March 28, 2024, 09:50:57 AM
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Topic: Combined treatment of migration and diffusion of a cation on dissolution  (Read 2408 times)

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Offline samuel

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Hi,
I've to get an equation that consider the electrical charge flow due to a cation Oxz+ that   is reduced on an inert electrode in high overpotential conditions (diffusion control) and without supporting electrolyte (so I have to consider also migration).

I would appreciate it if you would look through my results and if I've made some mistakes give me an advice about how to correct them.

1) Starting point: The Nernst-Plank equation but making 0 the convection term.
eq (1) where J is the ions flux
2) Term of diffusion: using the Nernst diffusion layer model, being δ the Nernst diffusion layer width it can be solved as: eq (2)
3)Term of migration: using the transport index eq (4), considering that (∂ϕ/∂x) is the electric field (E) and considering the concentration of Ox close to the electrode i get by combination the eq (3) and (4) the eq (5) as a final result
(the last step would be convert ion flux to electric flux by jelect=J·Z·F)
*The equations are in the attached picture
Notation:
uOx= ion mobility
tOx=ion transport index
Ktot=total conductivity of the solution
KOx=conductivity of the ion
COxelectrode= concentration of Ox close to the electrode
COxsolution= concentration of Ox in the middle of the solution
F=Faraday constant
Z= charge of the ion
E (with |E| ande vector) = electric field module

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