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Coupling problem: Nernst-Planck equation with Poisson not converging
Posted Mar 25, 2014, 12:43 p.m. EDT Chemical Reaction Engineering, Electrochemistry, Studies & Solvers Version 4.4 5 Replies
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Hi,
I am unsuccessfully trying to implement to Poisson equation through the Electrostatic Module into the Module "Transport of Diluted species" for a stationary case.
Beside those modules I use the laminar flow module to account for the fluidics.
The model is supposed to describe a biochemical cell, with a fixed ion concentration streaming into a reaction chamber onto a sensor. The variable of interest would be the resulting ion concentrations for both species. On that sensor species of one kind are transported out of the model, accounted for with the "flux" boundary condition.
I activated both migration through the Electrical field and convection through the fluid in the ion transport module.
As I understand the Electrical field created by the ion species are not automatically accounted for by these modules, so I created a space charge density as
with z the respective ion charges and c the respective ion concentrations.
Without the space-charge density everything converges fine, with the space charge density implemented however, the solution does not converge. I tried different solver combinations, first solving for the fluidics, finer grid resolution and no steep gradients, but without any success.
Does anybody have any experience in coupling Poisson with NP? I'm starting to think some of the boundary conditions are not set up correctly...
It would be awesome if anybody could have a look at my model.
Thanks a lot,
Raphael
I am unsuccessfully trying to implement to Poisson equation through the Electrostatic Module into the Module "Transport of Diluted species" for a stationary case.
Beside those modules I use the laminar flow module to account for the fluidics.
The model is supposed to describe a biochemical cell, with a fixed ion concentration streaming into a reaction chamber onto a sensor. The variable of interest would be the resulting ion concentrations for both species. On that sensor species of one kind are transported out of the model, accounted for with the "flux" boundary condition.
I activated both migration through the Electrical field and convection through the fluid in the ion transport module.
As I understand the Electrical field created by the ion species are not automatically accounted for by these modules, so I created a space charge density as
with z the respective ion charges and c the respective ion concentrations.Without the space-charge density everything converges fine, with the space charge density implemented however, the solution does not converge. I tried different solver combinations, first solving for the fluidics, finer grid resolution and no steep gradients, but without any success.
Does anybody have any experience in coupling Poisson with NP? I'm starting to think some of the boundary conditions are not set up correctly...
It would be awesome if anybody could have a look at my model.
Thanks a lot,
Raphael
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5 Replies Last Post Jul 7, 2015, 2:25 a.m. EDT
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Posted:
1 decade ago
Raphael:
Can you please explain how your cell works in more detail? As far as I can understand, there is an inlet tube where 2 species c and c2 enter the cell and an outlet tube where they leave the cell. Once they are inside the cell, they interact with a circular sensor which only allows "c" to pass through and not c2. How is this selection done? Are you applying any external current or an electric field?
Also, if you have the electrochemistry module, I suggest you use the Tertiary current distribution which will take care of all these modules together.
Sri.
Can you please explain how your cell works in more detail? As far as I can understand, there is an inlet tube where 2 species c and c2 enter the cell and an outlet tube where they leave the cell. Once they are inside the cell, they interact with a circular sensor which only allows "c" to pass through and not c2. How is this selection done? Are you applying any external current or an electric field?
Also, if you have the electrochemistry module, I suggest you use the Tertiary current distribution which will take care of all these modules together.
Sri.
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Posted:
1 decade ago
Hi Sri,
Thanks for your reply.
Yes, an electrolyte with two species is washed through the cell, entering through the inner tube and leaving through the outer tube. One of the species is transported through a transporter protein on a biomembran and is thus leaving the model (as this area is conntected to ground, no electrostatic force is built up. Now, with one species leaving, the concentration changes and therfore the space charge density, which over the Poisson-equation
and 
and the defined space charge density should have influence on the migration-term in the nernst-planck equation 
as far as I understand. No external field or voltage is applied, my goal is to check whether these concentration gradients reach the electrode (next to the tubes) by migration in the presence of convection by the fluid. The diffusion term can be ignored in this case I think.
I had a look at the Tertiary current distribution, but it appears to neglect the self-induced migration term through the concentration change as well as sets up a electroneutrality condition, which is not applicable to my model.
I set up the model in accordance to the diffuse double layer model in the libraries....
I still don't understand why I don't get convergence in my case...
thanks for any help,
Raphael
Thanks for your reply.
Yes, an electrolyte with two species is washed through the cell, entering through the inner tube and leaving through the outer tube. One of the species is transported through a transporter protein on a biomembran and is thus leaving the model (as this area is conntected to ground, no electrostatic force is built up. Now, with one species leaving, the concentration changes and therfore the space charge density, which over the Poisson-equation
and and the defined space charge density should have influence on the migration-term in the nernst-planck equation as far as I understand. No external field or voltage is applied, my goal is to check whether these concentration gradients reach the electrode (next to the tubes) by migration in the presence of convection by the fluid. The diffusion term can be ignored in this case I think.I had a look at the Tertiary current distribution, but it appears to neglect the self-induced migration term through the concentration change as well as sets up a electroneutrality condition, which is not applicable to my model.
I set up the model in accordance to the diffuse double layer model in the libraries....
I still don't understand why I don't get convergence in my case...
thanks for any help,
Raphael
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Posted:
9 years ago
Hi Raphael,
I was wondering if you found a solution to your problem, and if yes what the solution was because I am stuck with a similar problem and don't know what to change besides exclude the space charge density from the model, which I cannot do.
Thanks in advance.
Arpita Iddya
I was wondering if you found a solution to your problem, and if yes what the solution was because I am stuck with a similar problem and don't know what to change besides exclude the space charge density from the model, which I cannot do.
Thanks in advance.
Arpita Iddya
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Posted:
9 years ago
Recently, in simulating Induced charge electroosmotic flow by coupling P-N-P-NS equations in Comsol, I encountered similar converging issues, and yet have not resolved~~
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Posted:
9 years ago
There is an inherent problem: N-P uses electroneutrality condition which you try to overrule by P-B. In an older version of Comsol there was physics "N-P without electroneutrality" (or something like that). It has been removed - maybe Comsol developers realized that it did not work properly?
I have used P-B according to Gouy-Chapman theory, i.e.
Nabla^2 phi = - SUM{c_i^b*exp(-(z_i*F/RT)*phi)}
In a physiological solution the electric double layer is very thin, ca. 1 nm, so do you really need that?
br
Lasse
I have used P-B according to Gouy-Chapman theory, i.e.
Nabla^2 phi = - SUM{c_i^b*exp(-(z_i*F/RT)*phi)}
In a physiological solution the electric double layer is very thin, ca. 1 nm, so do you really need that?
br
Lasse