# Boundary conditions in a closed system for diffusion (2nd Fick's law) in a porous medium

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!

• 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. – porphyrin Apr 9 '20 at 20:44