Modeling air phase diffusion w radioactive decay

John Tauxe

Greetings, folks. I am not a CFD modeler, but I do have an engineering PhD and get the basic concepts if not all the jargon. I concentrate on the migration of environmental contaminants through natural and engineered materials. Here's my current challenge:

I am modeling the diffusion of radioactive gases (e.g. radon) through a partially-saturated porous medium, using a 1-D finite difference scheme. Each compartment in the FD setup is assumed to be instantaneously mixed, as usual, and therefore introduces some numerical dispersion (or numerical diffusion, as some here have called it). That's to be expected, of course, and there are various ways of compensating for that.

However... things get much trickier when dealing with a diffusing gas that decays (to other radioactive materials that are not gases) and also partitions into any water present in the soil. So there are several competing mechanisms going on simultaneously:

- instantaneous mixing by the FD compartment (undesirable) - diffusion in the air phase within the porous medium - partitioning into the adjacent water phase (assumed instantaneous and reversible -- in the end this just serves to retard transport) - radioactive decay

and these other factors need also to be considered:

- dimensions of the compartment parallel to flow - diffusive length modified by tortuosity of the air phase - reduced diffusive area due to porous medium

As you can see, it is a complex problem. But all that is a setup to this question:

Is there something like the Damkohler number to evaluate the influence of radioactive decay compared to the diffusive transport? Would it be fair to call this relationship a Damkohler number, or is there some other construct that people have used. The literature is sparse on the subject, so I wanted to bounce the idea of calling the relationship of radioactive decay to diffusion a Damkohler number.

What thinks ye all?