## 3 Results and Discussion
In the current study the ratio (\(\sqrt{\frac{Stt}{Pr}}\)) in lowest temperature conditions becomes as low as 0.15, stressing that the wetting dynamics during the spreading phase are not much affected by phase change mechanism. Therefore, comparison of the maximum spreading diameter with that of hydrodynamic energy balance models at specfic temperatures can be performed. After analysis of the impacting supercooled water drop in the still air, the effect of stagnation flow on the impacting water drop seems an interesting topic. The resulting shear and normal force of the air flow might lead to important changes in wetting dynamics of an impacting water drop. Furthermore, it significantly changes thermal transport properties of air-liquid interface by evaporation cooling [16]. However, quantitative analysis of temporal evolution of spreading diameter, illustrated in Figure 3, shows that the effect of incoming cold air flow has an insignificant effect on wetting dynamics on hydrophilic and hydrophobic surfaces which arise from strong crystallization process at solid-liquid interface combined with sever increase in contact line viscosity up to 8 and 4.3 fold at \(-30\)\({}^{\circ}\)C and \(-20\)\({}^{\circ}\)C, respectively [41; 42]. Furthermore, the effect of the capillary ridge become important where exposed air flow on thin film of super cooled water comes into contact with solid material [46]. On the other hand, due to the fact that both homogeneous nucleation, which weakens surface tension, and heterogeneous nucleation, which results in an increase in hydrophilicity by changing contact angle [17], enhances the chance of pinning on a polished aluminum surface and the resulting normal and shear force of stagnation flow cannot overcome the formed capillary ridge. However, incoming air flow has an observable and important outcome on the superhydrophobic surface. Figure 4 shows the sequential images of supercooled water droplet impacting on a coated superhydrophobic substrate along with quantitative analysis of temporal spreading diameter. The droplet diameter, impact velocity, Weber and Reynolds, Stefan, and Prandtl number are 2.6 mm, 1.6 m/s, 88, 2170, 0.128, 14.83, respectively. Droplet sphericity is changed after impact due to rapid raise in pressure and gets flattened cylindrical shape at 3 ms with no differences between the cases with and without air flow. However, at recoiling phase when the air jet velocity is increased (i.e., an increase in dynamic pressure), droplet bouncing and jet formation is dramatically suppressed, as depicted in Figure 4.  
Figure 3: Temporal evolution of impacting supercooled water drop on aluminum (**A**) and Teflon substrate (**B**) exposed to cold air flow. Droplet size and impact velocity are 2.6 mm and 1.6 m/s, respectively. The recoiling phase is almost initiated right after finishing the relaxation phase and lasts up to 0.2 ms. Strong retraction force due to high receding contact angle and partial slip velocity [47; 48] results in droplet detachment at 14 ms. Droplet contact time is not a function of impact velocity when it is sufficiently higher than the critical velocity of drop repulsion (i.e., \(V_{c}=\left(gR_{o}^{3}/lc^{2}\right)^{1/2}\), where \(lc\) is capillary length of water drop, \(lc=\sqrt{\gamma/\rho g}\)) and it varies with \(R^{2/3}\)[49]. On the other hand, quantitative analysis of the impacting supercooled water drop on superhydrophobic substrate accompanied with different air speeds shows different phenomena, as depicted in Figure 4. Striking results were observed when air velocity was increased. A droplet detached from the surface in a considerably smaller time than that of the still air case as a function of air speed. Contact time is reduced up to almost 30% at air velocity up to 10 m/s highlighting the effect of another physical factor. Recent study of droplet impact on dry ice shows that there is rapid generation of gas vapor formed beneath of the impacting droplet on a dry ice surface [50].