Convection-Diffusion in a Semi-Infinite Region

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The dimensionless concentrations ( is surface concentration []) in a semi-infinite region are plotted (steady state in orange, transient in blue) up to the space coordinate [].


Only one slider is used to adjust the parameters: space [], time [], the flow velocity [], the hydrodynamic dispersion coefficient [] ( is dispersivity []), the first-order reaction rate [], and the frame length [].

The model is described by the partial differential equation subject to the conditions , , .

For a fixed time parameter, the space determines black points on the orange curve and on the blue curve , so that you can see the corresponding numerical values. Smilarly for any parameter the precise values of the steady state and transient dimensionless concentrations are available.


Contributed by: Mikhail Dimitrov Mikhailov (March 2011)
Open content licensed under CC BY-NC-SA



The solution programmed includes all possible special cases. The general case is given by Bear and used to compute multispecies transport problems by Sun, et al.

J. Bear, Hydraulics of Groundwater, New York: McGraw-Hill, 1979.

Y. Sun, J. N. Petersen, T. P. Clement, and R. S. Skeen, "Development of Analytical Solutions for Multispecies Transport with Serial and Parallel Reactions," Water Resources Research, 35(1), 1999 pp. 185–190.

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