## 2 Materials and Methods
High-magnification SEM image analysis was utilized in order to document the impact flame conditions had on the morphology of the carbonaceous films. Once SEM analysis was completed the flame-treated substrates were classified as hydrophobic, superhydrophobic, or hydrophilic via CA analysis. As shown in Figure 2d the CA was measured by placing a water droplet on the surface of the substrate, capturing a photograph of the water droplet resting on the surface, and using digital micrograph software to measure the CA of the water droplet. Note that the contact angle, \(\theta\), is measured between the line parallel to the surface of the substrate at the base of the water droplet and the line tangent to the water droplet (Figure 2d). C-layers were formed on SS substrates using three different flames (Flame I, II, and III), as shown in Table 2. Changes in surface morphology/structure, degree of hydrophobicity, and mass of the flame deposits were observed based on the following: (a) substrate insertion height into the flame; (b) fuel types used in the burner (CME vs. CH\({}_{4}\)); and (c) amount of oxygen in the oxidizer stream (21%, 35%, and 50%). Initially, the effect of flame height on the C-layer formed was explored by inserting the substrate into the CME/air flame at four different heights (10, 12, 15 and 20 mm) for a resident time of 5 min (Table 2--Flame I); the total length of the CME/air flame was approximately 22 mm. Next, the effect of fuel type was investigated by using a methane/air flame (Table 2--Flame II). The substrate was inserted into the CH\({}_{4}\)/air flame for a residence time of 1 min at 50 and 60 mm HAB; the total height of CH\({}_{4}\)/air flame was approximately 85 mm. The final flame, Flame III, utilized CME as the fuel and the oxygen content within the oxidizer stream was increased from 21% (air) to 35% and then 50% O\({}_{2}\) (N\({}_{2}\) made up the balance of the oxidizer). The SS disk was inserted into the flame volume at approximately three-quarters the flame height for a residence time of 5 min for all oxygen contents. At 21% O\({}_{2}\) the flame was \(\sim\)21 mm in height and the substrate was inserted at \(\sim\)15 mm HAB; at 35% O\({}_{2}\) the flame was \(\sim\)12 mm in height and the substrate was inserted at \(\sim\)9 mm HAB; and at 50% O\({}_{2}\) the flame was \(\sim\)10.6 mm in height and the substrate was inserted at \(\sim\)8 mm HAB. All tested flame parameters are shown in Table 2. A shortened residence time was utilized for the methane-air flame due to increased flame temperatures, to limit thermal strain to the substrate holder and to avoid rapid oxidation of deposited soot. The CME-air flame ranged from \(\sim\)490 \({}^{\circ}\)C near the burner inlet (HAB = 1.4 mm) to \(\sim\)870 \({}^{\circ}\)C at the tip of the flame (20 mm), while the methane-air flame temperature ranged from \(\sim\)740 \({}^{\circ}\)C near the burner inlet (HAB = 9.8 mm) to \(\sim\)1200 \({}^{\circ}\)C at the tip of the flame (HAB = 80 mm). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Flame** & **Fuel** & **Oxidizer (\% O\({}_{2}\))** & **HAB (mm)** & **Residence Time (min)** \\ \hline Flame I & CME & 21 & 10, 12, 15, 20 & 5 \\ Flame II & CH\({}_{4}\) & 21 & 50, 60 & 1 \\ Flame III & CME & 21, 35, 50 & 3/4 Flame Height \({}^{\dagger}\) & 5 \\ \hline \hline \end{tabular} \({}^{\dagger}\) 21%, 35%, and 50% O\({}_{2}\) corresponds to respective HABs of 15, 9, and 8 mm.  
\end{table} 
Table 2: Summary of flame parameters for C-layer formation.