Example 5.2E Mozzarella
Back in 2010, Italian police seized more than 70,000 balls of mozzarella because they turned blue! It turns out that the water with which the mozzarella was brined was contaminated.
Suppose that this contamination comes from a landfill where, for 10 years, they have been dumping contaminated garbage. This contamination has been penetrating the soil due to rainwater seeping through the ground. This process can be seen as an effective diffusion process, with a diffusion coefficient of D = 2.0 x 10^-10 m^2/s. Assume that the contaminated garbage layer was so big that at the top of the soil layer, the concentration of the contamination is always equal to the solution of the contamination c*. The value of c* = 2.0 kg/m^3.
In 10 years, the contamination has penetrated the soil to a depth of h = 0.45 m. Assume a linear concentration profile throughout the contaminated layer.
What is the gradient of the concentration in the soil?
The government has decided that they will not just remove the garbage, but also the top 30 cm of the contaminated soil layer. Is this deep enough for the concentration in the remaining soil to not surpass?
