Charge screening by electrolytes

[Gavroy]

if I have a not necessarily homogenous electric field of a charge distribution in an electrolyte and i want to find out what the electric field at some position in the electrolyte is. is there any equation that i could use to consider also electric screening by the ions, so that I will get a different electric field that is lowered by the screening?

So basically I am looking for an equation that takes an electric field or potential and gives me the screened one.

 

[Baluncore]

You must define conductive equipotential boundary conditions for problems like this. For trivial geometric examples there will be an equation, but finite element analysis might be more appropriate here.

If you imagine your electrolyte to be made of many small cubes, each with a specified dielectric constant, then you can model those elements as an array of series and parallel capacitors. The electric field gradient will be greatest in elements that have the lowest dielectric constant.