On 04/17/2008 Composite Analytica
To obtain the mass uptake of a sample, which is not only exposed to chemicals in the x direction, but also in the y or z direction, you can do the following (in case of a rectangular sample, with plane walls):
- Take the analytical solution of Fick's second law for the mass uptake of a sample in one dimension, for example the x direction: Mx(t).
Make sure that the boundary conditions and initial conditions are right. One appropriate source for this analytical mass uptake solution is the book "Diffusion in Polymers", edited by Crank and Park.
- Now for the y (2D) and z (3D) direction you can take the same formula: My(t) and/or Mz(t) Again make sure that the diffusion distance, boundary and initial condition are right.
- The total mass uptake in 2 dimensions now follows from Mtotal(t) = Mx(t) x My(t). For 3 dimensions it is: Mtotal(t)=Mx(t) x My(t) x Mz(t).