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Analytical Solution for Two-Region Diffusion with Two Well-Mixed End Chambers

Soils and Biogeochemistry, Dep. of Land, Air, and Water Resources, Univ. of California, Davis, CA 95616

L. W. Petersen

Danish Ministry of Agriculture, Inst. of Plant and Soil Science, Research Center Foulum, P.O. Box 23, DK-8830 Tjele, Denmark

R. D. Glauz

Dep. of Mathematics, Univ. of California, Davis, CA 95616

*Corresponding author (yhelfarhan{at}ucdavis.edu).

ABSTRACT

Many methods have been developed for determining the effective gaseous diffusion coefficient (D_p) in soils. Some commonly used methods are the one- and two-chamber apparatuses. In addition, laboratory apparatuses for the study of vapor diffusion, sorption, and biodegradation may consist of soil and vapor chambers. Existing analytical solutions for such apparatuses cannot accommodate diffusion through regions containing two distinct layers of differing porosity and diffusion coefficient. Such dual porosities can represent stagnant air layers, or crusting-compaction at core ends. We developed an analytical solution for gaseous diffusion in a four-region chamber system. The system consists of two diffusion regions (with two different porosities), and a well-mixed end chamber attached at either end. The solution was used to simulate one-dimensional gas diffusion in an apparatus consisting of two diffusion regions with constant-concentration boundary conditions. The solution was also used to quantify errors made in estimating D_p using the one-chamber apparatus when the air chamber is not mixed, or when a stagnant air layer exists above the soil surface. Errors due to non-mixing decreased with time and increased with water content and air-chamber size when analysis was done using concentrations at a point close to the soil surface. Analysis of the effects of a stagnant air layer showed that errors increased with time and air-chamber size and decreased with increasing water content. Analysis done to test the effects of soil crusting on diffusion showed that, despite the thinness of the soil crust, large estimation errors in D_p are possible.

Received for publication October 16, 1995.