**Author details**

characteristics of hydrophobicity can be enhanced. *θ*<sup>c</sup> is always larger than *θ* on the

**Figure 5** shows a droplet sitting on a textured surface in a Cassie-Baxter state. It

(the first level of hierarchy) as shown in **Figure 5b**. If the contact line is divided into much smaller lines, viz., the second level of hierarchy, the related contact angle *θ*<sup>2</sup>

**Figure 5c**. These phenomena will be kept on until a homogeneous wetting interface achieved when reaching a level *n*. Consequently, the contact angle either increases or decreases by adding multiple length scales of roughness at all smaller levels depending on the pinned fraction of each level of hierarchy, which is critical for

The droplet on a solid surface will exhibit a certain value of contact angle to achieve the equilibrium of the interfacial tensions. In addition, surface roughness will influence the contact angle, based on Wenzel's and Cassie-Baxter's theories, with the assumption of overhangs. It reveals that the contact angle can be controlled by the intentionally fabricated textured surfaces, and the surface with the fabricated textures can be changed from hydrophilic to hydrophobic, and vice versa, without considering whether the original material is hydrophilic or hydrophobic.

<sup>r</sup> of the first level of hierarchy as shown in

<sup>r</sup> (the zeroth level) to *θ*<sup>1</sup>

*. (b) The apparent contact line of the drop is*

r

*r .*

r

depicts the real contact line of the droplet, which is changed into many smaller

In fact, numerous investigations have been devoted to the wettability on different surfaces, particularly for the surfaces inspired by Nature Mother [18–26]. Paxson et al. [27] fabricated a surface with the hierarchical textures initiated by lotus leaves and revealed the relevant mechanism of the variation or evolution of the adhesion force per unit length of the projected contact line distributed on natural textured surfaces. Results show that the adhesion force varies with the

*Schematic of self-similar contact line pinning. (a) A liquid droplet that rests in a Cassie-Baxter state on a*

*divided into many smaller first-level contact lines, each at the top of a first-level roughness feature with width* w *and spacing* s*. each of these first-level contact lines sits at the base of a first-level capillary bridge, which has a*

*divided into smaller second-level contact lines, each atop a second-level roughness feature. Each second-level contact line sits at the base of a second-level capillary bridge, which has a local receding contact angle* θ*<sup>2</sup>*

*r*

*. (c) The apparent contact line of each second-level capillary bridge is further*

rough surface [14–17].

*local receding contact angle* θ*<sup>1</sup>*

**Figure 5.**

pinned fraction of each level of hierarchy.

*hierarchical surface exhibits an apparent receding angle* θ*<sup>0</sup>*

*21st Century Surface Science - a Handbook*

*r*

is distinctively different from *θ*<sup>1</sup>

**6. Conclusion**

**120**

lines. Meanwhile, the contact angle also changes from *θ*<sup>0</sup>

designing surfaces with various adhesion [28–33].

Yeeli Kelvii Kwok Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong

\*Address all correspondence to: yeelikwok@yahoo.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
