Discussion Forum

Hey - I'm an undergrad working on a summer project, and this is an absolute "newbie" set of questions, but if you can help me in any way, I'd appreciate it (alot!):

I have a 2D rectangular geometry problem, modeling the concentration of oxygen in a basic rectangular microfluidic channel with advection and diffusion, for steady state. My "simple" subdomain being a rectangle, there are 4 boundaries. The first boundary (on the left) is the maximum solubility of oxygen in cell culture media, so it is (obviously) a concentration. The bottom boundary is a constant flux of cells consuming oxygen, which I approximate with a set of kinetics to obtain a consistent mol/m^2*s value. The right boundary is the outlet (convective flux). But the top is where the trick is. I have a value for a mass transfer coefficient k, and the flux through the top is generated by the difference between the saturated concentration of oxygen in the material that is above the channel Csat (which is higher than the max solubility of oxygen in the media that is flowing through the channel) and whatever the value is for the concentration along the top of the channel (call it Ctop) at each x. i.e. flux through the top =k*(Csat-Ctop(x)) [eq 1]

So, Questions:

1. I want to limit myself to downward diffusion (i.e. anisotropic) how do I do that? I know that it's the matrix for anisotropic diffusion (under subdomain settings), but what does each value there represent? How do I get my diffusion "just down"?
2. I believe that I use one of the "coupling variable" features, but how can I extract the concentration from the interior of the boundary at the top of the channel to make it available for the expression that I will use to generate the flux at the top? [eq 1]
3. how can I limit the maximum concentration of oxygen in the channel, so that it cannot go above the media's saturation concentration value?

Thanks - like I said - I'm new to, well, everything that I am doing - and I haven't been able to talk to someone who knows how to do this, nor find answers within the "help files. Whatever you can tell me - I'd be very grateful!

Kindest Regards,
Mike