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Poisson-Boltzmann Equation
Posted Nov 17, 2009, 11:11 p.m. EST 9 Replies
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Anyone experienced in modelling a simple charge surface with Poisson-Boltzmann equation?
I follow this paper:
-Pham et al. "Numerical Simulation of the Electrical Double Layer Based on the Poisson-Boltzmann Models for AC Electroosmosis Flows",
-Built the model in Figure3, use equation (7),
-I couldnt reproduce figure 4, my potential profile is linear instead of exponential.
I upload my model, I appreciate your kind attention in this problem.
Best Regards,
yang
Attachments:
Hello Wee Yang NG
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in your model, I think you simply forgot to multiply the bulk concentration by 10^3*NA (as explained in the second page of the article)
SO I advice you to define the constant c as 1e-2*1e3*6.022*10^23 and to refine your mesh near the boundary 1 to see the exponential...
Best,
Patrick
Dear All,
Anyone experienced in modelling a simple charge surface with Poisson-Boltzmann equation?
I follow this paper:
-Pham et al. "Numerical Simulation of the Electrical Double Layer Based on the Poisson-Boltzmann Models for AC Electroosmosis Flows",
-Built the model in Figure3, use equation (7),
-I couldnt reproduce figure 4, my potential profile is linear instead of exponential.
I upload my model, I appreciate your kind attention in this problem.
Best Regards,
yang
Please login with a confirmed email address before reporting spam
Why you did not use Poisson equation in Comsol to do so?? It would be easier for you (to understand) rather doing it with PDE. the Poisson equation was not really distinguished!!
As Patrick said, your model is missing lots of things: The Avogadro number, epsilon..etc
Note that the concentration in Comsol are expressed in Mol/m^3 so be careful with that.
Also, Pham et.al., used two different PB equation : the classical one and the modified PB (take a look to the reference of Bazant)
This means that your applied potential should not be so high!!!
I have attached a PB model. you can take a look and try to understand, it is quite easy.
Good luck
Attachments:
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Actually, Yang did use the epsilon number, but you dont see it because he converted the value numerically (see the value of c)...
expect of the fact that he didnt convert the unit with the avogadro number, his model seems ok to me...
Best,
Patrick
Hi,
Why you did not use Poisson equation in Comsol to do so?? It would be easier for you (to understand) rather doing it with PDE. the Poisson equation was not really distinguished!!
As Patrick said, your model is missing lots of things: The Avogadro number, epsilon..etc
Note that the concentration in Comsol are expressed in Mol/m^3 so be careful with that.
Also, Pham et.al., used two different PB equation : the classical one and the modified PB (take a look to the reference of Bazant)
This means that your applied potential should not be so high!!!
I have attached a PB model. you can take a look and try to understand, it is quite easy.
Good luck
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Thank you both for your tips.
With the model i posted earlier, if i just multiply by *Na*10e3, i would have gotten a exponential profile.
But if i add divide by /esp0*espr to the equation, the profile would be linear.
I have read Faycal model, it is very well defined ;)
But, if i try to change my existing model to Faycal's parameter, seems like the solution is not correct.
I posted the model i.e. PB_eqn (2)
Also, i try to write a new model with Poisson (poeq) duplicating Faycal's example, again i cant get it to converge.
Due to the large file size, I posted the model before mesh and solve i.e. Repeat_Faycal
Any comments or reason why i cant get them to run correctly?
Regards,
yang
Attachments:
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(-2*e*N*z*Cb/er*e0)*sinh(z*e*u/(k*T))
instead of
(-2*e*N*z*Cb/er*e0)*sinh(z*e*u/k*T).
Two more comments:
1. All your variables have no units. It is easy to make mistakes if you are solving complicated physical problems.
2. You used free mesh parameters to refine the mesh at all boundaries. This is totally unnecessary for such a simple problem.
Hope the attached file can help.
Best,
Hainan
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Thank you very much for looking through and correcting my code.
Sorry for the poor documentation of the file, i was trying to do a quick one to compare with Faycal's.
I go through the equation, i think i have another mistake, should be
(-2*e*N*z*Cb/(er*e0))*sinh(z*e*u/(k*T))
With the first correction (k*T), the profile is exponential.
But with the second correction (er*e0), the profile is linear again.
Regards,
yang
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e0=8.854*10^(-12) [A^2*s^4/(kg*m^3)]
You missed the minus sign... After correcting this, you will exponential drop. Be careful!
Hainan
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I have tried to reproduce your model with Helmholtz PDE model model. But I have not get the results obtained by you. Can you help me what is wrong with my model.
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i am working on dielectrophoresis of CNT and for that i need to solve the poisson's equation for the electrodes of any geometry in 3-D space.and export the solution to Matlab in a 200*200*200 grid.
can you tell me how can i solve this problem in comsol 4.0.
Regards
Gaurav