Discussion: “The Effect of Anisotropy on the Percolation Threshold of Sealing Surfaces” (Yang, Z., Liu, J., Ding, X., and Zhang, F., 2019, ASME J. Tribol., 141(2), p. 022203)

Abstract

A recent paper by Yang et al. [1] shows interesting results on the percolation threshold, the ratio of real contact area to nominal contact area A/A0 when the first leak channel appears across a seal interface. Percolation is a very general phenomenon, which perhaps originated from the problem of conduction in mixtures where Bruggeman gave his “effective medium theory” or “effective medium approximation” (EMA) [2] already in 1935. It is known that the threshold values are in general not correctly predicted in three-dimensions [3] (factor 2 errors observed in experiments), but in two-dimensions, the EMA turns out to model percolation relatively well, with a prediction of a threshold of 50%. In the context of the flow in a seal between rough (anisotropic) interfaces; today, it can be said that EMA gives the percolation threshold, the ratio of real contact area to nominal contact area A/A0 when the first leak channel appears across a seal interface, as(1)Ap/A0=γ/(1+γ)where γ is Peklenik number, introduced in 1967 [4], as the ratio between the characteristic lengths in the autocorrelation functions (ACF) in x and y directions, at which the ACF has reduced by 50%.