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Diffusion and sorption in particles and two‐dimensional dispersion in a porous medium
Author(s) -
Rasmuson Anders
Publication year - 1981
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr017i002p00321
Subject(s) - laplace transform , dispersion (optics) , dimensionless quantity , diffusion , mathematical analysis , dispersion relation , porous medium , differential equation , steady state (chemistry) , mathematics , point source , integral transform , taylor dispersion , partial differential equation , mechanics , physics , materials science , thermodynamics , porosity , chemistry , optics , composite material
A solution of the two‐dimensional differential equation of dispersion from a disk source, coupled with a differential equation of diffusion and sorption in particles, is developed. The solution is obtained by the successive use of the Laplace and the Hankel transforms and is given in the form of an infinite double integral. If the lateral dispersion is negligible, the solution is shown to simplify to a solution presented earlier. Dimensionless quantities are introduced. A steady state condition is obtained after long times. This is investigated in some detail. An expression is derived for the highest concentration which may be expected at a point in space. An important relation is obtained when longitudinal dispersion is neglected. The solution for any value of the lateral dispersion coefficient and radial distance from the source is then obtained by simple multiplication of a solution for no lateral dispersion with the steady state value. A method for integrating the infinite double integral is given. Some typical examples are shown.