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Boundary Conditions for Displacement Experiments through Short Laboratory Soil Columns¹

ABSTRACT

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.

¹ Joint contribution from the U.S. Salinity Lab., 4500 Glenwood Drive, Riverside, CA 92501, and the Dep. of Agronomy, Virginia Polytechnic Inst. and State Univ., Blackburg, VA 24061.

² Research Soil Scientist, U.S. Salinity Lab., and Assistant Professor, Dep. of Agronomy, Virginia Polytechnic Inst. and State Univ., respectively.

Received for publication November 10, 1983. Accepted for publication March 2, 1984.

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