Slow Motion of a Non-Newtonian Liquid Past a Sphere

Rathna, S. L.

doi:10.1093/qjmam/15.4.427

Cited by 17 publications

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“…15,21 The flow patterns, hold-up, and pressure drop were also studied for cocurrent upward and downward flow of air−water in coiled tubes. 22 The flow patterns in coiled tubes were observed similar to the flow patterns in inclined tubes reported by Spedding et al 23 integral momentum boundary layer approach 10−100 0.5−1.0 >100 applicable for both laminar and turbulent flow Rathna et al 16 analytical method solution is obtained up to first order term boundary layer approach 20−100 0.5−1.5 1−20 Reported that flow rate is independent of curvature ratio. Takami et al 17 numerical time marching method 10−100 0.5−1.5 1−1000 Relations f c and N De can be expressed with a single curve dependent on n. Nigam et al 18 Analytical perturbation method solution is found up to second order term 10−100 0.5−1.5 1−30 Flow rate is found as a function of curvature ratio, Reynolds number, and power-law index.…”

Section: Literature Reviewsupporting

confidence: 67%

“…Rathna et al 16 analytical method solution is obtained up to first order term boundary layer approach 20−100 0.5−1.5 1−20 Reported that flow rate is independent of curvature ratio. Takami et al 17 numerical time marching method 10−100 0.5−1.5 1−1000 Relations f c and N De can be expressed with a single curve dependent on n. Nigam et al 18 Analytical perturbation method solution is found up to second order term 10−100 0.5−1.5 1−30 Flow rate is found as a function of curvature ratio, Reynolds number, and power-law index.…”

Section: Literature Reviewmentioning

confidence: 99%

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Flow Characteristics of Power-Law Fluids in Coiled Flow Inverter

Singh¹,

Verma²,

Nigam³

2013

Ind. Eng. Chem. Res.

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A novel device coiled flow inverter (CFI) has shown great potential as a heat exchanger and inline mixer. 1−3 The device offers negligible thermal and concentration gradient in the radial direction. CFI may find potential applications in food industry for different processes such as pasteurization and sterilization, due to its ideal characteristic. Therefore, in the present study, the hydrodynamic of single and two-phase non-Newtonian fluid flow in CFI have been investigated experimentally and numerically. The experiments have been performed in three different CFI geometries. The aqueous solution of carboxymethyl cellulose (CMC) of three different concentrations has been used as a working fluid. The single-phase Reynolds number ranged from 100 to 10000, while the two-phase liquid and gas Reynolds numbers ranged from 100 to 10000 and 100 to 8500, respectively. The various flow patterns for two-phase non-Newtonian fluid flow in CFI have been observed during experimental investigation. The effects of the gas and liquid flow rates, curvature ratio and concentration of non-Newtonian fluid on frictional pressure drop have been investigated. The correlation for the friction factor in CFI has been developed for single and two-phase air non-Newtonian fluid flow under laminar condition. The development of velocity fields has been demonstrated for single and two-phase non-Newtonian fluid flow in CFI. The contours of the volume fraction are plotted at different axial length and after each 90°bend. The contour plots bring about an understanding of flow inversion and flow distribution of pseudoplastic fluids after each 90°bend in CFI.

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Section: Literature Reviewsupporting

confidence: 67%

Section: Literature Reviewmentioning

confidence: 99%

Flow Characteristics of Power-Law Fluids in Coiled Flow Inverter

Singh¹,

Verma²,

Nigam³

2013

Ind. Eng. Chem. Res.

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“…The lowerscript in (11) symbolize the 0 th , 1 st , 2 nd order approximations of the related quantities, and retaining the terms in the power series expansion of S up to 2 nd order only. Therefore, the stream functions ψ 0 , ψ 1 and ψ 2 satisfy, respectively, the following differential equations [25,33]: The differential equations depicted by Eq. (12) yield the following solutions for stream function corresponding 0 th , 1 st and 2 nd order of approximations as and Stokes operator E 2 has the following form…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…4. When λ = 0, ε = 0, Rathna's formula [33] in corrected form for Reiner-Rivlin liquid past a rigid sphere F z = −6bπμ e U 1 − 0.005 7 S 2 .…”

Section: Application To An Oblate Spheroidmentioning

confidence: 99%

“…Sharma [38] contemplated the slow viscous movement of a non-Newtonian 2 nd order fluid over a body of spherical in shape. Rathna [33] examined the creeping flow of Reiner-Rivlin liquid streaming over a rigid spherical body, and acquired a solution by utilizing the approximation given by Stokes. Later, the similar kind of technique utilized and implemented by Ramkissoon [25] to consider the fundamentally the same problem for a fluid sphere, and deduced that sphere encounters very much drag as compared Newtonian case.…”

Section: Introductionmentioning

confidence: 99%

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Steady Stokes flow of a non-Newtonian Reiner-Rivlin fluid streaming over an approximate liquid spheroid

Jaiswal

2020

ACM

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The investigation is carried out to study steady Stokes axisymmetrical Reiner-Rivlin streaming flow over a fixed viscous droplet, and this droplet to be deformed sphere in shape. As boundary conditions, vanishing of radial velocities, continuity of tangential velocities and shear stresses at the droplet surface are used. The very common configuration of approximate sphere governed by polar equation $\tilde{r} =a[1 +\alpha_m \vartheta_m(\zeta)]$ has been considered for the study to $o(\varepsilon)$ describing the distortion. Based on the Stokes approximation, an analytical investigation is achieved in the orthogonal curve linear framework in an unbounded region of a Reiner-Rivlin fluid. In constraining cases, some earlier noted outcomes are obtained. Also, the yielded outcomes for the drag have been compared with solution existing in the literature. Further, the change for both force and pressure are evaluated with deflection w.r.t. the parameters of interest and shown through table and graphs.

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An experimental investigation of the flow of aqueous non‐Newtonian high polymer solutions past a sphere

Turian

1967

AIChE Journal

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The terminal velocities of spheres falling in aqueous solutions of hydraxyethyl cellulose and polyethylene oxide were determined with ruby and steel spheres. For each sphere the terminal velocity was obtained in seven cylinder sizes covering a range of sphere-to-cylinder diameter ratio from 0.0067 to 0.18. The data were used in an extrapolation to correct for the cylindrical wall effect. Several alternative extrapolation procedures for estimating the zero shear viscosity were attempted and the results were compared. An empirical correlation for the drag coefficient was developed in terms of the Ellis parameters of the fluids, and the Faxen wall correction for Newtonian flow. The correlation gives the drag coefficient within 4% for all cases in which the quantity qovt/Dtl/a is less thon 0.3. N E W T O N I A N F L O W PAST A SPHEREThe drag force exerted on a sphere of radius R resulting from the flow past it of an unbounded incompressible Newtonian fluid of viscosity To and approach velocity v, is given by Stokes' law ( 1 2 ) :Equation (1) Oseen's approximation is represented by taking the terms up to and including N R e in Equation (2), whereas Goldstein's solution, purportedly an extension of Oseen's approximation, does not include the logarithmic term. These solutions are classified as the low Reynolds number flow approximations to the Navier-Stokes equations, and they possess certain interesting features, some of which have been discussed by Chester ( 4 ) (with regard to the Oseen approximation) and also by Proudman and Pearson (1 7). to (D/D,) = 0.32. Ladenburg (11) has also presented a correction for the effect of the bottom of the cylinder. This correction, based on the solution for a sphere falling in an infinite fluid bounded at the bottom by an infinite flat plate, appears to overestimate the bottom correction. More recently, Tanner (24) carried out a numerical calculation in which the effects of both the cylindrical wall and the bottom of the container were taken into account. He found that the top and bottom corrections are negligible, provided the sphere is at least one cylinder radius away from either end. These conclusions are corroborated by experimental evidence and, consequently, the need for a top and bottom correction can be eliminated by appropriate design of the falling-sphere system.Many other studies on the flow of Newtonian fluids past a sphere have been reported. These have been reviewed (8, 13) and will not be discussed inasmuch as the results are not employed in the present study. N O N -N E W T O N t A N F L O W PAST A SPHEREReported studies on non-Newtonian flow past a sphere include solutions based on perturbation procedures, solutions based on variational schemes, and empirical correlations and associated experimental studies. Solutions Bored o n Perturbation ProceduresA perturbation approximation for the flow of a ReinerRivlin-Prager fluid ast a sphere was obtained by Rathna ity are constant. The rheological model subject to these restrictions is inadequate in describing non-Newton...

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Slow Motion of a Non-Newtonian Liquid Past a Sphere

Cited by 17 publications

References 0 publications

Flow Characteristics of Power-Law Fluids in Coiled Flow Inverter

Flow Characteristics of Power-Law Fluids in Coiled Flow Inverter

Steady Stokes flow of a non-Newtonian Reiner-Rivlin fluid streaming over an approximate liquid spheroid

An experimental investigation of the flow of aqueous non‐Newtonian high polymer solutions past a sphere

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