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The dispersion of a buoyant solute in laminar flow in a straight horizontal pipe. Part 2. The approach to the asymptotic state

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.
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Abstract

Chatwin (1970) has described the approach to normality of a cloud of solute which is injected into a pipe containing solvent in steady laminar flow. This paper is concerned with the modification of Chatwin's theory when there is a small density difference between the solvent and the dissolved solute. Asymptotic series are derived for the induced density currents and for the distribution of solute in the case when the molecular diffusivity is constant throughout the pipe's cross-section. These series lead to the asymptotic forms of the moments of the distribution, thereby describing some additional deviations from normality caused by buoyancy effects at large times. The theory predicts that the additional dispersion due to buoyancy effects is proportional to the square of the Rayleigh number and depends on the Péclet number of the flow. There is excellent agreement between the results and those previously obtained by the author (1976) from Erdogan & Chatwin's (1967) model of dispersing buoyant solutes. The results confirm that Erdogan & Chatwin's intuitive theory correctly models the significant features of the situation for large Schmidt numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 74 , Issue 1 , 9 March 1976 , pp. 91 - 112
Copyright
© 1976 Cambridge University Press

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References

Aris, R. 1956 Proc. Roy. Soc. A, 235, 67.
Barton, N. G. 1976 J. Fluid Mech. 74, 81.
Chatwin, P. C. 1970 J. Fluid Mech. 43, 321.
Erdogan, M. E. & Chatwin, P. C. 1967 J. Fluid Mech. 29, 465.
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.