A Drag Correlation for Single Spheres in Pseudoplastic Tube Flow

Subramaniam, Girish; Zuritz, Carlos A.; Ultman, James S.

doi:10.13031/2013.31839

Cited by 8 publications

(7 citation statements)

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“…Subsequently, this has been extended to cylindrical particles, albeit the particle shape is not a significant factor here. 25,26 Similarly, both Subramaniam and Zuritz 27 Industrial & Engineering Chemistry Research ARTICLE et al 28 have measured drag force on spheres (fixed at the axis of a pipe) immersed in the laminar flow of power-law fluids and correlated their results empirically In summary, therefore as far as known to us, the drag on a sphere in the shearing flow of power-law fluids has not been investigated systematically and this work aims to alleviate this situation. In particular, the continuity and momentum equations describing the laminar flow of power-law fluids past a sphere fixed at the axis of a long pipe have been solved numerically over wide ranges of conditions as: Reynolds number (1 e Re e 100), powerlaw index (0.2 e n e 1), and blockage ratio (0.05 e λ e 0.5).…”

Section: Previous Workmentioning

confidence: 99%

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

Song

Gupta

Chhabra

2011

Ind. Eng. Chem. Res.

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The effect of finite boundaries on the drag experienced by a sphere exposed to the Poiseuille flow of power-law fluids in cylindrical vessels has been investigated numerically. In particular, the momentum equations have been solved over the following ranges of conditions: sphere Reynolds number based on the area average velocity in the pipe, Re 1-100; power law index, n: 0.2-1, and sphere-to-tube diameter ratio, λ: 0-0.5. Due to the obstruction in the path of the fluid caused by the sphere fixed at the axis of the tube and the corresponding changes in the velocity field close to the sphere, there is extra viscous dissipation at the walls and this, in turn, leads to an increase in the drag force acting on the sphere. Conversely, there is an extra pressure drop caused by the fixed sphere for the flow of the fluid in the tube. The effect, however, is more significant at low Reynolds numbers than that at high Reynolds numbers. Similarly, the additional drag due to the confining walls increases with the increasing degree of obstruction, i.e., sphere-to-tube diameter ratio. Overall, all else being equal, the wall effect is seen to be less severe in power-law fluids than that in Newtonian fluids. Furthermore, the confining walls also influence the onset of flow separation and subsequently the size of the recirculation region. The present numerical predictions are consistent with the scant experimental results available in the literature for Newtonian and power-law fluids.

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Section: Previous Workmentioning

confidence: 99%

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

Song

Gupta

Chhabra

2011

Ind. Eng. Chem. Res.

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“…They proposed a correlation for the drag coefficient in terms of a generalized particle Reynolds number and power-law index. They extended their experimental work for a wider range of blockage ratios and lower range of Re p in the non-Newtonian fluid …”

Section: Background and Scopementioning

confidence: 96%

“…They extended their experimental work for a wider range of blockage ratios and lower range of Re p in the non-Newtonian fluid. 27 Graham and Jones 2 concluded that due to the nonlinearity introduced by the viscosity term in non-Newtonian fluid flow and fluid inertia, numerical methods may have to be used for studying the drag effects. They analyzed flow of power-law fluids past a sphere in the particle Reynolds number range of 0.2−100.…”

Section: Background and Scopementioning

confidence: 99%

“…From the above literature review involving non-Newtonian fluids, it may be noted that most of the studies have considered creeping flow regime, , fluid approaching the particle with a constant velocity , as well as the cases where the particle was located centrally in the tube ,, for a wide range of Re p . The conditions considered in these studies are summarized in the Supporting Information (Table S1).…”

Section: Background and Scopementioning

confidence: 99%

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Effects of Particle Blockage and Eccentricity in Location on the Non-Newtonian Fluid Hydrodynamics around a Sphere

Krishnan

Kannan

2012

Ind. Eng. Chem. Res.

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The flow of an incompressible non-Newtonian fluid over an eccentrically located sphere confined in a circular tube was investigated using three-dimensional steady state Computational Fluid Dynamics simulations. Pseudoplastic fluids with different power-law indices of 0.57, 0.76, and 0.94 were considered. The effects of ratio of particle diameter to tube diameter (blockage ratio, BR) and ratio of offset of the sphere position from the tube axis to the tube radius (eccentricity, E c ) on the hydrodynamic phenomena around the sphere are reported over a range of particle Reynolds numbers (Re p ). The simulations were carried out in the range (0.1 ≤ Re p ≤ 40, 0.01 ≤ BR ≤ 0.5, and 0.0 ≤ E c ≤ 0.6). The drag coefficient predictions for an unconfined sphere were found to be sensitive to the value of the consistency index parameter (K) in the viscous flow regime, especially at lower n values. At lower particle Reynolds numbers and centrally located sphere, the enhancement in drag coefficient due to blockage ratio was felt least by the fluid with the lowest n value. Even at higher Re p , higher blockage ratios still could cause significant enhancements in the drag coefficients (∼20%) for centrally located spheres. Irrespective of the power-law index, eccentric location of the sphere caused a decline in the overall drag coefficient due to the dominant influence of the lower hemisphere which was closer to the tube wall. At the highest particle Reynolds numbers, eccentricity, and blockage ratio, asymmetric fluid flow distribution caused opposing effects by decreasing the viscous drag coefficient and increasing the form drag coefficient relative to those obtained with the centrally confined sphere. Sharp variations in the shear rate dependent viscosity at the sphere surface could be associated with boundary layer separation. Wall effects at higher blockage ratio suppressed the boundary layer separation in the case of the fluid with the highest power-law index. Eccentricity also caused accelerated boundary layer separation at the upper hemisphere and absence of boundary layer separation along the lower hemisphere. At lower blockage ratios a maximum in the lift coefficient versus particle Reynolds number was usually observed. This study will be relevant in applications such as aseptic food processing, petroleum well drilling, fluidization, and particle transport in microfluidic devices.

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“…p K a has been documented essential for many applications and research areas, namely food science, pharmacology, toxicology, pathology, environment, and therapy . p K a also effects on the base‐pairing behavior , plays a critical role in various protein functions , and therefore is of wide interest in biochemical and metabolomics. Moreover, systematical p K a evaluation of the acidic property enables establishing appropriate characterization for the nature organic matter in complex samples .…”

Section: Introductionmentioning

confidence: 99%

Capillary electrokinetic fractionation mass spectrometry (CEkF/MS): Technology setup and application to metabolite fractionation from complex samples coupled at‐line with ultrahigh‐resolution mass spectrometry

Harir

Gougeon

et al. 2014

Electrophoresis

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Capillary electrokinetic fractionation (CEkF) is investigated as a new, simple, and robust approach for semipreparative and analytical sample analysis based on pKa -dependant pH-driven electrophoretic mobility. CEkF was optimized with contactless conductivity detection and conducted with 10 kV reverse voltage for 10 min, then coupled on/at-line to ESI/MS. We propose a semi-empirical model with 14 representative compounds based on the correlation between sample/medium pH regulating the partial charge, the electrokinetic loading of the capillary and intensity (I) of analytes. According to the model, an empirical function (I = f (pH)) could be derived to calculate the acid dissociation constant (pKa ) of various model compounds based on their pH-dependant MS intensity profiles with the RSD < 4.05. Using the ultrahigh-resolution of ion cyclotron resonance Fourier transform MS, the pKa model was further illustrated in real samples into the structure prediction of important compounds in wine over two vintages. The established CEkF was successfully used to selectively fractionate sulfur compounds from the complex wine samples at pH 1.66. The proposed CEkF approach should allow in the future the simultaneous pKa evaluation of multiple constituents without complicated separation out of a complex mixture in metabolomics or environmental chemistry.

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A Drag Correlation for Single Spheres in Pseudoplastic Tube Flow

Cited by 8 publications

References 0 publications

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

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

Effects of Particle Blockage and Eccentricity in Location on the Non-Newtonian Fluid Hydrodynamics around a Sphere

Capillary electrokinetic fractionation mass spectrometry (CEkF/MS): Technology setup and application to metabolite fractionation from complex samples coupled at‐line with ultrahigh‐resolution mass spectrometry

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