Wenzel state: where λp = linear fraction of contact line on the asperities θr,0 = receding contact angle of a smooth substrate θair = contact angle between liquid and air (typically assumed to be 180°) Unitary versus hierarchical roughness structures M. Nosonovsky and B. Bhushan studied the effect of unitary (non-hierarchical) structures of micro and nano roughness, and hierarchical structures (micro roughness covered with nano roughness). They found that hierarchical structure was not only necessary for a high contact angle but essential for the stability of the water-solid and water-air interfaces (the composite interface). Due to an external perturbation, a standing capillary wave can form at the liquid–air interface. If the amplitude of the capillary wave is greater than the height of the asperity, the liquid can touch the valley between the asperities; and if the angle under which the liquid comes in contact with the solid is greater than h0, it is energetically profitable for the liquid to fill the valley. The effect of capillary waves is more pronounced for small asperities with heights comparable to the wave amplitude. An example of this is seen in the case of unitary roughness, where the amplitude of asperity is very low. This is why the likelihood of instability of a unitary interface will be very high. However, in a recent study, Eyal Bittoun and Abraham Marmur found that multiscale roughness is not necessarily essential for superhydrophobicity but beneficial for mechanical stability of the surface. Examples in nature Many very hydrophobic materials found in nature rely on Cassie's law and are biphasic on the submicrometer level. The fine hairs on some plants are hydrophobic, designed to exploit the solvent properties of water to attract and remove sunlight-blocking dirt from their photosynthetic surfaces. Inspired by this lotus effect, many functional superhydrophobic surfaces have been developed. Water striders are insects that live on the surface film of water, and their bodies are effectively unwettable due to specialized hairpiles called hydrofuge; many of their body surfaces are covered with these specialized "hairpiles", composed of tiny hairs spaced so closely that there are more than one thousand microhairs per mm, which creates a hydrophobic surface. Similar hydrofuge surfaces are known in other insects, including aquatic insects that spend most of their lives submerged, with hydrophobic hairs preventing entry of water into their respiratory system. The skin surface of some species of lizards, such as geckos and