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Effect of boundary absorption upon longitudinal dispersion in shear flows

Published online by Cambridge University Press:  20 April 2006

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

Boundary absorption causes a depletion of contaminant. Since the boundary tends to be the region of lowest velocity and of strongest shear, the remaining contaminant experiences on average an increased advection velocity, a reduced rate of shear dispersion, and a tendency to develop skewness towards the rear. Here it is shown how all these effects can be incorporated into a delay-diffusion description of the longitudinal dispersion process (Smith 1981). It is the accurate reproduction of the skewness that permits a delay-diffusion equation to become applicable at an earlier stage than the more conventional diffusion-equation models for longitudinal dispersion, and before there has been an undue loss of contaminant through the boundary.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 134 , September 1983 , pp. 161 - 177
Copyright
© 1983 Cambridge University Press

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References

Aris, R. 1959 On the dispersion of a solute by diffusion convection and exchange between phases Proc. R. Soc. Lond. A252, 538–550.Google Scholar
Chatwin, P. C. 1970 The approach to normality of the concentration distribution of a solute in solvent flowing along a straight pipe J. Fluid Mech. 43, 321–352.Google Scholar
De Gance, A. E. & Johns, L. E. 1978a The theory of dispersion of chemically active solutes in a rectilinear flow field Appl. Sci. Res. 34, 189–225.Google Scholar
De Gance, A. E. & Johns, L. E. 1978b On the dispersion coefficients for Poiseuille flow in a circular cylinder Appl. Sci. Res. 34, 227–258.Google Scholar
Elder, J. W. 1959 The dispersion of marked fluid in turbulent shear flow J. Fluid Mech. 5, 544–560.Google Scholar
Fife, P. C. & Nicholes, K. R. K. 1975 Dispersion in flow through small tubes Proc. R. Soc. Lond. A344, 131–145.Google Scholar
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.
Gill, W. N. & Ananthakrishnan, V. 1967 Laminar dispersion in capillaries: Part 4. The slug stimulus. AIChE J. 13, 801–807.Google Scholar
Jayaraj, K. & Subramanian, R. S. 1978 On relaxation phenomena in field-flow fractionation Sep. Sci. Tech. 13, 791–817.Google Scholar
Lungu, E. M. & Moffatt, H. K. 1982 The effect of wall conductance on heat diffusion in duct flow J. Engng Math. 16, 121–136.Google Scholar
Maron, V. I. 1978 Longitudinal diffusion through a tube Intl J. Multiphase Flow 4, 339–355.Google Scholar
Nordin, C. F. & Troutman, B. M. 1980 Longitudinal dispersion in rivers: the persistence of skewness in observed data. Water Resources Res. 16, 123–128.Google Scholar
Sankarasubramanian, R. & Gill, W. N. 1973 Unsteady convective diffusion with interphase mass transfer Proc. R. Soc. Lond. A333, 115–132.Google Scholar
Sankarasubramanian, R. & Gill, W. N. 1975 Correction to: ‘Unsteady convective diffusion with interphase mass transport’. Proc. R. Soc. Lond. A341, 407–408.Google Scholar
Smith, R. 1981 A delay-diffusion description for contaminant dispersion J. Fluid Mech. 105, 469–486.Google Scholar
Smith, R. 1982 Non-uniform discharges of contaminants in shear flows J. Fluid Mech. 120, 71–89.Google Scholar
Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube Proc. R. Soc. Lond. A219, 186–203.Google Scholar
Thacker, W. C. 1976 A solvable model of shear dispersion J. Phys. Oceanogr. 6, 66–75.Google Scholar
Watson, G. N. 1966 A Treatise on the Theory of Bessel Functions. Cambridge University Press.