 Diffusion in two dimensions

Posting by sue on April 17, 2008 at 14:21:15.

I'm interested to learn about Fick's First and Second Laws. From the Fick's Law (1D), how to derive into 2 or 3 dimensions? How about the similarities of mass transfer with heat transfer equations?

On 04/17/2008 Composite Analytica posts: 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).

Good luck,
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