Fluid leakage near the percolation threshold

TL;DR

This paper challenges the universality of percolation theory by showing that fluid leakage near the sealing point depends critically on microscopic details, making it difficult to predict leakage behavior from macroscopic surface statistics.

Contribution

The study demonstrates through simulations that leakage behavior near the percolation threshold is governed by microscopic details, contradicting the universal powerlaw assumption.

Findings

Leakage critical behavior depends on microscopic constriction details.

Universal powerlaws do not apply to fluid leakage near sealing points.

Predicting leakage from surface statistics alone is fundamentally limited.

Abstract

Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation theory asserts that most percolative processes are universal, that is, the emergent powerlaws only depend on the general, statistical features of the macroscopic system, but not on specific details of the random realisation. In contrast, our computer simulations of the leakage through a seal---applying common assumptions of elasticity, contact mechanics, and fluid dynamics---show that the critical behaviour (how the flow ceases near the sealing point) solely depends on the microscopic details of the last constriction. It appears fundamentally impossible to accurately predict from statistical properties of the surfaces alone how strongly we have to tighten a water tap to make it stop dripping and also how it starts dripping once we loosen it again.