Creeping flow past a sphere of a Reiner-Rivlin fluid

Foster, Robert D.; Slattery, John C.

doi:10.1007/bf03184973

Cited by 6 publications

(1 citation statement)

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“…Falling sphere data on the few such fluids encountered in the experimental study carried out by Turiiiri (27) indicate that the results for Nmvtonian flow are entirely adequate. Foster and Slattery (6) used a variational method to obtain the approximation to the drag force for the Reiner-Hivlin-Prager fluid with constant viscosity and cross visc~osity. This is the same model used by I b t h n a ( 1 8 ) in his perturbation scheme, and the solution is therefore subject to the same objections, namely, that the model is inadequate and objectionable on the basis of the second lnw of therinodynamics.…”

Section: Solutions Based On Voriotionol Proceduresmentioning

confidence: 99%

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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Section: Solutions Based On Voriotionol Proceduresmentioning

confidence: 99%