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Anybody ??

Hi,
I think some more information is warranted. I am trying to model deposition inside a 100 nm dia. pore and trying to determine the final pore shape (conformal or non-conformal) I am using COMSOL 4.3. I am employing two physics-

(1) Transport of Diluted Species- The flux on the pore walls i.e the BC is set to be equal to k*c (mol/m^2.s), which is the first order rate expression.

(2) Moving Mesh- Used to convert the reaction rate to a mesh velocity by multiplying it with molar volume of the deposited species

Since the deposition process is carried out at very low pressures and since the pore radius is very small I have to use a Knudsen diffusion coeff. instead of a continuum diffusion coeff. This coeff value varies as material deposits in the pore and as the pore becomes narrower and narrower making it more difficult for reactant species to diffuse inside.

I have been successful in simulating the deposition profiles with a constant diffusion coeff and the results are consistent with the theory. But i have been unable to define a variable diffusion coefficient.

Can anybody guide me to a useful resource or some example ?

Thank you for your help
Sanket

Hi

do not forget when the scales goes really down as for you case, your molecules become amost at the size of the mesh, then one could ask oneself if the "coninuum" hypothesis of FEM is still respected, or if one should rather use some molecular simulation methods

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Good luck
Ivar

Hi Ivar,

Thank you for your response. Indeed, you are right that using continuum assumption for nanometric length scale is indeed a stretch. Basically there are two approaches to model deposition in nanoscale features-

(1) Free molecular models- These models consider molecular collisions of the reacting molecules with the feature walls, in this case a certain fraction of the colliding molecules "stick" to the walls and contribute to the material on the wall. This is controlled by a "sticking coefficient" . This is the rigorous approach. I am mainly an experimentalist and I don't have assess to these sophisticated models.

(2) Continuum-like Models- This model assumes continuum behavior inside the features and uses a Knudsen diffusion coefficient instead of a continuum diffusion coefficient. Although the assumption is not fully correct, this model has been used in many studies as it is easy to implement and gives analogous results to the free molecular models.

I have been getting pretty good results using a relatively simple model. In this model the diffusion coefficient that I am employing is close to an average Knudsen diffusion coeff value. I have calculated this value at halfway closure of the pore. Now, I want to be more exact and incorporate a diffusion ceofficient which changes with the pore radius. This will be a cross-section averaged value.

I am thinking of incorporating a PDE physics into my model. This PDE equation will describe the mesh velocity. I think I should be able to find out the thickness of the material deposited by integrating this equation along the reacting boundary. Is this the right approach ? I am not sure if there is an easier way out.

Thank you,
Sanket

Hi

I'm working definitively in 2) contiuum models so I do not feel reall competent for your 1) case,
but talking about sticking, you have the particle module that allows you to play with that kind of features ;)

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Good luck
Ivar

Hi

I'm working definitively in 2) contiuum models so I do not feel reall competent for your 1) case,
but talking about sticking, you have the particle module that allows you to play with that kind of features ;)

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Good luck
Ivar

Hi Ivar,

I think I have not explained the problem properly. I am working with continuum hypothesis and my problem is essentially a continumm diffusion/Reaction problem. My question is pretty broad-based and I think it applies irrespective of the fact whether the features are small or not. This is a broad-based problem statement.

Consider diffusion in a pore with reactive pore walls (say catalyst coated). Material diffuses to this wall and reacts with it and deposits on it. Due to deposition of material the pore gets constricted and the pore radius keeps on decreasing. In such circumstances, I have the following questions-

(1) How do I create a variable that can track the thickness of the material deposited inside the pore as a function of z (depth inside the pore) ? Constantly changing geometry is another complication here. There is a custom-built variable called " thickness" in the electrodeposition module. But how can I incorporate a similar variable in my model ? I have tried different in-built variables, but none of them seem to do the job.

(2) Should I add "PDE" physics to my model to track the thickness ? I am thinking of adding an expression like (du/dt = k*c*rho) where u is the thickness of the deposited material. My initial efforts in this area have not yielded any results yet . Is there an easier way to deal with this problem ?

Thank you for your time,
Sanket

Hi

This is really not my "pot of tea" as domain, among other because I lack the module I believe you should study closer here: electro-deposition, where you have also geometry changes (probably with the DG physics)

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Good luck
Ivar