Academic literature on the topic 'Euler's numbers. Newtonian fluids Fluid dynamics'
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Journal articles on the topic "Euler's numbers. Newtonian fluids Fluid dynamics"
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Wang, Qixuan. "Optimal Strokes of Low Reynolds Number Linked-Sphere Swimmers." Applied Sciences 9, no. 19 (September 26, 2019): 4023. http://dx.doi.org/10.3390/app9194023.
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Optimal gait design is important for micro-organisms and micro-robots that propel themselves in a fluid environment in the absence of external force or torque. The simplest models of shape changes are those that comprise a series of linked-spheres that can change their separation and/or their sizes. We examine the dynamics of three existing linked-sphere types of modeling swimmers in low Reynolds number Newtonian fluids using asymptotic analysis, and obtain their optimal swimming strokes by solving the Euler–Lagrange equation using the shooting method. The numerical results reveal that (1) with the minimal 2 degrees of freedom in shape deformations, the model swimmer adopting the mixed shape deformation modes strategy is more efficient than those with a single-mode of shape deformation modes, and (2) the swimming efficiency mostly decreases as the number of spheres increases, indicating that more degrees of freedom in shape deformations might not be a good strategy in optimal gait design in low Reynolds number locomotion.
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Luo, Zheng Yuan, and Bo Feng Bai. "Dynamics of capsules enclosing viscoelastic fluid in simple shear flow." Journal of Fluid Mechanics 840 (February 14, 2018): 656–87. http://dx.doi.org/10.1017/jfm.2018.88.
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Previous studies on capsule dynamics in shear flow have dealt with Newtonian fluids, while the effect of fluid viscoelasticity remains an unresolved fundamental question. In this paper, we report a numerical investigation of the dynamics of capsules enclosing a viscoelastic fluid and which are freely suspended in a Newtonian fluid under simple shear. Systematic simulations are performed at small but non-zero Reynolds numbers (i.e. $Re=0.1$) using a three-dimensional front-tracking finite-difference model, in which the fluid viscoelasticity is introduced via the Oldroyd-B constitutive equation. We demonstrate that the internal fluid viscoelasticity presents significant effects on the deformation behaviour of initially spherical capsules, including transient evolution and equilibrium values of their deformation and orientation. Particularly, the capsule deformation decreases slightly with the Deborah number De increasing from 0 to $O(1)$. In contrast, with De increasing within high levels, i.e. $O(1{-}100)$, the capsule deformation increases continuously and eventually approaches the Newtonian limit having a viscosity the same as the Newtonian part of the viscoelastic capsule. By analysing the viscous stress, pressure and viscoelastic stress acting on the capsule membrane, we reveal that the mechanism underlying the effects of the internal fluid viscoelasticity on the capsule deformation is the alterations in the distribution of the viscoelastic stress at low De and its magnitude at high De, respectively. Furthermore, we find some new features in the dynamics of initially non-spherical capsules induced by the internal fluid viscoelasticity. Particularly, the transition from tumbling to swinging of oblate capsules can be triggered at very high viscosity ratios by increasing De alone. Besides, the critical viscosity ratio for the tumbling-to-swinging transition is remarkably enlarged with De increasing at relatively high levels, i.e. $O(1{-}100)$, while it shows little change at low De, i.e. below $O(1)$.
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AFONSO, A. M., P. J. OLIVEIRA, F. T. PINHO, and M. A. ALVES. "Dynamics of high-Deborah-number entry flows: a numerical study." Journal of Fluid Mechanics 677 (April 13, 2011): 272–304. http://dx.doi.org/10.1017/jfm.2011.84.
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High-elasticity simulations of flows through a two-dimensional (2D) 4 : 1 abrupt contraction and a 4 : 1 three-dimensional square–square abrupt contraction were performed with a finite-volume method implementing the log-conformation formulation, proposed by Fattal & Kupferman (J. Non-Newtonian Fluid Mech., vol. 123, 2004, p. 281) to alleviate the high-Weissenberg-number problem. For the 2D simulations of Boger fluids, modelled by the Oldroyd-B constitutive equation, local flow unsteadiness appears at a relatively low Deborah number (De) of 2.5. Predictions at higher De were possible only with the log-conformation technique and showed that the periodic unsteadiness grows with De leading to an asymmetric flow with alternate back-shedding of vorticity from pulsating upstream recirculating eddies. This is accompanied by a frequency doubling mechanism deteriorating to a chaotic regime at high De. The log-conformation technique provides solutions of accuracy similar to the thoroughly tested standard finite-volume method under steady flow conditions and the onset of a time-dependent solution occurred approximately at the same Deborah number for both formulations. Nevertheless, for Deborah numbers higher than the critical Deborah number, and for which the standard iterative technique diverges, the log-conformation technique continues to provide stable solutions up to quite (impressively) high Deborah numbers, demonstrating its advantages relative to the standard methodology. For the 3D contraction, calculations were restricted to steady flows of Oldroyd-B and Phan-Thien–Tanner (PTT) fluids and very high De were attained (De ≈ 20 for PTT with ϵ = 0.02 and De ≈ 10000 for PTT with ϵ = 0.25), with prediction of strong vortex enhancement. For the Boger fluid calculations, there was inversion of the secondary flow at high De, as observed experimentally by Sousa et al. (J. Non-Newtonian Fluid Mech., vol. 160, 2009, p. 122).
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Tian, Fang-Bao. "Deformation of a Capsule in a Power-Law Shear Flow." Computational and Mathematical Methods in Medicine 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/7981386.
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An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.
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Arafin, Sayyadul, and S. M. Mujibur Rahman. "Dynamical Properties of Omani Crude Oils for Flow Through a Vertical Annulus and a Cylindrical Pipe." Sultan Qaboos University Journal for Science [SQUJS] 16 (December 1, 2011): 102. http://dx.doi.org/10.24200/squjs.vol16iss0pp102-117.
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We have initially investigated the temperature dependence of density and viscosity of a number of crude oils, collected from various hydrocarbon reservoirs in Oman. The measured data are then utilized to investigate the flow dynamics of these hydrocarbon fluids under gravity and applied pressures at various temperatures. We have modeled the flow of the various crude oil samples through a vertical (a) annulus and (b) cylindrical pipe - all treated within the Newtonian fluid flow approximation of a laminar flow - to investigate the flow properties of these samples. A computer program is developed so that the temperature dependence of the fluid flow distinctly separates the laminar mode from a turbulent mode with respect to Reynolds numbers within the ranges Re<2000 and Re>2000. The adopted models of the velocity profiles, mass rate of flow and viscous force on the solid surface are not novel, but the present calculations aim to specifically use the various Omani crude oil samples with various AIP values; the calculated results shed some light on the dynamics of these specific samples within Newtonian approximation. The measured physical properties and the subsequent calculations of the relevant dynamical properties might be useful for various purposes e.g. extraction and transportation of crude oils through pipes.
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Zinani, F. S. F., and S. Frey. "GALERKIN LEAST-SQUARES APPROXIMATIONS FOR FLOWS OF CASSON FLUIDS THROUGH AN EXPANSION." Revista de Engenharia Térmica 5, no. 2 (December 31, 2006): 82. http://dx.doi.org/10.5380/reterm.v5i2.61855.
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Among non-Newtonian fluid models, purely viscous constitutive equations play an important role in industrial applications regardless their lack of accuracy in non-viscometric flows. In this work we are concerned with the flow of viscoplastic shear-thinning fluids in complex geometry. Viscoplastic fluids are those that behave as extremely high viscosity materials when submitted to low stresses and that flow when submitted to stresses higher than a yield stress value. Usually, they also present shearthinning behavior. Fluids such as molten chocolate, xanthan gum solutions, blood, wastewater sludges, muds, and polymer solutions present viscoplastic shear-thinning features. In order to approximate numerically viscoplastic shear-thinning flows we first describe a mechanical model based on continuum mechanics conservation laws of mass and momentum. The description of material behavior is such as to respect certain principles of objectivity and generality in continuum mechanics. The Generalized Newtonian Liquid constitutive equation with Casson viscosity function is able to predict viscoplasticity and shear-thinning. The numerical approximation of the equations is performed by a finite element method. To prevent the model from pathologies known for the classic Galerkin method, we employ a stabilized method based on a Galerkin least-squares (GLS) scheme, which is designed to circumvent Babuška-Brezzi condition and deal with the asymmetry of the advective operator. We present approximations for the flow through a planar 4:1 sudden expansion. We investigate the influence of Reynolds and Casson numbers on the flow dynamics.
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Shahsavar Goldanlou, Aysan, Mohammad Badri, Behzad Heidarshenas, Ahmed Kadhim Hussein, Sara Rostami, and Mostafa Safdari Shadloo. "Numerical Investigation on Forced Hybrid Nanofluid Flow and Heat Transfer Inside a Three-Dimensional Annulus Equipped with Hot and Cold Rods: Using Symmetry Simulation." Symmetry 12, no. 11 (November 14, 2020): 1873. http://dx.doi.org/10.3390/sym12111873.
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A 3D computational fluid dynamics method is used in the current study to investigate the hybrid nanofluid (HNF) flow and heat transfer in an annulus with hot and cold rods. The chief goal of the current study is to examine the influences of dissimilar Reynolds numbers, emissivity coefficients, and dissimilar volume fractions of nanoparticles on hydraulic and thermal characteristics of the studied annulus. In this way, the geometry is modeled using a symmetry scheme. The heat transfer fluid is a water, ethylene–glycol, or water/ethylene–glycol mixture-based Cu-Al2O3 HNF, which is a Newtonian NF. According to the findings for the model at Re = 3000 and ϕ1 = 0.05, all studied cases with different base fluids have similar behavior. ϕ1 and ϕ2 are the volume concentration of Al2O3 and Cu nanoparticles, respectively. For all studied cases, the total average Nusselt number (Nuave) reduces firstly by an increment of the volume concentrations of Cu nanoparticles until ϕ2 = 0.01 or 0.02 and then, the total Nuave rises by an increment of the volume concentrations of Cu nanoparticles. Additionally, for the case with water as the base fluid, the total Nuave at ϕ2 = 0.05 is higher than the values at ϕ2 = 0.00. On the other hand, for the other cases, the total Nuave at ϕ2 = 0.05 is lower than the values at ϕ2 = 0.00. For all studied cases, the case with water as the base fluid has the maximum Nuave. Plus, for the model at Re = 4000 and ϕ1 = 0.05, all studied cases with different base fluids have similar behavior. For all studied cases, the total Nuave reduces firstly by an increment of the volume concentrations of Cu nanoparticles until ϕ2 = 0.01 and then, the total Nuave rises by an increment of the volume concentrations of Cu nanoparticles. The Nuave augments are found by an increment of Reynolds numbers. Higher emissivity values should lead to higher radiation heat transfer, but the portion of radiative heat transfer in the studied annulus is low and therefore, has no observable increment in HNF flow and heat transfer.
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Vannozzi, Carolina. "Relaxation and coalescence of two equal-sized viscous drops in a quiescent matrix." Journal of Fluid Mechanics 694 (January 25, 2012): 408–25. http://dx.doi.org/10.1017/jfm.2011.559.
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AbstractHead-on collisions of two equal-sized viscous drops in a biaxial extensional flow were simulated using the boundary integral method in the Stokes flow limit, for capillary numbers of the order of $1{0}^{\ensuremath{-} 4} $–$1{0}^{\ensuremath{-} 1} $, typical of flow-induced coalescence experiments. At a certain point in time, during the drainage process, the flow was abruptly stopped and the time-dependent dynamics of drop deformation (relaxation) was followed to discern whether the pair of drops would eventually coalesce. The concept of coalescence probability was used to study the evolution of probable collisions. The polymeric system of polybutadiene (PBd) drops undergoing head-on collisions in a polydimethylsiloxane (PDMS) matrix, previously well-characterized both experimentally and numerically by Yoon et al. (Phys. Fluid, vol. 19, 2007, 102102), in which both fluids were Newtonian under the experimental conditions, was used as our reference. Film shapes, velocity profiles and pressure distributions were studied for initially parabolic or dimpled thin film shapes. It was shown that micrometre-sized drops undergoing relaxation can coalesce in the capillary number range studied, which also included cases of hindered coalescence and cases in which the flow interaction time for the collision was smaller than the drainage time; thus, this phenomenon could influence the final drop size distribution of blends. Further, these findings could be of interest in interpreting stop–strain experiments, in the case of a sudden change in flow conditions and in population balance studies of drops in blends.
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Aminian Dehkordi, Javad, and Arezou Jafari. "CFD Investigation of Al2O3 Nanoparticles Effect on Heat Transfer Enhancement of Newtonian and Non-Newtonian Fluids in a Helical Coil." Chemical Product and Process Modeling 14, no. 3 (March 16, 2019). http://dx.doi.org/10.1515/cppm-2018-0057.
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Abstract The present study applied computational fluid dynamics (CFD) to investigate the heat transfer of Newtonian (water) and non-Newtonian (0.3 %wt. aqueous solution of carboxymethylcellulose (CMC)) fluids in the presence of Al2O3 nanoparticles. To analyze the heat transfer rate, investigations were performed in a vertical helical coil as essential heat transfer equipment, at different inlet Reynolds numbers. To verify the accuracy of the simulation model, experimental data reported in the literature were employed. Comparisons showed the validity of simulation results. From the results, compared to the aqueous solution of CMC, water had a higher Nusselt number. In addition, it was observed that adding nanoparticles to a base fluid presented different results in which water/Al2O3 nanofluid with nanoparticles’ volume fraction of 5 % was more effective than the same base fluid with a volume fraction of 10 %. In lower ranges of Reynolds number, adding nanoparticles was more effective. For CMC solution (10 %), increasing concentration of nanoparticles caused an increase in the apparent viscosity. Consequently, the Nusselt number was reduced. The findings reveal the important role of fluid type and nanoparticle concentration in the design and development of heat transfer equipment.
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Mkacher, Hakim, and Abdelhak Ayadi. "Thermo-Convective Flow of a Yield-Stress Fluid Between Two Horizontal Plates for Rayleigh Numbers Greater Than the Critical Value." Journal of Thermal Science and Engineering Applications 12, no. 3 (November 4, 2019). http://dx.doi.org/10.1115/1.4045119.
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Abstract In this paper, two-dimensional unsteady simulations of yield-stress fluids in the Poiseuille–Rayleigh–Bénard flow between two horizontal plates were performed. The laminar flow of these fluids is characterized by the existence of high- and low-viscous zones. The thermal and hydrodynamic behaviors were studied in the case where the convective instability was developed, and the high-viscous zones were minimized. The commercial computational fluid dynamics (CFD) package fluent was adopted to perform the different simulations. The average Nusselt number over time of the two plates was chosen to characterize the thermal transport, while the average of the maximum vertical velocity component over time in the horizontal mid-plane described the hydrodynamics of the flow. It was found that the fluid behaved according to a range of viscosities with the same order of magnitude as the plastic viscosity. The effect of the dimensionless numbers on the flow showed that the yield-stress fluid could mimic a Newtonian behavior in the pre-described conditions. Although, the fluid still held the non-Newtonian character distinguished by the dependency on the Bingham number Bn. This returned to the increase of the apparent viscosity with Bn which contributed to the weakening of the convective streams, and consequently, reduced convective thermal transport.
Dissertations / Theses on the topic "Euler's numbers. Newtonian fluids Fluid dynamics"
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Yildirim, B. Gazi. "A global preconditioning method for the Euler equations." Master's thesis, Mississippi State : Mississippi State University, 2003. http://library.msstate.edu/etd/show.asp?etd=etd-07152003-164237.
Full textConference papers on the topic "Euler's numbers. Newtonian fluids Fluid dynamics"
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Vempati, Bhadraiah, Mahesh V. Panchagnula, Alparslan O¨ztekin, and Sudhakar Neti. "Flow Regimes of Newtonian Fluids in Vertical Co-Axial Flows." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14111.
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This paper presents experimental and numerical results of the interfacial dynamics of liquid-liquid flows when a dispersed phase liquid introduced in a continuous phase liquid flow with an arbitrary inlet velocity profile. The flow dynamics are studied as a function of the individual phase Reynolds and Capillary numbers, viscosity ratio, flow rate ratio, and Bond number. Fully-developed (or self-similar solution) model predicted multiple (one to three) solutions of jet diameter for a range of dimensionless numbers. The critical bifurcation parameters are identified in order to study the jet instability. The fully developed jet diameter solutions are plotted in terms of flow ratio of liquid phases and indicate three solution branches. Experiments have been carried out using Poly Ethylene Glycol (PEG)-Canola oil to investigate the three possible solutions predicted by fully developed theory. The measured values of inner fluid radius agree very well with the lower branch of the three branched solution and the deviation of the experimental results for the rest of the branches is observed to be more than 50 percent. Numerical simulations also have been performed to compare the self-similar solution results of liquid jet radius using FLUENT® software. The results predicted by numerical simulations agree very well with both the lower and upper branches of solution predicted by fully developed theory.
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Stangl, Michael, Johannes Gerstmayr, and Hans Irschik. "A Large Deformation Finite Element for Pipes Conveying Fluid Based on the Absolute Nodal Coordinate Formulation." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34771.
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A novel pipe finite element conveying fluid, suitable for modeling large deformations in the framework of Bernoulli Euler beam theory, is presented. The element is based on a third order planar beam finite element, introduced by Berzeri and Shabana, on basis of the absolute nodal coordinate formulation. The equations of motion for the pipe-element are derived using an extended version of Lagrange’s equations of the second kind for taking into account the flow of fluids, in contrast to the literature, where most derivations are based on Hamilton’s Principle or Newtonian approaches. The advantage of this element in comparison to classical large deformation beam elements, which are based on rotations, is the direct interpolation of position and directional derivatives, which simplifies the equations of motion considerably. As an advantage Lagrange’s equations of the second kind offer a convenient connection for introducing fluids into multibody dynamic systems. Standard numerical examples show the convergence of the deformation for increasing number of elements. For a cantilever pipe, the critical flow velocities for increasing number of pipe elements are compared to existing works, based on Euler elastica beams and moving discrete masses. The results show good agreements with the reference solutions applying only a small number of pipe finite elements.
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Ovando, Guillermo E., Juan C. Prince, and Sandy L. Ovando. "Flow in Cavities With Curved Boundaries." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78076.
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Fluid dynamics for a Newtonian fluid in the absence of body forces in a two-dimensional cavity with top and bottom curved walls was studied numerically. The vertical walls are fixed and the curved walls are in motion. The Navier-Stokes equations were solved using the finite element method combined with the operator splitting scheme. We analyzed the behaviour of the velocity fields, the vorticity fields and the velocity profiles of the fluid inside the cavity. The analysis was carried out for two different Reynolds numbers of 50 and 500 with two ratios (R = 1, −1) of the top to the bottom curved lid speed. For these values of parameters the flow is characterized by vortex formation inside the cavity. The spatial symmetry on the flow patterns are also investigated. We found that when the velocities of the top and bottom walls have opposite direction only one cell is formed in the central part of the cavity; however when the velocities of the top and bottom walls have the same direction the vortex formation inside the cavity is more complex.
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Kumar, Purushotam, Kai Jin, and Surya Pratap Vanka. "Numerical Simulation of a Gas Bubble Rising in Power-Law Fluids Using a Sharp Surface Force Implementation." In ASME-JSME-KSME 2019 8th Joint Fluids Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/ajkfluids2019-4769.
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Abstract In this paper, we have applied a recently-developed numerical technique to study the three-dimensional dynamics of a confined air bubble rising in shear thinning and shear-thickening power-law fluids. The method is a blend of Volume of Fluid and Level Set methods and incorporates a Sharp Surface Force Method (SSF) for surface tension forces by solving a second Pressure Poisson Equation (PPE). The gas-liquid interface is captured by an equation for the liquid volume fraction and advected using the geometry reconstruction method. The interface normal and curvature are computed using level-set and height function methods. The accurate representation of the interface and interfacial forces significantly suppressed the spurious velocities commonly observed with conventional volume of fluid method and the Continuum Surface Force (CSF). The algorithm is implemented in a in-house code called CUFLOW and runs on multiple GPUs platform. We explored the effects of fluid rheology, Bond number, and wall confinement on bubble’s transient shape, rise velocity, rise path, and generated vortex structures. The power-law index is varied from 0.25 to 1.50 covering shear-thinning and shear-thickening regimes. Three Bond numbers (Bo = 2, 10 and 50) and three confinement ratios (Cr = 4, 6 and 8) are considered, and their impacts on bubble’s dynamics are analyzed. For the range of parameters examined here, bubble motion in a shear-thinning fluid is seen to be unsteady with significant shape oscillations. The bubble rises with a secondary motion in the cross-sectional plane along with its primary vertical rise. However, in the Newtonian and shear-thickening fluids, the bubble’s shape is seen to reach a steady-state in a relatively short time and rise with only minor deviations from the vertical path.