Potentiometry

I feel like my issue should not be that hard, but I am struggling to model this.

I have a system in which there is a very nonpolar (organic) membrane between two aqueous solutions. I am trying to model the flux (diffusion) of a charged species out of the membrane into one of the aqueous solutions due to a change in thickness of the Nernstian diffusion layer governed by the stirring rate of the system.

One of the biggest considerations is that there is no net current change, just a change in potential (phase boundary potential differences). This makes it difficult to justify with other ion transfer models out there.

Any help would be appreciated!