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Second-order recombination in a parallel shear flow

Published online by Cambridge University Press:  26 April 2006

Ronald Smith
Ronald Smith
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

For a reactive solute, with weak second-order recombination, an investigation is made of the near-source behaviour (where concentrations are high), and of the far field (where the recombination has an accumulative effect). Despite the loss of material and increased spread due to recombination, the far-field concentration distribution is shown to be nearly Gaussian. This permits a simplified (Gaussian) treatment of the chemical nonlinearity. Explicit solutions are given for the total amount of solute, variance and kurtosis for solutes with no first-order reactions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 200 , March 1989 , pp. 389 - 407
Copyright
© 1989 Cambridge University Press

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References

Barton, N. G.: 1984 An asymptotic theory for dispersion of reactive contaminants in parallel flow. J. Austral. Math. Soc. B 25, 287–310.Google Scholar
Barton, N. G.: 1986 Solute dispersion and weak second-order recombination at large times in parallel flow. J. Fluid Mech. 164, 289–303.Google Scholar
Chatwin, P. C.: 1970 The approach the normality of the concentration distribution of a solute in solvent flowing along a straight pipe. J. Fluid Mech. 43, 321–352.Google Scholar
Chatwin, P. C.: 1980 Presentation of longitudinal dispersion data. J. Hydraul. Div. ASCE 106, 71–83.Google Scholar
De Gance, A. E. & Johns, L. E. 1978 The theory of dispersion of chemically active solutes in a rectilinear flow field. Appl. Sci. Res. 34, 189–225.Google Scholar
Erdelyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G., 1954 Tables of Integral Transforms, vol. II. McGraw Hill.
Lungu, E. M. & Moffatt, H. K., 1982 The effect of wall conductance on heat diffusion in duct flow. J. Engng Maths 16, 121–136.Google Scholar
Sankarasubramanian, R. & Gill, W. N., 1973 Unsteady convective diffusion with interphase mass transfer. Proc. R. Soc. Lond. A 333, 115–132.Google Scholar
Smith, R.: 1982 Gaussian approximation for contaminant dispersion. Q. J. Mech. Appl. Maths 35, 345–366.Google Scholar
Smith, R.: 1983 Effect of boundary absorption upon longitudinal dispersion in shear flows. J. Fluid Mech. 134, 161–177.Google Scholar
Smith, R.: 1987 Shear dispersion looked at from a new angle. J. Fluid Mech. 182, 447–466.Google Scholar
Taylor, G. I.: 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186–203.Google Scholar
Taylor, G. I.: 1954 Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion. Proc. R. Soc. Lond. A 225, 473–477.Google Scholar