## 3 Results and Discussion
Therefore, the droplet moves on a compressed layer of vapor and not the surface. Consequently, occurrence of full slip condition rather than partial one promotes capillary force (i.e., ideally no contact line viscous dissipation is present at full slip condition) and leads to the achievement of complete repellency as observed on superhydrophobic surfaces. Therefore, it can be inferred that stagnation flow may result in the presence of a thin moving layer of air underneath the impacting water drop and superhydrophobic surface. By increasing incoming air velocity, the accelerated flowing thin air layer in the viscous region helps to reduce the droplet contact time by two mechanisms. First, the generated rim of the droplet in contact with the thin layer of air underneath promotes the ligament of the impacting water droplet to spread without significant viscous dissipation compared to the still air case. In fact, near the wall boundary layer thickness is not same as still air conditions. Secondly, K-H instability [31] which is promoted by increasing air speeds at either interface (solid-air or air-liquid) results in a more unstable spreading ligament. In fact, contribution of the full slip boundary condition along with K-H instability results in faster detachment of the water droplet during the recoiling phase. Furthermore, impacting the water drop in the presence of air flow is not fully axisymmetrical as the drop might not impact exactly at the stagnant point. In fact, numerical simulation of the impinging air flow shows that the stagnation domain has a diameter of about 1 mm where air radial velocity in this  
Figure 2:0 Sequential images of supercooled water droplet impacts on superhydrophobic substrate maintained at \(-10\)\({}^{\circ}\)C (**A**) along with analysis of temporal spreading diameter (**B**). Droplet size and impact velocity are 2.6 mm and 1.6 m/s, respectively. area is negligible (i.e., below 2% of air jet velocity (see Supplementary Materials). Therefore, the spread drop might face the nonaxisymmetric shear and normal force of the air flow. Similarly to the study of [PERSON] et al. [PERSON] et al. (2013), droplet contact time is reduced significantly when receding velocity is no longer axisymmetric for normal drop impacts. However, it was shown to be independent of surface inclination for oblique drop impact [PERSON] et al. (2013). To this end, the same results was observed for an impacting supercooled water drop with temperature as low as \(-3.5\)\({}^{\circ}\)C on superhydrophobic surfaces maintained at temperature as cold as \(-20\)\({}^{\circ}\)C. In Figure 5, dimensionless contact time based on capillary-inertia time scale versus specific viscosity (\(\frac{\mu_{d}}{\mu_{d}}\)), for various supercooled water droplet temperatures is presented where \(\mu_{sd}\) is the viscosity of supercooled water and \(\mu_{d}\) is the viscosity of water at room temperature. In addition, we have added results of water-glycerol solution having the same viscosity as that of a supercooled water drop to properly evaluate the net effect of increasing viscosity on the detachment time of an impacting supercooled water drop [PERSON] et al. (2013). On the other hand, supercooled water droplet dynamics on superhydrophobic substrate maintained at \(-30\)\({}^{\circ}\)C which is below critical temperature of heterogeneous nucleation (i.e., \(-24\)\({}^{\circ}\)C) has a systematically different behavior (see Supplementary Materials). Although the spreading phase remains unaffected (e.g., measuring both advancing dynamic contact angle and maximum spreading diameter, along with calculation of ratio of Stefan to Prandtl ratio (i.e., 0.15)) by both ice nucleation mechanisms and sever increase in contact line viscosity with and without air flow, dramatic changes were observed in the relaxation and receding phases. Time at the maximum spreading diameter (i.e., relaxation time) was significantly increased up to 2 ms causing a significant increase in heat transfer cooling rate due to the large wetting area.