Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-20T05:54:23.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of finite boundaries on the Stokes resistance of an arbitrary particle

Published online by Cambridge University Press:  28 March 2006

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

Abstract

A general theory is put forward for the effect of wall proximity on the Stokes resistance of an arbitrary particle. The theory is developed completely for the case where the motion of the particle is parallel to a principal axis of resistance. In this case, the wall-effect correction can be calculated entirely from a knowledge of the force experienced by the particle in an unbounded fluid, providing (i) that the wall correction is already known for a spherical particle and (ii) that the particle is small in comparison to its distance from the boundary. Experimental data are cited which confirm the theory. The theory is extended to the wall effect on a particle rotating near a boundary.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 12 , Issue 1 , January 1962 , pp. 35 - 48
Copyright
© 1962 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

Birkhoff, G. 1950 Hydrodynamics, p. 38. Princeton University Press.
Brenner, H. & Happel, J. 1958 J. Fluid Mech. 4, 195.
Chang, I. D. 1961 ZAMP, 12, 6.
Cunningham, E. 1910 Proc. Roy. Soc. A, 83, 357.
Famularo, J. 1960 D.Eng. Sci. Thesis, New York University (unpublished).
Haberman, W. L. & Sayre, R. M. 1958 Motion of rigid and fluid spheres in stationary and moving liquids inside cylindrical tubes. David Taylor Model Basin Report no. 1143.Google Scholar
Hall, E. W. 1956 Ph.D. Thesis, Birmingham.
Happel, J. & Pfeffer, R. 1960 J. Amer. Inst. Chem. Engrs, 6, 129.
Heiss, J. F. & Coull, J. 1952 Chem. Engng Progr. 48, 133.
Jeffery, G. B. 1915 Proc. Lond. Math. Soc. (2), 14, 327.
Kynch, G. J. 1959 J. Fluid Mech. 5, 193.
Lamb, H. 1932 Hydrodynamics, 6th ed. Cambridge University Press.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, p. 67. Reading, Mass.: Addison Wesley Publ. Co.
Love, A. E. H. 1927 A Treatise on the Mathematical Theory of Elasticity, 4th ed. Cambridge University Press.
Oseen, C. W. 1927 Neuere Methoden und Ergebnisse in der Hydrodynamik. Leipzig: Akademische Verlagsgesellschaft.
Péres, J. 1929 C.R. Acad Sci., Paris, 188, 310.
Pettyjohn, E. S. & Christiansen, E. B. 1948 Chem. Engng Progr. 44, 157.
Pfeffer, R. 1958 The motion of two spheres following each other in a viscous fluid. M.Ch.E. Thesis, New York University.
Squires, L. & Squires, W. 1937 Trans. Amer. Inst. Chem. Engrs, 33, 1.
Stimson, M. & Jeffery, G. B. 1926 Proc. Roy. Soc. A, 111, 110.
Villat, H. 1943 Leçons sur les Fluides Visqueux, p. 120. Paris: Gauthier-Villars.
Wakiya, S. 1957 J. Phys. Soc. Japan, 12, 1130 (with corrigenda, Ibid. p. 1318).
Wakiya, S. 1959 Effect of a submerged object on a slow viscous flow-spheroid at an arbitrary angle of attack. Research Report no. 8, College of Engineering, Niigata Univ. (in Japanese).Google Scholar