Labs on Chip

7.4.4    DIFFUSION EQUATION BASIC SOLUTIONS: DIFFUSION IN LIMITED VOLUMES

Diffusion solution in conditions of free diffusion are very useful in several practical cases, however it is also frequently the case in which the fact that diffusion happens in a limited volume cannot be ignored. In this case, boundary conditions are added to the initial condition and the free diffusion Green methods cannot be used. In labs on chip, the ducts and chambers where diffusion happens are generally squared, due to the processes that produce them. Thus, the case of a square domain for diffusion is not only particularly simple, but it is also important in our case.

Let us imagine that diffusion happens in a chamber of dimensions L_i (i = 1, 2, 3) whose vertex with ...