DOI: 10.1017/s0022112067002551. On the slow motion of a sphere parallel to a nearby plane wall

On the slow motion of a sphere parallel to a nearby plane wall

10.1017/s0022112067002551

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

Abstract

A new method using a matched asymptotic expansions technique is presented for obtaining the Stokes flow solution for a rigid sphere of radius a moving uniformly in a direction parallel to a fixed infinite plane wall when the minimum clearance ea between the sphere and the plane is very much less than a. An ‘inner’ solution is constructed valid for the region in the neighbourhood of the nearest points of the sphere and the plane where the velocity gradients and pressure are large; in this region the leading term of the asymptotic expansion of the solution satisfies the equations of lubrication theory. A matching ‘outer’ solution is constructed which is valid in the remainder of the fluid where velocity gradients are moderate but it is possible to assume that ε = 0. The forces and couples acting on the sphere and the plane are shown to be of the form (α0+α1ε) log ε + β0 + O(ε) where α0, α1 and β0 are constants which have been determined explicitly.

Bibliography

OâNeill, M. E., & Stewartson, K. (1967). On the slow motion of a sphere parallel to a nearby plane wall. Journal of Fluid Mechanics, 27(4), 705â724.

Authors 2

M. E. O'Neill (first)
K. Stewartson (additional)

References 14 Referenced 196

O'NEILL, M. E. 1964a Mathematika,11,67.
Kynch, G. J. 1959 J. Fluid Mech. 5,193. (10.1017/S0022112059000155)
Faxén, H. Z. 1927 Angew. Math. Mech. 7,79. (10.1002/zamm.19270070110)
Stimson, M. & Jeffrey, G. B. 1926 Proc. Roy. Soc. A,111,110. (10.1098/rspa.1926.0053)
Smoluchowski, M. 1911 Bull. Inter. acad. Polonaise Sci. lett. 1A,28.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics .New York:Prentice-Hall.
Thompson, B. W. 1964 M.Sc. Thesis,Melbourne.
Gross, W. A. 1962 Gas Film Lubrication .New York:Wiley.
Langlois, W. E. 1964 Slow Viscous Flow .New York:Macmillan.
Burgers, J. M. 1941 Proc. Koningl. Akad. Wetenschap (Amsterdam) 44,1054.
O'NEILL, M. E. 1964b University of London Ph.D. Thesis.
Pinkus, O. & Sternlicht, B. 1961 Lubrication Theory .New York:McGraw-Hill.
Dean, W. R. & O'NEILL, M. E. 1963 Mathematika,10,13.
Majumdar, S. R. 1965 University of London Ph.D. Thesis.

Dates

Type	When
Created	19 years, 5 months ago (March 28, 2006, 7:56 a.m.)
Deposited	6 years, 4 months ago (April 1, 2019, 3:35 p.m.)
Indexed	3 weeks, 3 days ago (Aug. 6, 2025, 9:24 a.m.)
Issued	58 years, 5 months ago (March 20, 1967)
Published	58 years, 5 months ago (March 20, 1967)
Published Online	19 years, 5 months ago (March 28, 2006)
Published Print	58 years, 5 months ago (March 20, 1967)

Funders 0

None

BibTeX

@article{O_Neill_1967, title={On the slow motion of a sphere parallel to a nearby plane wall}, volume={27}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112067002551}, DOI={10.1017/s0022112067002551}, number={4}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={O’Neill, M. E. and Stewartson, K.}, year={1967}, month=mar, pages={705–724} }

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