Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T08:25:30.471Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-uniform discharges of contaminants 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
Get access Rights & Permissions [Opens in a new window]

Abstract

For a non-uniform discharge of contaminant in a shear flow the initial advection velocity and the amount of shear across the contaminant cloud depend upon the discharge shape across the flow. Here i t is shown how the continuing influence of the discharge non-uniformity can be incorporated into a delay-diffusion description of the dispersion process (Smith 198 1). An important improvement over the variable coefficient diffusion equation derived by Gill 85 Sankarasubramanian (1971) is that the solutions have the physically correct superposition property.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 120 , July 1982 , pp. 71 - 89
Copyright
© 1982 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aris, R. 1956 On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235, 67–77.Google Scholar
Chatwin, P. C. 1970 The approach to normality of the concentration distribution of a solute in solvent flowing along a pipe. J. Fluid Mech. 43, 321–352.Google Scholar
Dewey, R. J. & Sullivan, P. J. 1982 Longitudinal diffusion at small times. J. Fluid Mech. (submitted).Google Scholar
Gill, W. N. & Sankarasubramanian, R. 1970 Exact analysis of unsteady convective diffusion. Proc. R. Soc. Lond. A 316, 341–350.Google Scholar
Gill, W. N. & Sankarasubramanian, R. 1971 Dispersion of a non-uniform slug in timedependent flow. Proc. R. Soc. Lond. A 322, 101–117.Google Scholar
Krishnamurthy, S. & Subramanian, R. S. 1977 Exact analysis of field-flow fractionation. Sep. Sci. Tech. 12, 347–379.Google Scholar
Jayaraj, K. & Subramanian, R. S. 1978 On relaxation phenomena in field-flow fractionation. Sep. Sci. Tech. 13, 791–871.Google Scholar
Maron, V. I. 1978 Longitudinal diffusion in a flow through a tube. Int. J. Multiphase Flow 4, 339–355.Google Scholar
Smith, R. 1981 A delay-diffusion description for contaminant dispersion. J. Fluid Mech. 105, 469–486.Google Scholar
Smith, R. 1982 Gaussian approximation for contaminant dispersion. Quart. J. Mech. Appl. Math. (to appear).
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. 1959 The present position in the theory of turbulent diffusion. Adv. Geophys. 6, 101–111.Google Scholar
Thacker, W. C. 1976 A solvable model of shear dispersion. J. Phys. Oceanogr. 6, 66–75.Google Scholar