Discussion Forum

Dear Rutger,
I see your point.

In your model, only the domain condition (current conservation) is used. The tubes (the edges) will need an additional condition. In principle, this would go as follows:

In the tube, you've got a potential, with a potential gradient. Now, if you multiply this potential gradient (in the direction of the tube) with the tube's conductivity and the tube's cross section you get:

-Vx[V/m]*sigma[S/m]*A[m^2] = I[A].

As this current can leave and enter the tube along it's length, you have a current loss/gain per meter.

-Vxx[V/m^2]*sigma[S/m]*A[m^2] = I[A/m].

Where Vxx is the second order derivative of V in the direction of the tube.

Per meter of tube length, this is equal to the current that enters/leaves the domain around the tube. So in the domain, you can define (as an edge condition) a current source per meter length of the tube.

I've once implemented this as a weak contribution:
pi*wr^2*ws*-(V2Tx*test(V2Tx)+V2Ty*test(V2Ty)+V2Tz*test(V2Tz))
Here, "pi*wr^2" is the tube cross section and ws is the tube's conductivity.

The problem however, is that it's not mesh convergent. If you implement this, you will discover the conductivity of your bulk material depends on how fine the mesh is near the tubes. And it won't converge when your mesh goes to infinitely fine, because your tube is infinitely thin.

Alternatively,
You can model one single tube in different orientations, average the results and use that as an average material property:

Let's assume the tubes are evenly distributed, but their orientation is random (also evenly distributed). Let's say we've got one tube per cubic millimetre on average. I would model one cubic millimetre with one tube and use various orientations. If you average the results of these studies you can determine a kind of average bulk material property. You can use this average property for your macroscopic model.

In order to simplify the tube, I would use a triangular one with a swept mesh.
Please see the attached file for further details.

Kind regards,

If the conductivity of your fibres is orders of magnitude larger than the conductivity of the epoxy you can assume constant potential throughout every single fibre.
Or it would be more correct to say that you can do this when the resistance between any two points on the same fibre is orders of magnitude lower than the resistance between any two points on any two different fibres.

Indeed, we've tried that as well.
If I'm not mistaken, that implementation too resulted in singular behaviour.
So when you follow the equipotential implementation, please check for mesh convergence!

By the way, the geometry as implemented in the file I've uploaded earlier, doesn't require much more mesh elements than the edge implementation. I suppose this geometry is also suitable if you want 20+ tubes.

Hi Durk,

I am distributing CNT's inside a polymer, I solved the problems for meshing but i want to know "how to input tunneling properties between CNT's and tunneling between CNT's and my terminals". I like to find the resistance change in the model after application of force, because the CNT'S are moved closer to the contacts which should create conduction or tunneling effects. But there is no change in resistance after apply the force, still the CNT's are gone near the contacts..

I am bad in explaining, If you understood something please help to solve the problem..

I tried to attact the file but i cant. I m having the file, i can send it to you for checking...

Dear Laveen,

Please take into consideration the electric currents interface solves an ordinary diffusion equation (Poisson's equation or "heat" equation), for current conservation.

It treats the medium as well as the electrons as a continuum. Quantum mechanical effects like tunnelling are not included. At best, the electric currents interface, combined with solid mechanics and presumably, moving mesh is able to model an increase in conductivity just because the material is squeezed, resulting in a thinner insulator between your conductors. This should be a more-or-less linear effect.

Even so, the insulators and conductors are treated as a continuum: It's a macroscopic approach.

Please check if this is applicable in your case. Otherwise, it might be useful to investigate a Quantum approach. Perhaps the following tutorial model may be of use to you: www.comsol.com/model/conical-quantum-dot-723

Lastly, you could consider mimicking the tunnelling behaviour by including a strain dependent conductivity or something like that. It's a simplification, but perhaps it's good enough.

Thanks Durk.

I will check with moving mesh and also check with the example..

Thanks for your valauble suggestion.


Regards,
Laveen

Dear Laveen,

Please take into consideration the electric currents interface solves an ordinary diffusion equation (Poisson's equation or "heat" equation), for current conservation.

It treats the medium as well as the electrons as a continuum. Quantum mechanical effects like tunnelling are not included. At best, the electric currents interface, combined with solid mechanics and presumably, moving mesh is able to model an increase in conductivity just because the material is squeezed, resulting in a thinner insulator between your conductors. This should be a more-or-less linear effect.

Even so, the insulators and conductors are treated as a continuum: It's a macroscopic approach.

Please check if this is applicable in your case. Otherwise, it might be useful to investigate a Quantum approach. Perhaps the following tutorial model may be of use to you: www.comsol.com/model/conical-quantum-dot-723

Lastly, you could consider mimicking the tunnelling behaviour by including a strain dependent conductivity or something like that. It's a simplification, but perhaps it's good enough.