Enhanced load-carrying capacity of hairy surfaces floating on water

Abstract

Water repellency of hairy surfaces depends on the geometric arrangement of these hairs and enables different applications in both nature and engineering. We investigate the mechanism and optimization of a hairy surface floating on water to obtain its maximum load-carrying capacity by the free energy and force analyses. It is demonstrated that there is an optimum cylinder spacing, as a result of the compromise between the vertical capillary force and the gravity, so that the hairy surface has both high load-carrying capacity and mechanical stability. Our analysis makes it clear that the setae on water striders' legs or some insects' wings are in such an optimized geometry. Moreover, it is shown that surface hydrophobicity can further increase the capacity of a hairy surface with thick cylinders, while the influence is negligible when the cylinders are thin.

Floating Versus Sinking

“…As expected based on the results for a single horizontal cylinder in Section 3.2, the precise value of the contact angle plays only a minimal role, provided that θ > π/2. Xue et al (2014) also found that, when the separation between the hairs becomes very small, d c , the total load that can be supported by the raft becomes insensitive to the value of d. (This agrees with the generalization of Archimedes' principle, as this force is simply the weight of liquid displaced.) However, the authors also observed that there is in fact an optimum value of d, www.annualreviews.org • Floating Versus Sinking at which the load supported is maximized.…”

“…Indeed, as r hair / c → 0, the importance of this optimum diminishes (i.e., the maximum supported load becomes closer to that supported by close-packed hairs, d / c → 0). The numerical results of Xue et al (2014) show that d optimal ∼ Bo 1/3 hair where Bo hair = (r hair / c ) 2 is the Bond number of the hairs (see Figure 5c). This simple scaling result is valid over a remarkably large range of Bond numbers and is not, to my knowledge, understood.…”

“…Nevertheless, detailed calculations of the maximum load that can be supported by a raft of two-dimensional hairs at an interface (Xue et al 2014) are of considerable interest. Xue et al (2014) varied the microscopic contact angle of the hairs, θ, the separation between hairs, d, and the radius of the hairs, r hair .…”

“…Xue et al (2014) varied the microscopic contact angle of the hairs, θ, the separation between hairs, d, and the radius of the hairs, r hair . As expected based on the results for a single horizontal cylinder in Section 3.2, the precise value of the contact angle plays only a minimal role, provided that θ > π/2.…”

How Solid–Liquid Adhesive Property Regulates Liquid Slippage on Solid Surfaces?

“…[6][7][8][9][10][11] Slip lengths on smooth hydrophobic surfaces have been reported at the nanoscale, and can reach as high as tens or hundreds of microns 12,13 when hydrophobic surfaces are rendered superhydrophobic by manufacturing micro/nano structures. [14][15][16][17][18] This is attributed to the high area fraction of shear-free liquid-air interfaces at solid surfaces.…”