# Dissolved ion distribution under the influence of an external electric field

1. Aug 9, 2007

### Thorr

Hello,

I'm a medical student and a few days ago a rather interesting question arose when I was doing some research. The gist of the problem is estimating how dissolved ions in a solution will distribute themselves when an external electric field is applied. Now I had basic physics and electrostatics but even just writing down equations to try and describe this problem is a bit over my head.

I drew an illustration of the dilemma to make it clearer.

Exact description of the problem:
- we have a sealed container of dimension d, filled with a solution of ions A and B. For simplicity, lets assume both A and B have +1 and -1 charges respectively. (you can also ignore the undissolved part of compound AB for now)

- we apply an external homogeneous electric field of strength E to the container. Obviously ions A drift in the direction of the electric field, ions B the other way around until an equilibrium state is achieved.

The thing I'd like to know is how the concentration of A (B) changes in relation to x.

I know the computation might get a bit involved but I hope I can at least get pointers on how to write down some initial equations or perhaps where a solution (with full derivation preferably) to this problem can be found.

I'm not just interested in the final functions, I'd like to see the path to the solution at least in part or at crucial steps.

The problem is a bit akin to something like the Debye's shielding effect...

Thanks so much for your help!

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Last edited: Aug 9, 2007