Solution to the Diffusion Equation with a Step in Concentration

Solution to the Diffusion Equation with a Step in Concentration 

Sometimes the boundary conditions can be approximated as a step in concentration instead of a step in mass released. This subtle difference in boundary conditions changes the solution from one that is related to pulse boundaries (known mass release) to one resulting from a concentration front with a known concentration at one boundary. 

EXAMPLE 2.7 Dichlowbenzene concentration in lake sediments due to a plating facility discharge (solution to a concentration front) 

There are three known techniques to solve equation (E2.7.1) Laplace transforms, Fourier transforms, and change of variables, which incorporates both luck and skill We will use change of variables  

We will now apply equation (E2.7.6) to estimate the dichlorobenzene penetration versus time from spillage. The results are given in Table E2.7.1, which gives the interstitial dichlorobenzene concentrations. 

---

E. SOLUTION TO THE DIFFUSION EQUATION WITH A STEP IN CONCENTRATION... 

---