Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-20T13:32:06.456Z Has data issue: false hasContentIssue false
  • English
  • Français

Slow viscous flow past a sphere in a cylindrical tube

Published online by Cambridge University Press:  28 March 2006

Howard Brenner  and
John Happel
Howard Brenner
Affiliation:
Department of Chemical Engineering, New York University
John Happel
Affiliation:
Department of Chemical Engineering, New York University
Get access Rights & Permissions [Opens in a new window]

Abstract

A theoretical treatment is presented for the slow flow of a viscous fluid through a cylindrical container within which a small spherical particle is confined. The sphere is situated in an arbitrary position within the cylinder and moves at constant velocity parallel to the walls. Approximate expressions are derived which give the frictional drag, rotational couple, and permanent pressure drop caused by the presence of this obstacle in the original Poiseuillian field of flow. The primary parameters involved are the ratio of sphere to cylinder radius and fractional distance of the particle from the longitudinal axis of the cylinder. With appropriate modifications, the results are also applicable to a sphere settling in a quiescent fluid. This yields the necessary boundary corrections to Stokes law arising in connection with devices such as the falling ball viscometer when the sphere is eccentrically located.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 4 , Issue 2 , June 1958 , pp. 195 - 213
Copyright
© Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Faxen, H. 1923 Ark. f. Mat. Astr. og Fys. 17, no. 27.
Faxen, H. 1927 Ark. f. Mat. Astr. og Fys. 20, no. 8.
Haberman, H. 1956 Wall effect for rigid and fluid spheres in slow motion, David Taylor Model Basin Report; also Proc. 9th Intern. Cong. Appl. Mech. (Brussels).Google Scholar
Haberman, H. 1957 Wall effect for rigid and fluid spheres in slow motion within a moving liquid, David Taylor Model Basin Report.Google Scholar
Happel, J. & Byrne, B. J. 1954 Industr. Engng. Chem. 46, 1181 (with corrigenda, Ibid. 1957, 49, 1029).
Happel, J. & Brenner, H. 1957 J. Amer. Inst. Chem. Engrs 3, 506.
Lamb, H. 1932 Hydrodynamics, 6th Ed. Cambridge University Press.
Lorentz, H. A. 1907 Abhandlungen über Theoretische Physik, p. 23. Leipzig.
Oseen, C. W. 1928 Neure Methoden und Engebrisse in der Hydrodynamik. Leipzig.
Peres, J. 1929 C. R. Acad. Sci., Paris 188, 310.
Simha, R. 1936 Kolloidzschr. 76, 16.
Wakiya, S. 1953 J. Phys. Soc. Japan 8, 254.
Watson, G. N. 1922 A Treatise on the Theory of Bessel Functions. Cambridge University Press.