# Spreading Dynamics of Droplet Impact on a Wedge-Patterned Biphilic Surface
## 3 Results and Discussion
### Effects of Impact Velocity
[20] and [PERSON] et al. [21]. The resolutions are shown in Table 1.9  
The static contact angle has an effect on the maximum spreading diameter. For the static contact angle \(\theta_{1}=68^{\circ}\) and \(\theta_{2}=142^{\circ}\), the maximum spreading factor varies widely. As the apex angle is relatively small, the homogeneous surface model should be analyzed first. Taking the static contact angle \(\theta=\theta_{2}=142^{\circ}\), the comparison between the different models are listed in \[E_{k0}=\frac{\pi\rho D_{0}^{3}v_{0}^{2}}{12} \tag{17}\]0  
In Figure 10a, there is not much difference between the different models. The model of [PERSON] et al. [21] agrees well with the experimental data for a homogeneous superhydrophobic surface. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Contact Angle**} & \multicolumn{1}{c}{_We_} & **0.5** & **1.9** & **2.7** & **4.8** \\ \cline{2-6}  & **Exp. Data** & **1.18** & **1.33** & **1.43** & **1.58** \\ \hline \multirow{2}{*}{\(\theta_{1}=68^{\circ}\)} & Pasandideh-Fard [20] & 2.51 & 2.52 & 2.54 & 2.59 \\  & Zhao [21] & 2.20 & 2.48 & 2.62 & 2.92 \\  & Equation (31) & 2.07 & 2.12 & 2.15 & 2.24 \\ \hline \multirow{2}{*}{\(\theta_{2}=142^{\circ}\)} & Pasandideh-Fard [20] & 1.51 & 1.57 & 1.60 & 1.67 \\  & Zhao [21] & 0.90 & 1.33 & 1.46 & 1.73 \\  & Equation (31) & 0.88 & 1.04 & 1.15 & 1.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum spreading factor of the different Weber numbers for different models. Figure 9: Recorded positions after impacting on the wedge-patterned biphilic surface. For a wedge-patterned biphilic surface with apex angle \(\alpha\), the equivalent diameter is promoted to be estimated according to the spreading area \(S\):  
\[S=\frac{\pi\overline{D}_{\max}^{2}}{4} \tag{33}\]  
\[S_{1}=\frac{\alpha D_{\max,1}^{2}}{8} \tag{34}\]  
\[S_{2}=\frac{(2\pi-\alpha)D_{\max,2}^{2}}{8} \tag{35}\]  
\[S=S_{1}+S_{2} \tag{36}\]  
where \(D_{\max,1}\) and \(D_{\max,2}\) represent the maximum spreading diameters on the hydrophilic surfaces and superhydrophobic surfaces, separately. Combining Equations (33)-(36), one can get:  
\[\overline{D}_{\max}=\sqrt{\frac{\alpha D_{\max,1}^{2}+(2\pi-\alpha)D_{\max,2} ^{2}}{2\pi}} \tag{37}\]  
Taking the apex angle \(\alpha=36.9^{\circ}\), the equivalent maximum spreading diameters, calculated on different models are listed in Figure 10b. Based on Equation (37), the equivalent maximum spreading diameters are calculated for apex angle \(\alpha=36.9^{\circ}\), as shown in Figure 10b. From Figure 10b, the maximum spreading diameters based on Equation (31) agree well with the experimental data, better than those two models of [PERSON] et al. [20] and [PERSON] et al. [21]. In order to derive a relation for the maximum spreading factor of the impact on wedge patterned surfaces, the first oscillation has been paid more attention. The maximum spreading factor during the first oscillation is shown in Figure 11 for different Weber numbers. Taking account of the expression of [PERSON] et al. [27], an exponential function is promoted, then \(\beta_{\max}\sim We^{x}\). Using the least squares procedure on the experimental results for maximum spreading diameters, one can find that \(x\approx 1/5\). The experimental data of the maximum spreading diameters under different Weber numbers and the fitting exponential curve are plotted in Figure 11.  
Based on the limited experimental data during the first oscillation under different Weber numbers, the maximum diameter then has a relation with the Weber number:  
\[\beta_{\max}\sim We^{1/5} \tag{38}\]  
Figure 10: Maximum spreading factor for different Weber numbers (**a**) and different apex angles (**b**).