**2. Experimental Methods**

Figure 1 shows an outline of the experimental setup. The experimental equipment consisted of a paint sprayer that sprayed paint and an observation unit that observed how paint adheres to and forms a coating film. The gravity feed spray gun (CREAMY(KP)5A-12, Kinki Factory Co., Ltd., Osaka, Japan) was used. The nozzle diameter of the spray gun was 1.2 mm, and the injection pressure was set to *P*in = 0.1, 0.2, and 0.3 MPa. The paints used in the experiment were colorless acrylic resin paints (Econet EB Two Pack Paints, Origin Electric Co., Ltd., Saitama, Japan), and their components are 40%–45% for acrylic polyol, 35%–40% for butyl acetate, and 15%–20% for diisobutyl ketone. Three types of viscosities were prepared by changing the amount of thinner. As a result of measuring each paint viscosity with an Iwata type viscosity cup, *μ* = 0.023, 0.033, and 0.037 Pa·s, respectively. Coumarin 153, which is a fluorescent agent, was used in order to assess the droplet adhesion behavior and the paint film formation. It was mixed with each paint at a ratio of 2.0 g/L. The absorption wavelength range of Coumarin 153 is 360 to 480 nm, the maximum absorption wavelength is 423 nm, and the maximum fluorescence wavelength is 530 nm. Phosphorescent powder was also mixed with the paint to measure the flow characteristics of the paint film. The wavelengths of lights used were 420 and 480 nm. The 420 nm light is near the absorption wavelength range of Coumarin 153. The phosphorescence from the powder was emitted by the 420 and 480 nm lights.

### **Figure 1.** Experimental setup.

In the observation section, a transparent acrylic plate, with a length of 100 mm, a width of 100 mm, and a thickness of 3 mm, was installed as a painted surface at 300 mm downstream from the tip of the spray gun. Since the wavelength of light that can be transmitted through the transparent acrylic plate is about 400 nm or more, it was able to transmit the 420 and 480 nm lights used here. The paint mixed with the fluorescent agent and the phosphorescent powder was measured for fluorescence and phosphorescence by shining light of a specific wavelength from the underside of this acrylic plate.

The coating film formation process for the paint sprayed on the acrylic plate was photographed using a digital camera (DMC-GH4, Panasonic Corporation, Osaka, Japan) fitted with a microscope (VZM1000, Edmund Optics, Tokyo, Japan). In addition, a long pass filter (Φ 25 mm 500 nm High-Performance Longpass Filter, Edmund Optics) for blocking light at a wavelength of 490 nm or less was inserted between the microscope and camera to block the violet light, and only the light of fluorescence and phosphorescence wavelengths was photographed. In order to measure the paint film thickness quantitatively, the fluorescence intensities were calibrated. Paint containing a fluorescent agent was sandwiched between two glass plates, as shown in Figure 2, and the fluorescence intensities with against the various gap distances between the glass and acrylic plate were obtained. Figure 3 shows the calibrated data. From these data, the relationship between the fluorescence intensity and the thickness of the paint film was ascertained.

**Figure 2.** Experimental setup for calibrations of the relationship between fluorescence intensity and the coating film thickness.

**Figure 3.** Calibration curve showing the coating film thickness in relation to the fluorescence intensity.

The obtained image was binarized to determine the adhesion area of the paint and the size distribution of the adherent droplets. In addition, to evaluate the film formation process, we defined the area ratio, *α*(*t*), and the overlap ratio, *β*(t), from a previous study [12]. Figure 4 shows an example of the time dependence of the area and overlap ratios. The area ratio is the ratio of the droplet adhesion area to the measurement range. The overlap ratio is the value obtained by subtracting *α*(*t*) from the value that multiplies the increase ratio, *α*'0, of the area ratio at the initial stage of the droplet adhesion by the elapsed time *t*[s]. If the droplets do not overlap, the area ratio is considered to increase as *α* <sup>0</sup>·*t*, and the overlap ratio indicates how much extra paint is attached as compared with do not overlap case.

**Figure 4.** Model of coating formation [12] (adapted with permission from The Japanese Society for Experimental Mechanics).

In addition, the temporal change in the coating film thickness was determined by measuring the fluorescence intensity distribution on across-section of the fluorescence image. Additionally, the smoothness of the coating film was evaluated by examining the standard deviation of the fluorescence intensity distribution over the entire fluorescence image.
