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Concentration boundary condition - v 3.5a

Posted Apr 27, 2011, 12:26 p.m. EDT Modeling Tools & Definitions, Parameters, Variables, & Functions Version 3.5a 2 Replies

J
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Hello there,

I have a question regarding a concentration boundary condition.

In COMSOL version 3.5a, if you take the "Convection and Diffusion" module and you go to "Boundary settings" you'll see that if one wants to impose a "concentration" as BC, the value of the concentration is expressed in mol/m^3 (in my case I am working with a 2D-axialsymmetric model but with a 3D case it's the same). Since we are talking of a boundary (a surface in 3D) shouldn't be mol/m^2?

I asked Comsol support and I got this answer that still left me a bit puzzled:

The unit of the concentration variable is mol/m^3. If you integrate it in space, in 3D, you get the number of moles of the substance. When you set the concentration you specify the concentration on that boundary (in mol/m^3). If that is integrated on that surface you get mol/m. This can be interpreted as the number of moles per m distance in the out of plane direction. That is if you extrude that surface 1m, the volume created would contain 1mol.

This explanation is still not clear to me. Do you have a "clearer" explanation? And in the case of a 2D-axialsymmetric geometry?

Any suggestion is more than welcome,

J
2 Replies Last Post May 21, 2011, 10:49 a.m. EDT
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Apr 27, 2011, 3:04 p.m. EDT
Hi

do not forget that "D is only a simplified 3D in the sense that the third dimension "Z", our out of paper direction, is assumed to have a dimension of 1[m], hence all values are given in per meter.

If you are in 2D-axi, you have cylindrical dimensions, and the "depth" or "phi" direction (still out of paper) is defined by the value "2*pi*r" what I often call the "loop length"

So an edge in 2D is in fact an area of 1[m] depth, just like an edge in 2D-axi has a depth of 2*pi*r (which might vary, and is only constant if we consider vertical edges at r=cte)

Hope this helps ;)

--
Good luck
Ivar
Hi do not forget that "D is only a simplified 3D in the sense that the third dimension "Z", our out of paper direction, is assumed to have a dimension of 1[m], hence all values are given in per meter. If you are in 2D-axi, you have cylindrical dimensions, and the "depth" or "phi" direction (still out of paper) is defined by the value "2*pi*r" what I often call the "loop length" So an edge in 2D is in fact an area of 1[m] depth, just like an edge in 2D-axi has a depth of 2*pi*r (which might vary, and is only constant if we consider vertical edges at r=cte) Hope this helps ;) -- Good luck Ivar
J
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Posted: 1 decade ago May 21, 2011, 10:49 a.m. EDT
Thanks for your reply Ivar, and sorry for my late one.

I understand what you say, and of course I know that in 2D every edge in reality is a surface with 1 m depth. The point is that in 3D the boundary is a surface and therefore you can count the number of molecules on this area, giving then an area-density of mol/m^2.

I still don't grasp why we define the boundary concentration as mol/m^3.

Thanks for your reply.

J
Thanks for your reply Ivar, and sorry for my late one. I understand what you say, and of course I know that in 2D every edge in reality is a surface with 1 m depth. The point is that in 3D the boundary is a surface and therefore you can count the number of molecules on this area, giving then an area-density of mol/m^2. I still don't grasp why we define the boundary concentration as mol/m^3. Thanks for your reply. J

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