Questions about the electric field in an air/ionic media interface

[Sancor]

Hi there. I'm trying to consider a system in which you have an electric field applied by a capacitor over two media, namely an air gap and then a solution containing a bivalent ionic concentration.


++++++++
air
-------------
ionic media
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If a DC potential is applied between the top and bottom electrodes, you should be able to consider the electric field using the boundary condition supplied by conservation of charge:

Layer 1 (Dielectric, air, conductivity = s1 = 0) : Layer 2 (conductivity = s2)
Jn1=Jn2 Current density continuation equation (n is the normal component)
E1n*s1=E2n*s2 Ohms law
0=E2n*s2 Since Jn1=0
E2n=0 Since s2 =/= 0


This implies that the vertical electric field in the ionic media must be zero. I'm having a hard time believing this. Could someone offer some physical reasoning as to why this is?

 

[mfb]

An electric field in a conductor would lead to a current - and that current reduces the electric field. In equilibrium, you don't have a current and therefore you don't have an electric field.
That is equivalent to your equations, just with words.

 

[DrZoidberg]

A capacitor with an ionic media (aka electrolyte) and without an insulating layer is called a "double layer capacitor"
http://en.wikipedia.org/wiki/Double-layer_capacitor
There is no field inside the electrolyte since it's a conductor. There is however a strong field in the double layer.