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How to implement discontinuity in derivative of electric potential across boundary?
Posted 21 janv. 2012, 17:49 UTC−5 Fluid & Heat, Studies & Solvers 3 Replies
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Hello,
I am building a model (in the general PDE mode of COMSOL 4.1) to simulate the behavior of a device using mixed ionic/electronic conductors. I'm using the generalized transport equation (Nernst-Planck) for all charge carriers, and the Poisson equation for the electric potential.
At the interface between two different materials, the relevant boundary condition for the electric potential is that the electric displacement field normal to the boundary is constant. Let's assume here that the direction normal to the boundary is the "x" direction. Therefore, since the electric displacement field is the electric field times the material's permittivity, and the electric field is simply the gradient of the electric potential, we can write this boundary condition in the following way:
e(left)*phi_x(left) = e(right)*phi_x(right)
... where e is the permittivity, phi is the electric potential, and phi_x is the component of the gradient of phi normal to the boundary. (left) and (right) indicate the position relative to the boundary.
Clearly, according to the above equation, when the permittivity changes at the interface between two materials, there will be a discontinuity in the derivative of the electric potential. However, I just can't figure out how to implement this in COMSOL.
How can I specify a discontinuity in the derivative of one of my dependent variables at a boundary? Please note that I am using the general PDE mode rather than one of the physics modules. I like to see what's going on under the hood, and since I'm working with diffusive transport as well as electric potential, it seemed best to keep things general.
I apologize if this is obvious or if it has already been asked -- I have tried my best to look around before posting.
Thanks!
John
I am building a model (in the general PDE mode of COMSOL 4.1) to simulate the behavior of a device using mixed ionic/electronic conductors. I'm using the generalized transport equation (Nernst-Planck) for all charge carriers, and the Poisson equation for the electric potential.
At the interface between two different materials, the relevant boundary condition for the electric potential is that the electric displacement field normal to the boundary is constant. Let's assume here that the direction normal to the boundary is the "x" direction. Therefore, since the electric displacement field is the electric field times the material's permittivity, and the electric field is simply the gradient of the electric potential, we can write this boundary condition in the following way:
e(left)*phi_x(left) = e(right)*phi_x(right)
... where e is the permittivity, phi is the electric potential, and phi_x is the component of the gradient of phi normal to the boundary. (left) and (right) indicate the position relative to the boundary.
Clearly, according to the above equation, when the permittivity changes at the interface between two materials, there will be a discontinuity in the derivative of the electric potential. However, I just can't figure out how to implement this in COMSOL.
How can I specify a discontinuity in the derivative of one of my dependent variables at a boundary? Please note that I am using the general PDE mode rather than one of the physics modules. I like to see what's going on under the hood, and since I'm working with diffusive transport as well as electric potential, it seemed best to keep things general.
I apologize if this is obvious or if it has already been asked -- I have tried my best to look around before posting.
Thanks!
John
3 Replies Last Post 24 juil. 2012, 03:33 UTC−4
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Posted:
1 decade ago
Hi
take a look how COMSOL implements their equations for a thin resistive layer (internal boundary) condition in HT. That should give you some ideas I expect
--
Good luck
Ivar
take a look how COMSOL implements their equations for a thin resistive layer (internal boundary) condition in HT. That should give you some ideas I expect
--
Good luck
Ivar
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Posted:
1 decade ago
Hi Ivar
I have a similar problem and I need your help.
I am modeling a two phase flow problem under electrostatic forces using moving mesh. The electrostatic force depends on the gradient in dielectric coefficient (relative permittivity) across the internal boundary between the two phases. The problem is that I get zero gradient although the values of the dielectric constant are very different (80 and1). I believe this is because the differentiation takes place in each domain separately and the dielectric coefficient is not differentiated across the internal boundary line. Do you have any suggestions?
By the way, when I use the level set (LS) model, I donot have this problem because the boundary itself has a finite thickness, but the problem with LS is that it is not suitable for very thin jets, where the LS interface thickness is compared with jet thickness itself.
Many thanks Ivar
Ahmed
I have a similar problem and I need your help.
I am modeling a two phase flow problem under electrostatic forces using moving mesh. The electrostatic force depends on the gradient in dielectric coefficient (relative permittivity) across the internal boundary between the two phases. The problem is that I get zero gradient although the values of the dielectric constant are very different (80 and1). I believe this is because the differentiation takes place in each domain separately and the dielectric coefficient is not differentiated across the internal boundary line. Do you have any suggestions?
By the way, when I use the level set (LS) model, I donot have this problem because the boundary itself has a finite thickness, but the problem with LS is that it is not suitable for very thin jets, where the LS interface thickness is compared with jet thickness itself.
Many thanks Ivar
Ahmed
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Posted:
1 decade ago
Hi Ivar
I'm doing such similar simulation about electrokinetics, and I also met a problem of interface of different materials.
I used Transport of diluted species model to govern the Nernst-Planck equation, and Electrostatics model to govern Poisson equation.
I believed that in the whole domain the current (or flux of species) should be uniform, but at the interface of two domains in which ions have different diffusivities and mobilities, the current is much higher or lower. Even though I meshed the model very well near the interface, it still changes sharply.
Need I add some other conditions?
many thanks
Mingjie
I'm doing such similar simulation about electrokinetics, and I also met a problem of interface of different materials.
I used Transport of diluted species model to govern the Nernst-Planck equation, and Electrostatics model to govern Poisson equation.
I believed that in the whole domain the current (or flux of species) should be uniform, but at the interface of two domains in which ions have different diffusivities and mobilities, the current is much higher or lower. Even though I meshed the model very well near the interface, it still changes sharply.
Need I add some other conditions?
many thanks
Mingjie