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Academic literature on the topic 'Newtonian bubble'

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Published: 6 September 2023

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Journal articles on the topic "Newtonian bubble"

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Rosenbaum, Eilis, Mehrdad Massoudi, and Kaushik Dayal. "Surfactant stabilized bubbles flowing in a Newtonian fluid." Mathematics and Mechanics of Solids 24, no. 12 (June 26, 2019): 3823–42. http://dx.doi.org/10.1177/1081286519854508.

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Bubbles suspended in a fluid cause the suspension to have different rheological properties than the base fluid. In general, the viscosity of the suspension increases as the volume fraction of the bubbles is increased. A current application, and motivation for this study, is in wellbore cements used for hydrocarbon extraction and carbon sequestration. In these settings, the gas bubbles are dispersed into the cement to reduce the density as well as improve the properties for specific conditions or wellbore issues. In this paper, we use Stokesian dynamics to numerically simulate the behavior of a large number of bubbles suspended in a Newtonian fluid. Going beyond prior work on simulating particles in suspension, we account for the nature of bubbles by allowing for slip on the bubble surface, the deflection on the bubble surface, and a bubble–bubble pairwise interaction that represents the surfactant physics; we do not account for bubble compressibility. We incorporate these interactions and simulate bubble suspensions of monodisperse size at several volume fractions. We find that the bubbles remain better dispersed compared with hard spherical particles that show a greater tendency to structure or cluster.
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De Kee and, D., C. F. Chan Man Fong, and J. Yao. "Bubble Shape in Non-Newtonian Fluids." Journal of Applied Mechanics 69, no. 5 (August 16, 2002): 703–4. http://dx.doi.org/10.1115/1.1480822.

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The study of the behavior of bubbles in complex fluids is of industrial as well as of academic importance. Bubble velocity-volume relations, bubble shapes, as well as viscous, elastic, and surfactant effects play a role in bubble dynamics. In this note we extend the analysis of Richardson to a non-Newtonian fluid.
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Kontaxi, Georgia, Yorgos G. Stergiou, and Aikaterini A. Mouza. "Experimental Study of Bubble Formation from a Micro-Tube in Non-Newtonian Fluid." Micromachines 12, no. 1 (January 11, 2021): 71. http://dx.doi.org/10.3390/mi12010071.

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Over the last few years, microbubbles have found application in biomedicine. In this study, the characteristics of bubbles formed when air is introduced from a micro-tube (internal diameter 110 μm) in non-Newtonian shear thinning fluids are studied. The dependence of the release time and the size of the bubbles on the gas phase rate and liquid phase properties is investigated. The geometrical characteristics of the bubbles are also compared with those formed in Newtonian fluids with similar physical properties. It was found that the final diameter of the bubbles increases by increasing the gas flow rate and the liquid phase viscosity. It was observed that the bubbles formed in a non-Newtonian fluid have practically the same characteristics as those formed in a Newtonian fluid, whose viscosity equals the asymptotic viscosity of the non-Newtonian fluid, leading to the assumption that the shear rate around an under-formation bubble is high, and the viscosity tends to its asymptotic value. To verify this notion, bubble formation was simulated using Computational Fluid Dynamics (CFD). The simulation results revealed that around an under-formation bubble, the shear rate attains a value high enough to lead the viscosity of the non-Newtonian fluid to its asymptotic value.
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Kontaxi, Georgia, Yorgos G. Stergiou, and Aikaterini A. Mouza. "Experimental Study of Bubble Formation from a Micro-Tube in Non-Newtonian Fluid." Micromachines 12, no. 1 (January 11, 2021): 71. http://dx.doi.org/10.3390/mi12010071.

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Over the last few years, microbubbles have found application in biomedicine. In this study, the characteristics of bubbles formed when air is introduced from a micro-tube (internal diameter 110 μm) in non-Newtonian shear thinning fluids are studied. The dependence of the release time and the size of the bubbles on the gas phase rate and liquid phase properties is investigated. The geometrical characteristics of the bubbles are also compared with those formed in Newtonian fluids with similar physical properties. It was found that the final diameter of the bubbles increases by increasing the gas flow rate and the liquid phase viscosity. It was observed that the bubbles formed in a non-Newtonian fluid have practically the same characteristics as those formed in a Newtonian fluid, whose viscosity equals the asymptotic viscosity of the non-Newtonian fluid, leading to the assumption that the shear rate around an under-formation bubble is high, and the viscosity tends to its asymptotic value. To verify this notion, bubble formation was simulated using Computational Fluid Dynamics (CFD). The simulation results revealed that around an under-formation bubble, the shear rate attains a value high enough to lead the viscosity of the non-Newtonian fluid to its asymptotic value.
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Shan, Jie, and Xiaojun Zhou. "The Effect of Bubbles on Particle Migration in Non-Newtonian Fluids." Separations 8, no. 4 (March 24, 2021): 36. http://dx.doi.org/10.3390/separations8040036.

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The movement of the gas–liquid interface caused by the movement of the bubble position will have an impact on the starting conditions for particle migration. This article quantifies the influence of moving bubbles on the starting conditions of particle migration in non-Newtonian fluids, and it aims to better understand the influence of bubbles moving in non-Newtonian fluids on particle migration to achieve more effective control. First, the forces and moments acting on the particles are analyzed; then, fluid dynamics, non-Newtonian fluid mechanics, extended DLVO (Derjaguin Landau Verwey Overbeek theory), surface tension, and friction are applied on the combined effects of particle migration. Then, we reasonably predict the influence of gas–liquid interface movement on particle migration in non-Newtonian fluids. The theoretical results show that the movement of the gas–liquid interface in non-Newtonian fluids will increase the separation force acting on the particles, which will lead to particle migration. Second, we carry out the particle migration experiment of moving bubbles in non-Newtonian fluid. Experiments show that when the solid–liquid two-phase flow is originally stable, particle migration occurs after the bubble movement is added. This phenomenon shows that the non-Newtonian fluid with bubble motion has stronger particle migration ability. Although there are some errors, the experimental results basically support the theoretical data.
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Aquino, Andrea, Davide Picchi, and Pietro Poesio. "Modeling the motion of a Taylor bubble in a microchannel through a shear-thinning fluid." E3S Web of Conferences 312 (2021): 05006. http://dx.doi.org/10.1051/e3sconf/202131205006.

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Applications of multiphase flows in microchannels as chemical and biological reactors and cooling systems for microelectronic devices typically present liquid slugs alternated with bubbles of elongated shape, the Taylor bubbles. These occupy almost entirely the cross-section of the channel and present a hemispherical front and a liquid layer, the lubrication film, which separates the gas from the tube wall. The Taylor bubble perturbs the surrounding fluids activating many transport mechanisms in the proximity of the gas-liquid interface; therefore, the bubble motion significantly influences the heat and mass transfer rates. Although many works deeply investigate the bubble hydrodynamics in Newtonian fluids, the knowledge about the relation between bubble hydrodynamics and rheological properties is insufficient, and studies where the continuous phase exhibits a shear-thinning behavior are missing. Our numerical analysis tries to fill this gap by investigating the motion of a Taylor bubble in a non-Newtonian shear-thinning fluid, modeled by the Carreau viscosity model. First, we validate the results against the Newtonian case and a recent theory for shear-thinning fluids (Picchi et al., Journal of Fluid Mechanics, 2021, 918). Then, we investigate the bubble hydrodynamics far from the validity range of the current models. Finally, we study the scaling of the bubble velocity and lubrication film thickness, extending the current theory to shear-thinning fluids.
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Islam, Md Tariqul, P. Ganesan, and Ji Cheng. "A pair of bubbles’ rising dynamics in a xanthan gum solution: a CFD study." RSC Advances 5, no. 11 (2015): 7819–31. http://dx.doi.org/10.1039/c4ra15728a.

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The motion and interaction of a bubble pair in a non-Newtonian fluid are numerically simulated by a volume of fluid method. The effects of initial horizontal bubble interval, oblique alignment and fluid rheological properties on the pair of rising bubbles are evaluated.
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Truby, J. M., S. P. Mueller, E. W. Llewellin, and H. M. Mader. "The rheology of three-phase suspensions at low bubble capillary number." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2173 (January 2015): 20140557. http://dx.doi.org/10.1098/rspa.2014.0557.

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We develop a model for the rheology of a three-phase suspension of bubbles and particles in a Newtonian liquid undergoing steady flow. We adopt an ‘effective-medium’ approach in which the bubbly liquid is treated as a continuous medium which suspends the particles. The resulting three-phase model combines separate two-phase models for bubble suspension rheology and particle suspension rheology, which are taken from the literature. The model is validated against new experimental data for three-phase suspensions of bubbles and spherical particles, collected in the low bubble capillary number regime. Good agreement is found across the experimental range of particle volume fraction ( 0 ≤ ϕ p ≲ 0.5 ) and bubble volume fraction ( 0 ≤ ϕ b ≲ 0.3 ). Consistent with model predictions, experimental results demonstrate that adding bubbles to a dilute particle suspension at low capillarity increases its viscosity, while adding bubbles to a concentrated particle suspension decreases its viscosity. The model accounts for particle anisometry and is easily extended to account for variable capillarity, but has not been experimentally validated for these cases.
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Zhao, Xinxin, Xiangzhen Yan, Hongwei Jiang, Guang Yang, Jintang Wang, Xiaohui Sun, Yonghai Gao, and Faling Yin. "Simulation Analysis of Gas Bubble Formation and Escape in Non-Newtonian Drilling Fluids." Geofluids 2021 (April 9, 2021): 1–14. http://dx.doi.org/10.1155/2021/6680653.

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In this study, the formation and escape movements of a bubble injected in non-Newtonian drilling fluid through a pore were numerically simulated using a volume of fluid method. The pattern of a single bubble and the pressure and velocity fields of the surrounding liquid phase during the bubble formation were analyzed and compared with experimental results; based on the comparison, the formation and escape properties of the bubble were further studied. In particular, the effects of static shear force, consistency coefficient, and flow behavior index on the growth and escape time of the bubble were analyzed. The results show that, owing to the effect of velocity on the viscosity of a non-Newtonian drilling fluid, the escape time and volume of the bubble increase with an increase in static shear force, consistency coefficient, and flow behavior index. Among the three parameters, the flow behavior index has the greatest effect. This is because the shear disturbance of a bubble to its surrounding fluid during its growth and escape, caused by the shear thinning of a yield-power-law fluid, reduces the fluid viscosity. The shear thinning decreases, and the resistance to the bubble increases as the flow behavior index approaches 1, leading to larger bubble formation times and separation volumes. An empirical formula for predicting the equivalent radius of bubbles considering the liquid yield stress, inertial force, viscous force, and surface tension is established. The average error of predicting the equivalent radius of detached bubble is 0.80%, which can provide a reference for the better study of bubble migration and flow pattern in non-Newtonian fluid.
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Fakhari, Ahmad, and Célio Fernandes. "Single-Bubble Rising in Shear-Thinning and Elastoviscoplastic Fluids Using a Geometric Volume of Fluid Algorithm." Polymers 15, no. 16 (August 17, 2023): 3437. http://dx.doi.org/10.3390/polym15163437.

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The motion of air bubbles within a liquid plays a crucial role in various aspects including heat transfer and material quality. In the context of non-Newtonian fluids, such as elastoviscoplastic fluids, the presence of air bubbles significantly influences the viscosity of the liquid. This study presents the development of an interface-capturing method for multiphase viscoelastic fluid flow simulations. The proposed algorithm utilizes a geometric volume of fluid (isoAdvector) approach and incorporates a reconstructed distance function (RDF) to determine interface curvature instead of relying on volume fraction gradients. Additionally, a piecewise linear interface construction (PLIC) scheme is employed in conjunction with the RDF-based interface reconstruction for improved accuracy and robustness. The validation of the multiphase viscoelastic PLIC-RDF isoAdvector (MVP-RIA) algorithm involved simulations of the buoyancy-driven rise of a bubble in fluids with varying degrees of rheological complexity. First, the newly developed algorithm was applied to investigate the buoyancy-driven rise of a bubble in a Newtonian fluid on an unbounded domain. The results show excellent agreement with experimental and theoretical findings, capturing the bubble shape and velocity accurately. Next, the algorithm was extended to simulate the buoyancy-driven rise of a bubble in a viscoelastic shear-thinning fluid described by the Giesekus constitutive model. As the influence of normal stress surpasses surface tension, the bubble shape undergoes a transition to a prolate or teardrop shape, often exhibiting a cusp at the bubble tail. This is in contrast to the spherical, ellipsoidal, or spherical-cap shapes observed in the first case study with a bubble in a Newtonian fluid. Lastly, the algorithm was employed to study the buoyancy-driven rise of a bubble in an unbounded elastoviscoplastic medium, modeled using the Saramito–Herschel–Bulkley constitutive equation. It was observed that in very small air bubbles within the elastoviscoplastic fluid, the dominance of elasticity and capillary forces restricts the degree of bubble deformation. As the bubble volume increases, lateral stretching becomes prominent, resulting in the emergence of two tails. Ultimately, a highly elongated bubble shape with sharper tails is observed. The results show that by applying the newly developed MVP-RIA algorithm, with a tangible coarser grid compared to the algebraic VOF method, an accurate solution is achieved. This will open doors to plenty of applications such as bubble columns in reactors, oil and gas mixtures, 3D printing, polymer processing, etc.
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Dissertations / Theses on the topic "Newtonian bubble"

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Redmon, Jessica. "Stochastic Bubble Formation and Behavior in Non-Newtonian Fluids." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case15602738261697.

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Boehm, Michael. "EXPERIMENTAL INVESTIGATION OF TWO-PHASE PENETRATING FLOW OF NEWTONIAN AND NON-NEWTONIAN POLYMERIC FLUIDS AND DEVELOPMENT OF PRACTICAL APPLICATIONS IN DRUG/GENE DELIVERY." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1253548237.

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Wang, Yijie. "The Effect Of Non-Newtonian Rheology On Gas-Assisted Injection Molding Process." The Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=osu1053622915.

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Mouline, Youssef. "Dynamique des bulles de gaz dans les milieux rhéologiquement complexes." Vandoeuvre-les-Nancy, INPL, 1996. http://www.theses.fr/1996INPL063N.

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Dans les procédés gaz-liquide, l'efficacité des transferts de matière et de chaleur est essentiellement contrôlée par la dynamique des bulles dans la phase liquide. L’étude du comportement des bulles de gaz dans un milieu liquide est donc d'un intérêt certain, tant sur le plan fondamental que sur le plan industriel, surtout lorsque le milieu liquide est non-newtonien. Notre étude a révélé que les propriétés rhéologiques de la phase liquide et la fréquence d'injection du gaz dans la colonne ont une influence importante sur la vitesse d'ascension des bulles. Dans les milieux viscoélastiques, des bulles de volume identique coalescent en ligne à partir d'une certaine hauteur de la colonne. Comme le confirme la simulation rhéologique, la coalescence en ligne des bulles est induite par la présence de contraintes résiduelles dans le fluide. L’utilisation des techniques spécifiques à l'analyse des systèmes dynamiques dissipatifs a montré que la coalescence en ligne est de nature chaotique déterministe. Enfin, un modèle de formation de bulle a été élaboré dans le but de prédire le volume et la forme des bulles au moment du détachement pour diverses conditions expérimentales
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Cappello, Vincenzo. "Extrapolation des réacteurs agités gaz-liquide par modélisation tridimensionnelle de l'hydrodynamique, transferts et cinétique." Thesis, Université Clermont Auvergne‎ (2017-2020), 2020. http://www.theses.fr/2020CLFAC040.

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Dans le cadre de la production de bio-carburants, les fermenteurs agités aérés sont utilisés la culture de micro-organismes car ils permettent d’assurer un bon transfert d’oxygène entre gaz et liquide, tout en homogénéisant de manière efficace la concentration en substrats. Dans le cas de la production d’enzyme par le champignon filamenteux Trichoderma reesei (une étape clef de la production d’éthanol 2G), le transfert d’oxygène est dégradé par la rhéologie non-newtonienne du moût fermentaire. Par ailleurs, les volumes fermentaires nécessaires aux futures unités de production de bioéthanol sont tellement élevés, de l’ordre de plusieurs centaines de m3 ou plus, que l’homogénéité des substrats n’est plus assurée.Dans ce contexte, la finalité des travaux présentés était de développer un outil de prédiction de performances et d’extrapolation des fermenteurs aérés, basé sur la mécanique des fluides numériques (ou CFD : Computational Fluid Dynamics), et permettant de coupler l’hydrodynamique, la rhéologie, le transfert de matière ainsi que le métabolisme simplifié des microorganismes. Pour arriver à cela, plusieurs étapes expérimentales ont été préalablement menées.Les tailles de bulles présentes dans divers milieux (filtrat fermentaire, milieux modèles) ont été caractérisées à l’aide d’une technique de sonde optique développée à IFPEN lors de travaux antérieurs, mais encore jamais appliquée aux milieux non-newtoniens. Ces mesures inédites de tailles de bulles ont été complétées par la caractérisation du transfert gaz/liquide (kLa) dans chaque système étudié, et la combinaison des différents résultats a permis de développer un modèle de coefficient de transfert (kL) à implémenter dans le modèle CFD. Par ailleurs, des caractérisations hydrodynamiques de type Temps de mélange (par colorimétrie et traitement d’image) et Vélocimétrie (par tube de Pavlov) ont été menées dans les milieux visqueux aérés pour valider les simulations hydrodynamiques.Le modèle développé, basé sur une approche diphasique Eulérienne, et une description moyennée des champs de vitesse (approche dite RANS : Reynolds Averaged Navier-Stokes équations) est utilisé pour illustrer la dégradation du mélange lors de l’extrapolation de la production d’enzymes. Ce phénomène se traduit par l’apparition de gradients de concentrations en substrats (sucres, oxygène dis- sous). Les résultats issus du modèle seront utilisés pour guider les futurs développements technologiques de fermenteurs, ainsi que pour mener des cultures biologiques représentatives de type scale-down, en fermenteurs multizones. Les simulations numériques et les expériences de scale-down permettront d’évaluer la résistance des microorganismes aux gradients de concentrations en substrats subis dans les fermenteurs industriels
Mechanically-agitated reactors are widely used in aerobic fermentation, because they provide good mixing of reactants and high performance in terms of oxygen mass transfer. In the enzyme production process by filamentous fungi Trichoderma reesei, the mass transfer is hindered by the complex rheology of the fermentation broth. This process is a key step in the production of second-generation ethanol; however, because of the high fermentation volumes (∼ 100 m3) required for future bioethenol production units, the reactor scale-up is challenging. In fact, by increasing the size of the fermenter, large scale substrate gradients tend to appear.In this framework, the objective of this study is to develop a predictive tool based on Computational Fluid Dynamics (CFD) for the design and scale-up of aerated reactors. The numerical model here proposed, allows one to characterize such systems by coupling hydrodynamics, rheology, mass transfer, and a simplified metabolic model. To assess the fidelity of the model, several experimental analyses were carried out. Bubble size in shear-thinning liquids and in fermentation broth was measured thanks to a novel technique that was previously developed at IFPEN. This measuring techniques is based on phase- detective optical probes, and its use in stirred tank reactors and in viscous liquids was validated during this study. Bubble size measurements were supplemented with gas-liquid transfer coefficient (kLa) and gas holdup measurements. By combining these data, it was possible to develop a dimensional model for the liquid-side mass transfer coefficient (kL), that served to model the mass transfer mechanism in the CFD simulations.Moreover, the reactor hydrodynamics was characterized in terms of mixing time (via colorimetric method and image processing), and liquid velocity (with the Pavlov tube). These data were then used to quantify the accuracy of the simulations. The numerical model — based on the two-phase Eulerian model, and on Reynolds-averaged Navier-Stokes equations — was used to highlight the mixing degradation that accompanies the scale-up of the protein production process. Results from coupled simulations (distribution of substrate and oxygen concentrations) will be used to guide future design and technology optimization of fermenters, as well as to develop more representative scale-down models for microbial cultures. CFD simulations and scale-down data will assess the microorganisms’ resistance to exposure to substrate content variation inside industrial reactors
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Mendes, Caroline Eliza. "Avaliação das condições hidrodinâmicas, de transferência de oxigênio e de cisalhamento em diferentes modelos e escalas de reatores pneumáticos." Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/7928.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Due to the high capacity of oxygen transfer and versatility, pneumatic reactors have been constantly used in bioprocesses. However, aiming to expand the use of these bioreactors in the industry, as well as increase the understanding of the complex phenomena that occur in these devices, this thesis aimed to evaluate the hydrodynamic, oxygen transfer and shear conditions in three models of pneumatic reactors (bubble column, concentric-tube airlift and split-cylinder airlift) in the scales of 5 and 10 L, using as liquid phase four Newtonian fluids and eight non-Newtonian fluids, and five specific air flow rate (air of 1 to 5 vvm). Related to the hydrodynamic were studied the global gas hold-up (g), the gas hold-ups in the riser (R) and in the downcomer (D), liquid circulation time (tC), superficial liquid velocity in the riser (ULR) and in the downcomer (ULD), and the percentage energy losses in the riser (%ER+%EFR), in the downcomer (%ED+%EFD), and in the bottom (%EB) of airlift reactors. The values of g, R, D, ULR and ULD showed increasing behaviour with increase of air and decreasing behaviour with the kinematic liquid viscosity (L) and the rheologic properties (K e n), and observed the opposite for tC. The higher values of g, R, D and tC were obtained for concentric-tube airlift reactor (ACC) and scale of 10 L. With exception of ULR of Newtonian fluids, the others liquid velocity tests resulted in higher values for split-cylinder airlift reactors (ASC) and scale of 10 L. This result was attributed to the greater driving force (R-D) to liquid circulation obtained in the ASC reactors and the higher energy losses in the riser and in the downcomer observed in the ACC reactors. In the bottom of the airlift reactors, the higher values of %EB were obtained to the ASC reactor. To evaluate the mass transfer were studied, the average bubble diameter (Db), the volumetric oxygen transfer coefficient (kLa) and the terms that compose the kLa, the convective mass transfer coefficient (kL) and the specific interfacial area of mass transfer (aL). With the increase of air, L, K and n, the air bubbles were predominantly coalescent in water, presenting distorted shape, and non-coalescent with spherical/elliptical shape in the other solutions. It was observed a similar behavior between the kLa and aL parameters, which were directly proportional to the air and inversely proportional to the L, K and n. In water, the aL values were lower than glycerol solutions due to the higher Db values observed in this liquid. For the kL, it was observed a decreasing behaviour with the increase of the air in the most solutions. The magnitude of kL values was due mainly the oxygen difusivity in the liquid, and the higher values were observed to the water, following by the non-Newtonian solutions. In general, the higher values of the mass transfer parameters were obtained in the ACC reactor and in the scale of 10 L. The proposed method to the estimate the average shear rate velocity based on Kolmogorov’s theory of isotropic turbulence showed results consistent with the literature relative to the behavior and magnitude of this variable, as well as the results obtained by the analysis of the morphological changes of Streptomyces clavuligerus in two models of airlift reactors and two aeration conditions. Were proposed correlations to predict all evaluated parameters. Were obtained in all cases a good fit with the experimental data, with deviations between the calculated and experimental values below 20%.
Devido à alta capacidade de transferência de oxigênio e versatilidade, reatores pneumáticos têm sido constantemente utilizados em bioprocessos. Entretanto, visando ampliar a utilização destes reatores na indústria, assim como aumentar a compreensão dos fenômenos complexos que ocorrem nestes dispositivos, na presente tese teve-se como objetivo avaliar as condições hidrodinâmicas, de transferência de oxigênio e de cisalhamento em três modelos de reatores pneumáticos (coluna de bolhas, airlift de cilindros concêntricos e airlift split-cylinder) nas escalas de 5 e 10 L, utilizando como fase líquida quatro fluidos newtonianos e oito fluidos nãonewtonianos e cinco vazões específicas de ar (ar de 1 a 5vvm). Em termos hidrodinâmicos foram estudadas as retenções gasosas global (g), no riser (R) e no downcomer (D), tempo de circulação do líquido (tC), velocidade superficial do líquido no riser (ULR) e no downcomer (ULD) e as perdas percentuais de energia no riser, no downcomer e na base (%EB) de reatores airlift. Os valores de g, R, D, ULR e ULD apresentaram comportamento crescente com o aumento de ar e decrescente com a viscosidade cinemática do líquido (L) e propriedades reológicas (K e n), sendo observado o oposto para tC. Os maiores valores de g, R, D e tC foram obtidos em reator airlift de cilindros concêntricos (ACC) e escala de 10 L. Com exceção de ULR de fluidos newtonianos, os demais testes de velocidade do líquido resultaram em maiores valores nos reatores airlift split-cylinder (ASC) e escala de 10 L. Tal resultado foi atribuído a maior força motriz (R-D) para circulação do líquido obtida em ASC e às maiores perdas de energia no riser e no downcomer observadas em reatores ACC. Na base dos reatores, os maiores valores de %EB foram obtidos para reator ASC. Para avaliação da transferência de massa foram estudados o diâmetro da bolha (Db), o coeficiente volumétrico de transferência de oxigênio (kLa) e os termos que o compõe, coeficiente convectivo de transferência de massa (kL) e área interfacial específica de transferência de massa (aL). Bolhas de ar, com o aumento de ar, L, K e n foram predominantemente coalescentes em água, apresentando formato distorcido e nãocoalescentes com formato esférico/elíptico nas demais soluções. Observou-se um comportamento análogo entre kLa e aL, com relação direta à ar e inversa à L, K e n. Em água, os valores de aL foram inferiores às soluções de glicerol em virtude do maior Db observado neste líquido. Para kL, observou-se um comportamento decrescente com o aumento de ar na maioria das soluções. A magnitude dos valores de kL obedeceu principalmente a difusividade do oxigênio no líquido, sendo os maiores valores observados para água, seguido das soluções não-newtonianas. De maneira geral, os maiores valores dos parâmetros de transferência de massa foram obtidos em reator ACC de 10 L. O método proposto para estimativa da taxa de cisalhamento com base na teoria de turbulência isotrópica de Kolmogorov apresentou resultados condizentes com a literatura em termos de comportamento e magnitude desta variável, assim como com os resultados obtidos pela análise das alterações morfológicas de Streptomyces clavuligerus em dois modelos de reatores airlift e duas condições de aeração. Para todos os parâmetros avaliados foram propostas correlações para sua predição, sendo obtidos em todos os casos bons ajustes aos dados experimentais com desvios inferiores à 20%. Palavras-chave: reatores pneumáticos, retenção gasosa, kLa, diâmetro da bolha, velocidade
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Mary, Gilles. "Prise en compte des effets du produit et du procédé au cours de l’opération de foisonnement par battage en continu - Analyse dimensionnelle." Thesis, Paris, AgroParisTech, 2011. http://www.theses.fr/2011AGPT0054/document.

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L'objet de cette étude est de mieux formaliser et modéliser de façon générique le processus de structuration d'un produit par le procédé de foisonnement, en reliant les paramètres opératoires aux propriétés des mousses formées et de contribuer ainsi à un meilleur pilotage de l'opération. Une ligne de foisonnement par battage en continu a été instrumentée et l'évolution du diamètre des bulles en fonction des paramètres du produit et du procédé a été suivie pour des milieux modèles newtoniens et rhéofluidifiants. L'analyse dimensionnelle à l'échelle du procédé a permis d'aboutir à un modèle physique de l'opération, et donc d'avoir une compréhension des phénomènes en présence. Elle a aussi permis d'intégrer les paramètres du produit et du procédé et de simplifier la représentation des résultats expérimentaux. Enfin, la cohérence de ce modèle avec d'autres issus de la littérature et une première approche de validation avec un produit réel, semble justifier son caractère générique
The aim of this study is to better formalize and model in a generic way the structuring of a product by the foaming operation process, by linking the operating parameters to the foams properties and contribute to a better steering of the operation. A continuous whipping line was instrumented and the evolution of bubble diameter depending on both product and process parameters was characterized for Newtonian and shear-thinning model fluids. Dimensional analysis of the process has lead to a physical model of the operation, and therefore makes possible the understanding of the phenomena involved. It also helped to integrate the product and the process parameters and simplify the representation of experimental results. Finally, the consistency of this model with others from the literature and a first validation with a real product seems to justify his relevance
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Dewsbury, Kevin H. "Hydrodynamic study of free rise of solid particles and gas bubbles in non-Newtonian fluids." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0017/MQ58025.pdf.

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Zhang, Yuning. "Analysis of radial oscillations of gas bubbles in Newtonian or viscoelastic mediums under acoustic excitation." Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/55427/.

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Acoustic cavitation plays an important role in a broad range of biomedical, chemical and oceanic engineering problems. For example, kidney stone can be crushed into the powder (being discharged naturally) by the acoustic cavitation generated by carefully controlled focused ultrasonic beams. Therefore, the prediction of generation of acoustic cavitation is essential to the aforementioned emerging non-invasive technique for kidney stone crushing. The objective of this PhD program is to study the generation of acoustic cavitation (e.g. through rectified mass diffusion across bubble interface) theoretically in the Newtonian fluids (e.g. water) or viscoelastic mediums (e.g. human soft tissue) under acoustic excitation of single or dual frequency. The compressibility and the viscosity of the liquid, heat and mass transfer across bubble-medium interface are all considered in this study. During this PhD program, the established works in the literature on the above topic have been re-examined. More physically general formulas of natural frequency and damping of gas bubble oscillations in Newtonian or viscoelastic mediums has been derived and further employed for solving the problem of bubble growth under acoustic field (i.e. rectified mass diffusion). For rectified mass diffusion of gas bubbles in Newtonian liquids, the predictions have been improved for high-frequency region of megahertz and above. Effects of medium viscoelasticity and dual-frequency acoustic excitation on rectified mass diffusion have also been studied. To facilitate the fast growth of bubble under acoustic field, dynamic-frequency and dual-frequency techniques have been proposed and demonstrated.
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10

Fu, Taotao. "Ecoulements gaz-liquide et comportement des bulles en microcanaux." Thesis, Vandoeuvre-les-Nancy, INPL, 2010. http://www.theses.fr/2010INPL030N/document.

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Les écoulements gaz-liquide constituent un axe de recherche très actif en microfluidique. Le rapport des débits entre les deux phases, la formation de bulles et les champs de vitesse des microcanaux ont été étudiés dans cette thèse, en utilisant une caméra numérique rapide et un microsystème de Particule Image Velocimetry (micro-PIV). En particulier, le diagramme des phases gaz-liquide ont été établi dans des microcanaux carrés ; la formation des bulles en fluides tant newtoniens que non newtoniens a été étudiée en détail dans plusieurs configurations géométriques telles que T-injonction et flow-focusing. Les mécanismes régissant la formation d'une bulle ont été modélisés pour chaque étape : expansion, amincissement et rupture. L'étape amincissement de la traînée d'une bulle est notamment contrôlée par une pression orthogonale qui dépend du débit du liquide. Dans le cadre de flow-focusing, le mécanisme de la rupture du film gazeux peut être décrit par une loi d'échelle reliant l'épaisseur minimale du film au temps restant juste avant la rupture avec un exposant 1/3. Le caractère non newtonien de fluides PAAm allonge la traînée d'une bulle par rapport aux fluides newtoniens. Enfin, l'étude de la coalescence entre bulles a été entreprise à l'échelle microscopique ainsi que le comportement complexe des trains de bulles dans des réseaux de microcannaux
Gas-liquid two-phase flow is an important research project in microfluidics. The gas-liquid two-phase flow, the bubble formation and moving behaviours in microchannels were investigated, by using a high speed digital camera and a micro Particle Image Velocimetry (micro-PIV). The gas-liquid two-phase flow in vertical rectangular microchannels was investigated and a flow pattern map was constructed; the bubble formation in both Newtonian and non-Newtonian fluids in cross-flowing microfluidic T-junctions and flow-focusing devices was investigated; the bubble formation process could be divided into expansion, collapse and pinch-off stages; the collapse speed of the gaseous thread in the second stage is controlled by the squeezing pressure, and is proportional to the liquid flow rates; while the minimum width of the neck of the gaseous thread in the third stage for bubble formation in flow-focusing devices could be scaled with the remaining time to the ultimate pinch-off as a power law relationship with an exponent of 1/3; the PAAm solutions prolong the gaseous thread in the tangential direction of the neck; bubble coalescence in a microchannel with an expansion section was studied; the bubble behavior in a microchannel with a loop was also investigated
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Books on the topic "Newtonian bubble"

1

Carew, Peter Simon. Bubble dynamics of non-Newtonian flows in inclined pipes for the prediction of gas kicks in oilwells. Birmingham: University of Birmingham, 1993.

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Bubbles, drops, and particles in non-Newtonian fluids. 2nd ed. Boca Raton, FL: CRC Taylor & Francis, 2007.

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Bubbles, drops, and particles in non-Newtonian fluids. Boca Raton, Fla: CRC Press, 1993.

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Coopersmith, Jennifer. The Principle of Virtual Work. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198743040.003.0004.

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The meaning behind the mysterious Principle of Virtual Work is explained. Some worked examples in statics (equilibrium) are given, and the method of Virtual Work is compared and contrasted with the method of Newtonian Mechanics. The meaning of virtual displacements is explained very carefully. They must be ‘small’, happen simultaneously, and do not cause a force, result froma force, or take any time to occur. Counter to intuition, not all the actual displacements can be allowed as virtual displacements. Some examples worked through are: Feynman’s pivoting (cantilever) bar, a “black box,” a weighted spring, a ladder, a capacitor, a soap bubble, and Atwood’s machine. The links between mechanics and geometry are demonstrated, and it is shown how the reaction or constraint forces are always perpendicular to the virtual displacements. Lanczos’s Postulate A and its astounding universality are explained.
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Chhabra, R. P. Bubbles, Drops, and Particles in Non-Newtonian Fluids. Taylor & Francis Group, 2006.

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Chhabra, R. P. Bubbles, Drops, and Particles in Non-Newtonian Fluids. Taylor & Francis Group, 2006.

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Chhabra, R. P. Bubbles Drops and Particles in Non-Newtonian Fluids. Taylor & Francis Group, 2021.

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Chhabra, R. P. Bubbles, Drops, and Particles in Non-Newtonian Fluids. Chemical Industries. Taylor & Francis Group, 2010.

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Chhabra, R. P. Bubbles, Drops, and Particles in Non-Newtonian Fluids, Second Edition (Chemical Industries Series). 2nd ed. CRC, 2006.

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Book chapters on the topic "Newtonian bubble"

1

Brujan, Emil-Alexandru. "Bubble Dynamics." In Cavitation in Non-Newtonian Fluids, 63–116. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15343-3_3.

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Kumawat, Kapil Dev, Sachin Balasaheb Shinde, and Lalit Kumar. "Experimental Investigation of Bubble Rising in Newtonian and Non-Newtonian Fluids: A Comparative Assessment." In Green Energy and Technology, 769–78. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-2279-6_68.

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Chhabra, Raj P., and Swati A. Patel. "Non-Newtonian Fluid Behavior." In Bubbles, Drops, and Particles in Non-Newtonian Fluids, 7–44. 3rd ed. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9780429260759-2.

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Chhabra, Raj P., and Swati A. Patel. "Fluid Particles in Non-Newtonian Media." In Bubbles, Drops, and Particles in Non-Newtonian Fluids, 175–238. 3rd ed. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9780429260759-6.

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Chhabra, Raj P., and Swati A. Patel. "Rigid Particles in Time-Independent Liquids without a Yield Stress." In Bubbles, Drops, and Particles in Non-Newtonian Fluids, 45–104. 3rd ed. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9780429260759-3.

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Chhabra, Raj P., and Swati A. Patel. "Fluidization and Hindered Settling." In Bubbles, Drops, and Particles in Non-Newtonian Fluids, 331–61. 3rd ed. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9780429260759-8.

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Chhabra, Raj P., and Swati A. Patel. "Wall Effects." In Bubbles, Drops, and Particles in Non-Newtonian Fluids, 471–508. 3rd ed. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9780429260759-11.

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Chhabra, Raj P., and Swati A. Patel. "Introduction." In Bubbles, Drops, and Particles in Non-Newtonian Fluids, 1–6. 3rd ed. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9780429260759-1.

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Chhabra, Raj P., and Swati A. Patel. "Heat and Mass Transfer in Particulate Systems: Free and Mixed Convection." In Bubbles, Drops, and Particles in Non-Newtonian Fluids, 417–69. 3rd ed. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9780429260759-10.

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Chhabra, Raj P., and Swati A. Patel. "Non-Newtonian Fluid Flow in Porous Media and Packed Beds." In Bubbles, Drops, and Particles in Non-Newtonian Fluids, 239–330. 3rd ed. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9780429260759-7.

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Conference papers on the topic "Newtonian bubble"

1

Bamberger, Judith Ann, Carl W. Enderlin, and S. Tzemos. "Air Sparging for Mixing Non-Newtonian Slurries." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-40833.

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The mechanics of air sparger systems have been primarily investigated for aqueous-based Newtonian fluids. Tilton et al. (1982) [1] describes the fluid mechanics of air sparging systems in non-Newtonian fluids as having two primary flow regions. A center region surrounding the sparger, referred to as the region of bubbles (ROB), contains upward flow due to the buoyant driving force of the rising bubbles. In an annular region, outside the ROB, referred to as the zone of influence (ZOI), the fluid flow is reversed and is opposed to the direction of bubble rise. Outside the ZOI the fluid is unaffected by the air sparger system. The flow regime in the ROB is often turbulent, and the flow regime in the ZOI is laminar; the flow regime outside the ZOI is quiescent. Tests conducted with shear thinning non-Newtonian fluid in a 34-in. diameter tank showed that the ROB forms an approximately inverted cone that is the envelop of the bubble trajectories. The depth to which the air bubbles reach below the sparger nozzle is a linear function of the air-flow rate. The recirculation time through the ZOI was found to vary proportionally with the inverse square of the sparging air-flow rate. Visual observations of the ROB were made in both water and Carbopol®. The bubbles released from the sparge tube in Carbopol® were larger than those in water.
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Niazi, Erfan, Mehrzad Shams, and Goodarz Ahmadi. "Population Balance Modeling for Non-Homogeneous Bubble Column: Effect of Fluid Rheology on Gas Dispersion." In ASME 2012 Fluids Engineering Division Summer Meeting collocated with the ASME 2012 Heat Transfer Summer Conference and the ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/fedsm2012-72360.

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This work describes the development of a two-dimensional CFD model for gas-liquid flows in a bubble column. Population balance dynamic equation is solved for babbles including bubbles coalescence and break up in the column. Prince and Blanch model for bubbles coalescence extended to non-Newtonian rheology and used in the analysis. Luo and Svendsen model is used for bubbles breakup modeling and the k-e model equations are solved for analysis of primary fluid turbulence. Solutions of carboxy methyl cellulose in water with different concentrations are used as a non-Newtonian pesudoplastic liquid. Raise velocity of bubbles, which play an important role in population balance modeling, is discusses in details for non-Newtonian fluid. As a first step the results for Newtonian bubble column are presented and verified by comparison with the previous studies. Then the effect of changing fluid rheology is discussed in terms of gas volume fraction and continuous liquid velocity.
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Niazi, Erfan, Mehrzad Shams, Arash Elahi, and Goodarz Ahmadi. "Simulation of Gas – Non-Newtonian Liquid Flow in a Rectangular Bubble Column by Considering Bubbles Interactions." In ASME 2012 Fluids Engineering Division Summer Meeting collocated with the ASME 2012 Heat Transfer Summer Conference and the ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/fedsm2012-72361.

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In this article a CFD model of a three-dimensional Eulerian-Lagrangian is developed for a gas - non-Newtonian liquid flow in a rectangular column. The model resolves the time-dependent, three-dimensional motion of gas bubbles in a liquid to simulate the trajectory of bubbles. Our model incorporates drag, gravity, buoyancy, lift, pressure gradient and virtual mass forces acting on a bubble rising in a liquid, and accounts for two-way momentum coupling between the phases. Population balance equation is solved to model bubble coalescence and break up. In bubble coalescence, Prince and Blanch model is used which can consider the effect of fluid rheology. Luo and Svendosen model was selected for bubble break up. The standard k-e turbulence model is selected for calculating turbulent flow properties. Power-law non-Newtonian liquid is selected for analysis of effect of different solutions of carboxy methyl cellulose in water. The effect of changing fluid to non-Newtonian is discussed in terms of velocity profile and gas hold up.
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Ihmoudah, Abdalsalam, Mohamed M. Awad, Aziz Rahman, and Stephen D. Butt. "Numerical Study on Gas-Yield Power-Law Fluid in T-Junction Minichannel." In ASME 2019 17th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/icnmm2019-4253.

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Abstract In this study, a computational examination of Taylor bubbles was performed for gas/non-Newtonian fluid two-phase flows developed in a minichannel T-junction mixer with a hydraulic diameter of 1 mm. The investigations employed three separate aqueous xanthan gum solutions at concentrations of 0.05, 0.1 and 0.15 w/w, which are referred to as non-Newtonian (yield power-law) fluids. The effective concentration of the xanthan gum solutions and superficial velocity of the inlet liquid phase on the length, velocity, and shape of the Taylor bubbles was studied using the ANSYS FLUENT 19 software package. The simulation results show an increase in bubble velocity with increasing film thickness, particularly in solutions of higher viscosity XG-0.15%. Furthermore, bubble lengths decreased as the xanthan gum concentrations increased, but bubble shapes underwent alterations when the concentrations increased. Another interesting result of the tests shows that when the liquid inlet velocity increases, bubble lengths decrease during lower liquid superficial velocity, whereas during higher velocities, they change only slightly after increases in concentration. Finally, with increasing XG concentration, the liquid film thickness around the bubble increased. The results show good agreement with correlations after modifying a capillary number (Ca*) for non-Newtonian liquids in all cases.
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Williams, P. Rhodri, Rodhri L. Williams, and A. Al-Hussany. "Cavitation Phenomena in Thin Films of Newtonian, Non-Newtonian and Viscoelastic Fluids Due to Rapid Bubble Expansion Under Pulses of Negative Pressure." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45001.

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We report studies of the growth of a cavitation bubble in terms of the development of hydrodynamic pressures within the liquid close to the expanding bubble’s surface. The results of this study are discussed in terms of the possible consequences of cavitation bubble expansion in Newtonian and non-Newtonian, shear-thinning fluids (such as synovial fluid). Contrary to previous indications in the literature, non-Newtonian (specifically, shear-thinning) behaviour is found to be significant in this context, insofar as it may result in markedly enhanced tensions due to the pressure waves developed about a growing bubble during the latter stages of its expansion phase. The magnitude of the tensions so developed are compared with estimates of cavitation thresholds (Fc ) which are obtained from experiments involving the reflection of pulsed ultrasound at a flexible boundary. Under some circumstances the tensions developed about the growing cavity are shown to be commensurate with Fc. The possible consequences of these findings are discussed in terms of cavitation damage to blood vessels or other biological tissues.
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6

De Kee, D., D. Rodrigue, and C. F. Chan Man Fong. "The Motion of Bubbles in Non-Newtonian Fluids." In ASME 1996 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/imece1996-0226.

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Abstract The drag and the rise velocity of a spherical bubble rising freely and slowly in an inelastic Carreau fluid are calculated by a perturbation method. Measurements of the rise velocity of gas bubbles in several Newtonian and non-Newtonian fluids are reported. The transition from the Stokes to the Hadamard-Rybczynski regimes has been observed and in the case of viscoelastic fluids a jump discontinuity in the velocity has also been recorded. An equation is proposed to predict the volume at which the jump discontinuity occurs and the prediction is in good agreement with the experimental data.
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7

Williams, P. R. "Cavitation phenomena in thin films of Newtonian and non-Newtonian fluids due to rapid bubble expansion." In BIOMEDICINE 2003, edited by R. L. Williams and A. Al-Hussany. Southampton, UK: WIT Press, 2003. http://dx.doi.org/10.2495/bio030091.

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8

Jing, Silin, Xianzhi Song, Zhaopeng Zhu, Buwen Yu, and Shiming Duan. "Settling Behavior of Particles in Bubble Containing Newtonian Fluids: Experimental Study and Model Development." In ASME 2021 40th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/omae2021-62756.

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Abstract Accurate description of cuttings slippage in the gas-liquid phase is of great significance for wellbore cleaning and the control accuracy of bottom hole pressure during MPD. In this study, the wellbore bubble flow environment was simulated by a constant pressure air pump and the transparent wellbore, and the settling characteristics of spherical particles under different gas volume concentrations were recorded and analyzed by highspeed photography. A total of 225 tests were conducted to analyze the influence of particle diameter (1–12mm), particle density (2700–7860kg/m^3), liquid viscosity and bubble volume concentration on particle settling velocity. Gas drag force is defined to quantitatively evaluate the bubble’s resistance to particle slippage. The relationship between bubble drag coefficient and particle Reynolds number is obtained by fitting the experimental results. An explicit settling velocity equation is established by introducing Archimedes number. This explicit equation with an average relative error of only 8.09% can directly predict the terminal settling velocity of the sphere in bubble containing Newtonian fluids. The models for predicting bubble drag coefficient and the terminal settling velocity are valid with particle Reynolds number ranging from 0.05 to 167 and bubble volume concentration ranging from 3.0% to 20.0%. Besides, a trial-and-error procedure and an illustrative example are presented to show how to calculate bubble drag coefficient and settling velocity in bubble containing fluids. The results of this study will provide the theoretical basis for wellbore cleaning and accurate downhole pressure to further improve the performance of MPD in treating gas influx.
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9

Leishear, Robert A., Michael L. Restivo, and David J. Sherwood. "Bubble Formation in a Large Scale System." In ASME 2008 Fluids Engineering Division Summer Meeting collocated with the Heat Transfer, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/fedsm2008-55013.

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The complexities of bubble formation in liquids increase as the system size increases, and a photographic study is presented here to provide some insight into the dynamics of bubble formation for large systems. Air was injected at the bottom of a 28 feet tall by 30 inch diameter column. Different fluids were subjected to different air flow rates at different fluid depths. The fluids were water and non-Newtonian, Bingham plastic fluids, which have yield stresses requiring an applied force to initiate movement, or shearing, of the fluid. Tests showed that bubble formation was significantly different in the two types of fluids. In water, a field of bubbles was formed, which consisted of numerous, distributed, 1/4 to 3/8 inch diameter bubbles. In the Bingham fluid, large bubbles of 6 to 12 inches in diameter were formed, which depended on the air flow rate. This paper provides comprehensive photographic results related to bubble formation in these fluids.
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10

Pillapakkam, Shriram B. "Dynamics of Drops and Bubbles in Newtonian and Viscoelastic Flows." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-1227.

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Abstract A finite element code based on the level set method is developed for simulating the motion viscoelastic free-surfaces in two-dimensions. This method is a generalization of the one described in Osher and Sethian (1988) where the free-surface problems of inviscid and viscous fluids were simulated. The code is used to study deformation of drops in simple shear and Poisuelle flows over a wide range of dimensionless capillary (Ca) and Deborah numbers (De). Simulations show that there are limiting values of these two parameters below which the drops assume steady state shapes. For values greater than these limiting values, on the other hand, there is no steady state shape and the drop continued to deform. For a Newtonian bubble rising in a quiescent viscoelastic liquid we again find that there are limiting values of the parameters De and Ca, above which the bubble assumes a characteristic shape with a cusp-like trailing edge. The numerical results show that the viscoelastic stresses near the trailing edge are extensional and act in the direction normal to the drop surface. The front of the bubble however remains round as the local viscoelastic and viscous stresses act to round the bubble. These results are in good agreement with the experimental results.
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