calculate backflow through reed valve

[meekg]

I'm looking to calculate the backflow through a (closed) reed valve, given the pressure difference and the viscosity.

For simplicity, the reed is circular with radius R, and is sitting over a hole with radius r. The reed remains flat and so contacts the flange over an (R-r) anulus.

I'm not even sure what is the principal mechanism by which backflow occurs...
- Is the flow due to surface imperfections?
- Is there a thin film of fluid that is held together by surface tension?
- Is there a mechanism by which equilibrium is reached? specifically - if the flow stops, then the pressure on both sides of the reed (over the contact area) equalizes.

Thanks,
Ben.