Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-11T04:40:37.122Z Has data issue: false hasContentIssue false
  • English
  • Français

The initial dispersion of soluble matter in three-dimensional flow

Published online by Cambridge University Press:  17 February 2009

N. G. Barton
N. G. Barton
Affiliation:
School of Mathematics, University of N.S.W., Kensington, N.S.W.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The dispersion of a passive solute in three-dimensional flow is examined for short times after the injection of solute. If the diffusivity is constant, the solute at first diffuses isotropically about the fluid particle originally coincident with the injection point whilst, at longer times, the effect of diffusion across a velocity shear becomes more important. An asymptotic expansion is derived for the concentration of solute at small times after its injection into the fluid flow and the use of the theory is illustrated for three representative flows. Some critical remarks on the applicability and limitations of the results conclude the note.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 3 , June 1978 , pp. 265 - 279
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Abramowitz, M. and Stegun, I. A.Handbook of mathematical functions (Dover, New York, 1965).Google Scholar
[2]Aris, R., ‘On the dispersion of a solute in a fluid flowing slowly through a tube’, Proc. Roy. Soc. A 235 (1956), 67–77.Google Scholar
[3]Barton, N. G., ‘The dispersion of a buoyant solute in laminar flow in a straight horizontal pipe. Part 1. Predictions from Erdogan & Chatwin's (1967) paper’, J. Fluid Mech. 74 (1976), 81–89.CrossRefGoogle Scholar
[4]Barton, N. G., ‘The dispersion of a buoyant solute in laminar flow in a straight horizontal pipe. Part 2. The approach to the asymptotic state’, J. Fluid Mech. 74 (1976), 91–112.CrossRefGoogle Scholar
[5]Chatwin, P. C., ‘The approach to normality of the concentration distribution of solute in solvent flowing along a straight pipe’, J. Fluid Mech. 43 (1970), 321–352.CrossRefGoogle Scholar
[6]Chatwin, P. C., ‘A calculation illustrating effects of the viscous sub-layer on longitudinal dispersion’, Q. J. Mech. Appl. Math. 26 (1973), 427–439.CrossRefGoogle Scholar
[7]Chatwin, P. C., ‘The initial dispersion of contaminant in Poiseuille flow and the smoothing of the snout’, J. Fluid Mech. 77 (1976), 593–602.CrossRefGoogle Scholar
[8]Chatwin, P. C., ‘The initial development of dispersion in straight tubes’, J. Fluid Mech. 80 (1977), 33–48.CrossRefGoogle Scholar
[9]Elder, J. W., ‘The dispersion of marked fluid in turbulent shear flow’, J. Fluid Mech. 5 (1959), 544–560.CrossRefGoogle Scholar
[10]Erdogan, M. E. and Chatwin, P. C., ‘The effects of curvature and buoyancy on the laminar dispersion of solute in a horizontal tube’, J. Fluid Mech. 29 (1967), 465–484.CrossRefGoogle Scholar
[11]Lighthill, M. J., ‘Initial development of diffusion in Poiseuille flow’, J. Inst. Maths Applics 2 (1965), 97–108.CrossRefGoogle Scholar
[12]Saffman, P. G., ‘On the effect of the molecular diffusivity in turbulent diffusion’, J. Fluid Mech. 8 (1960), 273–283.CrossRefGoogle Scholar
[13]Sullivan, P. J., ‘Longitudinal dispersion within a two-dimensional turbulent shear flow’, J. Fluid Mech. 49 (1971), 551–576.CrossRefGoogle Scholar
[14]Taylor, G. I., ‘Dispersion of soluble matter in solvent flowing slowly through a tube’, Proc. Roy. Soc. A 219 (1953), 186–203.Google Scholar
[15]Taylor, G. I., ‘The dispersion of matter in turbulent flow through a pipe’, Proc. Roy. Soc. A 223 (1954), 446–468.Google Scholar