Theory of the leak-rate of seals

TL;DR

This paper develops a theoretical framework for understanding the leak-rate of seals based on percolation theory and contact mechanics, supported by molecular dynamics simulations and a proposed experimental test.

Contribution

It introduces a novel theory of seal leak-rate that combines percolation and contact mechanics, validated by molecular dynamics results.

Findings

Percolation occurs at a contact area ratio of about 0.4.

Molecular dynamics simulations support the percolation-based leak mechanism.

A simple experiment is proposed to test the theory.

Abstract

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 dynamics 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 order 0.4, in accor dance with percolation theory. We suggest a simple experiment which can be used to test the theory.