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Integrating several Physics and problem with average current distribution
Posted 2015年9月11日 GMT-4 13:02 Fluid & Heat, Chemical Reaction Engineering, Electrochemistry, Mesh, Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers Version 5.1 5 Replies
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I am trying to solve nernst plank equation in 2D space. I have inert electrodes.
I used 2 methods for approaching and both have a common problem - the mesh (copper deposition) does not move ahead.
Additionally each one has a specific problem
1. In Nernst Plank, I am using flux on both the ends, but I do not want the flux to be constant, and more like how it would be experimentally (higher near the other electrode)
2. In the tertiary current distribution, I would like the equilibrium of water to work properly (OH ion concentration should not drop below zero).
The models may have other problems that I am not aware of.
Any suggestions is greatly appreciated.
Due to size restriction, I am unable to attach file, so I have given the google drive link
drive.google.com/open?id=0B5sTHUmnJxmEdUk0STlnRTR6QUU
Thanks,
Chitvan
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I did not download your model, but let me reply something.
1. Current at both electrodes must be equal. Of course you can set the flux boundary condition time dependent, but the fluxes cannot be different, it would violate electroneutrality.
2. Did you include the autoprotolysis of water? Usually it is not necessary as water is an infinite source of H+ and OH-. It is tricky to take these ions into account in the model.
In the case of copper deposition, the thickness of Cu layer advances at the rate of
v = I*M/(n*F*d)
I = current density
M = molar mass (63.5 g/mol)
n = number of electrons = 2
F = Faraday constant = 96500 As/mol
d = density = 9 g/cm^3
For example, setting I = 100 A/m² = 0.01 A/cm² gives
v = 3.6 nm/s
This is why metal electrolysis requires high current densities (typically 300-500 A/m²), large electrode areas (thousands of m²) and long deposition time (a couple of days).
BR
Lasse
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You have made some valid points, and I have considered all of them. The problem is that I can not include autoprotolysis of water, and I wish to include that.
Any suggestions will be a great help.
Thanks,
Chitvan
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I suggest leaving OH- out from the simulation, assume pH constant. If possible, I still has not downloaded your model ;)
BR
Lasse
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That is how I started to model, for testing. But the equation on the anode is something like this:
2OH- => H2O + 0.5 O2 + 2e-
I modelled this in Nerst Plank equation physics as it has equilibrium equation, but it does not have other features like average current density (as I would like to observe how the copper deposition front changes as time progresses) and electrode reactions as that models the electrode potential (due to the reactions taking place at the electrodes).
Thanks for helping out,
Chitvan
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Equilibria are tricky in transport equations. Due to the nature of the calculus, it is better to use kinetic equations. For water autoprotolysis the reaction rate constant is
2.45e-5 1/s
and for the recombination of H+ and OH- the 2. order rate constant is
1.35e11 1/(M*s)
(This is normal phys chem textbook knowledge.)
BR
Lasse