**2. Theoretical basis of wettability**

Contact angle (CA) assigned as θ, which can give the quantitative measurement of wetting of a solid by a liquid. Therefore, it can be defined as the angle measured by a liquid where the liquid-gas interface meets at solid surface as shown in **Figure 1**.

*A Triphasic Superwetting Catalyst for Photocatalytic Wastewater Treatment DOI: http://dx.doi.org/10.5772/intechopen.109509*

**Figure 1.** *Schematic illustration of the triple-phase contact line.*

### **2.1 Theoretical models**

Wettability is an essential property of solid materials. When liquid droplet contacts a solid surface in air, a three-phase contact line is formed at the three-phase junction. The contact line expands outward up to the droplet reaches a static state. In a steady-state system, a three-phase contact line is contact because of an equilibrium tangential forces created by the interfacial and surface tensions. The wetting properties of the liquid on solid surface is measured by the CA such as when θ < 90°, the surface considered to be hydrophilic and when θ > 90°, the surface is hydrophobic. However, when the θ > 150° , the surfaces are highly hydrophobic and called superhydrophobic. Similarly, superhydrophilic surfaces have a θ < 10° .

The Wetting properties of the solid surfaces is governed by the Young, Wenzel, and Cassie-Baxter equation. The young are derived by balancing the interfacial forces at a three-phase contact line Eq. (1).

$$\cos \theta = \frac{\mathcal{Y}\_{sv} - \mathcal{Y}\_{sl}}{\mathcal{Y}\_{lv}} \tag{1}$$

Here θ is the CA of the liquid droplet, γsv (solid-gas) γlv (liquid-gas), and γsl (solidliquid) interfacial force per unit length of the contact line which is surface tension. Moreover, the balance of angle formed by the liquid at the three-phase boundary is defined as young's contact angle (**Figure 2a**). According to the value of contact angle, the surface should be hydrophilic (θ < 90°, γS > γSL) and hydrophobic (θ > 90°, γS < γSL) (**Figure 2b** and **c**).

For the solid surface which has rough morphology, then Wenzel introduced the factor of surface roughness, r, into Young's equation after considering the influence of rough surface structure on wettability. Therefore, the definition is the actual surface area to the projected surface area is "r". In this case, the liquid fills the microstructure of the solid surface (**Figure 3a**). For a liquid droplet in the Wenzel state, the measured/apparent CA ( Θ*w* ) can be expressed by the Wenzel equation Eq. (2) which can be expressed the surface roughness.

$$r\cos\Theta w = r.\cos\theta\tag{2}$$

**Figure 2.**

*(a) The wetting regime for Young's model, measurement of contact angle for (b) hydrophilic and (c) hydrophobic surfaces.*

#### **Figure 3.**

*Various states of droplets on a solid surface (a) Wenzel model, and (b) Cassie–Baxter model.*

For hydrophobic surfaces, the roughness is very high and large r value. Sometimes, the liquid does not penetrate in to the roughness, so that the layer of trapped air between the solid surface and the liquid. In this case the contact interface between liquid and the solid surface consists of liquid-solid contact and liquid-air contact (**Figure 3b**) and expressed by Cassie equation Eq. (3)

$$
\cos\Theta\_c = f\_1 \cdot \cos\Theta\_1 + f\_2 \cdot \cos\Theta\_2 \tag{3}
$$

Where θ*c* is the CA, θ1, θ2 are the CA of the liquid droplet on the solid and air phases and f1, f2 are the area ratio of liquid-solid contact and the liquid-air contact, respectively. Again, for solid microstructure surface, if the liquid-solid contact area fraction is f, then liquid-air contact will be (1 − f). So that, the Cassie equation will be Eq. (4):

$$
\cos \theta \mathbf{c} = f \cos \theta\_1 + (1 - f) \cos \mathbf{1} \mathbf{8} \mathbf{0}^\circ \tag{4}
$$

According to wettability, superwetting materials are generally categorized into four types: superhydrophobic, superhydrophilic, superoleophilic, and superoleophobic states. Specially, the first two kinds of superwetting materials which can be used for oil/water separation. These superwetting materials are believed to be promising

materials for removing pollutants from water due to their superwetting property towards oils and water [7, 8].
