Abstract
Understanding the distribution of interfacial separations between contacting rough surfaces is integral for providing quantitative estimates for adhesive forces between them. Assuming non-adhesive, frictionless contact of self-affine surfaces, we derive the distribution of separations between surfaces near the contact edge. The distribution exhibits a power-law divergence for small gaps, and we use numerical simulations with fine resolution to confirm the scaling. The characteristic length scale over which the power-law regime persists is given by the product of the rms surface slope and the mean diameter of contacting regions. We show that these results remain valid for weakly adhesive contacts and connect these observations to recent theories for adhesion between rough surfaces.
Highlights
Interest has turned to systems including attractive interactions that lead to macroscopic adhesion
Two opposite limits exist in the classical literature on the adhesion of smooth spheres: in the Derjaguin–Muller–Toporov (DMT) [32] limit, weak attractive forces between solids do not alter the geometry of contact, but do reduce the global mean pressure; in the opposite limit, known as the Johnson–Kendall–Roberts (JKR) [33] limit, strong attractive forces significantly change the structure of the contact edge and can lead to contact hysteresis
The roughness profile of each periodic, L × L surface with nominal area A0 = L2 is described by a self-affine fractal between an upper cutoff length scale max and a lower cutoff min, where length scales are given in terms of the pixel size a0. This means that the power spectral density (PSD)
Summary
Rough surfaces has been the subject of study for countless experimental, analytical, and numerical investigations over the past century [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]. A universal theme found in most cases is that contact is limited to the peaks or asperities of the rough topography and the real area of contact Arep is much less than the apparent projected area A0. Substantial progress has been made in determining the relationship between Arep and the applied normal force F in non-adhesive, frictionless systems
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