Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-18T18:48:17.236Z Has data issue: false hasContentIssue false
  • English
  • Français

Viscous flow in a cylindrical tube containing a line of spherical particles

Published online by Cambridge University Press:  29 March 2006

Henry Wang  and
Richard Skalak
Henry Wang
Affiliation:
Department of Civil Engineering and Engineering Mechanics, Columbia University, New York
Richard Skalak
Affiliation:
Department of Civil Engineering and Engineering Mechanics, Columbia University, New York
Get access Rights & Permissions [Opens in a new window]

Abstract

The viscous, creeping flow through a cylindrical tube of a liquid, which contains rigid, spherical particles, is investigated analytically. The spheres are located on the axis of the cylinder and are equally spaced. Solutions are derived for particles in motion and fixed, with and without fluid discharge. Numerical results are presented for the drag on each sphere and the mean pressure drop for a wide range of sizes and spacings of the spheres. The study is motivated by possible application to blood flow in capillaries, where red blood cells represent particles of the same order of magnitude as the diameter of the capillary itself. The results may also be of interest in other applications, such as sedimentation and fluidized beds. It is shown that there is little interaction between particles if the spacing is more than one tube diameter, and that the additional pressure drop over that for Poiseuille flow is less than 50% if the sphere diameter is less than 0·8 of the tube diameter.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 1 , 14 August 1969 , pp. 75 - 96
Copyright
© 1969 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

Atsumi, A. 1960 J. Appl. Mech. 82E, 87–92.
Brandt, A. & Bugliarello, G. 1965 Annual Conf. on Engineering in Med. and Biol. 7, 159.
Gregersen, M. I. 1967 Colloque International organisé pour la circulation, Paris. Masson et Cie, pp. 231–244.
Haberman, W. L. & Sayre, R. M. 1958 David Taylor Model Basin Report 1143. Washington, D.C.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. New Jersey: Prentice-Hall.
Happel, J. & Byrne, B. J. 1954 Ind. Engng Chem. 46, 1181–1186.
Haynes, R. H. 1961 Trans. Soc. Rheol. 5, 85–101.
Hobson, E. W. 1955 The Theory of Spherical and Ellipsoidal Harmonics. New York: Chelsea.
Lighthill, M. J. 1968 J. Fluid Mech. 34, 113.
Ling, C. B. 1963 The Collected Papers of C. B. Ling. Taipei: Academia Sinica.
Macrobert, T. M. 1948 Spherical Harmonics. New York: Dover.
Sonshine, R. M. & Brenner, H. 1966 Appl. Sci. Res. 16, 425–454.
Wang, H. 1967 Ph.D. Thesis, Columbia University.
Wang, H. & Skalak, R. 1967 Tech. Rept. 1, Project NR 062–393. New York: Colombia University.
Watson, G. N. 1944 Theory of Bessel Functions. Cambridge University Press.
Whitmore, R. L. 1967 Proc. Int. Conf. on Hemorheology (Copley, ed.). Oxford: Pergamon.