Diffusion Exercises

The diffusion software supports two different types of initial conditions. These are selected under the "Flow Problem" menu. The default problem solves the problem for diffusion of a chemical with initial concentration Co in the soil to some user-specified depth and a concentration of zero below that mixing depth. No chemical enters or leaves the soil surface (x=0) in this case. This case will be called the initially mixed condition below.

The second case considers a soil with an initial concentration of zero throughout. The chemical concentration is then maintained at a concentration of Co at the inlet x = 0 so chemical diffuses into the soil as time passes. This case will be called the constant concentration case below.

I. Consider the initially mixed transport problem with the chemical mixed to a depth of 5 cm. Begin with the maximum depth to plot equal to 20 cm and make adjustments as needed.

  1. Using a diffusion coefficient of 1.0 cm2/day, how far has the chemical moved into the soil after 10, 20, 30, 40, and 50 days? Draw a graph of the depth of penetration as a function of time. Repeat this for Diffusion coefficients of 2.0, 3.0, 4.0, and 5.0 cm2/day. (Draw lines for all values of D on a single graph.) Describe the way the depth of penetration changes with diffusion coefficient at a specific time.

  2. Retain the line corresponding to a diffusion coefficient of 1.0 cm2/day and time of 50 days. Increase the diffusion coefficient to 2.0 cm2/day. Adjust the time of interest so that the curve for D=2.0 cm2/day coincides with the curve for 1.0 cm2/day and 50 days. At what time do the curves coincide? Repeat this for diffusion coefficients of 3.0, 4.0, and 5.0 cm2/day. What do you conclude from these results?

  3. The effective diffusion coefficient depends upon the water content and the porosity (and hence the bulk density) of the soil. Does an increase in water content increase or decrease the effective diffusion coefficient? Why?

  4. Does an increase in porosity increase the diffusion coefficient? Why or why not?

  5. Assume the soil has an organic carbon content of 1.5%. The soil contains two chemicals with diffusion coefficients of 5.0 cm2/day and with Koc values of 0 and 10 ml/g OC. Which will diffuse the greatest distance in 30 days? Does sorption have a large effect on diffusion? What diffusion coefficient for the chemical with Koc of 0 produces the same curve as the soil with a diffusion coefficient of 5 and Koc of 10 ml/g OC?

  6. Repeat 5 for a soil having an organic carbon content of 1.0%. What is the effect of organic carbon?

II. Repeat the exercises above for the constant concentration initial condition. What similarities and differences do you observe?