Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T12:34:02.686Z Has data issue: false hasContentIssue false
  • English
  • Français

The dispersion of a buoyant solute in laminar flow in a straight horizontal pipe. Part 1. Predictions from Erdogan & Chatwin's (1967) paper

Published online by Cambridge University Press:  29 March 2006

N. G. Barton
N. G. Barton
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Australia 4067 Present address: University of New South Wales, P.O. Box 1, Kensington, Australia 2033.
Get access Rights & Permissions [Opens in a new window]

Abstract

This work is concerned with the dispersion of a buoyant solute in a straight horizontal pipe of circular cross-section where dispersion is affected by molecular diffusion, the laminar flow along the pipe and density currents. Erdogan & Chatwin (1967) have derived an equation for the mean concentration $\overline{C}$ of a buoyant solute using a relatively simple asymptotic model, and have predicted that the dispersion induced by buoyancy effects depends on the Péclet number of the flow. In this part of this study an approximate expression is derived for $\overline{C}$ from Erdogan & Chatwin's equation, and an asymptotic form is obtained for the second moment of distributions of buoyant solutes. The examination of the second moment leads to a simple, but important, result: the dispersion induced by density currents at large times is small compared with the dispersion induced by density currents at times when transient effects are significant.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 74 , Issue 1 , 9 March 1976 , pp. 81 - 89
Copyright
© 1976 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

Ananthakrishnan, V., Gill, W. N. & Barduhn, A. J. 1965 A.I.Ch.E. J. 11, 1063.
Aris, R. 1956 Proc. Roy. Soc. A, 235, 67.
Barton, N. G. 1976 J. Fluid Mech. 74, 91.
Bournia, A., Coull, J. & Houghton, G. 1961 Proc. Roy. Soc. A, 261, 227.
Chatwin, P. C. 1970 J. Fluid Mech. 43, 321.
Erdogan, M. E. & Chatwin, P. C. 1967 J. Fluid Mech. 29, 465.
Green, A. E. & Naghdi, P. M. 1969 University of California, Berkeley, Appl. Mech. Rep. AM-69-4.
Reejhsinghani, N. S., Gill, W. N. & Barduhn, A. J. 1966 A.I.Ch.E. J. 12, 916.
Taylor, G. I. 1953 Proc. Roy. Soc. A, 219, 186.