EnPEn
There it is. The code producing all of my dissertation. It's academic and therefore it's ugly, won't compile and will lead to people code up the same stuff, just better (tm).
What it does
EnPEN solves the coupled Nernst-Planck-Poisson equations in one dimension, while accounting for chemical reactions. It can handle any ion exchange membrane setup you can think of (multilayered assemblies, bipolar membranes). Add some convection, why not. It can simulate electrical impedance spectroscopy up to unmeasurable frequencies and down to unmeasurable frequencies. It's tailored C code, so it'll solve the problem faster and better than stuff you can buy.
You think you have a problem that EnPEn can solve?
Don't be afraid to ask. Mail me. I can tell you if EnPEn can do it out of the box or what parts of the code you might want to change. For instance, change anything but files in the impl/ directory, or be careful about it. Since this is kind of a library, I wrote several python scripts to wrap around it, for instance: impedance spectroscopy lends itself to having several simulations at the same time.
Citing and validation
In the spirit of good scientific practice, you could cite, for steady state code:
https://www.nature.com/articles/srep11583
and for anything dynamic code:
http://www.sciencedirect.com/science/article/pii/S0376738816311140
License
Academia? Go ahead. Otherwise ask me.