# Dropwise Condensation Mechanism on Smooth Hydrophilic Surfaces
## 2 Materials and Methods  
The visualization of dropwise condensation was carried out using the SPRi instrument, which is an in-house developed microscope [14]. The schematics of the dropwise condensation experiments are detailed in Figure 1. The substrate is 50 nm gold with 2.5 nm of titanium as an adhesive layer, coated on a glass substrate. The root-mean-square of surface roughness is 1.10 \(\pm\) 0.02 nm and a static contact angle of water on a surface is 78\({}^{\circ}\). SDC was conducted at the droplet growth rate of 1 \(\upmu\)m/s in diameter. As Figure 1a shows, an ITO-coated glass is placed 4-5 mm above the gold surface as a heater and a water column with a volume of 10-15 \(\upmu\)L is formed between the substrate and the heater. By heating the water bridge, the water evaporates and condenses on the gold surface. During the visualization of the dropwise condensation, the temperature of the gold surface was 35 \({}^{\circ}\)C, the local temperature of air above the gold surface was 45 \({}^{\circ}\)C, and the relative humidity (RH) was 60%. The thermocouples are not shown in the schematics of Figure 1. For the USDC, a 3-D printed chamber with an inlet and outlet was placed on top of the gold surface as an enclosure (see Figure 1b). The relative humidity (RH = 99%) and temperature (T = 97 \({}^{\circ}\)C) were monitored inside the enclosure using a combined temperature and RH sensor (DHT22 sensor based on an Arduino Mega 2560 controller). Steam was introduced into the chamber from the inlet and vented from the outlet of the chamber. As dropwise condensation of steam occurs on a smooth gold surface and no drainage mechanism was designed for this surface, the setup makes it intuitive to see the degradation of dropwise condensation in the long term. The SPRi visualization was carried out at 550 nm and 680 nm for both stable and unstable dropwise condensation. More details about the experimental procedure, visualization, and analysis of data are provided in our previous work [14].  
In the case of SDC at the RH of 60%, the condensation rate was approximately 0.0009 \(\upmu\)L/(mm\({}^{2}\) s), or a heat transfer rate of 0.2 W/cm\({}^{2}\). The droplet growth rate was roughly calculated to be around 1 \(\upmu\)m/s in diameter. In the case of USDC, the droplet growth rate was calculated roughly to be around 20 \(\upmu\)m/s in diameter. SDC and USDC were repeated 3-5 times at both wavelengths of 680 nm and 550 nm. The incident angle was set at 43.15 degrees (0.15 degrees below the SPR angle for air at 680 nm) and 44.80 degrees (1.5 degrees below the SPR angle of air at 550 nm) for SPRi with intensity modulation (IM) at 680 nm and 550 nm, respectively. Figure 2 shows the theoretical reflectance curve for SPRi of a 1 nm layer of water at wavelengths of 550 nm and 680 nm. The experimental angles shown in these plots are the incident angle of 44.80 degrees and 43.15 degrees implemented for SPRi with intensity modulation at 550 nm and 680 nm, respectively. At 550 nm and an experimental angle of 44.80 degrees, a 1 nm water film can result in a \(\sim\)4% change in the reflectance of the recorded signal. At 680 nm and an experimental angle of 43.15 degrees, a 1 nm film of water on the gold surface can produce a \(\sim\)16% change in the reflectance. Therefore, SPRi with a higher wavelength provides a better resolution in measuring ultrathin films. On the other hand, SPRi at 550 nm provides a better lateral resolution for our imaging; the lateral resolutions at 550 nm and 680 nm are 4 \(\upmu\)m and 10 \(\upmu\)m, respectively. Because of the trade-off in resolutions, we repeated the dropwise condensation experiments at both wavelengths of 550 nm and 680 nm.  
Figure 1: Schematic of the experimental setup for (**a**) stable dropwise condensation (SDC) and (**b**) unstable dropwise condensation (USDC) studies. Two wavelengths of 550 nm and 680 nm with the incident angles (\(\theta\)) of 44.80 degrees and 43.15 degrees, respectively, were studied.