Theory of the leak-rate of seals

Seals are extremely useful devices to prevent fluid leakage. However, the exact mechanism of roughness induced leakage is not well understood. We present a theory of the leak-rate of seals, which is based on percolation theory and a recently developed contact mechanics theory. We study both static and dynamic seals. We present molecular dynamics results which show that when two elastic solids with randomly rough surfaces are squeezed together, as a function of increasing magnification or decreasing squeezing pressure, a non-contact channel will percolate when the (relative) projected contact area, A/A(0), is of the order 0.4, in accordance with percolation theory. We suggest a simple experiment which can be used to test the theory.