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Transport of diluted species and electrostatics

Posted 1 mar 2011, 21:33 GMT-5 Low-Frequency Electromagnetics, Chemical Reaction Engineering, Electrochemistry, Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers Version 4.0, Version 4.2, Version 4.3a 35 Replies

Nils Baumann

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Dear Community,

I am trying to combine the physics of the poisson equation (electrostatics) with the nernst-planck (transport of diluted species) in Comsol 4.1 for like 6 weeks now, and all I get is errors. Does anyone have experience with these two models combined?

Eventually I wanna model the concentration and potential and flux fields in a nanopore, but I took a step backwards, and just try to get the physics right, by modeling an electrical double layer next to a charged surface.

Some details on my model. I use the potential field from the electrostatics as input for the potential in the nernst-planck, and in return I defined a space charge density of F*(c-c2) (c and c2 being the electrolyte ions) for the electrostatics. That should be enough to couple the two physics, or am I wrong?
Moreover I have a -1 mC/m2 surface charge on one side and ground on the other side (just rectangle). Electrolyte concentrations are fixed on the ground side to 1 mM.

All I get as error is that the maximum number of newton iterations is reached and the solution is not converged. I tried a whole bunch of different initial conditions and solver configurations, but nothing is working.

Does anyone have any ideas?

Best
Nils

35 Replies Last Post 21 apr 2015, 03:43 GMT-4

R. F. Hamou

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Posted: 1 decade ago

Hi Nils,

It seems that your Physics is a bit wrong:
In the electrostatic module you have to set the space charge density equal to rho=N*e*z1*c1+N*e*z2*c2 as it is usually defined for an electrolyte containing ionic species c1 and c2.
N:Avogadro Number
z: valency
e: electron charge
c1, c2: ionic concentration (the variable used in the NP equation)

Your BCs seem correct.
You should start with low bulk concentration and low potential (or surface charge). However, increasing the potential or the concentration would need a refined mesh near the electrode!

If you face other problems, I can upload a V4.1 MPH file in which you can get the correct model.

I hope it helps

Cheers

Nils Baumann

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Posted: 1 decade ago

First, if you recall that F=N*e and that z1=1 and z2=-1, you recognize that I've been using the same model for the space charge density, as you propose. So this can't be the error.

Also, I tried using low surface charges (as low as 1e-8 C/m2) and a refined mesh at the electrode, but still I get only errors. It'd be nice, if you could upload a file to which I can compare my model.

Best
Nils

R. F. Hamou

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Posted: 1 decade ago

So, you have something wrong somewhere ;-).
The file is attached.

Good Luck

Attachments:

test41_EDL.mph

Nils Baumann

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Posted: 1 decade ago

Ok,

I looked at it and there are a couple of questions.

First, I see that your equation for rho is orange, which means that Comsol does not recognize it. Did you ever run this model?
Second, you're using an electric potential at one side, whereas I try to do it with a surface charge. Have you ever tried that?
Third, in the transport of diluted species physics under Diffusion and Migration you defined the electric potential as V. Don't you need to use the es/ccn1, i.e. the potential output from the electrostatics interface, to ensure that the physics are talking with each other?

Best
Nils

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago

Hi

one comment: orange is a warning of inconsistent units, no error as such,

but, I agree it's better to add units on the parameters because it's easier to check the formulas thereafter => proof:

If you push the units from the comment line back into the parameter list you will end up with all black formulas

EXCEPT for Deb = sqrt(.. where "eps0" not being defined any longer, as in v4 it's "epsilon0_const".

Apart from that I do not see anything specific to put in doubt.
Specially since Deb, referred to by eps0 seems not to be used either ;)

--
Good luck
Ivar

Nils Baumann

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Posted: 1 decade ago

What about the potential? Do you not need to couple the electrostatics to the transport of diluted species by using es/ccn1 (the output from the electrostatics) in the diffusion and migration part?

I found that in one of the tutorial models and it makes sense to me.

Best
Nils

R. F. Hamou

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Posted: 1 decade ago

Apart from that I do not see anything specific to put in doubt.
Specially since Deb, referred to by eps0 seems not to be used either ;)

Hi Ivar,
Thanks
Yes, because I had to remove many variables and things from the original file ;-) and also it was just a simple test for Nils!
I am discovering the 4.1 !! because I was not satisfied with the philosophy of Comsol 4!!! But now I have to follow you ;-))

Cheers

R. F. Hamou

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Posted: 1 decade ago

There is no need to couple!
It is already coupled via "V" in the NP equation and via "rho" in the electrostatic interface.

Nils Baumann

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Posted: 1 decade ago

Okay,

first, thanks for the help. However, when I changed everything to match with the previous upload, I don't get the right result. Now I don't get an error message anymore but the potential field and the concentration fields are uniform and zero or one respectively (same as starting values).

How can I upload a file, so that you can have a look at it and maybe catch an error? I see the attach file button, but nothing happens when I click on it.

Best
Nils

R. F. Hamou

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Posted: 1 decade ago

The upload in this forum needs the Flash, Silverlight or HTML5!! check your web browser ;-)

Nils Baumann

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Posted: 1 decade ago

Ok, here goes.

I looked over it again and cannot find any difference between my model and the other.

Thanks for the help.

Best
Nils

Attachments:

double layer axisymmetric.mph

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago

Hi

first of all it's easy to give a first estimate for the electric field, I believe it should rather start with a constant gradient of the type -0.1[V]*(1-z[1/um])

Then if you turn on the Results while solving of the Fully Coupled node you will see the progress, basically the system is highly unstable, your voltage gradient is destroid by the concetration explosion (going from 0 to 1e10 in one step. Are you sure you do not have a sign or a dimension issue in the space charge density, or in the transport case there ?

By adding a few probes more you can better see what is happening

--
Good luck
Ivar

Nils Baumann

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Posted: 1 decade ago

I'm sorry, i don't know what you mean by dimension issue. As for the sign, I don't think there is an error, but you can look for yourself in the file.

Also, if I check the plot while solving box, how do I add probes?

Thanks
Nils

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago

Hi

Probes are In the Definition Node try a right click

You have an issue with some dimensions tat make the solver go crazy, so "probing" it would help, I would probe C,c2 and V somewhere or along the axis, but you need a log scale !

Then you have the two coupled physics, you should check that thy solve independently and set initial conditions to their "static" solution, this often helps for the convergence.

Try to uncouple the charge feedback to ES by adding a *0 or disabling it to the charge distribution and solve only the ES, is it OK ? then add the CHDS to the solver but keep the ES uncoupled, is the result reasonable ?
and so on

Could it be that you have a scaling issue ? you can get more solver info is you turn on the "Detailed Log in the Advanced Solver node

--
Good luck
Ivar

R. F. Hamou

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Posted: 1 decade ago

Hi,

After three clicks, your model seems correct now!! But you are already near the limit of the validity of the PNP-EDL model.

Since that you were paying attention to the warnings concerning the units, so I think you should pay more attention to the writing of your mathematical expressions !!

# The mobilities UK and UC were wrong it is Dk/(R*T) or Dk/R/T but not Dk/R*T
# This is also valid for the expression of your UNITS like the R [J/mol/K] and not [J/mol*K]

And the main source of the problem was the expression of your volume charge density as I have claimed before ;-)) but...you were so confident

I let you discover the error by yourself !! This is kind of ...

Good luck man for the next ;-)

Cheers

Attachments:

double layer axisymmetric.mph

Nils Baumann

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Posted: 1 decade ago

Hm,
thanks man.
I did not know the thing with the units and expressions. But then, I"ve only been using Comsol for a couple of weeks now. So I guess it needs some time to learn your way around.

Also, I still don't understand what the problem with the space charge density was. As you had it in the file you uploaded, I had it before as well. Also, since F=N*e, I should have got it right, in my file. Can you please explain, why you think my space charge density was incorrect?

I appreciate it
Nils

R. F. Hamou

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Posted: 1 decade ago

Also, I still don't understand what the problem with the space charge density was. As you had it in the file you uploaded, I had it before as well. Also, since F=N*e, I should have got it right, in my file. Can you please explain, why you think my space charge density was incorrect?

;-)) I was just kidding !! There was no problem with the charge density! I just wanted to make you understand that you should be careful when editing expressions. Try to Avoid compact formulation, i.e., charge density, express your formulas as they are written in the text book or even as in the Comsol equations. This would help you in detecting errors. Keep the use of "z" even if it is equal to 1!!

However, the error was the wrong expression of the mobility! That's it. This caused you a problem of convergence. In other words, you were not solving the NP equation but something else!! This means that the Boltzmann distribution (ZF/RT) which is the center of your migration part was missing or kaput ;-)

Cheers

Pooria Mostafalu

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Posted: 1 decade ago

Hi

Could you solve your problem? I wan to simulate cyclic voltametry , but when I apply voltage with electrostatics or other AC/DC module I did not gain reasonable result, how can relate these module?

Thank you

Nils Baumann

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Posted: 1 decade ago

Well,
partly. I could solve my problem for a simple geometry (i.e. an electrical double layer).

I assume you're combining Electrostatics and Transport of Diluted Species?

First you need to make sure that the electrical potential has the same name in both physics, typically V.
Second, you need to define a space charge density in the electrostatics interface, defined as rho = Sum (ziCi). Z = charge number, C= concentration.

Also, you need to refine the mesh at the electrode to make sure that the electrical double layer is accurately modelled.
When you're doing CV, I am sure you need to define the surface concentrations at the electrides, including the redox potential of your molecule. That has been done in the past (look up some papers).
Also you need to define a scan rate (you can do that in parameters) and define the potential at your electrode as scan rate * t (of course you need to make a time dependent study).

Hope that helps

Best
Nils

Pooria Mostafalu

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Posted: 1 decade ago

Hi Nills

Thank you so much for your fast response, I am not professional in COMSOL. yes I combine Electrostatics and Transport of Diluted Species, as you said I applied charge surface density in electrode but this boundary could not accept because in that boundary I applied volatage . my geometry is 2D, and my electrode is a line without thickness so It was not effective!! I think COMSOL do not understand redox . I am right? If you could send me your model may be I can understand more. my problem is:[my comsol is 4.0 version]

1- 2 module are not relate.
2-I could not set redox and double layer .

I would be Thankful I you help me.

Nils Baumann

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Posted: 1 decade ago

Hm...
what did you set the out of plane thickness to? If that's to small that's gonna be a problem. Put at least 1 mm in there, better 1 m, or go to a axialsymmetric geometry.

Second, I can not send you the file, as it will not help you, if you have 4.0. I doubt that you can open it. If you wanna have a look anyway, use the file that someone uploaded here earlier.

Good luck

Best
Nils

JS Shen

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Posted: 1 decade ago

Hi:
I tried to model ionic current flowing through a nanochannel with non-uniform surface charge. My model is 2D axis-symmetric having KCl as electrolyte with voltage applied across the nanochannel. I want to perform integration over the upper or lower boundary to know the flux, but do not know how to do so in 2-D axis-symmetric case (since it's not simply a line integration anymore..)
Also, some literature says to use weak constraint along with Lagrange multiplier could help calculating flux.. Could anyone please explain in more detail how to implement that? Thank you!

Niya Sa

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Posted: 1 decade ago

Ok, here goes.

I looked over it again and cannot find any difference between my model and the other.

Thanks for the help.

Best
Nils

Hi, Nils

I have a question based on the "double layer axisymmetric" model u uploaded. Why the initial values under transport of diluted species was not set? In this model it seems that c and c2 are set as 0. I am wondering is this supposed to be 1 mM?

Niya

Yihua Luo

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Posted: 1 decade ago

Hi Nils,

It seems that your Physics is a bit wrong:
In the electrostatic module you have to set the space charge density equal to rho=N*e*z1*c1+N*e*z2*c2 as it is usually defined for an electrolyte containing ionic species c1 and c2.
N:Avogadro Number
z: valency
e: electron charge
c1, c2: ionic concentration (the variable used in the NP equation)

Your BCs seem correct.
You should start with low bulk concentration and low potential (or surface charge). However, increasing the potential or the concentration would need a refined mesh near the electrode!

If you face other problems, I can upload a V4.1 MPH file in which you can get the correct model.

I hope it helps

Cheers

Dear Sir:
I am now trying to build a model about ion transportation inside a molding compound of a microelectronic package
due to the migration and diffusion effect under electric bias.I kinda have the same trouble as the guy had.I coupled the poisson equation and Nernst-Planck Eqution and the result shows error.I guess I must be set something wrong.Since you mention a V4.1 MPH file in which we can see the similar model,could you please send one copy to me ?Thanks a lot!

Purushottam Tiwari

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Posted: 1 decade ago

Dear R. F. Hamou,
I am new user to COMSOL. While reading the forum discussions at the aim of learning how to model the systems, I found "test41_EDL" model. I tried to do the same thing but my result came out different than the one posted. Could you please help me why this happened? I couldn't figure out the problem. I have attached my model herein.
Thank You

Attachments:

Rectangular box.mph

Purushottam Tiwari

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Posted: 1 decade ago

I got it. I forgot to assign domain for the space charge density.

Fatemeh Bahmani

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Posted: 1 decade ago

I am trying to solve the PNP and Navier-Stokes equations in a nanochannel. There are two reserviors on the left and right and the nanochannel is in the middle. I am using COMSOL 4.4. I have added Fluid flow physics ( Laminar, stokes flow: creeping flow), Nernst-Plank and electrostatic physics. But the simulation does not converge. There should be something wring with the Nernst-Plank simulation. I tested the fluid flow simulation separately and it worked perfectly. Could anyone look at my simulation and help me.

Attachments:

channel1.mph

Lasse Murtomäki

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Posted: 1 decade ago

You have two electric potentials, V and V2. Nernst-Planck equation assumes electroneutrality but you apparently wish to have electroosmosis, as you have assigned surface charge in the nanochannel. That creates an electric double layer which violates electroneutrality and thus N-P equation. I also noticed that the space charge density condition was not assigned to the domain.

I have not made any electroosmosis simulations myself, but there must plenty of models available. I would use transport of diluted species, activate both migration and convection, take the electric potential for the former from electrostatics and the flow field for the latter from creeping flow.

wish this helps
lasse

Fatemeh Bahmani

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Posted: 1 decade ago

Thank you very much, it was great help. I need to have 30 grid points across the nanochannel to make sure that I capture the EDL correctly, is it possible in COMSOL that I can generate virtual boundaries and make a finer mesh inside the channel and around the corners?
, and one more question is that should I necessarily specify a pressure for the inflow boundary? how if I just assume zero pressure for the inflow?

Lasse Murtomäki

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Posted: 1 decade ago

Meshing is of course possible, look at the boundary mesh.

About the zero pressure, I am not quite sure, but there are the boundary conditions "Open Boundary" and "Inlet". In the former Normal stress to 0 N/m^2 (= Pa!), the latter Pressure, no viscous stress 0 Pa.

Fatemeh Bahmani

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Posted: 1 decade ago

Thank you Lasse, could you help me how to create a boundary layer mesh for the geometry which I have. I need to have 30 meshes in the EDL adjacent to the charged surface and stretch the mesh out toward the center of the channel.
Thank you

Lasse Murtomäki

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Posted: 1 decade ago

Your model is axisymmetric, i.e. de facto 3D. Attached a file with two alternative meshes. Enjoy!

Lasse

Attachments:

channel_mesh.mph

Fatemeh Bahmani

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Posted: 1 decade ago

Thank you very much Lasse.

Fatemeh Bahmani

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Posted: 1 decade ago

Does anybody have any experience with convergence problems for nanofluidics simulation? I set number of iteration =140 and the error goes down to 1e-6, but the simulation returns no solution and reports convergence problems. Does anybody have an idea how to adjust the parameters to get convergence? My simulation is attached.

Attachments:

channel_mesh_refined.mph

Tanaya Dhar

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Posted: 10 years ago

hello ivar
i was trying to model streamer discharge in a needle-plane configuration in axis 2D symmetric space.
i could not run my model. i would like to give the modelling details to you, so plz read it and give me your suggestions if you see any error i commited.
My model description:

one poisson's equation
and three continuity equations
do i need to couple them or they will automatically get coupled via variables that i would define
plz tell
will the fine meshing at needle tip will solve the problem of singularity

Thanks

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Transport of diluted species and electrostatics

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