How do geckoes stick to surfaces?

Tokay geckos are remarkable for their ability to cling to vertical and even inverted surfaces using an average of 227 mm${}^2$‍ of highly specialized toepads. The toepads are covered with hydrophobic hairs called setae, with a density of approximately 5,300 setae$\cdot$‍mm${}^{-}$‍${}^2$‍, arranged in plate-like layers known as lamellae. Each setae branches into 100 to 1,000 flat, highly deformable tips called spatulae that allow each setae to make multiple contact points with the surface. Gecko toepads are able to produce adhesive forces, drawing the animal toward a surface, and frictional forces, preventing the animal from sliding along the surface.

It is generally agreed that geckos adhere to both hydrophobic and hydrophilic surfaces primarily via attractive van der Waals forces between setae and a surface. Researchers disagree about whether or not capillary adhesion plays a significant role in gecko toe adhesion. Capillary adhesion depends on the formation of a thin layer of water between the two surfaces (a “capillary bridge”), which attracts two hydrophilic surfaces toward each other. The water is thought to arise from normal environmental humidity. Experimental evidence has shown that it takes approximately 4.2 ms for capillary bridges to form, which must occur for capillary adhesive forces to be generated.

To further explore the interplay between van der Waals forces and capillary adhesion, a group of scientists investigated the forces generated by actual setae at different humidities. Arrays of setae were scraped from gecko toepads and artificially attached to a device capable of recording sensitive measurements of force. The setal arrays were dragged 100 nm across various surfaces at a constant velocity of 5 $\mu$‍m per second. The resulting adhesive and frictional forces were measured, as shown in Figure 1.

Figure 1: The influence of humidity on the adhesion and friction of isolated gecko setal arrays during steady-state drag. Each symbol represents the mean of a group of trials (n=6). Silicon dioxide is a hydrophilic semiconductor. Gallium arsenide is a hydrophobic semiconductor. Experiments were carried out at a constant temperature of 25${}^{\circ }$‍C. Adapted from: Puthoff, Jonathan B., Michael S. Prowse, Matt Wilkinson, and Kellar Autumn. "Changes in materials properties explain the effects of humidity on gecko adhesion." The Journal of experimental biology 213, no. 21 (2010): 3699-3704.

When a gecko is clinging motionless to a perfectly vertical surface, which of the following must be true?