ANALYTICAL SOLUTION FOR 2-REGION DIFFUSION WITH 2 WELL-MIXED END CHAMBERS

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 apparatu ses 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 contain ing two distinct layers of differing porosity and diffusion coefficien t, Such dual porosities can represent stagnant air layers, or crusting -compaction at core ends. We developed an analytical solution for gase ous diffusion in a four-region chamber system. The system consists of two diffusion regions (with two different porosities), and a well-mixe d end chamber attached at either end. The solution was used to simulat e one-dimensional gas diffusion in an apparatus consisting of two diff usion regions with constant-concentration boundary conditions. The sol ution was also used to quantify errors made in estimating D-p using th e one-chamber apparatus when the air chamber is not mixed, or when a s tagnant air layer exists above the soil surface, Errors due to non-mix ing decreased with time and increased with water content and air-chamb er size when analysis was done using concentrations at a point close t o the soil surface. Analysis of the effects of a stagnant air layer sh owed that errors increased with time and air-chamber size and decrease d with increasing water content. Analysis done to test the effects of soil crusting on diffusion showed that, despite the thinness of the so il crust, large estimation errors in D-p are possible.