On stickiness of multiscale randomly rough surfaces

Abstract

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

A Criterion for the Effective Work of Adhesion in Loading and Unloading of Adhesive Soft Solids from Rough Surfaces

“…Actually, the present results reinforce the growing consensus that extremely accurate measurement of roughness should not be needed but it is the long wavelength content of roughness which matters most [1][2][3][4][5]. While Dalvi et al [13] have used a more precise calculation of the roughnessinduced increase of area A true ∕A 0 which indeed seems to improve the correlation with experiments that they reported, it remains true that the role of A true ∕A 0 seems insufficient to explain adhesion enhancement, and that the Guduru effect (which is still not entirely understood for random roughness), has some chance in explaining the adhesion enhancement.…”

“…-The Dalvi variant of PT criterion [13] where and h ′ rms is evaluated from ((5), second equation) 5 ; -The modified version of the Guduru model (10) proposed in the present paper.…”

“…Roughness is usually responsible for destroying adhesion, and in particular after some debate, there is some consensus that it is the longest wavelength of roughness which is responsible for this so that extremely accurate measurement of roughness should not be needed [1][2][3][4][5]: in other words, the roughness root-mean-square (rms) is the first simple parameter of choice in "killing" adhesion. Fifty years ago, indeed to first measure adhesion, very smooth soft rubber spheres and optically smooth glass was used ( [6] JKR in the following, generalizing the Hertz contact theory to short range adhesion).…”

Two-dimensional finite element analysis of elastic adhesive contact of a rough surface

“…which is convergent for H ≥ 0.5. This convergence of ⁎ γ is similar to the conclusions found in references [32][33][34][35][36][37][38] and in contrast with work done in refs. 39,40 .…”

A Numerical Study on Roughness-Induced Adhesion Enhancement in a Sphere with an Axisymmetric Sinusoidal Waviness Using Lennard–Jones Interaction Law

“…Adhesion is a challenging topic in tribology [1][2][3] with relevance in several engineering applications that range from biomimetics [4], soft matters [5], soft robots [6], grippers [7], friction [8][9][10][11][12]. Although roughness is usually responsible for adhesion reduction [13][14][15], Briggs and Briscoe [16] showed already in 1977 that relatively small random roughness amplitude could enhance adhesion in pull-off experiments as well as relative rolling resistance by a factor up to 2.5. Later, Guduru [17] showed that in the contact between a rigid sphere and a soft halfspace with an axisymmetric single wavelength waviness, adhesion could be enhanced by a factor up to 20 with respect to the Johnson-Kendall-Roberts smooth case ( [18], JKR in the following).…”