Abstract
Wettability has been explored for 100 years since it is described by Young’s equation in 1805. It is all known that hydrophilicity means contact angle (θ), θ < 90°; hydrophobicity means contact angle (θ), θ > 90°. The utilization of both hydrophilic surfaces and hydrophobic surfaces has also been achieved in both academic and practical perspectives. In order to understand the wettability of a droplet distributed on the textured surfaces, the relevant models are reviewed along with understanding the formation of contact angle and how it is affected by the roughness of the textured surface aiming to obtain the required surface without considering whether the original material is hydrophilic or hydrophobic.
Keywords
- wettability
- droplet
- hydrophilic
- hydrophobic
- surface tension
- contact angle
- textured surface
- Wenzel model
- Cassie-Baxter model
1. Introduction
It is well known that when a small droplet of liquid is deposited on the solid surface, it forms a shape with a contact angle to the solid. This phenomenon is firstly described by Young in 1805, and he proposed that surface energy is the interaction between the forces of adhesion and the forces of cohesion which determine whether the wetting occurs or not (i.e., the spreading of a liquid over a surface) [1]. If it does not occur the complete wetting, the liquid in a bead shape will be formed. In the same time, as a function of the surface energies, a contact angle is defined in the system.
When the liquid wets the solid, three different interfacial boundary surfaces, viz., solid-air (sv), solid-liquid (sl), and liquid-air (lv), are involved. The contact angle, which is included between the interfaces of sl and lv, has to reach a certain value to satisfy the equilibrium state of the three interfacial tensions. It is all known that there are two requirements for the equilibrium.
2. Static equilibrium
The first requirement for keeping a balance of the three interfacial tensions in horizontal direction is described by Young’s Eq. (1):
where
3. Dynamic equilibrium
Another requirement is the dynamic equilibrium determined by the interface energy which can be calculated from
where
It should be noticed that
For the system applied on a hydrophobic surface as shown in Figure 2b, with the effect of the contracting of liquid, the area of the sl interface decreases with increasing lv interface. Because
It should be noted that (
4. Effect of surface roughness on contact angle
It should be noticed that there distinctively exists a difference between the geometric surface and the actual surface and their interface is not ideal as a proposed model in the textbooks. Actually, the surface of any real solid is not a perfect plane. Due to the surface roughness, the real area of the actual surface is larger than the so-called ideal (geometric) surface. Consequently, the surface roughness affects the contact angle and the contact angle distinctively varies with the surface roughness. As a result, in order to keep the equilibrium, the profile of a droplet will vary with the effect of the surface roughness. For studying
Wenzel model.
According to the model described by Wenzel in 1936 [9], the solid surface completely contacts with liquid under the droplet as shown in Figure 3. The
With a variation of the geometric
In addition, the lv interface is not affected by the surface roughness. So the equilibrium with the new contact angle of
Compared with Eq. (1),
Taken
where
5. Cassie-Baxter model
In 1944, Cassie applied and explored Wenzel equation on porous materials [13]. According to Cassie-Baxter model, air can be trapped below the drop as shown in Figure 4. The area of the
With a variation of the profile of the droplet, the amount of energy transited among the interfaces is changed:
The equilibrium with the new contact angle of
Compared with Eq. (1),
Taken
where
In fact, numerous investigations have been devoted to the wettability on different surfaces, particularly for the surfaces inspired by Nature Mother [18, 19, 20, 21, 22, 23, 24, 25, 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 pinned fraction of each level of hierarchy.
Figure 5 shows a droplet sitting on a textured surface in a Cassie-Baxter state. It depicts the real contact line of the droplet, which is changed into many smaller lines. Meanwhile, the contact angle also changes from
6. Conclusion
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.
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