By Michael Nosonovsky, Bharat Bhushan
Multiscale Dissipative Mechanisms and Hierarchical Surfaces covers the speedily constructing themes of hierarchical surfaces, roughness-induced superhydrophobicity and biomimetic surfaces. The examine in those themes has been progressing quickly within the contemporary years because of the advances within the nanosciences and surfaces technological know-how and because of capability purposes in nanotechnology. the 1st in its box, this monograph presents a finished assessment of those matters and offers the heritage creation in addition to fresh and new leads to the area.
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Additional info for Multiscale dissipative mechanisms and hierarchical surfaces : friction, superhydrophobicity, and biomimetics
Nosonovsky  considered a very simple model which, however, can account for adhesion hysteresis. Physically the van der Waals adhesion force and the elastic force are both caused by the atomic interaction. However, at the scale of nanometers, the contacting bodies can still be treated as a continuum, but the effects of adhesion forces are important . The usual approach for the elasto-adhesive problems is to consider the bodies in contact as a continuum media and the interaction between them governed by an adhesive potential.
7 Discussion In summary, there are several mechanisms of dry friction. They all are associated with a certain type of heterogeneity or nonideality, including surface roughness, chemical heterogeneity, contamination, and irreversible forces. All these mechanisms are also characterized by the interface forces being small compared to the bulk force. In the following chapters, we will discuss linearity of friction as a result of the presence of a small parameter, nonlinearity of friction, related to heterogeneity and hierarchical structure and multiscale nature of the frictional mechanisms.
6. 3 Friction as a Linear Phenomenon 43 using the corresponding load. The dependence of total contact area upon W is then given by integration of the individual contact areas by r as  a Ar ∝ W (1/3) 1 − r 2 /a 2 2/3 2πr dr 0 π ∝ W (1/3) cos φ 2/3 2π(a sin φ)a cos φ dφ 0 ∝ W (2/9) a 2 ∝ W (2/9) W (2/3) ∝ W (8/9) . 6) were used. The integral of the trigonometric functions can be easily calculated, however, its value is not important for us, because it is independent of a and W . If the small asperities are covered by the “third-order” asperities of an even smaller radius, the total area of contact can be calculated in a similar way as a Ar ∝ W (1/3) 1 − r 2 /a 2 8/9 2πr dr ∝ W (8/27) a 2 ∝ W (26/27) .
Multiscale dissipative mechanisms and hierarchical surfaces : friction, superhydrophobicity, and biomimetics by Michael Nosonovsky, Bharat Bhushan