## 2 Materials and Methods  
In this study a flame deposition process was used to form hydrophobic C-layers on stainless steel substrates. The stainless steel (SS) substrates consist of disks that are 19 mm in diameter and resistant to high temperatures. A modified version of the co-flow burner developed by [PERSON] et al. [32] for studying methane/ethane flames was used to create methane and biodiesel flames. Once the flames were formed, the SS substrate was mounted on an aluminum substrate holder and positioned at specified heights above the burner nozzle (HAB). Once the C-layers were deposited the coated SS substrates were imaged using scanning electron microscopy (SEM). Finally, a water droplet test was used to determine the hydrophobicity of the flame-formed deposits: a water droplet is placed on the coated substrate's surface and an image is taken of the resting water droplet. Computer software is used to determine the CA. If the measured CA is less than 90\({}^{\circ}\) the surface is considered hydrophilic, at CAs greater than 90\({}^{\circ}\) the surface is considered hydrophobic, and at CAs greater than 150\({}^{\circ}\) the surface is considered superhydrophobic (Figure 2d). Flames for this study were produced as shown in Figure 2a,b. Various types of generated flames (two different fuels and varying oxygen content in the oxidizer stream) were tested for forming the carbonaceous deposits on the SS substrate. Fuel (gaseous or vapor) enters the burn zone through a central inlet with the oxidizer flowing through an annular region around the fuel inlet. The oxidizer used consisted of 21% O\({}_{2}\) (air), 35% O\({}_{2}\), and 50% O\({}_{2}\), with N\({}_{2}\) as the balance. The oxidizer was funneled through the annulus created by concentric pipes 11 mm and 82 mm in diameter. The central pipe carried the fuel, and the outer pipe supplied the oxidizer via four inlet ducts (Figure 2b). The co-flow burner housed an arrangement of glass balls and a honeycomb lattice within the annulus that acted to stabilize the air flow and ensure a uniform, laminar flow (Figure 2b). The fuel and air were not mixed until they were introduced by diffusion to the flame zone. Using a syringe pump the liquid CME fuel was introduced at a rate of 6 mL/h to the fuel evaporator line. The evaporator line was heated via heating tapes, and the CME was  
Figure 2: Experimental setup is shown. (**a**) Two-dimensional representation of the deposition process of soot on an SS substrate from the co-flow flame; (**b**) detailed co-flow reactor schematic; (**c**) photograph of the CME/oxygen-enriched air flame at O\({}_{2}\) contents of 21%, 35%, and 50%; (**d**) photographs of water droplets on a hydrophobic and hydrophilic surface with contact angles illustrated. evaporated. A nitrogen flow was used as a carrier gas (<0.1 Lpm) to move the evaporated CME through the fuel line, allowing for a more stable and easily ignitable flame. Methane, being a gas, did not require a carrier gas; therefore, a methane flow rate of 0.45 Lpm was used. For both fuels the oxidizer utilized a flow rate of 36 Lpm. To allow for accurate deposition of the flame-formed C-layers the burner was placed on a 2-D positioning system controlled by an 8300 series stepping motor controller (Model VXM-2, Velmex, Inc., Bloomfield, NJ, USA). The burner could be moved horizontally and vertically for optimal flame positioning [33]. By repositioning the burner, it was possible to form C-layers at a range of different heights within the flame. A hood and series of ducts were used to direct exhaust gases away from the setup. Figure 2a depicts the deposition process that allowed for formation of hydrophobic carbon films on the substrate. The soot deposition process created a black layer of material on the surface of the substrate. After deposition, the formed C-layers/flame deposits were analyzed using a light microscope and scanning electron microscope (SEM).