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Three‐Dimensional Solutions for Solute Transport in an Infinite Medium With Mobile and Immobile Zones
Author(s) -
Goltz Mark N.,
Roberts Paul V.
Publication year - 1986
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/wr022i007p01139
Subject(s) - laplace transform , porous medium , partial differential equation , mathematical analysis , fourier transform , mechanics , advection , coupling (piping) , flow (mathematics) , boundary value problem , materials science , mathematics , porosity , physics , thermodynamics , geology , geotechnical engineering , metallurgy
Tailing of breakthrough responses, which has been experimentally observed during flow through porous media, can be modeled by dividing the porous medium into regions of mobile and immobile water, and coupling the advective‐dispersive solute transport equation with expressions to describe diffusional transfer between the two regions. Three‐dimensional solutions to this coupled set of partial differential equations with infinite boundary conditions are derived by applying the Laplace transform to the equations with respect to time, and the Fourier transform with respect to space. The solutions presented herein may be useful in applying the two‐region models to field settings.