## 4 Passive Anti-Biofouling Nanoc Coatings
### Fouling Release Strategies
#### 4.2.2 Biomimetic Hierarchical Micro- and Nanostructured Superhydrophobic Surfaces  
with Low-Adhesion and Self-Cleaning Properties  
Wetting can be described as the displacement of a gaseous phase (in particular air) at the surface of a solid by a liquid phase (in particular water). The wettability of a solid surface by a liquid is described by the contact angle (\(\theta\)), which is the angle at which the liquid-air interface meets the solid-liquid interface. Hydrophilic surfaces are characterised by contact angles to water lower than 90\({}^{\circ}\), while if the water contact angle is higher than 90\({}^{\circ}\), the surface is said to be hydrophobic. In the case of an ideal flat (smooth) surface, the contact angle (\(\theta_{0}\)) is given by the Young Equation (1):  
\[\cos\theta_{0}\ =\ \frac{\gamma_{\rm SA}-\gamma_{\rm SL}}{\gamma_{\rm LA}} \tag{1}\]  
where \(\gamma_{\rm SA}\), \(\gamma_{\rm SL}\), and \(\gamma_{\rm LA}\) are the surface tensions at the solid-air, solid-liquid, and liquid-air interfaces. On a real rough surface having roughness details smaller in size than the liquid droplets, the actual contact angle is the angle between the tangent to the liquid-air interface and the actual local surface of the solid. However, the actual contact angle is usually not a measurable quantity, and what is currently amenable to measurement is the apparent contact angle defined as the angle between the tangent to liquid-air interface and the apparently solid surface, as macroscopically observed. The apparent or measured contact angle \(\theta\) is often modeled using either the Wenzel's Equation (2) or the Cassie-Baxter Equation (3) depending on whether the liquid penetrates or not into the grooves of the rough solid surface [116; 117; 118; 119; 120]. [PERSON]'s model assumes that the liquid droplet fills up the grooves completely on a rough surface, forming a homogenous interface with the solid (see schematic representation in Figure 3). According to [PERSON], the apparent contact angle (\(\theta\)) can be related to the Young contact angle on an ideal smooth surface (\(\theta_{0}\)) by Equation (2). The proportionality constant \(R_{\rm f}\) in Equation (2) is called the roughness factor, which accounts for the extension of the surface area due to the roughness being defined as the ratio of the actual surface area of the liquid-solid interface (\(A_{\rm SL}\)) to the geometrically projected area, or in another word, the flat solid-liquid contact area (\(A_{\rm F}\)). \[\cos\theta\ =\ R_{\rm f}\cos\theta_{0} \tag{2}\]  
\[R_{f}\ =\ \frac{A_{\rm SL}}{A_{\rm F}}\]  
The Wenzel Equation (2) predicts that the wettability caused by the chemistry of the surface is reinforced by roughness. Since the roughness factor is always supraunitary, \({\rm R_{r}}>1\), if the solid surface is mostly hydrophilic, i.e., if \(\theta_{0}<90^{\circ}\), and \(\cos\!\theta_{0}>0\), then \(\cos\!\theta>\cos\!\theta_{0}\), meaning that \(\theta<\theta_{0}\). On the other hand, if the solid surface is mostly hydrophobic (\(\theta_{0}>90^{\circ}\), \(\cos\!\theta_{0}<0\)), then \(\cos\!\theta<\cos\!\theta_{0}\), which means that \(\theta>\theta_{0}\). In other words, a hydrophilic surface becomes even more hydrophilic, and a hydrophobic surface becomes even more hydrophobic if the roughness increases. However, in practice, the Wenzel model is mostly applicable to hydrophilic surfaces, since, on rough hydrophobic surfaces, the liquid cannot wet the whole surface [121]. In fact, Equation (2) is valid only for moderate values of the roughness factor, \(R_{\rm f}\). For non-wetting surfaces, as the roughness increases, it becomes harder and harder for the water to penetrate into the grooves, resulting in the partial wetting and formation of trapped air pockets between the liquid and the rough solid surface (see Figure 4).