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Mathematical Analysis of One‐Dimensional Solute Transport in a Layered Soil Profile
Author(s) -
Leij Feike J.,
Genuchten M. Th.,
Dane J. H.
Publication year - 1991
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1991.03615995005500040008x
Subject(s) - laplace transform , classification of discontinuities , layering , boundary value problem , advection , soil horizon , mechanics , inlet , conservation of mass , constant (computer programming) , soil science , chemistry , thermodynamics , environmental science , soil water , geology , mathematics , mathematical analysis , physics , geomorphology , botany , computer science , biology , programming language
Solute transport studies involving layered media are important for investigating how restricting layers affect rates of solute migration in the soil profile and, more generally, for examining the influence of soil heterogeneity on solute transport. Analytical solutions of the one‐dimensional advection‐dispersion equation (ADE) were obtained with the help of Laplace transforms for transport in a two‐layered soil profile. Assuming that the layers are, in effect, semi‐infinite, solutions were obtained for first‐type (constant concentration) and third‐type (constant flux) conditions at both the inlet boundary and the interface of the two layers. Concentration profiles were also obtained for a finite first layer via numerical inversion of the Laplace transform solution, using a third‐type condition at the inlet, and, simultaneously, a first‐ and third‐type condition at the interface. Volume‐averaged or resident‐type concentrations were used in all cases. First‐type conditions did not meet our criterion of mass conservation, whereas third‐type conditions caused discontinuities in the concentration at the interfaces of layers with differing transport parameters. The concentration at the interface was found to be continuous, and no mass‐balance error occurred, when first‐ and third‐type conditions were imposed simultaneously at the interface. Serveral example calculations show the effect of soil layering on solute transport in a one‐dimensional soil profile.