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On the method of moments for solute dispersion

Published online by Cambridge University Press:  20 April 2006

N. G. Barton
N. G. Barton
Affiliation:
CSIRO Division of Mathematics and Statistics, P.O. Box 218, Lindfield, N.S.W., Australia 2070
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Abstract

A cloud of solute injected into a pipe or channel is known to spread out by a dispersion process based on cross-sectional diffusion across a velocity shear. The original description of the process is due to Taylor (1953, 1954), and an important subsequent contribution was by Aris (1956), who framed and partially solved equations for the integral moments of the cloud of contaminant. The present work resolves some technical difficulties that occur when Aris’ solution method (separation of variables) is pursued in depth. In particular, it is shown that Aris’ technique has to be modified to give the moments at short and moderate times after the injection of solute into the flow. The paper is concerned with dispersion in those parallel flows for which an associated eigenvalue problem has a discrete spectrum of eigenvalues; fortunately, this case appears to be the rule rather than the exception. Expressions are obtained for the second and third moment about the mean, and the theory is applied to three cases of interest.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 126 , January 1983 , pp. 205 - 218
Copyright
© 1983 Cambridge University Press

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