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Boundary Conditions for Displacement Experiments through Short Laboratory Soil Columns
Author(s) -
Genuchten M. Th.,
Parker J. C.
Publication year - 1984
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/sssaj1984.03615995004800040002x
Subject(s) - inlet , effluent , mechanics , boundary value problem , boundary (topology) , flux (metallurgy) , mass flux , péclet number , displacement (psychology) , finite volume method , chemistry , mathematics , physics , mathematical analysis , environmental science , geology , environmental engineering , psychology , organic chemistry , geomorphology , psychotherapist
This paper presents a discussion of the physical and mathematical significance of various boundary conditions applicable to one‐dimensional solute transport through relatively short laboratory soil columns. Based on mass balance considerations, it is shown that a first‐type or concentration‐type condition at the inlet boundary incorrectly predicts the volume‐averaged or resident concentration inside both semi‐infinite and finite systems. A third‐type or flux‐type inlet boundary condition preserves mass in semi‐infinite systems, but underpredicts effluent concentrations from finite columns unless a local transformation is used to convert volume‐averaged concentrations into flux‐averaged concentrations. This transformation leads to an expression for the effluent concentration that is identical to the solution for the semi‐infinite system using a concentration‐type boundary condition. For column Peclet numbers greater than about five, the resulting analytical expression for the effluent curve is shown to be nearly identical to the analytical solution for a finite system based on a flux‐type inlet boundary condition and a zero‐concentration gradient at the exit boundary. Both solutions correctly preserve mass in the system; other solutions of the convective‐dispersive transport equation are shown to be inappropriate for analyzing column effluent data.