# Biomimetic Liquid-Repellent Surfaces by Ultrafast Laser Processing
## 3 Superhydrophobic, Self-Cleaning, and Antifouling Surfaces
In this case the contact angle of liquid on the structured surface is given by the Wenzel equation, introducing the structure parameter \(\tau\) (\(\tau>1\) for rough surface), defined as the ratio of the structured enlarged surface area to its flat projected area [56]:  
\[\cos\theta_{\rm W}=\tau\cos\theta_{\rm Y}.\]  
Due to the realization of this wetting state, the interface and therefore adhesion between the solid and liquid is increased compared to that on a flat surface of the same material. In the second state, the liquid wets the structured surface incompletely; a composite solid/liquid-air interface is formed. In this case the contact angle of liquid on the structured surface is given by the following equation, introducing the structure parameter \(\hat{t}_{\rm sl}\) (\(0<t_{\rm sl}<1\), ideally, close to 0), defined as the ratio of the solid surface in contact with liquid to the flat surface projected area [57]:  
\[\cos\theta_{\rm CB}=f_{\rm sl}(\cos\theta_{\rm Y}+1)-1\;.\]  
This equation is a particular case of the general Cassie-Baxter expression \(\cos\theta_{\rm CB}=f_{1}\cos\theta_{\rm Y1}+\,f_{2}\cos\theta_{\rm Y2}\). This expression was developed for application to a chemically heterogeneous surface consisting of two materials, each of them characterized by its own \(\theta_{Y}\) and its own portion of the total area \(f\) (\(f_{1}+f_{2}=1\)). The superhydrophobic stage is a special case where a chemically heterogeneous surface is formed from solid and air. As a result, the interface between liquid droplets and solid can be strongly reduced. An important characteristic of liquid-repellent surfaces is small contact angle hysteresis (\(\Delta\theta\)). Hysteresis is defined as the difference between the advanced and receding angles of a liquid droplet. Shortly before a droplet starts to move over the inclined solid surface, the advancing contact angle can be observed at the front droplet side and receding at the back side. It is important to note that retentive force, which describes drop retention on a tilted surface, is directly proportional to \(\cos\theta_{\text{advancing}}-\cos\theta_{\text{receding}}\)[58]. Another parameter often used for characterization of liquid-repellency is tilt angle \(\alpha\) (also known as the tilting or sliding angle), which is required for the initiation of droplet sliding from the surface. The droplet mobility on the surface is characterized by contact angle hysteresis and tilt angle. The low values of contact angle hysteresis and tilt angle are intrinsic characteristics of a nearly defect-free surface that enables liquid repellency. Dry superhydrophobic liquid-repelling surfaces (if the liquid is water, they are referred to as water-repelled or superhydrophobic) is a special case of realization of the state, which is described by the Cassie-Baxter equation. In the case of superhydrophobic plants, low-energy wax makes the surface hydrophobic, and the hierarchical structure of leaves makes them superhydrophobic. Water drops on superhydrophobic leaves are supported by a hierarchical structure on the composite solid-air interface. Studies with AFM and confocal light microscopy found that hierarchical roughness results in a reduction of the contact area by more than 95% compared to the projected area of a water droplet [59]. The superhydrophobic plant surfaces are characterized by a static contact angle of \(\geq\)150\({}^{\circ}\) and contact angle hysteresis and tilt angle \(\leq\)10\({}^{\circ}\)[50; 51]. Inspired by biomimetic models, superhydrophobic surfaces were fabricated on different materials by ultrafast laser ablation. The first works demonstrated superhydrophobic modification of silicon using a columnar structure superimposed with LIPSS or nanoroughness in combination with low-energy surface coating [60; 61], following the application of this functionalization technique to other materials. Superhydrophobic modification of metals was realized analogous to silicon solely by structuring [62; 63; 64; 65; 66] or in combination with a coating [38; 67].