Hello everyone,
I am having problems trying simulate a basic problem of electro chemistry. I know I could just use the build in NPP solver, but I want to do equation-based modeling using "Coefficient Form PDE" to gain a better understanding of what I am actually doing.
I am working in 1D, and I have two AgCl electrodes with distance 
from each other. My electrolyte is KCl (0.5 mol) and I would like to solve for the x depending concentration 
and 
, respectively. The applied potential on the one electrode is 100 mV, the other electrode is on ground. Electrode reactions can be neglected for the moment.
So far, I have been able to solve Laplace's equation 
, which is pretty straightforward. This yields a linearly decreasing line from 
to 
, as expected.
The Nernst-Planck equation is as follows: 
.
So how do I couple those equations? I have been able to formulate both equations but how do I call 
? Is it something like grad(phi) or d(phi,x)? Unfortunately, I have not found any satisfying solution.
Any help will be highly appreciated! Thanks in advance.
Cheers, Junis