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Hello Michael Z

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Okay, maybe if I line my question a little better, someone will know what I am talking about:

I am wondering about this example "dialysis" model: www.comsol.com/showroom/gallery/258/ (convection and diffusion / diffusion model)
- it uses something called "stiff-spring" (SS) boundary conditions. I know that stiff spring conditions let the model deal with the "jump" in concentrations that has to do with the difference in solubilities for the gas moving between the different regions - I am just wondering how this particular set of BCs derived and works. I have looked through the two references that were listed in the model's documentation, and I could find no references to such BCs for this kind of transport. I also had trouble finding anything in Comsol's help file.

So:

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 through stiff spring BCs:

i.e. between region one and two (it is similar between regions 2 and 3):
(-D?c1+c1u)?n= M(c2 - Kc1) -> (that is, M(c2 - Kc1)is the inward flux approx. on the c1 side)
(-Dm?c2)?n= M(Kc1- c2) -> (that is, M(Kc1- c2) is the 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
- M is an arbitrary large (???) stiff spring velocity

My question(s):
- how is this particular SS condition derived with all of the variables listed?
- I have some sense of how it works (what goes in equals what comes out) but why is it an effective approx. in this case? (the way that it is set up with the variables that it includes) - M is very strange to me.

ANY thoughts/hints/suggestions that you could provide would be greatly appreciated. I am trying to determine the scope of this approximation, because it seems to work very well for a case that I am trying to analyze.