Integrating several Physics and problem with average current distribution

Hi there,

I am trying to solve nernst plank equation in 2D space. I have inert electrodes.
I used 2 methods for approaching and both have a common problem - the mesh (copper deposition) does not move ahead.

Additionally each one has a specific problem
1. In Nernst Plank, I am using flux on both the ends, but I do not want the flux to be constant, and more like how it would be experimentally (higher near the other electrode)
2. In the tertiary current distribution, I would like the equilibrium of water to work properly (OH ion concentration should not drop below zero).

The models may have other problems that I am not aware of.
Any suggestions is greatly appreciated.

Due to size restriction, I am unable to attach file, so I have given the google drive link
drive.google.com/open?id=0B5sTHUmnJxmEdUk0STlnRTR6QUU

Thanks,
Chitvan