calculate backflow (leak rate) through closed reed valve

[meekg]

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

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 reed is in equilibrium, then the pressure on both sides of the reed (over the contact area) equalizes. removing most of the seating force

Thanks,
Ben.