## 4 Passive Anti-Biofouling Nanoc Coatings
### Fouling Release Strategies
#### 4.2.2 Biomimetic Hierarchical Micro- and Nanostructured Superhydrophobic Surfaces
That leads to a composite interface consisting of solid-liquid, solid-air, and liquid-air interfaces where the solid-air interfaces and the liquid-solid contact zones are located into the troughs of the rough surface and, at the top of the asperities, respectively. In this situation, increasing the surface roughness will no longer result in an increase ofthe solid-liquid contact area. For the case of partial wetting and considering a flat composite interface under the droplet, the apparent contact angle \(\theta\) is given by the Cassie-Baxter Equation (3). \[\cos\theta\ =\ R_{\mathrm{f}}f_{\mathrm{SL}}\cos\theta_{0}-f_{\mathrm{LA}}\ =\ R_{ \mathrm{f}}f_{\mathrm{SL}}\cos\theta_{0}-1+f_{\mathrm{SL}} \tag{3}\]  
where \(f_{\mathrm{SL}}\) and \(f_{\mathrm{LA}}\) are the flat geometric areas of the solid-liquid and liquid-air interfaces, respectively. The Cassie-Baxter Equation (3) predicts that for higher roughness (lower pitch between the asperities), the solid-liquid contact area dramatically decreases, \(f_{\mathrm{SL}}\) approaches zero, and \(\theta\) approaches \(180^{\circ}\). Hence, the surface becomes superhydrophobic; the adhesion of the liquid to the solid is greatly reduced, which aids a droplet on the surface to roll off easily even at a low inclination. Moreover, the adhesion of the dirt particles to such a surface is minimal because of the very small contact area between the particles and the rough surface. Hence, if the rolling liquid droplet encounters a particle lying on the surface, it readily picks up the particle because the contact area between the droplet and the particle is much larger than that one between the particle and the rough solid surface. Consequently, the dirt particle will adhere to the liquid droplet, being carried away from the surface by the rolling drop. This is the underlying mechanism behind the well-known self-cleaning ability of the _Nelumbo nucifera_ (Lotus) leaves. In conclusion, the formation of a stable composite interface with air pockets between the liquid and the solid appears to be of critical importance in order to attain superhydrophobicity and self-cleaning properties. However, the composite interface is fragile, and a series of destabilising factors such as the formation of capillary waves at the liquid-air interface, nanodroplet condensation, as well as liquid pressure can irreversibly transform it into a homogenous interface [118; 119; 122; 123]. SEM (Scanning Electron Microscopy) micrographs revealed the peculiar hierarchical surface morphology of the Lotus leaves. The upper epidermis of a Lotus leaf has a distinctive hierarchical structure consisting of micro-bumps of epidermal cells (papillae) coated with a dense covering of agglomerated nano-scale epicuticular wax tubules [111] (see Figure 5 for SEM micrographs of Lotus leaf at three magnifications). It is this combination between the hydrophobic coating and the peculiar surface topography with dual hierarchical roughness on micro- and nano-length scales that are responsible for the Lotus effect. These specific topographical features enhance the stability of the composite interface, as demonstrated by [PERSON] and [PERSON]. These authors showed that the higher micro-scale papillae resist the capillary waves, while nanoscale epicuticular tubules prevent nanodroplets from filling the grooves between the papillae [118]. There are several methods to fabricate biomimetic superhydrophobic surfaces with hierarchical roughness. They can be categorised as \"top-down\" or \"bottom-up\" approaches. In the top-down approaches, the nano-scale topographical details of the surface are obtained by the gradual removal of material from a larger bulk substrate [124].