# The Wettability and Numerical Model of Different Silicon Microstructural Surfaces
## 1 Introduction  
Wettability describes the spreading of a liquid on a surface, and is one of the important characteristics of a solid surface [1]. Wettability has been widely used in many industries, such as surface self-cleaning [2; 3; 4], antibacterial products [5], fluid drag reduction [6], inkjet printing [7; 8], anti-fouling products [9], anti-adhesives [10], and environmental applications [11]. Moreover, surface wettability plays an important role in boiling and condensation, such as in homogeneous nucleation, vapor condensation, and bubble growth [12; 13]. The contact angle is the main parameter that characterizes the wettability of the solid surface, and it changes following variations in the surface morphology or chemical properties. The contact angle refers to the angle formed by the tangent of the gas-liquid interface at the gas-liquid-solid intersection on the sample surface, when the droplet reaches a thermodynamic equilibrium on the solid surface. The relationship between surface tension and contact angle can be expressed as [PERSON]'s equation [14], and the wetting model is shown in Figure 0(a). \[\cos\theta_{Y}=\left(\gamma_{sg}-\gamma_{sl}\right)/\gamma_{\rm lg} \tag{1}\]  
where \(\theta_{Y}\) is [PERSON]'s contact angle, \(\gamma_{sg}\), \(\gamma_{sl}\) and \(\gamma_{lg}\), andare the surface tension at the solid-gas, solid-liquid, and liquid-gas interfaces, respectively. [PERSON]'s equation is applied to smooth ideal surfaces, which greatly limits its practical applications. On the basis of [PERSON]'s theory, [PERSON] [15]proposed a contact-angle prediction theory for practical surfaces, and the wetting model is shown in Figure 1b. \[\cos\theta_{W}^{*}=r\cos\theta_{Y} \tag{2}\]  
where \(r\) represents the roughness and is defined as the ratio of the true surface area to the projected surface area, namely \(r\geq 1\). The [PERSON] theory assumes that the liquid is in full contact with the rough structure on the solid surface. However, when \(|r\cos\theta_{Y}|>1\), the surfaces do not satisfy this rule in practical applications. The Cassie-Baxter theory [16] assumes that the solid-gas composite surface is in contact with the droplet on the rough surface; in other words, the groove under the droplet is filled with gas. The wetting model is shown in Figure 1c, such that  
\[\cos\theta_{\rm C}^{*}=f_{s}\cos\theta_{Y}+f_{s}-1 \tag{3}\]  
where \(f_{s}\) is the solid-liquid fractional surface area. The Cassie-Baxter theory indicates that the solid-liquid fractional surface area plays a decisive role in determining the apparent contact angle. Smaller \(f_{s}\) values generate greater Young's contact angles and apparent contact angles (\(\theta_{\rm C}^{*}\)). Both the [PERSON] and Cassie-Baxter theories indicate that the contact angle of the actual surface is determined by both the surface morphology and Young's contact angle. In recent years, many scholars have examined the properties of superhydrophobic surfaces owing to their excellent performances in industrial applications. The wettability of a solid surface is determined by its surface chemical energy and surface roughness. To increase the contact angle of the surface, it is necessary to reduce the surface chemical energy and to increase the surface roughness [17]. [PERSON] et al. [18], [PERSON] et al. [19], and [PERSON] et al. [20] characterized the surfaces of different materials using different chemical methods, all of which enlarged the surface roughness and reduced the surface free energy with the aim of generating a hydrophobic surface and augmenting the surface contact angle. In addition, some scholars changed the surface wettability by increasing the surface roughness. [PERSON] [21] prepared a stable and wear-resistant coating on a stainless steel surface using nanosecond laser processing, which enhanced the surface roughness and the contact angle. [PERSON] et al.