## 1 Introduction  
Icing on key parts of an aircraft, such as wings, tails and engines, poses a threat to flight safety [1]. To tackle this issue, various ice protection systems have been developed and widely used, including thermal, pneumatic, electro-mechanic and anti-/de-icing fluid systems [2; 3]. Although these ice protection systems have been effective, the increasing emphasis on safety requirements and limited aircraft energy capacity have exposed the conflict between the two. For instance, the hot-air ice protection system utilizes engine-generated hot air that affects engine power. In adverse weather conditions, when the hot air is insufficient, surface heating cannot ensure the complete evaporation of impinging water droplets, and part of the supercooled water impinging on the surface will freeze and form runback ice after flowing over the protected area [4]. That is the major cause of the ATR72 accident in Roselawn in 1994 [5]. The thermoelectric ice protection system has been widely used in helicopter blades, windshields, instruments, etc. However, with components such as wings and tails, due to the limited power supply of the aircraft, it typically operates periodically or continuously provides less heat only to maintain water on the surface in its liquid state [6], resulting in weak ice protection. Pneumatic, electro-mechanic ice protection system and anti-/de-icing fluid would negatively impact aerodynamic performance or add extra weight. With advances in material technology, researchers attempted to develop a kind of icephobic coating that can passively reduce or delay ice formation without energy consumption. However, almost all coatings could not achieve the desired goal [7; 8; 9]. Alternatively,hydrophobic or superhydrophobic coatings have been used to decrease the power required for ice protection by facilitating droplet removal when subjected to shear flow. In 2007, [PERSON] et al. [10] tested a mixture of acrylic urethane resin and polytetrafluoroethylene named AIS, and the results showed less difference in performance when no heating was performed. There was less ice on the AIS, but the test did not reflect whether it was due to the icephobic or hydrophobic properties. In 2009, [PERSON] et al. [11] examined the ice formation process of supercooled water drops on surfaces with different hydrophobic characteristics and confirmed that the hydrophobic property had a significant impact on icing. In subsequent studies, [PERSON] et al. [12] investigated the reasons why superhydrophobic coatings reduce energy consumption and determined that they reduced water droplet aggregation on the surface and promote water droplets' falling off the surface, resulting in fewer droplets freezing. [PERSON] et al. [13], by comparing runback ice formed on a hydrophilic surface and a superhydrophobic surface, believed that surface wetting state played an important role in the icing process. [PERSON] et al. [14] found that the decreasing contact angle would lead to an increase in the angle needed for droplet inclined rolling. The movement of water droplets on the surface deteriorates rapidly under the condition of high relative humidity and low temperature. In 2011, [PERSON] et al. [15] combined thermoelectric and hydrophobic coatings and evaluated the behavior of various hydrophobic coatings under glaze and rime icing conditions. The energy savings achieved were about 33% for glaze ice and about 13% for rime ice compared to ice protection systems used with no coating [15]. In 2017, [PERSON] et al. [16] studied the behavior of superhydrophobic coating on an airfoil model equipped with a thermal ice protection system and found no ice formation when maintaining the superhydrophobic coating surface temperature above 4 \({}^{\circ}\)C, while the ice protection system surface with no coating needs at least 70 \({}^{\circ}\)C in the same condition.