The Stokes Flow from Half-Space to Semi-Infinite Circular Cylinder

Wu Wang-yi; Richard Skalak

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Wu Wang-yi, Richard Skalak. The Stokes Flow from Half-Space to Semi-Infinite Circular Cylinder[J]. Applied Mathematics and Mechanics, 1985, 6(1): 9-23.

Citation:

Wu Wang-yi, Richard Skalak. The Stokes Flow from Half-Space to Semi-Infinite Circular Cylinder[J]. Applied Mathematics and Mechanics, 1985, 6(1): 9-23.

Citation:

Wu Wang-yi, Richard Skalak. The Stokes Flow from Half-Space to Semi-Infinite Circular Cylinder[J]. Applied Mathematics and Mechanics, 1985, 6(1): 9-23.

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The Stokes Flow from Half-Space to Semi-Infinite Circular Cylinder

Wu Wang-yi¹,
Richard Skalak²

1.
Department of Mechanics, Peking University;
2.
Department of Civil Engineering and Engineering Mechanics, Columbia University

Received Date: 1984-01-06
Publish Date: 1985-01-15

Abstract

Abstract

The infinite-series solutions for the creeping motion of a viscous imcomperssible fluid from half-space to semi-infinite circular cylinder are presented. The results show that inside the cylinder beyond a distance equal to 0.5 times the radius of tube from the pore opening, the deviation of the velocity profile from the Poiseuille one becomes equal to or less than 1%.The inlet length in this case is considerably shorter than Dagan's finite circular cylinder one. In the half-space outside the cylinder pore the region, strongly affected by the tube wzll, is restricted within a narrow limit no more than one radius of the tube from the orifice. Beyond this region the solutions match almost exactly the Sampson's one for a flow through an orifice of Zero thickness, The relationship between the pressure drop and the volumetric flow rate is also considered in this paper.

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References(7)

References

[1]	Dagan,Z.,S.Weinbaum and R.Pfeffer.An infinite-series solution for the creeping motion through an orifice of finite length.J.Fluid Mech.,115(1982).502-523.
[2]	吴望一,R. Skalak,应用数学和力学,4, 6(1983), 743-756.
[3]	Parmet,I.L.and E.Saibel,Axisymmetric creeping flow an orifice in a plane wall.Comm.Pure Appl.Math.18(1965),17.
[4]	Sampson, R.A Phil, Trans, Roy.Soc, Lond.,A182(1891), 449
[5]	Erdelyi.A.,W.Magnus,F.Oberhettingen and F.G.Tricomi.Tables of Integral Transforms.Vol.11.McGraw-Hill.New York(1954).
[6]	Oberhettinger.F.,Table of Bessel Transforms,Springer Verlag.New York(1972).
[7]	Watson.G.M.,A Treatise on the Theory of Bessel Functions.2nd edition.Cambridge University Press.Cambridge,U.K.(1958).