Let me see if I can line out my question a little better to hopefully get some sort of input. I am trying to understand where a type of boundary condition approx. called(adsbygoogle = window.adsbygoogle || []).push({}); stiff spring BCs. I have, among a couple of other examples, an example comsol "dialysis" model that uses it. I have been searching references for quite some time on this topic and I haven't been able to find anything that gives an adequate explanation (a full one) of where this approx. comes from and "how" it works. Even people I know who work with comsol all the time have not heard of this before:

how the "dialysis" model is set up: you define three separate concentrations for 3 regions, which you solve independently - c1 (region 1) c2 (region 2) and c3 (region 3). Region 1 (convection and diffusion of a gas moving through a fluid) is linked to region 2 (diffusion of a gas moving through a membrane) which is in turn linked to region 3 (convection and diffusion of a gas moving through a fluid). They are linked throughstiff spring BCs:

between region one and two (it is similar between regions 2 and 3):

(-D∇c1+c1u)⋅n=M(c2 - Kc1)--> (inward flux approx. on the c1 side)

(-Dm∇c2)⋅n=M(Kc1- c2)--> (inward flux approx. on the c2 side)

where:

*** Dm is the diffusivity of the gas in the membrane

*** D is the likewise in the fluid

*** K=c2/c1 is a partition coefficient derived from Henry's law (which I assume means that they are referring to the saturation concentrations under the conditions in question)

*** M is an arbitrary large (???) stiff spring velocity

I am trying to understand this approximation better and determine whether or not it is good to use in my case (I have two regions, a diffusive layer and a channel with convection and diffusion). ANY input that you could give at this point would be greatly appreciated (even if it's a guess or just pointing me in a certain direction given something similar that you've seen).

Questions:

- why does this work (I can guess intuitively from playing around with it, but I would rather not - I'd like a more complete explination)?
- where does it come from?
- how is it derived?

Notes:

- the documentation for the model in question if you would like to check it out: http://www.engineering.uiowa.edu/~cbe_217/Misc/dialysis.pdf
- this guy seems to have used stiff spring boundary conditions in the way that I would like to: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2678100/pdf/1742-4682-6-5.pdf
- another example of someone who used them: cds.comsol.com/access/dl/papers/1530/Clark.pdf
- I did some searching, and I've found other people with similar hesitations/problems:

http://www.comsol.se/community/forums/general/thread/6473

http://www.comsol.nl/community/forums/general/thread/3314

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# Stiff spring boundary conditions?

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