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Lo, Lilian L.

The meniscus on a needle - A lesson in matching. (English) Zbl 0554.76038

J. Fluid Mech. 132, 65-78 (1983).
The height of the meniscus on a slender vertical cylinder, which had been calculated by D. F. James [J. Fluid Mech. 63, 657-664 (1974; Zbl 0287.76005)] using the method of matched asymptotic expansions, is reconsidered. The erroneous result in James’ work has been pointed out and corrected by Fraenkel’s restricted form of the matching principle. Besides, a less restricted matching principle is also suggested, and show that the last known term of order \(Re^ 3\ln (Re)\) in the drag on a sphere in low-Reynolds-number flow is correct, even though it was found in a way that violates Fraenkel’s warning.
Reviewer: F.Jiang

Cited in 11 Documents

MSC:

76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects

Keywords:

meniscus on a slender vertical cylinder; matching principle; drag on a sphere in low-Reynolds-number flow

Citations:

Zbl 0287.76005
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Full Text: DOI

References:

[1] DOI: 10.1016/0021-9797(69)90399-3 · doi:10.1016/0021-9797(69)90399-3
[2] Fraenkel, Proc. Camb. Phil. Soc. 65 pp 209– (1969)
[3] Crighton, Proc. R. Soc. Lond. A335 pp 313– (1973) · Zbl 0314.76062 · doi:10.1098/rspa.1973.0128
[4] DOI: 10.1017/S0022112069000851 · Zbl 0175.52003 · doi:10.1017/S0022112069000851
[5] DOI: 10.1017/S0022112057000105 · Zbl 0077.39103 · doi:10.1017/S0022112057000105
[6] Stokes, Camb. Phil. Trans. 9 pp 8– (1851)
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[8] DOI: 10.1137/1014002 · Zbl 0311.34068 · doi:10.1137/1014002
[9] Kaplun, J. Math. Mech. 6 pp 585– (1957)
[10] DOI: 10.1017/S0022112074002126 · Zbl 0287.76005 · doi:10.1017/S0022112074002126
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