Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T20:54:01.743Z Has data issue: false hasContentIssue false
  • English
  • Français

Stokes flow through periodic arrays of spheres

Published online by Cambridge University Press:  20 April 2006

A. A. Zick  and
G. M. Homsy
A. A. Zick
Affiliation:
Department of Chemical Engineering, Stanford University, California 94305
G. M. Homsy
Affiliation:
Department of Chemical Engineering, Stanford University, California 94305
Get access Rights & Permissions [Opens in a new window]

Abstract

We treat the problem of slow flow through a periodic array of spheres. Our interest is in the drag force exerted on the array, and hence the permeability of such arrays. It is shown to be convenient to formulate the problem as a set of two-dimensional integral equations for the unknown surface stress vector, thus lowering the dimension of the problem. This set is solved numerically to obtain the drag as a function of particle concentration and packing characteristics. Results are given over the full concentration range for simple cubic, body-centred cubic and face-centred cubic arrays and these agree well with previous limited experimental, asymptotic and numerical results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 115 , February 1982 , pp. 13 - 26
Copyright
© 1982 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

Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317.Google Scholar
Martin, J. J., McCabe, W. L. & Monard, C. C. 1951 Pressure drop through stacked spheres — effect of orientation. Chem. Engng Prog. 47, 91.Google Scholar
Rallison, J. M. & Acrivos, A. 1978 A numerical study of the deformation and burst of a viscous drop in an extensional flow. J. Fluid Mech. 89, 191.Google Scholar
Saffman, P. G. 1973 On the settling speed of free and fixed suspensions. Stud. Appl. Math. 52, 115.Google Scholar
Snyder, L. J. & Stewart, W. E. 1966 Velocity and pressure profiles for Newtonian creeping flow in regular packed beds of spheres. A.I.Ch.E. J. 12, 167.Google Scholar
Sorensen, J. P. & Stewart, W. E. 1974 Computation of forced convection in slow flow through ducts and packed beds. II. Velocity profile in a simple cubic array of spheres. Chem. Engng Sci. 29, 819.Google Scholar
Susskind, H. & Becker, W. 1967 Pressure drop in geometrically ordered packed beds of spheres. A.I.Ch.E. J. 13, 1155.Google Scholar
Youngren, G. K. & Acrivos, A. 1975 Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech. 69, 377.Google Scholar
Youngren, G. K. & Acrivos, A. 1976 On the shape of a gas bubble in a viscous extensional flow. J. Fluid Mech. 76, 433.Google Scholar