New to FEM? Get Answers about Stiff-Spring Method & Partition Coefficient

[howtophysics]

New to FEM - have started using COMSOL. Trying to adapt a "stiff-spring" method that was used in this example:
http://www.engineering.uiowa.edu/~cbe_217/Misc/dialysis.pdf
Questions:
1. How does this "stiff-spring" approximation method work? I got the books that where listed as references, but I still can't seem to piece it together. I guess I am wondering how it's derived.
2. Could I use the "stiff-spring" boundary conditions at only one boundary (i.e. create two domains, with different saturation values, and then link them with a stiff-spring boundary condition in order to solve for steady state?)
3. The partition coefficient confuses me a little. It's set as the ratio of concentrations? But which concentrations? Apparently it's a constant - so where is it coming from?

If you guys and gals could help me on any of the following questions (or just point me in the right direction) I'd be grateful. Thanks.

 

[Navin A S]

1. The "stiff-spring" approximation method is based on a linear relationship between the pressure gradient across a medium and the displacement of the spring. This is expressed as a differential equation, which can be solved to get the displacement of the spring at any given point in time. The idea is that the pressure gradient across the medium can be approximated by a spring with a certain stiffness, so that when the pressure gradient changes, the displacement of the spring will also change. This allows for a simplified solution to the problem of finding the pressure gradient. 2. Yes, it is possible to use the "stiff-spring" boundary conditions at only one boundary. The two domains will need to be connected via a stiff-spring boundary condition in order to solve for the steady state. This means that the stiffness of the spring should be chosen such that it is appropriate for the given pressure gradient.3. The partition coefficient is a constant that is typically determined experimentally. It describes the ratio of concentrations of a particular species between two phases, such as a liquid and a gas. For example, the partition coefficient for water between air and water would be the ratio of the concentration of water in the air to the concentration of water in the liquid.