On Stokes flow about a torus

Pell, William H.; Payne, L. E.

doi:10.1112/s0025579300001601

Cited by 53 publications

(47 citation statements)

References 7 publications

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“…Theory can predict shape factors for spheroids and needles (Gans, 1911;Pell and Payne, 1960a), lenses and hemispheres (Payne and Pell, 1960). hollow spherical caps (Collins, 1963;Dorrepaal et al, 1978), and toroids (Pell and Payne, 1960b), and some combination of these shapes (Bowen and Masliyah, 1973); however, most particles in nature do not have these simple shapes.…”

Section: Introductionmentioning

confidence: 99%

Drag on Nonspherical Objects

Leith¹

1987

Aerosol Science and Technology

187

131

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Stokes's law describes drag force on a sphere in creeping flow. This law can be extended to a nonspherical object by allocating the interaction of the fluid with the object into its interaction with two analogous spheres, one with the same projected area and one with the same surface area as the object. This approach was used to characterize dynamic shape factor for objects whose shape factors are reported in the literature. Agreement between data and the equation for shape factor based on this approach was excellent for prisms: RZ = 0.998. This equation and empirical equations from the literature were used to predict shape factor for a sphere, cylinders, prisms, spheroids, and double conicals whose shape factors have been reported. The equation based on the Stokes's law extension predicted shape factors better than the empirical equations, as judged by a least-squares index of performance.

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Section: Introductionmentioning

confidence: 99%

Drag on Nonspherical Objects

Leith¹

1987

Aerosol Science and Technology

187

131

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“…When the boundary profile consists of a closed curve C in the upper half of the plane, W -% on C and W should be expressed [7] in the form…”

Section: Smentioning

confidence: 99%

“…Again the analysis can be switched to Pell and Payne's [7] by noting that P B _j(0 satisfies the equation When j> and $ have been determined, W is given by (27) which corresponds to Pell and Payne's (3.34) (in which there is a misplaced brace).…”

Section: Stokes Flow Past a Torusmentioning

confidence: 99%

“…The method will be illustrated in some problems in the Stokes flow of a viscous fluid which are analogous to the problems in in viscid flow mentioned above; in these problems the stream function xp satisfies the equation L'ij,(y)) = 0. Payne and Pell [5,6,7] have discussed these Stokes flow problems and have carried out the difficult analysis required to produce the solutions. As would be expected, essentially the same detailed calculations are required however the problems are approached but the new procedure proposed here sets these calculations in a unified context and provides a natural approach to them.…”

Section: Introductionmentioning

confidence: 99%

“…The result of this is to change the parameter X which occurs in the solution for <j> to n = A-p -1 = -^p+l-n. The rest of the procedure remains the same and when <j> and $> have both been obtained, (14) gives The method is illustrated by showing how to find the stream function for axially symmetric Stokes flow of a viscous fluid in two cases previously considered by Pell and Payne [6,7] who have solved the problems in detail. The account given here will be limited to demonstrating the systematic approach provided by the present method, the analysis being carried only far enough to link it to the original authors' presentation.…”

Section: If a New Variable G = Y H L 2 F Is Introduced (19) Shows Thmentioning

confidence: 99%

See 2 more Smart Citations

The iterated equation of generalized axially symmetric potential theory. V. Generalized weinstein correspondence principle

Burns

1970

J. Aust. Math. Soc.

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The translational friction of toroids

Allison¹,

Easterly²,

Teller³

1980

Biopolymers

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SynopsisAn approximate analytic expression for the translational friction coefficient of a toroid modeled a s a continuous shell of frictional elements is derived using the Kirkwood approximation. The accuracy of this expression was determined by comparing the friction coefficients predicted by it to those predicted,by extrapolated shell-model calculations using the modified Oseen tensor. T o show that these calculatiops do indeed yield the correct friction coefficients, actual translational friction coefficients were determined by observing settling rates of macroscopic model rings or toroids in a high-viscosity silicone fluid. Our conclusion is that the approximate expression yields friction coefficients that are about 1.5-3%) low for finite rings. For thin rings, a comparison is also made with the exact result of Yamakawa and Yamaki [J. Chem. Phys. 57,1572Phys. 57, (1972 58,2049(1973l for the translational friction of plane polygonal rings. This comparison shows that the approximate expression yields results which are low by 2-3% unless t h e rings are extremely thin, in which case the error is larger. I n the limit of a n infinitely thin ring the approximate expression reduces to the Kirkwood result [ J . Polym. Sci. 12, 1 (1954)], which is low by 8.3%. We discuss hriefly how this work may he useful in determining the structure of DNA compacted by various solvent-electrolyte systems and polyamines.

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On Stokes flow about a torus

Cited by 53 publications

References 7 publications

Drag on Nonspherical Objects

Drag on Nonspherical Objects

The iterated equation of generalized axially symmetric potential theory. V. Generalized weinstein correspondence principle

The translational friction of toroids

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