## 1 Introduction  
Nano-micro topography of solid surfaces exhibits different characteristics when interaction of solid-liquid ranging from severe adhesion to strong repellency is taken into consideration [1]. They have shown different outcomes when a hot [2] or cold surface [3] has been used for heat transfer and wetting dynamics evaluation. Cloud droplets leading to icing are supercooled water droplets in metastable equilibrium, a better understanding of the mechanism of phase change is essential for numerous applications. These applications range from electrical transmission power line, wind turbine to aerospace industries [4; 5; 6]. It was shown that having a surface with low wettability is a key prerequisite for ice formation mitigation [7] which is related to the substrates receding contact angle [8]. [PERSON] et al. [7] defined a correlation between ice adhesion strength and contact angle hysteresis (the difference between advancing and receding contact angle) for different solid surfaces with various wettabilities. An extremely low wettable surface, namely superhydrophobic surface, typically has a static and hysteresis contact angle larger than \(150^{\circ}\) and \(10^{\circ}\), respectively [9; 10]. These surfaces exhibit a tremendous water repellency whether in room or low temperature conditions above the critical temperature of freezing (i.e., \(-24\)\({}^{\circ}\)C) [11]. Indeed, superhydrophobicity is produced by combing rough surfaces coated with low surface-energy materials. Entrapped air underneath of an impacting water drop on rough surface changes the thermal transport property by increasing thermal resistance due to the low thermal conductivity of entrapped air [12; 13; 14]. This unique features of superhydrophobic surfaces act as a good insulator [15] used for decreasing solid-liquid interface temperature during the impact of the supercooled water droplet. Solid-liquid interface temperature plays a critical role in cthe crystallization process. It generally plays a dual role when a supercooled water droplet impacts on cold substrates. Larger solid-liquid interfacial area of impacting drop causes a significant increase in the heat transfer cooling rate [15]. Furthermore, both induced homogeneous nucleation [16] (i.e., due to evaporation cooling) and heterogeneous nucleation (solid-liquid interaction) [17] are related to liquid interface temperature. In fact, in real atmospheric cold conditions, induced homogeneous nucleation can happen even above the critical temperature of homogeneous nucleation (i.e., \(-37\)\({}^{\circ}\)C) [18; 19] due to the presence of air flow which systematically increases the rate of evaporation cooling at low and high humidity environments [16]. Therefore, gas-liquid interface temperature becomes as important as solid-liquid interface temperature (i.e., Gibbs free surface energy is related to interface temperature whether gas-liquid or solid-liquid) when evaluation of both nucleation mechanisms on wetting dynamics of an impacting supercooled water drop are taken into account. When a supercooled water drop impacts on a substrate the interface temperature becomes very close to the substrate temperature. Analysis of heat penetration length [1] showed that liquid water drop viscosity increases several times depending on substrate temperature. Dramatic changes in near wall viscosity results in rapid increase of viscous dissipation rate during drop impact, particularly at recoiling phase [20]. For moderate and high inertia impact conditions, partial meniscus penetration also happens which promotes viscous dissipation rate owing to contact line friction. Therefore, droplet receding velocity is reduced [21] which is the main reason for an increase in droplet contact time up to almost 75% and 20% for droplet Weber number (i.e., ratio of inertia to surface tension force) up to 236 and 100, respectively.