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Modelling diffusion-reaction equation with two diffusion terms

Trygvi Zachariassen Laksafoss

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I am currently trying to model the movement of bacteria cells using diffusion reaction equations. I have had great success using the "Transport of diluted species" where only one diffusion term was nessesary, but we want to model the phenomena called Chemotaxi which can be modelled using two diffusion terms. The PDE for cell concentration has a standard diffusion term describing the spatial spreading of cells and an additional diffusion term describing the movement of cells towards a concentration of chemoattractant. The equation excluding growth terms and other is: . My challenge is how to implement the second diffusion term which is based on the gradient of the concentration of the chemoattractant S. Is it possible to model it using the "Transport of diluted species" physics module, or do i have to move to equation based modelling?

Thanks in advance, Trygvi


4 Replies Last Post Feb 19, 2019, 4:17 AM EST

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Posted: 1 year ago Feb 13, 2019, 11:07 PM EST

Hi Tygvi, If it was me I would set up 2 dependent variables: bacteria and chemoattractant. That way I can describe the diffusion of each separately. Or if their transport mechanism is different, for example if only chemoattractant can be transported by both convection and diffusion, I would set up 2 separate transport of diluted species physics, one discribing bacteria the other chemoattractant. Good luck

Claire

Hi Tygvi, If it was me I would set up 2 dependent variables: bacteria and chemoattractant. That way I can describe the diffusion of each separately. Or if their transport mechanism is different, for example if only chemoattractant can be transported by both convection and diffusion, I would set up 2 separate transport of diluted species physics, one discribing bacteria the other chemoattractant. Good luck Claire

Trygvi Zachariassen Laksafoss

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Posted: 1 year ago Feb 14, 2019, 3:24 AM EST

Hi Claire, thanks alot for the reply. I do have a separate dependant variable describing the change and diffusion of chemoattractant which works correctly. It is only the diffusion of the bacteria that cause issue. From the equation mentioned, the diffusion of cells is dependant on two gradients, the cells and chemoattractant. I have not yet found a way to have two diffusion terms in one equation using the COMSOL interface, but i am looking into using equation based mdoelling which might solve the issue.

Trygvi

Hi Claire, thanks alot for the reply. I do have a separate dependant variable describing the change and diffusion of chemoattractant which works correctly. It is only the diffusion of the bacteria that cause issue. From the equation mentioned, the diffusion of cells is dependant on two gradients, the cells and chemoattractant. I have not yet found a way to have two diffusion terms in one equation using the COMSOL interface, but i am looking into using equation based mdoelling which might solve the issue. Trygvi

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Posted: 1 year ago Feb 14, 2019, 10:37 AM EST
Updated: 1 year ago Feb 14, 2019, 1:03 PM EST

Hi,

I presume you could still use the transport in dilute species, only additional step being adding a "reaction" or "species source" term in the domain contribution. Because the units are consistent, i.e. mol/m3/s.

I do not know your terms well, but for demonstration purposes, let us simplify your extra diffusion term as:

grad.(De*gradS) - where De is some effective coefficient, then in the above domain contributions (either reaction or species source), you can just type:

d(De*d(S,x),x)+d(De*d(S,y),y)

Alternatively, you can also use weak form (domain contribution), if you want to, for which you can refer to the user manual.

So effectively, you are augmenting equation based modelling with the existing module to minimize your work.

The above is in 2D, so you can extend it to 3D. But be careful with 2D axisymmetric because you will need to add additional terms, which I did not discuss.

I am sorry, if this turns out to be wrong.

Suresh

Hi, I presume you could still use the transport in dilute species, only additional step being adding a "reaction" or "species source" term in the domain contribution. Because the units are consistent, i.e. mol/m3/s. I do not know your terms well, but for demonstration purposes, let us simplify your extra diffusion term as: grad.(De\*gradS) - where De is some effective coefficient, then in the above domain contributions (either reaction or species source), you can just type: d(De\*d(S,x),x)+d(De\*d(S,y),y) Alternatively, you can also use weak form (domain contribution), if you want to, for which you can refer to the user manual. So effectively, you are augmenting equation based modelling with the existing module to minimize your work. The above is in 2D, so you can extend it to 3D. But be careful with 2D axisymmetric because you will need to add additional terms, which I did not discuss. I am sorry, if this turns out to be wrong. Suresh

Trygvi Zachariassen Laksafoss

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Posted: 1 year ago Feb 19, 2019, 4:17 AM EST

Hi Suresh

Thanks a bunch for your reply. Your solution makes sense and i also think i should work. I'll try it out and report back.

Cheers Trygvi

Hi Suresh Thanks a bunch for your reply. Your solution makes sense and i also think i should work. I'll try it out and report back. Cheers Trygvi

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