Numerical Simulation of a Gas Bubble Rising in Power-Law Fluids Using a Sharp Surface Force Implementation

2019 ◽  
Author(s):  
Purushotam Kumar ◽  
Kai Jin ◽  
Surya Pratap Vanka
Keyword(s):  
Level Set ◽  
Power Law ◽  
Shear Thickening ◽  
Surface Force ◽  
Shear Thinning ◽  
Volume Of Fluid ◽  
Liquid Volume ◽  
Reconstruction Method ◽  
Power Law Fluids ◽  
Bubble Rising

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.

Drops of power-law fluids falling on a coated vertical fibre

2014 ◽  
Vol 751 ◽  
pp. 184-215
Author(s):  
Liyan Yu ◽  
John Hinch
Keyword(s):  
Solitary Waves ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Bond Number ◽  
Power Law Fluid ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Shear Thickening Fluids ◽  
The Stability

AbstractWe study the solitary wave solutions in a thin film of a power-law fluid coating a vertical fibre. Different behaviours are observed for shear-thickening and shear-thinning fluids. For shear-thickening fluids, the solitary waves are larger and faster when the reduced Bond number is smaller. For shear-thinning fluids, two branches of solutions exist for a certain range of the Bond number, where the solitary waves are larger and faster on one and smaller and slower on the other as the Bond number decreases. We carry out an asymptotic analysis for the large and fast-travelling solitary waves to explain how their speeds and amplitudes change with the Bond number. The analysis is then extended to examine the stability of the two branches of solutions for the shear-thinning fluids.

scholarly journals Collapse of a neutrally buoyant suspension column: from Newtonian to apparent non-Newtonian flow regimes

2017 ◽  
Vol 826 ◽  
pp. 918-941 ◽  
Author(s):  
A. Bougouin ◽  
L. Lacaze ◽  
T. Bonometti
Keyword(s):  
Power Law ◽  
Temporal Evolution ◽  
Volume Fraction ◽  
Fluid Model ◽  
Particle Diameter ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Rheological Parameters ◽  
Power Law Fluids ◽  
Neutrally Buoyant

Experiments on the collapse of non-colloidal and neutrally buoyant particles suspended in a Newtonian fluid column are presented, in which the initial volume fraction of the suspension $\unicode[STIX]{x1D719}$, the viscosity of the interstitial fluid $\unicode[STIX]{x1D707}_{f}$, the diameter of the particles $d$ and the mixing protocol, i.e. the initial preparation of the suspension, are varied. The temporal evolution of the slumping current highlights two main regimes: (i) an inertial-dominated regime followed by (ii) a viscous-dominated regime. The inertial regime is characterized by a constant-speed slumping which is shown to scale as in the case of a classical inertial dam-break. The viscous-dominated regime is observed as a decreasing-speed phase of the front evolution. Lubrication models for Newtonian and power-law fluids describe most of situations encountered in this regime, which strongly depends on the suspension parameters. The temporal evolution of the propagating front is used to extract the rheological parameters of the fluid models. At the early stages of the viscous-dominated regime, a constant effective shear viscosity, referred to as an apparent Newtonian viscous regime, is found to depend only on $\unicode[STIX]{x1D719}$ and $\unicode[STIX]{x1D707}_{f}$ for each mixing protocol. The obtained values are shown to be well fitted by the Krieger–Dougherty model whose parameters involved, say a critical volume fraction $\unicode[STIX]{x1D719}_{m}$ and the exponent of divergence, depend on the mixing protocol, i.e. the microscale interaction between particles. On a longer time scale which depends on $\unicode[STIX]{x1D719}$, the front evolution is shown to slightly deviate from the apparent Newtonian model. In this apparent non-Newtonian viscous regime, the power-law model, indicating both shear-thinning and shear-thickening behaviours, is shown to be more appropriate to describe the front evolution. The present experiments indicate that the mixing protocol plays a crucial role in the selection of a shear-thinning or shear-thickening type of collapse, while the particle diameter $d$ and volume fraction $\unicode[STIX]{x1D719}$ play a significant role in the shear-thickening case. In all cases, the normalized effective consistency of the power-law fluid model is found to be a unique function of $\unicode[STIX]{x1D719}$. Finally, an apparent viscoplastic regime, characterized by a finite length spreading reached at finite time, is observed at high $\unicode[STIX]{x1D719}$. This regime is mostly observed for volume fractions larger than $\unicode[STIX]{x1D719}_{m}$ and up to a volume fraction $\unicode[STIX]{x1D719}_{M}$ close to the random close packing fraction at which the initial column remains undeformed on opening the gate.

Two Dimensional Unsteady Laminar Flow of Power Law Fluids Past a Square Cylinder: A Numerical Study

2008 ◽  
Author(s):  
Akhilesh K. Sahu ◽  
Raj P. Chhabra ◽  
V. Eswaran
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Shear Thickening ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Shear Thinning ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Shear Thickening Fluids ◽  
Edge Separation

The two-dimensional and unsteady flow of power-law fluids past a long square cylinder has been investigated numerically in the range of conditions 60 ≤ Re ≤ 160 and 0.5 ≤ n ≤ 2.0. Over this range of Reynolds numbers, the flow is periodic in time for Newtonian fluids. However, no such information is available for power law fluids. A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. The macroscopic quantities such as drag coefficients, Strouhal number, lift coefficient as well as the detailed kinematic variables like stream function, vorticity and so on, have been calculated as functions of the pertinent dimension-less groups. In particular, the effects of Reynolds number and of the power-law index have been investigated in the unsteady laminar flow regime. The leading edge separation in shear-thinning fluids produces an increase in drag values with the increasing Reynolds number, while shear-thickening behaviour delays the leading edge separation. So, the drag coefficient in the above-mentioned range of Reynolds number, Re, in shear-thinning fluids (n < 1) initially decreases but at high values of the Reynolds number, it increases. As expected, on the other hand, in case of shear-thickening fluids (n > 1) drag coefficient reduces with Reynolds number, Re. Furthermore, the present results also suggest the transition from steady to unsteady flow conditions to occur at lower Reynolds numbers in shear-thickening fluids than that in Newtonian fluids. Also, the spectra of lift signal for shear-thickening fluids show that the flow is truly periodic in nature with a single dominant frequency in the above range of Reynolds number. In shear-thinning fluids at higher Re, quasi-periodicity sets in with additional frequencies, which indicate the transition from the 2-D to 3-D flows.

Spread of a non-Newtonian liquid jet over a horizontal plate

2008 ◽  
Vol 613 ◽  
pp. 411-443 ◽  
Author(s):  
JIANGANG ZHAO ◽  
ROGER E. KHAYAT
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Hydraulic Jump ◽  
Shear Thickening ◽  
Flow Region ◽  
Shear Thinning ◽  
Similarity Solutions ◽  
Viscous Boundary Layer ◽  
Power Law Fluids ◽  
Shear Thickening Fluids

The flow of an impinging non-Newtonian jet onto a solid flat plate is examined theoretically in this study. Similarity solutions are sought for both shear-thinning and shear-thickening fluids of the power-law type. The jet is assumed to spread out in a thin layer bounded by a hydraulic jump. In addition to the stagnation-flow region, the flow domain is divided into three main regions: a developing boundary layer, fully viscous boundary layer and hydraulic jump. The anomalous behaviour of power-law fluids at small shear rate is remedied by seeking a two-layer solution in each domain. Such anomalies include the singularity of viscosity for shear-thinning fluids, and the vanishing of viscosity as well the overshoot in velocity for shear-thickening fluids. Although the rate of shear-thinning appears to affect significantly the film profile and velocity, only the overall viscosity influences the position of the hydraulic jump.

Drag on a Sphere in Poiseuille Flow of Shear-Thinning Power-Law Fluids

2011 ◽  
Vol 50 (23) ◽  
pp. 13105-13115 ◽  
Author(s):  
Daoyun Song ◽  
Rakesh K. Gupta ◽  
Rajendra P. Chhabra
Keyword(s):  
Power Law ◽  
Poiseuille Flow ◽  
Shear Thinning ◽  
Power Law Fluids

Fully Developed Flow of Power-Law Fluid Through a Cylindrical Microfluidic Pipe: Pressure Drop and Electroviscous Effects

2008 ◽  
Author(s):  
Ram P. Bharti ◽  
Dalton J. E. Harvie ◽  
Malcolm R. Davidson
Keyword(s):  
Pressure Drop ◽  
Field Strength ◽  
Charge Density ◽  
Power Law ◽  
Maximum Velocity ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Electrical Field ◽  
Electrical Field Strength ◽  
Fluid Behaviour

Pressure drop and electroviscous effects in the axisymmetric, steady, fully developed, pressure-driven flow of incompressible power-law fluids through a cylindrical microchannel at low Reynolds number (Re = 0.01) have been investigated. The Poisson-Boltzmann equation (describing the electrical potential) and the momentum equations in conjunction with electrical force and power-law fluid rheology have been solved numerically using the finite difference method. The pipe wall is considered to have uniform surface charge density (S = 4) and the liquid is assumed to be a symmetric electrolyte solution. In particular, the influence of the dimensionless inverse Debye length (K = 2, 20) and power-law flow behaviour index (n = 0.2, 1, 1.8) on the EDL potential, ion concentrations and charge density profiles, induced electrical field strength, velocity and viscosity profiles and pressure drop have been studied. As expected, the local EDL potential, local charge density and electrical field strength increases with decreasing K and/or increasing S. The velocity profiles cross-over away from the charged pipe wall with increasing K and/or decreasing n. The maximum velocity at the center of the pipe increases with increasing n and/or increasing S and/or decreasing K. The shear-thinning fluid viscosity is strongly dependent on K and S, whereas the shear-thickening viscosity is very weakly dependent on K and S. For fixed K, as the fluid behaviour changes from Newtonian (n = 1) to shear-thinning (n < 1), the induced electrical field strength increases and maximum velocity reduces. On the other hand, the change in fluid behaviour from Newtonian (n = 1) to shear-thickening (n > 1) decreases the electrical field strength and increases the maximum velocity. The non-Newtonian effects on maximum velocity and pressure drop are stronger in shear-thinning fluids at small K and large S, the shear-thickening fluids show opposite influence. Electroviscous effects enhance with decreasing K and/or increasing S. The electroviscous effects show complex dependence on the non-Newtonian tendency of the fluids. The shear-thickening (n > 1) fluids and/or smaller K show stronger influence on the pressure drop and thus, enhance the electroviscous effects than that in shear-thinning (n < 1) fluids and/or large K where EDL is very thin.

Wetting behavior of the shear thinning power law fluids

2013 ◽  
Vol 11 (1) ◽  
pp. 95-102 ◽  
Author(s):  
Sima Didari ◽  
Zakaria Y. Ahmad ◽  
James D. Veldhorst ◽  
Tequila A. L. Harris
Keyword(s):  
Power Law ◽  
Shear Thinning ◽  
Wetting Behavior ◽  
Power Law Fluids
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