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

Barton N.G. (1976) The dispersion of a buoyant solute in laminar flow in a straight horizontal pipe. Part 2. The approach to the asymptotic state. Journal of Fluid Mechanics, 74 1: 91-112. doi:10.1017/S0022112076001705


Author Barton N.G.
Title The dispersion of a buoyant solute in laminar flow in a straight horizontal pipe. Part 2. The approach to the asymptotic state
Journal name Journal of Fluid Mechanics   Check publisher's open access policy
ISSN 1469-7645
Publication date 1976-03-09
Sub-type Article (original research)
DOI 10.1017/S0022112076001705
Volume 74
Issue 1
Start page 91
End page 112
Total pages 22
Subject 2210 Mechanical Engineering
2211 Mechanics of Materials
3104 Condensed Matter Physics
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.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
 
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Created: Tue, 12 Jul 2016, 01:59:17 EST by System User