conveniently increasing the value of a Korteweg stress parameter. This finding is certainly reassuring, since it substantiates the surface tension-like role of such stresses for miscible flows, and also indicates the effectiveness and reliability of our numerical scheme.
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Huang, Yu-Sheng, and 黃裕盛. "A Robust Diffuse-Interface Method for both Miscible and Immiscible Hele-Shaw Flows." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/29043678583908791522.
Full textAbstract:
博士<br>國立交通大學<br>機械工程系所<br>103<br>In this study, we successfully use diffuse-interface method with high-order numerical scheme to simulate the Hele-Shaw flows. Diffuse-interface method helps us to simulate both miscible and immiscible flows by changing the interface energy profile. To verify our numerical scheme and diffuse-interface method, a rotating Hele-Shaw flow is simulated. In the results, we found that the number of viscous finger is a function of a dimensionless parameter, Bond number (Bo), which is a ratio of surface tension to centrifugal force, the function can be described as: N=√(1⁄((3*〖Boe〗))). Also, some features of viscous fingers what mentioned in references are captured in our simulations. We also compare the results of different fluid viscosity ratio, which is well-known dimensionless parameter Atwood number (A). When the viscosity of inner fluid is smaller than outer fluid (A<0), the length of each inward fingers keeps almost same; otherwise, when A>0, the outward fingers’ length almost keeps same. In the end, we try to find out the effect of Coriolis force. According to the comparison between the result with and without Coriolis force, the Coriolis force acts along the azimuthal direction. Because this azimuthal direction, the fingering patterns present a bending growing process, and increase the number of pinch-off tips. To control the growing of viscous fingers in suction and injection Hele-Shaw flows, a constant and linear flow rate, which have same flow volume and flow time, are considered in our simulations. For suction, the results show us that the linear flow rate cannot inhibit the viscous fingers’ growing, not only in immiscible condition, but also in fully miscible and partial miscible conditions. It is worth to noticed that the number of fingers of immiscible fluid flow follows the formula from the reference, which described as: n_max≈√((1⁄3)*(1+((Ca*exp(R)*r))⁄8)). For injection flow, the linear flow rate provides a great job of inhibit the fingers’ growing when flow exist the surface tension or Korteweg stress effect, which means the immiscible and partial miscible flow. Without the Korteweg stress, the linear flow rate does constrain the flow direction of viscous fingers, but it does not inhibit the growing process.
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Yu-Chia, Liu, and 劉于嘉. "Numerial Simulation of Interfacial Instabilities on Miscible Rotating Hele-Shaw Flows with the Effects of Coriolis Forces and Korteweg Stresses." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/77971765241422065248.
Full textAbstract:
碩士<br>大葉大學<br>機械工程研究所碩士班<br>92<br>The Hele-Shaw flows driven by centrifugal force have been the subject of recent studies due to their potential applications of in the technology of spin coating. In the common practices of spin coating process, a liquid drop is initially deposited on the top of rotating target substrate, and spreads outward by the centrifugal force. Since the coating film is extremely thin, the process bears similarities to a rotating Hele-Shaw flow. The rotational effects to the fingering instability differ from the radial flows in many ways. Instabilities in radial flows are mainly due to the viscosity contrast, and decay as radial distance increases. Fingerings are triggered if the displacing fluid is less viscous and more vigorous near the origin. However, in the rotational Hele-Shaw cell, the centrifugal force is generated by the density difference, and proportional to the radial distance. A stronger unstable mechanism is expected if the heavier fluid, usually more viscous, is the driving fluid and more pronounced away from the center. Numerical simulations of interfacial stabilities for miscible interfaces of confined annulus in a rotating Hele-Shaw cell have been presented by means of highly accurate numerical schemes. The influences of Coriolis forces, rotating speed, viscosity contrast, Korteweg stresses and injection are simulated systematically. The fingering patterns are detailed demonstrated by images of concentration, vorticity fields and streamlines systematically to depict the influences of various parameters