Fluid leakage in seals: An approach based on percolation theory

We use the formalism developed by Persson et al. [Contact area between a viscoelastic solid and a hard, randomly rough, substrate. J Chem Phys 2004;120(18):8779–93], which we briefly review for the reader convenience, to calculate the fluid leakages in seals. The methodology makes use of the percolation theory and theory of contact mechanics to show how the statistical properties of the surface, the applied load and the geometry of the seal affect the leakages in such systems. The problem is relevant in a countless number of applications, e.g. in ball valves, or common rail systems. The basic idea is to describe the nominal contact area as a square lattice where each square can be black or white depending on whether contact between the two surfaces takes place or not. The probability to find a black site is then equal to the ratio between the apparent contact area at a given magnification and the nominal contact area. Since the apparent contact area decreases as the magnification is increased, a critical value of the magnification exists at which the probability to find a white square reaches the critical value given by the percolation theory. When this happens, a percolation channel is formed and fluid leakage occurs.