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[Help] AC electroosmosis, defining the electrode-electrolyte boundary condition

Posted 2 nov 2009, 03:13 GMT-5 10 Replies

Wee Yang NG
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Dear all,

I am working on a 2D AC electroosmosis problem, the model consists of a pair of electrodes.
The models which I adopt are (1) Conductive DC media, and (2) Incompressible Navier-Stoke.
I have some difficulties in defining the boundary conditions at the electrodes.

Electrode BC (for Conductive DC media):
cond n dphi/dy=iwC_DL (phi-V_applied)
Electrode BC (for Incompressible Navier-Stoke):
u_slip=-eA/4n d|phi-V_applied|^2/dx
(refer to document for equations)

I would like to write the above two equations in COMSOL.
Any advice would be deeply appreciated.

Best Regards,
yang

Reference:
Loucaides N., Ramos A., Georghoiu G.E., Novel systems for configurable AC electroosmotic pumping, Microfluidics and Nanofluidics, Vol3, pp709-714, 2007. www.springerlink.com/content/171127n275151g66/

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10 Replies Last Post 8 feb 2016, 05:37 GMT-5
Tom Myers
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Posted: 2 decades ago 3 nov 2009, 06:21 GMT-5
Dear Yang,

This is an interesting problem. I am a microfluidics researcher and have been working on similar problems.


I have some difficulties in defining the boundary conditions at the electrodes.

Electrode BC (for Conductive DC media):
cond n dphi/dy=iwC_DL (phi-V_applied)
Electrode BC (for Incompressible Navier-Stoke):
u_slip=-eA/4n d|phi-V_applied|^2/dx
(refer to document for equations)


Where does your difficulty lie? You have posed quite a general question.

I would be uncertain of how to implement derivative terms in the boundary condition. How are you extracting the other terms in your equations from your model, boundary integration? This paper provides some interesting further reading:


Green NG, Ramos A, Gonzalez A, Morgan H, Castellanos A (2002)
Fluid flow induced by nonuniform ac electric fields in electrolytes
on microelectrodes iii Observation of streamlines and
numerical simulation. Phys Rev E 66:026305


I am interested in finding a solution to this - so keep me in the loop.

Regards,
Tom
Dear Yang, This is an interesting problem. I am a microfluidics researcher and have been working on similar problems. [quote] I have some difficulties in defining the boundary conditions at the electrodes. Electrode BC (for Conductive DC media): cond n dphi/dy=iwC_DL (phi-V_applied) Electrode BC (for Incompressible Navier-Stoke): u_slip=-eA/4n d|phi-V_applied|^2/dx (refer to document for equations) [/quote] Where does your difficulty lie? You have posed quite a general question. I would be uncertain of how to implement derivative terms in the boundary condition. How are you extracting the other terms in your equations from your model, boundary integration? This paper provides some interesting further reading: [quote] Green NG, Ramos A, Gonzalez A, Morgan H, Castellanos A (2002) Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes iii Observation of streamlines and numerical simulation. Phys Rev E 66:026305 [/quote] I am interested in finding a solution to this - so keep me in the loop. Regards, Tom
Wee Yang NG
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Posted: 2 decades ago 6 nov 2009, 01:29 GMT-5
Dear Tom,

Thanks for your reference :)

I tried to write the boundary conditions according to the paper that i mentioned (Loucaides et al. 2007).
My solution does not converge, and the unconverged results vary on different runs.
My guess could be that I didnt write the boundary conditions correctly on the electrodes.

Below are the BC that i used:

Conductive DC Media (dc)
BC: Inward Current Flow
Electrode1: Jn = -(zeta-Vpp)/Zdl
Electrode2: Jn = -(zeta+Vpp)/Zdl
where Zdl = 1/i*2*pi*f*Cdl (its in complex form)

Incompressible Naiver-Stokes (mmglf)
BC: Inflow/Outflow velocity
Electrode1: u = -eo*er*A*(zeta-Vpp)*Ex_dc/eta
Electrode2: u = -eo*er*A*(zeta+Vpp)*Ex_dc/eta

Refer to the attached document for the schematics/equations.
I look forward to any suggestions and comments, many thanks in advance.

Best Regards,
yang
Dear Tom, Thanks for your reference :) I tried to write the boundary conditions according to the paper that i mentioned (Loucaides et al. 2007). My solution does not converge, and the unconverged results vary on different runs. My guess could be that I didnt write the boundary conditions correctly on the electrodes. Below are the BC that i used: Conductive DC Media (dc) BC: Inward Current Flow Electrode1: Jn = -(zeta-Vpp)/Zdl Electrode2: Jn = -(zeta+Vpp)/Zdl where Zdl = 1/i*2*pi*f*Cdl (its in complex form) Incompressible Naiver-Stokes (mmglf) BC: Inflow/Outflow velocity Electrode1: u = -eo*er*A*(zeta-Vpp)*Ex_dc/eta Electrode2: u = -eo*er*A*(zeta+Vpp)*Ex_dc/eta Refer to the attached document for the schematics/equations. I look forward to any suggestions and comments, many thanks in advance. Best Regards, yang

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Tom Myers
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Posted: 2 decades ago 7 nov 2009, 16:27 GMT-5
Dear Yang,

Would you be willing to share your COMSOL model with me?

Regards,
Tom
Dear Yang, Would you be willing to share your COMSOL model with me? Regards, Tom
Xin Guo
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Posted: 2 decades ago 10 nov 2009, 16:41 GMT-5
Hi,

I followed the paper in the past as well, but what I used was the model of "electrostatic" or "PDE coeff form" directly. I did not try to use"conductive media DC" to solve this problem before. I m wondering how you define the subdomain for the electric problem so as to solve phi (i.e. zeta in ur own equations) with ur BCs? What I can figure out at this moment is that the gradient of phi should not be zero at non electrodes, but the normal factor is zero. Also, ur Jn eqn at electrode boundaries seems not to establish a pde for solving phi at electrodes, so the subdomain function (supposed to be the laplace eqn involving phi) is not associated with boudnary conditions. That is my opinion and I am still new to Comsol too.

Regards
Hi, I followed the paper in the past as well, but what I used was the model of "electrostatic" or "PDE coeff form" directly. I did not try to use"conductive media DC" to solve this problem before. I m wondering how you define the subdomain for the electric problem so as to solve phi (i.e. zeta in ur own equations) with ur BCs? What I can figure out at this moment is that the gradient of phi should not be zero at non electrodes, but the normal factor is zero. Also, ur Jn eqn at electrode boundaries seems not to establish a pde for solving phi at electrodes, so the subdomain function (supposed to be the laplace eqn involving phi) is not associated with boudnary conditions. That is my opinion and I am still new to Comsol too. Regards
Wee Yang NG
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Posted: 2 decades ago 11 nov 2009, 21:08 GMT-5
Dear All

Sorry for the late response, and thank you so much for your interest in the problem.

Re Tom: I attached the model for your reference.

Re Guo Xin: I think electrostatic (es), laplace (lpeq), conductive dc media (dc) are similiar, i am not familiar with PDE coeff form (c). The reason that i choose conductive dc media is because i can change the conductivity value easier.

Your interest and help is greatly appreciated.

Regards,
yang
Dear All Sorry for the late response, and thank you so much for your interest in the problem. Re Tom: I attached the model for your reference. Re Guo Xin: I think electrostatic (es), laplace (lpeq), conductive dc media (dc) are similiar, i am not familiar with PDE coeff form (c). The reason that i choose conductive dc media is because i can change the conductivity value easier. Your interest and help is greatly appreciated. Regards, yang

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Neophytos Loucaides
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Posted: 1 decade ago 11 dic 2009, 04:23 GMT-5
If a boundary condition contains a pde you have to use weak form to get correct results, i.e. you have to solve the Laplace equation with the continuity PDE relating the derivative of the potential on the edge of the double layer using the weak form mode. Therefore, you can not solve this problem using the conductive dc media mode.
The Comsol Modeling guide has a chapter , page 345 in my version, on how to convert to weak form.

Regards,
Dr Neophytos Loucaides
If a boundary condition contains a pde you have to use weak form to get correct results, i.e. you have to solve the Laplace equation with the continuity PDE relating the derivative of the potential on the edge of the double layer using the weak form mode. Therefore, you can not solve this problem using the conductive dc media mode. The Comsol Modeling guide has a chapter , page 345 in my version, on how to convert to weak form. Regards, Dr Neophytos Loucaides
Wee Yang NG
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Posted: 1 decade ago 14 dic 2009, 02:34 GMT-5

If a boundary condition contains a pde you have to use weak form to get correct results, i.e. you have to solve the Laplace equation with the continuity PDE relating the derivative of the potential on the edge of the double layer using the weak form mode. Therefore, you can not solve this problem using the conductive dc media mode.
The Comsol Modeling guide has a chapter , page 345 in my version, on how to convert to weak form.

Regards,
Dr Neophytos Loucaides


Hi Dr Loucaides,

You are the best person to address my question, as the paper i am following is written by you :)
Thank you for you tip, i am now studying the weak form chapter.
Just a quick check, is it possible to use a weak constraints in the existing conductive DC media mode rather then converting all to weak form mode?
I hope to communicate with you further on this topic.

With Best Regards,
yang
[QUOTE] If a boundary condition contains a pde you have to use weak form to get correct results, i.e. you have to solve the Laplace equation with the continuity PDE relating the derivative of the potential on the edge of the double layer using the weak form mode. Therefore, you can not solve this problem using the conductive dc media mode. The Comsol Modeling guide has a chapter , page 345 in my version, on how to convert to weak form. Regards, Dr Neophytos Loucaides [/QUOTE] Hi Dr Loucaides, You are the best person to address my question, as the paper i am following is written by you :) Thank you for you tip, i am now studying the weak form chapter. Just a quick check, is it possible to use a weak constraints in the existing conductive DC media mode rather then converting all to weak form mode? I hope to communicate with you further on this topic. With Best Regards, yang
Neophytos Loucaides
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Posted: 1 decade ago 14 dic 2009, 03:03 GMT-5
From what I am aware of, no. If you want to have a PDE on a boundary you have to use the Weak form.
From what I am aware of, no. If you want to have a PDE on a boundary you have to use the Weak form.
naheed ferdous
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Posted: 1 decade ago 10 mar 2011, 09:48 GMT-5
Dear all,
I am having difficulty to model the AC electroosmosis whether it is equilibrium or non equilibrium method.
what models do i suppose to take for these poisson, nernst plank and navier stokes equation?
how do i place the boundary conditions?


How do i create an AC field?

please help
i am in great danger
Dear all, I am having difficulty to model the AC electroosmosis whether it is equilibrium or non equilibrium method. what models do i suppose to take for these poisson, nernst plank and navier stokes equation? how do i place the boundary conditions? How do i create an AC field? please help i am in great danger

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Abraham Mansouri
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Posted: 9 years ago 8 feb 2016, 05:37 GMT-5
Hi Yang

sub: electrode boundary condition

My problem is a pressure driven flow inside a microchannel, that generates ionic current due to
electric double layer formation. there is no external electric field. I solve Poisson Nernst Planck equations along with Navier Stokes, in my case ionic current is (velocity)w*(np-nn) (net charge density),

What I want to model is the "streaming current measurement, no potential exists in streaming current mode due to electrodes", when in practice we put two electrodes at the ends of channel....how can I change the streaming potential modeling to streaming current modeling? I need an electrode boundary condition at exit ? thats my problem now, can you help?

thank you
Abraham



QUOTE]

If a boundary condition contains a pde you have to use weak form to get correct results, i.e. you have to solve the Laplace equation with the continuity PDE relating the derivative of the potential on the edge of the double layer using the weak form mode. Therefore, you can not solve this problem using the conductive dc media mode.
The Comsol Modeling guide has a chapter , page 345 in my version, on how to convert to weak form.

Regards,
Dr Neophytos Loucaides


Hi Dr Loucaides,

You are the best person to address my question, as the paper i am following is written by you :)
Thank you for you tip, i am now studying the weak form chapter.
Just a quick check, is it possible to use a weak constraints in the existing conductive DC media mode rather then converting all to weak form mode?
I hope to communicate with you further on this topic.

With Best Regards,
yang


Hi Yang sub: electrode boundary condition My problem is a pressure driven flow inside a microchannel, that generates ionic current due to electric double layer formation. there is no external electric field. I solve Poisson Nernst Planck equations along with Navier Stokes, in my case ionic current is (velocity)w*(np-nn) (net charge density), What I want to model is the "streaming current measurement, no potential exists in streaming current mode due to electrodes", when in practice we put two electrodes at the ends of channel....how can I change the streaming potential modeling to streaming current modeling? I need an electrode boundary condition at exit ? thats my problem now, can you help? thank you Abraham QUOTE] [QUOTE] If a boundary condition contains a pde you have to use weak form to get correct results, i.e. you have to solve the Laplace equation with the continuity PDE relating the derivative of the potential on the edge of the double layer using the weak form mode. Therefore, you can not solve this problem using the conductive dc media mode. The Comsol Modeling guide has a chapter , page 345 in my version, on how to convert to weak form. Regards, Dr Neophytos Loucaides [/QUOTE] Hi Dr Loucaides, You are the best person to address my question, as the paper i am following is written by you :) Thank you for you tip, i am now studying the weak form chapter. Just a quick check, is it possible to use a weak constraints in the existing conductive DC media mode rather then converting all to weak form mode? I hope to communicate with you further on this topic. With Best Regards, yang [/QUOTE]

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