Evolution of the free volume between rough surfaces in contact

TL;DR

This paper investigates how the free volume between rough fractal surfaces in contact evolves with separation, contact area, and pressure, revealing fractal spatial distributions and proposing a synthetic interpretative formula.

Contribution

It provides a fundamental analysis of free volume evolution on fractal surfaces, considering surface fractal dimension and resolution effects, with theoretical bounds and a new probabilistic formula.

Findings

Free volume domains exhibit fractal spatial distributions.

Bounds of fractal dimensions are theoretically derived.

A synthetic formula based on probability distribution explains observed trends.

Abstract

The free volume comprised between rough surfaces in contact governs the fluid/gas transport properties across networks of cracks and the leakage/percolation phenomena in seals. In this study, a fundamental insight into the evolution of the free volume depending on the mean plane separation, on the real contact area and on the applied pressure is gained in reference to fractal surfaces whose contact response is solved using the boundary element method. Particular attention is paid to the effect of the surface fractal dimension and of the surface resolution on the predicted results. The free volume domains corresponding to different threshold levels are found to display fractal spatial distributions whose bounds to their fractal dimensions are theoretically derived. A synthetic formula based on the probability distribution function of the free volumes is proposed to synthetically interpret the numerically observed trends.