## 3 Results and Discussion
It increases up to almost 2-fold at 10 m/s air velocity, which highlights a significant difference on impacting drop dynamics on a superhydrophobic surface where stagnation flow is present. In Figure 7, comparison of the maximum spreading diameters was carried out by three different approaches. The first is the energy based model proposed by [PERSON] et al. [44] which is based on the balance of all energies before and after impacts, and the second model is an analytical hydrodynamic model proposed by [PERSON] [54] derived from continuity and momentum equations. Both the hydrodynamic and energy based model were used to compare with experimental data. For a superhydrophobic surface, a scaling law analysis proposed by [PERSON] et al. [55] is used for proper  
Figure 2:2 Temporal evolution of impacting water droplet on superhydrophobic substrate at different temperature (**A**); Effect of air flow on impacting supercooled water drop on superhydrophobic substrate below critical temperature of heterogeneous nucleation (**B**). Droplet size and impact velocity are 2.6 mm and 1.6 m/s, respectively. evaluation. As depicted in Figure 7C, for supercooling conditions, the scaling law predicts very well the supercooled water drop at \(-2\)\({}^{\circ}\)C. However, it overestimates the maximum spreading diameter for the lowest temperature supercooled water drop (i.e., \(-5.5\)\({}^{\circ}\)C) with mean value deviation up 3%. The best agreement was observed for the energy balanced model at supercooling condition. This model fits very well with experimental data with mean value deviation of up to 1%. However, the analytical hydrodynamic model predicts relatively well the mean value deviation up to 14% for supercooled water drop at \(-5.5\)\({}^{\circ}\)C. In addition to supercooled water droplet experiments, the droplet impact of water-glycerol solution with various specific viscosity ranging from 1.9 (corresponding supercooled water at \(-2\)\({}^{\circ}\)C) to 2.2 (corresponding \(-5.5\)\({}^{\circ}\)C supercooled water) were carried out to mimic an increased viscosity in supercooled water due to temperature reduction. The results show a very good agreement with that of supercooled water drop experiments. The same comparison was carried out for aluminum and Teflon substrates, as depicted in Figure 2:3 Both the energy based model and hydrodynamic model agree very well with experimental results. Associated errors for the energy based model become slightly larger than those of the hydrodynamic model for room temperature conditions on an aluminum substrate with mean value deviation of 4.6% and 3.5%, respectively. The same results were found for Teflon substrate for both models with almost the same mean value deviation up to 8% for room temperature conditions. However, when viscosity is increased, the difference between experimental results and the two aforementioned models becomes larger. For a higher water drop degree of subcooling (i.e., \(-5.5\)\({}^{\circ}\)C), the mean value deviation for energy based and hydrodynamic models for aluminum substrates become 12% and 15%, and 10% and 14% for Teflon substrates, respectively. The difference between experimental results with that of the aforementioned models stems from water drop interface temperature moving through cold air before impacting on the substrates. Thermal transport analysis (see Supplementary Materials) shows that the Biot number becomes larger than 0.1 when air flow is present. Furthermore, the Fourier number becomes as small as 0.00045. Therefore, we can expect an interfacial temperature change. Calculation of heat penetration lengths [1], \(\delta_{h}\approx(\alpha_{w}t_{c})^{\frac{1}{2}}\), shows that this length varies up to 0.1 mm (\(\alpha_{w}=0.13\)\(10-6\)\(\left(\frac{m^{2}}{s}\right)\) and \(t_{c}\approx 85\) ms).