Consider two bars of the same pure semi-infinite metal A, being joined at their edges, and that between them is a thick layer at concentration of pure metal B, a solute that is going to diffuse into the interior of the two bars. This system is presented in Figure 2.2.21 in a graphic of concentration of species C of the atom or molecule diffusing (solute) as a function of distance x. The origin of the system is located in the center of the middle material.
The following boundary conditions or hypothesis should be assumed in this case:
a- For x < - h or x > + h, it follows that C = 0 when t = 0.
b- For -h < x < +h, it follows that C =C0 when t = 0.
The application of the boundary conditions above of Fick’s second law, Eq. (2.7), results in the following solution:
\[ C(x,t) = \frac{C _ {0}}{2}[erf(\frac{h-x}{2\sqrt{Dt}})+erf(\frac{h+x}{2\sqrt{Dt}})] \tag{2.27} \]
