2
$\begingroup$

I would like to calculate the chloride redistribution in concrete (assumption: porous and homogeneous structure, purely diffusion-controlled mass transfer, closed system). For this I have derived a solution of the differential equation of Fick's 2nd law.

Since the chloride ions cannot leave the system at the borders, I have assumed the following boundary condition:

$$\frac{dc(0,t)}{dx} = \frac{dC(L,t)}{dx} =0, ~~~t>0$$

I have taken this boundary condition from another post on this site (When is diffusion steady-state?)

My solution of the differential equation assuming this boundary condition is correct. I have checked it with the help of an FEM simulation. Now to my question:

Does anyone know of a literature source with which I can prove my chosen boundary condition? Can one generally assume that the derivative of the concentration at the edges is always zero when the system is closed?

Thanks a lot for your help in advance!

$\endgroup$
1
  • $\begingroup$ There are two classic texts on this well studied topic J. Crank, 'The Mathematics of Diffusion' publ. 1979 OUP, and Carlsaw & Jaeger 'Conduction of Heat in Solids', publ. 1959, Clarendon Press. Either or both are well worth looking at. $\endgroup$
    – porphyrin
    Apr 9, 2020 at 20:44

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.