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We derive a very simple and effective stickiness criterion for solids having random roughness using a new asymptotic theory, which we validate with that of Persson and Scaraggi and independent numerical experiments. Previous claims that stickiness may depend on small scale quantities such as rms slopes and/or curvatures, obtained by making oversimplified assumptions on the contact area geometry, are largely incorrect, as the truncation of the PSD spectrum of roughness at short wavelengths is irrelevant. We find stickiness is destroyed typically at roughness amplitudes up to three orders of magnitude larger than the range of attractive forces. With typical nanometer values of the latter, the criterion gives justification to the qualitative well known empirical Dalhquist criterion for stickiness which demands adhesives to have elastic modulus lower than about 1MPa.The results clarifies a much debated question in both the scientific and technological world of adhesion, and may serve as benchmark for better comprehension of the role of roughness.3/2 rms ∆γ/ R 1/2 E * where E * is the plane strain elastic modulus, ∆γ is interface energy. The choice of R seems critical in view of its sensitivity to "resolution" or "magnification" [13], i.e. on the shortest wavelength in the roughness spectrum. In the "fractal limit", i.e. for an infinite number of wavelength R → 0, there would be no stickiness for any surface, irrespective of the geometrical characteristics, like fractal dimension, or root mean square heigths (rms) amplitude. Hence, FT apparent good correlation with the theory despite the many limitations (see [14]), may have been due to a fortuitous choice of R at a

Surface roughness affects several tribological phenomena and in particular adhesion. For many years, multiasperity models have been the most used in the study of rough contacts notwithstanding their evident limitations. In this work, we propose a fair assessment of improved asperity models with adhesion modeled according to the Derjaguin, Muller and Toporov theory, which assumes attractive forces do not deform the surface profiles. Results are given for three enhanced asperity models: the discrete Greenwood and Williamson model, where the effective heights and curvatures of the surface asperities are used rather than a statistical description; the interacting Hertzian asperities model, where the elastic coupling effects are included; the interacting and coalescing Hertzian asperities model, where the coalescence of contact spots is also conveniently considered. A comparison with advanced contact mechanics theories shows that only the interacting and coalescing Hertzian asperities model correctly captures the physics of the problem at all roughness scales.

In this work, we investigate dissipative effects involved during the detachment of a smooth spherical glass probe from a viscoelastic silicone substrate patterned with micro-asperities. As a baseline, the pull-off of a single asperity, millimeter-sized contact between a glass lens and a smooth poly(dimethylsiloxane) (PDMS) rubber is first investigated as a function of the imposed detachment velocity. From a measurement of the contact radius ( ) and normal load during unloading phase, the dependence of the strain energy release rate on the velocity of the contact line = ∕ is determined under the assumption that viscoelastic dissipation is localized at the edge of the contact. These data are incorporated into Muller's model (Muller, 1999) in order to predict the time-dependence of the contact size. Similar pull-off experiments are carried out with the same PDMS substrate patterned with spherical micro-asperities with a prescribed height distribution. From in situ optical measurements of the micro-contacts, scaling laws are identified for the contact radius and the contact line velocity . On the basis of the observed similarity between macro and microscale contacts, a numerical solution is developed to predict the reduction of the contact radius during unloading.

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