## 2 Materials and Methods  
Two nanostructured coatings (hereafter labeled as 1 and 2) [24] were applied with an aerograph with a layer-by-layer process, as a usual paint, on three different substrates: (1) 5 \(\times\) 5 cm \(\times\) cm flat composite samples made of carbon fiber and epoxy resin painted with a commercial aeronautical paint purchased from Akzo-Nobel (labeled as C); (2) 5 \(\times\) 5 cm \(\times\) cm flat samples in stainless steel (hereafter labeled as S) pretreated with a sandpaper P40 to increase the roughness surface and improve the coating's adhesion, and; (3) two wing profiles NACA0015 manufactured with a 3D printing machine, having a length of 135 mm and a chord of 100 mm made of acrylonitrile butadiene styrene (hereafter labeled as A). Samples were named as: X-i with X = Substrate, which is C, S, or A, and I = Surface, namely, R for Reference, and 1 or 2 for coatings. Hence AR, CR, and SR are the references, whereas A1, A2, C1, C2, S1, and S2 are the coated samples. Unlike samples C and S, sample A had one-half painted with coatings, leaving the other half uncoated as a reference to better compare the coating and reference. The roughness of substrates before and after the application of the coating was measured by employing a SAMA SA6260 surface roughness meter. Roughness measurements, performed according to the ISO 4288 [25], were reported as Ra, which represents the arithmetic average of the absolute values of the profile height deviations from the mean line. The optical images were acquired with a microscope USB Dino-Lite AM4815 ZTL at 140\(\times\). The contact angle (CA) measurements were performed at 23 \({}^{\circ}\)C in compliance with the ASTM D7490-13 [26] standard, with 3 \(\mu\)L of water (H\({}_{2}\)O) and diiodomethane (CH\({}_{2}\)I\({}_{2}\)), by acquiring at least six measurements. Contact angles were rapidly acquired, within 30 s of depositing the drop, to avoid changes in angles. The mean values and standard deviations of CA were the input data of a Matlab tool (a CIRA home-made tool) which solves the two equations (1), derived by the application of the Owens-Wendt-Kaelble method [27; 28] for the assessment of the solid surface free energy (SFE). Due to the stochastic nature of the CA experimental measurements, a third liquid was introduced, i.e., formamide (HCONH\({}_{2}\)) [29; 30]. The software uses the third liquid to minimize the error on the third Equations (2) and (3), giving as output the optimized values of the CA, along with an assessment of polar and dispersive components of SFE, which is useful to calculate the SFE through Equation (4), the work of adhesion (W\({}_{\text{A}}\)) through Equation (5), and the surface polarity (SP) through Equation (6). \[\left\{ \begin{array}{c}\frac{\gamma_{l_{1}}(1+\cos\theta_{1})}{2}=\left( \gamma_{l_{1}}^{d}\gamma_{s}^{d}\right)^{1/2}+\left(\gamma_{l_{1}}^{p}\gamma_ {s}^{p}\right)^{1/2}\\ \frac{\gamma_{l_{2}}(1+\cos\theta_{2})}{2}=\left(\gamma_{l_{2}}^{d}\gamma_{s} ^{d}\right)^{1/2}+\left(\gamma_{l_{2}}^{p}\gamma_{s}^{p}\right)^{1/2}\end{array} \right. \tag{1}\]  
\[\underset{\gamma_{s}^{d}\gamma_{s}^{p}}{\min}\bigg{(}\left(\gamma_{l_{3}}^{d} \gamma_{s}^{d}\right)^{1/2}+\left(\gamma_{l_{3}}^{p}\gamma_{s}^{p}\right)^{1/ 2}-\frac{\gamma_{l_{3}}(1+\cos\theta_{3})}{2}\bigg{)} \tag{2}\]  
\[\small\begin{array}{c}s.t.\left\{\begin{array}{c}\left(\gamma_{l_{1}}^{d} \gamma_{s}^{d}\right)^{1/2}+\left(\gamma_{l_{1}}^{p}\gamma_{s}^{p}\right)^{1/ 2}-\frac{\gamma_{l_{1}}(1+\cos\theta_{1})}{2}=0\\ \left(\gamma_{l_{2}}^{d}\gamma_{s}^{d}\right)^{1/2}+\left(\gamma_{l_{2}}^{p} \gamma_{s}^{p}\right)^{1/2}-\frac{\gamma_{l_{2}}(1+\cos\theta_{2})Here \(\gamma_{li}^{P}\) and \(\gamma_{li}^{D}\) are the polar and dispersive components of the liquid \(i\), \(\gamma_{s}^{P}\) and \(\gamma_{s}^{D}\) are the polar and dispersive components of the solid, respectively, and \(\theta i\) is the CAs measured with the liquid \(i\).