From micro to nano contacts in biological attachment devices

Abstract

Animals with widely varying body weight, such as flies, spiders, and geckos, can adhere to and move along vertical walls and even ceilings. This ability is caused by very efficient attachment mechanisms in which patterned surface structures interact with the profile of the substrate. An extensive microscopic study has shown a strong inverse scaling effect in these attachment devices. Whereas microm dimensions of the terminal elements of the setae are sufficient for flies and beetles, geckos must resort to sub-microm devices to ensure adhesion. This general trend is quantitatively explained by applying the principles of contact mechanics, according to which splitting up the contact into finer subcontacts increases adhesion. This principle is widely spread in design of natural adhesive systems and may also be transferred into practical applications.

Fig. 1.

Terminal elements (circles) in animals with hairy design of attachment pads. Note that heavier animals exhibit finer adhesion structures.

Fig. 2.

Dependence of the terminal element density (N_A) of the attachment pads on the body mass (m) in hairy-pad systems of diverse animal groups (log·N_A(m^–2) = 13.8 + 0.699·log·m(kg), R = 0.919).

Fig. 3.

Interpretation of Fig. 2 in light of contact theory. A fit to all data (red line) gives a slope of ≈2/3, corresponding to the self-similarity criterion. Within each lineage, a lower slope of ≈1/3 is found, suggesting curvature invariance of the contacts with radius R (green lines). The approximate limit for such attachment devices (limit of maximum contact) is shown as a blue line.

Fig. 4.

Two cases of contact scaling. (a) Self-similarity: contact radius R scales with contact size s.(b) Curvature invariance: contact radius is independent of contact size.