# Recent Advances in Femtosecond Laser-Induced Surface Structuring for Oil-Water Separation
## 4 Oil-Water Separation Mechanism  
The superwetting characteristic of water and oil phases on a solid surface is predominantly responsible for oil-water separation in membrane technology. The wetting response of a surface to a liquid is characterized by the contact angle of a liquid droplet on the surface. When such a droplet is placed on a surface, it forms a hemispherical shape due to the minimization of the surface free energy. The contact angle, \(\theta\), depending on the surface free energy of the solid, liquid, and vapor interfaces, is described by [PERSON]'s equation [50]:  
\[\cos\theta=(\gamma_{\mathrm{SV}}-\gamma_{\mathrm{SL}})/\gamma_{\mathrm{LV}} \tag{1}\]  
where \(\gamma_{\mathrm{SV}}\), \(\gamma_{\mathrm{SL}}\), and \(\gamma_{\mathrm{LV}}\) are the surface free energy of the solid/vapor, solid/liquid, and liquid/vapor interfaces, respectively (Figure 6a). [PERSON]'s state explains the wettability response of the material on an ideally flat surface. However, microscopic surface roughness has a crucial influence on the wetting response. The effect of the surface roughness on the wettability has been widely described by two different models (Figure 6c,d). In the [PERSON] model, the liquid is assumed to completely penetrate the entire rough surface, described as a homogeneous wetting state, without leaving any air pockets underneath. The apparent contact angle, \(\theta_{\mathrm{w}}\), is then given by a modified [PERSON]'s equation:  
\[\cos\theta_{\mathrm{w}}=r(\gamma_{\mathrm{SV}}-\gamma_{\mathrm{SL}})/\gamma_ {\mathrm{LV}}=r\cos\theta \tag{2}\]  
where the roughness factor \"\(r\)\" is the ratio of the unfolded to the projected surface area [51] and \(\theta\) is the contact angle on a flat surface of the same nature as the rough. Because \(r\) is always greater than unity, this model predicts that the contact angle will decrease/increase with surface roughness for an initially hydrophilic (\(\theta<90^{\circ}\))/hydrophobic (\(\theta>90^{\circ}\)) surface. In other words, a hydrophobic rough surface  
Figure 6: Different wetting states of water and oil droplets. (**a**) Young state of a droplet on a flat surface; (**b**) definition of the sliding angle (SA) or roll-off angle; (**c**) Wenzel state where the liquid completely wets the surface structures; (**d**) transitional or partial wetting state; (**e**) Cassie–Baxter state, where the droplet sits on the microstructures and air is trapped beneath it; and (**f**) oil droplet underwater in the Cassie–Baxter state. becomes more hydrophobic, while a hydrophilic one becomes more hydrophilic. Furthermore, contrary to the [PERSON]'s droplet state, [PERSON]'s state, i.e., an ideally flat surface, exhibits limited hydrophobicity, as the effect of the surface energy alone is not enough to realize superhydrophobicity. Contrary to the Wenzel state, in the case of the Cassie-Baxter droplet state (Figure 6d), the droplet sits on the surface microstructures, and air pockets are trapped beneath the liquid [52]. In this case, the apparent contact angle \(\theta_{CB}\) is provided by the following relation:  
\[\cos\theta_{CB}= f\cos\theta+f-1 \tag{3}\]  
where \(f\) is the area fraction of the liquid in direct contact with the surface structures and \(\theta\) is the Young's contact angle. As \(f\) is always lower than unity, this model always predicts the enhancement of hydrophobicity independently of the value of the initial contact angle \(\theta\). In practice, a transitional stage between the [PERSON] and Cassie state is more likely to occur, in which the liquid only partially permeates the rough surface (Figure 6e). As a result, the droplet forms a composite solid-liquid/air-liquid interface with the surface in contact.